jmbussat/physics290e/fall-2006/tcad_document… · contents sxtract iv chapter 5 bsim3...

SXtractVersion Y-2006.06, June 2006

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SXtract, Y-2006.06

SXTRACT CONTENTS

SXtractAbout this manual ...............................................................................................................................vii

Audience ........................................................................................................................................................... viiiRelated publications.......................................................................................................................................... viiiTypographic conventions .................................................................................................................................. viiiCustomer support.............................................................................................................................................. viiiAcknowledgments ............................................................................................................................................... ix

Chapter 1 Using SXtract .......................................................................................................................1About SXtract ......................................................................................................................................................1Integration within Synopsys tools ........................................................................................................................2Starting SXtract ...................................................................................................................................................2

Editing a project of Sentaurus Workbench .....................................................................................................3Requirements for the extraction .....................................................................................................................3Running Sentaurus Device.............................................................................................................................3Running SXtract .............................................................................................................................................4Running a second Sentaurus Device .............................................................................................................4Results ...........................................................................................................................................................4

Chapter 2 Creating a project of Sentaurus Workbench.....................................................................5Overview .............................................................................................................................................................5Grid and doping files ...........................................................................................................................................5Template file of Sentaurus Device ......................................................................................................................6Editing parameters ..............................................................................................................................................7

Chapter 3 Extraction input file .............................................................................................................9Overview .............................................................................................................................................................9

Reserved keywords for section names ..........................................................................................................9Reserved keywords in sections......................................................................................................................9

DEVICE section ................................................................................................................................................10PSETTABLE section .........................................................................................................................................11COMPACTMODEL section ...............................................................................................................................12NAMESMAPPING section ................................................................................................................................12STEP section ....................................................................................................................................................13MATHEMATICS section ....................................................................................................................................14DESSIS section .................................................................................................................................................15

Chapter 4 Extraction and optimization procedures .........................................................................17Sequence of parameter extraction ....................................................................................................................17Physically oriented optimization sequence .......................................................................................................19Optimization algorithm ......................................................................................................................................20Goal functions ...................................................................................................................................................21Convergence conditions ....................................................................................................................................22

Goal function tolerance ................................................................................................................................22Maximum number of iterations .....................................................................................................................23Gradient criterion..........................................................................................................................................23Additional stopping criterion .........................................................................................................................23

Root-mean-square evaluation ...........................................................................................................................24Random starting-point generation .....................................................................................................................24Estimating standard error of extracted parameters ...........................................................................................24

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SXTRACTCONTENTS

Chapter 5 BSIM3 extraction................................................................................................................27Device size requirements ..................................................................................................................................27Schematic .........................................................................................................................................................28Data for extraction .............................................................................................................................................29

IV curves ......................................................................................................................................................29CV curves.....................................................................................................................................................31

Extracting single-device parameters .................................................................................................................32Defining process-dependent parameters .....................................................................................................32Defining SPICE parameters .........................................................................................................................32Model control parameters.............................................................................................................................33DC parameters .............................................................................................................................................33

Single-device extraction: Parameters to be extracted..........................................................................33Single-device extraction: Predefined parameters .................................................................................35Single-device extraction strategy ..........................................................................................................35

CV parameters .............................................................................................................................................36Single-device extraction: Parameters to be extracted...........................................................................36Single-device extraction: Predefined parameters .................................................................................37CV model control parameters ...............................................................................................................37Single-device extraction strategy ..........................................................................................................38

BSIM3 objects ...................................................................................................................................................38BSIM3 DC objects: nbsim3dc and pbsim3dc ...............................................................................................38BSIM3 CV objects: nbsim3cv, pbsim3cv, nbsim3cv1, pbsim3cv1 ...............................................................43

Goal functions ...................................................................................................................................................45Current goal function ....................................................................................................................................45Capacitance goal function ............................................................................................................................46

Chapter 6 BSIM3 self-consistent DC and CV extraction..................................................................47BSIM3 objects: nbsim3 and pbsim3 ..................................................................................................................47Goal function .....................................................................................................................................................53Extraction strategy ............................................................................................................................................54

Chapter 7 BJT Gummel–Poon model extraction..............................................................................55Schematic .........................................................................................................................................................55BJT objects: npnbjt and pnpbjt ..........................................................................................................................55Goal function .....................................................................................................................................................58Extraction strategy ............................................................................................................................................58

Chapter 8 Diode extraction.................................................................................................................59Schematic .........................................................................................................................................................59Diode object: diode ...........................................................................................................................................59Extraction strategy ............................................................................................................................................60

Chapter 9 BSIM4 DC, CV, and RF extraction ....................................................................................61Schematic .........................................................................................................................................................61BSIM4 DC, CV, and RF objects: nbsim4, pbsim4 .............................................................................................61

Considerations when extracting BSIM4 model parameters .........................................................................76Range of parameters ............................................................................................................................76The geomod parameter.........................................................................................................................77The rshg parameter...............................................................................................................................77Model selector parameters....................................................................................................................78

Goal function .....................................................................................................................................................78Extraction strategy ............................................................................................................................................78

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SXTRACT CONTENTS

Chapter 10 BSIMPD extraction...........................................................................................................81Overview ...........................................................................................................................................................81Schematic .........................................................................................................................................................81BSIMPD objects: nbsimpd2.2.2 and pbsimpd2.2.2 ...........................................................................................82Extraction strategy ............................................................................................................................................92

Chapter 11 Mextram 504 parameter extraction ................................................................................93Schematic .........................................................................................................................................................93Mextram object: ts504 .......................................................................................................................................93Circuits for capacitance and Y-matrix calculation .............................................................................................98Goal function .....................................................................................................................................................99Extraction strategy ..........................................................................................................................................100

Appendix A Extracting DC parameters ...........................................................................................101

Appendix B Extracting transient parameters .................................................................................103

Bibliography ......................................................................................................................................105

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SXTRACTCONTENTS

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SXTRACT ABOUT THIS MANUAL

SXtract

About this manual

SXtract is a simulation-based extractor of compact model parameters. In circuit analysis, differentsemiconductor devices are usually represented by so-called compact models. The compact models in alarge circuit are solved simultaneously to predict the behavior of the circuit. To adjust a compact modelto a specific device, parameters of the compact model are extracted from measurements. In TCADapplications, the device may not exist, and measurements are performed using a device simulator.Within Synopsys TCAD software, the measurements are made using the device simulator SentaurusDevice. Using both process and device simulations allows for the provision of predictive SPICE modelparameters including statistical information if necessary.

The main chapters are:

Chapter 1 introduces a simple example of extraction of DC BSIM3 model parameters fromSentaurus Device ‘simulated’ data.

Chapter 2 describes a sequence of steps in the Sentaurus Workbench projects, which allows for thecomputation of all data needed for an extraction.

Chapter 3 presents a detailed description of the sections of the SXtract input file.

Chapter 4 describes the mathematical approach used in SXtract for parameter extraction.

Chapter 5 describes the shared objects and single-device extraction technique for sequentialextraction of DC and CV BSIM3 model parameters.

Chapter 6 describes the shared objects for simultaneous extraction of DC and CV BSIM3 modelparameters.

Chapter 7 describes the shared objects for the extraction of bipolar model parameters. Both DC andCV parameters can be extracted simultaneously.

Chapter 8 describes the shared object for the extraction of DC and CV diode parameters.

Chapter 9 describes the shared objects for BSIM4 extraction. All DC, CV, and RF parameters canbe extracted simultaneously or separately.

Chapter 10 describes the shared objects for the extraction of BSIMPD model parameters. Threeapproaches to extraction are supported: extract parameters for the body contact device only; extractparameters for the floating body device only; and extract parameters simultaneously for the bodycontact and floating body devices.

Chapter 11 describes the shared object for the extraction of parameters of the Mextram 504 bipolartransistor model.

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SXTRACTABOUT THIS MANUAL

AudienceThis manual is intended for users of the SXtract software package.

Related publicationsFor additional information about SXtract, see:

Documentation on the Web, which is available through SolvNet athttps://solvnet.synopsys.com/DocsOnWeb.

Synopsys Online Documentation (SOLD), which is included with the software for CD users or isavailable to download through the Synopsys Electronic Software Transfer (EST) system.

Typographic conventions

Customer supportCustomer support is available through SolvNet online customer support and through contacting theSynopsys Technical Support Center.

Accessing SolvNet

SolvNet includes an electronic knowledge base of technical articles and answers to frequently askedquestions about Synopsys tools. SolvNet also gives you access to a wide range of Synopsys onlineservices including software downloads, documentation on the Web, and “Enter a Call to the SupportCenter.”

Convention Explanation

Blue text Identifies a cross-reference (only on the screen).

Bold text Identifies a selectable icon, button, menu, or tab. It also indicates the name of a field, window, dialog box, or panel.

Courier font Identifies text that is displayed on the screen or that the user must type. It identifies the names of files, directories, paths, parameters, keywords, and variables.

Italicized text Used for emphasis, the titles of books and journals, and non-English words. It also identifies components of an equation or a formula, a placeholder, or an identifier.

Menu > Command Indicates a menu command, for example, File > New (from the File menu, select New).

NOTE Identifies important information.

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http://solvnet.synopsys.com/DocsOnWeb

SXTRACT ABOUT THIS MANUAL

To access SolvNet:

1. Go to the SolvNet Web page at http://solvnet.synopsys.com.

2. If prompted, enter your user name and password. (If you do not have a Synopsys user name andpassword, follow the instructions to register with SolvNet.)

If you need help using SolvNet, click HELP in the top-right menu bar or in the footer.

Contacting the Synopsys Technical Support Center

If you have problems, questions, or suggestions, you can contact the Synopsys Technical Support Centerin the following ways:

Open a call to your local support center from the Web by going to http://solvnet.synopsys.com(Synopsys user name and password required), then clicking “Enter a Call to the Support Center.”

Send an e-mail message to your local support center:

• E-mail [email protected] from within North America.

• Find other local support center e-mail addresses at http://www.synopsys.com/support/support_ctr.

Telephone your local support center:

• Call (800) 245-8005 from within the continental United States.

• Call (650) 584-4200 from Canada.

• Find other local support center telephone numbers at http://www.synopsys.com/support/support_ctr.

Contacting your local TCAD Support Team directly

Send an e-mail message to:

[email protected] from within North America and South America.

[email protected] from within Europe.

[email protected] from within Asia Pacific (China, Taiwan, Singapore, Malaysia,India, Australia).

[email protected] from Korea.

[email protected] from Japan.

AcknowledgmentsBSIM3 was developed by the Device Research Group of the Department of Electrical Engineering andComputer Science (EECS), University of California, Berkeley, and is copyrighted by the University ofCalifornia.

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http://solvnet.synopsys.com

http://solvnet.synopsys.com

http://www.synopsys.com/support/support_ctr

http://www.synopsys.com/support/support_ctr

SXTRACTABOUT THIS MANUAL

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SXTRACT CHAPTER 1 USING SXTRACT

SXtract

CHAPTER 1 Using SXtract

This chapter presents a short tutorial to illustrate how SXtract works.

About SXtractThe extraction procedure is illustrated by using a simple example: IV curves for a single device arecomputed, and the DC parameters of the BSIM3 compact model are extracted using those curves asinput (single-device extraction technique). Figure 1 shows the flow chart of an extraction example inSentaurus Workbench. The generation of grid and doping files (input for Sentaurus Device) is notincluded as they were computed earlier using Dios and Mdraw.

Figure 1 Model parameter extraction methodology based on Synopsys TCAD

Model Parameter

Grid GenerationDevice Simulation

‘Measured Data’

Compact ModelParameter Extraction

Parameter Validation

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SXTRACTCHAPTER 1 USING SXTRACT

Integration within Synopsys toolsTo extract compact model parameters from Sentaurus Device simulation results, these important stepsmust be performed:

1. Create a project to obtain all necessary IV curves. Sentaurus Workbench is a tool designed to handlelarge simulation projects. Different template files of Sentaurus Device are available to generate aproject. Users can modify these templates, use their own templates, or create the necessary IVcurves in a different way.

2. Extract the parameters. For this, the user must describe each device, the input and output data, andthe extraction strategy. The extraction input file for SXtract is designed to define the extractionprocedure.

3. Validate the extracted parameter set. (This step is optional.)

The extraction strategy is stored in the extraction input file. This file also contains input and output filenames, specific information about each device, initial guesses for compact model parameter sets, and soon. If extr_input_file_name.cmd is the name of the extraction input file, the extracted compact modelparameters are stored in the file named extr_input_file_name.scf. For convenience, the template forcreating projects of Sentaurus Workbench can also be stored in the extraction input file, although it isnot needed for SXtract.

For example, a BSIM3 model parameter extraction project can be very large. In a standard approach, atleast 20 IV curves must be obtained for each device (see DEVICE section on page 10 and Data forextraction on page 29). If five different devices are used for the parameter extraction, 100 IV curvesmust be generated. To simplify the generation of such a project, Sentaurus Workbench uses the templateof the parameterized input file of Sentaurus Device. The IV curves that are computed using SentaurusDevice are supplied as measurements to SXtract. After the parameter extraction, the same IV curves canbe computed using the compact models with the extracted parameter set.

To avoid confusion, the initial IV curves computed with Sentaurus Device will be called measurementsand the IV curves obtained with the compact model will be referred to as simulation results.

Starting SXtractSXtract can be started as a stand-alone tool by using the command:

sxtract extr_input_file_name.cmd

Comments to each step of this tool flow are presented here.

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SXTRACT CHAPTER 1 USING SXTRACT

Editing a project of Sentaurus WorkbenchTo start a project:

1. Click the Example Library icon.

2. Open the folder Manual_Examples/Tools/SXtract/ISE_bsim3/SingleDevice.

3. Select the project nbsim3_DC.

4. Edit > Duplicate.

These actions duplicate the entire example. A new folder appears, named COPIED_OBJECT_username,where the user name is your user name. This folder has a copy of the project DC_SXtractProject. Thefiles are no longer write protected. This allows users to modify anything as required. Work with theduplicated project from this point onwards.

5. Click the Status icon.

6. Drag the copied project to the Status window.

7. Click Edit in the Status window.

8. Open the tool flow.

The tools in the tool flow are Sentaurus Device, SXtract, a second instance of Sentaurus Device, andInspect.

Requirements for the extractionSXtract requires measured data to perform the extraction. This measured data is generated by usingSentaurus Device. The family of curves that is needed for a DC BSIM3 single-device extraction strategyis described in Data for extraction on page 29.

Running Sentaurus DeviceThe input file des.cmd of Sentaurus Device contains the parameter SWEEP of Sentaurus Workbench. Eachvalue of this parameter corresponds to a certain IV curve needed for the extraction. The calculatedcurves are saved in .plt files, for example, idvg_1__des.plt (see IV curves on page 29 for file-namingdetails).

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SXTRACTCHAPTER 1 USING SXTRACT

Running SXtractWhen all simulations of Sentaurus Device are finished, that is, all measured data is obtained, SXtractstarts. SXtract executes the sequence of extraction steps, which are described in the extraction input fileisx.cmd. When SXtract is finished, the obtained parameters are saved in the library file with theextension .scf.

Running a second Sentaurus DeviceIn the second run of Sentaurus Device, the same simulations as in the first run are performed. However,instead of the physical device, the BSIM3 compact model of the MOSFET transistor is used. Theparameters of the model are taken from the file *.scf, that is, the previously extracted set of parametersare used. The purpose of the second run of Sentaurus Device is to compare the measured IV curves withthe simulated ones. The input file for the second simulation of Sentaurus Device is called mod.cmd. Thenames of the IV curves obtained after two runs are similar, for example, idvg_1__des.plt is the name ofthe measured curve and idvg_1_mod_des.plt is the name of the corresponding simulated curve.

ResultsWhen both measured and simulated data are obtained, Inspect can be used to validate the extractedparameters. The Inspect script contains a set of plots with a comparison of the measured and simulatedresults.

To display these plots in Inspect:

Script > Continue Script.

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SXTRACT CHAPTER 2 CREATING A PROJECT OF SENTAURUS WORKBENCH

SXtract

CHAPTER 2 Creating a project of Sentaurus Workbench

This chapter discusses how to create a project of Sentaurus Workbench.

OverviewThe creation of a project of Sentaurus Workbench is the first step of the parameter extraction procedure.Assume that you want to extract BSIM3 model parameters using standard 2D simulations for fivedifferent devices. As explained in Data for extraction on page 29, for the extraction of the DCparameters, 20 IV curves must be computed for each device. If one characteristic corresponds to eachSentaurus Device simulation, then 100 Sentaurus Device simulations must be performed to create100 .plt files.

The names of the created files must correspond to the appropriate symbolic names defined in the DEVICEsections of the extraction input file. Such a correspondence must be correctly performed for each device.Of course, the correct geometry and doping files must be used for the appropriate devices. To simplifythe procedure of project creation and maintenance, the following approach is recommended:

Use names of geometry and doping files that include unique information about the device (such aslength and width of the devices).

Use names of the output .plt files that directly correspond to the simulation conditions.

Use an automatic procedure for the creation of the project of Sentaurus Workbench.

All this is performed with the help of an appropriate des.cmd file of Sentaurus Device.

NOTE In this example, only the project that starts from Sentaurus Device is discussed, assuming thatthe necessary geometry and doping files have been created earlier.

Grid and doping filesGeometric parameters for each device are specified in the DEVICE section of the extraction input file.However, this specification must correspond to the appropriate data of the geometry .grd and .datdoping files of the input file of Sentaurus Device.

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SXTRACTCHAPTER 2 CREATING A PROJECT OF SENTAURUS WORKBENCH

This can be performed by using the following parameterization:

Grid = "@DEVICE@_mdr.grd"Doping = "@DEVICE@_mdr.dat"

In this case, the user must ensure that appropriate .grd and .dat files exist in the working directory. Ifthese files are created elsewhere, they must be copied to the working directory of Sentaurus Workbench.Examples of geometry and doping files are:

large_mdr.dat mshort2_mdr.dat small_mdr.datlarge_mdr.grd mshort2_mdr.grd small_mdr.grdmshort1_mdr.dat mshort3_mdr.datmshort1_mdr.grd mshort3_mdr.grd

Template file of Sentaurus DeviceThe template input file (des.cmd) of Sentaurus Device can be stored in the DESSIS section of the extractioninput file. However, for now, this section is not used directly. Before the creation of a project ofSentaurus Workbench, the contents of this section must be copied to a separate des.cmd file. Of course,this section cannot exist in the extraction input file, and the des.cmd file must be stored in the workingdirectory as a separate file.

The input file of Sentaurus Device is a parameterized file, which uses parameters and variables ofSentaurus Workbench. Based on the possible values of the parameters, the simulation tree of SentaurusWorkbench is created. The variables of Sentaurus Workbench allow for the setting of the required datato different branches of the tree. In the Synopsys examples, the following parameters of SentaurusWorkbench are selected:

@SWEEP@@DEVICE@

The variables that are used in the examples are Ramp1_Name, Ramp1_V, Ramp2_Name, Ramp2_V, Ramp3_Name,Ramp3_V, and Ramp3_step.

The parameter @SWEEP@ is a string variable. It can be equal to idvg_1 or idvd_2, which correspond to thenames of the curves (see Data for extraction on page 29 and Table 5 on page 30). The parameter @DEVICE@is also a string variable. For example, it can be equal to large, which corresponds to the device names inFigure 8 on page 28. The Sentaurus Workbench variables such as Ramp1_Name and Ramp1_V define theelectrode names, applied biases, and the values of voltage steps how these biases change. Table 5 showsan example with standard values of these variables. The parameters and variables of SentaurusWorkbench are used in the template of the input file of Sentaurus Device.

From the example of the Sentaurus Device template (see Appendix A on page 101), the parameters andvariables of Sentaurus Workbench appear in different places in the des.cmd file. They are used in the Filesection to define geometry and doping files, in the Solve section to specify voltages and steps duringvoltage ramps, and in the NewCurrent statement to define the names of the output .plt files. Afterpreprocessing of the project, an experiment tree of Sentaurus Workbench is created. Figure 2 on page 7is an example of such a tree.

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SXTRACT CHAPTER 2 CREATING A PROJECT OF SENTAURUS WORKBENCH

Figure 2 Typical parameter extraction project in Sentaurus Workbench

Editing parametersThe parameters of Sentaurus Workbench can be edited in Sentaurus Workbench using dialog boxes. Forexample, users can change the device name, the curve name, and so on. It is also possible to add or deleteparameters. However, in this case, it can influence the extraction flow strategy, and it is possible thatsome changes have to be performed in the extraction flow definition (that is, in the STEP sectionspecifications and in the sequence of STEP sections).

For example, if in the extraction flow process, the threshold voltage parameters are extracted from thelong channel device and this device has been deleted, the user must change the extraction flowspecification to ensure that the threshold voltage parameters are extracted correctly in another step.

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SXTRACTCHAPTER 2 CREATING A PROJECT OF SENTAURUS WORKBENCH

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SXTRACT CHAPTER 3 EXTRACTION INPUT FILE

SXtract

CHAPTER 3 Extraction input file

This chapter presents a detailed description of the sections of the SXtract input file.

OverviewThe extraction strategy is defined in the extraction input file. This file contains all other necessaryinformation for the actual extraction and (optionally) the generation of the project of SentaurusWorkbench:

Description of each device

Information for generating the extraction project of Sentaurus Workbench

Description of the compact model

Initial values of the compact model parameters and their limits

Specification of the extraction strategy

The extraction input file consists of different sections.

Reserved keywords for section namesThe keywords reserved to recognize the sections are DEVICE, PSETTABLE, COMPACTMODEL, NAMESMAPPING, STEP,FUNCTION, MATHEMATICS, DESSIS, and DEPEND. Braces define the beginning and end of a section. Onlyuppercase letters can be used for these keywords.

Reserved keywords in sectionsIn the extraction input file, the reserved keywords that are used inside of sections are quadratic,diff(.,.), absolutechangemax, absolutechangerms, d1gradient_tol, function_tol, gradient_tol, max(.),max_outer_iter, maxiter, min(.), rand, ref_value, relativechangemax, relativechangerms, and weight(.). Forthese keywords, only lowercase letters are allowed.

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SXTRACTCHAPTER 3 EXTRACTION INPUT FILE

DEVICE sectionThe DEVICE section contains information about the device. The device name immediately follows thekeyword DEVICE. A typical DEVICE section is:

DEVICE DEVICENAME {l = valuew = value...idvg_1 = "DeviceName.idvg_1_des.plt"...

}

DeviceName is the unique name of the device that is used in the extraction input file when it is needed torefer to this particular device. Inside the section, the parameters of the SPICE1 device are specified (l isthe length of the device, w is the width of the device, and so on). These parameters must correspondexactly to the appropriate parameters of the SPICE model as described in the Compact Models manual.

For each curve of the device, users must specify a symbolic name of the curve, such as idvg_1, thatcorresponds to the real name of the curve, which will be created in the project of Sentaurus Workbench.For example, if it is specified as:

idvg_1 = "DeviceName.idvg_1_des.plt"

idvg_1 is a symbolic name and DeviceName.idvg_1_des.plt is the real name of the .plt file in the project.Symbolic names are used widely in the input file to describe extraction strategy, for example, in STEPsection on page 13. An example of a DEVICE section is:

DEVICE large {l = 10e-6 w = 10.0e-6ad = 2e-12as = 2e-12pd = 20.4e-6ps = 20.4e-6nrd = 0.02nrs = 0.02temp = 27

idvg_1 = "large.idvg_1_des.plt"idvg_2 = "large.idvg_2_des.plt"idvg_3 = "large.idvg_3_des.plt"idvg_4 = "large.idvg_4_des.plt"idvg_5 = "large.idvg_5_des.plt"

idvgh_1 = "large.idvgh_1_des.plt"idvgh_2 = "large.idvgh_2_des.plt"idvgh_3 = "large.idvgh_3_des.plt"idvgh_4 = "large.idvgh_4_des.plt"idvgh_5 = "large.idvgh_5_des.plt"

1. The SPICE circuit simulator was developed by the Department of Electrical Engineering and Computer Science(EECS), University of California, Berkeley, and is copyrighted by the University of California.

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idvd_1 = "large.idvd_1_des.plt"idvd_2 = "large.idvd_2_des.plt"idvd_3 = "large.idvd_3_des.plt"idvd_4 = "large.idvd_4_des.plt"

idvd2_1 = "large.idvd2_1_des.plt"idvd2_2 = "large.idvd2_2_des.plt"idvd2_3 = "large.idvd2_3_des.plt"idvd2_4 = "large.idvd2_4_des.plt"

isubvg_1= "large.isubvg_1_des.plt"isubvg_2= "large.isubvg_2_des.plt"

}

PSETTABLE sectionPSETTABLE is a required section of the extraction input file. An example of this section is:

PSETTABLE ModelName {ModelParameterName InitialValue MinValue MaxValue...

}

where ModelName is an arbitrary name of the model (specified by the user). For each parameter, an initialvalue is specified, as well as the allowed minimal and maximal values for the parameter. Initial valuesare used as a starting point for the extraction. The parameters MinValue and MaxValue specify restrictionsfor the extracted value of the parameter; the extracted parameter cannot be outside the specified range.

An example of a PSETTABLE section is:

PSETTABLE UserModelName {// initial min maxvth0 7.000000e-01 0.000e+00 1.000e+00 // Threshold voltagek1 5.000000e-01 0.100e+00 1.500e+00 // Bulk effect coefficient 1k2 0.000000e+00 -1.000e-01 1.000e-01 // Bulk effect coefficient 2k3 8.000000e+01 -1.000e-01 1.000e+02 // Narrow width effect coefficient...

}

NOTE The set of SPICE device parameters is different from the SPICE model parameters. Theformer set is predefined for each device, but the latter set is extracted with SXtract.

11


COMPACTMODEL sectionTo accelerate the extraction procedure and support different possibilities needed for the extraction, thecompact models to be used by the extraction program are modified. The executable of the compactmodel (or a path to it) is specified in the COMPACTMODEL section:

COMPACTMODEL {Name_of_shared_object

}

where Name_of_shared_object is a compiled executable, that is, it is the name of the shared object that isloaded at run-time. The supported shared objects are:

NAMESMAPPING sectionIn input files of Sentaurus Device, the names of electrodes are specified in the Electrode section, forexample:

Electrode {{Name="drain" Voltage=0.05}

}

Similarly, this name appears in the .plt file as:

"drain OuterVoltage"

diode For the extraction of diode parameters.

nbsim3, pbsim3 For the self-consistent extraction of DC and CV BSIM3 parameters (capmod=0,1,2,3).

nbsim3cv, pbsim3cv For the extraction of CV BSIM3 parameters (capmod=3).

nbsim3cv1, pbsim3cv1 For the extraction of CV BSIM3 parameters (capmod=0,1,2). The executable, which starts with the letter n, corresponds to an NMOS transistor. If it starts with the letter p, it is a PMOS transistor object.

nbsim3dc, pbsim3dc For the extraction of DC BSIM3 parameters.

nbsim4_dc_cv, pbsim4_dc_cv For the extraction of DC, CV, and RF BSIM4 parameters.

nbsimpd2.2.2, pbsimpd2.2.2 For the extraction of BSIMPD version 2.2.2 model parameters.

npnbjt, pnpbjt For the extraction of bipolar Gummel–Poon model parameters, DC, CV, and transient for n-p-n-type and p-n-p-type, respectively.

ts504 For the extraction of the parameters of the Mextram 504 bipolar transistor model.

12


In the SPICE model (that is, in the executable specified in the COMPACTMODEL section), the drain electrodeis used with the name Vd. The NAMESMAPPING section is used to establish a correspondence between SPICEand Sentaurus Device names:

NAMESMAPPING {SpiceName = DessisName...

}

An example of the NAMESMAPPING section for DC parameter extraction is:

NAMESMAPPING {Vd = "drain OuterVoltage"Vs = "source OuterVoltage"Vg = "gate OuterVoltage"Vb = "subs OuterVoltage"Id = "drain TotalCurrent"Ib = "subs TotalCurrent"Is = "source TotalCurrent"

}

Users must specify the names of all electrode voltages. Some current name specifications may beomitted if they are not used for the extraction (for example, gate TotalCurrent).

STEP sectionThe extraction procedure is described in the STEP section. The input file can have an arbitrary number ofSTEP sections, and they are executed in the order in which they appear in the input file. The possibility tospecify different STEP sequences, to define any set of parameters to be extracted, and to use any set ofcurves for the extraction of the specified parameters in the particular extraction step allows users toemulate arbitrary extraction strategies. The syntax of the STEP section is:

STEP step_number {parameter1parameter2...FUNCTION {IV curves1}FUNCTION {IV curves2}...MATHEMATICS {...}DEPEND...

}

Each STEP operator must have a unique number step_number. In the body of the STEP section, a list ofparameters, which are used for the optimization, must be listed. In the subsection FUNCTION, users mustdefine a type of function to be used for the optimization, and a set of IV curves that is supposed to fit inthis step by using parameter variations. The subsection FUNCTION must be present in the body of the STEPsection and looks like:

FUNCTION Type_Function {DEVICENAME.CurveName.[CurrentName1][[CurrentName2]...]...

}

13


Type_Function is the type of the goal function used for the optimization. The supported goal functiontypes are:

quadratic Least squares function is used (see Goal functions on page 21).

diff(CurrentName, VoltageName, Weight)

The least square function is applied for the optimization of the derivatives of thefirst dataset with respect to the second dataset. The datasets are defined by theirnames (CurrentName and VoltageName, respectively). For example, ifdiff(Id, Vd, 1.0) is specified, the least squares function is applied to thederivative with weight equal to 1.0.

An example of the STEP section is:

STEP 1 {vth0k1k2u0FUNCTION quadratic {

large.idvg_1.[Id]large.idvg_2.[Id]large.idvg_3.[Id]large.idvg_4.[Id]large.idvg_5.[Id]

} //END FUNCTIONFUNCTION diff(Id,Vd, 1.0) {

large.idvd_4.[Id]} //END FUNCTIONMATHEMATICS {

min(Vg) = 0.5min(Id) = 1e-6maxiter = 100

}} // END STEP 1

MATHEMATICS sectionThe MATHEMATICS section is optional. In this section, the parameters that control the optimizationprocedure are specified. This section can be global or can be specified inside any STEP section. In thelatter case, the values inside this section are local for a particular STEP, and the global values areoverwritten by the local ones. The most important parameters of the MATHEMATICS section are:

MATHEMATICS {min(Spice_Name) = valuemax(Spice_Name) = valuemaxiter = value

}

where maxiter is the maximum number of iterations in the optimization process, and min(V) and max(V)are the minimum and maximum values of the variable V with the name Spice_Name (seeNAMESMAPPING section on page 12).

dId dVd⁄

14


The optimization procedure is performed only for the values that satisfy the condition:

min(V) < V < max(V) (1)

Table 1 lists the keywords of the MATHEMATICS section.

DESSIS sectionThe DESSIS section contains a template of the command file (des.cmd) of Sentaurus Device. This templateis used to create a project of Sentaurus Workbench, so parameters and variables of Sentaurus Workbenchare used in the template. The template is used to generate an input file of Sentaurus Device for a projectof Sentaurus Workbench.

It is important that the files with IV curves are saved in .plt files, which have names described in thecorresponding DEVICE section of the extraction input file. This section is not used directly and is storedinside of the extraction input file for convenience. To create a project of Sentaurus Workbench, thissection must be copied to the des.cmd file in the project directory. An example of a command file templateof Sentaurus Device is presented in Appendix A on page 101.

Details of the creation of a project are described in Chapter 2 on page 5.

Table 1 Keywords of MATHEMATICS section

Parameters Description

absolutechangemax Absolute change of maximum error on outer iterations in percent.

absolutechangerms Absolute change of RMS on outer iterations in percent.

d1gradient_tol=1e-3 Minimum of gradient norm of the goal function for one dimension minimization.

function_tol=1e-10 Function tolerance (see Goal function tolerance on page 22).

gradient_tol=1e-6 Minimum of gradient norm of the goal function, (see Gradient criterion on page 23).

max(.) Maximum value of variable (see Eq. 1).

max_outer_iter Maximum number of outer iterations.

maxiter=100 Maximum number of iterations at one optimization step (see Maximum number of iterations on page 23).

min(.) Minimum value of variable (see Eq. 1).

rand Generates a random starting point for optimization.

ref_value=1e-6 Minimum (reference) value for the goal function estimation (see Eq. 3).

relativechangemax Relative change of maximum error on outer iterations in percent.

relativechangerms Relative change of RMS on outer iterations in percent.

weight(.) Weight of variable in goal function (see Eq. 3).

fmin

15


16

SXTRACT CHAPTER 4 EXTRACTION AND OPTIMIZATION PROCEDURES

SXtract

CHAPTER 4 Extraction and optimization procedures

This chapter describes the mathematical approach used in SXtract for parameter extraction.

Sequence of parameter extractionSXtract supports different extraction strategies, which can be specified in the extraction input file. As inany optimization procedure, the optimization strategy in SXtract consists of a sequence of optimizationsteps. The STEP sections in the extraction input file are designed to describe one step of the optimizationprocedure. The steps are executed sequentially or, if necessary, loops can be created. This sequence ofoptimization steps together with the STEP section specification defines the whole extraction strategy. Anextraction step includes:

A set of unknown parameters {Xi} that are to be extracted.

A set of devices {Di} and a set of corresponding curves {Ci}, which compose a dataset{Datai}={Di}U{Ci}. This dataset is used for {Xi} extraction.

The type of the goal function F(Xi) and the appropriate mathematical parameters.

When completed, an optimal value for the parameter set {Xi} is extracted.

During each step, the extraction (optimization) is performed with the help of the optimization module,which is a part of SXtract. This module optimizes the goal function F(Xi) over the parameter set {Xi}. Toavoid confusion, it is worthwhile to define the difference between extraction and optimization.

The term extraction means the calculation of parameter values from measured data and the termoptimization is the iterative adjustment of parameter values to achieve the best fit between measured andsimulated data. As SXtract uses only optimization, there is no differentiation between extraction andoptimization.

SXtract can perform an arbitrary sequence of extraction steps as shown in Figure 3 on page 18. Toprovide this general extraction strategy, a fully separate optimization module exists in SXtract. Thismodule needs an input, which is generated by SXtract from the data defined in the STEP section of theextraction input file (see STEP section on page 13). The extracted set of parameters is an output of theoptimization module. SXtract processes each step of the optimization procedure as follows:

1. An input file stepN.ext for the optimization module is created. This input file includes:

a) A shared object name, which corresponds to the selected compact model.

b) A set of SPICE device parameters for each .plt file.

17

SXTRACTCHAPTER 4 EXTRACTION AND OPTIMIZATION PROCEDURES

c) A type of goal functions for each .plt file.

d) A full list of parameters of the compact model, their initial, and lower and upper limit values.Each parameter has an attribute ‘Y’ or ‘N,’ which means either to recompute the parameter oruse its initial value.

e) Mathematical control parameters for the optimization module.

Figure 3 General parameter extraction flow

Optimization STEP1

Devices Curves Parameters STEP

CurvesDevices Parameters

Check No

Yes

Optimization STEP2CurvesDevices Parameters

Check No

Yes

Optimization STEPNCurvesDevices

Check No

Yes

Model Parameters

Parameters

18


2. After completion of the optimization module, the following output files are created:

a) Log file stepN.log, which contains detailed information about the optimization process duringthe N-th optimization step.

b) A file stepN.smo, which contains a full list of SPICE parameters (the specified SPICE modelparameters have been updated at this optimization step); a root mean square (RMS) errorseparately for each .plt file; and the total error (averaged over all curves).

3. SXtract ‘remembers’ the new values of the extracted parameters and uses them at the next extractionstep.

In a standard parameter extraction procedure, users do not need to consider these three steps. However,it may be necessary to analyze the intermediate data and the intermediate output.

Physically oriented optimization sequenceThe very general approach described in Sequence of parameter extraction on page 17 allows users tocreate an arbitrary extraction strategy. One strategy is described here. It combines the mathematicalaccuracy of the optimization procedure with some deductive knowledge of the sensitivity of devicecharacteristics on specific parameters (which is usually based on experience and device physicsknowledge).

The main assumption of any physically oriented extraction is that it is possible to subdivide the full setof data (curves and devices) into subsets, which are mainly responsible for the appropriate subset of theSPICE model parameters. It can be shown that those subsets of parameters can be determinedindependently with some error.

To remove this error, optimization is performed over all parameters, but the extraction over the subsetof parameters is used as the initial guess for the global step. This approach is:

1. Assume that after execution of the (N–1)-th extraction step, the optimal values of the vector are obtained. These optimal values minimize the goal function for the dataset .

2. During the N-th extraction step, the optimal value of the unknown vector is determined. Itconsists of the union of the vector and the subset of the parameters, which must be determinedat this step (they are denoted as ).

Then, the vector can be written as . The vector will minimize the datasubset and the whole dataset is a union of the previous dataset and a newlydetermined one, .

3. The values of the vector are a result of solving the following optimization problem, where the initial guess is a union of and the user-

specified values for the initial guess for .

At the N-th step, the optimization is performed for the whole vector , although mostly, this step isdesigned to extract a subvector . The other components of will only slightly change at this step,but they stabilize the behavior of the goal function. To accelerate the optimization procedure, first a

XN 1–opt

XN 1– DataN 1–

XNXN 1–

XNnew

XN XN XN 1– XNnew

,{ }= XNnew

DataNnew DataN

DataN DataNnew DataN 1–∪=

XNopt XN

XNopt

min F XN DataN,( )( )arg= XNinit

XN 1–opt

XNnew

XN

XNnew XN

19


smaller optimization problem (intermediate-STEPN) such as issolved and then the previously described optimization problem is solved for STEPN. The values of theparameters after the intermediate step are used as the initial guess for the full STEPN optimization.

This optimization procedure is depicted in Figure 4, where STEPN-1 corresponds to the intermediate-STEPN. STEPN is the final N-th step of the optimization.

Figure 4 Extraction strategy

Optimization algorithmThe SXtract optimization module uses an algorithm that is based on theBroyden–Fletcher–Goldfarb–Shanno algorithm [1], which itself uses the quasi-Newton approach tominimization problems. The algorithm is complemented by the possibility to impose two-side linearlimits on the unknown parameters. This algorithm enhancement is based on the method of anti-gradientprojections onto linear limitations. During optimization, partial derivatives of the goal function must becomputed. In our approach, derivatives are computed numerically, but special precautions are used toguarantee a high accuracy of the numeric differentiation procedure. The optimal step of derivativescalculation in the optimization process is dynamically evaluated using information about goal functionbehavior [2]. The schematic of the optimization module is presented in Figure 5 on page 21.

XNnew opt,

min F XNnew

DataNnew,( )( )arg=

Optimization

Optimization

Optimization

Optimization

Optimization

Model Parameters

Devices Curves Parameters STEP

Devices

Set1

Curves

Set1

Parameters

Set1

Devices

Set2

Curves

Set2

Parameters

Set2

Devices

SetN-1

Curves

SetN-1

Parameters

SetN-1

STEP1

STEP2

STEP3

STEPN-1

STEPN

Devices

∪ Seti3

i=1

Curves

∪ Seti3

i=1

Parameters

∪ Seti3

i=1

Devices

∪ SetiN

i=1

Curves

∪ SetiN

i=1

Parameters

∪ SetiN

i=1

20


Figure 5 Schematic of optimization procedure

Goal functionsSXtract allows for the construction of very general goal functions for the optimization procedure. First,the general least square goal function is formulated. Let:

(2)

be the vector function of the independent input vector , the set of model parameters , and the set ofinstance device parameters . This vector function depends of a specific optimization task to be solved,so in order to make SXtract general and flexible, this function is programmed in a separate shared object,which is linked at run-time (see COMPACTMODEL section on page 12). The general goal function canbe written as:

(3)

Function

Measured Data

ConvergenceConditions

Stop

Gradient

Evaluation of Evaluation of

Evaluation of Stepsfor DerivativeComputation

Inverse HessianMatrix

1D Minimization

Direction ofMinimization

Initial Guessof Parameters

f f V X P, ,( )=

V XP

Ff

X( ) Wifi n,meas fi n,

sim X( )–

max fi n,meas fmin,( )

------------------------------------------⎝ ⎠⎜ ⎟⎛ ⎞

2

n 0=

N

∑i∑

curves∑

devices∑=

21


Here, devices is a set of devices selected for the optimization, curves is a set of sweeps selected for theoptimization for each device, N is the number of points on the curve during the sweep, and is the i-thcomponent of the vector function .

The superscript meas corresponds to the measured data that is obtained using Sentaurus Device and simcorresponds to the data after the simulation with the compact model. is the goal function weight forthe i-th component of vector function , and is the constant defined in Table 1 on page 15.

As described in STEP section on page 13, the type of the goal function immediately follows the keywordFUNCTION; the function presented by Eq. 3 is called quadratic.

For some special applications, it is necessary to optimize the derivative of vector function . The goalfunction activated by the name diff has the form:

(4)

where is the goal function weight for the derivative. Here, the total goal function has the form:

(5)

In some extraction strategies, DC and CV parameters are extracted simultaneously. Then, the goalfunction consists of the current and the diagonal components of the Y-matrix, , where and are conductivity and capacitance, i and j are the electrodes, and is the operating frequency. Insuch an approach, capacitances are multiplied by the frequency, which means the components of the goalfunction can have the same weight for both the real and imaginary parts of the impedance.

Convergence conditionsThe optimization process stops when one or more of the following convergence conditions is reached.

Goal function toleranceOptimization stops when the difference of the goal function at two successive iterations is less than thevalue specified by the function_tol parameter:

(6)

fif

Wif fmin

f

FV∂

∂ fX( ) Wi j,

Vj∂∂fi n,

meas

Vj∂∂ fi n,

sim X( )–

Vj∂∂fi n,

meas------------------------------------------------

⎝ ⎠⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎛ ⎞ 2

n 0=

Nj

∑×

i 0=

curves

∑devices∑

j∑=

Wi j, Vj∂∂fi

F X( ) Ff

X( ) FV∂

∂ fX( )+=

yij Aij ωCij+= AijCij ω

Fi 1+ X( ) Fi X( )–

Fi X( )-------------------------------------------- function_tol≤

22


The default value of function_tol is . It is possible to redefine this value in the global or localMATHEMATICS section of the extraction input file, for example:

function_tol = 1e-6

Maximum number of iterationsOptimization stops when the number of iterations exceeds the number specified by the maxiterparameter. The default value of maxiter is 100. It is possible to redefine this value in the global or localMATHEMATICS section of the extraction input file, for example, maxiter = 200.

Gradient criterionThe optimum is assumed to be reached when the gradient norm of the goal function is less than the valuespecified by the gradient_tol parameter. It corresponds to the expression:

(7)

The default value of gradient_tol is . This value can be redefined, for example, gradient_tol =1.e-5.

Additional stopping criterionThe optimization module always takes the next iteration step approximately in the anti-gradientdirection of the goal function, that is, the value of the goal function at each iteration must be smaller thanat the previous one. It may happen that, at an iteration, the goal function cannot be further reduced. Somereasons for this could be a too highly specified accuracy and computational noise due to rounding errors,nonsmooth derivatives of the goal function, and errors in the computation of derivatives. In this case,SXtract still exits with zero error code, although the final decision as to whether the obtained solution isacceptable must be made by the user, for example, on RMS error estimations.

NOTE No special action is required if the program terminates with such a criterion during anintermediate step.

1 10 10–×

F X( )∇ gradient_tol≤

F X( )∇ maxi Xi∂

∂ F X( )⎝ ⎠⎛ ⎞=

1 10 6–×

23


Root-mean-square evaluationThe root-mean-square error is used to evaluate the achieved accuracy. It is evaluated (in percent) by:

(8)

where N is a total number of measured points, and and are the components of output vector.

Random starting-point generationThe selection of an initial guess is very important for the successful solution of an optimization problem.In difficult cases, the initial values may be completely unknown. SXtract allows users to select an initialguess (starting point) randomly. The command for this selection is:

rand = M

where M is an integer. This command generates a sequence of random vectors of unknown parameters, which reproduces the appropriate sequence of values of goal function .

The starting point of optimization is selected to satisfy the condition: : ,that is, is the vector for which the functional F will reach the minimum among M randomselections.

Estimating standard error of extracted parametersThe important message we want to deliver is that fitting of parameters is not the end-all of parameterestimation. To be genuinely useful, a fitting procedure should provide (i) parameters, (ii) errorestimates on the parameters, and (iii) a statistical measure of goodness-of-fit. When the third itemsuggests that the model is an unlikely match to the data, then items (i) and (ii) are probably worthless.Unfortunately, many practitioners of parameter estimation never proceed beyond item (i). They deema fit acceptable if a graph of data and model “looks good.” This approach is known as chi-by-eye.Luckily, its practitioners get what they deserve.1

The estimation of the standard error is a more difficult part of parameter extraction than the extractionitself because of the lack of a mature mathematical theory for the nonlinear optimization problem.

1. W. H. Press, et al., Numerical Recipes in C: The Art of Scientific Computing, Cambridge: Cambridge UniversityPress, 2nd ed., 1992.

RMS 100 1N----

Inmeas In

sim X( )–

max Inmeas Imin,( )

-------------------------------------------⎝ ⎠⎜ ⎟⎛ ⎞

2

n 0=

N

∑×=

Inmeas In

sim

Xi i, 1 M÷= Fi Xi( ) i, 1 M÷=

Xstart mini

Fi Xi( )( ) i 1 M÷=,⎩ ⎭⎨ ⎬⎧ ⎫

Xstart

24


With some assumptions allowing simplification of the goal function behavior to a nearly optimalsolution, the standard error of a parameter can be calculated by using:

(9)

where is the standard error of -th parameter, is the value of the goal function at theoptimal solution , and is the -th diagonal element of the inverse Hessian matrix.

To activate the estimation of the standard error program procedure, users must define the flagstandarderror in the MATHEMATICS section (local or global) of the SXtract input file, for example:

MATHEMATICS {...standarderror...

} //END LOCAL MATHEMATICS

The resultant table of parameter values and their standard errors can be found in the *.log file of theappropriate extraction step. An example of this table for the BSIM3 model is:

Parameter Expected Standardname value error(%)vth0 = 5.000000e-01 +/- 5.000000e+00%k1 = 6.000000e-01 +/- 5.000000e+00%k2 = -5.000000e-03 +/- 2.000000e+02%k3 = -1.000000e+00 +/- 1.000000e+02%k3b = 1.000000e-01 +/- 4.000000e+02%nlx = 1.000000e-07 +/- 3.000000e+01%...

Note 1

Usually, the standard error of parameters that have clear physical meanings, such as vth0 in this example,is relatively small. The standard error for some parameters may be large. Apart from the obvious reason– the extracted value is far from the optimal value – there could be other reasons for this, such as:

The set of input data is not sufficient and an appropriate physical effect is not present there.

The model is not accurate enough to capture some effects.

The input data is noisy, which often occurs for parameters that are responsible for derivatives of thecurves.

The parameter is not needed for this particular situation.

Note 2

SXtract computes only estimated values and not exact values of standard errors. From this perspective,the standard error does not have a strong mathematical meaning. However, if two sets of parameters areextracted from some input data, the ratio of the standard errors of the two parameter sets reflects therelative quality of the extracted parameter sets.

ΔXi F Xoptim( ) Hii1–×=

ΔXi i F Xoptim( )Xoptim Hii

1– ii

25


26

SXTRACT CHAPTER 5 BSIM3 EXTRACTION

SXtract

CHAPTER 5 BSIM3 extraction

Given that CMOS is the most widely used technology and the BSIM3 compact model is the mostpopular compact model of MOSFET transistors, it is very important to provide fast and convenientextraction of BSIM3 model parameters. SXtract allows model parameters to be extracted for the originalBerkeley version of the BSIM3v3.2 model of MOS transistor [3].

SXtract uses its own extraction strategy, which is simple and accurate. Conversely, it allows any otherextraction strategy to be emulated (for example, the Berkeley strategy). SXtract allows static parametersto be extracted based on a set of IV curves (or their modifications, such as curve derivatives, ifnecessary) and transient parameters such as intrinsic capacitances. The latter can be extracted from CVcurves (as a result of direct AC analysis of the device) or by using a more complicated procedure ofextraction from special test structures. Moreover, SXtract allows for the use of advanced BSIM3extraction techniques, and the simultaneous and self-consistent extraction of DC and CV modelparameters (see Chapter 6 on page 47). This is especially important for very deep submicron devices.

Device size requirementsUsually, parameter extraction is performed for a set of devices: long-channel device, short-channeldevice, and a few intermediate devices. For 3D devices, the variation over the third dimension may benecessary.

In Figure 6, a set of devices recommended in the literature [3] is presented. The devices are called large,small, mshortN, and mnarrowN. Of course, other sets of devices are possible, for example, a setpresented in Figure 7 on page 28. On the other hand, because 3D simulation is time-consuming, the mostpopular will probably be a 2D simulation, without variation over the third dimension. This scheme ispresented as Figure 8 on page 28.

Figure 6 Scheme of set of MOSFET devices with various lengths and widths for parameter extraction

Width

Length

large

mshortN

mnarrowN

27

SXTRACTCHAPTER 5 BSIM3 EXTRACTION

Figure 7 Reduced set of MOSFET devices for parameter extraction

Figure 8 Set of 2D MOSFET devices for parameter extraction

SchematicThe NMOS and PMOS transistors are schematically drawn in Figure 9, where the letters correspond tothe names of the electrodes: s (source), d (drain), g (gate), and b (substrate (bulk)).

Figure 9 NMOS (left) and PMOS (right) transistors

Width

large

mshort1

mshort2mshort3

smallLength

Width

mshort3

small mshort1 large

mshort2

Length

g

s

d

b g

s

d

b

28


Data for extraction

IV curvesMost BSIM3 model parameters are extracted by fitting the DC curves, which are obtained from eithermeasurement or simulation. Here, it is assumed that all curves are obtained after numeric simulation,although users can also provide experimental curves as input for SXtract.

The commonly used bias conditions for DC simulations for each device are:

a) IdVg, Vd = 0.05 V For different bulk voltages Vb.

b) IdVg, Vd = Vdd V For different bulk voltages Vb.

c) IdVd, Vb = 0 For different gate voltages Vg.

d) IdVd, Vb = Vbb For different gate voltages Vg.

e) IbVg, Vb = 0 For different drain voltages Vd.

Here, Vdd and Vbb represent the maximum operating drain and bulk voltages, respectively. In Table 2,Table 3 on page 30, and Table 4 on page 30 are examples of curve specifications (for Vdd=2 V andVbb=2 V).

Table 2 IdVg

Curve name Vd Vg Vb Vs

idvg_1 0.05 0.0 2.0 0.05 0.0 0.0

idvg_2 0.05 0.0 2.0 0.05 –0.5 0.0

idvg_3 0.05 0.0 2.0 0.05 –1.0 0.0

idvg_4 0.05 0.0 2.0 0.05 –1.5 0.0

idvg_5 0.05 0.0 2.0 0.05 –2.0 0.0

idvgh_1 2.0 0.0 2.0 0.05 0.0 0.0

idvgh_2 2.0 0.0 2.0 0.05 –0.5 0.0

idvgh_3 2.0 0.0 2.0 0.05 –1.0 0.0

idvgh_4 2.0 0.0 2.0 0.05 –1.5 0.0

idvgh_5 2.0 0.0 2.0 0.05 –2.0 0.0

29


In the Vg column of Table 2 on page 29 and Table 4, and in the Vd column of Table 3, the first andsecond numbers represent the minimal and maximal values of the respective biases, and the thirdnumber is equal to the bias step during the bias ramp.

The curve names in the tables are used throughout in the extraction input file. These names arerecommended for use and are defined in the DEVICE section of the extraction input file, with the name ofthe respective .plt file. If users want to change these names, they must be changed appropriatelyeverywhere in the extraction input file (see Chapter 3 on page 9).

To create a project of Sentaurus Workbench, it is convenient to use the parameters of SentaurusWorkbench for bias specification (see Chapter 2 on page 5). In Table 5, the same parameters as in thetwo previous tables are presented using the parameter @SWEEP@ of Sentaurus Workbench, and theappropriate variables @Ramp1_Name@, @Ramp1_V@, @Ramp2_Name@, @Ramp2_V@, @Ramp3_Name@, @Ramp3_V@, and@Ramp3_step@.

Table 3 IdVd


idvd_1 0.0 2.0 0.05 0.7 0.0 0.0

idvd_2 0.0 2.0 0.05 1.2 0.0 0.0

idvd_3 0.0 2.0 0.05 1.7 0.0 0.0

idvd_4 0.0 2.0 0.05 2.0 0.0 0.0

idvd2_1 0.0 2.0 0.05 0.7 –2.0 0.0

idvd2_2 0.0 2.0 0.05 1.2 –2.0 0.0

idvd2_3 0.0 2.0 0.05 1.7 –2.0 0.0

idvd2_4 0.0 2.0 0.05 2.0 –2.0 0.0

Table 4 SubVg


isubvg_1 1.7 0.0 2.0 0.05 0.0 0.0

isubvg_2 2.0 0.0 2.0 0.05 0.0 0.0

Table 5 Specification of curves

SWEEP Ramp1_Name

Ramp1_V Ramp2_Name

Ramp2_V Ramp3_Name

Ramp3_V Ramp3_step

idvg_1 substrate 0.0 drain 0.05 gate 2.0 0.05

idvg_2 substrate –0.5 drain 0.05 gate 2.0 0.05



30


CV curvesTransient parameters can be extracted from the CV curves. Table 6 and Table 7 on page 32 list exampleswith bias conditions and the names of the variables of Sentaurus Workbench.


idvgh_1 substrate 0.0 drain 2.0 gate 2.0 0.05

idvgh_2 substrate –0.5 drain 2.0 gate 2.0 0.05




idvd_1 substrate 0.0 gate 0.7 drain 2.0 0.05




idvd2_1 substrate 2.0 gate 0.7 drain 2.0 0.05




isubvg_1 substrate 0.0 drain 1.7 gate 2.0 0.05

isubvg_1 substrate 0.0 drain 2.0 gate 2.0 0.05

Table 6 Capacitance curves


Cgg 0.0 –2.0 2.0 0.05 0.0 0.0

Cdd –0.6 2.0 0.05 0.0 0.0 0.0

Css 0.0 0.0 0.0 –0.6 2.0 0.05

Table 5 Specification of curves

SWEEP Ramp1_Name

Ramp1_V Ramp2_Name

Ramp2_V Ramp3_Name

Ramp3_V Ramp3_step

31


Extracting single-device parametersIn this section, an extraction technique applied to the IV and CV curves of a single device is presented.It is assumed that a 2D simulation of Sentaurus Device was used to obtain measured data.

Defining process-dependent parametersBefore any model parameters can be extracted, some process parameters must be provided. They arelisted in Table 8.

Defining SPICE parametersSXtract requires the following SPICE device parameters for each device.

Table 7 Specification of capacitance

CV Ramp1_Name Ramp1_V Ramp2_Name Ramp2_V Ramp2_step

Cgg vg.dc –2.0 vg.dc 2.0 0.05

Cdd vd.dc –0.6 vd.dc 2.0 0.05

Css vs.dc –0.6 vs.dc 2.0 0.05

Table 8 Process parameters

Parameter name Physical meaning

cit Interface state capacitance

nch Channel doping concentration

ngate Polygate doping

tnom Temperature at which parameters are extracted

tox Gate oxide thickness [m]

xj Junction depth [m]

Table 9 Device parameters


ad Area of the drain diffusions [m2]

as Area of the source diffusions [m2]

l Mask level channel length

32


Model control parametersTable 10 lists BSIM3 model control parameters that must be defined before an extraction simulation.

DC parameters

Single-device extraction: Parameters to be extracted

Table 11 lists the BSIM3 parameters to be extracted, their recommended initial values, and their limits.

nrd Number of squares of the drain diffusions

nrs Number of squares of the source diffusions

pd Perimeter of the drain junction [m]

ps Perimeter of the source junction [m]

temp Temperature at which device is simulated

w Mask level channel width

Table 10 User-defined model control parameters

Parameter name Meaning

capmod Flag for capacitance models

mobmod Mobility model selector

nmos/pmos Flag for transistor type

vbm Maximum body voltage

xpart Charge partitioning flag

Table 11 DC BSIM3 parameters for single-device extraction

Parameter name Initial value Minimum value Maximum value

a0 +1.000000e+00 +0.000e+00 +1.000e+01

a1 +0.000000e+00 -1.000e-00 +1.000e-00

ags +1.000000e-01 -1.000e+00 +1.000e+00

alpha0 +1.000000e-07 +1.000e-10 +1.000e-05

Table 9 Device parameters


33


b0 +0.000000e+00 -1.000e-01 +1.000e-01

beta0 +1.000000e+01 +1.000e+00 +1.000e+02

cdscb +0.000000e+00 -1.000e-02 +1.000e-02

cdscd +0.000000e+00 -1.000e-01 +1.000e-01

delta +1.000000e-02 +1.000e-04 +1.000e-00

eta0 +0.000000e+00 -1.000e+00 +1.000e+00

etab +0.000000e+00 -1.000e+00 +1.000e+00

k1 +5.000000e-01 +1.000e-01 +1.500e+00

k2 +0.000000e+00 -1.000e-00 +1.000e-00

keta +0.000000e+00 -1.000e+00 +1.000e+00

nfactor +1.000000e+00 +1.000e-02 +5.000e+00

ngate +3.000000e+20 +1.000e+19 +1.000e+22

pclm +1.300000e+00 +1.000e-02 +1.000e+02

pdiblc2 +8.600000e-03 +0.000e+00 +1.000e-00

pdiblcb 0.000000e+00 -1.000e+01 +5.000e-01

prwb +0.000000e+00 -1.000e-00 +1.000e+01

prwg +0.000000e+00 -1.000e-00 +1.000e+01

pscbe1 +4.240000e+08 +1.000e+04 +1.000e+09

pscbe2 +1.000000e-09 +0.000e+00 +1.000e-08

pvag +1.000000e-03 -1.000e+01 +1.000e+01

rdsw +1.000000e+02 +1.000e+00 +1.000e+04

u0 +6.700000e+02 +1.000e+01 +1.000e+03

ua +2.250000e-09 -1.000e-08 +1.000e-08

ub +5.870000e-19 -1.000e-16 +1.000e-16

uc -4.650000e-11 -1.000e-09 +1.000e-09

voff -8.000000e-02 -2.000e-01 +0.000e+00

vsat +8.000000e+04 +4.000e+04 +1.600e+05

vth0 +7.000000e-01 +1.000e-02 +1.000e+00

Table 11 DC BSIM3 parameters for single-device extraction


34


Single-device extraction: Predefined parameters

Table 12 lists the parameters that are not to be changed in a single-device extraction.

Single-device extraction strategy

Table 13 lists the parameters to be extracted at the appropriate optimization step and correspondingcurves used for optimization.

Table 12 Fixed DC BSIM3 parameters for single-device extraction

Parameter name Default value Parameter name Default value

alpha1 +0.000000e+00 lint +0.000000e+00

b1 +0.000000e+00 ll +0.000000e+00

cdsc +0.000000e+00 lln +1.000000e+00

cit +0.000000e+00 lw +0.000000e+00

drout +0.000000e+00 lwl +0.000000e+00

dsub +0.000000e+00 lwn +1.000000e+00

dvt0 +0.000000e+00 nlx +0.000000e+00

dvt0w +0.000000e+00 pdiblc1 +0.000000e+00

dvt1 +0.000000e+00 w0 +0.000000e+00

dvt1w +0.000000e+00 wint +0.000000e+00

dvt2 -3.200000e-02 wl +0.000000e+00

dvt2w +0.000000e+00 wln +1.000000e+00

dwb +0.000000e+00 wr +1.000000e+00

dwg +0.000000e+00 ww +0.000000e+00

k3 +0.000000e+00 wwl +0.000000e+00

k3b +0.000000e+00 wwn +1.000000e+00

Table 13 Single-device extraction strategy

Step Parameters Data

1 vth0, k1, k2, u0, ua, ub, uc, rdsw idvg.[Id] min(Id) = 1e-6

2 vth0, k1, k2, u0, ua, ub, uc, rdsw,prwb, voff, nfactor, cdscb

idvg.[Id] diff(Id,Vg) idvg.[Id] min(Id) = 1e-9

3 vth0, k1, k2, u0, ua, ub, uc, rdswprwb, voff, nfactor, cdscb,prwg, cdscd, eta0, etab, delta

idvg.[Id], idvgh.[Id]diff(Id,Vg) idvg.[Id]diff(Id,Vg) idvgh.[Id]min(Id) = 1e-9

35


CV parametersThe extraction of BSIM3 capacitance (CV) parameters must be performed after the extraction of the DCparameters, because some DC parameters are used during the CV extraction procedure. The user mustdefine the values of all DC parameters in the PSETTABLE section of the CV extraction input file.

Single-device extraction: Parameters to be extracted

Table 14 lists the BSIM3 CV parameters that are supposed to be extracted, their recommended initialvalues, and their limits.

4 vth0, k1, k2, u0, ua, ub, uc, rdswprwb, voff, nfactor, cdscb, prwg, cdscd, eta0, etab, delta, vsat, a0, ags, a1, pclm, pdiblc2, pscbe1, pscbe2, pvag, b0

idvg.[Id], idvgh.[Id]idvd.[Id] diff(Id,Vg) idvg.[Id] diff(Id,Vg) idvgh.[Id] diff(Id,Vd) idvd.[Id] min(Id) = 1e-9

5 vth0, k1, k2, u0, ua, ub, uc, rdswprwb, voff, nfactor, cdscb,prwg, cdscd, eta0, etab, delta,vsat, a0, ags, a1, pclm, pdiblc2, pscbe1, pscbe2, pvag, b0, keta

idvg.[Id], idvgh.[Id]idvd.[Id] idvd2[Id]diff(Id,Vg) idvg.[Id]diff(Id,Vg) idvgh.[Id]diff(Id,Vd) idvd.[Id]min(Id) = 1e-9

6 alpha0, beta0 isubvg.[Ib]

7 vth0, k1, k2, u0, ua, ub, uc, rdswprwb, voff, nfactor, cdscb,prwg, cdscd, eta0, etab, delta,vsat, a0, ags, a1, pclm, pdiblc2, pscbe1, pscbe2, pvag, b0,keta, (ngate if necessary)

idvg.[Id], idvgh.[Id]idvd.[Id] idvd2[Id]diff(Id,Vg) idvg.[Id]diff(Id,Vg) idvgh.[Id]diff(Id,Vd) idvd.[Id]min(Id) = 1e-9

Table 14 CV BSIM3 parameters for single-device extraction


acde 1.000000e+00 +1.000e-01 +1.600e+01

cf 1.000000e-11 +1.000e-15 +1.000e-10

cgdl 1.000000e-11 +1.000e-15 +1.000e-09

cgdo 1.000000e-10 +1.000e-15 +1.000e-09

cj 5.000000e-04 +1.000e-05 +1.000e-02

ckappa 6.000000e-01 +1.000e-02 +1.000e+01

clc 1.000000e-09 +1.000e-12 +1.000e-07

dlc 0.000000e+00 -1.000e-07 +1.000e-07



36


NOTE It is assumed in the provided shared objects for CV BSIM3 parameters (nbsim3cv, pbsim3cv,nbsim3cv1, pbsim3cv1) that cgso=cgdo and cgsl=cgdl.

Single-device extraction: Predefined parameters

Table 15 lists parameters that are not to be changed in a single-device CV extraction.

CV model control parameters

The following CV model control parameters must be defined.

mj 5.000000e-01 +1.000e-02 +1.000e+01

moin 1.500000e+01 +1.000e+00 +1.000e+05

noff 1.000000e+00 +1.000e-01 +1.000e+01

pb 1.000000e+00 +1.000e-01 +5.000e+00

vfbcv(capmod=0 only)

-1.000000e+00 -2.000e+00 -0.000e+00

voffcv 0.000000e+00 -5.000e-01 +5.000e-01

Table 15 Fixed CV BSIM3 parameters for single-device extraction

Parameter name Initial value Parameter name Initial value Parameter name Initial value

cgbo 0.000000e+00 llc 0.000000e+00 pbsw 1.000000e+00

cjsw 0.000000e+00 lwc 0.000000e+00 pbswg 1.000000e+00

cjswg 0.000000e+00 lwlc 0.000000e+00 wlc 0.000000e+00

cle 6.000000e-01 mjsw 3.300000e-01 wwc 0.000000e+00

dwc 0.000000e+00 mjswg 3.300000e-01 wwlc 0.000000e+00

Table 16 CV BSIM3 model control parameters

Parameter name Meaning

capmod Flag for capacitance models

xpart Charge partitioning flag

Table 14 CV BSIM3 parameters for single-device extraction


37


Single-device extraction strategy

A two-step extraction procedure is sufficient for the BSIM3 CV parameters. The parameters to beextracted and corresponding curves used for optimization are presented in Table 17.

BSIM3 objects

BSIM3 DC objects: nbsim3dc and pbsim3dcThe nbsim3dc and pbsim3dc shared objects are used for the calculation of the current vector as a functionof the voltage vector , the set of DC model parameters , and the set of instance device parameters :

(10)

The components of the voltage and current vectors are listed in Table 18 and Table 19 on page 39,respectively. The set of instance device parameters is shown in Table 20 on page 39. The BSIM3 DCshared objects use only the DC model parameters listed in Table 21 on page 39. Other BSIM3 DC modelparameters are not supported. All BSIM3 model parameters are described in the literature [3].

Use nbsim3dc and nmos=1 to specify an NMOS transistor. Use pbsim3dc and pmos=1 to specify a PMOStransistor.



1 cj, mj, pb cdd.[Cdd] css.[Css]

2 cj, mj, pb, dlc, noff, voffcv, acde, moin, clc, cf, cgdo, cgdl, ckappa

cgg.[Cgg][Cdd][Css]cdd.[Cdd][Cgg][Css]css.[Css][Cgg][Cdd]diff(Cgg, Vg) diff(Cdd, Vd)diff(Css, Vs)

Table 18 Input variables (BSIM3 DC)

Voltage name Description Unit

Vb External substrate–bulk voltage V

Vd External drain voltage V

Vg External gate voltage V

Vs External source voltage V

IV X P

I f V X P, ,( )=

38


Table 19 Output variables (BSIM3 DC)

Current name Description Unit

Ib Current at substrate–bulk terminal A

Id Current at drain terminal A

Is Current at source terminal A

Table 20 Instance device parameters (BSIM3 DC)

Name Description Unit

ad Drain area m2

as Source area m2

l Length m

nrd Number of squares in drain –

nrs Number of squares in source –

pd Drain perimeter m

ps Source perimeter m

temp Operating temperature oC

w Width m

Table 21 Model parameters (BSIM3 DC)


a0 Nonuniform depletion-width effect coefficient –

a1 Nonsaturation effect coefficient 1/V

a2 Nonsaturation effect coefficient –

ags Gate-bias coefficient of the bulk charge effect 1/V

alpha0 Substrate-current model parameter m/V

alpha1 Substrate-current model parameter 1/V

at Temperature coefficient of vsat m/s

b0 Bulk-charge effect coefficient for channel width m

b1 Bulk-charge effect width offset m

beta0 Substrate-current model parameter V

cdsc Drain–source and channel coupling capacitance F/m2

cdscb Body-bias dependence of cdsc F/Vm2

39


cdscd Drain-bias dependence of cdsc F/Vm2

cit Interface state capacitance F/m2

delta Effective Vds parameter V

drout DIBL coefficient of output resistance –

dsub DIBL coefficient in the subthreshold region –

dvt0 Short-channel effect coefficient 0 –

dvt0w Narrow-width coefficient 0 1/m


dvt1w Narrow-width effect coefficient 1 1/m

dvt2 Short-channel effect coefficient 2 1/V

dvt2w Narrow-width effect coefficient 2 1/V

dwb Width reduction parameter m/V1/2

dwg Width reduction parameter m/V

eta0 Subthreshold region DIBL coefficient –

etab Subthreshold region DIBL coefficient 1/V

ijth Diode-limiting current A

js Source–drain junction reverse saturation current density

A/m2

jsw Sidewall junction reverse saturation current density A/m

k1 Bulk-effect coefficient 1 V1/2

k2 Bulk-effect coefficient 2 –

k3 Narrow-width effect coefficient –

k3b Body-effect coefficient of k3 1/V

keta Body-bias coefficient of nonuniform depletion-width effect coefficient

1/V

kt1 Temperature coefficient of Vth V

kt1l Temperature coefficient of Vth Vm

kt2 Body coefficient of kt1 –

lint Length reduction parameter m

ll Length reduction parameter mlln



40


lln Length reduction parameter –

lw Length reduction parameter mlwn

lwl Length reduction parameter mlwn+lln

lwn Length reduction parameter –

mobmod Mobility model selector –

nch Channel doping concentration 1/cm3

nfactor Subthreshold swing coefficient –

ngate Polygate doping concentration cm–3

nj Source–drain junction emission coefficient –

nlx Lateral nonuniform doping effect parameter m

nmos Flag to indicate NMOS –

pclm Channel length modulation coefficient –

pdiblc1 Drain-induced barrier-lowering coefficient –


pdiblcb Body effect on drain-induced barrier lowering 1/V

pmos Flag to indicate PMOS –

prt Temperature coefficient of parasitic resistance

prwb Body effect on parasitic resistance V–1/2

prwg Gate-bias effect on parasitic resistance 1/V

pscbe1 Substrate-current body-effect coefficient V/m

pscbe2 Substrate-current body-effect coefficient m/V

pvag Gate dependence of output resistance parameter –

rdsw Source–drain resistance per width

rsh Source–drain sheet resistance /square

tnom Temperature at which parameters are extracted oC

tox Gate oxide thickness m

u0 Low-field mobility at tnom cm2/Vs

ua Linear gate dependence of mobility m/V

ua1 Temperature coefficient of ua m/V



Ω μm–

Ω μmwr–

Ω

41


ub Quadratic gate dependence of mobility (m/V)2

ub1 Temperature coefficient of ub (m/V)2

uc Body-bias dependence of mobilitymobmod=1,2mobmod=3

m/V2

1/V

uc1 Temperature coefficient of ucmobmod=1,2mobmod=3

m/V2

1/V

ute Temperature coefficient of mobility –

vbm Maximum applied body voltage V

voff Threshold voltage offset V

vsat Saturation velocity at tnom m/s

vth0 Threshold voltage V

w0 Narrow-width effect parameter m

wint Width reduction parameter m

wl Width reduction parameter mwln

wln Width reduction parameter –

wr Width dependence of rds –

ww Width reduction parameter mwwn

wwl Width reduction parameter mwwn+wln

wwn Width reduction parameter –

xj Junction depth m

xti Junction current temperature exponent –



42


BSIM3 CV objects: nbsim3cv, pbsim3cv, nbsim3cv1, pbsim3cv1The nbsim3cv, pbsim3cv, nbsim3cv1, and pbsim3cv1 shared objects are used for calculating the capacitancevector as a function of the voltage vector , the set of CV model parameters , and the set of instancedevice parameters :

(11)

where is a vector of BSIM3 DC model parameters (see BSIM3 DC objects: nbsim3dc andpbsim3dc on page 38).

The components of the voltage and capacitance vectors are listed in Table 18 on page 38 and Table 22,respectively. Table 20 on page 39 lists the set of instance device parameters. Table 23 lists the BSIM3CV shared objects use the CV model parameters.

Use nbsim3cv, nbsim3cv1, and nmos=1 to specify an NMOS transistor. Use pbsim3cv, pbsim3cv1, and pmos=1 tospecify a PMOS transistor.

nbsim3cv and pbsim3cv are used for capmod=3 only. nbsim3cv1 and pbsim3cv1 are used for capmod=0,1,2.

NOTE The nbsim3cv, pbsim3cv, nbsim3cv1, and pbsim3cv1 shared objects assume that cgso=cgdo,cgsl=cgdl.

Table 22 Output variables (BSIM3 CV)


Cbb Substrate–bulk capacitance F

Cdd Drain capacitance F

Cgg Gate capacitance F

Css Source capacitance F

Table 23 Model parameters (BSIM3 CV)


acde Exponential coefficient for finite charge thickness m/V

capmod Flag for capacitance models –

cf Fringe capacitance parameter F/m

cgbo Gate–bulk overlap capacitance per length F/m

cgdl Lightly doped gate–drain region overlap capacitance per width F/m

C V XP

C f V X P XDC, , ,( )=

XDC

43


cgdo Gate–drain overlap capacitance per width F/m

cgsl Lightly doped gate–source region overlap capacitance per width F/m

cgso Gate–source overlap capacitance per width F/m

cj Source–drain bottom junction capacitance per unit area F/m2

cjsw Source–drain sidewall junction capacitance per unit periphery F/m

cjswg Source–drain (gate side) sidewall junction capacitance per unit width

F/m

ckappa Coefficient for lightly doped region capacitance F/m

clc Vdsat parameter for C-V model m

cle Vdsat parameter for C-V model –

dlc Delta L for C-V model m

dwc Delta W for C-V model m

llc Length reduction parameter for CV mlln

lwc Length reduction parameter for CV mlwn

lwlc Length reduction parameter for CV mlwn+lln

mj Source–drain bottom junction capacitance grading coefficient –

mjsw Source–drain sidewall junction capacitance grading coefficient –

mjswg Source–drain (gate side) sidewall junction capacitance grading coefficient

–

moin Coefficient for gate bias–dependent surface potential V1/2

noff C-V switch on or off parameter –

pb Source–drain junction built-in potential V

pbsw Source–drain sidewall junction capacitance built-in potential V

pbswg Source–drain (gate side) sidewall junction capacitance built-in potential

V

tcj Temperature coefficient of cj 1/K

tcjsw Temperature coefficient of cjsw 1/K

tcjswg Temperature coefficient of cjswg 1/K

tpb Temperature coefficient of pb V/K

tpbsw Temperature coefficient of pbsw V/K



44


Goal functions

Current goal functionSXtract allows for the construction of very general goal functions for the optimization procedure.Usually, the optimization must be performed by using one terminal current, which corresponds to avoltage sweep. For example, during an IdVg sweep, the drain current must be included in the goalcurrent.

First, formulate the least square goal function for the drain current optimization only. This current goalfunction can be written as:

(12)

where I is the drain current Id, devices is a set of devices selected for the optimization of the draincurrent, curves is a set of sweeps selected for the optimization of the drain current for each device, andN is a number of biases in a Sentaurus Device simulation sweep for the appropriate IV curve, that is, thenumber of points on the IV curve during the sweep. The superscript meas corresponds to the measuredcurrent that is obtained with Sentaurus Device and sim corresponds to the current after the simulationwith the compact model. As described in STEP section on page 13, the type of the goal functionimmediately follows the keyword FUNCTION; the function presented by Eq. 12 is called quadratic.

tpbswg Temperature coefficient of pbswg V/K

vfbcv Flat-band voltage parameter for capmod=0 only V

voffcv C-V lateral shift parameter V

wlc Width reduction parameter for CV mwln

wwc Width reduction parameter for CV mwwn

wwlc Width reduction parameter for CV mwln+wwn

xpart Channel charge partitioning –



FI X( )Inmeas In

sim X( )–

max Inmeas Imin,( )

-------------------------------------------⎝ ⎠⎜ ⎟⎛ ⎞

2

n 0=

N

∑curves∑

devices∑=

45


The goal function activated by the name diff has the form:

(13)

where W is the goal function weight for the selected curve.

The total goal function has the form:

(14)

Instead of the drain current or together with the drain current, it is possible to include in the current goalfunction other values of terminal currents from each simulation sweep; for example, in an IdVdsimulation sweep, users can optimize not only the drain current, but also the bulk current. The names ofthe currents that must be included in the goal function are specified in brackets with every curvespecification in the body of the FUNCTION section. In Eq. 12 and Eq. 13, an additional sum sign over thespecified terminal currents must be added.

Capacitance goal functionTransient parameters of BSIM3 model can be extracted from the results of AC analysis. Similar toEq. 12, an appropriate goal function can be written as:

(15)

where C is equal to Cgg, Cdd, Css, or Cbb. If derivatives of capacitances are to be optimized, the goalfunction has the same form as Eq. 13:

(16)

where V is equal to Vg, Vd, Vs, or Vb. The total capacitance goal function has the form:

(17)

FV∂

∂IX( ) Wj

V∂∂In

meas

V∂∂ In

sim X( )–

V∂∂In

meas-----------------------------------------------

⎝ ⎠⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎛ ⎞

2

n 0=

Nj

∑×

j 0=

curves

∑devices∑=

FI X( ) FIdX( ) FIb

X( ) FVd∂

∂IdX( ) F

Vg∂∂Id

X( )+ + +=

FC X( )Cn

meas Cnsim X( )–

max Cnmeas Cmin,( )

-----------------------------------------------⎝ ⎠⎜ ⎟⎛ ⎞

2

n 0=

N

∑curves∑

devices∑=

FV∂

∂CX( ) Wj

V∂∂Cn

meas

V∂∂ Cn

sim X( )–

V∂∂Cn

meas---------------------------------------------------

⎝ ⎠⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎛ ⎞

2

n 0=

Nj

∑×

j 0=

curves

∑devices∑=

FC X( ) FCggX( ) FCdd

X( ) FCssX( ) F

Vg∂∂Cgg

X( ) FVd∂

∂CddX( ) F

Vs∂∂Css

X( )+ + + + +=

46

SXTRACT CHAPTER 6 BSIM3 SELF-CONSISTENT DC AND CV EXTRACTION

SXtract

CHAPTER 6 BSIM3 self-consistent DC and CV extraction

This chapter describes the BSIM3 shared objects that can be used for simultaneous and self-consistentDC and CV parameter extraction. In comparison with the strategy previously described, self-consistentextraction takes into account the coupling between DC and CV parameters of the BSIM3 model andgives more accurate results. However, such an extraction strategy can be more time-consuming than adecoupled one.

BSIM3 objects: nbsim3 and pbsim3The nbsim3 and pbsim3 shared objects are used for calculating the output vector function as a functionof the input vector , the set of model parameters , and the set of instance device parameters :

(18)

Table 24 lists the components of the input vector . If the input value of a component of this vector isnot defined in the input data, it is assumed to be equal to 0.

The components of the output vector function are listed in Table 25 on page 48 and consist of theterminal currents and the diagonal elements of the complex Y-matrix (in SentaurusDevice, Y-matrix isa result of small-signal AC analysis). The set of instance device parameters is shown in Table 26 onpage 48.

The nbsim3 and pbsim3 shared objects use only the model parameters listed in Table 27 on page 48. OtherBSIM3 model parameters are not supported. All BSIM3 model parameters is described in theliterature [4]. The nbsim3 and pbsim3 shared objects combine the functionality of DC and CV sharedobjects, which are used in the decoupled extraction approach (see BSIM3 objects on page 38).

Use nbsim3 and nmos=1 to specify an NMOS transistor. Use pbsim3 and pmos=1 to specify a PMOS transistor.

Table 24 Input variables (BSIM3)


F Frequency Hz





fV X P

f f V X P, ,( )=

V

f

47

SXTRACTCHAPTER 6 BSIM3 SELF-CONSISTENT DC AND CV EXTRACTION

Table 25 Output variables (BSIM3)


Abb Admittance bulk–bulk

Add Admittance drain–drain

Agg Admittance gate–gate

Ass Admittance source–source

Cbb Capacitance bulk–bulk F

Cdd Capacitance drain–drain F

Cgg Capacitance gate–gate F

Css Capacitance source–source F




Table 26 Instance device parameters (BSIM3)


ad Drain area m2

as Source area m2

l Length m






w Width m

Table 27 Model parameters (BSIM3)


a0 Nonuniform depletion width effect coefficient –

a1 Nonsaturation effect coefficient 1/V

a2 Nonsaturation effect coefficient –

acde Exponential coefficient for finite charge thickness m/V

Ω 1–

Ω 1–

Ω 1–

Ω 1–

48


ags Gate-bias coefficient of the bulk-charge effect 1/V

alpha0 Substrate current model parameter m/V

alpha1 Substrate current model parameter 1/V

at Temperature coefficient of vsat m/s

b0 Bulk-charge effect coefficient for channel width m

b1 Bulk-charge effect width offset m

beta0 Substrate current model parameter V

capmod Flag for capacitance models –

cdsc Drain–source and channel coupling capacitance F/m2

cdscb Body-bias dependence of cdsc F/Vm2

cdscd Drain-bias dependence of cdsc F/Vm2

cf Fringe capacitance parameter F/m

cgbo Gate–bulk overlap capacitance per length F/m

cgdl Lightly doped gate–drain region overlap capacitance per width

F/m

cgdo Gate–drain overlap capacitance per width F/m

cgsl Lightly doped gate–source region overlap capacitance per width

F/m

cgso Gate–source overlap capacitance per width F/m

cit Interface state capacitance F/m2

cj Source–drain bottom junction capacitance per unit area F/m2

cjsw Source–drain sidewall junction capacitance per unit periphery

F/m

cjswg Source–drain (gate side) sidewall junction capacitance per unit width

F/m

ckappa Coefficient for lightly doped region capacitance F/m

clc Vdsat parameter for C-V model m

cle Vdsat parameter for C-V model –

delta Effective Vds parameter V

dlc Delta L for C-V model m



49


drout DIBL coefficient of output resistance –

dsub DIBL coefficient in the subthreshold region –


dvt0w Narrow-width coefficient 0 1/m


dvt1w Narrow-width effect coefficient 1 1/m

dvt2 Short-channel effect coefficient 2 1/V

dvt2w Narrow-width effect coefficient 2 1/V

dwb Width reduction parameter m/V1/2

dwc Delta W for C-V model m

dwg Width reduction parameter m/V

eta0 Subthreshold region DIBL coefficient –

etab Subthreshold region DIBL coefficient 1/V

ijth Diode-limiting current A

js Source–drain junction reverse saturation current density A/m2

jsw Sidewall junction reverse saturation current density A/m

k1 Bulk-effect coefficient 1 V1/2

k2 Bulk-effect coefficient 2 –

k3 Narrow-width effect coefficient –

k3b Body-effect coefficient of k3 1/V

keta Body-bias coefficient of nonuniform depletion-width effect coefficient

1/V

kt1 Temperature coefficient of Vth V

kt1l Temperature coefficient of Vth Vm

kt2 Body coefficient of kt1 –

lint Length reduction parameter m

ll Length reduction parameter mlln

llc Length reduction parameter for CV mlln

lln Length reduction parameter –



50


lw Length reduction parameter mlwn

lwc Length reduction parameter for CV mlwn

lwl Length reduction parameter mlwn+lln

lwlc Length reduction parameter for CV mlwn+lln

lwn Length reduction parameter –

mj Source–drain bottom junction capacitance grading coefficient

–

mjsw Source–drain sidewall junction capacitance grading coefficient

–


–

mobmod Mobility model selector –

moin Coefficient for gate bias–dependent surface potential V1/2

nch Channel doping concentration 1/cm3

nfactor Subthreshold swing coefficient –

ngate Polygate doping concentration cm–3

nj Source–drain junction emission coefficient –

nlx Lateral nonuniform doping-effect parameter m

nmos Flag to indicate NMOS –

noff C-V switch on or off parameter –

pb Source–drain junction built-in potential V

pbsw Source–drain sidewall junction capacitance built-in potential

V

pbswg Source–drain (gate side) sidewall junction capacitance built-in potential

V

pclm Channel length modulation coefficient –



pdiblcb Body-effect on drain-induced barrier lowering 1/V

pmos Flag to indicate PMOS –

prt Temperature coefficient of parasitic resistance



Ω μm–

51


prwb Body effect on parasitic resistance V–1/2

prwg Gate-bias effect on parasitic resistance 1/V

pscbe1 Substrate-current body-effect coefficient V/m

pscbe2 Substrate-current body-effect coefficient m/V

pvag Gate dependence of output resistance parameter –

rdsw Source–drain resistance per width

rsh Source-drain sheet resistance /square

tcj Temperature coefficient of cj 1/K

tcjsw Temperature coefficient of cjsw 1/K

tcjswg Temperature coefficient of cjswg 1/K

tnom Temperature at which parameters are extracted oC

tox Gate oxide thickness m

tpb Temperature coefficient of pb V/K

tpbsw Temperature coefficient of pbsw V/K

tpbswg Temperature coefficient of pbswg V/K

u0 Low-field mobility at tnom cm2/Vs

ua Linear gate dependence of mobility m/V

ua1 Temperature coefficient of ua m/V

ub Quadratic gate dependence of mobility (m/V)2

ub1 Temperature coefficient of ub (m/V)2

uc Body bias dependence of mobilitymobmod=1,2mobmod=3

m/V2

1/V

uc1 Temperature coefficient of ucmobmod=1,2mobmod=3

m/V2

1/V

ute Temperature coefficient of mobility –

vbm Maximum applied body voltage V

vfbcv Flat-band voltage parameter for capmod=0 only V

voff Threshold voltage offset V



Ω μmwr–

Ω

52


Goal functionFor the extraction of CV parameters, the optimization fitting procedure is performed for a diagonalcomponents of Y-matrix, , where and are conductivity and capacitance, i and jare the electrodes, and is the operating frequency. Then, the output vector function can be writtenas:

(19)

that is, the capacitance components of the output vector function are multiplied by the frequency. Withsuch a definition of the output vector function, the general equations Eq. 3, Eq. 4, and Eq. 5 are valid.The goal function weight of the i-th component of vector function can be defined as described inTable 1 on page 15.

voffcv C-V lateral shift parameter V

vsat Saturation velocity at tnom m/s

vth0 Threshold voltage V

w0 Narrow-width effect parameter m

wint Width reduction parameter m

wl Width reduction parameter mwln

wlc Width reduction parameter for CV mwln

wln Width reduction parameter –

wr Width dependence of rds –

ww Width reduction parameter mwwn

wwc Width reduction parameter for CV mwwn

wwl Width reduction parameter mwwn+wln

wwlc Width reduction parameter for CV mwln+wwn

wwn Width reduction parameter –

xj Junction depth m

xpart Channel charge partitioning –

xti Junction current temperature exponent –



yij Aij ωCij+= Aij Cijω f

f Id Is Ib Add ωCdd Agg ωCgg Ass ωCss Abb ωCbb, , , , , , , , , ,{ }=

Wi f

53


NOTE If the i-th component of vector function is not selected for the optimization, is set to 0.

Extraction strategyThe examples of BSIM3 model parameter extraction using different extraction strategies, including self-consistent extraction of DC and CV parameters, can be found in the Manual Examples Library.

f Wi

54

SXTRACT CHAPTER 7 BJT GUMMEL–POON MODEL EXTRACTION

SXtract

CHAPTER 7 BJT Gummel–Poon model extraction

This chapter describes the bipolar junction transistor (BJT) shared objects used for extraction of theGummel–Poon model parameters as implemented in SPICE 3 Version 3F5.

SchematicThe n-p-n and p-n-p bipolar transistors are schematically depicted in Figure 10. The letters correspondto commonly used names of the electrodes: e (emitter), b (base), c (collector), and s (substrate).

Figure 10 n-p-n (left) and p-n-p (right) bipolar transistors

BJT objects: npnbjt and pnpbjtThe npnbjt and pnpbjt shared objects are used for calculating the output vector function as a functionof the input vector , the set of model parameters , and the set of instance device parameters :

(20)

The components of the input vector are listed in Table 28 on page 56. If the input value of somecomponent of this vector is not defined in the input data, it is assumed to be equal to 0. The componentsof the output vector function are listed in Table 29 on page 56 and consist of the terminal currents andthe diagonal elements of the complex Y-matrix. The set of instance device parameters is shown inTable 30 on page 56. The npnbjt and pnpbjt shared objects use only the model parameters are listed inTable 31 on page 56. Other Gummel–Poon model parameters are not supported. All Gummel–Poonmodel parameters are described in the literature [5].

Use npnbjt and npn=1 to specify an n-p-n transistor. Use pnpbjt and pnp=1 to specify a p-n-p transistor.

b

e

c

s b

e

c

s

fV X P

f f V X P, ,( )=

V

f

55

SXTRACTCHAPTER 7 BJT GUMMEL–POON MODEL EXTRACTION

Table 28 Input variables (BJT)


F Frequency Hz

Vb External base voltage V

Vc External collector voltage V

Ve External emitter voltage V

Vs External substrate voltage V

Table 29 Output variables (BJT)


Abb Admittance base–base

Acc Admittance collector–collector

Aee Admittance emitter–emitter

Ass Admittance substrate–substrate

Cbb Capacitance base–base F

Ccc Capacitance collector–collector F

Cee Capacitance emitter–emitter F

Css Capacitance substrate–substrate F

Ib Current at base terminal A

Ic Current at collector terminal A

Ie Current at emitter terminal A

Table 30 Instance device parameters (BJT)


area Area factor –

temp Instance temperature oC

Table 31 Model parameters (BJT)


bf Ideal forward beta –

br Ideal reverse beta –

cjc Zero-bias base–collector depletion capacitance F

cje Zero-bias base–emitter depletion capacitance F

Ω 1–

Ω 1–

Ω 1–

Ω 1–

56

SXTRACT CHAPTER 7 BJT GUMMEL–POON MODEL EXTRACTION

cjs Zero-bias collector–source capacitance F

eg Energy gap for IS temperature dependency eV

fc Forward bias junction fit parameter –

ikf Forward beta roll-off corner current A

ikr Reverse beta roll-off corner current A

irb Current for base resistance=(rb+rbm)/2 A

is Saturation current A

isc Base–collector leakage saturation current A

ise Base–emitter leakage saturation current A

itf High current dependence of TF A

mjc Base–collector junction-grading coefficient –

mje Base–emitter junction-grading coefficient –

mjs Substrate junction-grading coefficient –

nc Base–collector leakage emission coefficient –

ne Base–emitter leakage emission coefficient –

nf Forward emission coefficient –

npn Flag to indicate n-p-n transistor –

nr Reverse emission coefficient –

pnp Flag to indicate p-n-p transistor –

ptf Excess phase degree

rb Zero bias base resistance

rbm Minimum base resistance

rc Collector resistance

re Emitter resistance

tf Ideal forward transit time s

tnom Parameter measurement temperature oC

tr Ideal reverse transit time s

vaf Forward Early voltage V

var Reverse Early voltage V



Ω

Ω

Ω

Ω

57

SXTRACTCHAPTER 7 BJT GUMMEL–POON MODEL EXTRACTION

Goal functionFor the extraction of CV and transient parameters, the optimization fitting procedure is performed for adiagonal components of Y-matrix, , where and are conductivity and capacitance,i and j are the electrodes, and is the operating frequency. Then, the output vector function can bewritten as:

(21)

that is, the capacitance components of the output vector function are multiplied by the frequency. Withsuch definition of the output vector function, the general equations Eq. 3, Eq. 4, and Eq. 5 are valid. Thegoal function weight of the i-th component of vector function can be defined as described inTable 1 on page 15.


Extraction strategyThe examples of Gummel–Poon model parameter extraction using different extraction strategies,including self-consistent extraction of DC and CV parameters, can be found in the Manual ExamplesLibrary.

vjc Base–collector built-in potential V

vje Base–emitter built-in potential V

vjs Substrate junction built-in potential V

vtf Voltage giving VBC dependence of TF V

xcjc Fraction of base–collector capacitance to internal base

–

xtb Forward and reverse beta temperature exp. –

xtf Coefficient for bias dependence of TF –

xti Temperature exponent for IS –



yij Aij ωCij+= Aij Cijω f

f Ic Ib Ie Acc ωCcc Abb ωCbb Aee ωCee Ass ωCss, , , , , , , , , ,{ }=

Wi f

f Wi

58

SXTRACT CHAPTER 8 DIODE EXTRACTION

SXtract

CHAPTER 8 Diode extraction

This chapter describes the diode shared object used for extraction of the diode model, implemented inSPICE 3 Version 3F5 [5].

SchematicThe diode is schematically shown in Figure 11.

Figure 11 Diode

Diode object: diodeThe diode shared object is used for calculating the output vector function as a function of the inputvector , the set of model parameters , and the set of instance device parameters :

(22)

The components of the input vector are listed in Table 32. The components of the output vectorfunction are listed in Table 33 on page 60 and consist of the diode current and the elements of thecomplex Y-matrix. The set of instance device parameters is shown in Table 34 on page 60. The diodeshared object uses the model parameters listed in Table 35 on page 60 only. Other model parameters arenot supported. All diode model parameters are described in the literature [5].

Table 32 Input variables (Diode)


F Frequency Hz

Vd Diode voltage V

Id

Vd

fV X P

f f V X P, ,( )=

Vf

59

SXTRACTCHAPTER 8 DIODE EXTRACTION

Extraction strategyExamples of diode model parameter extraction are in the Manual Examples Library.

Table 33 Output variables (Diode)


Id Current through the diode A

ImY Imaginary part of complex conductance divided by F/Hz

ReY Real part of complex conductance

Table 34 Instance device parameters (Diode)


area Area factor –


Table 35 Model parameters (Diode)


bv Reverse breakdown voltage V

cjo Junction capacitance F

eg Activation energy eV

fc Forward bias junction fit parameter –

is Saturation current A

m Grading coefficient –

n Emission coefficient V

rs Ohmic resistance

tnom Parameter measurement temperature oC

tt Transit time s

vj Junction potential V

xti Saturation current temperature exp. –

ω

Ω 1–

Ω

60

SXTRACT CHAPTER 9 BSIM4 DC, CV, AND RF EXTRACTION

SXtract

CHAPTER 9 BSIM4 DC, CV, and RF extraction

This chapter describes the shared objects for BSIM4 extraction.

SchematicThe schematic structure of the BSIM4 model, including the gate electrode network, the substrateresistance network, and the source–drain parasitic resistances, is shown in Figure 12. A detaileddescription of each subcircuit element can be found in the literature [6].

Figure 12 BSIM4 schematic

BSIM4 DC, CV, and RF objects: nbsim4, pbsim4The nbsim4 and pbsim4 shared objects are used for the calculation of the output vector function as afunction of the input vector , the set of model parameters , and the set of instance device parameters

:

(23)

DS

B

G

Rgeltd

Rii

CgdoCgso

Rd(V)Rs(V)

RddiffRsdiff RBPS RBPD

RBPB

RBDBRBSB

fV X

P

f f V X P, ,( )=

61

SXTRACTCHAPTER 9 BSIM4 DC, CV, AND RF EXTRACTION

The components of the input vector are listed in Table 36.

If the input value of a component of this vector is not defined in the input data, the input value is assumedto be equal to 0. The components of the output vector function are listed in Table 37 and consist ofthe terminal currents and the diagonal element of the complex Y-matrix (in Sentaurus Device, the Y-matrix is a result of a small-signal AC analysis).

Table 36 Input variables (BSIM4 DC, CV, and RF)


F Frequency Hz





Table 37 Output variables (BSIM4 DC, CV, and RF)


Abb Admittance bulk–bulk

Add Admittance drain–drain

Agg Admittance gate–gate

Ass Admittance source–source

Cbb Capacitance bulk–bulk F

Cdd Capacitance drain–drain F

Cgg Capacitance gate–gate F

Css Capacitance source–source F



Ig Current at gate terminal A


V

f

Ω 1–

Ω 1–

Ω 1–

Ω 1–

62


Table 38 lists the set of instance device parameters, which must be specified by the user. Table 39 onpage 66 lists the set of model parameters, which can be extracted.

With the parameters capsel, diosel, rbsel, and rdssel, users can select a different extraction strategy. AC-style explanation of the meaning of these parameters is:

if( rdssel == 0 ) {

Asymmetric lightly doped drain–source resistance:

rsw != rdwrswmin != rdwmin}else {

Table 38 Instance device parameters (BSIM4 DC, CV, and RF)


ad Drain area m2

as Source area m2

capsel Asymmetric source–drain capacitance selector for extraction –

diosel Asymmetric source–drain junction diode selector for extraction –

l Length m

nf Number of fingers –





rbdb Resistance connected between dbNode and bNode

rbpb Resistance connected between bNodePrime and bNode

rbpd Resistance connected between bNodePrime and dbNode

rbps Resistance connected between bNodePrime and sbNode

rbsb Resistance connected between sbNode and bNode

rbsel Asymmetric substrate resistance network selector for extraction –

rdssel Asymmetric source–drain resistance selector for extraction –

rgeomod Source–drain resistance and contact model selector –


w Width m

Ω

Ω

Ω

Ω

Ω

63


Symmetric lightly doped drain–source resistance:

rsw = rdwrswmin = rdwmin}

As can be seen from the above definition, if rdssel=0, rsw and rdw (rswmin and rdwmin, respectively) aredifferent and must be extracted separately. Otherwise, they are the same (which is taken into accountduring extraction, and symmetry is guaranteed). In a similar way, all of the following construction canbe interpreted:

if( rbsel == 0 ) {

Asymmetric substrate resistance network:

(Table 39 on page 66)->rbpb != (Table 39 on page 66)->rbpd !=(Table 39 on page 66)->rbps != (Table 39 on page 66)->rbdb !=(Table 39 on page 66)->rbsb}else {

Symmetric substrate resistance network:

(Table 39 on page 66)->rbpd = (Table 39 on page 66)->rbpb(Table 39 on page 66)->rbps = (Table 39 on page 66)->rbpb(Table 39 on page 66)->rbdb = (Table 39 on page 66)->rbpb(Table 39 on page 66)->rbsb = (Table 39 on page 66)->rbpb}if( capsel == 0 ) {

Asymmetric source–drain capacitance:

cgso != cgdocgsl != cgdl

ckappas != ckappad}else {

Symmetric source–drain capacitance:

cgso = cgdocgsl = cgdlckappas = ckappad

}if( diosel == 0 ) {

Asymmetric source–drain junction diode:

ijthsrev != ijthdrevijthsfwd != ijthdfwdxjbvs != xjbvdbvs != bvdjss != jsdjsws != jswdjswgs != jswgdcjs != cjd

64


mjs != mjdmjsws != mjswdcjsws != cjswdcjswgs != cjswgdmjswgs != mjswgdpbs != pbdpbsws != pbswdpbswgs != pbswgdnjs != njdxtis != xtid}else {

Symmetric source–drain junction diode:

ijthsrev = ijthdrevijthsfwd = ijthdfwdxjbvs = xjbvdbvs = bvdjss = jsdjsws = jswdjswgs = jswgdcjs = cjdmjs = mjdmjsws = mjswdcjsws = cjswdcjswgs = cjswgdmjswgs = mjswgdpbs = pbdpbsws = pbswdpbswgs = pbswgdnjs = njdxtis = xtid}

To give more flexibility to the extraction of substrate resistance networks, the following rules apply forsubstrate resistance computation:

if( (Table 38 on page 63)->rbdb < 0. ) {instance->rbdb = (Table 39 on page 66)->rbdb}else {instance->rbdb = (Table 38 on page 63)->rbdb}if( (Table 38 on page 63)->rbsb < 0. ) {instance->rbsb = (Table 39 on page 66)->rbsb}else {instance->rbsb = (Table 38 on page 63)->rbsb}if( (Table 38 on page 63)->rbpb < 0. ) {instance->rbpb = (Table 39 on page 66)->rbpb}else {instance->rbpb = (Table 38 on page 63)->rbpb}if( (Table 38 on page 63)->rbps < 0. ) {instance->rbps = (Table 39 on page 66)->rbps

65


}else {instance->rbps = (Table 38 on page 63)->rbps}if( (Table 38 on page 63)->rbpd < 0. ) {instance->rbpd = (Table 39 on page 66)->rbpd}else {instance->rbpd = (Table 38 on page 63)->rbpd}

All instance device parameters that are not included in Table 38, but are listed among BSIM4parameters, are not supported in SXtract. (See the Compact Models manual for the complete list ofBSIM4 instance device parameters.) These parameters can be useful for circuit simulation but are notneeded for extraction.

The rgeomod instance parameter is used to select the rule for the calculation of the source–drain diffusionresistance. Only two possibilities are supported, which can be described as:

if{(rgeomod == 0)

The diffusion resistances Rs and Rd are not generated:

}else { Rd = nrd * rsh, Rs = nrs * rsh.}

The effective junction perimeter on the source and drain sides is calculated as follows:

if( permod == 0 ) PSeff = PS PDeff = PDelse PSeff = PS - Weffcj*NF PDeff = PD - Weffcj*NF

The nbsim4 and pbsim4 shared objects use only the model parameters listed in Table 39. Other BSIM4model parameters are not supported.

Use nbsim4 and nmos=1 to specify an NMOS transistor. Use pbsim4 and pmos=1 to specify a PMOS transistor.

Table 39 Model parameters (BSIM4 DC, CV, and RF)

Name Description Default value Unit

Model selectors or controllers

capmod Capacitance model selector 2 –

diomod Source–drain junction diode IV model selector 1 –

geomod Geometry-dependent parasitics model selector, specifying how the end source–drain diffusions are connected

0 –

66


igbmod Gate-to-substrate tunneling current model selector 0 –

igcmod Gate-to-channel tunneling current model selector 0 –

mobmod Mobility model selector 1 –

permod Pd and Ps model selector 1 –

rbodymod Substrate resistance network model selector 0 –

rdsmod Bias-dependent source–drain resistance model selector 0 –

rgatemod Gate resistance model selector 0 –

Process parameters

epsrox Dielectric constant of the gate oxide relative to vacuum 3.9 (SiO2) –

ndep Channel-doping concentration at the depletion edge for zero-body bias

1.7e17 cm–3

ngate Poly silicon gate-doping concentration 0.0 cm–3

nsd Source–drain doping concentration 1.0e20 cm–3

rsh Source–drain sheet resistance 0.0 /square

rshg Gate electrode sheet resistance 0.1 /square

toxe Electrical gate oxide thickness 3.0e-9 m

toxm Gate oxide thickness at which parameters are extracted 3.0e-9 m

toxp Physical gate oxide thickness 3.0e-9 m

xj Source–drain junction depth 1.5e-7 m

Basic model parameters

a0 Coefficient of channel-length dependence of bulk charge effect

1.0 –

a1 First nonsaturation effect parameter 0.0 V–1

a2 Second nonsaturation factor 1.0 –

ags Coefficient of Vgs dependence of bulk charge effect 0.0 V–1

b0 Bulk-charge effect coefficient for channel width 0.0 m

b1 Bulk-charge effect width offset 0.0 m

cdsc Coupling capacitance between source–drain and channel

2.4e-4 F/m2

cdscb Body bias dependence of cdsc 0.0 F/(Vm2)



Ω

Ω

67


cdscd Drain-bias dependence of cdsc 0.0 F/(Vm2)

cit Interface trap capacitance 0.0 F/m2

delta Parameter for DC Vdseff 0.01 V

drout Channel-length dependence of DIBL effect on Rout 0.56 –

dsub DIBL coefficient exponent in subthreshold region 0.56 –

dvt0 First coefficient of short-channel effect on Vth 2.2 –

dvt0w First coefficient of narrow-width effect on Vth for small-channel length

0.0 –

dvt1 Second coefficient of short-channel effect on Vth 0.53 –

dvt1w Second coefficient of narrow-width effect on Vth for small-channel length

5.3e6 m–1

dvt2 Body-bias coefficient of short-channel effect on Vth –0.032 V–1

dvt2w Body-bias coefficient of narrow-width effect for small-channel length

–0.032 V–1

dvtp0 First coefficient of pocket effect on Vth for long-channel devices

0.0 m

dvtp1 Second coefficient of pocket effect on Vth for long-channel devices

0.0 V–1

dwb Coefficient of body bias dependence of Weff 0.0 V1/2

dwg Coefficient of gate bias dependence of Weff 0.0 m/V

eta0 DIBL coefficient in subthreshold region 0.08 –

etab Body-bias coefficient for the subthreshold DIBL effect –0.07 V–1

eu Exponent for mobility degradation of mobmod=2 1.67 (NMOS)1.0 (PMOS)

–

fprout Effect of pocket implant on Rout degradation 0.0 V/m1/2

k1 First-order body-bias coefficient 0.5 V1/2

k2 Second-order body-bias coefficient 0.0 –

k3 Narrow-width coefficient 80.0 –

k3b Body-effect coefficient of k3 0.0 V–1

keta Body-bias coefficient of bulk-charge effect –0.047 V–1

lint Channel-length offset parameter 0.0 m



68


lpe0 Lateral nonuniform doping parameter at Vbs=0 1.74e-7 m

lpeb Lateral nonuniform doping effect on k1 0.0 m

minv Vgsteff-fitting parameter for moderate inversion condition

0.0 –

nfactor Subthreshold swing factor 1.0 –

pclm Channel length modulation parameter 1.3 –

pdiblc1 Parameter for DIBL effect on Rout 0.39 –


pdiblcb Body bias coefficient of DIBL effect on Rout 0.0 V–1

pdits Impact of drain-induced Vth shift on Rout 0.0 V–1

pditsd Vds dependence of drain-induced Vth shift for Rout 0.0 V–1

pditsl Channel-length dependence of drain-induced Vth shift for Rout

0.0 m–1

phin Nonuniform vertical-doping effect on surface potential 0.0 V

pscbe1 First substrate current-induced body-effect parameter 4.24e8 V/m

pscbe2 Second substrate current-induced body-effect parameter

1.0e-5 m/V

pvag Gate bias dependence of Early voltage 0.0 –

u0 Low-field mobility 0.067 (NMOS)0.025 (PMOS)

m2/(Vs)

ua Coefficient of first-order mobility degradation due to vertical field

1.0e-9 mobmod=0,11.0e-15 mobmod=2

m/V

ub Coefficient of second-order mobility degradation due to vertical field

1.0e-19 m2/V2

uc Coefficient of mobility degradation due to body-bias effect

–0.0465 mobmod=1–4.65e-11 mobmod=0,2

V–1; m/V2

vbm Maximum applied body bias in vth0 calculation –3.0 V

voff Offset voltage in subthreshold region for large W and L –0.08 V

voffl Channel-length dependence of voff 0.0 mV

vsat Saturation velocity 8.0e4 m/s



69


vth0 Long-channel threshold voltage at Vbs=0 0.7 (NMOS)–0.7 (PMOS)

V

w0 Narrow-width parameter 2.5e-6 m

wint Channel-width offset parameter 0.0 m

Parameters for asymmetric and bias-dependent Rds model

prwb Body bias dependence of LDD resistance 0.0 V–1/2

prwg Gate bias dependence of LDD resistance 1.0 V–1

rdsw Zero bias LDD resistance per unit width for rdsmod=0 200.0( m)wr

rdswmin LDD resistance per unit width at high Vgs and zero Vbs for rdsmod=0

0.0( m)wr

rdw Zero-bias lightly doped drain resistance Rd(V) per unit width for rdsmod=1

100.0( m)wr

rdwmin Lightly doped drain resistance per unit width at high Vgs and zero Vbs for rdsmod=1

0.0( m)wr

rsw Zero bias lightly doped source resistance Rs(V) per unit width for rdsmod=1

100.0( m)wr

rswmin Lightly doped source resistance per unit width at high Vgs and zero Vbs for rdsmod=1

0.0( m)wr

wr Channel-width dependence parameter of LDD resistance

1.0 –

Impact ionization current model parameters

alpha0 First parameter of impact ionization current 0.0 Am/V

alpha1 Isub parameter for length scaling 0.0 A/V

beta0 Second parameter of impact ionization current 30.0 V

Gate-induced drain leakage model parameters

agidl Pre-exponential coefficient for GIDL 0.0

bgidl Exponential coefficient for GIDL 2.3e9 V/m

cgidl Parameter for body-bias effect on GIDL 0.5 V3

egidl Fitting parameter for band bending for GIDL 0.8 V

Gate dielectric tunneling current model parameters

aigbacc Parameter for Igb in accumulation 0.43 (Fs2/g)1/2m–1



Ωμ

Ωμ

Ωμ

Ωμ

Ωμ

Ωμ

Ω

70


aigbinv Parameter for Igb in inversion 0.35 (Fs2/g)1/2m–1

aigc Parameter for Igcs and Igcd 0.43 (NMOS)0.31 (PMOS)

(Fs2/g)1/2m–1

aigsd Parameter for Igs and Igd 0.43 (NMOS)0.31 (PMOS)

(Fs2/g)1/2m–1

bigbacc Parameter for Igb in accumulation 0.054 (Fs2/g)1/2m–1 V–1

bigbinv Parameter for Igb in inversion 0.03 (Fs2/g)1/2m–1 V–1

bigc Parameter for Igcs and Igcd 0.054 (NMOS)0.024 (PMOS)

(Fs2/g)1/2m–1 V–1

bigsd Parameter for Igs and Igd 0.054 (NMOS)0.024 (PMOS)

(Fs2/g)1/2m–1 V–1

cigbacc Parameter for Igb in accumulation 0.075 V–1

cigbinv Parameter for Igb in inversion 0.006 V–1

cigc Parameter for Igcs and Igcd 0.075 (NMOS)0.03 (PMOS)

V–1

cigsd Parameter for Igs and Igd 0.075 (NMOS)0.03 (PMOS)

V–1

dlcig Source–drain overlap length for Igs and Igd 0.0 m

eigbinv Parameter for Igb in inversion 1.1 V

nigbacc Parameter for Igb in accumulation 1.0 –

nigbinv Parameter for Igb in inversion 3.0 –

nigc Parameter for Igcs, Igcd, Igs, and Igd 1.0 –

ntox Exponent for the gate oxide ratio 1.0 –

pigcd Vds dependence of Igcs and Igcd 1.0 –

poxedge Factor for gate oxide thickness in source–drain overlap regions

1.0 –

toxref Nominal gate oxide thickness for gate dielectric tunneling current model only

3.0e-9 m

Charge and capacitance model parameters

acde Exponential coefficient for charge thickness in capmod=2 for accumulation and depletion regions

1.0 m/V

cf Fringing field capacitance F/m

cgbo Gate–bulk overlap capacitance per unit channel length 0.0 F/m



71


cgdl Overlap capacitance between gate and lightly doped drain region

0.0 F/m

cgdo Non-LDD region drain–gate overlap capacitance per unit channel width

F/m

cgsl Overlap capacitance between gate and lightly doped source region

0.0 F/m

cgso Non-LDD region source–gate overlap capacitance per unit channel width

F/m

ckappad Coefficient of bias-dependent overlap capacitance for the drain side

0.6 V

ckappas Coefficient of bias-dependent overlap capacitance for the source side

0.6 V

clc Constant term for the short-channel model 1.0e-7 m

cle Exponential term for the short-channel model 0.6 –

dlc Channel-length offset parameter for CV model 0.0 m

dwc Channel-width offset parameter for CV model 0.0 m

moin Coefficient for the gate bias–dependent surface potential

15.0 –

noff CV parameter in Vgsteff,CV for weak to strong inversion

1.0 –

vfbcv Flat-band voltage parameter (for capmod=0 only) -1.0 V

voffcv CV parameter in Vgsteff, CV for weak to strong inversion

0.0 V

xpart Charge partition parameter 0.0 –

High-speed/RF model parameters

gbmin Conductance in parallel with each of the five substrate resistances

1.0e-12

rbdb Resistance connected between dbNode and bNode 50.0

rbpb Resistance connected between bNodePrime and bNode 50.0

rbpd Resistance connected between bNodePrime and dbNode

50.0

rbps Resistance connected between bNodePrime and sbNode

50.0

rbsb Resistance connected between sbNode and bNode 50.0



Ω

Ω

Ω

Ω

Ω

Ω

72


xrcrg1 Parameter for distributed channel-resistance effect for both intrinsic input resistance and charge-deficit NQS models

12.0 –

xrcrg2 Parameter to account for the excess channel diffusion resistance for both intrinsic input resistance and charge-deficit NQS models

1.0 –

Layout-dependent parasitics model parameters

ngcon Number of gate contact 1 –

xgl Offset of gate length due to variations in patterning 0.0 m

xgw Distance from gate contact to channel edge 0.0 m

Asymmetric source–drain junction diode model parameters

bvd Drain–diode breakdown voltage 10.0 V

bvs Source–diode breakdown voltage 10.0 V

cjd Bottom junction capacitance per unit area at zero bias for drain side

5.0e-4 F/m2

cjs Bottom junction capacitance per unit area at zero bias for source side

5.0e-4 F/m2

cjswd Isolation edge sidewall junction capacitance per unit length for drain side

5.0e-10 F/m

cjswgd Gate edge sidewall junction capacitance per unit length for drain side

5.0e-10 F/m

cjswgs Gate edge sidewall junction capacitance per unit length for source side

5.0e-10 F/m

cjsws Isolation edge sidewall junction capacitance per unit length for source side

5.0e-10 F/m

ijthdfwd Forward drain diode forward-limiting current 0.1 A

ijthdrev Reverse drain diode forward-limiting current 0.1 A

ijthsfwd Forward source diode forward-limiting current 0.1 A

ijthsrev Reverse source diode forward-limiting current 0.1 A

jsd Bottom drain junction reverse saturation current density

1.0e-4 A/m2

jss Bottom source junction reverse saturation current density

1.0e-4 A/m2



73


jswd Isolation edge sidewall drain junction reverse saturation current density

0.0 A/m

jswgd Gate edge drain junction reverse saturation current density

0.0 A/m

jswgs Gate edge source junction reverse saturation current density

0.0 A/m

jsws Isolation edge sidewall source junction reverse saturation current density

0.0 A/m

mjd Bottom junction capacitance grading coefficient for drain side

0.5 –

mjs Bottom junction capacitance grading coefficient for source side

0.5 –

mjswd Isolation edge sidewall junction capacitance grading coefficient for drain side

0.33 –

mjswgd Gate edge sidewall junction capacitance grading coefficient for drain side

0.33 –

mjswgs Gate edge sidewall junction capacitance grading coefficient for source side

0.33 –

mjsws Isolation edge sidewall junction capacitance grading coefficient for source side

0.33 –

pbd Bottom junction built-in potential for drain side 1.0 V

pbs Bottom junction built-in potential for source side 1.0 V

pbswd Isolation edge sidewall junction built-in potential for drain side

1.0 V

pbswgd Gate edge sidewall junction built-in potential for drain side

1.0 V

pbswgs Gate edge sidewall junction built-in potential for source side

1.0 V

pbsws Isolation edge sidewall junction built-in potential for source side

1.0 V

xjbvd Fitting parameter for drain–diode breakdown current 1.0 –

xjbvs Fitting parameter for source–diode breakdown current 1.0 –

Temperature-dependence parameters

at Temperature coefficient of vsat 3.3e4 m/s

kt1 Temperature coefficient for Vth –0.11 V



74


kt1l Channel-length dependence of the temperature coefficient for Vth

0.0 Vm

kt2 Body-bias coefficient of Vth temperature effect 0.022 –

njd Drain-junction emission coefficient 1.0 –

njs Source-junction emission coefficient 1.0 –

prt Temperature coefficient for rdsw 0.0 –m

tcj Temperature coefficient of cj 0.0 V/K

tcjsw Temperature coefficient of cjsw 0.0 V/K

tcjswg Temperature coefficient of cjswg 0.0 V/K

tnom Temperature at which parameters are extracted 27 oC

tpb Temperature coefficient of pb 0.0 V/K

tpbsw Temperature coefficient of pbsw 0.0 V/K

tpbswg Temperature coefficient of pbswg 0.0 V/K

ua1 Temperature coefficient of ua 1.0e-9 m/V

ub1 Temperature coefficient of ub –1.0e-18 (m/V)2

uc1 Temperature coefficient of uc 0.067 mobmod=10.025 mobmod=0,2

V–1

m/V2

ute Temperature coefficient of mobility –1.5 –

xtid Drain-junction current temperature exponent 3.0 –

xtis Source-junction current temperature exponent 3.0 –

dW and dL parameters

ll Coefficient of length dependence for length offset 0.0 mlln

llc Coefficient of length dependence for CV channel length offset

0.0 mlln

lln Power of length dependence for length offset 1.0 –

lw Coefficient of width dependence for length offset 0.0 mlwn

lwc Coefficient of width dependence for CV channel length offset

0.0 mlwn

lwl Coefficient of length and width cross term dependence for length offset

0.0 mlwn+lln



Ω

75


Considerations when extracting BSIM4 model parametersBSIM4 is a very complicated model and special precautions must be taken for successful parameterextraction.

Range of parameters

If some BSIM4 parameters (or internal BSIM4 variables) are outside of the allowed range, the BSIM4model behaves unpredictably, often resulting in a fatal error. Since SXtract allows users to set lower andupper bounds for possible values of the extracted parameters, it is strongly recommended that thesebounds are set so that parameters will be within the range that is acceptable for the model. Table 40shows the action of the BSIM4 model if a parameter is outside of the allowed range.

lwlc Coefficient of length and width cross term dependence for CV channel length offset

0.0 mlwn+lln

lwn Power of width dependence for length offset 1.0 –

wl Coefficient of length dependence for width offset 0.0 mwln

wlc Coefficient of length dependence for CV channel width offset

0.0 mwln

wln Power of length dependence of width offset 1.0 –

ww Coefficient of width dependence for width offset 0.0 mwwn

wwc Coefficient of width dependence for CV channel width offset

0.0 mwwn

wwl Coefficient of length and width cross term dependence for width offset

0.0 mwwn+wln

wwlc Coefficient of length and width cross term dependence for CV channel width offset

0.0 mwwn+wln

wwn Power of width dependence of width offset 1.0 –

Table 40 Limitations of BSIM4 parameters and variables

Condition BSIM4 action Condition BSIM4 action

toxe <= 0.0 Fatal error pscbe2 <= 0.0 Warning

toxp <= 0.0 Fatal error nf <= 0.0 Fatal error

toxm <= 0.0 Fatal error l <= xgl Fatal error

toxref <= 0.0 Fatal error ngcon < 1.0 Fatal error



76


The geomod parameter

The geomod parameter is not used directly, but is included for convenience.

The rshg parameter

The rshg parameter cannot be extracted using the 2D device simulation data. It is recommended that thisparameter is set equal to .

lpe0 < -leff Fatal error gbmin < 1.e-20 Warning

lpeb < -leff Fatal error clc < 0.0 Fatal error

phin < -0.4 Fatal error a2 < 0.01 Warning, a2=0.01

ndep <= 0.0 Fatal error a2 > 1.0 Warning, a2=1.0, a1=0.0

ngate <= 0.0 Fatal error prwg < 0.0 Warning, prwg=0.0

ngate > 1.e25 Fatal error rdsw < 0.0 Warning, rdsw=0.0

xj <= 0.0 Fatal error rdsmin < 0.0 Warning, rdsmin=0.0

dvt1 < 0.0 Fatal error fprout < 0.0 Fatal error

dwt1w < 0.0 Fatal error pdits < 0.0 Fatal error

w0 == -weff Fatal error pditsl < 0.0 Fatal error

dsub < 0.0 Fatal error nigbinv <= 0.0 Fatal error

b1 == -weff Fatal error nigbacc <= 0.0 Fatal error

u0temp <= 0.0 Fatal error nigc <= 0.0 Fatal error

delta < 0.0 Fatal error poxedge <= 0.0 Fatal error

vsattemp <= 0.0 Fatal error pigcd <= 0.0 Fatal error

pclm <= 0.0 Fatal error cgdo < 0.0 Warning, cgdo=0.0

drout < 0.0 Fatal error cgso < 0.0 Warning, cgso=0.0

Table 40 Limitations of BSIM4 parameters and variables

Condition BSIM4 action Condition BSIM4 action

1.0 10 3–×

77


Model selector parameters

For the best fit of the RF performance of the device, use the following values for BSIM4 model selectorparameters:

rdsmod=1, rgatemod=3, rbodymod=1

These values correspond to the schematic shown in Figure 12 on page 61.

Goal functionFor the extraction of CV and high-speed or RF model parameters, the optimization fitting procedure isperformed for diagonal components of the Y-matrix, , where and are conductivityand capacitance, i and j are the electrodes, and is the operating frequency. The output vector function

can then be written as:

(24)

The capacitance components of the output vector function are multiplied by the frequency. With thisdefinition of the output vector function, the general equations Eq. 3, Eq. 4, and Eq. 5 are valid. The goalfunction weight of the i-th component of vector function can be defined as described in Table 1on page 15.


Extraction strategySXtract supports a different BSIM4 extraction strategy, including:

DC parameter extraction only

CV parameter extraction

High-speed or RF parameter extraction

Simultaneous extraction of DC, CV, and high-speed or RF parameters

Single-device and multiple-device extraction

The following significant BSIM4 model parameters, which describe various physical effects ofMOSFET device operation, can be extracted:

Intrinsic input resistance (Rii) and the electrode gate resistance for RF, high-frequency analog, andhigh-speed digital applications

yij Aij ωCij+= Aij Cijω

f

f Id Ig I, s Ib Add ωCdd Agg ωCgg Ass ωCss Abb ωCbb, , , , , , , , , ,{ }=

Wi f

f Wi

78


Substrate resistance network parameters for RF modeling

Gate direct tunneling model parameters

Asymmetric or symmetric source–drain parasitic resistance, either internal or external to theintrinsic MOSFET

Mobility parameters for the all third mobility model

Gate-induced drain leakage (GIDL) current model parameters

Asymmetric or symmetric source–drain diode parameters

Quantum-mechanical charge-layer-thickness model parameters for both IV and CV characteristics

79


80

SXTRACT CHAPTER 10 BSIMPD EXTRACTION

SXtract

CHAPTER 10 BSIMPD extraction

This chapter describes the shared objects for the extraction of BSIMPD model parameters.

OverviewBSIMPD version 2.2 is a partially depleted (PD) silicon-on-insulator (SOI) MOSFET model. Thismodel was developed as an extension of another University of California Berkeley model, the bulksilicon BSIM3v3 model. The BSIMPD model shares the same basic equations related to generalMOSFET operation (non-SOI specific) with the bulk BSIM3v3 model. However, many new featuresand enhancements reflected in the complicated physics of SOI device are included in BSIMPD model,namely, floating body potential, parasitic lateral bipolar current, impact ionization current, gatetunneling current, gate-induced drain–source leakage current, and self-heating effects.

SchematicFigure 13 on page 82 shows the circuit elements that comprise the BSIMPD model for DC simulation.For convenience, temperature and substrate nodes are not indicated. In comparison with a conventionalbulk MOSFET model, a few current sources flowing into the internal body node are included in theBSIMPD model to provide high accuracy of the prediction of the floating-body potential. Detaileddescriptions of each current source can be found in the literature [7].

81

SXTRACTCHAPTER 10 BSIMPD EXTRACTION

Figure 13 Schematic of an SOI transistor

BSIMPD objects: nbsimpd2.2.2 and pbsimpd2.2.2The nbsimpd2.2.2 and pbsimpd2.2.2 shared objects are used for the calculation of the output vectorfunction as a function of the input vector , the set of model parameters , and the set of instancedevice parameters :

(25)

G

DS

P - External Body Node

B - Internal Body Node

Ids

Ibjt

Ibd

Igidl

Iii

Ibs

Igisl

Igb

Rbp

RdRs

f V XP

f f V X P, ,( )=

82


Table 41 lists the components of the input vector . If the input value of a component of this vector isnot defined in the input data, the input value is assumed to be equal to 0.

The components of the output vector function are listed in Table 42 and consist of the terminalcurrents.

Table 43 lists the set of instance device parameters, which must be specified by the user. The set ofmodel parameters, which can be extracted, is presented in Table 44 on page 84.

Table 41 Input variables (BSIMPD2.2)



Ve External substrate voltage V


Vp External body contact voltage V


Table 42 Output variables (BSIMPD2.2)


Ib Current at external body terminal A


Ig Current at gate terminal A


Table 43 Instance device parameters (BSIMPD2.2)


ad Drain area m2

aebcp Substrate-to-body overlap area for bc parasitics –

agbcp Gate-to-body overlap area for bc parasitics –

as Source area m2

bjtoff BJT on or off flag –

cth0 Instance thermal capacitance

float Flag for floating-body device:0 – body-contact device1 – floating-body device

–

frbody Layout-dependent body-resistance coefficient

l Length m

V

f

Ω

Ω

83


In addition to the instance device parameters described in the literature [7], users can select two otherparameters for different extraction strategies. The parameter temp can be used to specify one device atdifferent temperatures to extract isothermal and temperature-dependent parameters simultaneously. Theparameter float is used to specify explicitly that this particular device is either a floating-body device orbody-contact device. This is necessary if the parameter extraction for floating-body devices and body-contact devices is performed simultaneously in one optimization step of the extraction procedure.

nbc Number of body contact isolation edges –

nrb Number of squares in body –



nseg Number segments for width partitioning –


pdbcp Perimeter length for bc parasitics at drain side –


psbcp Perimeter length for bc parasitics at source side –

rth0 Instance thermal resistance


w Width m

Table 44 Model parameters (BSIMPD2.2)


Model control parameters

capmod Capacitance model selector 2 –

mobmod Mobility model selector 1 –

shmod Self heating mode selector0 – No self-heating

0 –

Process parameters

nch Channel doping concentration 1.7e17 cm–3

ngate Polysilicon gate doping concentration 0.0 cm–3

nsub Substrate doping concentration 6.0e16 cm–3

tbox Buried oxide thickness 3.0e-7 m

tox Gate oxide thickness 1.0e-8 m

Table 43 Instance device parameters (BSIMPD2.2)


Ω

84


tsi Silicon film thickness 1.0e-7 m

xj Source–drain junction depth tsi m

DC parameters

a0 Coefficient of channel-length dependence of bulk charge effect

1.0 –

a1 First nonsaturation effect parameter 0.0 V–1

a2 Second nonsaturation factor 1.0 –

aely Channel length dependency of Early voltage for bipolar current

0.0 V/m

agidl GIDL constant 0.0 –1

ags Coefficient of Vgs dependence of bulk charge effect

0.0 V–1

ahli High-level injection parameter for bipolar current 0.0 –

alpha0 First parameter of impact ionization current 0.0 m/V

b0 Bulk-charge effect coefficient for channel width 0.0 m

b1 Bulk-charge effect width offset 0.0 m

beta0 First Vds-dependent parameter of impact ionization current

0.0 V–1

beta1 Second Vds-dependent parameter of impact ionization current

0.0 –

beta2 Third Vds-dependent parameter of impact ionization current

0.1 V

bgidl GIDL exponential coefficient 0.0 V/m

cdsc Coupling capacitance between source–drain and channel

2.4e-4 F/m2

cdscb Body bias dependence of cdsc 0.0 F/(Vm2)

cdscd Drain bias dependence of cdsc 0.0 F/(Vm2)

cit Interface trap capacitance 0.0 F/m2

delta Parameter for DC Vdseff 0.01 V

drout Channel-length dependence of DIBL effect on Rout

0.56 –

dsub DIBL coefficient exponent in subthreshold region 0.56 –



Ω

85


dvt0 First coefficient of short-channel effect on Vth 2.2 –

dvt0w First coefficient of narrow-width effect on Vth for small channel length

0.0 –

dvt1 Second coefficient of short-channel effect on Vth 0.53 –

dvt1w Second coefficient of narrow-width effect on Vth for small channel length

5.3e6 m–1

dvt2 Body-bias coefficient of short-channel effect on Vth

–0.032 V–1

dvt2w Body-bias coefficient of narrow-width effect for small channel length

–0.032 V–1

dwb Coefficient of body bias dependence of Weff 0.0 m/V1/2

dwbc Width offset for body contact isolation edge 0.0 m

dwg Coefficient of gate bias dependence of Weff 0.0 m/V

esatii Saturation electric field for impact ionization 1.0e7 V/m

eta0 DIBL coefficient in subthreshold region 0.08 –

etab Body bias coefficient for the subthreshold DIBL effect

–0.07 V–1

fbjtii Fraction of bipolar current affecting the impact ionization

0.0 –

isbjt BJT injection saturation current 1.0e-6 A/m2

isdif Body to source–drain injection saturation current 0.0 A/m2

isrec Recombination in depletion saturation current 1.0e-5 A/m2

istun Reverse tunneling saturation current 0.0 A/m2

k1 First-order body-effect coefficient 0.6 V1/2

k1w1 First body-effect width-dependent parameter 0.0 m

k1w2 Second body-effect width-dependent parameter 0.0 m

k2 Second-order body-effect coefficient 0.0 –

k3 Narrow-width coefficient 80.0 –

k3b Body-effect coefficient of k3 0.0 V–1

kb1 Backgate body charge coefficient 1 –

keta Body-bias coefficient of bulk charge effect -0.6 V–1



86


ketas Surface potential adjustment for bulk charge effect 0.0 V

lbjt0 Reference channel length for bipolar current 2.0e-7 m

lii Channel-length dependent parameter at threshold for impact ionization current

0.0 m

lint Length offset fitting parameter from I-V without bias

0.0 m

ln Electron–hole diffusion length 2.0e-6 m

nbjt Power coefficient of channel length dependency for bipolar current

1.0 –

ndiode Diode non-ideality factor 1.0 –

nfactor Subthreshold swing factor 1.0 –

ngidl GIDL Vds enhancement coefficient 1.2 V

nlx Lateral nonuniform doping parameter 1.74e-7 m

nrecf0 Recombination non-ideality factor at forward bias 2.0 –

nrecr0 Recombination non-ideality factor at reverse bias 10.0 –

ntun Reverse tunneling non-ideality factor 10.0 –

pclm Channel length modulation parameter 1.3 –



pdiblcb Body-bias coefficient of DIBL effect on Rout 0.0 V–1

prwb Body-bias dependence of rdsw 0.0 V–1/2

prwg Gate-bias dependence of rdsw 0.0 V–1

pvag Gate bias dependence of Early voltage 0.0 –

rbody Intrinsic body contact sheet resistance 0.0 /square

rbsh Extrinsic body contact sheet resistance 0.0 /square

rdsw Parasitic resistance per unit width 100.0( m)wr

rhalo Body-halo sheet resistance 1.0e15 /m

rsh Source–drain sheet resistance 0.0 /square

sii0 First Vgs-dependent parameter for impact ionization current

0.5 V–1



Ω

Ω

Ωμ

Ω

Ω

87


sii1 Second Vgs-dependent parameter for impact ionization current

0.1 V–1

sii2 Third Vgs-dependent parameter for impact ionization current

0.0 V–1

siid Vds-dependent parameter of drain saturation voltage for impact ionization current

0.0 V–1

tii Temperature-dependent parameter for impact ionization current

0.0 –

u0 Low-field mobility at Temp=Tnom 0.067 (NMOS)0.025 (PMOS)

m2/(Vs)

ua Coefficient of first-order mobility degradation due to vertical field

2.25e-9 m/V

ub Coefficient of second-order mobility degradation due to vertical field

5.87e-19 m2/V2

uc Coefficient of mobility degradation due to body-bias effect

–0.0465 mobmod=3;–4.65e-11 mobmod=1,2

V–1; m/V2

vabjt Early voltage for bipolar current 10.0 V

vdsatii0 Nominal drain saturation voltage at threshold for impact ionization current

0.9 V

voff Offset voltage in subthreshold region for large W and L

–0.08 V

vrec0 Voltage-dependent parameter for recombination current

0.0 V

vsat Saturation velocity at Temp=Tnom 8.0e4 m/s

vth0 Threshold voltage at Vbs=0 for long and wide device

0.7 (NMOS)–0.7 (PMOS)

V

vtun0 Voltage-dependent parameter for tunneling current

0.0 V

w0 Narrow-width parameter 2.5e-6 m

wint Width offset fitting parameter from I-V without bias

0.0 m

wr Channel-width dependence parameter of rdsw 1.0 –



88


Gate-to-body tunneling parameters

alphagb1 First Vox-dependent parameter for gate current in inversion

0.35 V–1

alphagb2 First Vox-dependent parameter for gate current in accumulation

0.43 V–1

betagb1 Second Vox-dependent parameter for gate current in inversion

0.03 V–2

betagb2 Second Vox-dependent parameter for gate current in accumulation

0.05 V–2

deltavox Smoothing parameter in the Vox smoothing function

0.005 –

ebg Effective band gap in gate current calculation 1.2 V

igmod Gate current model selector 0 –

ntox Power term of gate current 1.0 –

toxqm Oxide thickness for Igb calculation tox m

toxref Target oxide thickness 2.5e-9 m

vecb Vaux parameter for conduction band electron tunneling

0.026 –

vevb Vaux parameter for valence band electron tunneling

0.075 –

vgb1 Third Vox-dependent parameter for gate current in inversion

300.0 V

vgb2 Third Vox-dependent parameter for gate current in accumulation

17.0 V

voxh Limit of Vox in gate current calculation 5.0 –

AC and capacitance parameters

acde Exponential coefficient for charge thickness in capmod=3 for accumulation and depletion regions

1.0 m/V

asd Source–drain bottom diffusion smoothing parameter

0.3 –

cf Gate to source–drain fringing field capacitance 0.0 F/m

cgdl Lightly doped drain–gate region overlap capacitance

0.0 F/m



89


cgdo Non-LDD region drain–gate overlap capacitance per channel length

0.0 F/m

cgeo Gate–substrate overlap capacitance per unit channel length

0.0 F/m

cgsl Lightly doped source–gate region overlap capacitance

0.0 F/m

cgso Non-LDD region source–gate overlap capacitance per channel length

0.0 F/m

cjswg Source–drain (gate side) sidewall junction capacitance per unit width (normalized to 100 nm Tsi)

1.0e-10 F/m2

ckappa Coefficient of bias-dependent for lightly doped region overlap capacitance

0.6 –

clc Constant term for the short channel model 1.0e-8 m

cle Exponential term for the short channel model 0.0 –

csdesw Source–drain sidewall fringing capacitance per unit length

0.0 F/m

csdmin Source–drain bottom diffusion minimum capacitance

0.0 F

delvt Threshold voltage adjust for C-V 0.0 V

dlbg Length offset fitting parameter for backgate charge

0.0 m

dlc Length offset fitting parameter for gate charge 0.0 m

dlcb Length offset fitting parameter for body charge 0.0 m

dwc Width offset fitting parameter for C-V 0.0 m

fbody Scaling factor for body charge 1.0 –

ldif0 Channel length dependency coefficient of diffusion cap

1.0 –


0.5 –

moin Coefficient for the gate bias–dependent surface potential

15.0 V0.5

ndif Power coefficient of channel length dependency for diffusion capacitance

1.0 –



90


pbswg Source–drain (gate side) sidewall junction capacitance build in potential

0.7 V

tt Diffusion capacitance transit time coefficient 1.0e-12 s

vsdfb Source–drain bottom diffusion capacitance flat-band voltage

0.0 V

vsdth Source–drain bottom diffusion capacitance threshold voltage

0.0 V

xpart Charge partitioning rate flag 0.0 –

Temperature parameters

at Temperature coefficient of vsat 3.3e4 m/s

cth0 Normalized thermal capacity 0.0 Ws/moC

kt1 Temperature coefficient for Vth –0.11 V

kt1l Channel-length dependence of the temperature coefficient for Vth

0.0 Vm

kt2 Body-bias coefficient of Vth temperature effect 0.022 –

ntrecf Temperature coefficient for nrecf 0.0 –

ntrecr Temperature coefficient for nrecr 0.0 –

prt Temperature coefficient for rdsw 0.0 –m

rth0 Normalized thermal resistance 0.0 moC/W

tcjswg Temperature coefficient of cjswg 0.0 1/oC

tnom Temperature at which parameters are extracted 27 oC

tpbswg Temperature coefficient of pbswg 0.0 V/oC

ua1 Temperature coefficient of ua 4.31e-9 m/V

ub1 Temperature coefficient of ub –7.61e-18 (m/V)2

uc1 Temperature coefficient of uc –0.056 mobmod=3-0.056e-9 mobmod=1,2

V–1

m/V2

ute Temperature coefficient of mobility –1.5 –

wth0 Minimum width for thermal resistance calculation 0.0 m

xbjt Power dependence of jbjt on temperature 1.0 –

xdif Power dependence of jdif on temperature 1.0 –



Ω

91


Extraction strategyParameter extraction of the BSIMPD model is more difficult than bulk device extraction, mainlybecause of floating body and self-heating effects. The existence of floating bodies makes a SOI deviceextremely sensitive to the physical effects, which could be negligible for the bulk device under the samebias conditions. Due to the low heat conductivity of the oxide, which surrounds the SOI device, the self-heating effect becomes important even for relatively low applied biases.

The commonly used extraction approach [8] is to extract parameters for the body-contact device andthen use the parameters for the floating-body devices. However, such an approach may not besufficiently accurate because the floating-body effect does not exist for the body-contact devices.SXtract enables extraction directly for the floating-body device only or extraction of parameterssimultaneously for body-contact devices and floating-body devices.

This is achieved by the special extraction strategy for BSIMPD developed in SXtract, which is differentfor the body contact–based extraction, the floating body–based extraction, and simultaneous bodycontact and floating-body extraction.

The extraction of device parameters with the self-heating effect is not supported.

xrec Power dependence of jrec on temperature 1.0 –

xtun Power dependence of jtun on temperature 0.0 –

dW and dL parameters

ll Coefficient of length dependence for length offset 0.0 mlln

lln Power of length dependence for length offset 1.0 –

lw Coefficient of width dependence for length offset 0.0 mlwn

lwl Coefficient of length and width cross term dependence for length offset

0.0 mlwn+lln

lwn Power of width dependence for length offset 1.0 –

wl Coefficient of length dependence for width offset 0.0 mwln

wln Power of length dependence of width offset 1.0 –

ww Coefficient of width dependence for width offset 0.0 mwwn

wwl Coefficient of length and width cross term dependence for width offset

0.0 mwwn+wln

wwn Power of width dependence of width offset 1.0 –



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SXTRACT CHAPTER 11 MEXTRAM 504 PARAMETER EXTRACTION

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CHAPTER 11 Mextram 504 parameter extraction

This chapter describes the bipolar junction transistor (BJT) shared objects used for extraction ofparameters of the Mextram 504 bipolar transistor model, version 4.1 [9]. The Mextram 504 modelcontains many features that are not in the widespread Gummel–Poon bipolar model. It can be used forstandard bipolar technology and advanced processes including double-poly and SiGe transistors, high-voltage power devices, and lateral n-p-n transistors in LDMOS technology.

SchematicThe n-p-n and p-n-p bipolar transistors are schematically depicted in Figure 14. The letters correspondto the commonly used names of the electrodes: c (collector), s (substrate), e (emitter), and b (base).

Figure 14 n-p-n (left) and p-n-p (right) bipolar transistors

Mextram object: ts504The ts504 shared object is used in SXtract for the calculation of the output vector function as afunction of the input vector , the set of model parameters , and the set of instance device parameters

:

(26)

The components of the input vector are listed in Table 45 on page 94. If the input value of acomponent of this vector is not defined in the input data, it is assumed to be equal to 0. The componentsof the output vector function are listed in Table 46 on page 94 and consist of the terminal currents,capacitances, and the diagonal and nondiagonal elements of the complex Y-matrix of a two-port circuitconfiguration. The set of instance device parameters is shown in Table 47 on page 94. The ts504 sharedobject uses the model parameters listed in Table 48 on page 95. The flicker noise parameters are listedfor completeness and cannot be extracted. A complete description of the Mextram 504 model is givenin the literature [9].

Use TYPE=1 to specify an n-p-n transistor. Use TYPE=-1 to specify a p-n-p transistor.

b

e

c

s b

e

c

s

fV X

P

f f V X P, ,( )=

V

f

93

SXTRACTCHAPTER 11 MEXTRAM 504 PARAMETER EXTRACTION

Table 45 Input variables (Mextram 504)


F Frequency Hz

Ibi Base current as input variable A

Vb External base voltage V

Vc External collector voltage V

Ve External emitter voltage V

Vs External substrate voltage V

Table 46 Output variables (Mextram 504)


Cbc Base–collector capacitance F

Cbe Base–emitter capacitance F

Csc Substrate–collector capacitance F

Ib Current at base terminal A

Ic Current at collector terminal A

Ie Current at emitter terminal A

Is Current at substrate terminal A

Y11_I Y11.im component of Y-matrix A/V

Y11_R Y11.real component of Y-matrix A/V







Table 47 Instance device parameter (Mextram 504)



94


Table 48 Model parameters (Mextram 504)


General parameters

DTA Difference between device temperature and ambient temperature oC

EXAVL Flag for extended modeling of avalanche current –

EXMOD Flag for extended modeling of the reverse current gain –

EXPHI Flag for distributed high-frequency effects in transient –

LEVEL Model level (LEVEL=504) –

MULT Multiplication factor –

TREF Reference temperature oC

TYPE Flag to indicate n-p-n (TYPE=1) or p-n-p (TYPE=–1) transistor (SXtract only)

–

Current parameters

BF Ideal forward current gain –

BRI Ideal reverse current gain –

IBF Saturation current of the non-ideal forward base current A

IBR Saturation current of the non-ideal reverse base current A

IK Collector–emitter high-injection knee current A

IS Collector–emitter saturation current A

MLF Non-ideality factor of the non-ideal forward base current –

VEF Forward Early voltage V

VER Reverse Early voltage V

VLR Crossover voltage of the non-ideal reverse base current V

XEXT Part of Iex, Qtex, Qex, and Isub that depends on Vbc1 instead of Vb1c1

–

XIBI Part of ideal base current that belongs to the sidewall –

Avalanche model parameters

SFH Current spreading factor of avalanche model (when EXAVL=1) –

VAVL Voltage determining curvature of avalanche current V

WAVL Epilayer thickness used in weak-avalanche model m

Resistance and epilayer parameters

AXI Smoothness parameter for the onset of quasisaturation –

95


IHC Critical current for velocity saturation in the epilayer A

RBC Constant part of the base resistance

RBV Zero-bias value of the variable part of the base resistance

RCC Constant part of collector resistance

RCV Resistance of the unmodulated epilayer

RE Emitter resistance

SCRCV Space charge resistance of the epilayer

Emitter–base depletion capacitance

CBEO Emitter–base overlap capacitance F

CJE Zero-bias emitter–base depletion capacitance F

PE Emitter–base grading coefficient –

VDE Emitter–base diffusion voltage V

XCJE Fraction of emitter–base depletion capacitance that belongs to the sidewall

–

Collector–base depletion capacitance

CBCO Collector–base overlap capacitance F

CJC Zero-bias collector–base depletion capacitance F

MC Coefficient for current modulation of collector–base depletion capacitance

–

PC Collector–base grading coefficient –

VDC Collector–base diffusion voltage V

XCJC Fraction of collector–base depletion capacitance under the emitter –

XP Constant part of Cjc –

Transit times parameters

MTAU Non-ideality factor of emitter stored charge –

TAUB Transit time of stored base charge s

TAUE Minimum transit time of stored emitter charge s

TAUR Transit time of reverse extrinsic stored base charge s

TEPI Transit time of stored epilayer charge s



Ω

Ω

Ω

Ω

Ω

Ω

96


SiGe parameters

DEG Band gap difference over the base eV

XREC Prefactor of the recombination part of Ib1 –

Temperature parameters

AB Temperature coefficient of resistivity of the base –

AC Temperature coefficient of resistivity of the buried layer –

AE Temperature coefficient of resistivity of the emitter –

AEPI Temperature coefficient of resistivity of the epilayer –

AEX Temperature coefficient of resistivity of the extrinsic base –

AQBO Temperature coefficient of zero-bias base charge –

DVGBF Band gap voltage difference of forward current gain V

DVGBR Band gap voltage difference of reverse current gain V

DVGTE Band gap voltage difference of emitter stored charge V

VGB Band gap voltage of base V

VGC Band gap voltage of collector V

VGJ Band gap voltage recombination emitter–base junction V

Noise parameters

AF Exponent of the flicker noise –

KF Flicker noise coefficient of the ideal base current –

KFN Flicker noise coefficient of the non-ideal base current –

Substrate terminal parameters

AS For a closed buried layer: AS=AC. For an open buried layer: AS=AEPI. –

CJS Zero-bias collector–substrate depletion capacitance F

IKS Base–substrate high injection knee current A

ISS Base–substrate saturation current A

PS Collector–substrate grading coefficient –

VDS Collector–substrate diffusion voltage V

VGS Band gap voltage of substrate V



97


NOTE The ts504 shared object does not support the self-heating effect.

NOTE The input variables Vb and Ibi cannot be defined simultaneously. If Ibi is defined, Vb isignored.

Circuits for capacitance and Y-matrix calculationThe various circuits that are needed for capacitance and Y-matrix parameter extraction are describedhere. In comparison to real measurement when at least two different structures are needed for DC andhigh-frequency parameter extraction, the TCAD-based extraction methodology allows parameters to beextracted from one device structure.

Figure 15 on page 99 shows four different circuits that are commonly used for capacitance and Y-matrixparameter extraction. Depending on capacitance or Y-parameters to be extracted, the ts504 shared objectautomatically selects appropriate circuit configuration. For example, subcircuit (a) is used if Cbe isspecified in the SXtract input file section among the parameters to be extracted at the particular step.

The correspondence between extracted (output) parameters and appropriate subcircuits generated insidethe ts504 shared object is presented in Table 49.

With any of these capacitances and Y-matrix circuit configurations, the Ic, Ib, Ie, and Is currents can beused as output variables. The circuits in Figure 15 are the voltage-controlled simulation and, therefore,the use of Ibi is not allowed.

Table 49 Output parameters and subcircuits

Output variable(see Table 46 on page 94)

Circuit configuration(see Figure 15)

Cbe Figure (a)

Cbc Figure (b)

Csc Figure (c)

Y11_R Y11_IY12_R Y12_IY21_R Y21_IY22_R Y22_I

Figure (d)

98


Figure 15 Circuits for capacitance and Y-matrix calculation for (a) base–emitter capacitance, (b) collector–base capacitance, (c) substrate–collector capacitance, (d) Y-matrix

Goal functionFor the extraction of CV and transient parameters, the optimization procedure is performed for acomplex Y-matrix of a two-port circuit configuration.

NOTE Sentaurus Device outputs the matrix of conductivities and capacitances between appropriateelectrodes.

Vcs = 0

Vbe

Vsc

Vbe = 0

Ves = 0

Vbc

+

–

+

– +

–

+

–

+

–

+

–

~

~

~

port1

port2

Vse

Cbe

Csc

Cbc

Two-Port Device

(a) (b)

(c) (d)

99


Table 50 lists the correspondence between the components of the Y-matrix, their Mextram notations, andappropriate output of Sentaurus Device.

Here, and are the conductivity and capacitance of appropriate terminals, and isthe operating frequency. Then, the output vector function can be written as:

(27)

With such a definition of the output vector function, the general equations Eq. 3, Eq. 4, and Eq. 5 arevalid. The goal function weight of the i-th component of vector function can be defined asdescribed in Table 1 on page 15.

NOTE If the i-th component of the vector function is not selected for optimization, is set to 0.

Extraction strategyAn example of an extraction of parameters of the Mextram 504 model can be found in the ManualExamples Library.

Table 50 Corresponding components of Y-matrix with Mextram and Sentaurus Device output

Component of Y-matrix Mextram 504 Sentaurus Device

Y11.real Y11_R

Y11.im Y11_I

Y12.real Y12_R

Y12.im Y12_I

Y21.real Y21_R

Y21.im Y21_I

Y22.real Y22_R

Y22.im Y22_I

a base base,( )

ω c base base,( )×

a base collector,( )

ω c base collector,( )×

a collector base,( )

ω c collector base,( )×

a collector collector,( )

ω c collector collector,( )×

a … …,( ) c … …,( ) ωf

f Ic Ib Ie Cbe Cbc Csc Yij i j, 1 2,=( ), , , , , ,{ }=

Wi f

f Wi

100

SXTRACT APPENDIX A EXTRACTING DC PARAMETERS

SXtract

APPENDIX A Extracting DC parameters

This is an example of a parameterized input file of Sentaurus Device for the generation of a project ofSentaurus Workbench for the extraction of DC parameters:

#if [string compare @SWEEP@ idvg_1] == 0#set Ramp1_Name subs#set Ramp1_V 0.0#set Ramp2_Name drain#set Ramp2_V 0.05#set Ramp3_Name gate#set Ramp3_V 2.0#set Ramp3_step 0.05#elif [string compare @SWEEP@ idvg_2] == 0...#elif [string compare @SWEEP@ idvd2_4] == 0#set Ramp1_Name subs#set Ramp1_V -2.0#set Ramp2_Name gate#set Ramp2_V 2.0#set Ramp3_Name drain#set Ramp3_V 2.0#set Ramp3_step 0.05#endifFile {

Grid ="@DEVICE@_mdr.grd"Doping ="@DEVICE@_mdr.dat"Current ="_"

}Electrode {

{Name="gate" Voltage=0.0 area=10}{Name="source" Voltage=0.0 area=10}{Name="drain" Voltage=0.0 area=10}{Name="subs" Voltage=0.0 area=10}

}Solve { #Inititial Solution: Vgs = 0.0, Vbs = 0.0, Vds = 0.0 Poisson Coupled { Poisson Electron Hole }# ramp 1 Quasistationary ( InitialStep=0.1 Increment=2 MaxStep=0.5 Minstep=1.0E-4 Goal { Name="@Ramp1_Name@" Voltage=@Ramp1_V@ } ) { Coupled { Poisson Electron Hole } }# ramp 2 Quasistationary ( InitialStep=0.1 Increment=2 MaxStep=0.5 Minstep=1.0E-4

101

SXTRACTAPPENDIX A EXTRACTING DC PARAMETERS

Goal { Name="@Ramp2_Name@" Voltage=@Ramp2_V@ } ) { Coupled { Poisson Electron Hole }}# ramp 3 NewCurrent="@DEVICE@.@SWEEP@" Quasistationary ( InitialStep=0.01 Increment=2 MaxStep=0.1 Minstep=1.0E-3 Goal { Name="@Ramp3_Name@" Voltage=@Ramp3_V@ } ) { Coupled { Poisson Electron Hole } CurrentPlot (Time=(range=(0.0 1.0) intervals= @< int(@Ramp3_V@ / @Ramp3_step@) >@)) }}

102

SXTRACT APPENDIX B EXTRACTING TRANSIENT PARAMETERS

SXtract

APPENDIX B Extracting transient parameters

This is an example of a parameterized input file of Sentaurus Device for the generation of a project ofSentaurus Workbench for the extraction of CV parameters:

#if [string compare @CV@ Cgg] == 0#set Ramp1_Name vg.dc#set Ramp1_V -2.0#set Ramp2_Name vg.dc#set Ramp2_V 2.0#set Ramp2_step 0.05#elif [string compare @CV@ Cdd] == 0#set Ramp1_Name vd.dc#set Ramp1_V -0.6#set Ramp2_Name vd.dc#set Ramp2_V 2.0#set Ramp2_step 0.05#elif [string compare @CV@ Css] == 0#set Ramp1_Name vs.dc#set Ramp1_V -0.6#set Ramp2_Name vs.dc#set Ramp2_V 2.0#set Ramp2_step 0.05#endifDevice nmos { Electrode { {Name="gate" Voltage=0.0 area=10 } {Name="source" Voltage=0.0 area=10 } {Name="drain" Voltage=0.0 area=10 } {Name="subs" Voltage=0.0 area=10 } } File { Grid ="@DEVICE@_mdr.grd" Doping ="@DEVICE@_mdr.dat" Current ="_" }} #end Device nmosFile { output = "@DEVICE@.@CV@" acextract = "@DEVICE@.@CV@"}system { nmos nmos_acdd (drain=d source=s gate=g subs=b) Vsource_pset vd(d 0){ dc=0 } Vsource_pset vs(s 0){ dc=0 } Vsource_pset vg(g 0){ dc=0 } Vsource_pset vb(b 0){ dc=0 } }Solve { # initial solution poisson Coupled { Circuit Poisson Electron Hole } # ramp 1

103

SXTRACTAPPENDIX B EXTRACTING TRANSIENT PARAMETERS

Quasistationary ( InitialStep=0.01 MaxStep=0.1 Minstep=1.e-5 increment=2 Goal {Parameter=@Ramp1_Name@ voltage=@Ramp1_V@}) { Coupled { Circuit Poisson Electron Hole }} # ramp 2 Quasistationary ( InitialStep=0.001 MaxStep=0.02 Minstep=1.e-5 increment=2 Goal {Parameter=@Ramp2_Name@ voltage=@Ramp2_V@}) { ACCoupled ( StartFrequency=1e5 EndFrequency=1e5 NumberOfPoints=1 Decade Node(d s g b) Exclude(vd vs vg vb) ) { Circuit Poisson Electron Hole } CurrentPlot (Time=(range=(0.0 1.0) intervals=@< int((@Ramp2_V@-@Ramp1_V@) / @Ramp2_step@) >@)) }}# end Solve

104

SXTRACT BIBLIOGRAPHY

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Bibliography

[1] M. Minoux, Mathematical Programming: Theory and Algorithms, Chichester: John Wiley & Sons,1986.

[2] M. Aoki, Introduction to Optimization Techniques: Fundamentals and Applications of NonlinearProgramming, Macmillan Series in Applied Computer Sciences, New York: The MacmillanCompany, 1971.

[3] W. Liu et al., BSIM3v3.2 MOSFET Model, User’s Manual, Department of Electrical Engineeringand Computer Sciences, University of California, Berkeley, CA, USA, 1998.

[4] Y. Cheng and C. Hu, MOSFET Modeling & BSIM3 User’s Guide, Boston: Kluwer AcademicPublishers, 1999.

[5] T. Quarles et al., SPICE 3 Version 3F5 User’s Manual, Department of Electrical Engineering andComputer Sciences, University of California, Berkeley, CA, USA, March 1994.

[6] W. Liu et al., BSIM4.1.0 MOSFET Model, User’s Manual, Department of Electrical Engineering andComputer Sciences, University of California, Berkeley, CA, USA, 2000.

[7] BSIMPD2.2 MOSFET Model, Users’ Manual, Department of Electrical Engineering and ComputerSciences, University of California, Berkeley, CA, USA, 1999.

[8] K. Goto et al., “80nm SOI CMOS Parameter Extraction for BSIMPD,” in IEEE International SOIConference, Durango, CO, USA, pp. 55–56, October 2001.

[9] J. C. J. Paasschens and W. J. Kloosterman, The Mextram Bipolar Transistor Model, level 504.4,Report NL-UR 2000/811, Koninklijke Philips Electronics N.V., April 2002.

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