deal-grove model predictions once b and b/a are determined, we can predict the thickness of the...
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Deal-Grove Model Deal-Grove Model PredictionsPredictions
Once B and B/A are determined, we Once B and B/A are determined, we can predict the thickness of the oxide can predict the thickness of the oxide versus timeversus time
Deal-Grove Model of Deal-Grove Model of OxidationOxidation
Oxide as a Diffusion BarrierOxide as a Diffusion Barrier Diffusion of As, B, P, and Sb are orders of magnitude Diffusion of As, B, P, and Sb are orders of magnitude
less in oxide than in siliconless in oxide than in silicon Oxide is excellent mask for high-temperature Oxide is excellent mask for high-temperature
diffusion of impuritiesdiffusion of impurities
BoronPhosphorus
10
1
0.1
0.010.1 1.0 10 100
Diffusion time (hr)
Mask thickness(m) 1200 C
1000 C
1200 C
1000 C 1100 C
900 C
1100 C
900 C
BP
10
1
0.1
0.010.1 1.0 10 100
Other ModelsOther Models A variety of other models have been suggested, A variety of other models have been suggested,
primarily to correct the deficiencies of the Deal-primarily to correct the deficiencies of the Deal-Grove model for thin oxidesGrove model for thin oxides
These includeThese include– The Reisman power law modelThe Reisman power law model– The Han and Helms model with parallel The Han and Helms model with parallel
oxidation pathsoxidation paths– The Ghez and van Meulen model to account for The Ghez and van Meulen model to account for
the effect of oxygen pressurethe effect of oxygen pressure Some of these models do a much better job for Some of these models do a much better job for
thin oxidesthin oxides None are widely acceptedNone are widely accepted
Other TopicsOther Topics
Several topics other than the simple Several topics other than the simple planar growth of wet and dry oxide planar growth of wet and dry oxide are importantare important
These includeThese include– Thin oxide growth kineticsThin oxide growth kinetics– Dependence on oxygen pressureDependence on oxygen pressure– Dependence on crystal orientationDependence on crystal orientation– Mixed ambient growth kineticsMixed ambient growth kinetics– 2D growth kinetics2D growth kinetics
Example: 2D GrowthExample: 2D Growth
Example: 2D GrowthExample: 2D Growth
Example: 2D GrowthExample: 2D Growth
There are several interesting There are several interesting observationsobservations– There is significant retardation of the There is significant retardation of the
oxide growth in sharp cornersoxide growth in sharp corners– The retardation is more pronounced for The retardation is more pronounced for
low temperature oxidation than for high low temperature oxidation than for high temperature oxidationtemperature oxidation
– Interior (concave) corners show a more Interior (concave) corners show a more pronounces retardation that exterior pronounces retardation that exterior (convex) corners(convex) corners
Example: 2D GrowthExample: 2D Growth
Example: 2D GrowthExample: 2D Growth
Several physical mechanisms are needed to Several physical mechanisms are needed to understand these resultsunderstand these results
1.1. Crystal orientationCrystal orientation
2.2. Oxidant diffusionOxidant diffusion
3.3. Stress due to volume expansionStress due to volume expansion Kao et al suggested changes to the linear-Kao et al suggested changes to the linear-
parabolic (Deal-Grove) model to correct for these parabolic (Deal-Grove) model to correct for these effectseffects
Most of these effects are built into the modeling Most of these effects are built into the modeling software such as SUPREM IV and ATHENA software such as SUPREM IV and ATHENA
Measurement MethodsMeasurement Methods
The parameters of interest includeThe parameters of interest include– ThicknessThickness– Dielectric constant and strengthDielectric constant and strength– Index of refractionIndex of refraction– Defect densityDefect density
There are three classes of measurementThere are three classes of measurement– Physical (usually destructive)Physical (usually destructive)– Optical (usually nondestructive)Optical (usually nondestructive)– Electrical (usually nondestructive)Electrical (usually nondestructive)
Physical MeasurementsPhysical Measurements Simple step height technique (DekTak)Simple step height technique (DekTak)
– Etch away oxide with HFEtch away oxide with HF– Use a small stylus to measure the resulting Use a small stylus to measure the resulting
step heightstep height– The resolution is <10 nmThe resolution is <10 nm
More complex technique uses one or more of the More complex technique uses one or more of the SFM concepts (AFM, MFM, etc)SFM concepts (AFM, MFM, etc)– Technique has atomic resolutionTechnique has atomic resolution
SEM or TEM (electron microscopy)SEM or TEM (electron microscopy) All require sample preparation that makes the All require sample preparation that makes the
tests destructive and not easy to use in tests destructive and not easy to use in productionproduction
Optical MeasurementsOptical Measurements Most optical techniques use the concept of Most optical techniques use the concept of
measuring reflected monochromatic lightmeasuring reflected monochromatic light– If monochromatic light of wavelength If monochromatic light of wavelength shines shines
on a transparent film of thickness xon a transparent film of thickness x00, some , some light is reflected directly and some is reflected light is reflected directly and some is reflected from the wafer-film interfacefrom the wafer-film interface
– For some wavelengths, the light will be in For some wavelengths, the light will be in phase and for others it will be out of phasephase and for others it will be out of phase constructive and destructive interferenceconstructive and destructive interference
Minima and maxima of intensity are observed as Minima and maxima of intensity are observed as is varied is varied
Optical TechniquesOptical Techniques
Color ChartColor Chart
http://www.htelabs.com/appnotes/sio2http://www.htelabs.com/appnotes/sio2_color_chart_thermal_silicon_dioxide.ht_color_chart_thermal_silicon_dioxide.htmm
Optical MeasurementsOptical Measurements
Instrument from Instrument from FilmetricsFilmetrics(http://www.filmetrics.com)(http://www.filmetrics.com)
Optical MeasurementsOptical Measurements
The positions of the minima and maxima The positions of the minima and maxima are given byare given by
m=1,2,3… for maxima and ½,3/2,5/2,… for minimam=1,2,3… for maxima and ½,3/2,5/2,… for minima
This is called reflectometry and works well This is called reflectometry and works well for thicknesses over a few 10’s of nmfor thicknesses over a few 10’s of nm
1
01
01maxmin,
sinsin
cos2
n
n
m
xn
Optical MeasurementsOptical Measurements
If one does not know n, or if the film is very thin, If one does not know n, or if the film is very thin, then ellipsometry is betterthen ellipsometry is better
When multiple wavelengths of light are used, the When multiple wavelengths of light are used, the instrument is known as a spectroscopic instrument is known as a spectroscopic ellipsometerellipsometer
Optical MeasurementsOptical Measurements
Here, one uses polarized light.Here, one uses polarized light.– The measurement may be performed at The measurement may be performed at
multiple angles of incidence to obtain a higher multiple angles of incidence to obtain a higher degree of accuracydegree of accuracy
One can get the index of refraction as a One can get the index of refraction as a function of wavelength as well as the function of wavelength as well as the extinction coefficientextinction coefficient– Can be used to measure thickness to <1 nmCan be used to measure thickness to <1 nm
Fitting routines are necessary to take into Fitting routines are necessary to take into account rough interfaces between Si and account rough interfaces between Si and SiOSiO22 layers. layers.
Cauchy EquationCauchy Equation
...)(42
CB
An
Sellmeier EquationSellmeier Equation
...1)(3
2
23
22
22
12
21
C
B
C
B
C
Bn
http://en.wikipedia.org/wiki/Cauchy%27s_equation
Electrical MeasurementsElectrical Measurements
These measure properties that correlate directly These measure properties that correlate directly to the performance of the devices fabricated to the performance of the devices fabricated using the oxidesusing the oxides
The dominant techniques is the C—V The dominant techniques is the C—V measurementmeasurement– The basic structure for the measurement is the MOS The basic structure for the measurement is the MOS
capacitorcapacitor
– The usual combination is Si-SiOThe usual combination is Si-SiO22-(Al or pSi)-(Al or pSi)
– Any conductor-dielectric-semiconductorAny conductor-dielectric-semiconductor can be usedcan be used
MOS CapacitorMOS Capacitor
tox
Al
Al
Si wafer V
+
-
http://www.mtmi.vu.lt/pfk/funkc_dariniai/transistor/mos_capacitors.htm
http://ece-www.colorado.edu/~bart/book/book/chapter6/ch6_3.htm#fig6_3_5
C-V PlotC-V Plot
C-V PlotC-V Plot
Differences between high frequency Differences between high frequency and low frequency C-V dataand low frequency C-V data– Doping concentration in Si near Si-oxide Doping concentration in Si near Si-oxide
interfaceinterface Voltage shift proportional to charged Voltage shift proportional to charged
defects within oxidedefects within oxide