Cllaplet1 Semiconductor Materials and Diodes 3
r2
Diode Circuits 49 Clwplet3
The Bipolar Junction Transisto r 97 Clllpltr4 Basic BJT Amplifiers 163 $ The Field-Efft Tr ansis tor 243 Cllll*t• Basic FET Amplifiers 313
Cllll*t1 Frequency Response 383 Cllll*t• Outp11t Stages and Power Amp lifiers 469 PMTll
ANALOG ELECTRONICS 519 CNpllrt The Ideal Operational Amplifier 52 l 10 Integrated Circuit Biasing and Active Loads 577 11 Differential and Multislage Amplifiers 639 CMplw12 Feedback and Stability 727
Clltjller 13 Operational Amplifier Circuits 817
CMplitfU Nonideil EtTo:ts in Operaliona l Amplifier Circuits 871
u Applie<1tions and Desisn of Integrated Circuits 923
... ·. . . .';.; .
·, · · .
. ; ·: . : -
: ; . : . . ·. ; . ; -'::'!: . ; :: ' . . ....
l 1173
llldtl 1211
PARTI
SEMICONDUCTOR DEVICES AND BASIC APPLICATIONS
Chtpltt'1 Semicootktetor Materials and Diodes 3 1.0 Pre\liew 3 I. I Semiconductor Materials a1141 Properties 4
I. I.I Intrinsic Semiconductors 4 1.1.2 Extrinsic Semiconductors 7
I . I . .3 Drift and Diffusion Currents 9
I. I .4 Excess Carriers 11
l.l The pn J•nction 12 1.2. I Th Equilibrium pn Junction 12
I . .:!.'.! Reverse-Biased pn Junction 14
1.2.J Forward-Biased pn Junction 16 12.4 Ideal Current-Voltage Relationship 17
I .:!.5 pn Junction Diode 18
t.3 Diode Circuits: DC Analysis and Models 23 I J. I Iteration and Graphical Analysis Techniques 24 I J.2 Piecewise Linear Model 27 LU (\)mputer Simulation and Analysis 30 l.J.4 Summary of Diode Models 31
1.4 Diode C ircuits: AC F..quhalent Circ•it 31 1.4.1 Sinusoidal Analysis 31
1.4.2 Small-Signal Equivalent Circuit 35
l.S Other Diode Types 35 I. 5.1 Solar Cell 35 1.5.2 PhiJtodiode 36 1.5 .. \ Ught·Emiuing Diode 36
1.5.4 Schottky Barrier Diode 37 LS .5 Zenr Diode 39
1.6 Summary 41
Design Problems 47
. . .-.· . :· .. :·
... .
· ·
..
• : : . . ·
. . ·· ·
.
. . :· ·
. . ::·":: . ..• :' · ·· .: •
. . .. :·. ·
. · . . :·:· ·
. ; · · ·:'. · '
· . ..
·
.
· .· . . .• · :. ·• ;····'
· : . .. . .
. . . · . · . :··· ,-. • ···. · . :
· ... ··'."··
.
·. .· ·
·
· ·
.. • ·
. ·:· .· ;· ·.· .
.. ··· ·' .• . :_·
2.0 Preview 49
2.1 Redifier Cir11its SO 2.1.1 Half-Wave Rectification 50 Problem-Solving Technique: Diode Circuits 51 2.1.l Full-Wave Rectificalion 53 2. U Filters. Ripple Voltage. and Diode Current 56 2.1.4 Voltage Doubler Circuit 63
2.2 Zener Diode Circuits 64 2.2. l Ideal Voltage Reference Circuit 64 2.2.2 Zener Resistance and Percent Regulation 67
2.J Clipper and Clamper Circuits 68 2.3. I Clippers 68 2.3.2 Clampers 72
2.4 MultipleeDiode Circuics 75 2.4.1 Example Diode Circuits 7S
Prot>lem·Solving Technique: Multiple Diode Circuits 79
2.4.2 Diode Logic Circuits 80 2.S Photodiode and LED Circuits 82
2.5. I Photodiode Circuit 82
2.5.2 LF.D Circuit 83 2.6 Summary 85 Cbe<'kpoint 85 Review Qu1ions 86
Problems 86 Compu ler Simulatio-o Problems 94
Design Problems '>S
The Bipolar J1111ctio• Transistor 97 3.0 Preview 97
3. I Basic Bipolar Junction Traa§istor 97 11.1 T rmsistor Str11ctures 9&
3.1.2 npn Transistor: Forward-Active Mode Operation 99 3.1.3 pnp Transistor: Fonvard-Acrive Mode Operation 104
3.1.4 Circuit Symbols and Conventions 105 ll.5 Current-Voltage Characteristics 107
3.1.6 Nonidcal Transistor Leakage Currenis and Breakdown Voltage 110
3.l DC Analysis of Tramistor Circuits 113
3.2..l Common-Emitter Circuit 114 3.2.2 Load Line and Modes of Operation 117
Problem-Solving Technique: Bipolar OC Analysis 120
3.2.3 Common Bipolar Circuits: DC Analysis 121
3.3 Bask Tramistor Applicaliom 131
3.3.1 Switch 13 l
3.3.2 Digital Logic 133 U.3 Amplifier 134 3.4 Bipolar Transistor Biasing 138 3.4.1 Single Base Resistor Biasing 138
3.4.2 Voltage Divider Biasing and Bias Stability 140
3.4.3 Integrated Circuit Biasing 145 3.5 M.altistage Circuits 147 3.6 Sum .. ary 150
Checkpoint 151
Cllll*r4
Basic BJl Amplifiers 163 4.D Preview 163
4.1 Analog Signals an• Linear Amplifiers 163 4.2 The Bipolar Linear Ampliler 165
4.2.1 Graphical Analysis and AC Equivalen1 Circuit 166
4.2.2 Small-Signal Hybrid-ir Equivalent Circuit of 1he Bipolar Transis1or 170
Pr()blem·Solving Technique: Bipolar AC Analysis 17S
Con ten ls
4.2.4 Expanded Hybrid-it Equivalenl Circuil 180
4.2.5 Other Small-Signal Parameters and Equi11alent Circuits 180
4.3 Bask Transistor Amplifier Configurations 18S 4.4 Common-Emitter l\mplifiers 189
4.4.1 Basic Commoo·Emitter Amplifier Circuit 190
4.4.2 Circuit with Emiuer Resistor 11)2
4.4.) Circuit with Emitter-8ypa-s Capaci1or 196
4.4.4 Advanced Common-Emitter Amplifier ConceplS 199
4.5 AC Load Line Analysis 200 4.5.1 AC Load Line 200 4.S.2 Maximum Symmetrical Swing 203
Problem-Solving Technique: Maximum Symmetrical Swing 204
4.6 Common-Collector (E .. itter-Follower) Amp1ifier 205
4.6.1 Small-Signal Voltage Gain 205
4.6.2 Input and Output Impedance 207
4.6.3 Small-Signal Current Gain 209
xviii
Contenls
4.7 Commo•Base Amplifter 214 4.7. I Small-Signal Voltage and Current Gains 214
4.7.2 Input and Output Impedance 216
4.8 The Three Basi( Amplifiers: Summary and Comparisoo 218
4.9 Multistage Amplifiers 219 4.9. I Multistage Analysis: Cascade Configuration 219
4.9.2 Cascode Configuration 223 4.10 Power CoMiderations 216
4.11 Smnmary 229 Checkpoint 229
Review Questio 229
5.0 Preview 243
S.1 MOS Field-Effect Trator 243 5.1.1 Two· Terminal MOS Str u..:ture 244
: .. < 5.1.2 n-Cbannel Enhancemenl-Mode MOSFET 246
· : • · .. • ·.
. . ': .
5. D Ideal MOSfET Current-Voltage Characteristics 248 5.1.4 Circuit Symbols and Conventions 253
5.J.5 Additional MOSFET Structures and Circuit Symbols 253
5.1.6 Summary of Transistor Operation 25
5.1.7 Nonideal Current-Vcltage Characteristics 259
S.2 MOSFET DC Circuit Analysis 262 5.'.!. I Contmon·Sourcc Cir(uit 263
5.2.2 Load Linc and Modes of Operation 267
Problem-Solving Tochnique: MOSFET DC Analysis 26&
5.2.J Common MOSFET Configurations: DC Analysis 269
5. 2 .4 Co11stant ..(' urrent Source Biasing 2.81
5.3 Basic MOSFET Applications: Switc•. Digital Logic Gate, and Amplifier 283
5.U NMOS I nverter 283
5.3.2 Digital Logic Gate 285
SJ.3 MOSFET Small-Signal Amplifier 287
5.4 Junction Field-Effect Traasistor 287 5.4. l pn JFET and MESFET Operat ion 288
5.4.2 Current-Voltage Characteristics 292
S.5 Swnmary 30 I
Problems J03
Design Problems 31 I
6.1.1 Graphical Analysis. Load Lines. and Small-Signal Parameter 314
ti.I. 2 Small-Signal Equivalent Circuit 318
Prohlcm·Solving fC(hnique: MOSFET AC AMlysis 320
6.1.J Modeling the Body Effe(t 32.!
6.2 Basic Trastor Amplifier Configurations 323
41.3 The Comroon-Source Amplifier 324 6. .I /\ Basic Common-Source Connguration 324
6.3.2 Common-Source Amplifier with Source Resistor 329
&.J3 Common-Source Circuit with Source Bypass C apacitor 31
6.4 l'he Source-Follower A .. plifter 334 (>.41 Small-Signal Voltage Gain 334
o.4. Input a11d Output Impedance .B9
6.5 The Common-Gate Configuratioo 341 6.5.1 Small-Signal Voltage and Current Gains 341
6.5.2 Input and Output Impedance 343
6.6 The Three Bask Amplifier Configurations: Summary and Comparison 345
<i. 7 Single-Stage Integrated Circllit MOSFET Amplifiers 34S fl. 7. I NMQS Amplifier with Enhancemenl Load .45 h.7.2 NMOS Amplifier with Depletion Load 350
t>.7.3 NMOS Amplifier with PMOS Load .i53 6.8 Multtage Amplifiers 355
(dU OC Analysis 356 h.K2 Small-Signal l\nalysis 360 6.9 Basic JFET Amplifiers 362 n.'>.l Small-Signal Equivalent Circuit 362
<•..2 Small-Signal Analysis 364
. .,, . :
··: • • •
• • • < :.
. ·. . . -:
· . . . :. : :
. . . : . .
; :· .·
. . .
. "
. . . , ·
Frequency Response J83
7.0 Preview 383
7.1 Amplifier Frequency Res))OllSe 384 7. l.I Equi,·alent Circuits 384
7.1.2 Frequency Response Analysis 385
7.2 System Transfer Functioos 386 7.2.l s·Domain Ana l ysis 386 i.2.2 First.Order Functions 388 7.2.3 Bode Plots 388
7.2.4 Short·Circuit and Opeo·Circui t Time Constants 394
7.3 Frequency Response: Transistor Amplifiers with Circuit Capacitors 398 7.3.1 C oupling Capacitor Effects 398
Problem.Solving Technique: Bode Plot of Gain Magnitude 404
7.3.2 Load Capacitor Effects 405
7.3.3 Coupling and Load Capacitors 407
7.3.4 Bypass Capacitor EITecls 410
7.3.S Combined Effects: Coupling and Bypass Capa citors 414
7.4 Frequency Res: Bipolar Tran.sistor 416 7.4.1 fapanded Hybrid·.ir Equivalent Circuit 416
7.4.2 Short-Circuit Current Gain 418
7.4J Cutoff Frequency 420
7.4.4 Miller Effect and Miller Capacitance 422
7.S Frequency Response: The FET 426 7.5.1 High-F"quency Equivalent Circuit 426
7.5.Z Unity·Gain Bandwidth 428 7.5.3 Miller Effect and Miller Capacitance 431
7.6 High-Frequency RespGnse of Transistor Circuits 433 7.6.1 Common·Emitter and Common.Source Cirtuits 433
7.6.2 Common· Base, Commo n-Gate, and Cascode Circuits 436
7.6.3 Emitter· and Source.Fo llower Circuits 444 7.6.4 High·Frequency Amplifier Design 448
7.7 Summary 4
CflePrS
Output Stages and Power Amplifiers 469 8.0 Preview 469 8.1 Power AmIJll.fiers 46'
8.2 Power Tratwistors 470 8.2. I Power BJTs 470
8.2.2 Power MOSFETs 474
8.2.3 Heat Sinks 477
8.3 Classes of Amplifiers 480 8.3. I Class-A Operatio n 48 l
8.3.2 Class-B Operation 484
8.3.3 Class-AB Operation 489
IU.4 Class-C Operation 493
8.4. I lnd11ctively Coupled Amplifier 494
8.4.2 Tra11sfonner-Coupled Common-Emitter Amplifier 495
8.4.3 Transformer-Coupled Emitter·Follower Amplifier 497
8.5 Class-AB Push-Pull Complementary Output Stages 499 8.S. I Class-AB Output Stage with Diode Biasng 499
8.5.2 Class-AB Biasing Using the JI Bf: Multiplier SOI
R.S.3 Class-AB Output Stage with Input Buffer Transistors 504
8.5.4 Class-AB Output Stage Utilizing the Darlington Configuration 507
8.6 Summary 508 Chfclpoint SO
Review Questions 509
PAllTI
9.1. I Ideal Parameters 522
91.2 Development of the Ideal Parameters S23
9 IJ Analysis Method 525
9 1.4 PSpice Modeling S26
9.? Inverting Amplifier 526 9.2.1 Basic Amplifier 527
Problem-Solving Technique: Ideal Op·Amp Circuits 529
9.2.2 Amplifier with a T-Network 530
9.2.1 Effect of Finite Gain 532
9.3 Summing Amplifier 534
9.4 Noainvertiag AmpWler 536
9.4.2 Volta£e foll<>wer 537
9.5 Op-Amp Applicaoons 539
9.5.2 Volrnge-to-Current Converter 540
9.5.J Differen Amplifier 54
9.5.6 Nonlinem Cin:uit l\pplica1ion$ 553
9.6 Op-Anip Circuit Oesigh 555
9.6. I Summing Op-Amp Circuit Design SSS
9.6.2 Reference Voilage Source Deign SSB
9.6.J Ditleren-ce Amplifier and Bridge Circuit Design 560
9.7 Summary 562 Checkpoint 563 Ptoblems 563
Computer Simulation Prob1e .. s 575
Chapter10
Integrated Ciruit Biasi1g and Active Loa4s 577 HJ.O Preview 517 JO.I Bipolar lra11sistor Current Sources 577
I0.1.1 Two-Tr..1nist(lf Current Somce 578 10.1. lmpm\'ed Current-Soul'ce ('in:ttits (1 Problc:rn·SQlvin Technique: BJr Current Sour C'ircuits 5\<9 10. U Widl;tr Current Source 589 10.1.4 Muhitrnn1'istor Curren1 Mirrors 595 1().2 FET Curre11t Sourcts 598 10.2.1 Basic Two· Transistor MOSFET Curren1 Source 598 Problem-Solvillg Thnique: MOSFET Current·Source Circuit b02
10.2.2 Multi-MOSFET Current-Source Circui1& 603
IO . .:u Bias-Independent Current Source 607 I0.2.4 JFET Current Sources 609
I0.3 Ciruits with Active Loads 611 JO.'.\. I DC l\nalysis: BJT Active Load Circuit 612
10 .. \2 Ve>llage Gain: BJT Activ Load Circuit 614
10..3 1x· Analysis: MOSFET Active Load Circuit 616
10.3.4 Voltage GJin: MOSFET Active Load Circuit 618
I0.3.5 Di<ocussi<>n 618
10.4 Small-Signal Analysis: Active Load Circuits 619 10.4. I Small-Signal Analysis: BJT Active Load Circui1 619 Problem-Solving 'Technique: Active Loads 621
10.4.2 Small-Signal Analysis: MOSFET Active Load Circuit 622
10.4.3 Small-Signal Analysis: Advanced MOSFET Active Load 623
I0.5 Summary 625
11.0 Preview 639
II. t The Differential Amplifier 639
J 1.2 Basic BJT Differential Pair 640 I I.:?. I Terminology and Qualitative Descriplion 640
11.2.2 0C Transfer Characteristics 643
11.:?..l Small·Signal Equivalent Circuit Analysis 641!
('ontent
11.2.4 nifTcrcntial· and Common·M('ode Gains 653 Problcm·Solvin{t Technique: DilT·Amps with Rcsitivc Loads 656
11.:!.5 Common-Mode Rejection Ratio 657
11 . :?.6 DilTerentia I· and Common· Mode Input Impedances 659 11.3 Basic FET Differential Pair 663
l I.JI DC Trnnsfer Characteristics 66J 11.1 '.! Differential- and Common.Mode Input I mpcdances 66S
II .U Small·Sigm1I Equivalent Circuit Analysis 6fi9 I U.4 JFFT Dirferential Amplifier 6 7:!
11.4 Differential Amplifier with Active Loa• 6i4
I 1.4. I BJT Diff·Amp with Active LlMd 674
11.4.2 Small·Signal Analysis of BJT Active Load 6 76
11.43 MOSFET Differential Amplifier with A·tive Load 679
11.4.4 MOSFET DifT·Amp with CaS(ooe Activ Load 683
l 1.5 BiCMOS Cir'Uits 686 11.5. I Basic Amplifier S1ages 686
11.5. 2 Current Sources 688
11.5 .. 1 BiCMOS Differential Amplifier 68S
( 1.6 (;ain Stage and Simple Ouq,ut Stage 690
11.6.1 Darlingron Pair and Simple Emitter-Follower Output 690
11.6.2 Input Impedance. Voltage Gain, and Output Impedance 691
11. 7 Simplified BJT Operational Amplifier Circ11it 695
Problem·Solving Technique: Multistage Circuits o9ll 11.8 DUT-Amp Fuency Response 699
I UU Due to Differential· Mode Input Signal 699
11.8.:! Due to Common-Mode Input Signal 700
I UU With Emitter-Degeneration Resistors 703
11.8.4 With. Active Load 704
.. .
· . .
Design Problems 724
12.0 Preview 727
12.2
12.3
12. I. I Advantages and Disadvantages of Negative Feedback 728
I 2.1.2 Use of Computer Simulation 729
Basic Feedback Concepts 729
12.2.2 Gain Sensitivity 1.32
12.2.3 Bandwidth Extension 734
l?.2.4 Noise Sensitivity 735
Ideal Feedbac.11 Topologies 738
12.3.1 Series-Shunt Configuration 739
12.3.2 Shunt-Series Configuration 743
12.3.3 Series-Series Configuration 746
12.3.4 Shunt-Shunt Configuration 747
12.4 Voltage {Series-ShtaO Amplifiers 749
12.4.1 Op-Amp Circuit Representation 749
12.42 Discrete Circuit Representation 752
12.5 Currrenf (Sllunt-&ries) Amplifiers 755
12.5. I Op-Amp Circuit Representation ?SS
12.5.2 Simple Discrete Circuit RepresentatiQll 757
12.5.3 Discrete Circuit Representation 758
12.6 Transoonductanc (Series-Series) Ainplifiets 762
12.6.1 Op-Amp Circuit Representation 7 6 2
12.6.2 Discrete Circuit Representation 764
12.7 Transresistance (Shunt-8hullt) Amplifiers 768
12. 7.1 Op-Amp Circuit Representation 768
12.7.2 Discrete Circuit Representation 770
12.8 Loop Gain 778 12.S. I Basic Approach 779
12.8.2 Computer Analysis 181
12.9.2 Bode Plots: One-, Two-, and Three-Pole Amplifiers 785
12.9.3 Nyquist Stability Criterion 789 12.9.4 Phase and Gain Margins 793
12.10 FrequeiM:y Cc.mpensation 795 12.10. I Basic Theory 795 Problem-Solving Technique: Frequency Compensation 796 12.10.2 Oosed-Loop Frequency Response 797 12.10.3 Miller Compensation 798
ll.11 Summary 800 Checkpoint 801
Review QuestioM 801 Problems 802 Computer Simulatlcm Problems 815 Design Problems 816
Cllaftlr13
13.0 Preview 817
13.1 General Op-Amp Cil'Cllit Design 817 13.1.1 General Design Philosophy 818 13.1.2 Circuit Element Matching 819
13.2 A Bipolar Operational A.mplfter Circuit 820 13. 2.1 Circuit Description 820 13.2.2 DC Analysis 823 13.2.3 Small-Signal Analysis 830 13.2.4 Frequency Response 838 P1oblem-Solving Technique: Operational Amplifier Circuits 839
13.3 CMOS Operation•! Amplifier Circuits 839 13.3. I MC14573 CMOS Operational Amplifier Circllit 840
Con ten Ls
13.3.2 Folded Cascode CMOS Operational Amplifier Circuit 843 13.3.3 CMOS Current-Mirror Operational Amplifier Circuit 846 13.3.4 CMOS Cascode Current-Mirror Op-Amp Circuit 847
13.4 BiCMOS Operational Amplifier Circuits 848 13.4.1 BiCMOS Folded Cascode Op-Amp 849 I J.4.2 CA3 l40 BiCMOS Circuit Description 850 13.4.3 CA3140 DC Analysis 852 13.4.4 CA3l40 Small-Signal Analysis 854
13.5 JFET Opentienal AmpUfler Orc:uits 856 IJ.5.1 Hybrid FET Op-Amp, LH0022/42/52 Series 857 13.5.2 Hybrid FET Op-Amp. LFISS Series 858
.•· .. · .· . .. ,.
. , : . • >: .
Chapter14 No1idtal Effects in Operational Amplifiu Circuits 871
14.@ Preview &71
14.l Practical Op·Amp Parameters 871 14.1.1 Prac1ica l Op-Amp Parameter Definition.; 872 14.1.2 Input and Output Voltage Limi1ations !173
14.2 Finite OpeLoop Gain 875
14.:?. I lnver1i1111 Amplifier Closed-L(}op Gain R75
14.2.2 Noninver1i11g Amplilier Clost>tl-Loop Gain R7
14.2.J Inverting Amplifie1· Clo-;ed-L(}op Input Resislam;e 1179 14.2.4 Noninverting Amplifier Closed-Lo<>p Input Rsb1ance 81!1
l4.2.5 Nonzero Output Resist;.nce in 14.3 Frequency Respome 885
14.3. J Open-Lt)op and Closed-Loop Frequency Response 885 14.3.2 Guin ·B<Jn<lwi<.Hh Product 111\7
14.3.J Slew Ra1 888
14.4 Offset Voltage 892
14.4.2 Offse1 Voltage Compen;ation 901
14.S lnpul Bias Current 906
14.5.1 Bias Cu rreol Effects 906 14.5.:! l:k1s Current Compensation 'ffl7
14.6 Additional Nonid-eal Eflects 909 14.6.1 Teinpernture Effects 909 14.6.2 Common-Mode Rejection Ratio 91 I
14.7 Summary 911 Checkpoint ')I?
Reiew Questions 9'12
Chapler15 Applications and Design of Integrated Circuits 923
IS.O Pre\'iew 923
IS.I Active Fillers 924 15. I.I Actiw Network Design 924 15.1.2 Gmc:ral Two-Pole Mlive Filter 926 15. l .3 Tw o·Pole Low-Pass Buuerworth Filler 927
I 5.1.4 Two-Pole High-Pass Butterworlh Filter 929
15.1.5 Higher-Order Buuerworth Filters 931
15 1 .6 Switched-Cap acitor Filter 933
IS.2 Oscillators 37
15.2. I Basic Principles of Oscillation 937
I S.2.2 Phase-Shift Oillator 938 I S.2.J Wien-Bridge Osdllator 941
15.2.4 Additional Oscillator Configurations 945
15.3 Sdtmitt Trigier Circuits 947 15 3.1 Comparator 948 1 5.:U Basic lnerting Schmitt Trigger 95 I
I SJ.3 l\dditional Schmill Trigger Configurations 954
15.3.4 Schmitt Triggers with Limiters 959
l S.4 Nonsinusoidal Oscillators and Timing Circuits %0 1 5.4. I Schmitt Trigger Oscillaior 961
15.4.2 Monostable Multivil>rator 963
15.4.3 The 555 Circuit 965
IS.5 Integrated Cire11it Power Amplifiers 972
15. S. I LM 30 Power Amplifier 972 15.5. PAl 2 Power Amplifier 975
15.S.3 Bridge Power Amplifier 977
I .6 Voltage Regulators 978 15.6. I Basic Regulator Descript;on 978
15.6.2 Output Resistance and Load Regulation 978
I S.6 .. l Simple Series-Pass Regulator 80
1 5.6.4 Positive Voltage Regulator 982
15.7 S•mmary 986
DIGIT AL ELECTRONICS 1001 CNptef 16
MOSFET Digital Circuits 1003
\f\. I . 3 Nois Margin 10\9
I fl. 1 .4 Body Effect 1024
lo.1.5 Transient Analysis of NMOS tnverlers 1026
Contents
16.2.1 NMOS NOR and NANO Gates 1028
16.2.2 NMOS Logic Circuirs I032
16.2.3 Fanout 1033
t6.3 CMOS f•verter 1034 16.3.1 p·Channe1 MOSFET Revisited 1035
!6.3.2 DC Analysis of the CMOS Inverter Ul36
16.3.J Power Dissipaticn 1043
16.3.4 Noise Margin 1045
16.4.1 Basic CMOS NOR and NANO Gates 1048
16.4.2 Complell CMOS Logic Circuits 1052
16.4.3 Fancut and Propagation Delay Time 1054
16.5 Clocked CMOS Logic Circuits 1055
16.6 Traasnais.iion Gates 1058 16.6.1 NMOS Transmission Gate 1058
16.6.2 NMOS Pass Ne1works 1063
16.6.3 CMOS Transmission Gate Hl65
16.6.4 CMOS Pass Networks 1067
16.7 Sequential Loaic Circuits 1067 16.7.1 Dynamic Shift Registers 1068
16.7.2 R-S Flip-Flop 1070
16.8 Memories: Classifications and Arthitectures 1075 16.8. I Classificalions of Memories 1075
16.8.2 Memory Architecture 1076
16.8.3 Address Decoders 1077
Ui.9 RAM Memory Cells 1&79 16.9.1 NMOS SRAM Cells 1079
16.9.2 CMOS SRAM Cells 1081
16.9.3 SRAM Read/Write Circuilry 1085
16.9.4 Dynamic RAM (DRAM) Cells 1087
16. H Read-Only M«nory I 089 16.10.1 ROM and PROM Cells 1089
16.L0.2 EPROM and EEPROM Cells l090
16.l l Summary 1093
Design Problems 1111
17 .0 Preview 1113
17.l Emitter-Coupled Logic (ECL) 1113 17.1. I Diiferential Amplifier Cireuil Revfaited 1114
17.U BasicECLLogicGate 1116
17. l.4 Voltage Transrer Characteristics 1124
17.2 Modified ECL Circuit Configurations 1125
17.2.1 Low-Power ECL 1125
17.2.3 Series Gating 1131
Transistor-Transistor Logic 1135 17.3.I Basic Diode-Transistor Logic Gate
17.3.2 The Input Transistor ofTIL 1138
17.3.3 Basic TIL NANO Circuit 1141
1136
17.3.S Tristate Output 1148
17.4,2 $(:ho11l<y lTf.. NAND Circuit 1152
17.4.3 Low-Power Schottky TTL Cif(:uits
17.4.4 Advanced Schottky TTL Circuits
BlCMOS Digital Circuits 1157
17.5.2 BiCMOS Logic Circuit
Contents
:nx :
8.4 Displaying Resorts of Simufatio11 I 177
8.5 Example Analyses 1177
-'PPelldll D Standard Resistor and Capacitor Values 1195
l>.l Carbon Resistors 1195
D.2 Precision Resistors (One Percent Torerae) 1190
0.3 Capacitors 1196
lnd81C 1211
Semiconductor Devices and Basic Applications
In the first part of the text, we introduce the physical characteristics and operation of the major semiconductor devices and the basic circuits in which lhey are used, to Illustrate how the device characteristics are utili2ed in switching.dig ital. and amplification applications
Chapter 1 briefly discusses semiconductor material characteristics and then introduces the semiconductor diode. Chapter 2 looks at various diode circuits ttiat demonstrate how the nonlinear characteristics of the diode Itself are used in switching and waveshaping applications. Chapter 3 intro­ duces the bipolar transistor. presents the de analysis of bipolar transistor circuits, and discusses basic applications of the transistor. rn Chapter 4, we design and anal yze fundamental bipolar transistor circuits, Including ampli­ fiers.
Chapter 5 introduces the field-effect 1ransistor (FET), and FET circuits are analyzed and designed in Chapter 6. Chapter 7 COMiders the frequency response of both bi polar and field·effect transistor circuits. Fi nafly, Chapter 8 discusses the designs and applications of these basic electronic circuits, including power amplifiers and various output stages.
C H A P T E R
1 Semiconductor Materials and Diodes
1.0 PREVIEW
This text deals with the analysis and design of circuits containing electronic devices. such as diodes and transistors. These electronic devices are fabricated using semiconductor materials, so we begin Chap1er I with a brief discussion of the properties and characteristics of semiconductors. The intent of this brief discussion i:; to become familiar with some of the semiconductor material terminology.
A basic electronic device is the pn junction diode. One of the more inter­ esting characteristics of the diode is its rionlinear urrent-voltuge properties. The rcsi:;tor. for example, has a linear relation between the current through it and the voltage across the element. The diode is also a two-terminal device, but the i-·1· relationship is nonlinear. The current i$ an exponential function of voltage in one direction and is essentially zero in the other direction. As we will sec. this nonlinear characteristic makes possible the generation of a de vollage frnm an ac voltage source and the design of digital logic circuits. for example.
Since the diode is a nonlinear element. the analysis of circuits containing diodes is not as straightfoward as is the an:dysis o-f simple resistor circuits. A mathematical model of the diode. describing the nonlinear i-1· properties. is developed. However. the circuit cannot be analyzed, in general. hy direct math­ ematical calculations. In many engineering problems. approximate '"back-of­ the-envelope" solutions replace difficult complell solutions. We develop one such approximation technique using the piecewise linear model of the diode. In this cae. we replace the nonlinear diode properties by linear characteristics that are approximately valid over a limited region of operatio n. This concept is used throughout the study of electronics.
Besides the pn junction diode, we consider five other types of diodes that are used in specialized electronic applications. These include the solar cell. photodiode. light-emitting diode. Schottky barrier diode, and the Zener diode.
The general propercies of the diode are considered in this chapter. Simple diode circuits are analyzed with the intent of developing a basic understanding of analysis techniques and diode circuit characteristics. Chapter 2 then con­ siders applications of diodes in circuits that perform various electronic functions.
3
1.1 SEMICONDUCTOR MATERIALS AND PROPERTIES
Most electronic devices are fabricated by using semiconductor materials along with conductors and insulators. To gain a belter understanding of the behavior of the electronic devices in circuits. we must first understand a few of the characteristics of the semiconductor material. Silicon is by far the most com­ mon semiconductor material used for semiconductor devices and integrated cin:uits. Other semiconductor materials are used for sialized applications. For example, gallium arsenide and related compounds are used for very-high­ speed devices and optical devices.
1.1.1 Intrinsic Semiconductors
An atom is composed of a nucleus. which contains positively charged protons and neutral neutrolls, and negatively charged electrons that, in the classical sense, orbit the nucleus. The electrons are distributed in various "shells" at different distances from the nucleus, and electron energy increases as shell radius increases. Electrons in the outermost shell are called valence electrom, and the chemical activity of a material is determined primarily by the number of such electrons.
Elements in the period table can be grouped according to the number of valence electrons. Table I. I shows a portion of the periodic table in which the more common semicollductors are found. Silicon (Si) and gennanium (Ge) are in group IV and are elemental semiconcluctors. In contrast, gallium arsenide is a group lll-V e:ompouncl stmicoaductor. We will show that the elements in group I l l and group V are also important in semiconductors.
Table 1.1 A portioo of the periodic table Ill IV v B c Al Si p Ga Ge As
Figure I .I (a) shows five noninteracting si1ico11 atoms, with the four valence electrons or each atom shown as dashed lines emanating from the atom. As silicon atoms come into close proximity to each other, the valence electrons interact to form a crystal. The final crystal structure is a tetrahedral configura­ tion in which each silicon .atom has four nearest neighbors, as shown in Figure I.l(b). The valence electrons are shared between atoms, forming what are called covalent boD41s. Germanium, gallium arsenide, and many other semicon· ductor materials have the same tetrahedral configuration.
Figure l . l(c) is a two-dimensional representation of the lattice fonned by the five silicon atoms in Figure l .l(a). An important property of such a lattice is that valence electrons are always available on the outer edge of the silicon crystal so that additional atoms can be added to form very large single-crystal structures.
A two-dimensional representation of a silicon single crystal is shown in Figure 1.2, for T = 0 °K, where T = temperature. Each line between atoms
- Si - l I
- Si - - Si - - Si -
- Si -
- Si -
l (a) {b)
Flgure 1.1 Silicon atoms in a Cf)'stal matrix: (a) five noninteraciing silicon atoms, each wittl tour valence electrons. (b) the te1rahedral conura1ioo, (c} a two-dimenSional representa1ion showing lhe covalent bonding
represents a valence electron. At T = 0 ''K, each electron is in its lowest pos­ sible energy slate, s.o each covalent bonding position is filled. If a small electric field is applied to this material, the electrons will not move, because they will still be bound to their individual atoms. Therefore, at T ::: 0 °K, silicon is an insulator: that is. no charge flows through it.
fr the temperature increases, the valence electrons will gain lhennal energy. Any such electron may gain enough thermal energy 10 break the covalent bond and move away from its original position (figure 1 .3). The electron will then be free to move within the crystal.
Since the net charge of the material is neutral, if a negatively charged electron breaks its covalent bond and moves away from its original position, a positively charged "empty state·· is created at that position (Figure 1.3). As the temperature increases, more covalent bonds .are broken and more free electrons and positive empiy stales are created.
In order 10 break the covalent bond, a valence electron must gain a mini­ mum energy, Ev called the banclgap energy. Materials that have large bandgap energies. in the range of 3 10 6 electron--volts1 (eV), are insulators because, at room temperature, essentially no free electrons exist in these materials. In contrast, materials that contain very large numbers of free electrons at room temperature are conductors.
In a semi('(mduc1or. the bandgap energy is on the order of I eV. The net flow of free electrons in a semiconductor causes a current. In addition. a valence electron that has a certain thermal eriergy and is adjacent to an empty state may move into that position, as shown in Figure l.4 making it appear as if a positive charge is moving through the semiconductor. This positively charged "particle" is called a hole. In semiconductors, then. two types of charged particles contribute to the current: the negatively charged free electron. and the positively charged hole. (This description of a hole is
1 An <lec1ron-voll is the energy of an electron 1hat ha$ been letated through a potential ditTerence of I volt. and I tV 1.6" 10-19 joules.
11 - Si -
l (c)
II II II II - Si = Si = Si = Si -
II II 11 II - Si = Si = Si = Si -
I I I I Figure 1.2 TwCK!imensiOnal represertation of the silieon crystal at T = o·K
Figure 1.3 The breaking ol a covalent bond f0< T > O' K
- Si = Si= Si = Si -
II II II II - Si = Si = Si = Si -
1 I I FlgUfe 1.4 A two­ dimelJS/onaJ 1epresenJation ot the silicon CfY$lal showing the movement of the wsitivety charged hol9
6 Part I Semiconductor Dcvi<:es and Ba•'ic Applications
greatly oversimplified. a.nd is mean! only to convey the concept of the moving positive charge.)
The concentrations (#/cm3) of eltrons and holes are important parameters in the charact eristics of a semiconductor material. because they
direc1ly inffuence the magnitude of the current An intrinsic semicooductor is a single-crystal semicondudor material with no other types of atoms within the crystal. In an inuinsic semiconductor, the densities of electrons and holes arc equal. since the lhermally generated electrons and holes are the only source of such particles. Therefore, we use the notation n; as the imrimk carriu ronce•­ Cration for the concentration of the free eletlrons. as well llS lhat of the holes. The equation for n; is as follows:
( 1.1)
where B is a constant related to the specific semiconductor material, £1 is the bandgap energy (eV), Tis 1he temperature ('K). and k is Boltzmann's constant (86 >< I o-6 e V ;nK ). Tile values for B and £1 for several semiconducLor maleri· als are given in Table 1 .2. The bandgap energy is not a strong function or temperature.
Table 1.2 Semiconductor constants
t.',(tV} I.I 1.4 0.66
Example 1.1 Ob)ecllw: Calculate the i111rinsic carrier concentration in silicon at T= oo·K.
s.tullotl: For silicon at T = 300°1<.. we can write·
n1 = BT)12e() = (.5.23 x 1015)(300)3/)) .... i-k,_)
()J
Comment: An intrinsic electron concen1ra1ion of 1.S x 1010 cm-3 may appear 10 be large. but it is relati\-ely small compared 10 the conccatration of si6con atoms. which is 5 x I022cm-l.
The inlrinsic concentration n, is an importani parameter that appears often in the current-voltage uations for semiconductor devices.
Chapter I Semiconduc1or Materials and Diodes
Tes1 Your Understandln9 1. t Calc11la1e the intrinsic carrier concentrarion in ;gailium arsenide and germanium at T ""' 300 'K. (Ans. GaAs, n; = 1.80 x 106cm-1: Ge. n; = 2.40 x J011 cm-J)
1.2 Determine the intrinsic carrier concentration in silicon. gallium arsenide, and germanium at T = 400"K. (Ans. Si. 111 = 4.76 x I012cm-J; GaAs, n; = 2.44 x IOq cm-.\: Ge. 11, = 9.06 x 1014 cm-'J
1.1.2 Extrinsic Semiconductors Becauc the electron and hole concentrations in an intrinsic semiconductor are relatively small, only very small currents are possible. However, these concen­ trations can be greatly increased by adding controlled amounts of certain impurities. A desirable impurity is one that enters the crystal lattice and replaces (i.e., substitutes for) one of lhe semiconductor atoms, even though the impurity atom does not have the same valence electron structure. For silicon. the desirable substitutional impurities ate from the group I l l and V elcmencs (sec Table 1 . 1) .
The most common group V elements used for this purpose are phosphorus and arsenic. For eKample, when a phosphorus atom substitutes for a silicon atom. as shown in Figure 1.5. four of its valence electrons are used to satisfy the covalent bond requirements. The fifth valence electron is more loosely boun<l to the phosphorus atom. At room temperature, this electron has enough thermal energy to bre-.tk the bond, thus being free to move through the crystal and contribute to the electron current in the semiconductor.
The phosphorus atom is called a dolKlr impwity, since it donates an elec­ tron that is free to move. Although che remaining phosphorus atom has a net positive charge, the atom is immobile in the crystal and cannot contribute to the current Therefore. when a donor impurity is added to a semiconductor. free electrons are created without generating holes. This process is called doping, and it allows us to control the concentration of free electrons in a semiconductor.
A semiconductor that contains donor impurity atoms is called an n-type semiconductor (for the negatively charged electrons).
The most common group 111 element used for silicon doping is boron. When a boron atom replaces a silicon atom. ics three valence electrons are used to satisfy the covalent bond requirements for three of the four nearest silicon atoms (Figure 1.6). This leaves one bond position open. At room tem­ perature, adjacent silicon valence electrons have sufficient thermal energy to move into this posicion, thereby creating a hole. The boron atom then has a net negative charge, but cannot move, and a hole is created that can ccnuibute to hole current.
Because the boron atom has accepted a valence electron, lhe boron is therefore called an accepttlr impurity. Acceptor atoms lead to the creation of holes without electrons being generated. This process, also called doping, can be used to control the concentration of holes in a semiconductor.
7
II II J..© II - Si =(V:: Si = Si -
11 II II II - Si = Si = Si Si -
Figure 1.5 Two-dimensiooal reJ)fesentation of a siliCOll lattice doped with a phosphorus atom
- Si = Si= Si = Si -
II II II II - Si = Si = Si = Si --
1 I I I Figure 1.6 Two-dimensional represemation of a siioon lattice doped with a boron atom
Pan I Semicond11c1or Devices aad Basic Appliuuiun
A semiconductor that contains aoceptor impurity atoms is called a p-type semiconductor (for the positively charged holes created).
The materials containing impurity atoms are called ntrinsic semicon•uc­
tors, or doped semkonch.l:tors. The doping process, which allows us to control the concentrations of free electrons and holes, determines the conductivity and currents in the material.
A fundamental relationship between the electron and hole concentrations in a semiconductor in thermal equilibrium is given by
(l.l) where "" is the thenna eqltilibrium concentration of free electrons, p6 is the thennal equilibrium conntration of holes, and n; is the intrinsic carrier concentration.
At room temperature (T = 300°K), each donor atom donates a free eltt­ tron to the semiconduccor. If the donor concentration N4 is much larger than the intrinsic concentration, we ca n approximate
11u :::: N,1
Then, from Equation (l.2). the hole concentration is ' ii" p" = "FJ­d
(1.3)
(1.4)
Similarly, at room temperature, each acceptor atom accepts a valence electron, creating a hole. If the acceptor concentration Na is much larger 1han the intrinsic concentration, we can approximate
J>,, lV,, (l.S) Then, from Equation ( 1.2), the electron concentration is
' Iii II., := N (1.6) " E11ample 1.2 Olljecllve: Calculate the thermal equilibrium electron and bole con­ ctntrations.
Consider silicon at T -= 300 °K doped with phosphorus at a concentration C>f N, = I016cm·>. Recall from Example I.I that 11; = l.S x I010cm·3•
Sotullon; Since N.1 » n;. the electron concentration is
n0 £!! N4 = 1014cm-l
and the hole conentration is 2 10 ' - - (l .S x 10 )· - 25 104 -)
Po - N4 - 1016 - •· x cm
Comment: In an extrinsic semiconduc1or, che electron and hole concentrations nor­ mally differ by many orders of magnitude.
Chapter I Semiconductor Materials and Diodes
In an n·type semiconductor, electrons are called the maj>rity carrier bause they far outnumber the holes, which are termed the minority carrier. The results obtained in Example 1.2 clarify this definition. In contrast, in a p-type semiconductor, the holes are the majority carrier and the electrons are the minority carrier.
Test Your Understanding
1.3 Calculate 1he majority and minority carrier concentrations in silicon at T =
300''K if (a} N0 = I017 cm-. and (b) Nd = 5 x 101s cm-J. (Ans. (a) p0 = 1017 cm-·1, "• = 2.5 x 101 cm-J. (b) n0 = 5 x IO" cm-3, p0 = 4.S x. 104 C111-3)
1.1.3 Drift and Diffusion Currents
The two basic processes which cause electrons and holes to move in a semi·
conducior are: (a) drift, which is the movement caused by electric fields; and (b) diff11Sion. which is the tlow caused by variations in the concentration, that is. c-0ncentration gradients. Such gradients can be caused by a nonhomoge­ neous doping distribution, or by the injection of a quantity of electrons or holes inlo a region, using methods to be discussed later in this chapter.
To understand drift, assume an electric field is applied to a semiconductor. The field produces a forct that acts on free electrons and holes, which then experience a net drifi velocity and net movement. Consider an n-type semicon­ ductor with a large number of free electrons (Figure 1.7(a)). An electric field E applied in one direction produces a force on 1he electrons in the opposite direction. because of the electrons' negative charge. The electrons acquire a drift velocity l'Jn (in cm/s) which can be written as
\"'" '"· 11,, 1; ( 1 .7)
where µ,, is a constant called the electron mobility and has units of cm2 /V-s. For low-doped silicon, the value ofµ.. is typically 1350 cm2 /V-s. The mobility can be thought of as a parameter indicating how well an electron can move in a semiconductor. The negative sign in Equation (1.7) indicates that the electron drift velocity is opposite to that of the applied electric field as shown in Figure l.7(a). The electron drift produces a drift current density J. (A/cm2) given by
.f,, .,,., · ···111 .. ,,, = -1•11(-11,,E) = +e111t11 t: (1.8)
where /1 is the electron concentration (#/cm3) and e is the magnitude of the electronic charge. The conventional drift current is in the opposite direction from the flow of negative charge, which means that the drift current in an it-type semiconductor is in che same direction as the applied electric field.
Ne1; t consider a p-t ype semiconductor with a large number of holes (Figure I .7(b)). An electric field E applied in one direction produces a force on the holes in rhe same direction, because of the posilive charge on the holes. The holes acquire a drift velocity v4, (in cm/s) which can be written as
(l .ll)
p·lype --.. f.
(b) Figure 1 . 7 Apj."4ied eleclrie field, carrier drift velocily, and drift current density in (a) an n·lype semiconduclor and (b) a p·type semiconductor
to Pan I mkonductor O.vices 3nd B&k Applications
where µP is a constant called the hole mobility, and again has units of cm2/V-s. for low-doped silicon, the value of µ,. is typically 480 cm/V-·s, which is slightly less than half !he v;ilue of the electron mobility. The positive sign in Equation (1.9) indicates 1hal the hole drift velocity is in the same direction as the applied electric field as shown in Figure I . 7(h. The hole drifl produces a drift current density Jr (A/cm2) given b
(I . I 0)
where p is the hole concentration (#/i;m·} and e is again the magnitude of the electronic charge. The conventional drift current is in the same direction as the flow of positive charge. which means that the drift current 1n a p-type material is also in the same direction as the applied elc<.1ric field.
Since a semico11ductor contains both electmn and holes. the tolill drifl current density is the sum of the electron and hole components. The total drift current density i then written as
J = c•nµ.E + ep111,E = nE <1 .1 l(a))
where
(1 .1 l(b))
and where u is the coadl!Cfil'ity of the semjconductor in (O-crn)"-1 . The con­
ductivity is related to the concentration of electrons and holes. If the electric field is the result of applying a voltage to the semiconductor, lhen Equation ( 1 . 1 l(a)) omes a linear relationship between current ;;.nd voltage and is one form ofOlun's law.
From Equation ( U I ( b)), we see that the CQnductivity can be changed from strongly n-type, /1 » p, by donor impurity doping to strongly p-type, p » n, by acceptor impurily doping. Being abk to roo.trol the ronductivity or a semicood1tetor by lective doping is l'rhll allows 11S to £abricalt die ,ariety of eleelronic devices that ar atallable.
With diffusion. particles flow from a region of high concentration to a region of lower concentratioa. This is a statistical phenomenon related to kinetic theory. To explain, the electrons and holes in a semiconductor are in continuous motion. with an average speed determined by the tempera· ture. and with the directions randomized by interactions with the Janice atoms. Statistically, we can assume that, at any particular instant. approximately half of the particles in the high-concentration region are moving away from that region toward 1he lower·c()ncentration region. We can also assume that, at the same time, approximately half of the particles in the lower.concentration region are moving toward the high-concentration region. However, by defini­ t.ion, there are fewer particles in the lower-concentration region than there arc in the high-concentration region. Therefore, the net result is a flow ofpanicles away from the high-concentration region and toward the lower-concentration region. This is the basic ditTusion proress.
"
p Hl il'fosioo
(b)
Figure 1.8 Current density caused by concentraliOn gradieots: (a) electron diffusion and cmresponding current density and (bl hole '1ifl\1$ioo and correspOllding c11f\'ent <!en$ily
ln Figure l .(b). the hole concentration is a function of distance. The diffusion of holes from a high-concenlration region to a low-concentration region produces a How of holes in the nega1ive x direction.
The fowl cu1rent density is 11\e sum of the drift and diffusion components. Fortunately. in most cases only one component dominates the current at any one time in a given region of a semiconductor.
t.1.4 Excess Carriers
Up to thi point. we have assumed that !he semiconductor is in thermal equi­ lillrium. In 1he discussion of drift and diffusion currents. we implicitly assumed that equilibrium was not significantly disturbed. Yet , when a voltage is applied lo, or a current exisls in. a semiconductor device. the semiconductor is really not in equilibrium. In this section. we will discuss the behavior of nonequi­ librium electron and hole concentrations.
Valence elec1rons may acquire sufficient energy to break the covalent bond and become free electrons if they interact with high-energy pho1ons incident on the semiconductor. When this occurs. both an ele<:tron and a hole are pro­ duced. thus generating an electron-hole pair. These additional electrons and holes are c<illed excess electrons and excess holes.
When these excess electrons and holes are created. the concentrations of free electrons and holes increase above their thermal equilibrium values. Thi may be represented by
" == "" + ,, ( 1. 12(a))
I'= /I .. + lip (t.12(b))
where 11,. and P .. are lhe thermal equilibrium co11centr<ltions of electrons and holes. and f>n and op are the excess electron and hole concentrations.
rr the semic1mductor is in a steady-stale condition. the cre-.uion of excess electrons and holes will not cause the carrier concentration to increase indefi­ nitely. because a free electron may recombine with a hole, in a process called elron-OOle recomllinalioa. Both the free electron and the hole disappear causing the excess concentration 10 reach a steady-state value. The mean time over which a n excess electron and hole exist before recombination is called the excess carrier lifecime.
1 1
Test Your Understanding
1.4 Consider silicon at r = J00°K. Assume 1itat ''• = 1350cm2 fV-s and 11,, =
480cm2/V--s. De1ennine the conductivity if (a) N,r= S x 1 016cm-1 and (b) N. = 5 x 1016 cm·.l. (Ans. (a) 10.8 (Gl--<:m)""1, lb) J.84ifl-<m)- 1•
1.5 A sample-0fs1licon at T = 300'K is doped to Nd = 8 x 101cm-.(a) Calculate n. and Pa· {b) If excess hole5 and eleClt(lOS are generated such lhat their respective concentrations are '1p = .Sn == 1014 cm-·3• determine the total concentrations of holes and electrons. (Ans. (a) n0 = 8 x I01$cm -. p,, = 2.81 x io•cm-\ (bl 110 = 8. 1 x 1015 an-1• p0 1014 cm-3) 1.e The conductivity of silicon iso = IO(nm)"1 . Detcnnine the driftcurren! den­
sity if an electric field of E = 1 5 V /cm is applied . (Ans. J = l 50 A/cmi)
1.2 THE pn JUNCTION
In the preceding sections. we looked at characteristics of semiconduct(lr materials. The real power of semiconductor ele<:tronics occurs when p- and n-regions are directly adjacent to each other, forming a po junction. One impor­ tant concept to remember is 'that in most integrated circuit applications, the encire semiconductor material is a single crystal, with one region doped to be p-type and the adjacent region doped to be n-type.
1.2.1 The Equilibrium pnJunctlon
Figure L9(a) is a simplified block dia gram or a pn junction. Figure l .9(b)
shows the respective p-type and n-type doping concentrations, assuming uni­ fonn doping in each region. as well as the minority carrier concentrations in each region, assuming thermal equilibrium.
1:;.. · . .:, . . .If.' . . Bl (8)
.t ()
(b)
Figure 1.9 The pn junction: (a) simplified geometry ol a pn jution and (b) doping profile of an ideal unifomlly doped po junciiQll
The incerface at x = -0 is called the metallurgical junction. A large densi1y gradient in both the hole and electron concentrations occurs across this junc­ tion. Initially, then, there is a diffusion of holes from the p-region into the n­
region, and a diffusion of electrons from the n-.region inro the p-region (Figure I. IO). The flow of holes from the p-region uncovers negatively charged acceptor i<lns, and the ftow of electrons from the n·region uncovers positively
Chapte1 I Semiconductor Ma1enals and Diodes
p-rog1on
p (•)
Potential
(b)
Figure 1.1 o Initial diffusion of electrons and holes at the metallurgical 1unction, eSlablishing thermal equilbrium
Figure 1.11 The pn junction in thermal equilibriim: (a) the sce-dlarge region and electric field and tbl the potential through the junction
charged donor ions. This action creates a charge separation (Figure 1 . 1 l(a)), which sets up an electric field orienled in the direction from the positive charge fo the negative charge.
If no voltage is applied to lhe pn junction. 1hc diffusion of holes and etrons must eventually cease. The dire<:tion of 1he induced electric field will ause the resulting force to repel the diffusion of holes from the p·region and 1he diffusion of electrons from the n-region. Thermal equilibrium occurs when the force produced by the electric field and the "force" produced by the density gradient exactly balance.
The positively charged region and the negatively charged region comprise the spacHharge region, or depletion region. of the pn junction. in which 1here are essentially no mobile electrons or holes. Because of the electric field in the space-charge region, there is a potential difference across that region (Figure 1 .1 l(b)). This potential difference i called the built-in potential barrier, or buih­ in voltage, and is given by
(l.13)
where VT = kT /e, k = Boltzmann·s constant. T = absolute lemperature, e = the magnitude of the electronic charge. and N. and Nd are the net acceptor and donor concentrations in the p- and n-regions. respectively. The parameter VT is called the 1hemal voltage and is approximately V r = 0.026 V at room tem­ perature. T = 300°K.
E11ampte 1.3 Ob1"1lv•: Calculate the built-in poten1ial barrier of a pn junction. Consider a silicon p11 junction at T = JOO•K, doped at N., .::. IO"'cm-1 in the p­
rcgion and N,1 • 1017 cm -J in the n·region.
Solution: 1-'rom the results of Example LL we have 11, .::. 1 .5 x I010cm·.1 ror silicon at
room temperature. We 1hen find
Vr. = V1 1 n = (0.026)1n 10 2 = 0.7S7 V (N N) [(101)(1017)]
llj (1.5 x 10 )
Part I Semiconducl0< vi.:es and Basic Applications
Comment Because of the log function. the magnitude of Vt>< is not a strong function of the doping concentrations. Therefore, the value of Vh, for silicon pn jur1ctions is usually within 0.1 to 0.2 V Qf this calculated value.
The potential difference, or built-in potential harrier, across the space­ chargt region cannot be measured by a voltmeter because new potential bar· riers form between the probes of the voltmeter and the semiconductor. cancel­ ing the effects of Vi,,. Jn essence. V), mainc.ains equilibrium. s-0 no current is produced by this voltage. However, the magniiude of Vh, becomes important when we apply a forwar<l-bias voltage, as diS<.:ussed later in this chapter.
Test Your Understanding
t.7 Determine Vh, for a silicon pn juncuon at T = 300"'K for (a) N,,""' l01icrn-). fll,1= l017 cm··1• and for (b) N. =. Nd = \()17 cm "3. (Ans. (a) VN =0.697V. (b) V01 ·= 0.817 V) t.8 Calculate V,,, for a GaAs pn junction at r = JOOK for N0 = 1016cm-·' and N., = 1011 cm->. (Ans. V,,, = 1.23 V)
1.2.2 Reverse-Biased pn Junction
Assume a positive voltage is applied to the n·region of a pn junction, as shown in Figure 1.12. The applied voltage V 11 induces an applied electric field, EA> in the semiconductor. The direction of this applied field is the same as that of the £-field in the space-charge region. Since che electric fields in the areas outside the space-charge region are essentially zero, the magnitude of the electric field in the space-charge region incieases above the lhennal equilibrium value. This increased elec1ric field holds back the holes in the p-region and !he electrons in the n-region, so there is essentially no current across the pn junction. By definition, this applied voltage polarity is called reverse bias.
When the electric field in the space-charge region increases, the number of positive and negative charges also increases. If the doping concentrations are not changed, the increases in the charges can only occur if the width W of the
Figure 1.12 A po juACtlon wilt! an applied revemH>ias voltage, sl1oWlng Ill& llir$Ction ol lhe electric fiekl Induced 17t' VR and of 1118 spaoe-chatgit electric field
(hapler I Senuconductor Material; a11d Diodes
spal-c-chargc region increases. Therefore. with an increasing reverse-bias volt­ age V11, spal'e·charge width W also increases.
Because or the addiiional positive and negative charges in the space-charge region. a capacitance is associated with 1he pn junction when a reverse-bias voltage ii; applied . This junction capacitaafe. or depletion layer capacitance, can be written in the form
(1. 14)
where C. is the junction capacitance at zero applied voltage. The capacitance-voltage characieristics make the pn junction useful for
electrically tunable resonant circuits. Junctions fabricated speci6cally for this purpose- are called varactor diodes. Varactor diodes can be used in electrically tunahle oscillarors. such as a Hartley oscillator. discussed in Chapter 15, or in tuned umplilicrs. considered in Chapter 8.
Example 1.4 Objectl11e: Calculate tile junction capacitance of a pn junction. Consider a silicon J'TI junction at T :::: JOO· K, with t.loping concentrations of N. ==
101'' cm " mid N,1 = 101cm 3. Assume that 11, = 1.5 x 1otocm .. and let C; .. = 0 . 5pF.
Calculate the junction capacitance at V,, = 1 V and ... R :::: 5 V.
Solution: Th1: huilt ·in polential is de1ermined by
The Jllllli1•n ,·apacitanct for VR = I V is th.;n found I(> be
( I' )_ , ,, ( I )_,, C, C,,. I + j . . = (0
. S) I + 0.637 . :: tU 12pF
For 1 ·11 =·: $ V
s ··I/ C, .· (0.5l( 1 + 0.3?) = 0.168 pF
Comment: The m.ignit udc of tnc junction ca paci tancc is usue11ly at or below the! pico­ fornd r ;111gc. •md it do:crcases as the reverse-bias voltage increases.
As implied in the previous section, !he magnitude of the electric field in tlte
space-charge region im:reases as the reverse-bias voltage increases. and the maximum dectric field occurs al the metallurgical junction. However, neither the dectrii.: field in the space-charge regiQn nor the applied reverse-bias voltage can increaso.: indefinitely becaui;e at some point, breakdown will oocur and a large reverse bias current will be generated. This concept will be described in detail later in this chapter.
15
Test Your Uriderstanding
t.9 A silicon pn juncti(ln at T = 300 "K is doped at N,, = !016cm- and N,, = 1017 -3 Th · . . . be C 0 . cm . e JUnetmn capac!tance 1s to 1 =- .8 pF when a reverse-bias volu1g of v R = s v is applied. Find the zern·biased junetiCln capacitance c, ... (Ans. c_. = 2.21 pF)
1.2.3 Forward-Biased pn Jundlon
To review briefly. the n-region contain:; many more free electrons than the p· region: similarly. the p-region contains many more holes than the n-n:gion. With zero applied voltage. the built-in potential barrier prevents these majority carriers from diffuing across the space-charge region; 1hus. the barrier main­ tains equilibrium between the carrier distributions on either side of the pn junction.
If a positiw voltage i:0 1s applied to the p-region. the potential barrier decreases (Fil(ure 1.13). The electric fields in the space-charge region are ver large comp<1red 10 those in the remainder of the p· and n-regions. so essentially all of the applied voltage exists acros the pn junclion region. The applied eloctric field. £,.. induced by the applied voltage is in the opposite dire<:tion rrom thilt of the thermal equilibrium space-drnrge £-field . The net result is that the electric field in the space-charge region is lower than the equilihrium value. This upsets the delicate balance between diffusion and the £-field force. Majority carrier electrons from the n-region diffue into the p-region, and majority carrier h<lles from the p-region diffuse into the 11-region. The process continues as long ;is the voltage v0 is applied, thus creating a current in the pn junction. This process would be analogous to lowering a dam wall slightly. A slighi drop in the wall height can send a large amoun t of water (current) over the barrier.
p
'------l1I.__-----' Flgu re 1.13 A pn jl.flction with ao applied forward-bias voltage, showing tile di recrion of ltie electric field EA induced by v0 and of the net spaoe·charge electric field E
This applied volt age polarity {i.e .. bias) is known as fo"'ard bias. The forward-bias voltage 1·n must always be less than the built-in potenti:1l barrier vbi.
As the majority carriers cross into the opposite regions, they become mi­ nority carriers in those regions, causing the minority carrier concentrations to increase. Figure 1 .14 shows the resulting excess minority carrier concentrations
Chapter I rniconductor Materials and Diodes
... x':O x:O x
Figure 1.14 S1eady·Slate mi'lority carrier concentrauoo in a pn junction under forward bias
at the spacc·charge region edges. These excess minority carriers diffuse into the neucrnl n- and p-regions, where they recombine with majority carriers, thus establishing a steady-state condition, as shown in Figure 1.14.
1.2.4 Ideal Current-Voltage Relationship
As shown in Figure 1.14, an applied voltage results in a gradient in the minority carrier concentrations, which in turn causes diffusion currents. The 1heore1kal relationship between the voltage and the current in the pn junction is given by
(J.15)
The rarnmelcr Is is the reverse-bias saturation cunent For silicon pn junctions. typical values of 15 are in the range of 10-15 to 10- 13 A. The actual value depenos on the doping concentrations and the cross-sectional area of the junc· ti{\11. Th 1rameter Vr is the thennal voltage. as defined in Equation (1 . 13). and is approximately VT = 0.026 V at room temperature. The parameter n is usually c.alled the emission coefficient or ideality factor. and its value is in the range I n :s 2.
The emission coefficient n takes into account any recombination of elec· trons and holes in the space-charge region. At very low current levels, recom­ bin:llion may be a significant factor and the value of n may be close to 2. Al higher current levels, recoml>ination is Jess a fac:tor. and the value of n will be I. Unless otherwise stated, we will assume the emission coefficient is n = I .
example 1.5 }eetlyt! Detennine the current in a pn juriction. Consider ll pn junclion al T = 300°K in which ls = 10-14 A and n = I. Find tbc
dil1Jc current for P = +0.70V and vD = -0.70 V.
Solution; For Y tJ "" +O. 70 V. the pn junc1ion is forward-biased and we find
for vp = -0.70 V, the pn junction is reverse-biased and we iind
17
13 Par1 l Semicondix:tor Devices and B,uic Applications
Comment Altho11gh J s is quite small, even a relatively small value of forward-bias vollage can induce a moderate junction current. With a reverse-bias voltage applied. the
junction current is virtually z.:-ro.
Test Your Understanding
1.10 · A silicon pn junction diode at T = 300" K has a reverse-saturation current of Ts = 10-1' A. (a) Determine the forward-bias diode current for (i) v0 = 0.5 V. (ii) v0 = 0.6 V. and (iii) ,.,., -= 0.7 V. (b) Find the reverse-bias diode current for (i) v0 = -0.5V, and (ii) V D = -2V. (Ans. (a) (i) 2.25µA. (ii) IOSµA. (iii) 4.93mA; (b) (i) 10-14 A. (ii) 10 14 A)
1.11 A silicon pn juncti-0n diode at T = 300 'K bas a reverse-saturation currem ol'
Is = 10- 13 A. The diode is forward-biased with a resulting current of I mA. Determine rp. (Ans . .. 0 .= 0.599 V)
1.2.5 pn Junction Diode
Figure l . l 5 is a plot of the derived currenl--vollage characteristics of a pn junction. For a forward-bias voltage. the current is an exponential function
- 1.0
Forward-bias region
F19ure1.1S Ideal 1-V chaslica ola pn junction diode tor Is = 10-u A
llJ(AJ I(» .l
w-"' .. ro-11 10·12 J 1r· I.I
111-14
0.1
F19ure 1.16 Ideal fOfWard·biastMI f-V dlaracteristics of a pn junction dio<le, with the wrren( plotted on a log S<:ale lor Is = 10 ·,. A and n = t
of vollag(. hgure 1.16 depicts the forward-bias current plotted on a Jog scale.
With only a small change in the forward-bias voltage, the corresponding forward-bias current increases by orders of magnitude. For a forward-bias vollagc ''J) > +0.1 V, the (-1) tenn in Equation ( 1 . 1 5) can be neglecled. In the reverse-bia dirtion. the current is almost Lero.
The semiconductor device that displays these f-V characteristics is called a pn j1nction diode. Figure 1 . 17 shows the diode circuit symbvl and the conven­ tional current direction and voltage polarity. The diode can be thought of and used as a voltage controlled switch that is .. off'" for a reverse-bias voltage and "'on .. for a forward-bias voltage. In the forward·bias 1Jr .. on·· state. a relatively large current is produced by a fairly small apphed voltage; in the reverse-bias. or --orr" state. only a very small current is created.
When a diode is reverse-biased by at least 0.1 V. the diode current is i1i = -/.-;. The current is in the reverse dir«:tion and is a constant. hence the name reverse-bias saturation current. Real diodes, however, exhibit reverse­ hias currents thal are considerably larger than /.'>· This addi1ional current is called a generation current and is due to eltf()ns and holes heing generated within the space-charge region. Whereas a typical value of Is may be io-
14 A, a typical value of reverse·bias current may be 10-9 A or I nA. Even though this current is much larger than Is. it is still small and negligible in most cases.
Temperature Eltects Since both l:; and 111 are funclions of temperature, lhe diode chan1cteristics
also vary with temperature. The temperature-related variations in forward-bias cllaracteristics •tre illustrated in Figure 1 . 1 8. For a given current, the required
19
(e)
(b)
Flgure1.17 The basic pn junction diode: (ai simpl1ed geomery and (b) circuit symbOI. and convenooal current direclion and volage polarity
!'art l SemiconductQI' Devi\:CS and &sic Applications
() Figure 1.18 Forward-bias characteristics verSIJs temperature
forward-bfas voltage decreases as temperature increases. For silicon diodes, the change is approximately 2 mV;°C.
The parameter Is is a function of the intrinsic carrier concentration n;. which in tum is strongly dependent on temperature. Consequently, the value of ls approximately doubles for every 5 •c increase in temperature. The actual reverse-bias diode current, as a general rule. doubles for every 10 °C rise in temperature. As an example of the importance of this effect, in gennanium, the relative value of n; is large, resulting in a large reverse-saturation current in germanium-based diodes. Increases in this reverse current with increases in the temperature malce the germanium diode highly impractical for most circuit applications.
Breakdown Voltage
When a reverse-bias voltage is applied to a pn junction, the.electric field in the space-charge region increases. The electric field may become large enough that covalent bonds are broken and electron-hole pairs are created. Electrons are swept to the n-region and boles to the p-region by the electric field generating a reverse-bias current. This breakdown mechanism is called the Zener effect. Another breakdown mechanism is caUed avalanche breakdown. which occur,; when minority carriers crossing the space-charge region gain sufficient kinetic energy to be able to break covalent bonds during a collision process. The generated electron-hole pairs can themselves be involved in a collision process generating additional electron-hole pairs, thus, the avalanche process. The reverse-bias current for each breakdown mechanism will be limited by the external circuit.
The voltage at which breakdown occurs depends on fabrication param­ eters of the pn junction. l>ut is usually in the range of 50 to 200 V for discrete devices, although brealdown voltages outside this range are possible-in excess of lOOOV, for example. A pn junction is usually rated in tenns of its
Cha?tet I Semic-0nd11e1or Mattrials and Piod.:s
peak iAverse voltage or PIV. The PIV of a diode must never be e11.cee<led in circuil operation if reverse breakdown is to be :avoided.
Zener diodes are fabricated with a specifically designed breakdown voltage and are designed to operate in the breakdown region. These diodes are dis­ cussed later in this chapter.
Switching Transient S i m .. -e the pn junction diode can be used a an electrical switch, an important parameter is its transient response, that is, its speed and characteristics, as it is switched from one state to the other. Assume. fo.r example. that the diode is switched from the forward-bias "on" stale to the reverse-bias "off" state. Figure 1 . 1 9 shows a simple circuit that will switch the applied voltage at time I = 0. For / < 0, the forward-bias current iv is
. J 0f' - ''1> ,,, = Ir = ···-:....-.......:.:. R,.
Figure 1 .19 Simple circuit tor switching a diode from foiward to reverse bias
(1 .16)
The minority carrier concentrations for an applied forward-bias voltage and an applied reverse-bias voltage are shown in Figure 1.20. Here, we neglecl lhe change in the space charge region width. When a forward·bias voltage is applied. excess minority carrier charge is s1ored in both the p- and n·regions. The execs:; charge is the difference between the minority carrier concentrations for a forward-bias voltage and those for a reverse-bias voltage as indicated in the figure. This charge mus1 be removed when the diode is switched from the forward to the reverse bias.
As the forward-bias voltage is removed, relatively large diffusion currents ore created in the reverse-bias direction. This happens b«ause the excess mi­ nority carrier electrons ftow back across the junction into the n·region, and the exces:; miMrity carrier holes flow back acros the junction into the p-region.
The large reverse-bias current is initially limited by resistor R11 to apprm<ima tel y
(1.17)
21
22 Part l Semiconductor Dcrn:es iln<l Baic Apphca!ions
p n
Figure 1.20 Stored excess minority carrier charge under lorward bias compared to reverse bias
The junction cap1dtances do not allow the junctic>n voltage lo change insran· taneously. The reverse current IR is approximately constant for O"" < / < t,. where '" is the storage time. which is the length of time required for the mi­ nority carrier concentrations at the space-charge region dges lei reach the thermal equilibrium values. After this time. the voltage ilcross the junction begins lo change. The fall t)me 11 is typically defined a the lime required for the current to fall to I 0 percent of its initial value. The total turn-off time is the sum of the storage time and the fall time. Figure 1 .21 shows the current characteristics as this entire proces!' takes place.
------ilf'
Figure 1 .21 Current characleristics versus time during diode switching
In order to switch a diode quickly. the diode must have a small excess minority carrier lifetime. and we must be able to ptoduce a large reverse current pulse. Therefore. in the design of diode circuits. we must provide a path for tile transient reverse-bias current pulse. These same transienl effects impact the switching of transistors. For example. the switcning speed of tran­ sistors i n digital circuits will affect the speed of computers.
The 1um-on transient occurs when the diode is switched from the "off ..
,;\ale to the forward-bias ··<>n .. slate, which can be initiated by applying a forward-bias current pulse. The transient lurnn time is the time required to establish the forward-bias minority carrier distributions. During this time. the
Chapter I Semiconductor Material and Di
voltage across the junction gradually increases toward ils steady-state value. Although the turn-on time for the pn junction diode is not zero. it is usually less than the transient turn-off time.
Test Your Understanding
1.12 R l'Cilll that tile forward-bias diode vol rage decreases approximately by 2 ml/ (C for silicQn duldcs with a given current. If VI> = 0.650 V at ID ; I mA for a temperature of 25 ·c de1.ermine the dio<k voltage at ID = I mA for T = 125 °C. (Ans. VD = 0.450 V)
1.3 DIODE CIRCUITS: DC ANALYSIS ANO MODELS
In this ection. we begin to study the diode in various circuit configuracions. As we hi1ve seen, the diode is a two-terminal device with nonlinear i-11 character­ istics. as opposed to a two-tenninal resistor, which has a linear relationship between current and voltage. The analysis of nonlinear electronic circuits is not as straightforward as the analysis of linear electric circuits. However. there are electronic functions that can be implemented only by nonlinear circui1s. Ex<imples include the generation of de voltages from sinusoidal voltages and the implementation of logic functions.
Mathematical relationships. or models. that describe 1he current-voltage characteristics of electrical elements allow us to analyze and design circuits without having to fabricate and test them in Che laboratory. An example is Ohm's law. which describes the properties of a resistor. ln this section, we will develop the de analysis and modeling techniques of diode circuits.
To begin lo understand diode circuits. consider a simple diode application. The current ·voltage characteristics of the pn junction diode were given in Fig.ure 1.15. An ideal diode (as opposed to a diode with ideal 1-V character­ istic) has the charac1eris1ics shown in Figure I .22(a). When a reverse-bias voltage is applied, the current through the diode is zero (Figure l.22(b)); when current through the diode is greater than zero, Che voltage across the diode is zero (Figure l .22(c)). An external circuit connected to the diode must be designed to control the forward current through the diode .
• •o -
(a) (b) (e)
Figure 1.22 The ideal diode: (a) 1-V cllaracteristic$, (b) equivaletit OO:u• under revene bias. and (c) equiYaleflt circuit In the cooduding stale
23
(cl
Paci I Semiconduc1or Devices and Basic Applications
One diode circuit is the rectifier circuit shown in Figure I .23(a). Assume that the input Yoltage v1 is a sinusoidal signal, as shown in Figure t .23(b), and the diode is an ideal diode (see Figure l.22(a). During the positive half.<:ycle of the sinusoidal input, a forward-bias current exists in the diode and the voltage across the diode is zero. The equivalent circuit for this condition is shown in Figure l .23(c). The output voltage v0 is then equal to the input voltage. During the negative half-cycle of the sinusoidal input, the diode is reverse biased. The equivalent circuit for this condition is shown in Figure 1.2l(d). In this part of the cycle, the diode aces as an open circuit, the current is zero, and the output voltage i8 mo. The output voltage cf the circuit is shown in figure l.23(e).
Over the entire cycle. the input signal is sinusoidal and has a zero average value; however, th.e outp'Ut signal contains only positive values and the1efore has a positive average value. Conseqently, this circuit is said to rectify the input signal. which is the first step in generating a de voltage from a sinusoidal (ac) voltage. A de voltage is required in virtually all electronic circuits.
As mentioned. the analysis of nonlinear circuits is nol as straightforward as that of linear circuits. Jn this section, we will look at four approaches to the de analysis of diode circuits: (a) iteration; (b) graphical techniques; (c) a i>iece­ wise linear modeling method; and (d) a computer analysis. Methods (a) and (b) are closely related and are therefore presented together.
+ "D -
(t)
-{J)J
Flgvre 1.23 The diOde nlcitlier: (a) circuit. (b} sinusoidal Input sigrial, (c) equivalent circuit lor v, > o, (cl} equiValenr circuit tor v1 < o. and (e) fied output signal
1.3.1 Iteration and Graphical Analysis Techniques
Iteration means using trial and error lo find a solution to a problem. The graphical analysis technique involves plotting two simultaneous equations and locating their point of intersection, which is the solution to the two equa· tions. We will use both techniques to solve the circuit equations, which include lhe diode equation. These equations are difficult to solve by hand because they contain both linear and exponential terms.
Cllapicr I SetnioonduelOr Materials and Diodes
Coosider, for eumple, the circuit shown in Figure l.24, with a de voltage Vps applied across a resistor and a diode. Kirchhoff's 'oltage law applies both to nonlinear and linear circuits, so we can write
Vps = lnR + JID which can be rewritten as
Vps Vn ln = - - ­R R
(1.18(•))
( l.18(b))
(Note: ln the remainder or this section in which de analysis is emphasized, the de variables arc denoted by uppercase letters anc:I uppercase subscripts.)
The diode voltage VD and current 11> are related by the ideal diock equa­ tion as
(1.19)
where 15 is assumed to be known for a particular diode. Combining Equations (J.l 8(a)) and (l. 19), we obtain
Vrs = lsR[e()-1 ]+vD (1.20)
which contains only one unknown, VD· However, Equation (1.20) is a trans­ cendental equation and cannot be solved directly. The use of iteration to find a solution to this equation is demonstrated in the following c:<ample.
Example 1 .6 Obfv.: Dete1111ine the diode vcltage and current for the circuit shown in figure 1.24.
Consider a diode with a given reverse-saturation current of Is = 10-n A.
Solullon: We can write .Equation (1.20) as
= ( IO-ll)(2 x to3>[ e()-1 }+ Vp (1.11)
If we first try VJ> = 0.60 V, the riaht sitU of Equation (\.21) is 2.7V, so the equation is not balanced and we must try again. If we next try V 1> = 0.65 V. the right side of Equation (l.21) is 15. l V. Again, the equation is not balanced, but wt can see that the solution for Y11 is between 0.6 and 0.6SV. If we continue rcftniQg ou.r guesses, we
will be able to show that, when VD = 0.619 V, the right sidc of Equation (1.21) is 4.99V, which is essenlially equal to the value of the lefl side ()f the equation.
The current in the circuit can then be determined by dividing the voltage difference across the resistor by the resistance, or
_ Vn- V0 _ S -0.619 _ 2 19mA lo - R - 2 - .
Comment Once the dio<le voltage is known, the cunent can also be determined from
•
----1 .
Part I Semiconductor Devices an Ba<ic l\pplications
To use a graphical approach to analyze the circuit, we go back to Kirchhoff's voltage law. as expressed by Equation ( l . 1 8(b)), which produces a straight-line relationship between current 10 and voltage Vv for a given Vps and R. This equation is referred to as the circuil load line, which can be plotted on a graph wi1h Tn and JI D as 1he axes. From Equation (1 . 18(b)). we see that if f 0 = 0, then VD = Vi's· Also from this equation. ii' V 0 = 0, then /0 = Ypsf R. The load line can be drawn between these two points. Using the values given in Example (l.6). we can plot the straight line shown in Figure l .25. The sec\.r.-: plot in tne figure is that of Equation ( 1 . 19). which is the ideal diode equation relating 1he diode curren I a.nd voll.age. The intersection of the load line and the device characteristics curve provides the de current 10 ::::: 2.2mA through the diode and the de voltage VD 0.62 V across the diode. This point is referred to as the q1iesce11t pohtt, or the poi11t.
10 lmAl
0 ..0.62 t 2 3 4 S VD (volts)
Rgv,.1.25 The dode and load line dlaracterislics for lhe circuit shown in Figure 1.24
The graphical analysis method can yield accurate resulls, but it is some­ what cumbersome. However, the concept of the load line and the graphical approach are useful for "visualizing" the response of a circuit, and the load line is use<! extensively in the evaluation of electronic circuits.
Test Your Understanding
•1.13 Consider the circuit in figure 1.24. Lei Vps = 4 V. R = 40k!J. and ls = 10-12 A. Detenninc V0 and ID, using the ideal diode equation and the iteration method. (Ans. Vi> = 0.S35V. lp = 0.&64mA) 1.14 Consider the diode and circuit in Exercise 1 .13. Determine I' 0 and 10, using the graphical technique. (Aos. V.o "" 0.54V. /0 :o:: O.ll7mA)
Chapltr I iconduc1or Ma1crials and L>iodes
1.3.2 Pieeewise Linear Model
Another. simpler way to analyze diode circuits is to approximate the diode·s current-voltage characteristics, using linear relationships or straight lines. Figurt' 1.26. for ex.ample, shows the ideal current-voltage characteristics and two linear arproximations.
1 ----t--"""ts ID -ts
1 Slope= ft
Figure 1.26 Tl\9 I diod& 1-V cl'laraclerl$1ics and two lfl&Br approidmatons
for V ll VY' we assume a straight-line appro"imation whose slope is lfr1, where Vy is the turn-on, or cat-in, YOltage of the diode, and r1 is the forward diode reslstan. The equivalent circuit for this linear approximation is a constant-voltage source in series with a resistor (Figure l.27(a)).2 For V n < Vr we assume a straight-line approx.imation parallel lo the V 0 ax.is at the zero current level. In this case, •he equivalent circuit is an open circuit (Figure I .27(b)).
't
+ - fD v,)
J Vy Vo
(b) (c)
Flour• 1.27 The diMe equival&!'lt eltc:uit (a) in ti'le •on• oondition wbon V0 :: Vr (bl in Ille "or condition when Vo < V,. and (<:) piecewise linear appro>Ctmation when r, = o
! It is imporltu 10 keep in mind that Ille voltage source in Figure I .27(a) only rtpments a voltage drop for V 0 :: v,. When V 0 < v,, the If SOUC(le does11111 prod11aa ncgarive diode aarrent. For Ve> < V,. the equivalent i11;ui1 in Figure I .27(b) must be used.
27
l8 Pa11 I Semicoaductor Dev and Basic Applications
This method models the diode with segments of straight lines; thus the name piecewise linen inodel. If we assume r1 = 0, the piecewise linear diode characteristics are shown in Figure I .27(c).
Example 1.7 Obi: Determine tne diode voltage and current in the circuit shown in Fi1urc 1.24. using a piecewise linear model.
Assume piecewise linear diode parameters of v, = 0.6 V and r1 :o IOQ. Solution: With the given input voltage polarity, the diode is forward biased or '"turned
on," so 10 > 0. The equivalent circuit is shown io Figure I .21(a). The diode current is determined by
I V,s - Vr 5 - 0.6
D "" R + r1 = 2 x JOl + I0 :::} 2.19mA
and the diode voltage is
110 = VY + lurr = 0.6 + (2.19 x 10-1)(10) = 0.622V
Comment: This solution, obtained using the piecewise linear modd, is nearly equal to the solution obtained in Example 1.6, in which the ideal diode equation wu used. However, the analysis using 1be piecewise-linear model in \his example is by far easier
than using the actual diode 1-V characteristics as was done in Elample 1.6. In general, we are willing to accept some slight analysis inaccuracy for ease of analysis.
Because the forward diode resistance r1 in Example 1 . 7 is much smaller than the circuit resistance R, the diode current Iv is essentially independent of the value of 'r· In addition, if the cut-in voltage is 0.7V instead of0.6V, the calculated diode current will be 2.15 mA. which is not significantly different from the previous results. Therefore, the calculated diode current is not a strong function of the cul-in voltage. Consequently, we will often assume a cut-in voltage of 0.7 V for silicon pn junction diodes.
The concept or the load line and rhe piecewise linear model can be com· bined in diode circuit analyses. Using Kirchhoff's voltage law, expressed as Equation l. 14(b). and the circuit in Figure 1.24. assume Vr = 0.7 V, 'I = 0, V15 "" +5 V, and R = 2 Hl. Figure l .28(a) shows the resulting load line and the piecewise linear c.haracteristic curves of the dio<le. The two curves intersect
10 <mA)
2.$ 2.IS
0.1 2 . .5 (b)
FlguM 1.28 PleceWIM inear 8PPfO)dmatlon (•)IOad line lof VPS "" SV and R"=' 2k0 and (b) IMW9flJ I09d Ines
Chapter l Semiconductor Materials and Diodes
at the Q-point, or diode current, I DQ 9! 2.15 mA. which is essentially a function of only V PS and R. Figure l .28(b) shows the same piecewise tioear character­ istics of the diode but with four different load lines, corresponding to: Vps = 5 v. R = 4 kn; v,s = 5 v, R = 2kS'2; v,s = 2.sv. R = 4 kS'l; and Y,.s = 2.sv, R = 2 k!l. The Q-point changes for each load line.
The load line concept is also useful when the diode is reverse biased. Figure l.29(a) shows the same diode circuit as before, but with the direction of the diode reversed. The diode current ID and voltage V 0 shown are the usual forward-biased parameters. Applying Kirchhoff's voltage Jaw. we can write
(1.22(•))
or
(1.ll(l>))
where I 0 = -I PS· Equation ( l.22(b)) is the load Line equation. The two end points are found by setting ID = 0, which yields V 0 = - V PS = -5 V, and by setting VD = O, which yields ID = -Vps/R = -5/2 ::::. -2.SmA. The diode characteristics and the load line are plotted in Figure l.29(b). We see that the load is now in the third quadrant, where it intersectS' the diode character· istics curve at V 11 = -5 V and II> = 0, demonstrating that the diode is reverse biased.
Ahhough the piecewise linear modd may yield solutions that are less accurate than those obtained with the ideal diode equation, the analysis is much easier.
lo
.,,.
Figure 1.29 Reverse-biased diode (a) circuit and (b) pieeewise finear approximation and load lille
T•st Your Und ... standing
1 . t a (a) Consider the circuit in Figutt 1.24. Let Vp.s = S V, R = 4 kn, and Vy= 0.7 V. Assume 'I = 0. Detennine 10• (b) Ir Yps is increased to 8 V, what must be the new value of R such that 10 is the same value as in part (a)? (c) Draw the diode character­ istics and load lines for parts (a) aod (b). (Ans. (a) 10 = l.08mA, (b) R = 6.79kQ)
30 Part I Semiconductor Devi(t'S ar.d Basic Appli<:alions
t, te The power supply (input) voltage in the circuit of Figure 1 .24 i-; 11 ps = 10 V and the diode cut-in voltage is Vy = 0. 7 V (assume r1 = 0). The power dissipated in the diode is to be no more than 1.0.SmW. Detennine the maximum diode current and the mini· mum value of R 10 meet Che power specification. (Am. 10 = 1.5 mA, R = 6.2 kO)
1 .3.3 Computer Simulation and Analysis
Today's computers are capable of using detailed simulation models of various components ancl performing complex circuit analyses quickly and relatively easily. Such models can factor in many diverse conditions, such as the temperature dependence of various parameters. One of the earliest, and now che most widely used, circuit analysis programs is the simulation program with integrated circuit emphasis (SPICE). This program, developed at the University of California at Berkeley. was first released about 1973. and has been continuously refined since that time. One outgrowth of SPICE is PSpicc. which is designed for use on personal computers.
Example 1.8 ObftCtl: Detennine the diode current and voltage characteristics of the cimiit shown in Figure 1.24 using a PSpice analysis.
SoluUcin: Fisure l.JO(a) is the PSpice cirruit schematic. A standard 1 N4002 diode from the PSpice libnuy was used in the analysis. The input voltage VI was varied ( d' sweep) from 0 to 5 V. Figure l.30(b) and (c) shows the diode voltage and diode current characteristics versus the input voltage.
? k +
(A) Di*.2A.dat (A} Diode 2A.dat I.() Y.------------. .o mA------------.
OY.s..---'-:-:----:-',....,,..---,,.,,., 0 I' 2.0 y 4.0 y 6.0 y a l'(Dl :I) y Pl
(lit
¥YI
(e)
Flture 1.30 (a) PSp circuit scllematic. (b) clode volta. and (c) diode CUll'8llt 1« Example 1.8
Chapter I ScmitonJuctor Ma1erials and Diodes
Discussion; Several observa1ions may be made from the rsult. The diode vohage incre-.iscs at a lmosl a linear rate up 10 approximately 400 m V without any discernible (mA) <11rrcnl heing measured. For an input vokage gre<.iter than