Lecture 11: MOSFET Modeling

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1 Digital Integrated Circuits (83-313) Lecture 11: MOSFET ing Semester B, Lecturer: Dr. Adam Teman TAs: Itamar Levi, Robert Giterman 18 June 2017 Disclaimer: This course was prepared, in its entirety, by Adam Teman. Many materials were copied from sources freely available on the internet. When possible, these sources have been cited; however, some references may have been cited incorrectly or overlooked. If you feel that a picture, graph, or code example has been copied from you and either needs to be cited or removed, please feel free to and I will address this as soon as possible.

2 MOSFET Current ing In Digital Electronic Circuits, we used the Shockley for hand-analysis of circuit operation. However, there are many models with varying levels of accuracy to estimate the I-V curves of a MOSFET. In this section, we will overview several models that will come in use throughout this course and your future. 2

3 3 Lecture Content

4 4 Basic MOS s

5 Switch The Switch The most simple MOSFET model is the Switch. V GS > V T R on S D I DS I DS 1/R on 5 V T V GS V DS

6 The Piece-Wise Linear The Switch As we know, when the channel pinches off, the current saturates. I DS This can be depicted with the simple Piece-Wise Linear Switch I DSAT linear saturation The Piece-wise Linear 1/R on V GT V DS 6

7 Adding Channel Length Modulation Channel Length Modulation modeled as a finite output resistance, causes a saturation current dependence on V DS. The Switch The Piece-wise Linear I DSAT 1/λIDSAT I DS D V DS I DSAT I DS Channel Length Modulation λi DSAT S 1/R on -1/λ V GT V DS 7

8 8 Square Law (Shockley) To get a more accurate model, we already are familiar with the Shockley or Square Law. Current is just charge times velocity, so at any point, x, along the channel: I x x Q x Wdx We found that charge can be approximated as: D Q x C ox V GS VCS x VT And the velocity is the mobility times the electrical field: dv x E x n dx The Switch The Piece-wise Linear The Square Law

9 Square Law (Shockley) The Switch So we get: I dx C W V V V dv D n ox GS T At pinch-off (V DS =V GS -V T ), the voltage over the channel is constant, so we get: This is where the Square-Law name comes from. And integrating from source to drain, we get L V DS W 1 I I dx C W V V V dv C V V V V L 2 DS D n ox GS T n ox DS GS T DS 0 0 W I C V V 2L 2 DSAT n ox GS T The Piece-wise Linear The Square Law 9

10 Square Law (Shockley) Replacing V DS with V DSeff =min(v GS -V T, V DS ) we get: 2 W V I C V V V V L 2 DSeff 1 DS n ox GS T DSeff DS The Switch The Piece-wise Linear The Square Law 10

11 The Velocity Saturation However, when looking at a short channel device, we see a linear dependence on V GS. This can be attributed to Velocity Saturation. sat 5 10 m s The Switch The Piece-wise Linear The Square Law The V-Sat 11

12 The Velocity Saturation A good approximation of the mobility curve is: 1 crit sat crit crit The Switch The Piece-wise Linear The Square Law The V-Sat 12 For continuity: crit After integration, we get: 2 sat C W I V V V 1 L 2 n ox DS DS GS T DS V DS L 2 crit V

13 The Velocity Saturation The Switch 13 This is hard to use, but we can reach an important conclusion. We found that: And we know that for a velocity saturated device: Equating, we get: V DSAT C W I V V V 1 L 2 n ox DS DS GS T DS V DS L 2 V V L GS T crit V V L GS T crit crit V I DS WCox VGS VDSAT VT sat DSAT crit GT GS T V L V V V pinch off V L V L vel sat DSAT crit GT crit The Piece-wise Linear The Square Law The V-Sat

14 The Unified for Hand Analysis A few simple estimations will make the V-Sat model more user-friendly: The mobility is piecewise linear, saturating at ξ>ξ crit /2 V DSAT is piecewise linear, saturating at V DSAT =ξ crit L/2, when V GT >ξ crit L/2 The Switch The Piece-wise Linear The Square Law The V-Sat The Unified 14

15 The Unified for Hand Analysis This brings us to the Unified : 2 W V DSeff I C V V V 1 V L 2 DS n ox GS T DSeff DS V min V V, V, V DSeff GS T DS DSAT V DSAT crit 2 L crit 2 sat The Switch The Piece-wise Linear The Square Law The V-Sat The Unified 15

16 16 Advanced MOS s

17 17 VT* Sometimes we want to use a really simple model. We can assume that if the transistor is on, it s velocity saturated. 2 V DSAT IDS kn VGS VT VDSAT 2 I DS VDSAT k V V V 2 * VT n GS T DSAT k V V V V V * 0 VGS VT * * n GS T DSAT GS T The Switch The Piece-wise Linear The Square Law The V-Sat The Unified The VT*

18 The Alpha Power Law Sakurai found that by changing the exponent of the square law, a better fit can be found with simple calculations. Shockley (α=2) Alpha (α=1.3) W I C V V 2L DSAT n ox GS T The Switch The Piece-wise Linear The Square Law The V-Sat The Unified The VT* The Alpha Power Law 18

19 BSIM The main model used by simulators today is the BSIM4 model. This model uses hundreds of parameters to achieve a good fit. This model takes into account all known physical effects, as well as many fitting parameters. The Switch The Piece-wise Linear The Square Law The V-Sat The Unified The VT* The Alpha Power Law BSIM 19

20 Newer s BSIM Group Webpage: Compact Coalition (CMC) Webpage: Newer BSIM s: BSIM6 Bulk CMOS BSIMSOI - SoI model standardized in 2001 (built on BSIM3.3) BSIM-CMG multi-gate FETs (FinFet, Nanowire) written in Verilog-A BSIM-IMG Independent Multi-Gate for UTBB-SoI EKV : Developed in 1995 to provide accuracy even in subthreshold PSP: Standard for current bulk CMOS The Switch The Piece-wise Linear The Square Law The V-Sat The Unified The VT* The Alpha Power Law BSIM And more 20

21 21 Threshold Voltage Revisited

22 Energy Band Diagrams To understand the threshold voltage and other secondary effects of the MOS device, we often use energy band diagrams. The first approach is looking in from the gate: 22

23 Energy Band Diagrams The second approach is looking from the source to the drain. 23

24 Threshold Voltage - Basic Theory Basic Theory The basic definition of threshold voltage is the gate voltage (V G ) required to invert the channel V Q OX T 0 MS 2 F Cox Q C dep ox Q 2qN 2 dep A si F N A F T ln T n i kt q 24

25 Body The appearance of a voltage difference between the source and body (V SB ) is known as The Body This can be modeled by the additional charge that needs to be depleted. Basic Theory Classic Body Q 2qN 2 V dep A si F SB V V 0 2 V 2 T T F SB F 25 V Q ox T 0 MS 2 F Cox Q dep0 C ox 2q si N A C ox

26 Modern Body A different approach is to look at the capacitive voltage divider between the gate and body (C GB ) Basic Theory Classic Body Modern Body C dep s W d max V S S V G G C C oxe 26 Q C V V V C V V inv oxe GS CS T 0 dep SB CS C dep Coxe VGS nvcs VT 0 n 1 1 C oxe 3T W oxe d max V B B C dep

27 Modern Body This can be shown to redefine V T as: C V V V V C ( ) dep T SB T0 SB oxe Basic Theory Classic Body Modern Body In modern technologies, C dep /C oxe is a constant, so V T is linearly dependent on V SB! 27

28 Poly Depletion and Channel Depth Basic Theory The threshold voltage is affected by two additional factors that we have disregarded until now: Polysilicon Depletion Since polysilicon is, itself, a semiconductor, the depletion layer into the poly effectively increases the oxide thickness. Classic Body Modern Body Channel Depth Since the channel is not a 2-dimensional line along the surface, the oxide thickness is essentially increased. n Cdep 1 1 C oxe 3T W oxe d max 28

29 Hot Carrier s Electrons can get so fast that they can tunnel into the gate oxide and increase the threshold voltage. V OX T 0 MS 2 F Cox This is a reliability issue as it happens over time. Q Q C dep ox Basic Theory Classic Body Modern Body Hot Carriers 29

30 V T Roll Off (Short Channel ) As channel length is reduced, effective channel length is reduced by depletion regions. Basic Theory Classic Body Modern Body Hot Carriers VT Roll-Off A trapezoid is created under the gate, dividing the channel into the region controlled by the gates and by the drain. 65nm technology. t ox =1.2nm V dd =1V K. Goto et al., IEDM In essence, V T is reduced.

31 DIBL (Drain Induced Barrier Lowering) In short channels, the barrier of the channel is essentially lowered, as the drain causes the energy band to drop closer to the source. This is exponentially dependent on V DS. Basic Theory Classic Body Modern Body Hot Carriers VT Roll-Off DIBL 31 V V V 0.4 T T,long DS C C d oxe

32 Roll Off / DIBL combined Basic Theory Classic Body Modern Body Hot Carriers VT Roll-Off DIBL 32

33 Reverse Short Channel (RSCE) V T actually increases at channel lengths a bit higher than minimum Basic Theory Classic Body Modern Body Hot Carriers VT Roll-Off DIBL RSCE 33

34 How to Measure VT There are various ways to measure V T One classic way takes a small V DS and sweeps V GS. Basic Theory Classic Body Modern Body 2 Id k ( Vgs Vt ) Vds 0.5V ds Vgs Vt So we can find the V GS at which the linear part crosses I ds =0. V T,gm V DS =50mV Hot Carriers VT Roll-Off DIBL RSCE Measuring VT 34

35 How to Measure VT One of the more common ways is to find the V GS at which I DS =100 na x W/L. For V T,lin, set a low V DS (V DS =50mV) For V T,sat set a high V DS (V DS =V DD ) Basic Theory Classic Body Modern Body Hot Carriers VT Roll-Off DIBL RSCE Measuring VT 35

36 OP and MP in Spectre Basic Theory Classic Body Modern Body Hot Carriers VT Roll-Off DIBL RSCE Measuring VT 36

37 Further Reading J. Rabaey, Digital Integrated Circuits 2003, Chapters 2.5, Weste, Harris CMOS VLSI Design, Chapter 7 C. Hu, Modern Semiconductor Devices for Integrated Circuits, 2010, Chapters 4-7 Tzividis, et al. Operation and ing of MOS Transistor Chapters 1-5 E. Alon, Berkeley EE-141, Lecture 9 (Fall 2009) M. Alam, Purdue ECE-606 lectures (2009) nanohub.org A. B. Bhattacharyya Compact MOSFET models for VLSI design, 2009, T. Sakurai, Alpha Power-Law MOS JSSC Newsletter Oct 2004 Managing Process Variation in Intel s 45nm CMOS Technology, Intel Technology Journal, 2008 Berkeley BSIM User s Manual 37

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