EE 330 Lecture 16. MOSFET Modeling CMOS Process Flow

Transcription

1 EE 330 Lecture 16 MOFET Modeling CMO Process Flow

2 Review from Last Lecture Limitations of Existing Models V V OUT V OUT V?? V IN V OUT V IN V IN V witch-level Models V imple square-law Model Logic ate V V BIA V OUT witch-level Models imple square-law Model } Voltage ain Input/Output Relationship? V IN Voltage Amplifier

3 Review from Last Lecture Model Extensions 300 I V A V Projections intersect V axis at same point, termed Early Voltage Typical values from -20V to -200V Usually use parameter λ instead of V A in MO model

4 Review from Last Lecture Model Extensions Id V VT W V I μcox V VT V V VT V V VT L 2 W 2 μcox V VT 1 V V VT V V VT 2L Note: This introduces small discontinuity (not shown) in model at AT/Triode transition Vds

5 Review from Last Lecture

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9 Model Extension ummary I I B V V T W V L 2 W 2 μc V V 1 V V V V V V 2L I μc V V V V V V V V OX T T T OX T T T V T V T0 V B Model Parameters : {μ,c OX,V T0,φ,γ,λ} esign Parameters : {W,L} but only one degree of freedom W/L

10 Id Operation Regions by Applications I Triode Region aturation Region Analog Circuits Cutoff Region Vds igital Circuits V Most analog circuits operate in the saturation region (basic VVR operates in triode and is an exception) Most digital circuits operate in triode and cutoff regions and switch between these two with Boolean inputs

11 Model Extension (short devices) 0 V V T W V L 2 W 2L I μc V V V V V V V V OX T T T 2 μc V V V V V V V OX T T T As the channel length becomes very short, velocity saturation will occur in the channel and this will occur with electric fields around 2V/u. o, if a gate length is around 1u, then voltages up to 2V can be applied without velocity saturation. But, if gate length decreases and voltages are kept high, velocity saturation will occur 0 V V T W I μc V V V V V V V OX T T 1 L 1 W μc V V V V V V 2 OX T T 1 L V V α is the velocity saturation index, 2 α 1 T T 2

12 Model Extension (short devices) 0 V V T W I μc V V V V V V V OX T T 1 L 1 W μc V V V V V V 2 OX T T 1 L V V α is the velocity saturation index, 2 α 1 T T 2 No longer a square-law model (some term it an α-power model) For long devices, α=2 Channel length modulation (λ) and bulk effects can be added to the velocity aturation as well egrading of α is not an attractive limitation of the MOFET

13 Model Extension (BIM model)

14 Model Errors with ifferent W/L Values I Actual Modeled with one value of L, W Modeled with another value of L, W V 3 V 2 V 1 V Binning models can improve model accuracy

15 BIM Binning Model - Bin on device sizes - multiple BIM models! With 32 bins, this model has 3040 model parameters!

16 Model Changes with Process Variations (n-ch characteristics shown) I TT F or FF (Fast n, slow p or Fast n, fast p ) or F (low n, slow p or low n, fast p ) V 3 V 2 V 1 V Corner models can improve model accuracy

17 BIM Corner Models with Binning - Often 4 corners in addition to nominal TT, FF, F, F, and - bin on device sizes With 32 size bins and 4 corners, this model has 15,200 model parameters!

18 How many models of the MOFET do we have? witch-level model (2) quare-law model quare-law model (with λ and bulk additions) α-law model (with λ and bulk additions) BIM model BIM model (with binning extensions) BIM model (with binning extensions and process corners)

19 The Modeling Challenge I Actual Modeled with one model V 3 (and W/L variations or Process Variations) Local Agreement with Any Model V 2 (and W/L variations or Process Variations) V 1 (and W/L variations or Process Variations) V (and W/L variations or Process Variations) I I V I = f V,V 1 I = f V,V 2 I = f V,V B 3 V I B V B = 0 ifficult to obtain analytical functions that accurately fit actual devices over bias, size, and process variations

20 Model tatus imple dc Model quare-law Model mall ignal Better Analytical dc Model ophisticated Model for Computer imulations BIM Model quare-law Model (with extensions for λ,γ effects) hort-channel α-law Model Frequency ependent mall ignal impler dc Model witch-level Models Ideal switches R W and C

21 In the next few slides, the models we have developed will be listed and reviewed quare-law Model witch-level Models Extended quare-law model hort-channel model BIM Model BIM Binning Model Corner Models

22 quare-law Model I V 4 V 3 V V 2 V 1 0 V V T W V L 2 W 2L I μc V V V V V V V V OX T T T 2 μc V V V V V V V OX T T T Model Parameters : {μ,c OX,V T0 } esign Parameters : {W,L} but only one degree of freedom W/L

23 witch-level Models rain ate ource R W C V witch closed for V = 1 witch-level model including gate capacitance and drain resistance C and R W dependent upon device sizes and process For minimum-sized devices in a 0.5u process 2KΩ n channel C 1.5fF R sw 6KΩ p channel Considerable emphasis will be placed upon device sizing to manage C and R W Model Parameters : {C,R W }

24 Extended quare-law Model I I B V V T W V L 2 W 2 μc V V 1 V V V V V V 2L I μc V V V V V V V V OX T T T OX T T T V T V T0 V B Model Parameters : {μ,c OX,V T0,φ,γ,λ} esign Parameters : {W,L} but only one degree of freedom W/L

25 hort-channel Model 0 V V T W I μc V V V V V V V OX T T 1 L 1 W μc V V V V V V 2 OX T T 1 L V V T T 2 α is the velocity saturation index, 2 α 1 Channel length modulation (λ) and bulk effects can be added to the velocity aturation as well

26 BIM model Note this model has 95 model parameters!

27 BIM Binning Model - Bin on device sizes - multiple BIM models! With 32 bins, this model has 3040 model parameters!

28 BIM Corner Models - Often 4 corners in addition to nominal TT, FF, F, F, and - five different BIM models! TT: typical-typical FF: fast n, fast p F: fast n, slow p F: slow n, fast p : slow n, slow p With 4 corners, this model has 475 model parameters!

29 Accuracy Complexity Hierarchical Model Comparisons BIM Binning Models Analytical Numerical (for simulation only) L Number of Model Parameters BIM Models Number of Model Parameters quare-law Models Number of Model Parameters witch-level Models Approx 3000 (for 30 bins) Approx to 6 W Number of Model Parameters 0 to 2

30 Corner Models Basic Model FF (Fast n, Fast p) F (Fast n, low p) TT Typical-Typical F (low n, Fast p) (low n, low p) Corner Model Applicable at any level in model hierarchy (same model, different parameters) Often 4 corners (FF, F, F, ) used but sometimes many more esigners must provide enough robustness so good yield at all corners

31 n-channel. p-channel modeling ource ate rain Bulk I 3 V n-channel MOFET V 3 V V V 1 V V V V > 0 V B (for enhancement devices) I V I I B B V B V 0 V VTn W V L 2 W 2L I =I =0 I μ C V V V V V V V V n OX Tn Tn Tn B 2 μ C V V V V V V V n OX Tn Tn Tn Positive V and V cause a positive I

32 Bulk ource n-channel. p-channel modeling ate rain (for enhancement devices) VTp 0 p-channel MOFET V I I B I B V B B V 0 V V Tp W V L 2 W 2L I =I =0 I -μ C V V V V V V V V p OX Tp Tp Tp B 2 -μ C V V V V V V V p OX Tp Tp Tp Negative V and V cause a negative I Functional form of models are the same, just sign differences and some parameter differences (usually mobility is the most important)

33 Bulk ource n-channel. p-channel modeling ate rain (for enhancement devices) VTp 0 p-channel MOFET B 0 V V Tp W V L 2 W 2L I =I =0 I -μ C V V V V V V V V p OX Tp Tp Tp B 2 -μ C V V V V V V V p OX Tp Tp Tp V I I B I B V B V V I B I B -I V B V Actually should use C OXp and C OXn but they are usually almost identical in most processes μ n 3μ p May choose to model I which will be nonnegative

34 n-channel. p-channel modeling Bulk ource ate rain V I I B I B V B V p-channel MOFET (for enhancement devices) 0 V V Tp W V L 2 W 2L I =I =0 I -μ C V V V V V V V V p OX Tp Tp Tp B 2 -μ C V V V V V V V p OX Tp Tp Tp Alternate equivalent representation 0 V V Tp W V L 2 W 2L I =I =0 B These look like those for the n-channel device but with I μ C V V V V V V V V p OX Tp Tp Tp 2 μ C V V V V V V V p OX Tp Tp Tp

35 n-channel. p-channel modeling B B I V I I B B V B V V I B I B V B V I I V 4 V 3 Models essentially the same with different signs and model parameters 1 V V V V V4 V3 V2 V 1> 0 0 V VTn W V L 2 W 2 μ C V V V V V V V 2L I =I =0 I μ C V V V V V V V V n OX Tn Tn Tn B n OX Tn Tn Tn 0 V V Tp W V L 2 W 2L I =I =0 I -μ C V V V V V V V V p OX Tp Tp Tp B 2 -μ C p OX V VTp V VTp V V VTp

36 Model Relationships etermine R W and C for an n-channel MOFET from square-law model In the 0.5u CMO process if L=1u, W=1u (Assume μc OX =100μAV -2, C OX =2.5fFu -2,V T0 =1V, V =3.5V, V =0) 0 V V T W V L 2 W 2L I μc V V V V V V V V OX T T T 2 μc V V V V V V V OX T T T when W is on, operation is deep triode

37 Model Relationships etermine R W and C for an n-channel MOFET from square-law model In the 0.5u CMO process if L=1u, W=1u (Assume μc OX =100μAV -2, C OX =2.5fFu -2,V T0 =1V, V =3.5V, V =0) When on operating in deep triode W V W L 2 L I μc V V V μc V V V OX T OX T V 1 1 R = 4K Q I W 1 V =V μc V V ( E 4) OX T L V =3.5V 1 C = C OX WL = (2.5fFµ -2 )(1µ 2 ) = 2.5fF

38 Model Relationships etermine R W and C for an p-channel MOFET from square-law model In the 0.5u CMO process if L=1u, W=1u ( C OX =2.5fFu -2,V T0 =1V, V =3.5V, V =0) Observe µ n \ µ p 3 0 V V T W V L 2 W 2L -I μc V V V V V V V V OX T T T 2 μc V V V V V V V OX T T T When W is on, operation is deep triode

39 Model Relationships etermine R W and C for an p-channel MOFET from square-law model In the 0.5u CMO process if L=1u, W=1u ( C OX =2.5fFu -2,V T0 =1V, V =3.5V, V =0) Observe µ n \ µ p 3 W V W L 2 L -I μ C V V V μ C V V V p OX T p OX T -V 1 1 R = 12K Q -I W 1 1 V =V μ C V V ( 4) p OX T L E V =3.5V 3 1 C = C OX WL = (2.5fFµ -2 )(1µ 2 ) = 2.5fF Observe the resistance of the p-channel device is approximately 3 times larger than that of the n-channel device for same bias and dimensions!

40 End of Lecture 16