How do I compute process constant "K" using BSIMSOI?


#1

Greetings! Thank you so much for taking the time to read over my problem.

I’m currently trying to figure out how to derive the process constant K used in the square law equation when a MOS is in saturation from below: (the process datasheet is here: http://www.onsemi.com/PowerSolutions/content.do?id=16693 but it reveals nothing on a general process constant)
At first, I thought it was K1 but a bit of reading on BSIMSOI manuals showed it was actually the bulk threshold parameter.

.MODEL NMOS NMOS ( LEVEL = 8
+VERSION = 3.1 TNOM = 27 TOX = 1.39E-8
+XJ = 1.5E-7 NCH = 1.7E17 VTH0 = 0.6696061
+K1 = 0.8351612 K2 = -0.0839158 K3 = 23.1023856
+K3B = -7.6841108 W0 = 1E-8 NLX = 1E-9
+DVT0W = 0 DVT1W = 0 DVT2W = 0
+DVT0 = 2.9047241 DVT1 = 0.4302695 DVT2 = -0.134857
+U0 = 458.439679 UA = 1E-13 UB = 1.485499E-18
+UC = 1.629939E-11 VSAT = 1.643993E5 A0 = 0.6103537
+AGS = 0.1194608 B0 = 2.674756E-6 B1 = 5E-6
+KETA = -2.640681E-3 A1 = 8.219585E-5 A2 = 0.3564792
+RDSW = 1.387108E3 PRWG = 0.0299916 PRWB = 0.0363981
+WR = 1 WINT = 2.472348E-7 LINT = 3.597605E-8
+XL = 0 XW = 0 DWG = -1.287163E-8
+DWB = 5.306586E-8 VOFF = 0 NFACTOR = 0.8365585
+CIT = 0 CDSC = 2.4E-4 CDSCD = 0
+CDSCB = 0 ETA0 = 0.0246738 ETAB = -1.406123E-3
+DSUB = 0.2543458 PCLM = 2.5945188 PDIBLC1 = -0.4282336
+PDIBLC2 = 2.311743E-3 PDIBLCB = -0.0272914 DROUT = 0.7283566
+PSCBE1 = 5.598623E8 PSCBE2 = 5.461645E-5 PVAG = 0
+DELTA = 0.01 RSH = 81.8 MOBMOD = 1
+PRT = 8.621 UTE = -1 KT1 = -0.2501
+KT1L = -2.58E-9 KT2 = 0 UA1 = 5.4E-10
+UB1 = -4.8E-19 UC1 = -7.5E-11 AT = 1E5
+WL = 0 WLN = 1 WW = 0
+WWN = 1 WWL = 0 LL = 0
+LLN = 1 LW = 0 LWN = 1
+LWL = 0 CAPMOD = 2 XPART = 0.5
+CGDO = 2E-10 CGSO = 2E-10 CGBO = 1E-9
+CJ = 4.197772E-4 PB = 0.99 MJ = 0.4515044
+CJSW = 3.242724E-10 PBSW = 0.1 MJSW = 0.1153991
+CJSWG = 1.64E-10 PBSWG = 0.1 MJSWG = 0.1153991
+CF = 0 PVTH0 = 0.0585501 PRDSW = 133.285505
+PK2 = -0.0299638 WKETA = -0.0248758 LKETA = 1.173187E-3
+AF = 1 KF = 0)
*
.MODEL PMOS PMOS ( LEVEL = 8
+VERSION = 3.1 TNOM = 27 TOX = 1.39E-8
+XJ = 1.5E-7 NCH = 1.7E17 VTH0 = -0.9214347
+K1 = 0.5553722 K2 = 8.763328E-3 K3 = 6.3063558
+K3B = -0.6487362 W0 = 1.280703E-8 NLX = 2.593997E-8
+DVT0W = 0 DVT1W = 0 DVT2W = 0
+DVT0 = 2.5131165 DVT1 = 0.5480536 DVT2 = -0.1186489
+U0 = 212.0166131 UA = 2.807115E-9 UB = 1E-21
+UC = -5.82128E-11 VSAT = 1.713601E5 A0 = 0.8430019
+AGS = 0.1328608 B0 = 7.117912E-7 B1 = 5E-6
+KETA = -3.674859E-3 A1 = 4.77502E-5 A2 = 0.3
+RDSW = 2.837206E3 PRWG = -0.0363908 PRWB = -1.016722E-5
+WR = 1 WINT = 2.838038E-7 LINT = 5.528807E-8
+XL = 0 XW = 0 DWG = -1.606385E-8
+DWB = 2.266386E-8 VOFF = -0.0558512 NFACTOR = 0.9342488
+CIT = 0 CDSC = 2.4E-4 CDSCD = 0
+CDSCB = 0 ETA0 = 0.3251882 ETAB = -0.0580325
+DSUB = 1 PCLM = 2.2409567 PDIBLC1 = 0.0411445
+PDIBLC2 = 3.355575E-3 PDIBLCB = -0.0551797 DROUT = 0.2036901
+PSCBE1 = 6.44809E9 PSCBE2 = 6.300848E-10 PVAG = 0
+DELTA = 0.01 RSH = 101.6 MOBMOD = 1
+PRT = 59.494 UTE = -1 KT1 = -0.2942
+KT1L = 1.68E-9 KT2 = 0 UA1 = 4.5E-9
+UB1 = -6.3E-18 UC1 = -1E-10 AT = 1E3
+WL = 0 WLN = 1 WW = 0
+WWN = 1 WWL = 0 LL = 0
+LLN = 1 LW = 0 LWN = 1
+LWL = 0 CAPMOD = 2 XPART = 0.5
+CGDO = 2.9E-10 CGSO = 2.9E-10 CGBO = 1E-9
+CJ = 7.235528E-4 PB = 0.9527355 MJ = 0.4955293
+CJSW = 2.692786E-10 PBSW = 0.99 MJSW = 0.2958392
+CJSWG = 6.4E-11 PBSWG = 0.99 MJSWG = 0.2958392
+CF = 0 PVTH0 = 5.98016E-3 PRDSW = 14.8598424
+PK2 = 3.73981E-3 WKETA = 5.292165E-3 LKETA = -4.205905E-3
+AF = 1 KF = 0)


#2

That’s a level 8 model. K depends on the mobility which in turn depends on the length. Have a look here:


#3

Hello! Thank you for your reply.
The main expression is in the manual and textbook (KP=UOCOX)
But oxide capacitance isn’t defined for Level 8.
I was thinking it might differ at various levels but after skimming a bunch of forums, it seems it’s just the same right? Hehe…
So…
COX=E0
Er/TOX
E0=8.854e-12F/m
Er=3.9 relative permittivity for SiO2
Need to ascertain that TOX is in meters.

Calculating KP for the NMOS case above: (carrier mobility=458.4396e-6)
KP=(458.439679e-6)*(3.9eo)/(1.39e-8)=1.139e-6 A/V^2

Now I can make theoretical and intuitive assumptions on my ckt. (^^,)


#4

By the way, the term for oxide capacitance (COX) excludes area from the standard capacitance equation so the unit is F/m^2.
Given the theories in electromagnetics, we should be able to derive COX for any MOSFET geometry.


#5

I am afraid your calculation is wrong. If you look at the level 8 equations you will see that the mobility is a function of the channel length, vgs, etc. page 98 and 99.
By default MOB=6, so you should prob use the eq at the bottom of page 99