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

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)

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

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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. (^^,)

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.

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

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