Extraction Procedure

14.3 Extraction Procedure

14.3.1Extraction Requirements

One large size device and two sets of smaller-sized devices are needed to extract parameters, as shown in Figure 13-1.

Large W and L

Orthogonal Set of W and L

W min L

L min

Figure 13-1. Device geometries used for parameter extraction

The large-sized device (W ≥ 10 µ m, L ≥ 10 µ m) is used to extract parameters which are independent of short/narrow channel effects and parasitic resistance. Specifically, these are: mobility, the large-sized device The large-sized device (W ≥ 10 µ m, L ≥ 10 µ m) is used to extract parameters which are independent of short/narrow channel effects and parasitic resistance. Specifically, these are: mobility, the large-sized device

(1) I ds vs. V gs @V ds = 0.05V with different V bs . (2) I ds vs. V ds @V bs = 0V with different V gs .

(3) I ds vs. V gs @V ds =V dd with different V bs .

(4) I ds vs. V ds @V bs =V bb with different V gs . (|V bb | is the maximum body bias).

14.3.2Optimization

The optimization process recommended is a combination of Newton- Raphson's iteration and linear-squares fit of either one, two, or three variables. A flow chart of this optimization process is shown in Figure 13-

2. The model equation is first arranged in a form suitable for Newton- Raphson's iteration as shown in (14.3.1):

The variable f sim () is the objective function to be optimized. The variable

f exp () stands for the experimental data. P 10 , P 20 , and P 30 represent the f exp () stands for the experimental data. P 10 , P 20 , and P 30 represent the

1 , P 2 and P 3 represent parameter values after the mth iteration.

(m)

(m)

Initial Guess of Parameters P i

Model Equations

Linear Least Squsre

Measured Data

Fit Routine

P =P + (m+1) (m) i i

no

(m)

yes STOP

Figure 13-2. Optimization flow.

To change (14.3.1) into a form that a linear least-squares fit routine can be used (i.e. in a form of y = a + bx 1 + cx 2 ), both sides of (14.3.1) are divided To change (14.3.1) into a form that a linear least-squares fit routine can be used (i.e. in a form of y = a + bx 1 + cx 2 ), both sides of (14.3.1) are divided

where i=1, 2, 3 for this example. The (m+1) parameter values for P 2 and P 3 are obtained in an identical fashion. This process is repeated until the

( incremental parameter change in parameter values m) ∆ P

are smaller than

a pre-determined value. At this point, the parameters P 1 ,P 2 , and P 3 have been extracted.

14.3.3Extraction Routine

Before any model parameters can be extracted, some process parameters have to be provided. They are listed below in Table 13-1:

Input Parameters Names Physical Meaning TOXE, TOXP, DTOX, or

Gate oxide thickness and dielectric con-

Doping concentration in the channel

TNOM

Temperature at which the data is taken

L drawn

Mask level channel length

W drawn

Mask level channel width

XJ

Junction depth

Table 13-1. Prerequisite input parameters prior to extraction process.

The parameters are extracted in the following procedure. These procedures are based on a physical understanding of the model and based on local optimization. (Note: Fitting Target Data refers to measurement data used for model extraction.)

Step 1

Extracted Parameters & Fitting Target Device & Experimental Data Data

VTH0, K1, K2 Large Size Device (Large W & L).

I ds vs. V gs @V ds = 0.05V at Different V bs Fitting Target Exp. Data: V th (V bs )

Extracted Experimental Data V th (V bs )

Step 2

Extracted Parameters & Fitting Target Devices & Experimental Data Data

UA, UB, UC, EU Large Size Device (Large W & L).

I ds vs. V gs @V ds = 0.05V at Different V bs Fitting Target Exp. Data: Strong Inver- sion region I ds (V gs ,V bs )

Step 3

Extracted Parameters & Fitting Target Devices & Experimental Data Data

LINT, R ds (RDSW, W, V bs ) One Set of Devices (Large and Fixed W & Different L).

Fitting Target Exp. Data: Strong Inver-

I ds vs. V gs @V ds = 0.05V at Different V bs sion region I ds (V gs ,V bs )

Step 4

Extracted Parameters & Fitting Target Devices & Experimental Data

Data

WINT, R ds (RDSW, W, V bs ) One Set of Devices (Large and Fixed L & Different W).

Fitting Target Exp. Data: Strong Inver- I ds vs. V gs @V ds = 0.05V at Different sion region I ds (V gs ,V bs )

V bs

Step 5

Extracted Parameters & Fitting Target Devices & Experimental Data Data

RDSW, PRWG, PRWB, WR R ds (RDSW, W, V gs ,V bs ) Fitting Target Exp. Data: R ds (RDSW, W,

V gs ,V bs )

Step 6

Extracted Parameters & Fitting Target Devices & Experimental Data Data

DVT0, DVT1, DVT2, LPE0, LPEB One Set of Devices (Large and Fixed W & Different L).

Fitting Target Exp. Data: V th (V bs , L, W )

V th (V bs , L, W )

Step 7

Extracted Parameters & Fitting Target Devices & Experimental Data Data

DVT0W, DVT1W, DVT2W One Set of Devices (Large and Fixed L & Fitting Target Exp. Data: V th (V bs , L, W ) Different W).

V th (V bs , L, W )

Step 8

Extracted Parameters & Fitting Target Devices & Experimental Data Data

K3, K3B, W0 One Set of Devices (Large and Fixed L & Different W).

Fitting Target Exp. Data: V th (V bs , L, W )

V th (V bs , L, W )

Step 9

Extracted Parameters & Fitting Target Devices & Experimental Data Data

MINV, VOFF, VOFFL, NFACTOR, One Set of Devices (Large and Fixed W & CDSC, CDSCB

Different L).

Fitting Target Exp. Data: Subthreshold

I ds vs. V gs @V ds = 0.05V at Different V bs region I ds (V gs ,V bs )

Step 10

Extracted Parameters & Fitting Target Devices & Experimental Data Data

CDSCD One Set of Devices (Large and Fixed W & Fitting Target Exp. Data: Subthreshold

Different L).

region I ds (V gs ,V bs )

I ds vs. V gs @V bs =V bb at Different V ds

Step 11

Extracted Parameters & Fitting Target Devices & Experimental Data Data

DWB One Set of Devices (Large and Fixed W & Fitting Target Exp. Data: Strong Inver-

Different L).

sion region I ds (V gs ,V bs )

I ds vs. V gs @V ds = 0.05V at Different V bs

Step 12

Extracted Parameters & Fitting Target Devices & Experimental Data Data

VSAT, A0, AGS, LAMBDA, XN, VTL, One Set of Devices (Large and Fixed W &

LC

Different L).

Fitting Target Exp. Data: I sat (V gs ,V bs )/W I ds vs. V ds @V bs = 0V at Different V gs A1, A2 (PMOS Only)

Fitting Target Exp. Data V dsat (V gs )

Step 13

Extracted Parameters & Fitting Target Devices & Experimental Data Data

B0, B1 One Set of Devices (Large and Fixed L & Fitting Target Exp. Data: I sat (V gs ,V bs )/W Different W).

I ds vs. V ds @V bs = 0V at Different V gs

Step 14

Extracted Parameters & Fitting Target Devices & Experimental Data Data

DWG One Set of Devices (Large and Fixed L & Fitting Target Exp. Data: I sat (V gs ,V bs )/W Different W).

I ds vs. V ds @V bs = 0V at Different V gs

Step 15

Extracted Parameters & Fitting Target Devices & Experimental Data Data

PSCBE1, PSCBE2 One Set of Devices (Large and Fixed W & Different L).

Fitting Target Exp. Data: R out (V gs ,V ds ) I ds vs. V ds @V bs = 0V at Different V gs

Step 16

Extracted Parameters & Fitting Target Devices & Experimental Data Data

PCLM, θ (DROUT, PDIBLC1, One Set of Devices (Large and Fixed W & PDIBLC2, L), PVAG, FPROUT, DITS, Different L). DITSL, DITSD

I ds vs. V ds @V bs = 0V at Different V gs Fitting Target Exp. Data: R out (V gs ,V ds )

Step 17

Extracted Parameters & Fitting Target Devices & Experimental Data Data

DROUT, PDIBLC1, PDIBLC2 One Set of Devices (Large and Fixed W & Fitting Target Exp. Data: θ (DROUT,

Different L).

PDIBLC1, PDIBLC2, L) θ (DROUT, PDIBLC1, PDIBLC2, L)

Step 18

Extracted Parameters & Fitting Target Devices & Experimental Data Data

PDIBLCB One Set of Devices (Large and Fixed W & Different L).

Fitting Target Exp. Data: θ (DROUT,

I ds vs. V gs @ fixed V gs at Different V bs PDIBLC1, PDIBLC2, L, V bs )

Step 19

Extracted Parameters & Fitting Target Devices & Experimental Data Data

θ DIBL (ETA0, ETAB, DSUB, DVTP0, One Set of Devices (Large and Fixed W & DVTP1, L)

Different L).

I ds vs. V gs @V ds =V dd at Different V bs Fitting Target Exp. Data: Subthreshold

region I ds (V gs ,V bs )

Step 20

Extracted Parameters & Fitting Target Devices & Experimental Data Data

ETA0, ETAB, DSUB One Set of Devices (Large and Fixed W & Different L).

Fitting Target Exp. Data: θ DIBL (ETA0,

I ds vs. V gs @V ds =V dd at Different V bs ETAB , L)

Step 21

Extracted Parameters & Fitting Target Devices & Experimental Data Data

KETA One Set of Devices (Large and Fixed W & Different L).

Fitting Target Exp. Data: I sat (V gs ,V bs )/W I ds vs. V ds @V bs =V bb at Different V gs

Step 22

Extracted Parameters & Fitting Target Devices & Experimental Data Data

ALPHA0, ALPHA1, BETA0 One Set of Devices (Large and Fixed W & Different L).

Fitting Target Exp. Data: I ii (V gs ,V bs )/W I ds vs. V ds @V bs =V bb at Different V ds

Step 23

Extracted Parameters & Fitting Target Devices & Experimental Data Data

ku0, kvsat, tku0, lku0, wku0, pku0, Set of Devices ( Different L, W, SA, SB). llodku0, wlodku0

I ds-linear @V gs =V dd, V ds = 0.05 Fitting Target Exp. Data: Mobility (SA, SB, L, W)

Step 24

Extracted Parameters & Fitting Target Devices & Experimental Data Data

kvth0, lkvth0, wkvth0, pvth0, llodvth, Set of Devices ( Different L, W, SA, SB). wlodvth

V th (SA, SB, L, W)

Fitting Target Exp. Data: V th (SA, SB, L, W )

Step 24

Extracted Parameters & Fitting Target Devices & Experimental Data Data Extracted Parameters & Fitting Target Devices & Experimental Data Data

k2 (SA, SB, L, W), eta0(SA, SB, L, W) W ), eta0(SA, SB, L, W)

Appendix A: Complete Parameter List