5.3 Linear Region

Step 1: Extract work function, interface charge and mobility model parameters for long gate length.

Extracted Parameters	Device and Experimental Data	Extraction Methodology
$PHIG$ , $CIT$	A long device $I_d$ vs. $V_g$ @ $V_d \sim 0.05V$	Observe subthreshold region offset and slope.
$U0_0$ , $UA_0$ , $UD_0$ , $EU$ , $ETAMOB$	A long device $I_d$ vs. $V_g$ @ $V_d \sim 0.05V$	Observe strong inversion region $I_{d,lin}$ and $G_{m,lin}$ .

Note: Larger length is better, as it will minimize the short channel effect and emphasize carrier mobility, work function and interface charge related parameters.

Step 2: Refine $V_{th}$ roll-off, DIBL and SS degradation parameters.

Extracted Parameters	Device and Experimental Data	Extraction Methodology
$DVT0$ , $DVT1$ , $CDSC$ , $DVT2$	Both short and medium devices $I_d$ vs. $V_g$ @ $V_d \sim 0.05V$	Observe subthreshold region of all devices in the same plot. Optimize $DVT0$ , $DVT1$ , $CDSC$ , $DVT2$ .

Note: We do not need very accurate fitting because mobility, series resistance parameters are not determined yet.

Step 3: Extract low field mobility $U0[L]$ for long and medium gate lengths.

Extracted Parameters	Device and Experimental Data	Extraction Methodology
$UP$ , $LPA$	Long and medium devices $I_d$ vs. $V_g$ @ $V_d \sim 0.05V$ . $U_0[L] = U0_0 \times (1 - UP \times L_{eff}^{-LPA} )$	Observe strong inversion region $I_{d,lin}$ and $G_{m,lin}$ , extract $U0[L]$ to get $UP$ , $LPA$ . For each $L_i$ , find $Y_i$ corresponding to $L_i$ , fit ( $L_i$ , $Y_i$ ) by Eq(1) to extract $UP$ , $LPA$ ). Refer to Fig. 16 for instance.

So far, we have good fit with data in subthreshold regions from long to short channel devices, and strong inversion for long channel devices. We need good fit for strong inversion in medium and short channel devices.

In linear region, current is to the first order, governed by low field mobility. So we start by tuning low field mobility values.

In short channel devices series resistance, coulombic scattering and enhanced mobility degradation effects are pronounced. To avoid the inuence of these effects, long and medium channel length devices are selected to especially extract low field mobility parameters.

Figure 16: Fit low field electron mobility with $L_g$

Step 4: Extract mobility model and series resistance parameters for short gate lengths.

Extracted Parameters	Device and Experimental Data	Extraction Methodology
$PARAM_0$ , $APARAM$ , $BPARAM$ , $LINT$ , $LL$ , $LLN$	Short and medium devices $I_d$ vs. $V_g$ @ $V_d \sim 0.05V$	1. Observe strong inversion region $I_{d,lin}$ and $G_{m,lin}$ . Similar to Step 3, find values of $UA[L]$ , $UD[L]$ , $RDSW[L]$ and $\Delta L[L]$ that gives good fit to experimental data, varying them simultaneously. $UA0$ , $UD0$ are provided from Step 1 and $RDSW0$ , $LINT$ are provided from parameter initialization. 2. Variation of each parameter with respect to $L$ should be kept minimal with smooth continuous trend. 3. From the length dependence of $UA[L]$ , $UD[L]$ , $RDSW[L]$ and $\Delta L[L]$ , find $AUA$ , $BUA$ , $AUD$ , $BUD$ , $ARDSW$ , $BRDSW$ , $LL$ , $LLN$ .

Note: Step 3 parameters are extracted from long and medium channel lengths, whereas, Step 4 involves short and medium channel lengths. As in Step 4 'exponential' corrections are particularly pronounced for small $L$ (short channel). Its Taylor expansion when $L_{eff}$ is medium can give appropriate modifications when power functions alone don't fit very well for medium lengths. Thus, the extracted parameters remain valid for all channel lengths to bring forth the intended length dependence in effect.

Step 5: Refine geometry scaling parameters for mobility degradation parameters.

Extracted Parameters	Device and Experimental Data	Extraction Methodology
$AUA$ , $AUD$ , $ARDSW$ , $LL$	Short and medium devices $I_d$ vs. $V_g$ @ $V_d \sim 0.05V$	Observe strong inversion region of all devices in the same plot. Optimize $AUA$ , $AUD$ , $ARDSW$ , $LL$ .

Step 6: Refine all Group 1 scaling parameters.

Further optimize the parameters by repeating Step 5 and 2. If not getting good fitting, tune $LLN$ , $BUA$ , $BUD$ , $BRDSW$ . If still not good, tune other parameters in Group 1 as appropriate. Iteration ends in Step 5 and then proceeds to Step 7. A sample fitting result up till this step is shown in Fig. 17.

Figure 17: $I_d$ vs $V_g$ and $G_m$ vs. $V_g$ @ $V_d \sim 0.05V$

5.3 Linear Region

5.3 Linear Region

results matching ""

No results matching ""