# SCIENTIA SINICA Informationis, Volume 47 , Issue 12 : 1730-1740(2017) https://doi.org/10.1360/N112016-00257

## A semi-empirical model of the drain/source resistance for MOSFET • AcceptedFeb 6, 2017
• PublishedJul 14, 2017
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### Abstract

A series resistance model is developed to accurately predict the drain/source resistance of MOSFETs in the ultra submicron regime. The series resistance model is based on the differential resistance concept and the mean value theorem of integrals. Three parameters of the model may be obtained through the multiple linear regression method. In this study, we employ numerical simulation data to fit three parameters for the planar nMOSFETs and nLDD-MOSFETs, of which the substrate doped concentration is $1\times10^{15}\sim~1\times10^{16}{\rm~cm}^{-3}$, and the channel length is 45$\sim$2000 nm. We also obtain a semi-empirical formula with a maximum error of only 9.5%. The theoretical model and calculation results of its semi-empirical formula show that the drain/source resistance is only related to the depth of the drain/source pn junction, resistivity, and length from the channel to the drain/source electrode, and that the influence of the channel length, stack-gate length, and electrode length is negligible. Because the semi-empirical formula is simple, with high precision and a clear physical concept, and allows for easy parameter extraction, it can be used in a characteristic analysis of MOSFETs and circuit simulators.

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• Figure 1

The structure diagram of MOSFET. (a) MOSFET used in thecalculation; (b) modern MOSFET with silicide

• Figure 2

The schematic diagram of drain / source differentialresistance

• Figure 3

(a) is comparison of simulation values of drain /source resistance and formula calculation when $l_{2~}$changed and channellength is 1000$\sim$2000 nm, $l$=1.6 $\mu~$m, $l_{1}=$ 0.01 $\mu~$m, $\rho~$$= 10 \Omega~\cdot\mu~m. The maximum error of (eq8) is 5% and for(8) is 5% (b) is simulation results of drain / source resistance whenl_{2} changed and channel length is 120\sim200 nm, l= 1.6 \mu~m,l_{1}= 0.01 \mu~m, \rho~$$=$ 10 $\Omega~\cdot\mu~$m. The maximum error of(eq8) is 5.9% and for (12) is 8%

• Figure 4

(a) is comparison of simulation values of drain/sourceresistance and formula calculation when $\rho~$changed and channel lengthis 45$\sim$80 nm, $l=$ 1.6 $\mu~$m, $l_{1}=$ 0.01 $\mu~$m, $l_{2}=$ 0.9 $\mu~$m. Themaximum error of (eq8) is 6.6% and for (16) is9% (b) is simulation results of drain/source resistance whenchanged and channel length is 120$\sim$200 nm, $l=$ 1.6 $\mu~$m, $l_{1}=$ 0.01 $\mu$m, $l_{2}=$ 0.9 $\mu~$m. The maximum error of (eq8) is 7.7% andfor (12) is 5%

• Figure 5

(a) is comparison of simulation values of drain/sourceresistance and formula calculation when $d$ changed and channel length is 45$\sim$80 nm, $l=$ 1.6 $\mu~$m, $l_{1}=$ 0.01 $\mu~$m, $\rho~$$= 8 \Omega~\cdot\mu~m. Themaximum error of (eq8) is 6.9% and for (16) is8.6% (b) is simulation results of drain/source resistance whenl_{2} changed and channel length is 120\sim200 nm, l= 1.6 \mu~m,l_{1}= 0.01 \mu~m, \rho~$$=$ 10 $\Omega~\cdot\mu~$m The maximum error of(eq8) is 3.9% and for (12) is 8.5%

• Figure 6

(a) is comparison of simulation values of drain/sourceresistance and formula calculation when changed and channel length is 45$\sim$80 nm, $l=$ 1.6 $\mu~$m, $l_{1}=$ 0.01 $\mu~$m, $\rho~$$= 8 \Omega~\cdot\mu~m. Themaximum error of (eq8) is 6.9% and for (16) is9.5% (b) is simulation results of drain/source resistance whenchanged and channel length is 120\sim200 nm, 45\sim80 nm, l= 1.6 \mu~m,l_{1}= 0.01 \mu~m, \rho~$$=$ 10 $\Omega~\cdot\mu~$m. The maximum error of(eq8) is 3.9% and for (12) is 8.5%

• Figure 7

(a) is the structure that channel length is 120$\sim$200 nm, $l=$ 1.6$\mu~$m, $l_{1}=$ 0.01 $\mu~$m, $\rho~$$_{1}= 10 \Omega~\cdot\mu~m, \rho~$$_{2}=$ protectłinebreak 100 $\Omega~\cdot\mu~$m, $a=$ 0.01 $\mu~$m, $d=$ 0.002 $\mu~$m. (b) is comparison of simulationresults of normal MOSFETs and LDD-MOSFETs drain/source resistance when $l_2$changed and $d$ is 0.02 $\mu~$m, 0.01 $\mu~$m and 0.005 $\mu~$m respectively. Themaximum error of (eq8) is 8.4% and for (12) is8.5%

• Table 1   The semi physical semi empirical formula of drain/source resistance between the different channel sections
 Channel length (nm) Formulas that the unit of length is $\mu$m Formulas of international unit system (the unit of length is $m$) 980$\sim$1980 $R_{\rm~DS}~=~\rho~^{0.76}\dfrac{6.87~\cdot~l_2~}{d^{0.6}}$ (8) $R_{\rm~DS}~=~\rho~^{0.76}\dfrac{5.9334\times~10^7~\cdot~l_2~}{d^{0.6}}$ (9) 580$\sim$980 $R_{\rm~DS}~=~\rho~^{0.77}\dfrac{6.27~\cdot~l_2~}{d^{0.63}}$ (10) $R_{\rm~DS}~=~\rho~^{0.77}\dfrac{4.2173\times~10^7~\cdot~l_2~}{d^{0.63}}$ (11) 120$\sim$200 $R_{\rm~DS}~=~\rho~^{0.82}\dfrac{3.63~\cdot~l_2~}{d^{0.8}}$ (12) ${{R}_{\rm~DS}}={{\rho~}^{0.82}}\dfrac{4.6832\times~{{10}^{6}}\cdot~{{l}_{2}}}{{{d}^{0.8}}}$ (13) 80$\sim$120 ${{R}_{\rm~DS}}={{\rho~}^{0.82}}\dfrac{5.40\cdot~{{l}_{2}}}{{{d}^{0.72}}}$ (14) ${{R}_{\rm~DS}}={{\rho~}^{0.82}}\dfrac{2.0555\times~{{10}^{7}}\cdot~{{l}_{2}}}{{{d}^{0.72}}}$ (15) 45$\sim$80 ${{R}_{\rm~DS}}={{\rho~}^{0.83}}\dfrac{9.21\cdot~{{l}_{2}}}{{{d}^{0.58}}}$ (16) ${{R}_{\rm~DS}}={{\rho~}^{0.83}}d\dfrac{1.3322\times~{{10}^{7}}\cdot~{{l}_{2}}}{{{d}^{0.58}}}$ (17)

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