PHT.301 Physics of Semiconductor Devices

## Electron and hole mobility of silicon

The charge carrier mobilities decrease as temperature increases due to the scattering from phonons and the mobilities decrease as the doping concentration increases due to the scattering from the dopants. N.D. Arora, J.R. Hauser, and D.J. Roulston [1] state that for temperatures in the range 250 K - 500 K and dopant concentrations in the range $10^{13}\text{ cm}^{-3}\text{ - }10^{20}\text{ cm}^{-3}$, the electron and hole mobilities of silicon can be approximated as,

$$\mu_e = 88\left(\frac{T}{300}\right)^{-0.57}+ \frac{7.4\times 10^8 T^{-2.33}}{1+ 0.88\left[ \frac{N_d}{1.26\times 10^{17}\left(\frac{T}{300}\right)^{2.4}}\right]\left(\frac{T}{300}\right)^{-0.146}}\quad\text{ cm}^2\text{/V s},$$ $$\mu_h = 54.3\left(\frac{T}{300}\right)^{-0.57}+ \frac{1.36\times 10^8 T^{-2.33}}{1+ 0.88\left[ \frac{N_a}{2.35\times 10^{17}\left(\frac{T}{300}\right)^{2.4}}\right]\left(\frac{T}{300}\right)^{-0.146}}\quad\text{ cm}^2\text{/V s}.$$
 $\mu_e$ [cm²/V s] $T$ [K]

 $\mu_h$ [cm²/V s] $T$ [K]
 $\mu_e$ [cm²/V s] $\text{log}(N_d)$ [1/cm³]

 $\mu_h$ [cm²/V s] $\text{log}(N_a)$ [1/cm³]

Silicon electron mobility calculator

$T=$ K $N_d=$ 1/cm³

$\mu_e=$ cm²/Vs

Silicon hole mobility calculator

$T=$ K $N_a=$ 1/cm³

$\mu_h=$ cm²/Vs

• [1] N.D. Arora, J.R. Hauser, and D.J. Roulston, “Electron and Hole Mobilities in Silicon as a Function of Concentration and Temperature”, IEEE, Vol. Ed-29, NO. 2, (1982). doi:10.1109/T-ED.1982.20698