Question

(iii) The graph below shows how the resistivity changes for n-type and p-type silicon as a function of doping density. Calculate the electron mobility for n-type Si at a doping density of 10'7cm Resistivity (22-cm) P-typ 92-type 0.001 0.0001 104 1019 1020 105 106 107 108 Doping density (cm)

Answer 1

Answer:

The electron mobility $\mu$ ​​​​​​ cm2/V-s given by

$\mu$ = vd/E .............(1)

vd = drift velocity

E = external electric field

Electrical conductivity $\sigma$ is given as:

$\sigma$=ne$\mu$ .......... (2)

Here n is no. Density of electrons per unit volume

e = charge on electron = 1.602* 10^-19 Coloumb

Also, Conductivity = 1/Resistivity..........(3)

Given that for electron density for (n-type) silicon, n = 10^17 cm-3 , from the graph the corresponding resistivity (red line) is found to be 0.1ohm-cm.

Substituting this value in equation 3

Or conductivity = 1/Resistivity

Conductivity = 1/0.1

Or $\sigma$ = 10 cm^-1 ohm^-1

Substituting this value inequation 2

$\sigma$ = ne$\mu$

10 cm^-1 ohm^-1 = 10^17 cm^-3 * 1.602* 10^-19 Coloumb *$\mu$

Solving we get,

10/(1.602*10^-2) = $\mu$

Or $\mu$ = electron mobility = 624.219 cm2/ Volt.sec