Question

Use Excel, MatLab or a similar program to plot carrier thermal velocity as a function of temperature for both electrons and holes for CdTe given that the effective mass ratio of the electron is 0.11 and the effective mass ratio of the hole is 0.35. Plot over a range of temperatures from 0K to 400K and use the expressi

Answer 1

Solution 2:

The thermal energy of any particle is given as =
`(1)/(2)mv^(2)`

where m= Effective mass of the particle,

v= Velocity of the particle

The average kinetic energy is given as =
`(3)/(2)KT,`

where K= Boltzmann Constant

T= Temperautre of the particle

At equilibrium,

1/2 mv² = 3/2 KT

Hence, v=
`\sqrt{(3KT)/(m)}`

As, effective mass ratio is calculated with respect to rest mass of electron,

melectron = 0.11 * 9.11 *10-31 kg

mhole = 0.35 *9.11 *10-31 kg

K = 1.38 × 10-23 m2 kg s-2 K-1

Plotting, over a range of temperature of 0 K to 400 K, we obtain the attached Graphs (attached).

Solution 3:

The above two curves plotted are not identical as seen. From the same value of Temperature, and under identical conditons, the Thermal velocity solely depends on effective mass ratio. And it is inversely proportional to effective mass ratio. More the effective mass ratio, less the thermal velocity and flatter the slope of the curve and vice versa. As, the mass ratio of holes is more than that of electrons, the curve of electrons has a steeper slope than that of holes. Hence, the curves are not just identical.