Question

Determine the total number of energy states in silicon between Ev and Ev-kT at T = 300 K. (For Si the effective mass of hole mp* = 0.56m0

Answer 1

Density of allowed quantum state in the valence band is given by formula

$$g_v (E) = \frac {4 \pi {(2m_p)}^\frac {3}{2}}{h^3} \sqrt{E_v - E} (1)$$

where h is the Planck's constant

Using (1) we have:

$$g_T (E) = \frac {4 \pi {(2m_p)}^\frac {3}{2}}{h^3} \int_{ E_v-kT }^ {E_v} \sqrt{E_v - E} dE (2)$$

After integrating (2) we got:

$$g_T (E) = \frac {4 \pi {(2m_p)}^\frac {3}{2}}{h^3} \frac {2}{3} {kT}^\frac {3}{2} (3)$$

where k is the Boltzmann constant

In our case, m_p=0.56m₀ (m₀=9.1×10^-31 kg), T=300 K

Using (3) we got:

g_T (E) = 4.08×10²³ m^-3

Answer:

4.08×10²³ m^-3