Answer to Question #88018 in Atomic and Nuclear Physics for ankit

Question #88018
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
1
Expert's answer
2019-04-19T10:29:31-0400

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, mp=0.56m0 (m0=9.1×10-31 kg), T=300 K


Using (3) we got:

gT (E) = 4.08×1023 m-3


Answer:

4.08×1023 m-3

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