A semiconducting material possesses a band gap of 1 eV . It is doped with acceptor impurities that establish acceptor levels 1 meV above the valence band. Suppose that a transition from one energy level to another is

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Correct answer: D. 20 K to 230 K

The energy required to excite an electron from the valence band to the acceptor level is

\Delta E_a = 1 \text{ meV} = 10^{-3} \text{ eV}

.

The acceptor levels achieve maximum population when

kT_1 = 2 \Delta E_a = 2 \times 10^{-3} \text{ eV}

.

Using the Boltzmann constant

k \approx \dfrac{1}{11600} \text{ eV/K}

, we get:

T_1 = 2 \times 10^{-3} \times 11600 = 23.2 \text{ K}

At this temperature, all acceptor levels are occupied by electrons, meaning the hole concentration in the valence band reaches a constant value.

The hole concentration remains constant until electrons from the valence band start getting excited to the conduction band. The band gap is

E_g = 1 \text{ eV}

.

This intrinsic transition begins when

kT_2 = \dfrac{1}{50} E_g = \dfrac{1}{50} \times 1 \text{ eV} = 0.02 \text{ eV}

.

T_2 = 0.02 \times 11600 = 232 \text{ K}

Thus, the hole concentration remains roughly constant in the temperature range of approximately

23.2 \text{ K}

to

232 \text{ K}

, which best matches

20 \text{ K}

to

230 \text{ K}

.

A semiconducting material possesses a band gap of 1 eV . It is...

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