Question

The energy gap between the valence band and the conduction band in the widely-used semiconductor gallium arsenide (GaAs) is Δ = 1.424 eV. Suppose that we consider a small piece of GaAs with 1020 available electrons, and use the equilibrium condition derived in the prelecture. 1) On average, how many electrons will be in the conduction band if T=274.15 K?

Answer 1

Answer:

$n_e = 8.139 *10^6$

Explanation:

Given that;

The energy gap between the valence band and the conduction band in the widely-used semiconductor gallium arsenide (GaAs) is Δ = 1.424 eV.

So; that implies that:

$\delta \ E = 1.424 \ eV$

Suppose that we consider a small piece of GaAs with 1020 available electrons, -- This is taking about the numbers of electrons used which is :

$n_i = 10^{20} \ electrons$

Temperature is given as:

$T = 274.15 \ K$

Number of electrons can be calculated by using the formula;

$n_e = n_i*e^-^{\frac{\delta E }{2 K_B*T}}$

$n_e = 10^{20}*e^-^{\frac{1.424}{2*8.617*10^{-5}*274.15}}$

$n_e = 8.139 *10^6$