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

`n_e = 8.139 *10^6`

Step-by-step 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^-^{(\delta E )/(2 K_B*T)}`

`n_e = 10^(20)*e^-^{(1.424)/(2*8.617*10^(-5)*274.15)}`

`n_e = 8.139 *10^6`