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?

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ajeigbeibraheem ajeigbeibraheem · Answer 1 · 2020-04-29T05:34:10+02:00

Answer:

[tex]n_e = 8.139 *10^6[/tex]

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:

[tex]\delta \ E = 1.424 \ eV[/tex]

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

[tex]n_i = 10^{20} \ electrons[/tex]

Temperature is given as:

[tex]T = 274.15 \ K[/tex]

Number of electrons can be calculated by using the formula;

[tex]n_e = n_i*e^-^{\frac{\delta E }{2 K_B*T}}[/tex]

[tex]n_e = 10^{20}*e^-^{\frac{1.424}{2*8.617*10^{-5}*274.15}}[/tex]

[tex]n_e = 8.139 *10^6[/tex]