Question

The band gap for silicon is 1.1 eV. (a) Find the ratio of the band gap to kT for silicon at room temperature 300 K. (b) At what temperature does this ratio become one tents of the value at 300 K? (Silicon will not retain its structure at these high temperatures.)

Answer 1

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Answer 2

a.The band gap for silicon at 300 K is 1.1 eV.

b. temperature at 300 K,T = 3000.4 K

Explanation:

It is given:

Temperature, $T=300 \mathrm{K}$

Silicon’s band gap,$E=1.1 \mathrm{eV}$

Constant of Boltzmann, $k=8.62 \times 10-5 \mathrm{eV} / \mathrm{K}$

(a) The ratio of the band gap to kT should be found out.

$\text { Ratio }=1.1 \mathrm{kT}$

$=1.18 .62 \times 3 \times 10-5 \times 102=42.53=43$

(b) 110th of the earlier ratio is the new ratio, which is 4.253.

New ratio $=4.253$

It is known already that Ratio = (Band gap)/(kT)

⇒ $4.253=1.18 .62 \times 10-5 \times \mathrm{T}$

⇒$\mathrm{T}=3000.4 \mathrm{K}$, which is approximately 3000 K.