Exhibit 22-2
The following question(s) pertain to the following equation which estimates the number of electrons per cubic centimeter excited to the conduction band as a function of temperature and the band gap energy. $\mathrm{n}_{\mathrm{e}}=\left(4.8 \times 10^{15} \mathrm{~cm}^{-3} \mathrm{~K}^{-3 / 2}\right) \mathrm{T}^{3 / 2} \mathrm{e}^{-\mathrm{E}_{\mathrm{e}} /(2 \mathrm{RT}) }$
Refer to Exhibit 22-2. The band gap of pure crystalline silicon is 1.94×10^-¹⁹ J at 300 K. How many electrons are excited from the valence band to the conduction band at this temperature in a 1.00 cm³ silicon crystal?

Question

Exhibit 22-2
The following question(s) pertain to the following equation which estimates the number of electrons per cubic centimeter excited to the conduction band as a function of temperature and the band gap energy.

\mathrm{n}_{\mathrm{e}}=\left(4.8 \times 10^{15} \mathrm{~cm}^{-3} \mathrm{~K}^{-3 / 2}\right) \mathrm{T}^{3 / 2} \mathrm{e}^{-\mathrm{E}_{\mathrm{e}} /(2 \mathrm{RT}) }

Refer to Exhibit 22-2. The band gap of pure crystalline silicon is 1.94×10^-¹⁹ J at 300 K. How many electrons are excited from the valence band to the conduction band at this temperature in a 1.00 cm³ silicon crystal?

Quizplus · Accepted Answer

The band gap energy is given as 1.94×10^-¹⁹ J. Substituting this value into the equation, we get:$\mathrm{n}_{\mathrm{e}}=\left(4.8 \times 10^{15} \mathrm{~cm}^{-3} \mathrm{~K}^{-3 / 2}\right) \mathrm{T}^{3 / 2} \mathrm{e}^{-\mathrm{E}_{\mathrm{e}} /(2 \mathrm{RT})}$$\mathrm{n}_{\mathrm{e}}=\left(4.8 \times 10^{15} \mathrm{~cm}^{-3} \mathrm{~K}^{-3 / 2}\right) (300 \mathrm{~K})^{3 / 2} \mathrm{e}^{-\left(1.94 \times 10^{-19} \mathrm{~J}\right) /(2 \times 8.62 \times 10^{-5} \mathrm{~eV/K} \times 300 \mathrm{~K})}$$\mathrm{n}_{\mathrm{e}}=1.70 \times 10^{9} \mathrm{~cm}^{-3}$

Exhibit 22-2 the Following Question(s) Pertain to the Following Equation

Exhibit 22-2
the Following Question(s) Pertain to the Following Equation