Question

The number of electrons excited to the conduction band per cubic centimeter in a semiconductor can be estimated from the following equation: n t ee e rtg = 脳( . )/ / /( ) 4 8 1015 3 3 2 3 2 2 cm k where t is the temperature in kelvins and eg the band gap in joules per mole. the band gap of diamond at 300 k is 8.7 10 19 j. how many electrons are thermally excited to the conduction band at this temperature in a 1.00-cm 3 diamond crystal?

Answer 1

The number of electrons thermally excited to the conduction band in a 1.00-cm³ diamond crystal at 300 K can be estimated using the given equation:
`\(n = \frac{e^{(-(E_g)/(2kT))}}{8 * 10^(15)}\)`, where
`\(E_g\)` is the band gap energy,
`\(k\)`is the Boltzmann constant, and
`\(T\)` is the temperature in Kelvin.

Step-by-step explanation:

The equation provided is an expression of the thermal generation of electrons in a semiconductor due to the excitation of electrons to the conduction band. In this context,
`\(E_g\)` represents the band gap energy,
`\(k\)`is the Boltzmann constant
`(\(8.617333262145 x 10^(-5)\) eV/K)`, and
`\(T\)` is the temperature in Kelvin.

For the given problem, the band gap energy
`(\(E_g\))` for diamond is provided as
`\(8.7 * 10^(-19)\)`joules. Plugging in the values into the equation, we get:
`\(n = \frac{e^{(-(8.7 * 10^(-19))/(2 * 8.617333262145 * 10^(-5) * 300))}}{8 * 10^(15)}\)`. Solving this expression will yield the number of electrons thermally excited to the conduction band per cubic centimeter.

Understanding and applying such equations are fundamental in semiconductor physics and materials science, allowing researchers and engineers to predict and analyze the behavior of materials under different conditions, especially at varying temperatures and band gap energies. In this case, the calculation will provide insights into the electron population in the conduction band of a diamond crystal at 300 K.