Question

Calculate the values of Fermi potential at a temperature of 300 K for p and n-type silicon with doping concentrations of 5×1017 cm⁻³ and 2×1016 cm⁻³ , respectively. The energy bandgap of silicon is 1.12 eV and the intrinsic carrier concentration is ni = 1.45×1010 cm⁻³

Answer 1

To calculate the Fermi potential, use the equation EF = Ec - (kBT/2) * (ln[Nc/n + 1] + ln[Nv/p + 1]), where Ec is the energy of the conduction band, kB is the Boltzmann constant, T is the temperature, Nc is the effective density of states in the conduction band, n is the doping concentration for n-type silicon, Nv is the effective density of states in the valence band, and p is the doping concentration for p-type silicon. Substitute the given values and calculate EF for both p-type and n-type silicon.

Step-by-step explanation:

The Fermi potential can be calculated using the formula:

EF = Ec - (kBT/2) * (ln[Nc/n + 1] + ln[Nv/p + 1])

where:

• EF is the Fermi potential
• Ec is the energy of the conduction band
• kB is the Boltzmann constant (8.617333262145 x 10^-5 eV/K)
• T is the temperature (300K)
• Nc is the effective density of states in the conduction band
• n is the doping concentration for n-type silicon
• Nv is the effective density of states in the valence band
• p is the doping concentration for p-type silicon

Using the given values:

• Ec = 1.12 eV
• Nc = 2 * (2 * pi * (2 * pi * (2 * m * k * T)^3/2)/(h^3))/(exp((Ec - EF)/(k * T)) + 1)
• Nv = 2 * (2 * pi * (2 * pi * (2 * m * k * T)^3/2)/(h^3))/(exp((EF - Ei)/(k * T)) + 1)
• m is the effective mass of carriers
• k is the Boltzmann constant
• h is the Planck's constant
• Ei is the energy level of the intrinsic carrier

Substitute the values into the formula and calculate EF for both p-type and n-type silicon.