Read the passage and answer the following questions :
The physics of semiconductor devices is dependent on the physics of semiconductors itself. The most important semiconductors are Germanium, Silicon and Gallium Arsenide. The GaAs has different properties than Silicon or Germanium. Pure silicon is intrinsic and contains negligibly small amount of impurities. Each silicon atom shares its four valance electrons with the four neighbouring atoms forming covalent bonds. An extrinsic silicon is achieved by introducing the impurities. The band structure of a solid can be obtained by solving a Schrodinger equation of an approximate one electron problem.
Deriving Ionized Donor Concentration Formula
The number of ionized donors ($N_D^+$) represents the concentration of donor atoms that have donated their electron, becoming positively charged. It is determined by the total donor concentration ($N_D$) and the probability of ionization.
Donor Ionization Equation
The concentration of ionized donors ($N_D^+$) is given by the total donor concentration ($N_D$) multiplied by the probability that a donor state is ionized. This probability is calculated as 1 minus the probability that the donor state is occupied (neutral).
The probability of a donor state being neutral is often described using a Fermi-Dirac-like function, modified by the degeneracy factor ($g$). For the given formula, the fraction of neutral donors is represented by:
$ P(\text{neutral}) = \frac{1}{1 + \frac{1}{g} \exp\left(\frac{E_D - E_F}{kT}\right)} $Where:
- $N_D$ is the total donor concentration.
- $g$ is the degeneracy factor of the donor level.
- $E_D$ is the energy level of the donor state.
- $E_F$ is the Fermi level energy.
- $k$ is the Boltzmann constant.
- $T$ is the absolute temperature.
The fraction of ionized donors is therefore $P(\text{ionized}) = 1 - P(\text{neutral})$.
Final Ionized Donor Formula
Multiplying the total donor concentration ($N_D$) by the ionization probability gives the number of ionized donors:
$ N_D^+ = N_D \times P(\text{ionized}) $ $ N_D^+ = N_D \left[ 1 - P(\text{neutral}) \right] $ $ N_D^+ = N_D \left[ 1 - \frac{1}{1 + \frac{1}{g} \exp\left(\frac{E_D - E_F}{kT}\right)} \right] $This equation calculates the concentration of positively ionized donor atoms based on the material's properties and temperature.
Important Questions from Semiconductor Materials
Which of the following IS a pentavalent impurity?
A bar of Gallium Arsenide (GaAs) is doped with Silicon such that the Silicon atoms occupy Gallium and Arsenic sites in the GaAs crystal. Which one of the following statements is true?
The outermost orbit of a Germanium atom has ________ electrons.
P-type extrinsic semiconductor doped with impurity having how much valence electron?
All semiconductors in their last orbit have
