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.
Fermi-Dirac Distribution Function Formula
The Fermi-Dirac distribution function, often denoted by $f(E)$, describes the probability that a given quantum state, characterized by energy $E$, will be occupied by a fermion at a temperature $T$. Fermions are particles like electrons that obey the Pauli exclusion principle.
The correct mathematical expression for the Fermi-Dirac distribution function is:
Where:
- $E$ is the energy level.
- $E_F$ is the Fermi energy (the highest occupied energy level at absolute zero temperature).
- $k$ is the Boltzmann constant.
- $T$ is the absolute temperature.
This formula specifically applies to fermions. The presence of '$+$' in the denominator distinguishes it from the Bose-Einstein distribution, which applies to bosons and has a '$-\;$' sign.
Option Analysis:
- Option 1: Incorrect due to the minus sign in the denominator.
- Option 2: Correct formula for Fermi-Dirac distribution.
- Option 3: Incorrect structure and includes $\Delta E$ inappropriately.
- Option 4: Incorrect structure and includes $\Delta E$ inappropriately.
Therefore, the correct representation is found in Option 2.
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
