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.
Intrinsic Semiconductor: Occupied Conduction Band Levels
In an intrinsic semiconductor, the number of occupied conduction band levels represents the electrons that have enough energy to move into the conduction band and potentially conduct electricity.
Understanding the Calculation
To find the total number of occupied states within a specific energy band, we need to consider:
- Density of States ($N(E)$): This function describes how many available electron states exist per unit energy at a given energy level $E$.
- Fermi-Dirac Distribution ($F(E)$): This function gives the probability that an available state at energy $E$ is actually occupied by an electron. For semiconductors, it's typically given by $F(E) = \frac{1}{1 + e^{(E - E_F) / (k_B T)}}$, where $E_F$ is the Fermi level, $k_B$ is Boltzmann's constant, and $T$ is the temperature.
The number of occupied states per unit energy is the product of the density of states and the probability of occupation: $N(E) \times F(E)$.
Defining the Conduction Band Range
The conduction band is the energy range where electrons can move freely. It starts at the lowest conduction band energy level, denoted as $E_C$, and extends upwards to the highest possible energy level within the band, denoted as $E_{top}$ (or theoretically, infinity).
Calculating Occupied Levels
The total number of occupied conduction band levels is obtained by integrating the product $N(E) F(E)$ over the entire energy range of the conduction band.
- The lower limit of integration is the bottom of the conduction band: $E_C$.
- The upper limit of integration is the top of the conduction band: $E_{top}$.
Therefore, the integral representing the number of occupied conduction band levels is:
$ \int_{E_C}^{E_{top}} N(E) F(E) dE $This integral sums up the contributions of all occupied states from the bottom to the top of the conduction band.
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
