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
- Match the LIST-I with LIST-IIChoose the correct answer from the options given below:
LIST-I LIST-II A. BJT I. Five layers and four junction device B. MOSFET II. Power switching device with fast acting features and high power capability with voltage control features C. IGBT III. Voltage controlled device D. DIAC IV. Current controlled device - A silicon solar cell has a short-circuit current of 100mA and an open circuit voltage of 0.8V under full solar illumination. The fill factor is given as 0.7, what is the maximum power delivered to a load by the cell?
The common drain circuit has a FET with $Y_{fs}$=3000 µS, $R_{gs}$=100 MΩ and $r_d$=50 KΩ. Determine the device input impedance.
- A solar cell consists of 400 cells with 40 elements series connected while 10 elements are parallely connected. If each cell can produce an output voltage and current of $V_o$=0.45 V and $I_o$=57 mA, the maximum charging voltage required is
- Given below are the two statements
I. Graphene in its purest and defect free form has electrical conductivity lesser than that of Gold and Copper
II. It is possible to develop graphene in the form of nano-ribbons and quantum dots
Choose the correct option from the list given below.
