I am interested in calculating the carrier concentration of both n-type and p-type semiconductors by using the Mott- Schottky plot. I would be very grateful if you could give me some suggestions for the calculation of carrier concentration for n-type S/C, and how to calculate the value of (1/c^2). Thank you.
Len Leonid Mizrah
Mott-Schottky Plot and Carrier Concentration: The Mott-Schottky plot is a useful tool in semiconductor electrochemistry. It describes the reciprocal of the square of capacitance versus the potential difference between bulk semiconductor and bulk electrolyte. For n-type semiconductors, the Mott-Schottky plot is linear. It allows us to determine system properties such as flat band potential, doping density, or Helmholtz capacitance. The formula to calculate the intrinsic carrier concentration (N_i) in an intrinsic semiconductor is: [ N_i = \sqrt{N_c \cdot N_v} \cdot e^{-\frac{E_g}{2kT}} ] where:(N_c) is the effective density of states in the conduction band. (N_v) is the effective density of states in the valence band. (E_g) is the band gap energy. (T) is the absolute temperature. (k) is the Boltzmann constant. n-Type Semiconductor Carrier Concentration: If the concentration of donor atoms (ND) is greater than the concentration of acceptor atoms (NA), the semiconductor material is n-type. In this case, the concentration of electrons (n) is greater than the concentration of holes (p): [ n = N_D - N_A ] The intrinsic carrier concentration (ni) can be calculated as: [ n_i = \sqrt{\frac{N_c \cdot N_v}{n}} ]\where (N_c) and (N_v) are the effective density of states in the conduction and valence bands, respectively. Value of (1/c^2): The term (\frac{1}{c^2}) is related to the Mott-Schottky plot. It represents the reciprocal of the square of the semiconductor electrode capacitance (CSC). Under depletion conditions, there is a relation between (\frac{1}{C_{SC}^2}) and the potential (V): [ \frac{1}{C_{SC}^2} = \frac{2}{\varepsilon \varepsilon_0 e N_D} \left(E - E_{fb} - \frac{kT}{e}\right) ] where:(\varepsilon) is the permittivity. (e) is the elementary charge.
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