To calculate the built-in potential, barrier height, and dopant concentration of a Au-n-GaAs Schottky-barrier diode, we'll use the given capacitance relation and diode area.
1. Calculate the built-in potential (Vbi):
The built-in potential (Vbi) is related to the capacitance (C) by the formula:
Vbi = 1 / sqrt(C^2)
Given: 1/C^2 = 1.57*10^15 to 2.12*10^15 V
Taking the lower limit of the capacitance range:
C^2 = 1.57*10^15 pF
C = sqrt(1.57*10^15) pF
Converting pF to F:
C = sqrt(1.57*10^15) * 10^(-12) F
Now, calculate the built-in potential:
Vbi = 1 / sqrt(C^2)
2. Calculate the barrier height (ϕb):
The barrier height (ϕb) is related to the built-in potential (Vbi) by the formula:
ϕb = Vbi - V0
Where V0 is the applied bias voltage, assumed to be 0 for the calculation of the barrier height.
3. Calculate the dopant concentration (Nd):
The dopant concentration (Nd) is related to the barrier height (ϕb) by the formula:
Nd = (2 * ε * ϕb) / (q * Nc * W^2)
Where ε is the permittivity of GaAs, q is the elementary charge, Nc is the effective density of states in the conduction band, and W is the depletion width of the diode.
Without the given values for ε, Nc, and W, it is not possible to calculate the exact dopant concentration (Nd) using the provided information.
Please note that the specific values for ε, Nc, and W should be provided in order to accurately calculate the barrier height and dopant concentration of the diode.