How to Calculate Voltage in a Depletion Region
- 1). Find the intrinsic carrier density, Ni, of the base material. For silicon at room temperature, Ni is about 1.5 x 10^10 carriers/cm^3.
- 2). Calculate the thermal voltage of the charge. VT is given by the equation
VT = k x T / q,
where k is Boltzmann’s constant — 1.38 x 10^-23 Joule/K,
T is measured in kelvin,
q is the electron charge — 1.6 x 10^-19 coulomb.
At 300K, this gives
VT = 1.38 x 10^-23 x 300 / 1.6 x 10^-19 = 0.025. - 3). Determine the acceptor and donor carrier densities. If you have an existing material, these will be determined by the fabrication process, and if you’re designing a material, you will choose these to match the characteristics you want. For purposes of illustration, assume the acceptor density, NA, is 10^18/cm^3 and the donor density, ND, is 10^16/cm^3.
- 4). Calculate the voltage across the depletion region with the equation
V = VT x ln(NA x ND / Ni^2)
For the example,
V = 0.025 x ln (10^18 x 10^16 / (1.5 x 10^10)^2),
V = 0.79 V.
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