How to Calculate Voltage in a Depletion Region

Nearly everything that uses electrical power has semiconductor circuits: your car, your coffeemaker, your computer. The performance of those circuits stems from the behavior of electrons within an ordered array of atoms, or a crystal lattice. Usually, the lattice is made from a base material of silicon atoms, with ̶0;dopants̶1; added to increase or decrease the number of electrons in the material.

̶0;N-type̶1; semiconductor is made by introducing a dopant such as phosphorus, which brings extra electrons, whereas ̶0;p-type̶1; has a dopant such as boron, which reduces the number of electrons compared to the base material. The interesting properties take place at the junction, where n- and p-type materials are brought into contact with one another. One of the things that happens is that the extra electrons from the n-type make their way to the p-side, and the missing electrons from the p-side, called ̶0;holes,̶1; make their way to the n-side. The region in between is emptied of charge, hence the name ̶0;depletion region.̶1;

Instructions

1. • 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 Boltzmann̵7;s constant ̵2; 1.38 x 10^-23 Joule/K,
     T is measured in kelvin,
     q is the electron charge ̵2; 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 you̵7;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.