Notes on Semiconductors: An Introduction

Preparing for a new semester, I’ve decided the best way to keep all my notes intact is to add them here to a website. My notes for semiconductors for example, are scattered upon 3 different textbooks and I’m personally annoyed to carry so much useless weight.

And so it begins:

Semiconductors are initially created from a metal, and is usually doped in order to allow a gradient that current can flow through. An INTRINSIC semiconductor is an un-doped material at which the statement n = p = ni is true.

Further explanation of n, p and ni: n stands for electrons that can be broken from their molecule and moved. p stands for holes which can be filled by electrons. ni is the material specific intrinsic carrier concentration. In a doped semiconductor, the equation n*p = ni^2
If doped with DONORS, the concentration Nd = n, if doped with ACCEPTORS, the concentration Na = p. If both were used the concentration depends on type. n = Nd-Na, p = Na-Nd.

With the general concept of holes, electron concentration, and doping covered, next is deriving a relationship between the energy band spectrum of the semiconductor and inferences to its type and concentrations. Normally, the intrinsic carrier concentration is known for the element, so solving for the type, and concentration of doping element is usually the problem structure.

Example of a band diagram

Note only the conduction band (Ec), Fermi level (Ef), the intrinsic level (Ei, which is in middle of band gap), and Valence band (Ev). In these semiconductor problems, you can identify the type off semiconductor by where a band labeled Ef is placed. If Ef is ABOVE Ei, then the semiconductor is N-type, if it is below Ei, it is P-type.

Now for the equations that relate to this->

Slides taken from: A.R. Hambley, Electronics, © Prentice Hall, 2/e, 2000 A. Sedra and K.C. Smith, Microelectronic Circuits, © Oxford University Press, 5/e, 2004


Note: K is the boltzmann constant (𝑘=8.62×10−5 eV/K) and T is temperature in Kelvin

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