Branch : Computer Science and Engineering
Subject : Fundamental of Electronic Devices
Compensation and Space Charge Neutrality
Following section explains the compensation and space charge neutrality for Si in details.
Compensation and space charge neutrality:
- When the concept of doping was introduced, we assumed the material contained either Nd donors or Na acceptors, so that the extrinsic majority carrier concentrations were n0 — Nd or p0 — Na, respectively, for the n-type or p-type material.
- It often happens, however, that a semiconductor contains both donors and acceptors.
- For example, Fig. given below illustrates a semiconductor for which both donors and acceptors are present, but Nd> Na.
- The predominance of donors makes the material n-type, and the Fermi level is therefore in the upper part of the band gap.
- Since EF is well above the acceptor level Ea, this level is essentially filled with electrons.
- However, with EF above Ei we cannot expect a hole concentration in the valence band commensurate with the acceptor concentration.
- In fact, the filling of the Ea states occurs at the expense of the donated conduction band electrons.
The mechanism can be visualized as follows:
- Assume an acceptor state is filled with a valence band electron, with a hole resulting in the valence band. This hole is then filled by recombination with one of the conduction band electrons.
- Extending this logic to all the acceptor atoms, we expect the resultant concentration of electrons in the conduction band to be Nd— Na instead of the total Nd. This process is called compensation.
- By this process it is possible to begin with an n-type semiconductor and add acceptors until Na = Nd and no donated electrons remain in the conduction band.
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In such compensated material, n0 = ni = p0 and intrinsic conduction is obtained. With further acceptor doping the semiconductor becomes p-type with
a hole concentration of essentially Na - Nd.
The exact relationship among the electron, hole, donor, and acceptor concentrations can be obtained by considering the requirements for space charge neutrality. If the material is to remain electrostatically neutral, the sum of the positive charges (holes and ionized donor atoms) must balance the sum of the negative charges (electrons and ionized acceptor atoms):
Thus in Fig. the net electron concentration in the conduction band is