Own semiconductor or i-type semiconductor or undoped semiconductor ( intrinsic - own) is a pure semiconductor , the content of impurities in which does not exceed 10 −8 ... 10 −9 %. The concentration of holes in it is always equal to the concentration of free electrons, since it is determined not by doping, but by the intrinsic properties of the material, namely, thermally excited carriers, radiation and intrinsic defects. The technology makes it possible to produce materials with a high degree of purification, among which it is possible to select indirect semiconductors: Si (at room temperature the number of carriers is n i = p i = 1.4 · 10 10 cm −3 ), Ge (at room temperature the number of carriers is n i = p i = 2.5 · 10 13 cm −3 ) and direct-gap GaAs .
A semiconductor without impurities has its own electrical conductivity , which has two contributions: electronic and hole. If no voltage is applied to the semiconductor, then the electrons and holes make thermal motion and the total current is zero. When a voltage is applied in a semiconductor, an electric field arises, which gives rise to a current, called the drift current i other . The total drift current is the sum of two contributions from the electron and hole currents:
- i dr = i n + i p ,
where the index n corresponds to the electron contribution, and p - to the hole contribution. The resistivity of a semiconductor depends on the carrier concentration and on their mobility , as follows from the simplest Drude model . In semiconductors with increasing temperature due to the generation of electron-hole pairs, the concentration of electrons in the conduction band and holes in the valence band increases much faster than their mobility decreases, therefore, with increasing temperature, the conductivity increases. The process of the death of electron-hole pairs is called recombination. In fact, the conductivity of an intrinsic semiconductor is accompanied by recombination and generation processes, and if their velocities are equal, then they say that the semiconductor is in an equilibrium state. The number of thermally excited carriers depends on the width of the forbidden band , so the number of current carriers in their own semiconductors is small compared with doped semiconductors and their resistance is much higher.
Calculation of the equilibrium concentration of free charge carriers
The number of allowed states for electrons in the conduction band (determined by the density of states ) and the probability of their filling (determined by the Fermi – Dirac function ) and the corresponding values for holes determine the number of own electrons and holes in a semiconductor:
- ,
- ,
where N c , N v are constants determined by the properties of a semiconductor, E c and E v are the position of the bottom of the conduction band and the ceiling of the valence band, respectively, E F is the unknown Fermi level , k is the Boltzmann constant , T is the temperature. From the electroneutrality condition n i = p i for the intrinsic semiconductor, one can determine the position of the Fermi level:
- .
This shows that in its own semiconductor the Fermi level is near the middle of the forbidden band. It gives for concentration of own carriers.
- ,
where E g is the band gap and N c (v) is defined by the following expression
where m c and m v are the effective masses of electrons and holes in a semiconductor, h is the Planck constant . This shows that the wider the band gap of a semiconductor, the less its own carriers are generated at a given temperature, and the higher the temperature, the more carriers in the semiconductor.
Literature
- Sze, Simon M. Physics of Semiconductor Devices (2nd ed.). - John Wiley and Sons (WIE), 1981. - ISBN 0-471-05661-8 .
- Kittel, Ch. Introduction to Solid State Physics. - John Wiley and Sons, 2004. - ISBN 0-471-41526-X .