Temperature Dependence of Carrier Concentrations
This section explains the temperature dependence of carrier concentrations in brief.
Temperature dependence of carrier concentrations:
The variation of carrier concentration with temperature is indicated by this
Initially, the variation of n0 and p0 with T seems relatively straight forward in these relations. The problem is complicated, however, by the fact that ni has a strong temperature dependence and that EF can also vary with temperature. Let us begin by examining the intrinsic carrier concentration. we obtain
The exponential temperature dependence dominates ni(T), and a plot of In ni vs. 103/T appears linear (Fig. given below). In this figure we neglect variations
due to the T3/2 dependence of the density-of-states function and the fact that Eg varies somewhat with temperature. The value of ni at any temperature is a definite number for a given semiconductor, and is known for most materials.Thus we can take ni, as given in calculating n0 or p0 from equ (1)
With ni and T given, the unknowns in Eq. (1) are the carrier concentrations and the Fermi level position relative to Ev One of these two quantities must be given if the other is to be found.
If the carrier concentration is held at a certain value, as in heavily doped extrinsic material, EF can be obtained from Eq. (1).
The temperature dependence of electron concentration in a doped semiconductor can be visualized as shown in Fig. above.
In this example, Si is doped n-type with a donor concentration Nd of 1015 cm-3. At very low temperatures (large 1/7), negligible intrinsic EHPs exist, and
the donor electrons are bound to the donor atoms.
As the temperature is raised, these electrons are donated to the conduction band, and at about 100K (1000/T = 10) all the donor atoms are ionized. This temperature range is called the ionization region.
Once the donors are ionized, the conduction band electron concentration is no= Nd = 1015 cm-3, since one electron is obtained for each donor atom.