Effect of Temperature on Semiconductor Properties

In this post impact of temperature on various properties of semiconductors used for electronic devices is examined. The semiconductors are highly influenced by temperatures. In this post temperature dependence of carrier concentration is explained. the variations in Fermi level, and how the mobility of carriers is affected by temperature and doping.

Key Questions:

What is the effect of temperature on carriers' concentration?
What is the effect of temperature on the Fermi level?
What is the effect of temperature and doping on mobility?

What is the effect of temperature on carriers' concentration?

An increase in the temperature of a semiconductor can result in a substantial increase in the number of free electrons, as a result, the number of holes. Electrons and holes are created in pairs called EHP (electron-hole pair). At higher temperatures inter-atomic bonds become weak. So the thermal energy is used to break the bonds. As a result electron and hole pairs are created. As electrons gain more energy make their way to the conduction band and leave a hole in the valence band. The electrons in the conduction band quickly lose energy fall back to the valence band and recombine with a hole. The merging of free electrons and holes is called Recombination.

The temperature dependence of electron concentration in a doped semiconductor can be visualised in figure 1. At low temperature (1/T is large) or only a few EHP exists. As the temperature increases, ionization occurs, and all the donor atoms donated electrons to the conduction band. After ionization, the conduction band concentration becomes no=Nd. Finally, at higher temperatures thermally generated EHP or intrinsic carriers are much greater than Nd.

Carrier concentration varies with temperature

What is the effect of temperature on the Fermi level?

The temperature and Fermi level have no direct relation or dependence. Fermi level is a theory that helps to understand semiconductor physics concepts. Fermi level falls indefinitely as the temperature increases.

As we know the Fermi level changes as the doping concentration changes. For n-type semiconductors, it lies just below the conduction band. For p-type semiconductors, it lies just above the valence band.

So, as the temperature increases, EHP is created. As the temperature is increased at a level where thermally generated EHP are much greater than doping concentration. The temperature dependence of the Fermi level can be seen from the following equation:

no=Nce-(Ec-Ef)/kT

Solving this equation

Ef=Ei+kT ln(no/ni)

What is the effect of temperature and doping on mobility?

Either increase in temperature or doping level tends to reduce the carrier mobility.

At higher temperatures, a carrier moving through the lattice experiences vibration of the lattice. These vibrations decrease the mobility of carriers. Or you can say carriers are scattered by lattice vibrations and hence mobility decreases. Collective vibrations of atoms in the crystal are called lattice vibrations or phonons (phonons are considered particles). The frequency of such scattering increases as temperature increases and hence mobility decreases.

On the other hand, at a lower temperature, a phenomenon called Impurity scattering is dominant. The thermal motion of the carrier is also slow at low temperatures. Now, what are ionized impurities? When a semiconductor is doped either with p-type or n-type, it will leave a hole or donate an electron and leaves behind ionized charged impurity. Slow-moving carriers are more likely to be scattered by these ionized impurities and hence decrease mobility. The phenomenon is dominant at low temperatures because at higher temperatures carriers are moving with greater momentum and are less likely to be scattered by ionized impurity.