Engineering Physics II - Ch. 6.4

Q.6.        Discuss mobility and conductivity of semiconductor.

Ans.        If n number of electrons cross the gap, n sites become vacant in the valence band. These vacant sites are called holes. Thus the number of electrons ne and number of the holes nh are equal    (ne = nh). both : electrons and the holes take part in semiconduction. Electrons conduct in the conduction band and the holes in the valence band. They move in opposite directions with certain drift velocity vd under an applied field gradient . This movement of electrons and holes is known as mobility. Mobility of an electron and of a hole is designated by  m_d and m_h respectively, and is defined as

   

Effect of temperatures:- Mobility is a temperature sensitive property, and decreases with increasing temperature. They vary with temperature as  and. Its value is more for electrons than for holes. Since both these charge carriers (electrons and holes) contribute towards conduction, hence conductivity a of an intrinsic semiconductor is obtained from.

                               

where ee = eh = e is electronic charge, ne and nh are carrier concentrations per unit volume of electrons and holes respectively. Intrinsic carrier concentration of a electron or a hole in germanium at 300 K is
.

Q.7.        Describe density of state of semiconductor material.

Ans.        Density of state:-

                                Density of state means the population density of electrons in a metal. It has relevance to fermi - dirac distribution. The fermi - probability function p (E) determines the probability of energy level E occupied by an electron. It tells us about the energy level but not about the number of electrons in those levels. The density of state N (E) indicates the number of electrons ne acrose the energy band. This number is not uniform across the energy band, rather it is geratest at the centre of the band. The product of p (E), N(E) and the number of electrons for metals are related by

                               

This relation is illustrated in figure over a range of band energy at 0 K and temperature above 0 K. It illustrates that only a small fraction of electrons within the energy range of k T can be excited above fermi level. Here k is boltzmann constant and T is absolute temperature. The effective density of energy states can be found by employing quantum mechanics. If the effective density of states at the conduction and the valence bands are NC and NV respectively, then    

           and      

Fig. -Illustration of density of state showing a small fraction of excited electrons possessing E > EF at T > 0 K.

                Where   and  is the effective mass of an electron and a hole respectively; and h is the planck’s constant. The number of negative and positive charge carriers ne and nh in their respective bands may be found from

                      

and                
where EF  is the fermi energy. Now the product of positive and negative charge carriers is

                          

and the term depends on the band structure of the semiconductor. For a specific material, the product

                      = constant.

Q.8.        Determine the intrinsic carrier density of pure silicon whose resistivity at room temperature is 3000 ohm m. The mobilities of electrons and holes in silicon at room temperature are 0.14 and 0.05 m2 / V s. Electron charge 

Ans.        We know that resistivity , and in an intrinsic semiconductor. Using  eq. (s = neeeme + nhehmh ) in which

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