Electrical properties of semiconductors

The fundamental difference between a metal and a semiconductor is that the former is unipolar and the semiconductor is bipolar. i.e metals conducted current by means of electrons only, whereas semiconductors conducts the current by charge carrying carriers like holes and electrons.

Conductivity

The electron carrier mobility is μn and the other is (positive) hole carrier mobility μp , these particles move in opposite direction in an electric field E,


Hence the current density is given by,

J=I/A


J=Current density


I=Current


A=Area

another representation of J is,

J=(N(μn)+P(μp)) qE = σE


where N=magnitude of free electron concentration


P=magnitude of hole concentration


σ=conductivity


Hence,σ= (N(μn)+P(μp)) q


For the pure semiconductor, N=P=ni

where ni=intrinsic concentration

Intrinsic concentration:

With increasing temperature, the density of hole-electron pairs increases and, correspondingly, the conductivity the conductivity increases. The intrinsic concentration ni is varies with temperature T as,

ni^2=AT^3е^(-Eg/kT)


where Eg= energy gap


k=Boltzmann constant

A is a constant independent of T

Energy Gap:

The forbidden energy Eg in a semiconductor depends upon temperature, expressed as for Si


Eg(T)=1.21-3.60*10^(-4) T


and at room temperature (300 degree kelvin), Eg=1.1ev


similarly for Germanium


Eg(T)= 0.785-2.23*10^(-4)T


and at room temperature,Eg=0.72ev

Mobility: 

The parameter μ varies as T^(-m) over a temperature range of 100 to 400 degree kelvin.For Si, m=2.5 for electrons and m=2.7 for holes, and for germanium (Ge) m=1.66 for electrons and m=2.33 for holes. 

The mobility also found to be a function of electric field intensity and remains constant only if E<10^(3) v/cm in n-type silicon. For 10^(3)<E<10^(4) v/cm, the mobility of n-type semiconductor varies approximately as E^(-1/2).For higher fields , the mobility of n-type semiconductor is inversely proportional to E and the carrier speed approaches the constant values of 10^7 cm/s.