# 4.11 Chapter2.2.3;2.2.4;2.2.5;insulator,semi-conductor,metal  (Page 2/3)

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Here N C = effective density of states at E C (the lower edge of Conduction Band) ~10 19 /cc for all the three semiconductors namely Ge,Si and GaAs.

Here N V = effective density of states at E V (the upper edge of Valence Band) ~10 19 /cc for all the three semiconductors namely Ge,Si and GaAs.

E g = Band-Gap(eV), k = Boltzmann Constant, T = Absolute Temperature in Kelvin.

Table 2.2.4.1 gives the intrinsic concentration of electrons and holes in Ge,Si and GaAs at Room Temperature (300K).

Table 2.2.4.1. Intrinsic Concentration of electrons and holes in Ge,Si and GaAs at Temperature 300K.

Semiconductor Band-Gap Temperature Effective Density of States n i = p i
Ge 0.67eV 300K ~10 19 /cc 2.4×10 13 /cc
Si 1.12eV 300K ~10 19 /cc 4×10 9 /cc
GaAs 1.4eV 300K N C ~5×10 17 /cc, N V ~7×10 18 /cc 3.3×10 6 /cc

Figure 2.2.24 in the previous section illustrates how the EHP are thermally generated and why they are always equal.

Equation 2.2.3.1 clearly shows that intrinsic concentration is very temperature sensitive.

Table.2.2.4.2.Intrinsic Concentration of Si from 300K to 360K

Temperature 300K 310K 320K 330K 340K 350K 360K
Intrinsic Conc(per cc) 4×10 9 8×10 9 1.5×10 10 2.8×10 10 5×10 10 9×10 10 1.45×10 11

From Table 2.2.4.2 it is evident that for an increment of 60K above Room Temperature, intrinsic concentration has increased by two-orders of magnitude i.e. nearly 100 times. Because of this undesirable feature of intrinsic concentration, Si suffers from a very serious drawback namely: the reverse leakage current in a reverse biased diode doubles for every 10K rise in temperature.

In Figure 2.2.26, the exponential rise in intrinsic concentration with temperature is plotted.

2.2.5. Extrinsic Semi-conductor, space-charge neutrality and compensation .

Electronic Grade Semiconductor with no doping is called Intrinsic Semiconductor and that with doping is called Extrinsic Semiconductor.

Semiconductor is Group IV element or compound semi-conductor is Group (III+V) Compound.

For Group IV element, Group III(namely B, Al) is acceptor or P-Type dopent and Group V(P, As) is donor or N-Type dopent.

For Group (III+V)Compound semiconductor, Group II is acceptor or P-Type dopent and Group VI is donor or N-Type dopent.

In Figure 2.2.27, the consequence of introducing a donor atom or the consequence of introducing an acceptor atom in a Silicon Crystalline Lattice is shown.

In case of Donor doped Silicon where doping density is N D donor atoms/cc , the octave condition is completed by 4 valence electrons of donor atom hence 5 th valence electron beomes the odd-man out and hence is very loosely held by the host donor atom. At Room Temperature, the 5 th valence electron is broken loose from the donor and becomes a wanderer in Si-lattice. In effect Donor atom gets (+)ve ly ionized and donates its negatively charged 5 th valence electron to the Si-lattice.Hence overall space-charge neutrality is maintained. Plus there are thermally generated EHP also.Overall thermal equilibrium is achieved and we have thermal equilibrium concentration value(n n -bar) of conducting electron and thermal equilibrium value (p n -bar) of holes. Here conducting electrons are many orders of magnitude larger than holes hence electrons are referred to as majority carriers and holes are referred to as minority carriers.

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