Silicon intrinsic carrier concentration

Silicon carbide-based sensors can operate at higher temperatures (above 600°C) because of a wide band gap and low intrinsic carrier concentration availability of SiC. Taking advantage of this trait, silicon carbide semiconductors have been used... 

This expression is derived from the more general case where the electron and hole concentrations in the conduction and valence bands are n and p with np = n2. At RT, taken as 300 K, the intrinsic carrier concentration n is 1.1 x 10111 cm in silicon, but it increases to about 4 x 1013 cm 3 in germanium to reach 2 x 1016 cm-3 in intrinsic InSb. 

Figure 18.16 plots the logarithm of the intrinsic carrier concentration n, versus temperature for both silicon and germanium. A couple of features of this plot are worth noting. First, the concentrations of electrons and holes increase with temperature because, with rising temperature, more thermal energy is available to excite electrons from the valence to the conduction band (per Figure 18.6h). In addition, at all temperatures, carrier concentration in Ge is greater than in Si. This effect is due to germanium s smaller band gap (0.67 vs. 1.11 eV, Table 18.3) thus, for Ge, at any given temperature, more electrons will be excited across its band gap.

Figure 18.16 Intrinsic carrier concentration (logarithmic scale) as a function of temperature for germanium and silicon.

Impurity Semiconductors, n-Type andp-Type. The discussion has been restricted so far to pure intrinsic semiconductors exemplified by germanium and silicon. In these substances, there is a low concentration of charge carriers (compared with metals). Further, the hole and electron concentrations are equal, and their product is a constant given by the law of mass action... 

It is essential that the silicon be intrinsic (/). It must neither be -type, containing free electrons from donor impurities, nor p-type, containing free holes from acceptor impurities in either type, the free charge carriers, at their usual concentrations, would overwhelm the few carriers produced by x-rays. Production of a reasonably large intrinsic crystal, which is not easy, requires two operations ... 

Silicon carbide in pure form is a semiconductor, and the resistivity depends on the impurity concentration. In the intrinsic form, the resistivity is less than 1000 Q cm, which is unsuitable for ordinary use. The addition of a small percentage (less than 1 percent) of BeO during the fabrication process increases the resistivity to as high as 10 Q cm by creating carrier-depleted layers around the grain boundaries. 

For a given semiconductor at temperature T, Equation (9.51) shows that as the number of free electrons increases, the number of holes proportionately decreases, so that their product remains the same. Thus the amount of the phosphorus dopant that is introduced controls the amount of both the electrons and the holes in the semiconductor. We call the carriers of higher concentration the majority carriers, while those of lower concentration are the minority carriers. Since electrons are the majority carrier when we dope silicon with phosphorous, we call this material an n-type semiconductor. When the number densities of minority and majority carriers are controlled by the amount of dopant, we say we have an extrinsic semiconductor. In the limit of small dopant concentrations, [P i] << p, there is no effect of the substitutional impurity of the electronic defects in the semiconductor, and it behaves similarly to an intrinsic semiconductor. 

Figure 2.10 A plot of the electron concentration in a piece of silicon doped with 10 cm donor atoms having an ionization energy of 0.04 eV. The steep slope at high temperature (low inverse temperature) corresponds to the intrinsic behavior for carriers crossing the energy gap. The lower temperature behavior occurs in the presence of the 10 cm electron donors. The slopes of the two curves correspond to the 1.1 eV energy gap and the 0.04 eV donor ionization energies, respectively.

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