Semiconductors intrinsic carrier concentration

In an intrinsic semiconductor, charge conservation gives n = p = where is the intrinsic carrier concentration as shown in Table 1. Ai, and are the effective densities of states per unit volume for the conduction and valence bands. In terms of these densities of states, n andp are given in equations 4 and... 

For an n-type semiconductor, if the donor impurity concentration is much greater than the intrinsic carrier concentration, Nd >nj, then no Nd. Equation (3.4.9) can then be written as... 

Indium nitride is a wide-gap semiconductor with negligible intrinsic carrier concentration and there are no reports of deliberate doping. Electron concentrations, most commonly of order 1020 cm 3, appear independent of growth method and are therefore assumed to be of native defect origin. The presence of... 

To describe the conductivity of an intrinsic semiconductor sample quantitatively, we need to calculate the concentrations of both types of charge carriers in the solid. The key quantity that controls the equilibrium concentration of electrons and holes in an intrinsic semiconductor is the band gap. Because the thermal excitation energy required to produce an electron and a hole is equal to Eg, the intrinsic carrier concentrations can be related to Eg using the Boltzmann relationship ... 

For most semiconductors, kT (0.0259 eV at 300 K) is much smaller than E. Thus, few electrons and holes are produced at room temperature in such semiconductors. Intrinsic samples are far too resistive for many applications additionally, in actual semiconductor samples, the concentration of unwanted impurities often exceeds the intrinsic carrier concentrations. Under these conditions, it is difficult to maintain quality control over the electrical properties of semiconductors. For these reasons, the conductivity of semiconductors is generally deliberately controlled through a process known as doping. 

Because the intrinsic carrier concentrations in semiconductors are so low, even impurity concentrations at the level of one part per billion can have a profound effect on the electrical properties of a semiconductor sample. To increase the sample conductivity and to control other electronic properties of the semiconductor, low concentrations of specific impurity atoms are often introduced into the crystal lattice. This process, which is called doping, serves to decrease the resistance... 

Again taking the effective masses to be equal to the electron mass, using 300 K for room temperature, and using 2.7 eV for the energy gap of the ladder-type PPPs, we obtain an intrinsic carrier concentration of 10 4 cm 3. This value will rise to 41 cm-3 upon increasing the temperature to 400 K. These values have to be compared to common inorganic semiconductors at room temperature 2.7... 

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... 

An intrinsic semiconductor does not possess impurities. Each valence band electron that is excited enough to transfer to the conduction band leaves behind a hole carrying a positive charge as a result, the concentrations in electron n and in hole p are equal, which is expressed as n = p = u u is the intrinsic carrier concentration. Integrating [3.20] and [3.21] yields the following relations for electron and hole concentrations ... 

In extrinsic semiconductors the carrier concentrations are perturbed such that n = p. Again the analogy with the addition of an acid or base to water is quite instructive here. Consider the case when donor impurities are added to a neutral semiconductor. Since the intrinsic carrier concentrations are so low (sub-parts per trillion), even additions in parts per billion levels can have a profound electrical effect. This process is known as doping of the semiconductor. In this particular case, the Fermi level shifts toward the CB edge (Fig. 4b). When the donor level is... 

Table 4.1-19 Intrinsic carrier concentration n, and electrical conductivity a, of Group IV semiconductors and FV-fV compounds...

For an intrinsic semiconductor, conductivity in terms of intrinsic carrier concentration... 

For intrinsic semiconductors, the intrinsic carrier concentration tij depends on temperatme, as follows ... 

TABLE 9.2 Intrinsic Carrier Concentration, n,[ in Selected Semiconductors... 

An intrinsic semiconductor has no impurities and the number of electrons, n, in the conduction band exactly matches the number of holes, p, in the valence band, n=p. The number of electrons or holes is named the intrinsic carrier concentration ni. This carrier concentration is given by the probability that a state at energy E is filled (as given by the Fermi function. Equation 2.11) multiplied by the density of states at that energy (Equation 2.22 for free electrons) integrated over all energies at or above the conduction band edge ... 

The most important point to note about Equation 2.30 is that ni depends exponentially with temperature on half of the semiconductor energy gap. Narrow-gap semiconductors will have large intrinsic carrier concentrations while wide-gap materials will have fewer mobile carriers at a given temperature. 

Calculate conductivity from charge carrier concentration, charge, and mobility. Differentiate between a conductor, insulator, semiconductor, and superconductor. Differentiate between an intrinsic and an extrinsic semiconductor. 

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