Free carrier density

The excess free carrier density decays (via recombination) with those recombination centers that have the largest cross section. 

Capture and emission processes at a deep center are usually studied by experiments that use either electrical bias or absorbed photons to disturb the free-carrier density. The subsequent thermally or optically induced trapping or emission of carriers is detected as a change in the current or capacitance of a given device, and one is able to deduce the trap parameters from a measurement of these changes. 

By studying the temperature dependence of the carrier concentration in a semiconductor sample, several things can be learned about its properties. Figure E10.1 shows the free carrier density (n +p) of a semiconductor sample measured as a function of temperature and plotted in a useful form. Based on the data in this plot, you should be able to discern ... 

A variety of experimental measurements can be used to determine free carrier densities (and thus dopant levels) in semiconductors. Four-point probe resistivity measurements are the most common because they are relatively painless, nondestructive, and can be performed on thin wafers. There is more to them than meets the eye, however. 

Figures 6.37 and 6.38 show the variation of electrical properties as a function of the dopant content of ZnO films. Figure 6.37 shows the case of AP-CVD ZnO F with fluorine as dopant (here, the fluorine atomic fraction is considered as dopant content). Figure 6.38 shows the case of LP-CVD ZnO B with boron as dopant (here, the B2H6/DEZ ratio is considered as dopant content). The electrical properties taken into consideration are the conductivity a, the resistivity p, the mobility //, and the free carrier density N.

The literature abounds with reports of thermal activation energies for shallow donors in GaN, obtained from Hall effect measurements over a range of temperatures, above and below room temperature, though their interpretation is rendered problematic by a number of complicating factors. At low temperatures there is clear evidence for impurity band conduction (see, for example, [31]) which severely limits the temperature range over which data may usefully be fitted to the standard equation for free carrier density n in terms of the donor density ND and compensating acceptor density NA ... 

The photoelectrical behaviour of an illuminated solid depends not only on its optical properties but also on the nature of the contacts made to it. If a resistive material is provided with ohmic contacts, there is no barrier to the transfer of electrons to and from the solid and the current that flows when a potential difference is applied between the contacts depends only on the density and mobility of charge carriers. The current will increase if illumination raises the free carrier density considerably and the material is then termed a photoconductor. In practice, illumination may serve either to promote electrons from the valence band to the conduction band or to release carriers trapped at impurity states in the band gap. In both cases, the light gives rise to a volume photoeffect [6]. 

Thus the higher the free-carrier concentration in the material, the smaller the penetration depth of the applied field into the medium. For electron concentrations of 10 cm (10 m ) or larger, the space charge is restricted to distances on the order of one atomic layer or less, because the large free-carrier density screens the solid from the penetration of the electrostatic field caused by the charge imbalance. For most metals, almost every atom contributes one free valence electron. Because the atomic density for most solids is on the order of 10 cm (10 m ), the free-carrier concentration in metals is in the range of 10 -10 cm (10 -10 m ). Thus Fv and d are small. For semiconductors or insulators, however, typical free-carrier concentrations at room temperatures are in the range of cm lO -... 

The power-law decay in Eq. (3) can be regarded as a decay of free carrier density or as a decay of the drift mobility. The tatter interpretation and the usual definition of the transit time tj lead to... 

The basis for this preliminary hypothesis is provided by the data from an approximate estimate of the vacancy concentrations [11] in undoped and doped single crystals of indium antimonide, which we obtained by comparing the x-ray (px) a.nd e erimental (pe) densities (Table 2). As may be seen from the table, the vacancy concentration in undoped indium antimonide is about 2 10 cm, and this value is maintained for doped indium antimonide up to a free-electron density of (1.2-1.5) 10 cm (i.e., a tellurium content of about 2 10 cm ). Only with a further increase in tellurium concentration in the crystal does the vacancy concentration iincrease. Therefore, with a further increase in tellurium content in the solid solution, the limitation in the free-carrier density may be due to both precipitation of tellurium from the solid solution and the formation of compensating acceptor vacancies by the mechanism given in [2]. 

In order to retain intrinsic conduction to temperatures as low as 150 K as observed in Figure 5.7, the gap must be virtu ly free of localized states. With AE 0.5 eV, for example, the free carrier density at 150 K is about n... 

In the absolute energy scale, the position of the conduction band with respect to the vacuum level is given by the electron affinity Ea (Figure 5). The position of the Fermi level depends on the free carrier density, n, and consequently on the doping. The electron affinity, Ea, is usually given in the... 

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