Free-Carrier Effects

We have assumed up to now that besides lattice absorption, intrinsic semiconductors were essentially transparent to photon energies less than the band gap at RT and below. Now, like electrons in metals, the free carriers in semiconductors can absorb electromagnetic radiation to increase their energies. In the calculation of the intrinsic free-carrier concentrations in the VB and CB of a semiconductor, one has to consider the effective densities of states 

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. 

In the classical electron transport model in metals or semiconductors, for a material with a free electron concentration n and an average electron scattering time (also called relaxation time) r, the DC conductivity is Oo = ne2r/to. In this classical expression, m (m or m ) is the conductivity effective mass, which is an average mass different from the DoS effective mass (see for instance [4]. In cubic semiconductors with degenerate CB extrema, the conductivity effective mass for electrons is  

For non-degenerate CBs, to is equal to mn. On the basis of a free-electron model, with an equation of motion analogous to expression (3.9) but without 

In a semiconductor, when considering expression (3.41), the contribution to the dielectric function of the high-frequency interband transitions at energies Eg is considered by replacing 1 by the high-frequency dielectric constant 

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Determination of free-carrier effective mass, mobility and concentration in doped semiconductors (for this application the use of magnetic fields and measurements in the far-infrared are required)... 

The uncertainty principle, according to which either the position of a confined microscopic particle or its momentum, but not both, can be precisely measured, requires an increase in the carrier energy. In quantum wells having abmpt barriers (square wells) the carrier energy increases in inverse proportion to its effective mass (the mass of a carrier in a semiconductor is not the same as that of the free carrier) and the square of the well width. The confined carriers are allowed only a few discrete energy levels (confined states), each described by a quantum number, as is illustrated in Eigure 5. Stimulated emission is allowed to occur only as transitions between the confined electron and hole states described by the same quantum number. 

Thus, sensor effect deals with the change of various electrophysical characteristics of semiconductor adsorbent when detected particles occur on its surface irrespective of the mechanism of their creation. This happens because the surface chemical compounds obtained as a result of chemisorption are substantially stable and capable on numerous occasions of exchanging charge with the volume bands of adsorbent or directly interact with electrically active defects of a semiconductor, which leads to direct change in concentration of free carriers and, in several cases, the charge state of the surface. 

Another type of absorption is also possible, i.e., exciton absorption which enriches the crystal in free excitons if the latter annihilate then on the lattice defects, causing a change in the charged state of the defects and leading to the appearance of free carriers in the crystal. In this case photoconduction arises as a secondary effect. 

The decrease in free carriers (holes) after hydrogenation of p-type Si is also evidenced by the decrease in IR absorption at the longer wavelengths, where free-carrier absorption dominates, and by a decrease in the device capacitance of Schottky-barrier diodes, due to the increase in the depletion width (at a given reverse bias) as the effective acceptor concentration decreases. 

Edward D. Palik and George B. Wright, Free-Carrier Magnetooptical Effects... 

Howard lA, Mauer R, Meister M, Laquai F (2010) Effect of morphology on ultrafast free carrier generation in polythiophene fullerene organic solar cells. J Am Chem Soc 132 14866... 

Figure 18 Free carrier (electron) concentration in SiC samples implanted with P ions at RT (circles) and 1200 ° C (squares) as a function of annealing temperature. Annealing was performed for 20 min in Ar atmosphere. The electron concentration was obtained from Hall effect measurement at RT.

There have been many investigations of photoinduced effects in -Si H films linked to material parameters. Changes have been observed in the carrier diffusion length, unpaired spin density, density of states in the gap, and infrared transmission. The transition from state A to B seems to be induced by any process that creates free carriers, including x-ray radiation and injection (double) from the electrodes. Because degradation in a solar cell is accentuated at the open-circuit voltage conditions, the A to B transition occurs upon recombination of excess free carriers in which the eneigy involved is less than the band gap. It has been pointed out that this transition is a relatively inefficient one and the increase in spin density takes place at a rate of 10-8 spins per absorbed photon. 

Bandgap measurements for Cu sulphides and selenides are complicated by the fact that these semiconductors are normally degenerate, with high free-carrier absorption in the near-infrared and possible Moss-Burstein shifts (due to saturation of the top of the valence band by holes) in the optical gap. It is quite possible that variations in bandgaps in these materials are due to differences in stoichiometry, phase, and doping rather than to any quantum size effect. Only studies where crystal size can be estimated and are possibly in the quantum size range are given here. 

A further application of the coplanar cell configuration showed in Fig. 3.1(c) concerns the study of the time dependence of the photocurrent following carrier excitation by means of a short pnlse of illnmination. This transient photodecay technique enables the examination of the interaction of initially free carriers with varions localized states. In principle, the decay of photocnrrent measured in this manner should (in the absence of recombination effects and phenomena associated with drift close to the surface of a thin film) correspond to the behavior in the initial pre-transit regime of a TOF pnlse. Becanse it allows measurements to be performed on very thin films under conditions appropriate to their nse in many device applications, and because the photocurrent may be examined over several decades of time withont the complications associated with carrier extraction, the techniqne has become rather popular over recent years. 

The polaron radius, if greater than (2), will be very sensitive to m —or, more exactly, to the bandwidth of the undistorted lattice. A particularly striking effect is that in materials like NiO doped with lithium, where the carriers are Ni3 + ions and in which the hole moves from one Ni2+ ion to another. The mass enhancement for a free carrier is rather small (about 5), while a bound carrier hopping round the Li+ ion on the sites available to it behaves like a small polaron with an activation energy for motion (see Bosman and van Daal (1970) and Chapter 6 below). 

A theoretical description of the a.c. conductivity has not been given. At low frequencies one would expect free-carrier absorption corresponding to the enhanced effective mass. At a frequency co comparable to E /h, where E is the unenhanced Fermi energy, we should expect the mass to go over to the unenhanced value. An example of this behaviour, taken from the infrared reflectivity of the vanadium oxides, is shown in Figs. 6.8 and 6.9. 

The Auger effect at a center can take place in various ways, since the three particles required for the process can be located on the particular center, on another center, and/or in the bands. The case of all three particles located at the center has been well treated fairly recently by Robbins and Dean (1978) and will therefore not be considered further. The remaining cases are those where either one or two particles are free (in one of the bands). For both these situations, the transition probability p depends on the free-carrier concentration it is customarily defined in terms of Auger coefficients and C, respectively, for one and two free carriers. For the case of one free hole,... 

The Auger effect involving one free carrier, by definition, must include two trapped carriers. These two trapped carriers can be either on the same defect or on nearby defects. A further subdivision is that the two trapped carriers can... 

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