Conductivity, Mobility and Carrier Density

The aim of our investigation was to study this very interesting phase, in the course of which we considered the dependences of the electrical conductivity, thermoelectric power, thermal conductivity, microhardness, coefficient of linear expansion, carrier mobility, and carrier density on composition in the most interesting concentration region (45 to 51 wt.% Si). Microstructure, x-ray structure, and chemical analysis were carried out on the most interesting alloys the dependence of a number of electrical properties on temperature was studied x-ray structure studies were carried out on single crystals. 

If the temperature dependence of the electronic conductivity of a semiconductor is to be accounted for, it is necessary to analyse how the density of charge carriers and their mobilities each depend upon T (see Eq. (2.25)). In the first place attention will be confined to the density n of electrons in the conduction band and the density p of holes in the valence band. When the intrinsic properties of the crystal are under consideration, rather than effects arising from impurities or, in the case of compounds, from departures from stoichiometry, the corresponding conductivity is referred to as intrinsic conductivity . The approach to the calculation of n and p in this instance is as follows. 

Fig. 6.37. Variation of (a) conductivity a, (b) carrier density N, and (c) mobility p as a function of the fluorine content for AP-CVD ZnO F films deposited at 400° C. Reprinted with permission from [15]...

The microwave reflectivity of a semiconductor depends on the sample conductivity, i.e. on the density and mobility of free electrons and holes. Photoexcitation of the sample brings about an instantaneous increase of electron and hole densities and a corresponding change in microwave reflectivity. After excitation by a laser pulse, the decay of minority carriers by bulk and surface recombination, as well as by trapping, can be followed by the change in microwave reflectivity. For small changes in carrier density, the relationship between microwave reflectivity and carrier density is linear. 

Figure 14.12 illustrates the electric conductivity of the selected two-dimensional materials. The data were obtained using a fleld-effect-transistor-fike microscopic device. The authors have measured the carrier mobilities and their density. 

The influence of the structure of the alloys on their physical properties was determined by measuring the room-temperature values of the electrical conductivity (Hall coefficient, the thermoelectric power (a), and the total thermal conductivity (>t). The carrier density (p), the carrier mobility (/i), and the thermoelectric figure of merit (z) were calculated. The samples used in these measurements were cut from the middle parts of the ingots and their compositions were checked by x-ray diffraction analysis. The results of the measurements are presented in Table 1. 

The extended 7t orbital of G has electron density above and below the sheet. This extended conjugation is responsible for the extremely high-electrical conductivity of G that can be even higher than the electrical conductivity of metals. Also charge mobility and the density of carriers in G are very high and, for this reason, many of the promising applications of G are in the domain of microelectronics. 

The conductivity is proportional to the product of mobility and carrier concentration. If we have n charge carriers per unit volume, the net flux of charge carriers per unit time is given by n Vd and the current density J = I/A by... 

Conductivity is the carrier density multiplied by mobility. The Marcus model may be used to calculate the mobility residence time and the Drude model may be used to obtain conductivity. We recall that the two parabolas are total energy curves for nuclear motion along a reaction coordinate. There are two equal minima (AG = 0) since the electron can be localized at two equivalent sites, as long as the field is negligible. If a field is switched on, there is an imbalance in the Marcus curves that leads to less barriers to jump in the field direction. Metallic conductivity is obtained when the height of the barrier, AG tends to zero. This happens when K < 2H,2 (Chapter 10). 2Hi2 is directly related to the band width. 

On lowering the temperature through Ty, a bandgap Eg = 0.1 eV appears in the FeB-ai(l) conduction band of Fig. 3 at Ep. The Hall coefficient increases as Rh exp(Ty/T), indicating that the charge-carrier density increases exponentially with T" , as in a normal semiconductor, and the Hall mobility increases from about 0.1 to 0.4 cm /Vs on lowering the temperature from Ty = 120 K to 77 K ... 

The mobilities of holes are always less than those of electrons that is fXh < Me- In silicon and germanium, the ratio [ie/[ih is approximately three and two, respectively (see Table 6.2). Since the mobilities change only slightly as compared to the change of the charge carrier densities with temperature, the temperature variation of conductivity for an intrinsic semiconductor is similar to that of charge carrier density. 

Unlike intrinsic semiconductors, in which the conductivity is dominated by the exponential temperature aud band-gap expression of Eq. (6.31), the conductivity of extrinsic semiconductors is governed by competing forces charge carrier density and charge carrier mobility. At low temperatures, the number of charge carriers initially... 

The basic assumption In conductance measurements Is the Independence of the sample resistance on electric field strength. However a deviation from the linear relation between current density and field strength will be observed If any field effect on the mobility and/or the number of free charge-carriers Is present. 

Pyrolyzed polyimide films at 480-530 °C can change the conductivity from 10-18 to 10 2 Scm-1 and mobility from 10-11 to 10 7m 2 V-1 s 1 (Fig. 55) [318], It has been shown that carrier density increases at the initial stage of the pyrolysis and then the increase of the mobility becomes predominant as the pyrolysis progresses. Hopping charge transfer is the main conductive mechanism. 

Localized states in the bulk of a semiconductor that have energies within the bandgap are known to capture mobile carriers from the conduction and valence bands.— The bulk reaction rate is determined by the product of the carrier density, density of empty states, the thermal velocity of the carriers and the cross-section for carrier capture. These same concepts are applied to reactions at semic ijiductor surfaces that have localized energy levels within the bandgap.— In that case the electron flux to the surface, F, reacting with a surface state is given by... 

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