Conductivity of semiconductors

All the types of charge carriers present in a medium contribute to the conductivity. In the case of semiconductors, both electrons and holes should be taken into account when conductivity is calculated, and the expression for the conductivity becomes (using Eqs. 7.6 and 7.7). 

The mobilities of electrons and holes are independent of the electric field over a wide range of carrier velocities, but they change with temperature. If the temperature decreases, the mobility of both carriers increases. The mobility of electrons and holes in pure germanium as a function of temperature is shown in Fig. 7.10. The mobility changes at /x with a 1.5, for T 80 K. For 

In a pure semiconductor, = Np and each one of these quantities is given by the equation 

The motion of the carriers in a semiconductor is also affected by the presence of impurities and defects of the crystal. A small amount of impurities is always present, although impurities are usually introduced deliberately to make 

For semiconductors, the probability that an electron will move from the valence to the conduction level is proportional to the factor (Eq. 7.3) 

In a semiconductor, the current is carried by both electrons and holes. Thus the current density may be written as 

Recall that for metals, we argued that r drift r th r p, and since the Fermi velocity was independent of the electric field and temperature, v was therefore independent of temperature. But in metals, Vp Uth because of the fact that every atom contributed at least free one electron to the Fermi distribution. (We do not coimt the boimd electrons in the iimer core of the atoms.) Similarly, the electrons in the valence band of a semiconductor are boimd and do not contribute to the Fermi level as long as they are in this bound state. Recall also that we placed the Fermi level between the valence and the conduction bands of an intrinsic semiconductor so that the probability of promoting an electron to the conduction band would equal the probability of creating a hole in the valence band. So for semiconductors, the Fermi velocity will be substantially less than the thermal velocity since the number of free electrons will be much less than for a metal. Therefore, we can assume for semiconductors that the average electron velocity v j.l/2. 

At very low temperatures ( 10K) scattering from lattice defects dominates in semiconductors, just as in metals. However, in the case of charged defects such as ionized donor 

Calculated conductivity for n-doped Si as a function of reciprocal temperature. The electron and hole mobilities were taken to be 0.14 and 0.048 m /V s, respectively at 300 K and were assumed to fall as the -3/2 power of temperature In the intrinsic region, a exp — (EJTkT). 

At higher temperatures, thermal scattering from collisions with the lattice ion cores dominates. We argued in the case of metals that the scattering cross section is proportional to T. This would also be true for semiconductors, except now the average electron velocity Hence the number of scattering events per unit time and the mobility 

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Semiconductors are a class of materials whose conductivity, while highly pure, varies witli temperature as exp (-Ag//cg7), where is tlie size of a forbidden energy gap. The conductivity of semiconductors can be made to vary over orders of magnitude by doping, tlie intentional introduction of appropriate impurities. The range in which tlie conductivity of Si can be made to vary is compared to tliat of typical insulators and metals in figure C2.16.1. 

The same Chapter contains results of studies of effects of adsorption of atom particles as well as simplest free radicals on electric conductivity of semiconductor zinc oxide films. 

Expressions (1.45) and (1.46) which are valid in case of applicability of above assumptions indicate on availability of direct proportionality between the value of the change of the surface-adjacent conductivity of semiconductor adsorbent and concentration of chemisorbed particles on its surface, the latter being in charged form. This results in the fact that when the surface is covered by adsorbed particles at degrees lower... 

The fair agreement of expressions (2.67) and (2.71) with experimental data as well as agreement of independently obtained experimental data concerning kinetics of the change of a with the data on equilibrium enabled the author of paper [89] to conclude that the proposed mechanism of effect of hydrogen on electric conductivity of semiconductors can be one of active mechanisms. The heat of total reaction (2.63) calculated from the values found was about 4.6 kcal. 

Thus, we have considered in detail various theoretical models of effect of adsorption of molecular, atom and radical particles on electric conductivity of semiconductor adsorbents of various crystalline types. Special attention has been paid to sintered and partially reduced oxide adsorbents characterized by the bridge type of intercrystalline contacts with the dominant content of bridges of open type because of wide domain of application of this very type of adsorbents as sensitive elements used in our physical and chemical studies. 

To detect radicals by means of semiconductor films there may be used both kinetic and stationary methods. The latter is based on relationship between the stationary conductivity of semiconductor film (e. g., ZnO, CdO, etc.) and stationary concentrations of active particles being detected. 

As for the energy transfer to the subsurface layers of zinc oxide from the singlet oxygen molecules, the transfer should lead to an intn ease in the electrical conductivity of semiconductor either due to ejection of electrons into the conduction band h-om shallow traps [67], or due to the injection of electrons into zinc oxide by excited particles [68]. Effects of this kind were observed in the interaction between a ZnO surface and excited pairs of benzophenone [70], and also in adsorption of singlet oxygen on the surface of ZnO monocrystal in electrolyte [69]. 

From general considerations it should be mentioned that only atoms of hydrogen can be present in gaseous phase in addition to atoms of antimony, molecules of antimony hydride and antimony hydride radicals in this system. Therefore, it is necessary to analyze plausible effects of each of above particles on conductivity of semiconductor sensor under experimental conditions. 

Compared with metals, semiconductors have quite high resistivity, as conduction of current requires a supply of activation energy. The conductivity of semiconductors increases with increasing temperature. 

There is a fundamental difference between electron-transfer reactions on metals and on semiconductors. On metals the variation of the electrode potential causes a corresponding change in the molar Gibbs energy of the reaction. Due to the comparatively low conductivity of semiconductors, the positions of the band edges at the semiconductor surface do not change with respect to the solution as the potential is varied. However, the relative position of the Fermi level in the semiconductor is changed, and so are the densities of electrons and holes on the metal surface. 

The conductance of MWCNTs is quantized. The experimental setup to measure the conducting properties involved the replacement of an STM tip with a nanotube fiber that was lowered into a liquid metal to establish the electrical contact. The conductance value observed corresponded to one unit of quantum conductance (Go = 2e /h = 12.9 kQ ). This value may reflect the conductance of the external tube because, for energetic reasons, the different layers are electrically insulated [150]. Finally, the conductance of semiconductor nanotubes depends on the voltage applied to the gate electrode their band gap is a function of their diameter and helicity [145] and the ON/OFF ratio of the transistors fabricated with semiconductor nanotubes is typically 10 at room temperature and can be as high as 10 at... 

The electrical conductance of semiconductors is derived from the mobility of charge carriers, holes h+ in the valence band and free electrons e in the... 

An important point to note about this explanation is it assumes that empty energy levels are available close in energy to the Fermi level. You will see later that the existence of such levels is crucial in explaining the conductivity of semiconductors. 

Equation (2) may be used for the rate constant k of a chemical reaction or applied to the diffusion coefficient in liquid or solid phases or to the fluidity of liquids (reciprocal of dynamic viscosity) or to the specific electrical conductivity of semiconductors. 

Flo. 9. Temperature dependence of conductivity of semiconductor pellets with and without added 10% wt of silver powder. The logarithm of structure-independent conductivity is plotted as a function of the reciprocal absolute temperature (degrees Celsius on top of the figure). Full lines are measured, dotted parts extrapolated (79). (Copyright by the Universite de Liege. Reprinted with permission.)... 

Now, for the semiconductor/solution interface, there are two reasons for the potential difference concentrating inside the semiconductor (Fig. 10.1) and being small at the conductivity interface with the solution. On the one hand, the electronic conduction of semiconductors is many orders of magnitude less than that of a... 

Unlike metals, the conductivity of semi-conductors and insulators is mainly due to the presence of interstitial electrons and positive holes in the solids due to imperfections. The conductivity of semiconductors and insulators increases with increase in temperature while that of metals decreases. 

The electric conductivity specifies the electric character of the material. Solid materials, in three groups of conductors, semiconductors, and insulators, exhibit a wide range of electric conductivities. Metals have conductivities on the order of 107 (fi m)-1, insulators have conductivities ranging between 10 10 and 10 20 (O m), and the conductivities of semiconductors range from 10 6 to 104 (O m). ... 

With the above description of the band structure and optical properties of semiconductors, it is now possible to describe the remaining key characteristic of semiconductors electrical conductivity. The electrical conductivity of semiconductors forms the basis for most of the modem electronics industry. Without precise control over the electrical conductivity of semiconductors, many modem electronic devices would not perform satisfactorily. The goal of this section is to understand the chemical basis for the electrical properties of semiconducting solids. 

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. 

The transduction mechanisms of these sensors are based on the conduction of semiconductors such as tin oxide [16], or polymers such as polypyrrole [17]. More sensitive are sensors that weigh impinging molecules [18] and more sensitive still is the biological nose. Recently there has been a renewal of interest in optical sensors incorporating fluorescent molecules [19]. Typically a device will have 3 to 30 sensors, the output of each being a voltage. This may be measured at the steady state, or the time development of the voltages may be monitored. Humidity and temperature control is important for many sensors. 

Figure 5.2 Conductivity of semiconductors and conductors as a function of temperature...

It seems natural to consider Eg (i.e., twice the chemical hardness), if transfer of electrons is the critical property. Certainly the fact that the gap is zero for metals accords with the great electrical conductivity of these solids. Also, the size of the gap determines the conductivity of semiconductors and insulators. In general, the conductivity, C, is given by... 

The conductivity of semiconductors can be increased by adding small amounts of other elements. 

D20.8 Semiconductors generally have lower electrical conductivity than most metals. Additionally, the conductivity of semiconductors increases as the temperature is raised whereas that of metals decreases. The difference occurs because of the relative balance between the excitation of electrons into electrical conductance and the scattering of electrons off the conductance path by collisions with vibrating atoms. The scattering process predominates with increasing temperature of a metal. The excitation process predominates for the semiconductor. 

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