Electron carrier concentration

Figure 22 (r.h.s.) illustrates the contact thermodynamics and its influence on ionic and electronic carrier concentrations. The level bending expresses the variation in the electrical potential, and the constancy of //ion and /ieon the electronic and ionic contact equilibrium.35 (Note that the electric potential term—as a non-configurational term—is to be included into the energy levels .) The constancy of the chemical potential of the neutral component is automatically fulfilled (see Fig. 22 r.h.s.). 

The electron-phonon coupling constant as a function of the doping level in silicon is presented in Fig. 2. The coupling is approximately directly proportional to the electron carrier concentration in the heavily doped silicon, but the electrical resistance of the silicon only slightly depends on the carrier concentration i n this range. This can be used for optimization of thermal characteristics of different microdevices operating at low tenqieratures. 

Yupko et al. (1974) have also measured the Hall coefficient and the electrical resistivity of La2C3, Ce2C3, Nd2C3 and Y2C3. The resulting electron carrier concentration data are, however, mutually inconsistent. 

Remember that throughout this process, the law of mass action holds which says that the product of hole and electron carrier concentration is a function only of the ratio of the effective masses of the electrons, the Eg, and the absolute temperature. The dopant concentration does not enter into the np product. Increasing the number of donor impurities raises n, but at the expense of p. Conversely, increasing the number of acceptor states increases p, but at the expense of n. In other words, for a given material at a given temperature, increasing the majority carrier concentration is done at the expense of the minority carrier concentration such that their product remains the same. 

Fig. 5.46 Dependences of the equilibrium concentrations in slightly positively (Nj ) doped FVenkel-disordered MX on Pxj, T, [N ]. At the working point characterized by P, C, T, the material still behaves intrinsically. The middle section in the T-dependence characterized by [V [] [h ] did not appear (Part c) in the case of AgCl owing to the very small electronic carrier concentration.

Material Cubic lattice constant, pm Band gap, eV Inttinsic carrier concentration, cm Relative dielectric constant, S Mobihty, Electrons cm"/(Vs) Holes... 

The carrier concentrations in doped or extrinsic semiconductors to which donor or acceptor atoms have been added can be deterrnined by considering the chemical kinetics or mass action of reactions between electrons and donor ions or between holes and acceptor ions. The condition for electrical neutraHty is given by equation 6. When the predominant dopants are donors, the semiconductor is... 

Lp = D r ) is the minority carrier diffusion length for electrons in the -region, (0) is the minority carrier concentration at the boundary between the depletion layer and the neutral region. The sign of this equation indicates that electron injection into the -region results in a positive current flow from p to n a.s shown in Figure 7. 

More precise coefficients are available (33). At room temperature, cii 1.12 eV and cii 1.4 x 10 ° /cm. Both hole and electron mobilities decrease as the number of carriers increase, but near room temperature and for concentrations less than about 10 there is Htde change, and the values are ca 1400cm /(V-s) for electrons and ca 475cm /(V-s) for holes. These numbers give a calculated electrical resistivity, the reciprocal of conductivity, for pure sihcon of ca 230, 000 Hem. As can be seen from equation 6, the carrier concentration increases exponentially with temperature, and at 700°C the resistivity has dropped to ca 0.1 Hem. 

For insulators, Z is very small because p is very high, ie, there is Htde electrical conduction for metals, Z is very small because S is very low. Z peaks for semiconductors at - 10 cm charge carrier concentration, which is about three orders of magnitude less than for free electrons in metals. Thus for electrical power production or heat pump operation the optimum materials are heavily doped semiconductors. 

As indicated in Figure 4, the basic thermoelectric parameters are all functions of carrier concentration. Thus adjusting the dopant level to increase the output voltage generally also increases the electrical resistance. In addition, it affects the electronic component of the thermal conductivity. However, there are limitations on what can be accompHshed by simply varying the carrier concentration in any given material. 

The relatively high mobilities of conducting electrons and electron holes contribute appreciably to electrical conductivity. In some cases, metallic levels of conductivity result ia others, the electronic contribution is extremely small. In all cases the electrical conductivity can be iaterpreted ia terms of carrier concentration and carrier mobiUties. Including all modes of conduction, the electronic and ionic conductivity is given by the general equation ... 

Parker [55] studied the IN properties of MEH-PPV sandwiched between various low-and high work-function materials. He proposed a model for such photodiodes, where the charge carriers are transported in a rigid band model. Electrons and holes can tunnel into or leave the polymer when the applied field tilts the polymer bands so that the tunnel barriers can be overcome. It must be noted that a rigid band model is only appropriate for very low intrinsic carrier concentrations in MEH-PPV. Capacitance-voltage measurements for these devices indicated an upper limit for the dark carrier concentration of 1014 cm"3. Further measurements of the built in fields of MEH-PPV sandwiched between metal electrodes are in agreement with the results found by Parker. Electro absorption measurements [56, 57] showed that various metals did not introduce interface states in the single-particle gap of the polymer that pins the Schottky contact. Of course this does not imply that the metal and the polymer do not interact [58, 59] but these interactions do not pin the Schottky barrier. 

The electrical conductivity in the solid state is determined by the product of the carrier concentration and the carrier mobility. In conjugated polymers both entities are material dependent and, i.e., are different for electrons and holes. Electrons or holes placed on a conjugated polymer lead to a relaxation of the surrounding lattice, forming so-called polarons which can be positive or negative. Therefore, the conductivity, o, is the sum of both the conductivity of positive (P+) and negative polarons (P ) ... 

Friend et at. studied the influence of electrodes with different work-functions on the performance of PPV photodiodes 143). For ITO/PPV/Mg devices the fully saturated open circuit voltage was 1.2 V and 1.7 V for an ITO/PPV/Ca device. These values for the V c are almost equal to the difference in the work-function of Mg and Ca with respect to 1TO. The open circuit voltage of the ITO/PPV/A1 device observed at 1.2 V, however, is considerably higher than the difference of the work-function between ITO and Al. The Cambridge group references its PPV with a very low dark carrier concentration and consequently the formation of Schottky barriers at the PPV/Al interface is not expected. The mobility of the holes was measured at KT4 cm2 V-1 s l [62] and that for the electrons is expected to be clearly lower. 

Photoelectrochemical techniques have been utilized to determine the minority (electron) diffusion length (L) and other electrical parameters of p-ZnTe [125] and p-type Cdi-jcZnjcTe alloys [126]. In the latter case, the results for a series of single crystals with free carrier concentration in the range 10 " -10 cm (L = 2-4 xm, constant Urbach s parameter at ca. 125 eV ) were considered encouraging for the production of optical and electro-optical devices based on heterojunctions of these alloys. 

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