Temperature dependence electron concentration

We have considered only one species of ion and have assumed the total number of ions is fixed. The extensions to more general cases, such as more than one species or a temperature dependent ion concentration, are obvious. We have neglected the thermal or electron-hole pair contribution to conductivity. 

The dominant role of the temperature-dependent carrier concentration implied by Fig. 5.8 permits us to draw some semi-quantitative conclusions about electronic transport in semiconducting liquid selenium. Using the simple semiconductor model, we can estimate the carrier mobility from Eq. 5.2 from the fitted prefactor in Eq. 5.1. For this purpose we assume that the carrier masses are not too different from the free electron mass, that is, nig — nif, mo- This yields an estimated carrier concentration at 400 °C, 2 3 x 10 cm. The corresponding... 

In the preceding chapters we have looked at temperature dependencies of concentrations of electronic defects and point defects, and we have looked at the conductivity and mobility of thermally activated diffusing species. In the following we consider the charge carrier mobilities of electrons and holes in some more detail. For instance for an intrinsic electronic semiconductor (where n=p) we can from Eq. 6.29 in combination with Eqs. 6.23 and 6.24 write an expression for... 

MIM or SIM [82-84] diodes to the PPV/A1 interface provides a good qualitative understanding of the device operation in terms of Schottky diodes for high impurity densities (typically 2> 1017 cm-3) and rigid band diodes for low impurity densities (typically<1017 cm-3). Figure 15-14a and b schematically show the two models for the different impurity concentrations. However, these models do not allow a quantitative description of the open circuit voltage or the spectral resolved photocurrent spectrum. The transport properties of single-layer polymer diodes with asymmetric metal electrodes are well described by the double-carrier current flow equation (Eq. (15.4)) where the holes show a field dependent mobility and the electrons of the holes show a temperature-dependent trap distribution. 

More recent B-NMR studies at room temperature have shown that (acyloxy)diethylboranes are monomeric also in non-polar solvents like chloroform [(5( B) - 60 ppm] [46]. Under the same conditions the corresponding 9-BBN derivatives are monomeric (both types I and II) or dimeric, depending on the electron-donating or -withdrawing effect of the substituent on the carboxyl group, the temperature, and the concentration of the... 

Mass-spectrometric research on silane decomposition kinetics has been performed for flowing [298, 302-306] and static discharges [197, 307]. In a dc discharge of silane it is found that the reaction rate for the depletion of silane is a linear function of the dc current in the discharge, which allows one to determine a first-order reaction mechanism in electron density and temperature [302, 304]. For an RF discharge, similar results are found [303, 305]. Also, the depletion and production rates were found to be temperature-dependent [306]. Further, the depletion of silane and the production of disilane and trisilane are found to depend on the dwell time in the reactor [298]. The increase of di- and trisilane concentration at short dwell times (<0.5 s) corresponds to the decrease of silane concentration. At long dwell times, the decomposition of di- and trisilane produces... 

An example of the temperature dependence of donor neutralization is shown in Fig. 3. Devices with a square van der Pauw geometry were exposed to H° for 30 min. at different temperatures. Hydrogenation reduces the free-electron concentration over the entire investigated temperature range, with a maximum reduction of approximately 40% at 140°C. In... 

Fio. 3. Dependence on hydrogenation temperature of the free-electron concentration (a) and the electron Hall mobility (b) in phosphorus-implanted n-type silicon (Johnson et al., 1987c). 

The equilibrium concentration of the ions A- and B- participating in the equlibrium can be directly observed by mass spectrometry. Thus, the free-energy change can be derived from the equilibrium constant, since the concentrations of the neutral species are known in advance. Similarly, by measuring the temperature dependence of the equilibrium constants, the associated enthalpy and entropy can be obtained from van t Hoff plots. By measuring a series of interconnecting equlibria, an appropriate scale can be established. The primary standard in such work has frequently been SO2 whose electron affinity is well established by electron photodetachment36. 

In either group of electrode reactions, the energy level of reacting particles (electrons or ions) in the electrode depends linearly on the electrode potential. Hence, the reaction afiinily (A = — AG) can be varied over a wide range by simply controlling the electrode potential. This is one of the characteristics of electrode reactions, in contrast with ordinary chemical reactions whose affinity can be varied in a relatively narrow range by controlling the temperature and the concentration of reaction particles. 

---