Semiconductors carrier concentrations

It is apparent from our discussion so far that the Hall factor is sometimes difficult to calculate and even more difficult to measure. However, it rarely varies by more than 20% from a value of 1.2 (Stillman et al., 1970 Debney and Jay, 1980). Such a situation is entirely tolerable, especially when one realizes the range of semiconductor carrier concentrations (103-1020 cm-3 in our laboratory) that can be measured by this simple technique. 

Additional issues arise when reduction of the size of a semiconductor is considered. In bulk semiconductors the valence and conduction bands bend. Because of the low carrier concentration, the electrical double layer in a bulk semiconductor/solution system extends into the interior of the semiconductor rather than into the solution. In terms of the Gouy Chapman model, the width of a diffuse double layer is inversely proportional to the square root of the carrier concentration for a typical semiconductor carrier concentration of 10 cm the band bending is calculated to occur over several hundred nanometers (in which region there is about one carrier). 

Note that the organic semiconductor used in OFETs should not be intentionally doped. Consequently, the semiconductor carrier concentration is very low, usually <10 " cm . When a voltage is applied... 

To solve the system of equations for the steady-state operation of semiconductor photoelectrodes, a definition of equilibrium must first be introduced. The law of mass action, in the context of semiconductor carrier concentration statistics, dictates that at equilibrium, the values of n and p are bound to a constant value ( ) in the following way ... 

In an intrinsic semiconductor, charge conservation gives n = p = where is the intrinsic carrier concentration as shown in Table 1. Ai, and are the effective densities of states per unit volume for the conduction and valence bands. In terms of these densities of states, n andp are given in equations 4 and... 

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... 

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. 

How can such problems be counterbalanced Since a large capacitance of a semiconductor/electrolyte junction will not negatively affect the PMC transient measurement, a large area electrode (nanostructured materials) should be selected to decrease the effective excess charge carrier concentration (excess carriers per surface area) in the interface. PMC transient measurements have been performed at a sensitized nanostructured Ti02 liquidjunction solar cell.40 With a 10-ns laser pulse excitation, only the slow decay processes can be studied. The very fast rise time cannot be resolved, but this should be the aim of picosecond studies. Such experiments are being prepared in our laboratory, but using nanostructured... 

Evaporation temperature, c Ag atoms flow intensity, isotope method, atoms s l Current carrier concentration variation rate in the film, semiconductor sensor method, Vg- 10 , electrons s Ve... 

The method of semiconductor sensors allows one to determine the flux of atoms, to which the sensor was exposed, from electric conductivity measurements (provided coefficients of ionization and reflection of oxygen atoms from zinc oxide films are known). In other words, the sensor technique can be used in this case as an absolute method [21]. Indeed, variation of electric conductivity of a semiconductor film Acrpi due to adsorption is known to be caused by variation of carrier concentration An in the film, rather than by variation of their mobility / [21] ... 

Fig. 4.12 Dependence of concentrations of negative charge carriers (ne) and positive charge carriers (np) on distance from the interface between the semiconductor (sc) and the electrolyte solution (1) in an w-type semiconductor. These concentration distributions markedly differ if the semiconductor/electrolyte potential difference A cp is (A) smaller than the flat-band potential AF

Perhaps not surprisingly, the most thorough NMR studies of Knight shifts, Korringa relaxation, metal-insulator transitions, and the NMR of the dopant nuclei themselves have been carried out for doped silicon. Since few semiconductors other than PbTe, which presents a considerably more complicated case, have been studied in such detail, it is worthwhile here to summarize salient points from these studies. They conveniently illustrate a number of points, and can shed light on the behavior to be expected in more contemporary studies of compound semiconductors, which are often hindered by the lack of availability of a suite of samples of known and widely-varying carrier concentrations. 

Figure 4.22 Schematic diagram of a field effect transistor. The silicon-silicon dioxide system exhibits good semiconductor characteristics for use in FETs. The free charge carrier concentration, and hence the conductivity, of silicon can be increased by doping with impurities such as boron. This results in p-type silicon, the p describing the presence of excess positive mobile charges present. Silicon can also be doped with other impurities to form n-type silicon with an excess of negative mobile charges.

An electric field in the semiconductor may also produce passivation, as depicted in Fig. 6.1c. In semiconductors the concentration of free charge carriers is smaller by orders of magnitude than in metals. This permits the existence of extended space charges. The concept of pore formation due to an SCR as a passivating layer is supported by the fact that n-type, as well as p-type, silicon electrodes are under depletion in the pore formation regime [Ro3]. In addition a correlation between SCR width and pore density in the macroporous and the mesoporous regime is observed, as shown in Fig. 6.10 [Thl, Th2, Zh3, Le8]. 

For an n-type semiconductor, if the donor impurity concentration is much greater than the intrinsic carrier concentration, Nd >nj, then no Nd. Equation (3.4.9) can then be written as... 

Eishchuk II, Arkhipov VI, Kadashchuk A, Heremans P, Bassler H (2007) Analytic model of hopping mobility at large charge carrier concentrations in disordered organic semiconductors polarons versus bare charge carriers. Phys Rev B 76 045210... 

It would seem that the carrier identification would be readily resolved by experiment. In fact, numerous experiments have found the carriers to be electrons in BaPb B Og (78)(79), the carrier concentration and Tc readily scaling with Bi content until a CDW decreases the carrier density. This interpretation is well supported by a magnetic susceptibility study (80). Even though the parent compound BaBiOg is a hole type semiconductor (81), the carrier type has been shown to be n or electronic in character (75) in Ba K BiOg. 

Calculate conductivity from charge carrier concentration, charge, and mobility. Differentiate between a conductor, insulator, semiconductor, and superconductor. Differentiate between an intrinsic and an extrinsic semiconductor. 

As the mobilities are likely to depend on temperature only as a simple power law over an appropriate region, the temperature dependence on conductivity will be dominated by the exponential dependence of the carrier concentration. We will have more to say about carrier mobility in the section on semiconductors. 

---