Conduction effective mass

In the classical electron transport model in metals or semiconductors, for a material with a free electron concentration n and an average electron scattering time (also called relaxation time) r, the DC conductivity is Oo = ne2r/to. In this classical expression, m (m or m ) is the conductivity effective mass, which is an average mass different from the DoS effective mass (see for instance [4]. In cubic semiconductors with degenerate CB extrema, the conductivity effective mass for electrons is ... 

At slightly lower frequencies, for u>2 = ujp/eoo, n goes to zero and the reflectance rises to values near unity. The determination of ujr=o when the free-carrier concentration and are known allows determination of the conductivity effective mass. For non-parabolic CBs, the values of m so obtained for different filling factors of the CB are different from those measured at the bottom of the CB. 

TABLE 2.8 Conductivity Effective Masses for Common Semiconductors... 

Reactor Configuration. The horizontal cross-sectional area of a reactor is a critical parameter with respect to oxygen mass-transfer effects in LPO since it influences the degree of interaction of the two types of zones. Reactions with high intrinsic rates, such as aldehyde oxidations, are largely mass-transfer rate-limited under common operating conditions. Such reactions can be conducted effectively in reactors with small horizontal cross sections. Slower reactions, however, may require larger horizontal cross sections for stable operation. 

Near a conduction band minimum the energy of electrons depends on the momentum ia the crystal. Thus, carriers behave like free electrons whose effective mass differs from the free electron mass. Their energy is given by equation 1, where E is the energy of the conduction band minimum, is the... 

Remarkably, although band stmcture is a quantum mechanical property, once electrons and holes are introduced, theit behavior generally can be described classically even for deep submicrometer geometries. Some allowance for band stmcture may have to be made by choosing different values of effective mass for different appHcations. For example, different effective masses are used in the density of states and conductivity (26). 

Where b is Planck s constant and m and are the effective masses of the electron and hole which may be larger or smaller than the rest mass of the electron. The effective mass reflects the strength of the interaction between the electron or hole and the periodic lattice and potentials within the crystal stmcture. In an ideal covalent semiconductor, electrons in the conduction band and holes in the valence band may be considered as quasi-free particles. The carriers have high drift mobilities in the range of 10 to 10 cm /(V-s) at room temperature. As shown in Table 4, this is the case for both metallic oxides and covalent semiconductors at room temperature. 

In most metals the electron behaves as a particle having approximately the same mass as the electron in free space. In the Group IV semiconductors, dris is usually not the case, and the effective mass of electrons can be substantially different from that of the electron in free space. The electronic sUmcture of Si and Ge utilizes hybrid orbitals for all of the valence elecU ons and all electron spins are paired within this structure. Electrons may be drermally separated from the elecU on population in dris bond structure, which is given the name the valence band, and become conduction elecU ons, creating at dre same time... 

The effective masses of holes and electrons in semiconductors are considerably less than that of the free electron, and die conduction equation must be modified accordingly using the effective masses to replace tire free electron mass. The conductivity of an intrinsic semiconductor is then given by... 

Fig. 36. Energy levels of excitonic states in CdS particles of various radii. Zero position of the lower edge of the conduction band in macrocrystalline CdS. Exc Energy of an exciton in macrocrystalline CdS. Effective masses of electrons and holes 0.19 m and 0.8 m respectively. The letters with a prime designate the quantum state of the hole...

The Schottky-Mott theory predicts a current / = (4 7t e m kB2/h3) T2 exp (—e A/kB 7) exp (e n V/kB T)— 1], where e is the electronic charge, m is the effective mass of the carrier, kB is Boltzmann s constant, T is the absolute temperature, n is a filling factor, A is the Schottky barrier height (see Fig. 1), and V is the applied voltage [31]. In Schottky-Mott theory, A should be the difference between the Fermi level of the metal and the conduction band minimum (for an n-type semiconductor-to-metal interface) or the valence band maximum (for a p-type semiconductor-metal interface) [32, 33]. Certain experimentally observed variations of A were for decades ascribed to pinning of states, but can now be attributed to local inhomogeneities of the interface, so the Schottky-Mott theory is secure. The opposite of a Schottky barrier is an ohmic contact, where there is only an added electrical resistance at the junction, typically between two metals. 

The application of an electric field E to a conducting material results in an average velocity v of free charge carriers parallel to the field superimposed on their random thermal motion. The motion of charge carriers is retarded by scattering events, for example with acoustic phonons or ionized impurities. From the mean time t between such events, the effective mass m of the relevant charge carrier and the elementary charge e, the velocity v can be calculated ... 

A very crude model to calculate the increase in bandgap energy is the effective-mass particle-in-a-box approximation. Assuming parabolic bands and infinitely high barriers the lowest conduction band (CB) level of a quantum wire with a square cross-section of side length w is shifted by AEC compared to the value Ec of the bulk crystal [Lei, Ho3] ... 

A and B being constants which need not interest us further. (We may assume that A B, which denotes approximate equality of the effective masses of free electrons and holes.) Thus, the electrical conductivity is diffeient in different cross sections parallel to the adsorbing surface (i.e., at different x). Chemisorption, by changing the bending of the bands, may lead to a noticeable change in the electrical conductivity of the subsurface layer of the crystal, which in the case of a sufficiently small crystal may effect the total electrical conductivity of the sample. Even more, so the very type of conductivity in the subsurface layer may change under the influence of chemisorption n conductivity (e < +) may go over into p conductivity (t > +), or vice versa (the so-called inversion of conductivity). 

Ncv = 2Mc v (27rm v KT/ h2 )3/2 where Mc v — the number of equivalent minima or maxima in the conduction and valence bands, respectively, and m cv = the density of states effective masses of electrons and holes. 

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