Effective masses of electrons and holes

Lead(II) sulfide occurs widely as the black opaque mineral galena, which is the principal ore of lead. The bulk material has a band gap of 0.41 eV, and it is used as a Pb " ion-selective sensor and IR detector. PbS may become suitable for optoelectronic applications upon tailoring its band gap by alloying with II-VI compounds like ZnS or CdS. Importantly, PbS allows strong size-quantization effects due to a high dielectric constant and small effective mass of electrons and holes. It is considered that its band gap energy should be easily modulated from the bulk value to a few electron volts, solely by changing the material s dimensionality. 

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...

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. 

Here /ie and are effective masses of electron and hole, respectively. Near to bottom of conductivity band and near to top of valent band where dependence E from k is close to parabolic, electron and hole move under action of a field as particles with effective masses fie — h2l(d2Ec(k)ldk1) and jUh = —h2l( E (k)ldk ) [6]. In particular, in above-considered onedimensional polymer semiconductor /ie — /ih — h2AEQj2PiP2d2 [6]. As a first approximation, it is possible to present nanocrystal as a sphere with radius R, which can be considered as a potential well with infinite walls [6], The value of AE in such nanocrystal is determined by the transition energy between quantum levels of electron and hole, with the account Coulomb interaction between these nanoparticles. 

The proportionality constant between the applied electric field and the resulting drift velocity is called the charge carrier mobility, jx. For electrons, = q r /ml ), for holes, ftp = 7(Trn/mj ). It should be noted that, owing to differences in the effective masses of electrons and holes, their mobilities within a semiconductor may be markedly different. The electrical conductivity, a, of a semiconductor is related to the free carrier concentrations by ... 

The effective masses of electrons and holes are estimated by parabolic approximation a large curvature corresponds to a small effective mass and a small curvature corresponds to a large mass. With this band concept, light absorption and luminescence are interpreted as follows Light is absorbed by the transition from valence band to conduction band. Therefore, the broadening of the absorption spectrum originates basically from the one dimensionality of the joint density of states, which is described by (E - g) . Excited electrons and holes relax to the bottom of the bands and then recombine radiatively. Therefore, the photoluminescence of the spectrum is very sharp. The energy difference between two peaks is called the Stokes shift. 

Electron and hole effective masses of various SiC polytypes have been determined by various methods, such as Hall measurements, Faraday rotation, Zeeman splitting of a photoluminescence line, electron cyclotron resonance, and infrared light reflection. There have also been several theoretical studies of the effective masses of 3C-SiC. The effective masses of electrons and holes thus obtained are listed in TABLE 1. 

Assuming that the effective mass of electrons and holes is independent of temperature, we obtain... 

Estimate the number of intrinsic electrons, n, and holes, p, and the product np, for a crystal of silicon at 300 K taking the effective mass of electrons and holes as equal to the electron rest mass, mg. The band gap. Eg, is 1.12 eV. 

A thin film of silver oxide, Ag20, forms on a silver surface. The band gap for silver oxide is 2.25 eV. What colour would be emitted by bulk silver oxide Treating the thin film as a quantum well, what film thickness is needed to obtain an emission in the blue region of the spectrum, at a wavelength of 413 nm Assume that the effective mass of electrons and holes in AgaO is equal to 0.3me. 

A film of zinc sulphide, ZnS, 4 nm in thickness, forms on metallic zinc. Treating the film as a quantum well, what is the wavelength of the transition Am = 2 The band-gap of ZnS is 3.54 eV, and the effective mass of electrons and holes is 0.4mi . 

Here, m and hole m are the effective masses of electron and hole, h is Plank s constant, and is the bandgap of the bulk material. The second term is the kinetic energy term. Third term corresponds to the Coulombic interaction between the electron and hole. 

The band gap of QDs can be expressed by the Schrodinger wave equation where me and mh, , h, and e are the effective masses of electrons and holes, optical dielectric constant, reduced Planck s constant, and charge of an electron, respectively. 

Table 4.1- -65 Effective masses of electrons ( ) and holes (mp) for gallium compounds (in units of the electron mass mo) ...

Here m i and mj are the effective masses of the electron and hole, respectively. For an estimate of the intrinsic charge carrier concentration, n, in a liquid insulator we may assume the effective masses of electron and hole to be equal to the free electron mass (0.91 x 10" kg). Equation 11 then becomes... 

One of the favorite materials studied so far is PbSe. Its advantage is that the effective mass of electrons and holes in a nanocrystal is nearly the same, that is, it can be expected that the energy levels are split symmetrically within the conduction and valence band with respect to the middle of the gap. The size dependence of the absorption spectra looks similarly as that determined for InP (compare with Figure 9.5). PbSe is also of great interest because the energy gap of the bulk material is 0.28 eV which makes it possible to study relaxation effects over a large range... 

Tableir.l-W Effective masses of electrons ( ) and holes (/Wp) for aluminium compounds (in units of the electron mass mo). Aluminium nitride (AIN), calculated values aluminium phosphide (AIP), calculated from band structure aluminium arsenide (AlAs), calculated from band structure data Aluminium antimonide (AlSb), theoretical estimates...

The effective mass model can be used in conjunction with the UVA isible spectrum of the CdS colloid to determine the approximate particle size (13). In this model, the effective mass of electrons and holes is determined by their interactions with other electrostatic charges within the lattice. Eqnation 2 shows how the semicondnctor band gap is related to the particle size ... 

The effective masses of electrons and holes can be measrued by irradiating the material with circularly polarized radio frequency (microwave) radiation in the presence of a magnetic field. The equation of motion is... 

Effective masses of electrons and holes have not been obtained experimentally and were deduced by a calculation (123). 

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