Energy level shallow

All teclmologically important properties of semiconductors are detennined by defect-associated energy levels in the gap. The conductivity of pure semiconductors varies as g expf-A CgT), where is the gap. In most semiconductors with practical applications, the size of the gap, E 1-2 eV, makes the thennal excitation of electrons across the gap a relatively unimportant process. The introduction of shallow states into the gap through doping, with either donors or acceptors, allows for large changes in conductivity (figure C2.16.1). The donor and acceptor levels are typically a few meV below the CB and a few tens of meV above the VB, respectively. The depth of these levels usually scales with the size of the gap (see below). 

Shallow impurities have energy levels in the gap but very close to a band. If an impurity has an empty level close to the VB maximum, an electron can be thennally promoted from the VB into this level, leaving a hole in the VB. Such an impurity is a shallow acceptor. On the other hand, if an impurity has an occupied level very close to the CB minimum, the electron in that level can be thennally promoted into the CB where it participates in the conductivity. Such an impurity is a shallow donor. 

The simplest example is that of tire shallow P donor in Si. Four of its five valence electrons participate in tire covalent bonding to its four Si nearest neighbours at tire substitutional site. The energy of tire fiftli electron which, at 0 K, is in an energy level just below tire minimum of tire CB, is approximated by rrt /2wCplus tire screened Coulomb attraction to tire ion, e /sr, where is tire dielectric constant or the frequency-dependent dielectric function. The Sclirodinger equation for tliis electron reduces to tliat of tlie hydrogen atom, but m replaces tlie electronic mass and screens the Coulomb attraction. 

The impurity atoms used to form the p—n junction form well-defined energy levels within the band gap. These levels are shallow in the sense that the donor levels He close to the conduction band (Fig. lb) and the acceptor levels are close to the valence band (Fig. Ic). The thermal energy at room temperature is large enough for most of the dopant atoms contributing to the impurity levels to become ionized. Thus, in the -type region, some electrons in the valence band have sufficient thermal energy to be excited into the acceptor level and leave mobile holes in the valence band. Similar excitation occurs for electrons from the donor to conduction bands of the n-ty e material. The electrons in the conduction band of the n-ty e semiconductor and the holes in the valence band of the -type semiconductor are called majority carriers. Likewise, holes in the -type, and electrons in the -type semiconductor are called minority carriers. 

The X-ray emission process followii the excitation is the same in all three cases, as it is also for the electron-induced X-ray emission methods (EDS and EMPA) described in Chapter 3. The electron core hole produced by the excitation is filled by an electron falling from a shallower level, the excess energy produced being released as an emitted X ray with a wavelength characteristic of the atomic energy levels involved. Thus elemental identification is provided and quantification can be obtained from intensities. The practical differences between the techniques come from the consequences of using the different excitation sources. 

The conclusion regarding the fact that constant current conductivity involves not all microcrystals of the sample is proved by results of measurements of electric conductivity in sintered ZnO films in case of alternating current (Fig. 2.10). The availability of barrier-free ohmic pathways is proved by a low value of initial resistivity in sintered samples ( 1 - 5 kOhm) in addition to exponential dependence of electric conductivity plotted as a function of inverse temperature having activation energy 0.03 - 0.5 eV, which coincides with ionization energy of shallow dope levels. The same value is obtained from measurements of the temperature dependence of the Hall constant [46]. 

The chemisorbed reaction product can be characterized by more shallow positioning of the energy level with respect to the bottom of conductivity band if contrasted to Z (A ) which results in emission of electron into the conductivity band in compliance with reaction... 

Shallow levels play an important part in electronic conductivity. Shallow donor levels lie close to the conduction band in energy and liberate electrons to it to produce n-type semiconductors. Interstitial metal atoms added to an insulating ionic oxide often act in this way because metal atoms tend to ionize by losing electrons. When a donor level looses one or more electrons to the conduction band, it is said to be ionized. The energy level representing an ionized donor will be lower than that of the un-ionized (neutral) donor by the same amount as required to move the electron into the conduction band. The presence of shallow donor levels causes the material to become an w-type semiconductor. 

Shallow LUMO energy level to block electrons... 

The next step is the definition of deep. The choice of quantitative values will again involve some arbitrariness. However, a further complication is that there is at present no universally accepted qualitative criterion. For instance, from the point of view of energy level calculations it is often convenient to define deep states as noneffective-mass-like or as those with a localized potential (see, for example, Bassani and Pastori Parravicini, 1975 Jaros, 1980). However, the disadvantage of this definition of deep is that it includes many isoelectronic states that are very shallow on an energy scale. On the other hand, if one uses an energy criterion, should the states be deep with respect to some fraction of the band gap, with respect to kT, or with respect to some shallow levels In this chapter we shall adopt an energy criterion for deep, and we shall require that our states be deep enough to be important in recombination. The importance of deep levels in recombination under many conditions of practical interest was already realized in the early work of Hall... 

Despite the success of purely optical methods such as luminescence and absorption in studying shallow energy levels, they are seldom used for characterization of deep states. This is mainly because the deeper levels of interest are usually nonradiative ones or killer centers for which such techniques are not applicable. In addition, the deep position within the energy gap means optical experiments must be performed in the infrared where... 

Figure 6.19 A schematic version of the potential energy well derived from the Fermi gas model. The highest filled energy levels reach up to the Fermi level of approximately 32 MeV. The nucleons are hound hy approximately 8 MeV, so the potential energy minimum is relatively shallow.

Fig. 2. The energy levels as a function of trap depth S for the onedimensional mixed crystal with guest concentration The manifold shown belongs to r = 0. The dotted curves are plots of the shallow-trap (left-hand) and deep-trap (right-hand) limiting approximations.

Note that this reasoning on the dependence of parameter A on the location depth of the recombination site has only a qualitative character. The actual samples of CdS have always a particle size distribution. Both the quencher adsorption constant and the luminescence emission spectrum depend on the particle size. This introduces a certain error into the A value obtained from fitting by the Eq. (2.19). The error should be particularly great for the deep and shallow energy levels of the surface recombination site. 

A deeper insight into the lateral electrical homogeneity of the films, the limiting mechanisms of the Hall mobility, and the thermal activation energies of shallow and deep defect levels can be gained by temperature-dependent Hall and deep level transient spectroscopy (DLTS) measurements [57,59,60]. To give an example, the temperature dependence of the Hall mobility and... 

In high resistivity GaN films, Glaser and co-workers observed ODMR on a broad band peaked at 3 eV and observed a second deep donor state at g = 1.978 [29]. Because the g value is between the effective mass donor and that of the first deep donor, they argued that the energy level was shallower than the first deep donor. Koschnick and co-workers [30] have also resolved a donor resonance atg - 1.96 in undoped fihns and a possibly different donor (also at g 1.96) in Mg-doped fihns using high frequency (70 GHz) ODMR. The existence of multiple donor levels was first proposed by Gotz and co-workers [31] based on their electrical measurements and these results seem to confirm that idea. 

If we consider a sample with shallow Gaussian traps and include PEE, the sample behaves as if there are no traps and the mobility is field dependent given by Eq. (3.56) far as the dependence of J on V is concerned. The zero field mobility and its temperature dependence are different in the two equations. If the traps are at a single energy level, <7t = 0 and the temperature variation of the mobility also becomes the same in the two cases. Eq. (3.58) represents both the models, it reduces to the existing shallow trap model (without PEE) when = 0 and to the existing field dependent mobility model when 6 = exp(-EtfkT). 

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