Hole energy levels

Figures. Radiative transition rates between electron and hole energy levels in 3.1 nm diameter quantum dot.

The calculation of the hole levels is much more complicated since the band structure of many important semiconductors has hole bands with fourfold degeneracy at k = 0. This leads to heavy and light holes with different effective masses. Consequendy, a double set of hole energy levels is formed in the QW with different spacings between levels—one set for the light holes, the second set for the heavy holes, as shown in Fig. 3.3. Solutions to the problem have been reported for both infinite (Bastard, 1981 Altarelli, 1985) and finite (Bastard and Brum, 1986) potential barriers. 

The saturation of the built-in potential in die Pt-Ca and the Al-Sm structures is caused by charging intrinsic states in the MEH-PPV fdm. The energy gap of MEH-PPV is about 2.4 eV with the electron and hole energy levels at about... 

The electronic properties of the new superlattice materials help to shed light on some major fundamental questions in amorphous semiconductors. Quantum size effects in the case of crystalline superlattices raise the lowest allowed electron and hole energy levels and give rise to a density of states that increases in discrete steps. This structure in the density of states is reflected in... 

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 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 uncertainty principle, according to which either the position of a confined microscopic particle or its momentum, but not both, can be precisely measured, requires an increase in the carrier energy. In quantum wells having abmpt barriers (square wells) the carrier energy increases in inverse proportion to its effective mass (the mass of a carrier in a semiconductor is not the same as that of the free carrier) and the square of the well width. The confined carriers are allowed only a few discrete energy levels (confined states), each described by a quantum number, as is illustrated in Eigure 5. Stimulated emission is allowed to occur only as transitions between the confined electron and hole states described by the same quantum number. 

Fig. 5. Energy levels of electrons and heavy holes confined to a 6-nm wide quantum well, Iuq 53GaQ 4yAs, with InP valence band, AE and conduction band, AE barriers. In this material system approximately 60% of the band gap discontinuity Hes in the valence band. Teasing occurs between the confined...

The equihbtium lever relation, np = can be regarded from a chemical kinetics perspective as the result of a balance between the generation and recombination of electrons and holes (21). In extrinsic semiconductors recombination is assisted by chemical defects, such as transition metals, which introduce new energy levels in the energy gap. The recombination rate in extrinsic semiconductors is limited by the lifetime of minority carriers which, according to the equihbtium lever relation, have much lower concentrations than majority carriers. Thus, for a -type semiconductor where electrons are the minority carrier, the recombination rate is /S n/z. An = n — is the increase of the electron concentration over its value in thermal equihbtium, and... 

A hst of some impurity semiconductors is given in Table 5. Because impurity atoms introduce new localized energy levels for electrons that are intermediate between the valence and conduction bands, impurities strongly influence the properties of semiconductors. If the new energy levels are unoccupied and He close to the top of the valence band, electrons are easily excited out of the filled band into the new acceptor levels, leaving electron holes... 

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. 

Figure 11-9. Measured (solid lines) and calculated (dashed lines) current density us a (unction o( voltage bias for MBH-PPV devices o( about 110 nut in thickness with Au us the electron injecting contact and Pt, Au, Cu. and Al us the hole injecting contact. The upper panel shows a schematic energy level diagram for the structures.

Figure 11-13. Calculated current density as a limelion of bias lor two-layer hole-only structures (0.1 eV injection barrier lor holes) with a 0.0, 0.3, and 0.5 eV energy harrier for holes at the interface between the polymer layers. The upper panel is a schematic of the energy level diagram for the sttuc-turcs.

The high electrical conductivity of metals as well as the high electron (and hole) mobility of inorganic covalently bound semiconductors have both been clarified by the band theory [I9, which slates that the discrele energy levels of individual atoms widen in the solid stale into alternatively allowed and forbidden bands. The... 

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