tween energy levels equal to a desired photon energy. Furthermore, the photoluminescence intensity is enhanced because of carrier confinement. These properties are advantageous in fabrication of lasers and photodetectors If a quantum well is placed between two thin barriers, the tunneling probability is greatly enhanced when the energy level in the quantum well coincides with the Fermi energy(resonant tunneling). The distance between nis"resonant"energy level and the Fermi level is controlled by the applied voltage. Consequently, the current peaks at the voltage corresponding to the resonant tunneling condition. The resulting negative differential resistance effect has been used to fabricate microwave generators operating at both room and cryogenic temperatures. Two kinds of superlattices are possible: compositional and doping Compositional superlattices are made of alternating layers of semiconductors with different energy gaps. Doping superlattices consist of alternating and p-type layers of the same semiconductor. The potential is modulated by electric fields arising from the charged dopants. Compositional superlattices can be grown as lattice matched or as strained layers. The latter are used for modification of the band structure, which depends on the lattice constant to produce desirable properties. In superlattices energy levels of individual quantum wells are split into minibands as a result of electron if the electro free perlattice period. In such structures the electron motion perpendicular to the layer is quantized. In a one dimensional tight binding approximation the miniband can be described as E(k)=Ell-cos(ka) (22.19) where a is the superlattice period and Eo is the half-width of the energy band. The electron group velocity h-lde(k)/ok=(e a/h) sin (ka) (2220) is a decreasing function of k(and hence of energy)for k> T/a. The higher energy states with k> T/2a may become occupied if the electrons are heated by the external field. As a result, a negative differential resistance can be achieved at high electric fields. The weak-field mobility in a superlattice may exceed that of the bulk material because of the separation of dopants if only barriers are doped In such modulated structures, the increased spatial separation between electrons and holes is also responsible for a strong increase in recomb nation lifetimes Disordered Semiconductors Both amorphous and heavily doped semiconductors are finding increasing applications in semiconductor technol- ogy. The electronic processes in these materials have specific features arising from the lack of long-range order. Amorphous semiconductors do not have a crystalline lattice, and their properties are determined by the arrangement of the nearest neighboring atoms. Even so, experimental data show that the forbidden energy band concept can be applied to characterize their electrical properties. However, the disordered nature of these materials results in a large number of localized quantum states with energies within the energy gap. The localized states in the upper and lower half of the gap behave like acceptors and donors, respectively. As an example, consider the density of states in hydrogenated amorphous silicon(a-Si)shown in Fig 22. 8. The distribution of the localized states is not symmetrical with respect to the middle of the energy gap. In particular, the undoped hydrogenated amorphous silicon is an n-type semiconductor. Usually amorphous semiconductors are not sensitive to the presence of impurity atoms, which saturate all their chemical bonds in the flexible network of the host atoms.( Compare this with a situation in crystallin silicon where an arsenic impurity can form only four chemical bonds with the host lattice, leaving the fifth responsible for the formation of the donor state. )Consequently, the doping of amorphous semiconductors difficult to accomplish. However, in hydrogenated a-Si(which can be prepared by the glow discharge decom position of silane), the density of the localized states is considerably reduced and the conductivity of this material can be controlled by doping. As in crystalline semiconductors, the charge carrier concentration in hydrogenated e 2000 by CRC Press LLC© 2000 by CRC Press LLC between energy levels equal to a desired photon energy. Furthermore, the photoluminescence intensity is enhanced because of carrier confinement. These properties are advantageous in fabrication of lasers and photodetectors. If a quantum well is placed between two thin barriers, the tunneling probability is greatly enhanced when the energy level in the quantum well coincides with the Fermi energy (resonant tunneling). The distance between this “resonant” energy level and the Fermi level is controlled by the applied voltage. Consequently, the current peaks at the voltage corresponding to the resonant tunneling condition. The resulting negative differential resistance effect has been used to fabricate microwave generators operating at both room and cryogenic temperatures. Two kinds of superlattices are possible: compositional and doping. Compositional superlattices are made of alternating layers of semiconductors with different energy gaps. Doping superlattices consist of alternating n￾and p-type layers of the same semiconductor. The potential is modulated by electric fields arising from the charged dopants. Compositional superlattices can be grown as lattice matched or as strained layers. The latter are used for modification of the band structure, which depends on the lattice constant to produce desirable properties. In superlattices energy levels of individual quantum wells are split into minibands as a result of electron tunneling through the wide-bandgap layers. This occurs if the electron mean free path is larger than the superlattice period. In such structures the electron motion perpendicular to the layer is quantized. In a one￾dimensional tight binding approximation the miniband can be described as (22.19) where a is the superlattice period and Eo is the half-width of the energy band. The electron group velocity v = \–1¶E(k)/¶k = (Eoa/\) sin(ka) (22.20) is a decreasing function of k (and hence of energy) for k > p/2a. The higher energy states with k > p/2a may become occupied if the electrons are heated by the external field. As a result, a negative differential resistance can be achieved at high electric fields. The weak-field mobility in a superlattice may exceed that of the bulk material because of the separation of dopants if only barriers are doped. In such modulated structures, the increased spatial separation between electrons and holes is also responsible for a strong increase in recombi￾nation lifetimes. Disordered Semiconductors Both amorphous and heavily doped semiconductors are finding increasing applications in semiconductor technol￾ogy. The electronic processes in these materials have specific features arising from the lack of long-range order. Amorphous semiconductors do not have a crystalline lattice, and their properties are determined by the arrangement of the nearest neighboring atoms. Even so, experimental data show that the forbidden energy band concept can be applied to characterize their electrical properties. However, the disordered nature of these materials results in a large number of localized quantum states with energies within the energy gap. The localized states in the upper and lower half of the gap behave like acceptors and donors, respectively. As an example, consider the density of states in hydrogenated amorphous silicon (a-Si) shown in Fig. 22.8. The distribution of the localized states is not symmetrical with respect to the middle of the energy gap. In particular, the undoped hydrogenated amorphous silicon is an n-type semiconductor. Usually amorphous semiconductors are not sensitive to the presence of impurity atoms, which saturate all their chemical bonds in the flexible network of the host atoms. (Compare this with a situation in crystalline silicon where an arsenic impurity can form only four chemical bonds with the host lattice, leaving the fifth responsible for the formation of the donor state.) Consequently, the doping of amorphous semiconductors is difficult to accomplish. However, in hydrogenated a-Si (which can be prepared by the glow discharge decom￾position of silane), the density of the localized states is considerably reduced and the conductivity of this material can be controlled by doping. As in crystalline semiconductors, the charge carrier concentration in hydrogenated E k E ka o ( ) = [1 - cos( )]