Semiconductors impurity states

Fig. 1. Photoexcitation modes iu a semiconductor having band gap energy, E, and impurity states, E. The photon energy must be sufficient to release an electron (° ) iato the conduction band (CB) or a hole (o) iato the valence band (VB) (a) an intrinsic detector (b) and (c) extrinsic donor and acceptor...

This transition has been emphasized by Mott for the case of localized impurity states in a semiconductor, forming a metallic band at some concentration of impurities (i.e. at some average distance between the impurities). It is referred to very often as the Mott (or Mott-Hubbard) transition. 

The basic idea of resonance tunneling relies on the reasonable assumption that there are impurity states in the oxide film (regarded as a semiconductor), the energy of which is in resonance with that of electrons in the metal on which the film has been formed. One considers the situation in terms of two coordinated tunnel transfers, one from the metal to the impurity state and then from the impurity state to an ion adsotbed at the oxide/solution interface. 

In the semiconductors of greater polarity, the dielectric constants are smaller and the effective masses larger, and the same evaluation leads to 0.07 eV in zinc selcnidc, for example many of the impurity states can be occupied at room temperature. As the energy of the impurity states becomes deeper, the effective Bohr radius becomes smaller and the use of the effective mass approximation becomes suspect the error leads to an underestimation of the binding energy. Thus, in semiconductors of greatest polarity- and certainly in ionic crystals— impurity states can become very important and arc then best understood in atomic terms. We will return to this topic in Chapter 14, in the discussion of ionic crystals. 

Enhancement of reactivity of incendiary components has been claimed by the introduction of impurity states, particularly into metallic oxides (Refs 56 86). Impurity states have a twofold effect they disturb the lattice structure of the oxide (and[ so increase the diffusivity of the reactants), and they disturb the electronic distribution on the surface as well as in the bulk. The argument is made that by doping the oxide, or by controlling the formation temp, one may change an oxide from an n-type to a p-type semiconductor and hence cause it to become a better electron acceptor, and vice versa... 

Doping a semiconductor by adding an electron acceptor impurity creates new states very near the top of the valence band. An electron can move to this impurity state from the valence band, leaving a positively charged hole in the valence band. The hole can move in response to an applied electric field. This doping process leads to a p-type semiconductor, in which the charge carrier is a hole. 

Defects or impurities in the semiconductor crystal structure create electronic states in the gap region. In the case of impurities, the valence character of the impurity determines whether the level acts as an electron donor or electron acceptor state. In doping semiconductors, impurities are deliberately used to generate either donor or... 

J. Chevallier, B. Pajot, Interaction of Hydrogen with Impurities and Defects in Semiconductors. Solid State Phenomena 85-86 203-284. (Scitec Publications, Switzerland, 2002)... 

The symmetry of an isolated atom is that of the full rotation group R+ (3), whose irreducible representations (IRs) are D where j is an integer or half an odd integer. An application of the fundamental matrix element theorem [22] tells that the matrix element (5.1) is non-zero only if the IR DW of Wi is included in the direct product x of the IRs of ra and < f. The components of the electric dipole transform like the components of a polar vector, under the IR l)(V) of R+(3). Thus, when the initial and final atomic states are characterized by angular momenta Ji and J2, respectively, the electric dipole matrix element (5.1) is non-zero only if D(Jl) is contained in Dx D(j 2 ) = D(J2+1) + T)(J2) + )(J2-i) for j2 > 1 This condition is met for = J2 + 1, J2, or J2 — 1. However, it can be seen that a transition between two states with the same value of J is allowed only for J 0 as DW x D= D( D(°) is the unit IR of R+(3)). For a hydrogen-like centre, when an atomic state is defined by an orbital quantum number , this can be reduced to the Laporte selection rule A = 1. This is of course formal, as it will be shown that an impurity state is the weighted sum of different atomic-like states with different values of but with the same parity P = ( —1) These states are represented by an atomic spectroscopy notation, with lower case letters for the values of (0, 1, 2, 3, 4, 5, etc. correspond to s, p, d, f, g, h, etc.). The impurity states with P = 1 and -1 are called even- and odd-parity states, respectively. For the one-valley EM donor states, this quasi-atomic selection rule determines that the parity-allowed transitions from Is states are towards np (n > 2), n/ (n > 4), nh (n > 6), or nj (n > 8) states. For the acceptor states in cubic semiconductors, the even- and odd-parity states labelled by the double IRs T of Oh or Td are indexed by + or respectively, and the parity-allowed transition take place between Ti+ and... 

The photoluminescent response is also used to study weak absorption coefficients due, for instance, to impurity states in the band gap of semiconductors, and it thus complements absorption measmements. 

The photophysical processes of semiconductor nanoclusters are discussed in this section. The absorption of a photon by a semiconductor cluster creates an electron-hole pair bounded by Coulomb interaction, generally referred to as an exciton. The peak of the exciton emission band should overlap with the peak of the absorption band, that is, the Franck-Condon shift should be small or absent. The exciton can decay either nonradiatively or radiative-ly. The excitation can also be trapped by various impurities states (Figure 10). If the impurity atom replaces one of the constituent atoms of the crystal and provides the crystal with additional electrons, then the impurity is a donor. If the impurity atom provides less electrons than the atom it replaces, it is an acceptor. When the impurity is lodged in an interstitial position, it acts as a donor. A missing atom in the crystal results in a vacancy which deprives the crystal of electrons and makes the vacancy an acceptor. In a nanocluster, there may be intrinsic surface states which can act as either donors or acceptors. Radiative transitions can occur from these impurity states, as shown in Figure 10. The spectral position of the defect-related emission band usually shows significant red-shift from the exciton absorption band. 

These lifetimes are, however, considerably longer than the sub-picosecond lifetimes typical of quantum well intersubband transitions of similar energy separation. This will aid the build up of a population inversion on the excited impurity states. In addition, the temperature stability of the intra-impurity lifetime (as measured up to 60 K), suggests that the use of the quantum dot properties of semiconductor impurities might provide a route to obtaining temperature stable far-infrared lasers. 

Volume 183 PROPERTIES OF IMPURITY STATES IN SUPERLATTICE SEMICONDUCTORS... 

In most covalent NCS it is found that AE, the thermal activation energy of the conductivity is about half the magnitude of the optical energy gap. This means that Ep is not far from the center of the mobility gap. Does this mean that these materials are intrinsic In the case of crystalline semiconductors the word intrinsic is used to mean that the conduction properties are not affected by the presence of localized impurity states. The position of Ep is then determined by the equality... 

Lerner [189] found that oxidized PAN fibers subjected to heat treatment temperatures of 715-945 K are semiconductors. The room temperature conductivity is dominated by the contributions of impurity states, but these are not related to defects in the polymer. There is a decrease in conductivity on ageing in air caused by a decrease in the electron-phonon scattering time. The conductivity increases at temperatures above 473 K, as the samples aged in air outgas. 

In n-type semiconductor, impurities like P, As are added and current flow is due to the movement of electrons from donor state to conduction band. 

Kastner M.,A.Bonding bands, lone-pair bands, and impurity states in chalcogenide semiconductors, Phys. Rev. Lett, 28, 355-357 (1972). 

Figure 9.6. Schematic illustration of shallow donor and acceptor impurity states in a semiconductor with direct gap. The light and heavy electron and hole states are also indicated the bands corresponding to the light and heavy masses are split in energy for clarity.

There are two kinds of surface states entrapment and polarization. The dangling bonds or surface impurities are subject to polarization, which add impurity states within the Eq of semiconductors. Termination of the dangling bonds by H adsorption could minimize the impurity states. The other is the entrapment in the relaxed surface region, which offsets the entire band strucmre down associated with Eq enlargement and the presence of band tails. 

Electronic polarization through a process of transition from the lower ground states (valence band, or the mid-gap impurity states) to the upper excited states in the conduction band takes the responsibility for complex dielectrics. This process is subject to the selection rule of energy and momentum conservation, which determines the optical response of semiconductors and reflects how strongly the electrons in ground states are coupling with the excited states that shift with lattice phonon frequencies [19]. Therefore, the of a semiconductor is directly related to its bandgap Eq at zero temperature, as no lattice vibration occurs at 0 K. 

Pure materials, or at least materials with no impurity states in the bandgap region, are called intrinsic semiconductors. The creation of an electron leaves a hole therefore, the number of holes must equal the number of electrons in an intrinsic material. The electron-hole product is directly proportional to the Boltzmann factor, exp —(Eg/fcT). The Fermi level, the energy for which the probability of creating a conduction electron is the same as creating a hole is shovm to be somewhere in the bandgap. 

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