Impurity states in semiconductors

A common application of extrinsic point defects is the doping of semiconductor crystals. This is a physical process of crucial importance to the operation of modem 

One important aspect of the impurity-related states is the effective mass of charge carriers (extra electrons or holes) due to band-structure effects, these can have an effective mass which is smaller or larger than the electron mass, described as light or heavy electrons or holes. We recall from our earlier discussion of the behavior of electrons in a periodic potential (chapter 3) that an electron in a crystal has an inverse effective mass which is a tensor, written as [(/n) ]o . The inverse effective mass depends on matrix elements of the momentum operator at the point of the BZ where it is calculated. At a given point in the BZ we can always identify the principal axes which make the inverse effective mass a diagonal tensor, i.e. [(m) ]a = as discussed in chapter 3. The energy of electronic 

We will assume the impurity has an effective charge which is the difference between the valence of the impurity and the valence of the crystal atom it replaces with this dehnition can be positive or negative. The potential that the presence of the impurity creates is then 

Substituting the expansion (9.15) into Eq. (9.16) and using the orthogonality of the crystal wavefunctions we obtain 

If we express the crystal wavefunctions in the familiar Bloch form, 

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An examination of the experimentally determined depth of various impurity states in semiconductors shows that the more covalent a semiconductor (the smaller the chemical splitting) the higher the defect formation energy and the farther states associated with that defect are from the appropriate band edge. This can be understood based on the approach outlined in Section 5.1. 

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. 

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. 

In this Datareview, we concentrate on deep levels measured by capacitance and admittance techniques those measured by other techniques are detailed in Datareview 4.1. For completeness, trap parameters for major defects and impurities obtained from all techniques are listed. Capacitance techniques have proven useful for the characterisation of deep states in semiconductor devices. In particular, states which are non-radiative can be analysed by this technique. If the state under study is one which principally determines the conductivity of the crystal, the techniques of admittance spectroscopy are used. The set-up for doing capacitance and admittance spectroscopy on SiC is identical to that used for other semiconductors with the exception of the necessity to operate the system at higher temperatures in order to access potentially deeper levels in the energy gap. The data are summarised in TABLE 1. 

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... 

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.

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. 

Several factors detennine how efficient impurity atoms will be in altering the electronic properties of a semiconductor. For example, the size of the band gap, the shape of the energy bands near the gap and the ability of the valence electrons to screen the impurity atom are all important. The process of adding controlled impurity atoms to semiconductors is called doping. The ability to produce well defined doping levels in semiconductors is one reason for the revolutionary developments in the construction of solid-state electronic devices. 

Electrochemical reactions at semiconductor electrodes have a number of special features relative to reactions at metal electrodes these arise from the electronic structure found in the bulk and at the surface of semiconductors. The electronic structure of metals is mainly a function only of their chemical nature. That of semiconductors is also a function of other factors acceptor- or donor-type impurities present in bulk, the character of surface states (which in turn is determined largely by surface pretreatment), the action of light, and so on. Therefore, the electronic structure of semiconductors having a particular chemical composition can vary widely. This is part of the explanation for the appreciable scatter of experimental data obtained by different workers. For reproducible results one must clearly define all factors that may influence the state of the semiconductor. 

The total energy of the system is one of the most important results obtained from any of the calculational techniques. To study the behavior of an impurity (in a particular charge state) in a semiconductor one needs to know the total energy of many different configurations, in which the impurity is located at different sites in the host crystal. Specific sites in the diamond or zinc-blende structure have been extensively studied because of their relatively high symmetry. Figure 1 shows their location in a three-dimensional view. In Fig. 2, some sites are indicated in a (110) plane... 

In addition to the electron energy bands and impurity levels in the semiconductor interior, which are three-dimensional, two-dimensional localized levels in the band gap exist on the semiconductor surface as shown in Fig. 2-28. Such electron levels associated with the surface are called surface states or interfacial states, e . The siuface states are classified according to their origin into the following two categories (a) the surface dangling state, and (b) the surface ion-induced state. 

The properties of the band gap in semiconductors often control the applicability of these materials in practical applications. To give just one example, Si is of great importance as a material for solar cells. The basic phenomenon that allows Si to be used in this way is that a photon can excite an electron in Si from the valence band into the conduction band. The unoccupied state created in the valence band is known as a hole, so this process has created an electron-hole pair. If the electron and hole can be physically separated, then they can create net electrical current. If, on the other hand, the electron and hole recombine before they are separated, no current will flow. One effect that can increase this recombination rate is the presence of metal impurities within a Si solar cell. This effect is illustrated in Fig. 8.4, which compares the DOS of bulk Si with the DOS of a large supercell of Si containing a single Au atom impurity. In the latter supercell, one Si atom in the pure material was replaced with a Au atom,... 

We first note that an isolated atom with an odd number of electrons will necessarily have a magnetic moment. In this book we discuss mainly moments on impurity centres (donors) in semiconductors, which carry one electron, and also the d-shells of transitional-metal ions in compounds, which often carry several In the latter case coupling by Hund s rule will line up all the spins parallel to one another, unless prevented from doing so by crystal-field splitting. Hund s-rule coupling arises because, if a pair of electrons in different orbital states have an antisymmetrical orbital wave function, this wave function vanishes where r12=0 and so the positive contribution to the energy from the term e2/r12 is less than for the symmetrical state. The antisymmetrical orbital state implies a symmetrical spin state, and thus parallel spins and a spin triplet. The two-electron orbital functions of electrons in states with one-electron wave functions a(x) and b(x) are, to first order,... 

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