Intentional impurities (dopants) can be introduced during epitaxial crystal growth in terms of either elemental doping sources or chemical compounds. This chapter is devoted to aspects of elemental doping sources and to the characteristics of these dopants. The following chapter discusses non-elemental, gaseous doping precursors. The incorporation of elemental doping impurities is mediated through thermal evaporation of the doping element from an effusion cell. Such elemental solid evaporation sources are commonly used for molecular-beam epitaxy (MBE) and related techniques discussed in Chap. 4.

Doping techniques and calibration

The incorporation of doping atoms originating from solid elemental doping sources is mediated through thermal evaporation within a vacuum environment. The solid source is heated to a temperature T at which the desired amount of the doping element evaporates. The rate of evaporation, the source and substrate geometry, and the sticking probability of impurity atoms on the crystal surface determine the incorporation rate of the impurities into the growing epitaxial crystal. These parameters are discussed below.

Doping impurity flux

The concentration of doping impurities in an epitaxial layer is usually controlled by the impurity-cell temperature. Consider an epitaxial crystal of GaAs that grows at a rate of 1 monolayer per second, i.e. at a rate of 6 × 1014 GaAs molecules per cm2 per second.

This chapter is devoted to the role of impurities in semiconductor structures which consist of different types of semiconductor materials. Semiconductor heterostructures, quantum wells and superlattices are structures in which the individual layers have spatial dimensions comparable to the carrier de Broglie wavelength. As a consequence, quantum effects cannot be neglected in such small semiconductor structures. Furthermore, the spatial dimensions of such structures can be comparable to the Bohr radius of impurities. As a consequence, the characteristics of impurities, e.g. ionization energy and wave function, are changed. The area of quantum semiconductor physics has gained much interest since the 1970s. The physical properties of several semiconductor quantum structures are closely related to the doping and to residual impurities in such structures. Among these structures are selectively doped heterostructures, doping superlattices, doped quantum wells, and doped quantum barriers, which will be discussed in this chapter.

Selectively doped heterostructures

Selectively doped heterostructures are structures which consist of a doped widegap semiconductor and an undoped narrow-gap semiconductor. Selectively doped heterostructures were first realized by Stormer et al. (1978) and Dingle et al. (1978) in an attempt to reduce scattering of carriers by ionized impurities. The electron mobilities obtained in AlxGa1−xAs/GaAs heterostructures at low temperatures can exceed 107 cm2/V s (Pfeiffer et al., 1989a).

The two growth technologies molecular-beam epitaxy (MBE) and vapor-phase epitaxy (VPE) are frequently employed for epitaxial growth, i.e. the crystalline growth of a thin layer on a crystalline substrate. High-quality epitaxial semiconductors with well controlled doping, composition, and thickness can be grown by MBE and VPE. Furthermore, the two growth methods MBE and VPE are capable of growing atomically abrupt doping and compositional profiles. This chapter covers the basic concepts of MBE, VPE, and related growth technologies.

Molecular-beam epitaxy

Molecular-beam epitaxy (MBE) is a powerful epitaxial growth technique whose historical origin dates back to the 1950s when Günther (1958) developed the ‘three temperature method’. For the epitaxial growth of a compound semiconductor, e.g. GaAs, by coevaporation, the temperatures of the effusion cells (Ga and As) and the GaAs substrate must conform with the three temperature rule. Günther showed that the substrate temperature must be between the two effusion cell temperatures for stoichiometric growth. In the experiments of Günther, the temperature of the group-V oven (As, Sb) was much lower than the temperature of group-III (In) oven. The substrate temperature was kept at a temperature between the two oven temperatures. Stoichiometric, polycrystalline growth of InAs and InSb was demonstrated on glass substrates using the three temperature method. The choice of the group-V to group-III flux ratio is of crucial importance.

Doping and other materials parameters influence the properties of III–V devices in a profound manner. Examples of device parameters which are strongly influenced by the defect and doping concentration are the radiative efficiency of a laser, the minority carrier lifetime in the base of a bipolar transistor, the carrier mobility in the channel of a field-effect transistor, or the quantum efficiency of a pin photo-diode. In this chapter, characterization techniques are discussed that relate directly to shallow impurities as well as deep centers. The characterization techniques are categorized as (i) electronic (ii) optical, and (iii) chemical and structural techniques. Fundamental aspects of characterization techniques as well as practical ‘hints’ for the experimentalist are emphasized.

Electronic characterization techniques

Many properties of semiconductors that relate directly to impurities or defects can be assessed by electrical measurements. Such measurements include current–voltage, capacitance–voltage, resistivity, magnetoresistance, and impedance measurements. Frequently, temporal transients of such measurements are of interest, for example the capacitance transient after a semiconductor has been subjected to an electrical pulse. In this section, the Hall effect, capacitance–voltage (CV) profiling technique, deep level transient spectroscopy (DLTS), thermally stimulated capacitance (TSCAP), thermally stimulated current (TSC), and admittance spectroscopy are discussed.

Hall effect measurements

Hall effect measurements (Hall, 1879) allow one to determine the (majority) Hall carrier concentration of unipolar semiconductors in which the minority carrier concentration can be neglected.

Deep centers are chemical impurities, native defects, or a combination of both, which have at least one energy level in the forbidden gap. The energy level or levels of deep centers are far removed from the conduction and valence band edges, which is in contrast to shallow impurities. The phenomenology of deep centers was discussed and analyzed in Chap. 2. In the present chapter, the characteristics of some specific deep centers will be summarized.

The DX-center is of primary technological importance in n-type AlxGa1−x As devices such as transistors and lasers. The properties of this center have puzzled researchers for more than a decade. The EL2 center can cause undoped bulkgrown GaAs to be semi-insulating. The EL2 center is of importance for the growth of GaAs bulk crystals and for the production of substrates. Hydrogen can be used in two different ways to influence the electronic properties of III–V semiconductors. First, protons implanted into III–V semiconductors cause damage to the crystal; the damaged regions can trap carriers. Second, hydrogen can passivate acceptor as well as donor impurities. Oxygen is also used to render III–V semiconductors semi-insulating. Chromium and iron are deep impurities which are used to make GaAs and InP highly resistive. Both Cr and Fe are deep acceptors and compensate for residual shallow donors in the two semiconductors.

Elemental impurities cannot be used as doping sources in vapor-phase epitaxial growth systems because such impurities would assume the ambient temperature in the reactor and condense on the reactor walls. Vapor-phase epitaxial (VPE) growth techniques therefore require gaseous doping compounds, i.e. chemical gases transporting the doping impurity. Such gaseous doping compounds are called doping precursors and are mandatory for growth techniques with a viscous gas flow such as VPE. Growth techniques with molecular flow can employ either elemental doping sources or doping precursors. Chemical-beam epitaxy (CBE) frequently employs gaseous doping compounds. The use of precursors in CBE is motivated by parasitic chemical reactions between the organometallic sources used for group-III elements and elemental doping sources which result in a degradation in elemental source purity (see Sect. 6.1). Thus the two techniques, VPE and CBE, use doping precursors for different reasons.

The use of non-elemental chemical precursors allows a wide selection of chemicals. The most obvious requirement for these chemicals are (i) a sufficient vapor pressure at room temperature (ii) thermal decomposition of the chemical at the growth temperature, and (iii) no parasitic chemical reactions before and after thermal decomposition. These requirements can be satisfied by either inorganic precursors, e.g. silane or disilane, or organometallic precursors, e.g. dimethylzinc (DMZn).

Impurities are the lifeblood of virtually all semiconductor devices. Impurities determine the semiconductive properties of materials and allow us to vary the conductivity from the semi-insulating via the semi-conductive to the semimetallic range of the conductivity spectrum. The species and concentration of impurities determine the conductivity type and the free carrier concentration of semiconductors. For p-type and n-type impurities the electronic conduction occurs predominantly in the valence and conduction band, respectively. Employment of both conductivity types in one semiconductor makes possible pn-junctions, i.e. rectifying devices. Employment of layered n-p-n-type conductivity allows amplification and switching of electronic signals in transistors. Finally, free carriers must be injected or extracted in all optoelectronic devices. Thus, impurities providing free carriers form the basis of light-emitting diodes, current-injection lasers, photodetectors, and solar cells.

Impurities incorporated into a semiconductor lattice predominantly occupy substitutional lattice sites. In compound semiconductors, the lattice site can be either a cation or an anion site. Which of the two sites is preferred by an impurity depends on a number of factors, including the valence electron correlation between impurity and host, the bond strength between the impurity atom and the surrounding host lattice, and the size of the impurity (strain effects). Examples of impurities incorporated into a III–V semiconductor lattice are schematically shown in Fig. 1. Such compound semiconductors have a zincblende structure, in which cations and anions are bonded with tetrahedral symmetry.

It was realized in the infancy of semiconductor science that impurities are the essential ingredient in these materials. The first usage of the term ‘impurities’ dates back to 1931 (Wilson, 1931):

The knowledge of the significant consequences of impurities motivated researchers to, first, purify the semiconductor materials, for example by zone refining, and, second, deliberately add ‘foreign atoms’ to purified semiconductors, for example by thermal diffusion of such ‘foreign atoms’ into the semiconductor. The deliberate doping of semiconductors with impurities required that the usage of the term ‘impurities’ was broadened. Such an extended definition was offered by Shockley (1950):

The term ‘dopant’ was non-existent in the English language until its introduction in 1963 by Seidman and Marshall (1963), who wrote about crystal growth from the melt:

Deep levels are states within the forbidden gap of a semiconductor that are far removed from either conduction or valence band. Many of the deep levels are closer to the center of the gap than to either of the band edges. The name midgap center is frequently used for such deep levels. Due to their ability to capture free electrons and holes, deep levels are also called traps or deep traps. Deep levels caused by substitutional, non-hydrogenic impurities are referred to as deep impurities. Chromium in GaAs and Fe in InP are examples of such deep impurities. Finally, deep levels can be due to point defect centers. Examples of such deep centers are anti-site defects and interstitials.

Deep levels can be caused not only by point defects but also by spatially extended defects. Examples for extended defects are dislocations such as threading dislocations, misfit dislocations, or screw dislocations. Another example of extended ‘defects’ are semiconductor surfaces. Electronic states at semiconductor surfaces are called surface states or Bardeen states after Bardeen (1947) who demonstrated the influence of such states on the surface potential. In many semiconductors, Bardeen states are located in the vicinity of the center of the gap (e.g. GaAs and InP) and have properties similar to deep levels occurring in the bulk.

Deep centers can be classified according to their charge state. Centers with a neutral and positively charged state are called donor-like states.

The incorporation and activation of impurities is governed by a number of physical and chemical laws. It is essential to know and apply them in order to predict experimental functional dependencies of impurity incorporation. For example, the incorporation of many impurities depends on the epitaxial growth temperature. How does the electrical activity, compensation, etc. depend on this growth temperature? How are the impurity characteristics influenced by the V/III flux ratio? These are some of the questions that are of interest. Furthermore, some incorporation characteristics are found only for certain impurity elements. Autocompensation is prominent among group-IV impurities. In order to minimize autocompensation, it is desirable to know the functional dependences of amphoteric impurity incorporation.

Another example of impurity characteristics is the doping efficiency. This is defined as the ratio of the free carrier concentration and the dopant concentration. The doping efficiency is unity for an ideal dopant element and an ideal doping procedure. However, it can be quite low. For example, the doping efficiency of impurities incorporated by implantation can be below 10% before activation. The understanding of the principles governing the doping efficiency is therefore desirable.

Finally, very high doping concentrations become increasingly important as the spatial dimensions of semiconductor structures shrink. What are the highest doping concentrations achievable in III–V semiconductors? What limits the maximum impurity concentration? These are some of the topics and questions that will be addressed in this chapter.

The concentration of neutral impurities, ionized impurities, and free carriers in a doped semiconductor depends on a large number of parameters such as the impurity atom concentration, the free carrier mass, the bandgap energy, and the dielectric constant. The interdependences of the free majority and minority carrier concentration, the impurity concentration, impurity ionization energy as well as some other constants and materials parameters are given by semiconductor statistics. Semiconductor statistics describes the probabilities that a set of electronic states are either vacant or populated.

Electronic states include localized impurity states as well as delocalized conduction and valence band states. In the simplest case, an impurity has a single state with no degeneracy (g0 = 1). However, an impurity may have a degenerate ground state (g0 > 1) as well as excited levels which may need to be considered. The states in the bands and their dependence on energy are described by the density of states. In semiconductor heterostructures, the free motion of carriers is restricted to two, one, or zero spatial dimensions. In order to apply semiconductor statistics to such systems of reduced dimensions, the density of states in quantum wells (two dimensions), quantum wires (one dimension), and quantum dots (zero dimensions), must be known. The density of states in such systems will also be calculated in this chapter.

Shallow impurities are of great technological importance in semiconductors since they determine the conductivity and the carrier type of the semiconductor. Shallow impurities are defined as impurities which are ionized at room temperature. This condition limits the ionization energy of such impurities to values « 100 meV. Shallow impurities can be either acceptors or donors, i.e. ‘accept’ electrons from the valence band or ‘donate’ electrons to the conduction band.

The hydrogen atom model can serve as the basis for the calculation of many properties of shallow impurities such as ionization energy and state wave functions. In this chapter, the hydrogen atom is analyzed in terms of Bohr's semi-classical model and in terms of a quantum mechanical approach. The hydrogen atom model is then applied to shallow impurities. Properties such as ionization energies, wave functions, central cell correction terms, and screening of impurity potentials by free carriers are summarized. Effects associated with high impurity or high free carrier concentrations are also discussed including the Mott transition, the Burstein–Moss shift, band tails, impurity bands, and bandgap shrinkage.

Hydrogenic impurities

Impurities in semiconductors can be incorporated on substitutional sites, interstitial sites, or as impurity complexes. Here, we restrict ourselves to substitutional, shallow impurities. Examples for such impurities are Be, Zn, Si, and Sn. These impurities are shallow, i.e. their ionization energy is comparable to the thermal energy kT at room temperature.

Technology revolutions mark their origin from a single breakthrough such as the demonstration of the transistor. Subsequent technological advances make the revolution a reality. The historical evolution from Si transistor to integrated circuits to high speed computers and telecommunications is one excellent example.

Active workers in the field know each advance represents a major expenditure of time and effort (really ‘blood and sweat’). Progress comes about in a competitive atmosphere involving creative ideas, personality forces and technology prognostications.

We are presently in the midst of the microelectronics revolution. Insatiable demands exist for greater data rates, for consumer electronics and for superior telecommunications. We envision a world of wireless communications, video transmissions and displays, and numerous applications of high speed data transmission. Satisfying this demand is the goal of current research.

For our field of microelectronics this means a systems analysis from the final product to the atomic configurations of the materials that make the product. This analysis itself is remarkable; we can precisely relate the macroscopic system properties – how fast will the system operate – to the microscopic atomic structure – where do the atoms sit in the solid.

Analysis of today's devices reveal the limitations of today's semiconductors – mostly silicon. Silicon has been the workhorse for the last thirty years. The ‘silicon community’ continues to squeeze all that is obtainable from this most robust and manufacturable semiconductor.

Spatial redistribution of impurities in semiconductors occurs at sufficiently high temperatures. That is, impurities may not remain on the site of their initial incorporation. As discussed in the previous chapter, the diffusive redistribution can even be used to incorporate impurities from the surface into the bulk of the semiconductor. However, impurity redistribution is most frequently an undesired effect; it leads to the smearing of doping profiles or, for example, can result in the displacement of the location of a pn-junction.

Redistribution of impurities can be isotropic or anisotropic. Conventional diffusion is an example for isotropic redistribution. On the other hand, anisotropic redistribution of impurities occurs in the presence of energy gradients. Such gradients can be the result of electric potential gradients, strain gradients, surfaces, etc. Preferential redistribution of impurities occurs along the energy gradient, i.e. towards regions of lower energy.

The vicinity of a semiconductor surface can lead to preferential redistribution of impurities. Some impurities tend to remain on the surface during epitaxial growth and do not readily incorporate into the bulk. The impurities segregate to the surface. Surface segregation is an undesired effect since it complicates the growth of well-defined impurity distributions. The effect of preferential redistribution of impurities (in the vicinity of a surface) towards the surface is called surface migration. This can be the result of potential gradients or defect gradients in the vicinity of a surface.