For over forty years, electron paramagnetic resonance was able to detect for the first time the acceptor resonance (EPR) has played a key role in the study of point defects in the absence of external strain, and confirm the complete in semiconductors. Because of the detailed structural J = 3/2 spectrum for the bound hole .
information available from the spectrum of a defect — This pioneering EPR work in silicon has served to set symmetry from its angular dependence, and the atomic and the pattern of undrstanding for all of the elemental and lattice structure from its hyperfine interactions — it has compound semiconductors. Similar shallow S = 1/2 proven to be uniquely able to identify a defect, to map out effective-mass donor resonances have subsequently been its wavefunction in the lattice, and determine its microscopic observed in many of the semiconductors, but the shallow structure. J = 3/2 acceptors have resisted detection, the valence In this short presentation, I can present only a very band maximum being at k = 0 for all. The acceptors few of the highlights, with apologies to the many, many have been observed in a very few cases, but only again EPR scientists who have made, and are continuing to either when stress was externally applied to the cubic make, vital contributions to our understanding of defects semiconductor, or when internally available for a few nonin semiconductors. cubic semiconductors.
I. Past 2. Deep Transition Element Impurities At about the same time, Ludwig and Woodbury initiated 1. Shallow Effective-Mass Impurities a systematic study of the 3d transition element impurities Over forty eyars ago, Feher  introduced the important in silicon, which continued through the 1960’s . Using technique of electron-nuclear double resonanse (ENDOR), EPR and ENDOR, several charge states of most of the 3d where the nuclear resonanse of nearby lattice atoms could transition element impurities were observed and a simple be detected as a change in the EPR signal of a defect. physical picture of their properties emerged.
With this, he was able for the first time to map out the This is summarized in fig. 1. The sign of the crystal fiels wavefunction of the S = 1/2 bound electron of the shallow experienced by the d-electrons is reversed for the interstitial donor in silicon over the surrounding silicon lattice sites . and substitutional sites. For the interstitial site, the crystal This served to establish in beautiful detail the correctness of field can be considered to arise primarily from the positive the theory of Kohn and Luttinger , which described the cores of the four nearest silicon atoms, which are exposed wavefunction as a large orbit hydrogenic envelope function because their charge compensating valence electrons are (effective-mass electron, dielectric shielded from the positive involved in bonds pointing away from the interstitial site.
core) multiphying a sum of the free electron states at the Therefore, as shown in the figure, the triply degenerate conduction band valley minima. d(t2) orbitals are lower in energy because they interact more The shallow acceptor in silicon was more difficult be- strongly with the neighbors than the doubly degenerate d(e) cause, for it, the top of the valence band is at the -point orbitals, which better avoid them. In the substitutional site, (k = 0), with orbital angular momentum L = 1, giving the negative charge of the electrons in the bonds to the J = 3/2 for the bound hole. The hole is therefore impurity dominate, and the level order is reversed.
strongly sensitive to random strains in the crystal and the Starting from the free ion 3d4s configuration for a acceptor resonance was too broad to detect. Feher solved particular charge state, all + electrons go into these the problem by applying uniaxial stress to the crystal, which orbitals for the non-bonding interstitial case, as expected. For lifted the degeneracy of the bound J = 3/2 hole and made the substitutional impurities, which require four electrons the resonance observable , again confirming the general to complete their bonds to the four silicon neighbors, features of the Kohn-Luttinger theory. Twenty years later, + - 4 remain to go into the d-orbitals. In both cases, with higher quality, lower internal strain crystals, Neubrand the levels are filled according to Hund’s Rule, electrons EPR of Defects in Semiconductors: Past, Present, Future Figure 1. Simple crystal field model deduced for 3d transition element impurities in silicon .
paired (maximum S), first filling the lower level, spin- 3. Vacancies and Self-interstitials up, then the upper, spin-up, before filling, spin-down, in Also, begun at about the same time, and continuing the lower, etc. The repulsive electron-electron interactions through the 1980’s, I and my students have systematically between the localized 3d orbitals, which force maximum probed the properties of the intrinsic defects — vacancies spin, therefore dominate over the crystal field energy.
and self-interstitials — in silicon [10–12]. The approach This general pattern, established very early for silicon, taken was to produce the defects by 1–3 MeV electron has been remarkable successful in interpreting the many irradiation in situ at cryogenic temperatures and to study subsequent EPR and optical results for transition elements by EPR the frozen-in isolated vacancies and interstitials, and in all of the semiconductors — elemental, III–V, and II–VI then to warm up and study their migrational properties.
alike. In the compound semiconductors, the impurities tend Fig. 2 summarizes the experiment and the overall pattern to enter substitutionally on the metal sublattice. For them, of results. Immediately after the irradiation, EPR of the the substitutional rules are the same as above, except that + isolated vacancy in two different charge states, V and + - 3 electrons go into the d-levels for the III–V’s, the V, is observed. Long range migration of the vacancy three electrons replacing now the three valence electrons with subsequent trapping by impurities occurs at 70 K associated with the neutral group–III atom that the impurity in n-type material, 200 K in high resistivity material, ion replaces. Similarly, for the II–VI’s, the d-level occupance and 150 K in p-type material. As shown, a whole number is + - 2.
host of trapped vacancies have been identified by EPR, Of course, the excitement, and new physics, comes when departures are found, although there have been few so confirming unambiguously that the annealing is indeed the result of long range diffusion of the vacancy. Kinetic studies far. One interesting one is that of the shallow manganese acceptor in GaAs. In that case it has been found that Mn0 of the annealing have revealed the activation energies for is not d4, as expected by the simple rules above, but the vacancy diffusion as shown in the figure, along with the Hund’s rule d5, with a shallow bound hole . Another corresponding defects charge states. This was the first departure has been found for substitutional Ni- in silicon  surprise. The high mobility well below room temperature, and also for the corresponding d  substitutional ions of the and its large dependence upon the vacancy charge state, 4d (Pd-) and 5d (Pt-,Au0) series. For them, a Jahn-Teller were not anticipated.
distortion sets in, which overcomes the electron-electron A second surprise was the experimantal observation that coupling, giving S = 1/2 for their e4t2 paramagnetic charge vacancy annealing can be stimulated even at 4.2 K by states. This anomaly has been explained as a result of strong shining near bandgap light on the sample or by injecting charge transfer of the paramagnetic d-orbitals onto the four electrons and holes electrically, This phenomenon, called neighbors in the particular case of the transition elements at recombination-enhanced migration, was also established to the end of each series . be occuring to a limited extent during the electron irradiation Физика твердого тела, 1999, том 41, вып. 828 G.D. Watkins Figure 2. Evolution of events after a vacancy-interstitial pair is produced by an electron irradiation event in silicon [11,12].
itself, which also generates substantial electron-hole pair Teller energy lowering for V over the one-electron energy + ionization. lowering for V, actually serves to overcome the Coulomb repulsion between the two electrons and lower the vacancy A third even greater surprise was the observation, in first donor level (0/+) to a position, below the second donor the p-type material studied, that the interstitial had already level (+/ ++). This rare phenomenon, called negative-U, migrated long distances during the initial electron irradiation implies a net attraction between electrons at the vacancy.
at 4.2 K. Immediately after the irradiation, only interstitials To account for this, the Jahn-Teller energy lowering for the trapped by impurities were observed, as illustrated in the figure, and in 1 : 1 concentration to the isolated vacan- vacancy single donor level (0/+) can be estimated to be at least 0.5eV . With relaxation energies this large cies. Apparently, the interstitial is even more efficient in (1/2 the bandgap!), it is easy to undrstand how capture of converting the capture of electrons and holes into the energy electrons and holes at the vacancy can supply the necessary required for its migration.
vibrational energy to overcome the small diffusion barriers Fig. 3 provides a simple interpretation of the electronic indicated in fig. 2, and explain its athermal 4.2 K migration and lattice structure of the vacancy that has evolved from the under electronic excitation.
EPR studies. Using the concept of simple molecular orbitals Inspection of the wide variety of observed configurations made up from the dangling bonds of the four vacancy for the trapped interstitials, combined with predictions of neighbors, the various charge states can be understood by recent ab initio calculations for interstitial boron  and their successive population with the appropriate number + silicon [15,16] has served to suggest a similar simple physical of electrons, two for V++, three for V, etc. Here, picture for predicting the properties of such interstitials.
the electron-electron interactions are weaker than in the Consider the s and p valence orbitals for the interstitial transition element ion case, being spread mostly over the atom when placed in the high symmetry Td interstitial four nearest atom neighbors, but also onto their neighbors position of the lattice. Populate them in the normal atomic as well, and each level is filled before proceeding to the next. The interesting feature here is that Jahn-Teller energy- order with electrons appropriate for the charge state of the interstitial. For B+(2s2), Al++(3s1) and Si++(3s2), lowering distortions occurs as soon as partial occupancy of i i i there is no orbital degeneracy, therefore no Jahn-Teller the degenerate t2 orbital occurs. A tetragonal distortion + distortion, and the interstitial should stay on-center, as indeed occurs for V, as observed in its EPR, because of its observed for Al++, and predicted by theory for the other single occupance in the t2 orbital. A much larger tetragonal i two. For B0(2s22p), C+(2s22p), Si+(3s23p1), and their distortion occurs for V0 being driven by the energy gain of i i i further degenerate p-level occupancy charge states, offtwo electrons in the orbital. For V, an additional dihedral center Jahn-Teller distortions should occur into symmetry distortion occurs.
lowering bonding configurations, as indeed observed for BThese distortions turn out to have important consei quences. For example, the increased two-electron Jahn- and C+,0,-, and predicted for all three atoms. Considering i Физика твердого тела, 1999, том 41, вып. EPR of Defects in Semiconductors: Past, Present, Future Figure 3. Simple one-electron model for the various charge states of the vacancy in silicon.
the large energies involved in p-bonding, it is again easy to Zn+(s1), has also been observed, and is on-center, as prei understand efficient recombination-enhanced migration for dicted . For the many other semiconductors about which the interstitial as it cycles back and forth between its various no clear experimental defect identifications exist, these configurations during electron and hole capture. models may provide useful predictive properties, which, incidentally, provide a remarkable consistent simple physical Remarkably, therefore, the electronic and lattice structures for vacancies and interstitials in silicon can be understood in almost identical fashion, as summarized in fig. 4. In each case, there is a non-degenerate (a1, s) level lowest and a three-fold degenerate (t2, p) level higher, which are filled by the electrons appropriate for the charge state of the defect.
Each level is filled before going to the next, and when orbital degeneracy results, symmetry-lowering Jahn-Teller destortions occur as bond reconstructions, rebonding configurations, etc.
The one-electron orbital pictures for vacancies and interstitials in fig. 4. must of course be generally applicable to all semiconductors — a vacancy always produces four dangling bonds, an interstitial in the undistorted tetrahedral site is Figure 4. An identical simple one-electron orbital model appears always an ion surrounded by four non-bonding neighbors. In to work for both vacancy and interstitial in silicon, the levels being the II–VI semiconductors, for example, it provides a natural filled, first the lower non-degenerate one, then the higher 3-fold explanation for the on-center character observed by EPR for degenerate one. When partial occupancy of the degenerate (t2, p) + the chalcogen vacancies, VVI(a1), and the trigonally distorted orbitals results, 0 < n < 5, large Jahn-Teller relaxations occur.
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