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New electron states of negative ions in semiconductors
Solid State Communications, Vol. 51, No. 6, pp. 411-414, 1984. Printed in Great Britain.
0038-1098/8453.00 + .00 Pergamon Press Ltd.
NEW ELECTRON STATES OF NEGATIVE IONS IN SEMICONDUCTORS M. Jaros Department of Theoretical Physics, The University, Newcastle upon Tyne, U.K.
(Received 2 May 1984 by F. Bassani) A theory is presented of a new class of localised states which are stabilised by enhanced correlation effects peculiar to the electronic structure of weakly-bonded defects in covalent semiconductors. A simple model of the correlation effect is employed and it is shown that it yields a consistent description of binding to N in GaPxAsl_ x.
BOUND ELECTRON STATES of negative ions (e.g. chemical impurities) in solids [1 ] are normally treated in a manner analogous to that used to describe the states of a free hydrogen atom with two electrons (H-) [2]. In some exceptional systems, the one-electron impurity potential is strong enough to bind an electron in a localised state [3 ]. In all cases of interest, only one (if any) bound state has been predicted. The purpose of this study is to show that in covalent semiconductors there is an important class of negatively charged defects with electron states that have not been accounted for in existing models. The origin and the number of these states are largely determined by an effect of enhancement of electron correlation peculiar to the electronic structure of such defects. As a result, there is an additional medium-range term in the potential which stabilizes new, relatively weakly localised bound states. A simple model of the many-electron effect is proposed to estimate the binding energy. The theory is successfully implemented to explain the ground state of N in GaPxASl_x . Other systems (e.g. GaP: O-)are also discussed. Not all negatively charged defects in semiconductors can be understood by analogy with free ions. Nitrogen impurities in GaPxASl-x alloys occupy the anion lattice sites. Since N is isoelectronic with P and As, the oneelectron impurity potential is of short range. It has recently been demonstrated that at least for certain alloy compositions (x ~ 0.5) N is capable of binding a single electron [4, 5]. Detailed one-electron calculations have confirmed that the nitrogen potential is sufficiently strong to form a well localised state near the conduction band edge [6, 7]. However, in spite of considerable computational effort, the existence of such a state in the forbidden gap has not been conclusively established [8]. In fact, it is now clear that the one-electron state reported in [6] and [9] for GapxAsl-x :N does not have the properties required to explain the experimental data. These data consist of well resolved luminescence spectra
depicting recombination of an exciton bound to a single nitrogen impurity in the alloy. The excitonic origin of these spectra was explained by Hopfield et al. [3] who proposed a model in which an electron is tightly bound to a neutral nitrogen and the excess negative charge then binds a hole into a large orbit characteristic of a shallow acceptor. It follows that the electron plays a key role in the spectra. Wolford et al. [10] plot the observed binding energy of the exciton EA, the separation energy AAB between the exciton states of total angular momentum J = 1 and 2, and the LO phonon coupling strength SLo as a function o f x . They show that EA, AAB and SLo first rise with decreasing x and rapidly decrease for x < 0.5. Since the magnitude of SLo is inversely proportional to the effective radius of the electron orbit, the drastic reduction of Sr.o for x < 0.5 implies that the localisation of the electron wave function collapses as Ea -~ 0. The one-electron calculations correctly predict the trend in Ea. However, the localisation of the calculated one-electron wave function does not change rapidly with x, in fact it is practically constant in the critical range 0.5 )" x > 0.3. This behaviour is characteristic of "deep" levels dominated by strong short-range forces [8]. The wave function is extended in the wave vector space and small changes in the distribution of the host crystal density of states do not lead to significant changes in localisation. This signature of deep levels is now well understood. It means that the discrepancy between the one-electron theory and the above mentioned experimental data cannot be reduced to details of the computational technique or potential. The experimental results imply that the dominant mechanism of binding is not correctly represented in the one-electron calculations. In a one-electron local density calculation, the Schrodinger equation is solved selfconsistently for a single (ground state) configuration of electron states. Sophisticated calculations have recently been performed for a number of neutral substitutional defects with a
411
412
NEW ELECTRON STATES OF NEGATIVE IONS IN SEMICONDUCTORS
energy ~
equation for energy t2 Q!
valence b~nd ~I Z.~//////1
oo
Vol. 51, No. 6
2s
Fig. 1. A sketch of the one-electron states of neutral nitrogen in GaPo.sAso.s invoked in the text. The energies obtained in the present calculation (measured with respect to the top of the valence band) are 3 . 1 , 2 . 4 , - 4.5, and -- 16.6 eV, respectively. The number of electrons in the occupied states associated with the neutral (NO) configuration is indicated. potential attractive to electrons [11,12]. A similar result is obtained in the present study for GaPo.sAso.s :N (see Fig. 1). The lowest state which lies deep below the valence band [7] accommodates the nitrogen 2s electrons. State 20 is localised on the impurity and may be viewed as a mixture of the nitrogen 2p orbitals and the dangling bond orbitals transforming as the t2 representation of the T d group. The localised resonances in the conduction band can be interpreted in a similar manner. The remaining states are weakly localised and will be left out of the present discussion as well as the tightly bound states representing the core electrons. The selfconsistent procedure ensures that for the ground state electron configuration shown in Fig. 1 the potential which appears in the Schrodinger equation returns all one-electron wave functions used to generate this potential. As in the conventional one-electron calculations for free atoms, the average electrostatic interactions between all electrons are included. However, the correlation between the instantaneous positions of electrons is not fully accounted for. To obtain a better estimate of the correlation effect, the total wave function can be expanded as a linear combination of Slater determinants corresponding to all electron configurations permitted by the exclusion principle. Since the states showed in Fig. 1 are well localised, the many-electron correction is dominated by the configurations involving these states. The strength of the correlation effect is then expressed in terms of the magnitude of the expansion coefficients associated with each of the virtually excited configurations. If it is assumed that there is a dominant configuration m, non-degenerate perturbation theory gives a generalised Schrodinger type
L'm :
Hmi Hira
Era
,
(1)
where Era = H m m is the unperturbed energy of the mth configuration and Hij are matrix elements of the Hamiltonian between the relevant determinantal wave functions. A rigorous implementation of the procedure implied by equation (1) lies outside the limits of present day theory. However, experimental results in question suggest that the correlation energy that may be sufficient to stabilise the ground state of N- is small (~< 0.1 eV) and that the charge distribution of the new state must contain a significant weakly localised component. It follows that under these circumstances it is possible to simplify the calculation of the correlation contribution by assuming that the extra electron moves slowly compared to the electrons (pictured in Fig. 1) which are well localised near nitrogen. The energy of the valence electrons can be evaluated for a fixed value of the extra electron coordinate. The effect of the virtual excitations is then expressed in terms of a "correlation potential" seen by the extra electron. This procedure is commonly used to describe excited states of some free ions [2]. Further simplifications can be achieved by expanding the electron-electron interaction term (r12)-~ in spherical harmonics and retaining only the dominant dipole contribution ri/rf cos O(rj > ri) where 0 is the angle between the position vectors r i and rj. The correlation energy due to the/th localised electron is
F~cj = ~ <~(r~) i' d~
x
dr
dO sinOcosOr3¢jCj*
r~
x ¢(r~)> (NjN; aE.,)-',
(2)
where Cj, Os' are the relevant solutions associated with the one-electron states shown in Fig. 1 normalised as fo 1¢il2 d7 = N i. The wave function of the extra electron ¢ must be obtained variationally by minimising energy
fiE, 5E = QblH0+ V/l~b)+~ Ecj, )
(3)
where Ho is the Hamiltonian of the virtual crystal and Vi is the effective impurity potential [8]. The one-electron solutions 4~j,e l , corresponding to the states showed in Fig. i, and the energy differences AEz, between configurations have been obtained numerically as described in [13] and [14]. The Schrodinger equation is solved by direct diagonalisation in the Bloch function
Vol. 51, No. 6
NEW ELECTRON STATES OF NEGATWE IONS IN SEMICONDUCTORS
representation. The sampling density employed is equivalent to dealing with clusters of more than 300 atoms. Although the details of charge localisation and topology are known to depend somewhat upon the choice of potentials and other technical considerations, it transpires that E c is insensitive to any but the most basic of properties of the states in question. The variational calculation of 6 E must be carried out numerically. Since the trial function is expected to be quite extended, q~can be approximated by an effecivemass-like solution with an envelope function of the form r v exp (--/3r). However, for most values of v and 18the matrix elements of rio and V/must be evaluated in the wave vector space so as to ensure that intra and interband effects peculiar to defects with medium range potentials and wave functions are correctly accounted for [15,181. The results of the calculation for GaPo.sAs0.s show that a stable N- configuration is possible with binding energy of about 12 meV. The contributions of rio and V i are 148 and --91 meV, respectively, and E c = Ej Eci -~ -- 69 meV. About 4% of the extra electron charge lies within the nearest neighbour distance from nitrogen. It can be seen that the binding energy is only a fraction of the correlation contribution which is obtained from a simplified model whose limits of applicability cannot be easily tested. Therefore, this calculation cannot provide any conclusive answer concerning the magnitude of the binding energy. However, it is clear that the correlation contribution is of correct order of magnitude to stabilise N-. The wave function of the weakly bound electron is much less localised than the one-electron solutions reported previously although it is significantly more localised than the wave function of a hydrogenic donor ground state in the same material. This is because in the present calculation the ground state of N- is controlled by the stabilising effect of the medium-range correlation potential. This potential depends on the well localised resonances shown in Fig. 1 and changes only slowly with x. However, since the electron wave function is delocalised, the expectation value of rio strongly reflects the properties of the band structure at the bottom of the conduction band. As x becomes smaller than 0.5, the F valley rapidly approaches the conduction band edge and for x ~<0.45 the material has a direct gap. Since the effective mass at F is very small, the positive contribution to 6 E rapidly increases near and below x -~ 0.5, and reduces the binding energy and the localisation of the wave function. This is precisely the behaviour observed in experiments. Not all isoelectronic impurities are expected to exhibit a stable negative-ion configuration. For example, GaP:As does not have a potential sufficientl7 strong to localise the states shown in Fig. 1 and both the correlation
413
contribution and V/are too small to stabilise a bound state. However, it has already been pointed out that the electronic structure which gives rise to the new state of N- in GapxAs~_x is characteristic of substitutional defects in covalent semiconductors which possess strong short-range potentials attractive to electrons. It is borne in mind that new stable configurations may be obtained in an analogous manner for other negatively charged systems. For example, this is the case for the substitutional donor oxygen in GaP. The relevant part of the electronic structure is qualitatively the same as that shown in Fig. 1. (For the neutral system of GaP :O°, there is one additional electron which occupies state al, with the corresponding level lowered deep into the forbidded gap.) The one-electron potential of O° is strong and binds deeply an extra electron [12, 16]. At low temperatures, the negative ion (O-) configuration is metastable at the perfect lattice site, with only small lattice relaxation present. Neither full scale one-electron calculations nor calculations analogous to those for H- produce stable excited states of O-. The excited states fail to materialise for very much the same reasons as they do at H-. However, if the effect of the electronic structure is fully taken into account, and the correlation contribution evaluated as above, both spin-triplet and spinsinglet excited configurations of O- are stable [17]. This is in agreement with recent experimental results [18] which show that the capture luminescence at GaP :O occurs via a weakly bound excited spin-singlet configuration of O-. To summarise, it has been shown that in covalent semiconductors correlation effects play an important part in stabilising new, weakly bound states of negativeion impurities. This effect derives its strength from the electronic structure which arises when the impurity potential pushes the valence s electrons at the foreign atom deep below the valence band. This modifies the covalent bond and leads to severall well localised states and enhanced configuration interactions. In the case of isoelectronic impurities the new stable state is the ground state of the negatively charged defect. In the case of hydrogen-like systems, the new states are the excited states of the negative ion. Although the approximate model of many-electron effects employed in this study leaves considerable uncertainty as far as the precise value of the binding energy is concerned, the significance of the correlation contribution is clearly demonstrated. In particular, the theory successfully explains recent experimental data concerning the formation of a stable state of negative nitrogen in GaPxASl_x. REFERENCES 1.
e.g. see A.M. Stoneham, T h e o r y o f D e f e c t s in Solids, Clarendon Press: Oxford (1975).
414 2. 3. 4. 5. 6. 7. 8. 9. 10.
NEW ELECTRON STATES OF NEGATIVE IONS IN SEMICONDUCTORS See H.S.W. Massey,Nagativelons, University Press: Cambridge (1976). J.J. Hopfield, D.G. Thomas & R.T. Lynch, Phys. Rev. Lett. 17,312 (1966). E. Cohen & M.D. Sturge,Phys. Rev. BIS, 1039 (1977). J.A. Kash, J.M. Collet, DJ. Wolford & J. Thompson,Phys. Rev. B27, 2294 (1983). M. Jaros & S. Brand, J. Phys. C12, 525 (1970). H.P. Hjalmarson, P. Vogl, DJ. Wolford and J.D. Dow,Phys. Rev. Lett. 44, 810 (1980). See M. Jaros, Deep Levels in Semiconductors, p. 97. (Hilger: Bristol (1982). P.W. Banks & M. Jaros,J. Phys. C14, 2333 (1981). DJ. Wolford, B.G. Streetman & J. Thompson, Physics of Semiconductors (1980); J. Phys. Soc. Japan 49, (Suppl. A), 223 (1980). A summary of
11. 12. 13. 14. 15. 16. 17. 18.
Vol. 51, No. 6
experimental and theoretical results concerning GaPxASl_x :N can be found in [8], p. 231. J. Bernholc, N.O. Lipari, S.T. Pantelides & M. Scheffler, Phys. Rev. B26, 5706 (1982). G.A. Baraff, E.O. Kane & M. Schluter,Phys. Rev. B25,548 (1982). See [8], p. 129 and M.J. Kirton, M. Jaros & S. Brand, Physica 116B, 79 (1983) (ICDS-12, Amsterdam, September 1982). MJ. Kirton, P.W. Banks, Lu da l_ian & M. Jaros, J. Phys. C. 14, 2487 (1984). D.C. Herbert &J. Inkson,J. Phys. CI0, L695 (1977); M. Altarelli, Phys. Rev. Lett. 46,205 (1981), M. Jaros,J. Phys. C8, 2455 (1975). M. Jaros, (to be published in J. Phys. 6). P.J. Dean, M.S. Skolnick, C.H. Uhlein & D.C. Herbert,J. Phys. C16, 2017 (1983).
0038-1098/8453.00 + .00 Pergamon Press Ltd.
NEW ELECTRON STATES OF NEGATIVE IONS IN SEMICONDUCTORS M. Jaros Department of Theoretical Physics, The University, Newcastle upon Tyne, U.K.
(Received 2 May 1984 by F. Bassani) A theory is presented of a new class of localised states which are stabilised by enhanced correlation effects peculiar to the electronic structure of weakly-bonded defects in covalent semiconductors. A simple model of the correlation effect is employed and it is shown that it yields a consistent description of binding to N in GaPxAsl_ x.
BOUND ELECTRON STATES of negative ions (e.g. chemical impurities) in solids [1 ] are normally treated in a manner analogous to that used to describe the states of a free hydrogen atom with two electrons (H-) [2]. In some exceptional systems, the one-electron impurity potential is strong enough to bind an electron in a localised state [3 ]. In all cases of interest, only one (if any) bound state has been predicted. The purpose of this study is to show that in covalent semiconductors there is an important class of negatively charged defects with electron states that have not been accounted for in existing models. The origin and the number of these states are largely determined by an effect of enhancement of electron correlation peculiar to the electronic structure of such defects. As a result, there is an additional medium-range term in the potential which stabilizes new, relatively weakly localised bound states. A simple model of the many-electron effect is proposed to estimate the binding energy. The theory is successfully implemented to explain the ground state of N in GaPxASl_x . Other systems (e.g. GaP: O-)are also discussed. Not all negatively charged defects in semiconductors can be understood by analogy with free ions. Nitrogen impurities in GaPxASl-x alloys occupy the anion lattice sites. Since N is isoelectronic with P and As, the oneelectron impurity potential is of short range. It has recently been demonstrated that at least for certain alloy compositions (x ~ 0.5) N is capable of binding a single electron [4, 5]. Detailed one-electron calculations have confirmed that the nitrogen potential is sufficiently strong to form a well localised state near the conduction band edge [6, 7]. However, in spite of considerable computational effort, the existence of such a state in the forbidden gap has not been conclusively established [8]. In fact, it is now clear that the one-electron state reported in [6] and [9] for GapxAsl-x :N does not have the properties required to explain the experimental data. These data consist of well resolved luminescence spectra
depicting recombination of an exciton bound to a single nitrogen impurity in the alloy. The excitonic origin of these spectra was explained by Hopfield et al. [3] who proposed a model in which an electron is tightly bound to a neutral nitrogen and the excess negative charge then binds a hole into a large orbit characteristic of a shallow acceptor. It follows that the electron plays a key role in the spectra. Wolford et al. [10] plot the observed binding energy of the exciton EA, the separation energy AAB between the exciton states of total angular momentum J = 1 and 2, and the LO phonon coupling strength SLo as a function o f x . They show that EA, AAB and SLo first rise with decreasing x and rapidly decrease for x < 0.5. Since the magnitude of SLo is inversely proportional to the effective radius of the electron orbit, the drastic reduction of Sr.o for x < 0.5 implies that the localisation of the electron wave function collapses as Ea -~ 0. The one-electron calculations correctly predict the trend in Ea. However, the localisation of the calculated one-electron wave function does not change rapidly with x, in fact it is practically constant in the critical range 0.5 )" x > 0.3. This behaviour is characteristic of "deep" levels dominated by strong short-range forces [8]. The wave function is extended in the wave vector space and small changes in the distribution of the host crystal density of states do not lead to significant changes in localisation. This signature of deep levels is now well understood. It means that the discrepancy between the one-electron theory and the above mentioned experimental data cannot be reduced to details of the computational technique or potential. The experimental results imply that the dominant mechanism of binding is not correctly represented in the one-electron calculations. In a one-electron local density calculation, the Schrodinger equation is solved selfconsistently for a single (ground state) configuration of electron states. Sophisticated calculations have recently been performed for a number of neutral substitutional defects with a
411
412
NEW ELECTRON STATES OF NEGATIVE IONS IN SEMICONDUCTORS
energy ~
equation for energy t2 Q!
valence b~nd ~I Z.~//////1
oo
Vol. 51, No. 6
2s
Fig. 1. A sketch of the one-electron states of neutral nitrogen in GaPo.sAso.s invoked in the text. The energies obtained in the present calculation (measured with respect to the top of the valence band) are 3 . 1 , 2 . 4 , - 4.5, and -- 16.6 eV, respectively. The number of electrons in the occupied states associated with the neutral (NO) configuration is indicated. potential attractive to electrons [11,12]. A similar result is obtained in the present study for GaPo.sAso.s :N (see Fig. 1). The lowest state which lies deep below the valence band [7] accommodates the nitrogen 2s electrons. State 20 is localised on the impurity and may be viewed as a mixture of the nitrogen 2p orbitals and the dangling bond orbitals transforming as the t2 representation of the T d group. The localised resonances in the conduction band can be interpreted in a similar manner. The remaining states are weakly localised and will be left out of the present discussion as well as the tightly bound states representing the core electrons. The selfconsistent procedure ensures that for the ground state electron configuration shown in Fig. 1 the potential which appears in the Schrodinger equation returns all one-electron wave functions used to generate this potential. As in the conventional one-electron calculations for free atoms, the average electrostatic interactions between all electrons are included. However, the correlation between the instantaneous positions of electrons is not fully accounted for. To obtain a better estimate of the correlation effect, the total wave function can be expanded as a linear combination of Slater determinants corresponding to all electron configurations permitted by the exclusion principle. Since the states showed in Fig. 1 are well localised, the many-electron correction is dominated by the configurations involving these states. The strength of the correlation effect is then expressed in terms of the magnitude of the expansion coefficients associated with each of the virtually excited configurations. If it is assumed that there is a dominant configuration m, non-degenerate perturbation theory gives a generalised Schrodinger type
L'm :
Hmi Hira
Era
,
(1)
where Era = H m m is the unperturbed energy of the mth configuration and Hij are matrix elements of the Hamiltonian between the relevant determinantal wave functions. A rigorous implementation of the procedure implied by equation (1) lies outside the limits of present day theory. However, experimental results in question suggest that the correlation energy that may be sufficient to stabilise the ground state of N- is small (~< 0.1 eV) and that the charge distribution of the new state must contain a significant weakly localised component. It follows that under these circumstances it is possible to simplify the calculation of the correlation contribution by assuming that the extra electron moves slowly compared to the electrons (pictured in Fig. 1) which are well localised near nitrogen. The energy of the valence electrons can be evaluated for a fixed value of the extra electron coordinate. The effect of the virtual excitations is then expressed in terms of a "correlation potential" seen by the extra electron. This procedure is commonly used to describe excited states of some free ions [2]. Further simplifications can be achieved by expanding the electron-electron interaction term (r12)-~ in spherical harmonics and retaining only the dominant dipole contribution ri/rf cos O(rj > ri) where 0 is the angle between the position vectors r i and rj. The correlation energy due to the/th localised electron is
F~cj = ~ <~(r~) i' d~
x
dr
dO sinOcosOr3¢jCj*
r~
x ¢(r~)> (NjN; aE.,)-',
(2)
where Cj, Os' are the relevant solutions associated with the one-electron states shown in Fig. 1 normalised as fo 1¢il2 d7 = N i. The wave function of the extra electron ¢ must be obtained variationally by minimising energy
fiE, 5E = QblH0+ V/l~b)+~ Ecj, )
(3)
where Ho is the Hamiltonian of the virtual crystal and Vi is the effective impurity potential [8]. The one-electron solutions 4~j,e l , corresponding to the states showed in Fig. i, and the energy differences AEz, between configurations have been obtained numerically as described in [13] and [14]. The Schrodinger equation is solved by direct diagonalisation in the Bloch function
Vol. 51, No. 6
NEW ELECTRON STATES OF NEGATWE IONS IN SEMICONDUCTORS
representation. The sampling density employed is equivalent to dealing with clusters of more than 300 atoms. Although the details of charge localisation and topology are known to depend somewhat upon the choice of potentials and other technical considerations, it transpires that E c is insensitive to any but the most basic of properties of the states in question. The variational calculation of 6 E must be carried out numerically. Since the trial function is expected to be quite extended, q~can be approximated by an effecivemass-like solution with an envelope function of the form r v exp (--/3r). However, for most values of v and 18the matrix elements of rio and V/must be evaluated in the wave vector space so as to ensure that intra and interband effects peculiar to defects with medium range potentials and wave functions are correctly accounted for [15,181. The results of the calculation for GaPo.sAs0.s show that a stable N- configuration is possible with binding energy of about 12 meV. The contributions of rio and V i are 148 and --91 meV, respectively, and E c = Ej Eci -~ -- 69 meV. About 4% of the extra electron charge lies within the nearest neighbour distance from nitrogen. It can be seen that the binding energy is only a fraction of the correlation contribution which is obtained from a simplified model whose limits of applicability cannot be easily tested. Therefore, this calculation cannot provide any conclusive answer concerning the magnitude of the binding energy. However, it is clear that the correlation contribution is of correct order of magnitude to stabilise N-. The wave function of the weakly bound electron is much less localised than the one-electron solutions reported previously although it is significantly more localised than the wave function of a hydrogenic donor ground state in the same material. This is because in the present calculation the ground state of N- is controlled by the stabilising effect of the medium-range correlation potential. This potential depends on the well localised resonances shown in Fig. 1 and changes only slowly with x. However, since the electron wave function is delocalised, the expectation value of rio strongly reflects the properties of the band structure at the bottom of the conduction band. As x becomes smaller than 0.5, the F valley rapidly approaches the conduction band edge and for x ~<0.45 the material has a direct gap. Since the effective mass at F is very small, the positive contribution to 6 E rapidly increases near and below x -~ 0.5, and reduces the binding energy and the localisation of the wave function. This is precisely the behaviour observed in experiments. Not all isoelectronic impurities are expected to exhibit a stable negative-ion configuration. For example, GaP:As does not have a potential sufficientl7 strong to localise the states shown in Fig. 1 and both the correlation
413
contribution and V/are too small to stabilise a bound state. However, it has already been pointed out that the electronic structure which gives rise to the new state of N- in GapxAs~_x is characteristic of substitutional defects in covalent semiconductors which possess strong short-range potentials attractive to electrons. It is borne in mind that new stable configurations may be obtained in an analogous manner for other negatively charged systems. For example, this is the case for the substitutional donor oxygen in GaP. The relevant part of the electronic structure is qualitatively the same as that shown in Fig. 1. (For the neutral system of GaP :O°, there is one additional electron which occupies state al, with the corresponding level lowered deep into the forbidded gap.) The one-electron potential of O° is strong and binds deeply an extra electron [12, 16]. At low temperatures, the negative ion (O-) configuration is metastable at the perfect lattice site, with only small lattice relaxation present. Neither full scale one-electron calculations nor calculations analogous to those for H- produce stable excited states of O-. The excited states fail to materialise for very much the same reasons as they do at H-. However, if the effect of the electronic structure is fully taken into account, and the correlation contribution evaluated as above, both spin-triplet and spinsinglet excited configurations of O- are stable [17]. This is in agreement with recent experimental results [18] which show that the capture luminescence at GaP :O occurs via a weakly bound excited spin-singlet configuration of O-. To summarise, it has been shown that in covalent semiconductors correlation effects play an important part in stabilising new, weakly bound states of negativeion impurities. This effect derives its strength from the electronic structure which arises when the impurity potential pushes the valence s electrons at the foreign atom deep below the valence band. This modifies the covalent bond and leads to severall well localised states and enhanced configuration interactions. In the case of isoelectronic impurities the new stable state is the ground state of the negatively charged defect. In the case of hydrogen-like systems, the new states are the excited states of the negative ion. Although the approximate model of many-electron effects employed in this study leaves considerable uncertainty as far as the precise value of the binding energy is concerned, the significance of the correlation contribution is clearly demonstrated. In particular, the theory successfully explains recent experimental data concerning the formation of a stable state of negative nitrogen in GaPxASl_x. REFERENCES 1.
e.g. see A.M. Stoneham, T h e o r y o f D e f e c t s in Solids, Clarendon Press: Oxford (1975).
414 2. 3. 4. 5. 6. 7. 8. 9. 10.
NEW ELECTRON STATES OF NEGATIVE IONS IN SEMICONDUCTORS See H.S.W. Massey,Nagativelons, University Press: Cambridge (1976). J.J. Hopfield, D.G. Thomas & R.T. Lynch, Phys. Rev. Lett. 17,312 (1966). E. Cohen & M.D. Sturge,Phys. Rev. BIS, 1039 (1977). J.A. Kash, J.M. Collet, DJ. Wolford & J. Thompson,Phys. Rev. B27, 2294 (1983). M. Jaros & S. Brand, J. Phys. C12, 525 (1970). H.P. Hjalmarson, P. Vogl, DJ. Wolford and J.D. Dow,Phys. Rev. Lett. 44, 810 (1980). See M. Jaros, Deep Levels in Semiconductors, p. 97. (Hilger: Bristol (1982). P.W. Banks & M. Jaros,J. Phys. C14, 2333 (1981). DJ. Wolford, B.G. Streetman & J. Thompson, Physics of Semiconductors (1980); J. Phys. Soc. Japan 49, (Suppl. A), 223 (1980). A summary of
11. 12. 13. 14. 15. 16. 17. 18.
Vol. 51, No. 6
experimental and theoretical results concerning GaPxASl_x :N can be found in [8], p. 231. J. Bernholc, N.O. Lipari, S.T. Pantelides & M. Scheffler, Phys. Rev. B26, 5706 (1982). G.A. Baraff, E.O. Kane & M. Schluter,Phys. Rev. B25,548 (1982). See [8], p. 129 and M.J. Kirton, M. Jaros & S. Brand, Physica 116B, 79 (1983) (ICDS-12, Amsterdam, September 1982). MJ. Kirton, P.W. Banks, Lu da l_ian & M. Jaros, J. Phys. C. 14, 2487 (1984). D.C. Herbert &J. Inkson,J. Phys. CI0, L695 (1977); M. Altarelli, Phys. Rev. Lett. 46,205 (1981), M. Jaros,J. Phys. C8, 2455 (1975). M. Jaros, (to be published in J. Phys. 6). P.J. Dean, M.S. Skolnick, C.H. Uhlein & D.C. Herbert,J. Phys. C16, 2017 (1983).