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The doping mechanism in amorphous silicon
Journal of Non-CrystallineSolids97&98 (1987) 495-498 North-Holland, Amsterdam
495
THE DOPING MECHANISM IN AMORPHOUS SILICON
C.S. NICHOLS (a), (b)*, L.H. YANG (a) and C.Y. FONG (a) (a) Physics Department, University of California, Davis, CA 95616 USA (b) Max-Planck-Institut fur Festkoperforschung, Heisenbergstrasse 1, D-7000 Stuttgart 80, Federal Republic of Germany We use the Slater-Koster scheme of the tight-binding method and ab-initio non-local pseudopotentials to study the electronic structure of P, As and B in threefold < 3 >and fourfold < 4 >-coordinated sites in periodic models of amorphous silicon and hydrogenated amorphous silicon. We have also investigated < 4 > P impurities with a second neighbor dangling bond. The properties of the impurity states are discussed with reference to local disorder. Comparisons are given to other theoretical calculations and to experimental results. The implications of our study for the doping mechanism in amorphous silicon are also discussed. INTRODUCTION Since the first successful doping of amorphous silicon (a-Si) by Spear and Le Comber [1] in 1975, two curious features of the doping process have emerged. First, the doping efficiency, that is, the fraction of impurity atoms in an a-Si sample which are electrically active, is usually very small, 0.1-1096 [2]. Second, an increase in the concentration of an impurity species is coupled to an increase in the dangling bond density [3]. To explain the low doping efficiency, it has been suggested, that Group III and Group V impurity atoms adopt configurations which satisfy their valency and hence render them electrically neutral. Furthermore, Adler [4] and, more recently, Street [5], have proposed that in order for an impurity to be incorporated into the a-Si network in a non-valencysatisfying configuration, it must be "paired" with a defect. Adler specifically invoked an intimate impurity-dangling bond (d.b.) pair. We have carried out a series of calculations which probe these two facets of the doping mechanism in a-Si. In the first instance, we compare the nature of the states produced by P, As and B impurities in < 4 > and < 3 > environments in a-Si and hydrogenated a-Si (a-Si:H). We also report preliminary results of a study of intimate P-d.b. pairs in a realistic supercell model of a-Si:H. CALCULATIONS As our calculational techniques have been described in greater length elsewhere [6, * Address aSterSeptember 1987: I B M T.J. Watson Research Center,Yorktown Heights,N e w York 10598
0022-3093/87/$03.50 ©Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
496
CS. Nichols et al. / The doping mechanism in amorphous silicon
7], we mention only a few relevant details here. For both a-Si and a-Si:H, we use the computer-generated models of Guttman [8]. The a-Si models have 54 Si atoms, while the a-Si:H model contains 54 Si atoms and 6 H atoms. For the tight-binding calculations, the Slater-Koster parameters for up to first neighbor interactions are scaled from those found by Li and Lin-Chung [9, 10]. For the pseudopotential calculations, we use the ab-initio pseudopotentials of Bachelet, Hamann and Schluter [11], and a plane wave basis, with the local density-functional formalism for the electron-electron interactions. Enough plane waves are included so that the cutoff energy is 3.1 Ryd. RESULTS Results for < 4 > As and P in a-Si and P and B in a-Si:H are summarized in Table Ia. This table also shows a comparison between our present findings and previous results calculated by Robertson [12]. We find that the impurity states depend sensitively upon the local bond-angle disorder. A variety of sites with differing angular distortions were studied. The greater the local bond-angle disorder around the impurity atom, the greater the donor/acceptor state binding energy. Furthermore, our calculations indicate that local distortion causes the impurity states to broaden into a band which can merge with the Si band edge. Generally we find the impurity states deeper in the gap and also considerably more broadened than does Robertson. Our results are, moreover, in better agreement in both respects to electron spin resonance experiments [13], than Robertson's. Table Ia. A comparison between the calculated properties of the impurity states of < 4 > As, P and B and previous results of Robertson.
(i): Tight-binding calculations; (ii):
Pseudopotential calculations. The values quoted are average quantities (same for Ib). Energy of the impurity state
Present Results
Robertson [12]
compared to the appropriate
P: Ec-0.2 eV (i)
P: Ec-0.1 eV
band edge.
Amount of broadening of impurity state caused by local angular distortion
Ec-0.25 eV (ii) As: Ec-0.2 eV (i)
As: Ec-0.3 eV
B: Ev+0.35 eV (ii)
B: Ev+0.1 eV
P, As: 0.3 eV (i)
P, As: 0.05 eV
0.3 eV (ii) B: 0.2 eV (ii)
B: 0.2 eV
The results for < 3 > impurities are summarized in Table Ib. Two sites for each impurity were studied. The average bond angle deviations, A0, from selected symmetries are listed in the second column of Table Ib. P has a lone pair orbital and B has a nonbonding p orbital perpendicular to the plane containing the B atom and its three neighbors.
C.S. Nichols et al. / The doping mechanism in amorphous silicon
497
Similar to previous calculations done by Robertson [14] and by Bernholc [15],we find the lone pair state of P at or below the valence band (VB) edge, Er. In contradiction, we find the non-bonding state of B above the conduction band (CB) edge, Ec. W e believe the difference is a manifestation of the dissimilar local environments of the two impurities from the previous calculations to ours. As with the < 4 > impurities, local bond-angle distortion causes a broadening of the impurity level. However, in contrast to < 4 > impurities, < 3 > impurities either always introduce no gap states (B) or only sometimes introduce gap states (P). Table Ib. A comparison of the impurity states of < 3 > P and B and previous results of Robertson and Bernholc. (a): pyramidal site; Csr symmetry; (b): planar site; Dsh symmetry. Energy of the impurity state
A0(°)
Present Results
Robertson [14]
Bernholc [15]
10.5
P: E~-0.35 eV
P: bottom of V B
P: E~-0.4 eV
10.5
B: E v + l . 5 eV (a)
B: E~+I.0 eV
B: E~+0.2 eV (a)
7.8
S~+0.9 eV (b)
E~+0.6 eV (b)
Amount of
P: 0.7 eV
P: none
P: none
broadening
B: 0.6 eV
B: none
B: 0.4 eV
Character of
P: p-like
P: s-like
P: p-like
impurity state
B: mixture
Lastly, two cases of intimate < 4 > P-d.b. pairs are studied. The existence of this defect complex is supported by arguments t h a t it is a lower energy configuration than an average-network-coordination-reducing (and hence strain relieving) < 3 > impurity. For b o t h pairs, the impurity state is found at Ec + 0.1 eV. The d.b. state is found at an average of E~ + 0.3 eV. Charge density plots, although not reproduced here, indicate a charge transfer from the < 4 > P to d.b. Whether it is the resulting Coulomb attraction between the two species or the local distortion which causes the occupied d.b. state ( D - ) to be 0.5 eV smaller than the measured value [16] must be determined by further calculations. Passivation of the d.b. by a single additional H atom moves the P impurity state to Ec - 0 . 1 eV. This downward shift can be attributed to the charge of the impurity state remaining around < 4 > P site in the presence of the H-atom. In summary, < 4 > P, As and B produce a band of states which can overlap either the CB or VB edge, respectively. The average energies, the amount of broadening, and the relative depths of the As and P levels agree well with the published experimental results [3], exclusive of B for which it is difficult to obtain unambiguous experimental results.
498
CS. Nichols et aL / The doping mechanism in amorphous silicon
< 3 > P and B produce a band of states either at the VB edge (P), or well into the CB (B). Both Robertson [14] and Bernholc [15] reported that < 3 > B produces a gap state. We have not located any experimental evidence for a non-bonding < 3 > B gap state. The presence of d.b.'s in a-Si:H relieves strain at the second neighbor site of the d.b., as evidenced by the small angular deviation of these sites (3.88 ° and 5.36 ° for the two sites studied here). Incorporation of a < 4 > P impurity at these sites introduces the impurity state at Ec + 0.1 eV. However, with an H second neighbor, the energy of the P impurity state is shifted down by 0.2 eV. Taken together, our results for < 4 > pod.b, pairs in a-Si:H are consistent with Street's [3] interpretation of numerous experimental data. The charged P states lie above the neutral P states. ACKNOWLEDGMENTS We thank the San Diego Supercomputer Center for partial support. One of us (CSN) would also like to acknowledge the support of the Hughes Aircraft Company in the form of a Hughes Predoctoral Fellowship and the Max-Planck-Institut fur Festkorperforschung. REFERENCES 1. W.E. Spear and P.G. Le Comber, Sol. State Comm. 17, 1193 (1975). 2. R.A. Street, D.K. Biegelsen, and J.C. Knights, Phys. Rev. B 24, 969 (1981) and references therein. 3. R.A. Street, J. Non-Cryst. Sol. 77 & 78, 1 (1985) and references therein. 4. D. Adler, Phys. Rev. Lett. 41, 1755 (1978). 5. R.A. Street, Phys. Rev. Lett. 49, 1187 (1982). 6. C.S. Nichols and C.Y. Fong, Phys. Rev. B, 35, 9360 (1987). 7. C.S. Nichols and C.Y. Fong, MRS Proceedings (1987), in publication. 8. L. Guttman, in "Tetrahedrally Bonded Amorphous Semiconductors" (Yorktown Heights), edited by M.H. Brodsky, S. Kirkpatrick and D. Weaire, AIP Conf. Proc. No. 20 (AIP, New York, 1974), p. 224 and L. Guttman, Phys. Rev. B 23, 1866
(1981). 9. Y. Li and P.J. Lin-Chung, Phys. Rev. B 27, 3465 (1983). 10. Y. Li and P.J. Lin-Chung, J. Phys. Chem. Solids 46, 241 (1985). 11. G.B. Bachelet, D.R. Hamann and M. Schluter, Phys. Rev. B 26, 433 (1982). 12. J. Robertson, Phys. Rev. B 28, 4647 (1983). 13. M. Stutzmann and R.A. Street, Phys. Rev. Lett. 54, 1836 (1985). 14. J. Robertson, Phys. Rev. B 28, 4666 (1983). 15. J. Bernholc, in 13th Intl. Conf. Proc. on Defects in Semicond., edited by L.C. Kimerling and J.M. Parsey, Jr., (Metallurgical Society, 1984), p. 781. 16. I. Hirabayashi, K. Morigaki and N. Nitta, J. Non. Cryst. Sol. 77 & 78, 519 (1985).
495
THE DOPING MECHANISM IN AMORPHOUS SILICON
C.S. NICHOLS (a), (b)*, L.H. YANG (a) and C.Y. FONG (a) (a) Physics Department, University of California, Davis, CA 95616 USA (b) Max-Planck-Institut fur Festkoperforschung, Heisenbergstrasse 1, D-7000 Stuttgart 80, Federal Republic of Germany We use the Slater-Koster scheme of the tight-binding method and ab-initio non-local pseudopotentials to study the electronic structure of P, As and B in threefold < 3 >and fourfold < 4 >-coordinated sites in periodic models of amorphous silicon and hydrogenated amorphous silicon. We have also investigated < 4 > P impurities with a second neighbor dangling bond. The properties of the impurity states are discussed with reference to local disorder. Comparisons are given to other theoretical calculations and to experimental results. The implications of our study for the doping mechanism in amorphous silicon are also discussed. INTRODUCTION Since the first successful doping of amorphous silicon (a-Si) by Spear and Le Comber [1] in 1975, two curious features of the doping process have emerged. First, the doping efficiency, that is, the fraction of impurity atoms in an a-Si sample which are electrically active, is usually very small, 0.1-1096 [2]. Second, an increase in the concentration of an impurity species is coupled to an increase in the dangling bond density [3]. To explain the low doping efficiency, it has been suggested, that Group III and Group V impurity atoms adopt configurations which satisfy their valency and hence render them electrically neutral. Furthermore, Adler [4] and, more recently, Street [5], have proposed that in order for an impurity to be incorporated into the a-Si network in a non-valencysatisfying configuration, it must be "paired" with a defect. Adler specifically invoked an intimate impurity-dangling bond (d.b.) pair. We have carried out a series of calculations which probe these two facets of the doping mechanism in a-Si. In the first instance, we compare the nature of the states produced by P, As and B impurities in < 4 > and < 3 > environments in a-Si and hydrogenated a-Si (a-Si:H). We also report preliminary results of a study of intimate P-d.b. pairs in a realistic supercell model of a-Si:H. CALCULATIONS As our calculational techniques have been described in greater length elsewhere [6, * Address aSterSeptember 1987: I B M T.J. Watson Research Center,Yorktown Heights,N e w York 10598
0022-3093/87/$03.50 ©Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
496
CS. Nichols et al. / The doping mechanism in amorphous silicon
7], we mention only a few relevant details here. For both a-Si and a-Si:H, we use the computer-generated models of Guttman [8]. The a-Si models have 54 Si atoms, while the a-Si:H model contains 54 Si atoms and 6 H atoms. For the tight-binding calculations, the Slater-Koster parameters for up to first neighbor interactions are scaled from those found by Li and Lin-Chung [9, 10]. For the pseudopotential calculations, we use the ab-initio pseudopotentials of Bachelet, Hamann and Schluter [11], and a plane wave basis, with the local density-functional formalism for the electron-electron interactions. Enough plane waves are included so that the cutoff energy is 3.1 Ryd. RESULTS Results for < 4 > As and P in a-Si and P and B in a-Si:H are summarized in Table Ia. This table also shows a comparison between our present findings and previous results calculated by Robertson [12]. We find that the impurity states depend sensitively upon the local bond-angle disorder. A variety of sites with differing angular distortions were studied. The greater the local bond-angle disorder around the impurity atom, the greater the donor/acceptor state binding energy. Furthermore, our calculations indicate that local distortion causes the impurity states to broaden into a band which can merge with the Si band edge. Generally we find the impurity states deeper in the gap and also considerably more broadened than does Robertson. Our results are, moreover, in better agreement in both respects to electron spin resonance experiments [13], than Robertson's. Table Ia. A comparison between the calculated properties of the impurity states of < 4 > As, P and B and previous results of Robertson.
(i): Tight-binding calculations; (ii):
Pseudopotential calculations. The values quoted are average quantities (same for Ib). Energy of the impurity state
Present Results
Robertson [12]
compared to the appropriate
P: Ec-0.2 eV (i)
P: Ec-0.1 eV
band edge.
Amount of broadening of impurity state caused by local angular distortion
Ec-0.25 eV (ii) As: Ec-0.2 eV (i)
As: Ec-0.3 eV
B: Ev+0.35 eV (ii)
B: Ev+0.1 eV
P, As: 0.3 eV (i)
P, As: 0.05 eV
0.3 eV (ii) B: 0.2 eV (ii)
B: 0.2 eV
The results for < 3 > impurities are summarized in Table Ib. Two sites for each impurity were studied. The average bond angle deviations, A0, from selected symmetries are listed in the second column of Table Ib. P has a lone pair orbital and B has a nonbonding p orbital perpendicular to the plane containing the B atom and its three neighbors.
C.S. Nichols et al. / The doping mechanism in amorphous silicon
497
Similar to previous calculations done by Robertson [14] and by Bernholc [15],we find the lone pair state of P at or below the valence band (VB) edge, Er. In contradiction, we find the non-bonding state of B above the conduction band (CB) edge, Ec. W e believe the difference is a manifestation of the dissimilar local environments of the two impurities from the previous calculations to ours. As with the < 4 > impurities, local bond-angle distortion causes a broadening of the impurity level. However, in contrast to < 4 > impurities, < 3 > impurities either always introduce no gap states (B) or only sometimes introduce gap states (P). Table Ib. A comparison of the impurity states of < 3 > P and B and previous results of Robertson and Bernholc. (a): pyramidal site; Csr symmetry; (b): planar site; Dsh symmetry. Energy of the impurity state
A0(°)
Present Results
Robertson [14]
Bernholc [15]
10.5
P: E~-0.35 eV
P: bottom of V B
P: E~-0.4 eV
10.5
B: E v + l . 5 eV (a)
B: E~+I.0 eV
B: E~+0.2 eV (a)
7.8
S~+0.9 eV (b)
E~+0.6 eV (b)
Amount of
P: 0.7 eV
P: none
P: none
broadening
B: 0.6 eV
B: none
B: 0.4 eV
Character of
P: p-like
P: s-like
P: p-like
impurity state
B: mixture
Lastly, two cases of intimate < 4 > P-d.b. pairs are studied. The existence of this defect complex is supported by arguments t h a t it is a lower energy configuration than an average-network-coordination-reducing (and hence strain relieving) < 3 > impurity. For b o t h pairs, the impurity state is found at Ec + 0.1 eV. The d.b. state is found at an average of E~ + 0.3 eV. Charge density plots, although not reproduced here, indicate a charge transfer from the < 4 > P to d.b. Whether it is the resulting Coulomb attraction between the two species or the local distortion which causes the occupied d.b. state ( D - ) to be 0.5 eV smaller than the measured value [16] must be determined by further calculations. Passivation of the d.b. by a single additional H atom moves the P impurity state to Ec - 0 . 1 eV. This downward shift can be attributed to the charge of the impurity state remaining around < 4 > P site in the presence of the H-atom. In summary, < 4 > P, As and B produce a band of states which can overlap either the CB or VB edge, respectively. The average energies, the amount of broadening, and the relative depths of the As and P levels agree well with the published experimental results [3], exclusive of B for which it is difficult to obtain unambiguous experimental results.
498
CS. Nichols et aL / The doping mechanism in amorphous silicon
< 3 > P and B produce a band of states either at the VB edge (P), or well into the CB (B). Both Robertson [14] and Bernholc [15] reported that < 3 > B produces a gap state. We have not located any experimental evidence for a non-bonding < 3 > B gap state. The presence of d.b.'s in a-Si:H relieves strain at the second neighbor site of the d.b., as evidenced by the small angular deviation of these sites (3.88 ° and 5.36 ° for the two sites studied here). Incorporation of a < 4 > P impurity at these sites introduces the impurity state at Ec + 0.1 eV. However, with an H second neighbor, the energy of the P impurity state is shifted down by 0.2 eV. Taken together, our results for < 4 > pod.b, pairs in a-Si:H are consistent with Street's [3] interpretation of numerous experimental data. The charged P states lie above the neutral P states. ACKNOWLEDGMENTS We thank the San Diego Supercomputer Center for partial support. One of us (CSN) would also like to acknowledge the support of the Hughes Aircraft Company in the form of a Hughes Predoctoral Fellowship and the Max-Planck-Institut fur Festkorperforschung. REFERENCES 1. W.E. Spear and P.G. Le Comber, Sol. State Comm. 17, 1193 (1975). 2. R.A. Street, D.K. Biegelsen, and J.C. Knights, Phys. Rev. B 24, 969 (1981) and references therein. 3. R.A. Street, J. Non-Cryst. Sol. 77 & 78, 1 (1985) and references therein. 4. D. Adler, Phys. Rev. Lett. 41, 1755 (1978). 5. R.A. Street, Phys. Rev. Lett. 49, 1187 (1982). 6. C.S. Nichols and C.Y. Fong, Phys. Rev. B, 35, 9360 (1987). 7. C.S. Nichols and C.Y. Fong, MRS Proceedings (1987), in publication. 8. L. Guttman, in "Tetrahedrally Bonded Amorphous Semiconductors" (Yorktown Heights), edited by M.H. Brodsky, S. Kirkpatrick and D. Weaire, AIP Conf. Proc. No. 20 (AIP, New York, 1974), p. 224 and L. Guttman, Phys. Rev. B 23, 1866
(1981). 9. Y. Li and P.J. Lin-Chung, Phys. Rev. B 27, 3465 (1983). 10. Y. Li and P.J. Lin-Chung, J. Phys. Chem. Solids 46, 241 (1985). 11. G.B. Bachelet, D.R. Hamann and M. Schluter, Phys. Rev. B 26, 433 (1982). 12. J. Robertson, Phys. Rev. B 28, 4647 (1983). 13. M. Stutzmann and R.A. Street, Phys. Rev. Lett. 54, 1836 (1985). 14. J. Robertson, Phys. Rev. B 28, 4666 (1983). 15. J. Bernholc, in 13th Intl. Conf. Proc. on Defects in Semicond., edited by L.C. Kimerling and J.M. Parsey, Jr., (Metallurgical Society, 1984), p. 781. 16. I. Hirabayashi, K. Morigaki and N. Nitta, J. Non. Cryst. Sol. 77 & 78, 519 (1985).