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Resonant interactions of phonons with donor continuum states in silicon
Solid State Communications, Vol. 54, No. 3, pp. 287-289, Printed in Great Britain.
1985.
0038-1098/85 $3.00 t .OO Pergamon Press Ltd.
RESONANT INTERACTIONS OF PHONONS WITH DONOR CONTINUUM STATES IN SILICON* H.R. Chandrasekhar, Meera Chandrasekhar Department of Physics and Astronomy, University of Missouri-Columbia, Missouri 652 11, USA K.K. Bajaj U.S. Air Force Wright Aeronautical Laboratories, Avionics Laboratory (AFWAL/AADR), Wright Patterson Air Force Base, Ohio 45433, USA N. Sclar Science Center, Rockwell International, Anaheim, California, USA (Received 26 September 1984 by M. Cardona)
A study of the extrinsic photoconductivity spectra of phosphorus and antimony donors in silicon at 1.5”K has revealed anti-resonances (dips) in the continuum photo response. These dips occur at 380, 437, 479, and 504cm-’ for both donors. We interpret these dips as due to a resonant interaction of the donor continuum states with the discrete phonon states. Analogous interaction of the zone center optical phonon at 520 cm-’ with the acceptor continuum state of boron as observed by Watkins et al. is not present in our spectra. This is attributed to the mismatch of the wave vector and the energy of the 520 cm-’ phonon with the conduction band minima along (1 0 0) directions. The specific phonons giving rise to antiresonances inour data are identified. INTRODUCTION A STUDY OF THE EXTRINSIC photoconductivity spectra of phosphorus and antimony donors in silicon at 1.5 K has revealed anti-resonances (dips) in the continuum photo response. These dips occur at 380, 437, 479, and 504cm-r for both donors. The samples are homogenously doped detector quality wafers obtained from zone-refined float-zone single crystals. The energies of the dips do not correspond to those of any other impurities in silicon. The energies, however, are in close proximity to the energies of the critical points in the vibrational density of states in silicon. We interpret these dips as due to a resonant interaction of the donor continuum states with the discrete phonon states. An analogous interaction of the zone center optical phonon at 520cm-’ with the acceptor continuum state of boron, as observed by Watkins et al. [l ] is not present in our spectra. This is attributed to the mismatch of the wave vector and the energy of the 520cm-’ phonon with the conduction band minima along (1 0 0) directions. The specific phonons giving rise to antiresonances in our data are identified. EXPERIMENTAL RESULTS AND DISCUSSION The samples were cut from single-crystal float zone silicon. The material was purified by zone refining prior *Supported by the U.S. Department of Energy under Contract No. DE-AC02 84ER 45048.
to growth. Residual impurities other than boron are vaporized or swept down to the ends of the boule. The boron concentration is in the range of lOi cm-‘. Doping with the impurity of interest was accomplished by insertion of calculated amounts before crystal growth. The doping concentration varies along the growth axis but has a very high radial uniformity. The samples are obtained from wafers cut in the radial plane. After lapping and polishing, phosphorus was diffused into surfaces to provide a heavily doped degenerate layer. The surfaces were then metallized sequentially with electroless nickel and electroplated indium. One of the contacts was fused to a tinned copper heat sink and the other soldered to the metal wire for the external circuitry. The infrared radiation reaches the detector transverse to these contacts via a light pipe arrangement. Room temperature radiation was minimized by placing a cold filter in front of the sample which was immersed in liquid helium. A FS-720 Fourier transform spectrometer equipped with a dedicated computer to perform a real time analysis of the data was used. We present here some preliminary results of extrinsic photoconductivity in silicon at low temperatures and controlled background radiation. Samples doped with antimony or phosphorus donors of various donor concentrations were used. Figure 1 shows the photoresponse of phosphorus (P) and antimony (Sb) doped silicon at 1.4K. These 287
RESONANT INTERACTIONS
288
Sl : P
0 200
I
400
600
PHOTON ENEMY
800
iOO0
Icm”l
Fig. 1. Photoresponse of phosphorus donors in silicon at 1.4K.
and antimony
spectra have not been corrected for the instrumental response which decreases rapidly with increasing photon energy above 500 cm-’ . A few features are worth noting in Fig. 1. The response increases sharply around 300-370 cm-’ . The ionization energies (8’r) of P and Sb donors in Si are 367.6 cm-’ and 344.9 cm-’ , respectively. The structure below EI is due to photothermal transitions of electrons from the impurity ground state to the excited states followed by thermal ionization to the conduction band. Due to the extremely low temperatures (1.4-4.2 K) at which the experiments were performed, the photothermal process is very weak as expected. The features which are new and observed for the first time are the relatively sharp dips in the electronic continuum of both Sb and P at 380, 394(weak), 437, 479 and 504 cm-’ and a broad dip at 720 cm-’ . A careful examination of the energy positions of the dips indicate that they do not correspond to any donor or acceptor impurity which may be present in trace quantities in our samples. We have also examined samples with impurity concentrations (No) ranging from 1014 cmv3 to 1016 cme3 and find that the position and intensity of the dips do not change with No. Hence we rule out localized vibrations of the impurities or the defect induced lattice absorption. We interpret these dips in the spectra as due to a resonant interaction between the localized phonons and the zero-phonon electronic excitations of the impurity to the continuum. An analogous effect has been observed in the boron acceptor spectrum of silicon by Watkins and Fowler [l]. They observed an antiresonance at 5 19 cm-’ and correctly interpreted it as due to a Breit-Wigner-Fano type resonant interaction of the continuum states of the impurity and the zonecenter optical phonon. Since the valence band maximum
OF PHONONS
Vol. 54, No. 3
and hence the acceptor states of silicon are at the zonecenter, the strongest interaction occurs for the zonecenter phonon. However, in the case of donors the situation is somewhat different. The donor states are tied to the conduction band minima which are along the (1 0 0) directions. There are six equivalent [ 1 0 0] valleys. The specific phonons which satisfy the energy and wavevector relation to be resonant with the electronic continuum are identified in Table 1. The interaction of some hydrogenic bound-tobound transitions of impurities in silicon with the optical phonons when the energy of the discrete state of the impurity coincides with that of the phonon has been studied [2-41. In the case of gallium and aluminum acceptors, the zone-center optic phonon (520 cm-‘) interacts strongly with some ls+2p transitions of the impurity. Phonons of other symmetry in particular the 477 cm-’ transverse optic phonons with wave-vectors in the (1 1 0) direction, do not mix with the acceptor states. In contrast, for bismuth donors in silicon [4], one of the 1s -+ 2p transitions strongly interacts with the 477 cm-’ phonon, whereas there is no interaction with the zone-center-optic phonon. The selection rule for interacting phonons of specific wavevectors to satisfy the energy and momentum conservation is similar to that observed by us. The principal difference between these experiments and ours is that the former deals with the bound-to-bound transitions and the latter with the impurity continuum. The observed structure at higher energies (greater than the highest energy in the one phonon density of states) can be ascribed to the interaction of phonon sidebands of the electronic excitations of the impurity and transitions to the no-phonon continuum. The zone center TO (520cm-‘) phonon sideband of the Is,, + 2p,, transition of boron, aluminum of gallium acceptors is seen to interact resonantly with the nophonon continuum of the acceptor to produce antiresonances in the absorption spectra [l] . Humphreys et al. [5] have observed dips in the no-phonon continuum of photo response of sulphur donors in silicon and interpret them as due to one-phonon sidebands of the bound-to-bound transitions. The phonon involved here is the 477 cm-’ TO phonon. Unlike the case of the acceptors in silicon where the impurity states and the phonons are at the zone center (k = 0), the donor states occur along approximately (0.8, 0, 0) direction. The interaction in this case would involve an intervalley scattering of the electron by phonons of the appropriate wavevector [6] . Onton [7] has ascribed some dips in the photoresponse of P, As and Sb donors in silicon to the one and two-phonon side bands of the ionization energy of the impurity. (Note that Ref. 7 did not include the O-500 cm-’ spectral range in which the first
Vol. 54, No. 3
RESONANT INTERACTIONS
Table 1. The BWF antiresonances in the photoresponse in (cm-’ ) and the associated phonons. Si(P)
Si(Sb)
Assignment
386 437 477 503 570
382 437 479 504 560
LA(l,O.21,0.21) LO(l,O.21,0.21) TO(1 10) TO<1 1 1)or 2LA(lO EI + LA (0.42,0,0)
720 820 (broad)
720 780-870 (broad)
971
970
Er+LA(I, 0.21,0.21) E1+LO(1,0.21,0.21) Er+TO(l 10) E1-tTO(l 11) Er + 2LA (0.42,0,0) EI + 3LA (0.42,0,0)
289
of Onton, and the additional structure observed in our spectra can easily be accounted for by the many possible phonons and the impurity states. In particular, the dips at 560,720 and 760 cm-’ can be assigned as in Ref. 7.
REFERENCES
0)
four dips are observed by us). Our data in the 50012OOcm-’ region is in qualitative agreement with that
OF PHONONS
1. 2 ’ 3. 4. 5
67:
G.D. Watkins & W.B. Fowler, Phys. Rev. B16, 4524 (1977). A. Onton, P. Fisher & A.K. Ramdas, Phys. Rev. Lett. 19,781 (1967). H.R. Chandrasekhar, A.K. Ramdas & S. Rodriguez, .Phys. Rev. B14,2417 (1976). N.R. Butler, P. Fisher & A.K. Ramdas,Phys. Rev. Bl2,3200 (1975). R.G. Humphreys, P. Migliorato & G. Fortunato, SolidState Commun 40,819 (1981). W.P. Dun&e, Phys. Rev. 118,938 (1960). A. Onton, Phys. Rev. Lett., 22,288 (1969).
1985.
0038-1098/85 $3.00 t .OO Pergamon Press Ltd.
RESONANT INTERACTIONS OF PHONONS WITH DONOR CONTINUUM STATES IN SILICON* H.R. Chandrasekhar, Meera Chandrasekhar Department of Physics and Astronomy, University of Missouri-Columbia, Missouri 652 11, USA K.K. Bajaj U.S. Air Force Wright Aeronautical Laboratories, Avionics Laboratory (AFWAL/AADR), Wright Patterson Air Force Base, Ohio 45433, USA N. Sclar Science Center, Rockwell International, Anaheim, California, USA (Received 26 September 1984 by M. Cardona)
A study of the extrinsic photoconductivity spectra of phosphorus and antimony donors in silicon at 1.5”K has revealed anti-resonances (dips) in the continuum photo response. These dips occur at 380, 437, 479, and 504cm-’ for both donors. We interpret these dips as due to a resonant interaction of the donor continuum states with the discrete phonon states. Analogous interaction of the zone center optical phonon at 520 cm-’ with the acceptor continuum state of boron as observed by Watkins et al. is not present in our spectra. This is attributed to the mismatch of the wave vector and the energy of the 520 cm-’ phonon with the conduction band minima along (1 0 0) directions. The specific phonons giving rise to antiresonances inour data are identified. INTRODUCTION A STUDY OF THE EXTRINSIC photoconductivity spectra of phosphorus and antimony donors in silicon at 1.5 K has revealed anti-resonances (dips) in the continuum photo response. These dips occur at 380, 437, 479, and 504cm-r for both donors. The samples are homogenously doped detector quality wafers obtained from zone-refined float-zone single crystals. The energies of the dips do not correspond to those of any other impurities in silicon. The energies, however, are in close proximity to the energies of the critical points in the vibrational density of states in silicon. We interpret these dips as due to a resonant interaction of the donor continuum states with the discrete phonon states. An analogous interaction of the zone center optical phonon at 520cm-’ with the acceptor continuum state of boron, as observed by Watkins et al. [l ] is not present in our spectra. This is attributed to the mismatch of the wave vector and the energy of the 520cm-’ phonon with the conduction band minima along (1 0 0) directions. The specific phonons giving rise to antiresonances in our data are identified. EXPERIMENTAL RESULTS AND DISCUSSION The samples were cut from single-crystal float zone silicon. The material was purified by zone refining prior *Supported by the U.S. Department of Energy under Contract No. DE-AC02 84ER 45048.
to growth. Residual impurities other than boron are vaporized or swept down to the ends of the boule. The boron concentration is in the range of lOi cm-‘. Doping with the impurity of interest was accomplished by insertion of calculated amounts before crystal growth. The doping concentration varies along the growth axis but has a very high radial uniformity. The samples are obtained from wafers cut in the radial plane. After lapping and polishing, phosphorus was diffused into surfaces to provide a heavily doped degenerate layer. The surfaces were then metallized sequentially with electroless nickel and electroplated indium. One of the contacts was fused to a tinned copper heat sink and the other soldered to the metal wire for the external circuitry. The infrared radiation reaches the detector transverse to these contacts via a light pipe arrangement. Room temperature radiation was minimized by placing a cold filter in front of the sample which was immersed in liquid helium. A FS-720 Fourier transform spectrometer equipped with a dedicated computer to perform a real time analysis of the data was used. We present here some preliminary results of extrinsic photoconductivity in silicon at low temperatures and controlled background radiation. Samples doped with antimony or phosphorus donors of various donor concentrations were used. Figure 1 shows the photoresponse of phosphorus (P) and antimony (Sb) doped silicon at 1.4K. These 287
RESONANT INTERACTIONS
288
Sl : P
0 200
I
400
600
PHOTON ENEMY
800
iOO0
Icm”l
Fig. 1. Photoresponse of phosphorus donors in silicon at 1.4K.
and antimony
spectra have not been corrected for the instrumental response which decreases rapidly with increasing photon energy above 500 cm-’ . A few features are worth noting in Fig. 1. The response increases sharply around 300-370 cm-’ . The ionization energies (8’r) of P and Sb donors in Si are 367.6 cm-’ and 344.9 cm-’ , respectively. The structure below EI is due to photothermal transitions of electrons from the impurity ground state to the excited states followed by thermal ionization to the conduction band. Due to the extremely low temperatures (1.4-4.2 K) at which the experiments were performed, the photothermal process is very weak as expected. The features which are new and observed for the first time are the relatively sharp dips in the electronic continuum of both Sb and P at 380, 394(weak), 437, 479 and 504 cm-’ and a broad dip at 720 cm-’ . A careful examination of the energy positions of the dips indicate that they do not correspond to any donor or acceptor impurity which may be present in trace quantities in our samples. We have also examined samples with impurity concentrations (No) ranging from 1014 cmv3 to 1016 cme3 and find that the position and intensity of the dips do not change with No. Hence we rule out localized vibrations of the impurities or the defect induced lattice absorption. We interpret these dips in the spectra as due to a resonant interaction between the localized phonons and the zero-phonon electronic excitations of the impurity to the continuum. An analogous effect has been observed in the boron acceptor spectrum of silicon by Watkins and Fowler [l]. They observed an antiresonance at 5 19 cm-’ and correctly interpreted it as due to a Breit-Wigner-Fano type resonant interaction of the continuum states of the impurity and the zonecenter optical phonon. Since the valence band maximum
OF PHONONS
Vol. 54, No. 3
and hence the acceptor states of silicon are at the zonecenter, the strongest interaction occurs for the zonecenter phonon. However, in the case of donors the situation is somewhat different. The donor states are tied to the conduction band minima which are along the (1 0 0) directions. There are six equivalent [ 1 0 0] valleys. The specific phonons which satisfy the energy and wavevector relation to be resonant with the electronic continuum are identified in Table 1. The interaction of some hydrogenic bound-tobound transitions of impurities in silicon with the optical phonons when the energy of the discrete state of the impurity coincides with that of the phonon has been studied [2-41. In the case of gallium and aluminum acceptors, the zone-center optic phonon (520 cm-‘) interacts strongly with some ls+2p transitions of the impurity. Phonons of other symmetry in particular the 477 cm-’ transverse optic phonons with wave-vectors in the (1 1 0) direction, do not mix with the acceptor states. In contrast, for bismuth donors in silicon [4], one of the 1s -+ 2p transitions strongly interacts with the 477 cm-’ phonon, whereas there is no interaction with the zone-center-optic phonon. The selection rule for interacting phonons of specific wavevectors to satisfy the energy and momentum conservation is similar to that observed by us. The principal difference between these experiments and ours is that the former deals with the bound-to-bound transitions and the latter with the impurity continuum. The observed structure at higher energies (greater than the highest energy in the one phonon density of states) can be ascribed to the interaction of phonon sidebands of the electronic excitations of the impurity and transitions to the no-phonon continuum. The zone center TO (520cm-‘) phonon sideband of the Is,, + 2p,, transition of boron, aluminum of gallium acceptors is seen to interact resonantly with the nophonon continuum of the acceptor to produce antiresonances in the absorption spectra [l] . Humphreys et al. [5] have observed dips in the no-phonon continuum of photo response of sulphur donors in silicon and interpret them as due to one-phonon sidebands of the bound-to-bound transitions. The phonon involved here is the 477 cm-’ TO phonon. Unlike the case of the acceptors in silicon where the impurity states and the phonons are at the zone center (k = 0), the donor states occur along approximately (0.8, 0, 0) direction. The interaction in this case would involve an intervalley scattering of the electron by phonons of the appropriate wavevector [6] . Onton [7] has ascribed some dips in the photoresponse of P, As and Sb donors in silicon to the one and two-phonon side bands of the ionization energy of the impurity. (Note that Ref. 7 did not include the O-500 cm-’ spectral range in which the first
Vol. 54, No. 3
RESONANT INTERACTIONS
Table 1. The BWF antiresonances in the photoresponse in (cm-’ ) and the associated phonons. Si(P)
Si(Sb)
Assignment
386 437 477 503 570
382 437 479 504 560
LA(l,O.21,0.21) LO(l,O.21,0.21) TO(1 10) TO<1 1 1)or 2LA(lO EI + LA (0.42,0,0)
720 820 (broad)
720 780-870 (broad)
971
970
Er+LA(I, 0.21,0.21) E1+LO(1,0.21,0.21) Er+TO(l 10) E1-tTO(l 11) Er + 2LA (0.42,0,0) EI + 3LA (0.42,0,0)
289
of Onton, and the additional structure observed in our spectra can easily be accounted for by the many possible phonons and the impurity states. In particular, the dips at 560,720 and 760 cm-’ can be assigned as in Ref. 7.
REFERENCES
0)
four dips are observed by us). Our data in the 50012OOcm-’ region is in qualitative agreement with that
OF PHONONS
1. 2 ’ 3. 4. 5
67:
G.D. Watkins & W.B. Fowler, Phys. Rev. B16, 4524 (1977). A. Onton, P. Fisher & A.K. Ramdas, Phys. Rev. Lett. 19,781 (1967). H.R. Chandrasekhar, A.K. Ramdas & S. Rodriguez, .Phys. Rev. B14,2417 (1976). N.R. Butler, P. Fisher & A.K. Ramdas,Phys. Rev. Bl2,3200 (1975). R.G. Humphreys, P. Migliorato & G. Fortunato, SolidState Commun 40,819 (1981). W.P. Dun&e, Phys. Rev. 118,938 (1960). A. Onton, Phys. Rev. Lett., 22,288 (1969).