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Resolved splitting of the free exciton luminescence band in silicon
5—7. Solid State Communications, Vol.31,in pp. Perganon Press Ltd. 1979. Printed Great Britain.
c~
RESOLVED SPLITTING OF THE FREE EXCITON LUMINESCENCE BAND IN SILICON R.R. Parsons, U.O. Ziemelis and J.A. Rostworowski Physics Department, The University of British Columbia Vancouver, B.C., V6T 1W5, Canada (Received 4 April 1979 by R. Barrie)
The exciton ground state splitting in silicon is resolved in the TA phonon assisted free exciton luminescence spectrum. The splitting is found to be 0.31 (+0.03,—0.06) meV.
was resolved into a doublet structure. N~split— ting could be observed for the PETO or FE~
The ground state of the indirect exciton in silicon is split into a lower state and an upper A 6 State due to’ the interaction of the hole in the degenerate valence bands with the1 The energy was first theoretically electron in splitting the anisotropic conduction bands. estimated by McLean and Loudon1 to be AE ~ 0.6 meV. The first experimental determination by Hammond et al. gave 0.3 < AE < 0.7 meV from a study of the temperature dependence of the LO and TO phonon assisted exciton luminescence, Thewalt and Parsons3 using both photolumines— cence and derivative absorption measurements obtained AE 0.2 ±0.05 meV. Smith et al.” improved the earlier determination by Hammond et al.2 to 0.3 < AE < 0.5 meV using lower temp— erature data. Capizzi et al.5 and later Balslev6 obtained AE = 0.13 meV and 0.3 < AE < 0.4 meV, respectively, using wavelength modulated absorption techniques. Timusk et aL7 deduced AE ~ 0.2 meV from far infrared absorp— tion measurements. Merle et al.8 obtained 0.24 < AE < 0.34 meV by extrapolating absorp— tion data for strained silicon to the zero strain limit. Very recently Hammond and Silver9 2’~ to determine refined earlier studies 10 theoretical gave AE 0.31 ±0.03 meV. Most recent 0.32 meV. estimates by Lipari and Altarelli In all, of the above studies the A 7 and A6 exciton states (in unstrained silicon) were not seen as two isolated structures in the spectro— 3’~’9photoluminescence spectra for scopic spectra. In particular, previously reported~’ the free exciton in silicon were completely devoid of structure associated with the ground 2’~’9 from a best fit of a state splitting and, consequently, the energy seven parameter function to featureless bands, splitting was deduced Furthermore the fitting procedure assumed parabolic densities of states, which is maccur— ate when kT is comparable to AE. In view of the interest in getting a more direct measurement of AE we have undertaken to improve significantly our instrumentation3 in order to resolve the A 7 and A6 exciton bands by photoluminescence measurement. In order to avoid the phonon broadening associated with the TO phonon assist— ed free exciton (VETO) we have studied the much weaker TA—assisted exciton jFETA) emission. As shown in the figure the FET band at T 1.6 K
(longitudinal optical phonon replica) bands. improve thetheapparatus3 A photo— To obtain FETA data asit follows. was necessary to multiplier with an lnGaAsP photocathode (model VPM—l59 manufactured by Varian Associates) and a grating blazed at 0.5 urn in first order with 1200 grooves/mm were installed in the Perkin— Elmer El double pass spectrometer. The high— purity (40,000 £1—cm) silicon sample was immersed in liquid helium at T 1.6 K. A 0.7 W, 4 mm diameter exciting beam from a cv argon—ion laser was unfocussed onto the sample in order to minimize local heating. Signal averaging with the use of an on—line minicompu— ter system11 was necessary to detect the weak FETA luminescence band with high resolution (slit width ,~ 0.08 meV) and large signal—to— noise ratio ~S/N ~ 15). The FE1-’ luminescence band is expected to be entirely due, within experimental accuracy, to exciton emission because the LO ~honon couples approximately three timesl2,9,Ll more strongly to the lower A A 7 state than the upper 6 State and, furthermore, the fact that the only a smallisthermal population the upper temperature low; i.e. KT ,~ AEofgives rise to state. As shown in the figure, the low energy portions of the 1~TAand FELO bands can be nearly superimposed by shifting the peaks up in energy by an amount equal to their phonon energy of the scaling A energiesposition and suitably the data. The 7 band edge obtained by a linear extrapolation of the low energy side of the FETA band is taken to be energy zero. FETO band indicates a phonon broadening The larger tail on the low—energy edge offorthe that particular replica which is not present in either the FETA or FE1~’°emissions. This broadening, which is comparable to the intrinsic broadening of 0.09 meV deduced by Hammond and Silver9 at the temperature of interest here explains the absence of observed structure of the VETO band. The result of subtracting the FETA and the FELO profiles is the band labelled FETA — FE in the figure. Since the A~Aand ~ components are cancelled out by this sub— traction, the PETA — VELO profile is the A6 emission band. The error flags shown in the figure indicate the 95 percent confidence inter— 5
6
RESOLVED SPLITTING OF THE FREE EXCITON LUMINESCENCE BAND
‘‘
\
\i”~
\
FETO FE~~
j
Vol. 31, No. 1
LSLIT IIWIDTH
\~fETA_FEL0
—,
o I -0.50
I—~O.3~mW (+,9)
•‘..
+ 0.50
0
+ 10
+ 1.50
ENERGY (meV) Fig. 1:
The TO, LO and TA phonon assisted luminescence bands associated with the indirect free exciton in intrinsic silicon.
The bands have
been shifted to higher energy by the energy of the phonon assisting the radiative recombination.
The spectra have been normalized
for easier comparison. The signal strengths for the FETO, LO TA FE and FE peaks are 4872, 3668 and 335 counts/sec, respectively. As the absolute photon energy is not important for the present work, the extrapolation position of the low energy edge of the TA band is set equal to zero.
This position is identified with the A
7
band edge, as shown by the vertical line labelled A7.
As
explained in the text, the extrapolation of the lower energy edge of the difference spectrum FETA
—
FELO gives the splitting
energy AE.
vals for the data points, together with an esti— mate of the mnac8uracy in achieving a match of the FETA and FEL A7—peaks. Extrapolating the low energy edge of the difference band, we obtain AE 0.31 (+O.03,—0.06) rneV, with uncertainties determined by the above—mentioned confidence intervals. This analysis and, conse— quently, the determination of AE does not depend on precise knowledge of the sample temperature and is rather insensitive to the instrumental broadening provided it is small compared with AE and the same for both the TA and LO replicas, which is the case here. The width at half
maximum intensity of the FELO band appears si — nificantly greater than that of the FETA_FEL profile. This could be due to a small A6 exciton contribution to the FELO band or, more likely, due to the non—parabolicity of the density of states of the lower exciton band for energies near AE. Neither of these effects should affect the above determination of AE. In summary, we have presented for the first time luminescence spectra which directly exhibit the ground state splitting of the free exciton in intrinsic silicon. It was necessary to study the weak TA replica which, unlike the stronger
Vol. 31, No. I
RESOLVED SPLITTING OF THE FREE EXCITON LUMINESCENCE BAND
TO replica, is not significantly ened. The present results, AE —0.06) meV are in good agreement 8’9 and experimental measurements detailed theoretical estimate10.
phonon—broad— 0.31 (+0.03, with other the most
This work was supported by NSERC grant #67—6714. We thank L.S. Yaggy and E.L. Kern of the Hughes Aircraft Company,which who was supplied ultra high purity silicon, grown the under contract No. F336l5—75—C—5283 for the U.S. Army and Air Force.
Acknowledgement—We thank Drs. R. Barrie and M.L.W. Thewalt for very helpful suggestions. REFERENCES
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.
T.P. McLEAN and R.J. LOUDON, J. Phys. Chem. Solids 13, 1 (1960). R.B. HAMMOND, D.L. SMITH and T.C. McGILL, Phys. Rev. Lett. 35, 1535 (1975). M.L.W. THEWALT and R.R. PARSONS, Solid State Commun. 20, 97 (1976). D.L. SMITH, R.B. HAMMOND, M. CHEN, S.A. LYON and T.C. McGILL, Proc. 13th mt. Conf. Phys. Semicond. Rome 1976, p. 1077. North Holland, Amsterdam (1976). M. CAPIZZI, F. EVANGELISTI, A. FROVA and P. VALFRE, Proc. 13th mt. Conf. Phys. Semicond. Rome 1976, p. 857. I. BALSLEV, Solid State Commun. 23, 205 (1977). T. TIMUSK, H. NAVARRO, N.O. LIPARI and M. ALTARELLI, APS Bull. 22, 351 (1977). 04. CAPIZZI, J.C. MERLE, P. FIORINI and A. FROVA, Solid State Commun. 24, 451 (1977); J.C. MERLE, M. CAPIZZI, P. FIORINI and A. FROVA, Phys. Rev. Bl7, 4821 (1978). R.B. HAMMOND and R.N. SILVER, Solid State Commun. 28, 993 (1978). N.O. LIPARI and M. ALTARELLI, APS Bull. 23, 426 (1978). M.L.W. THEWALT, M.Sc. Thesis, the University of British Columbia (1975), (unpublished). D.L. SMITH and T.C. McGILL, Phys. Rev. 814, 2448 (1976). A 6A7 labels are the same as Ref. 9, opposite to many earlier papers.
7
c~
RESOLVED SPLITTING OF THE FREE EXCITON LUMINESCENCE BAND IN SILICON R.R. Parsons, U.O. Ziemelis and J.A. Rostworowski Physics Department, The University of British Columbia Vancouver, B.C., V6T 1W5, Canada (Received 4 April 1979 by R. Barrie)
The exciton ground state splitting in silicon is resolved in the TA phonon assisted free exciton luminescence spectrum. The splitting is found to be 0.31 (+0.03,—0.06) meV.
was resolved into a doublet structure. N~split— ting could be observed for the PETO or FE~
The ground state of the indirect exciton in silicon is split into a lower state and an upper A 6 State due to’ the interaction of the hole in the degenerate valence bands with the1 The energy was first theoretically electron in splitting the anisotropic conduction bands. estimated by McLean and Loudon1 to be AE ~ 0.6 meV. The first experimental determination by Hammond et al. gave 0.3 < AE < 0.7 meV from a study of the temperature dependence of the LO and TO phonon assisted exciton luminescence, Thewalt and Parsons3 using both photolumines— cence and derivative absorption measurements obtained AE 0.2 ±0.05 meV. Smith et al.” improved the earlier determination by Hammond et al.2 to 0.3 < AE < 0.5 meV using lower temp— erature data. Capizzi et al.5 and later Balslev6 obtained AE = 0.13 meV and 0.3 < AE < 0.4 meV, respectively, using wavelength modulated absorption techniques. Timusk et aL7 deduced AE ~ 0.2 meV from far infrared absorp— tion measurements. Merle et al.8 obtained 0.24 < AE < 0.34 meV by extrapolating absorp— tion data for strained silicon to the zero strain limit. Very recently Hammond and Silver9 2’~ to determine refined earlier studies 10 theoretical gave AE 0.31 ±0.03 meV. Most recent 0.32 meV. estimates by Lipari and Altarelli In all, of the above studies the A 7 and A6 exciton states (in unstrained silicon) were not seen as two isolated structures in the spectro— 3’~’9photoluminescence spectra for scopic spectra. In particular, previously reported~’ the free exciton in silicon were completely devoid of structure associated with the ground 2’~’9 from a best fit of a state splitting and, consequently, the energy seven parameter function to featureless bands, splitting was deduced Furthermore the fitting procedure assumed parabolic densities of states, which is maccur— ate when kT is comparable to AE. In view of the interest in getting a more direct measurement of AE we have undertaken to improve significantly our instrumentation3 in order to resolve the A 7 and A6 exciton bands by photoluminescence measurement. In order to avoid the phonon broadening associated with the TO phonon assist— ed free exciton (VETO) we have studied the much weaker TA—assisted exciton jFETA) emission. As shown in the figure the FET band at T 1.6 K
(longitudinal optical phonon replica) bands. improve thetheapparatus3 A photo— To obtain FETA data asit follows. was necessary to multiplier with an lnGaAsP photocathode (model VPM—l59 manufactured by Varian Associates) and a grating blazed at 0.5 urn in first order with 1200 grooves/mm were installed in the Perkin— Elmer El double pass spectrometer. The high— purity (40,000 £1—cm) silicon sample was immersed in liquid helium at T 1.6 K. A 0.7 W, 4 mm diameter exciting beam from a cv argon—ion laser was unfocussed onto the sample in order to minimize local heating. Signal averaging with the use of an on—line minicompu— ter system11 was necessary to detect the weak FETA luminescence band with high resolution (slit width ,~ 0.08 meV) and large signal—to— noise ratio ~S/N ~ 15). The FE1-’ luminescence band is expected to be entirely due, within experimental accuracy, to exciton emission because the LO ~honon couples approximately three timesl2,9,Ll more strongly to the lower A A 7 state than the upper 6 State and, furthermore, the fact that the only a smallisthermal population the upper temperature low; i.e. KT ,~ AEofgives rise to state. As shown in the figure, the low energy portions of the 1~TAand FELO bands can be nearly superimposed by shifting the peaks up in energy by an amount equal to their phonon energy of the scaling A energiesposition and suitably the data. The 7 band edge obtained by a linear extrapolation of the low energy side of the FETA band is taken to be energy zero. FETO band indicates a phonon broadening The larger tail on the low—energy edge offorthe that particular replica which is not present in either the FETA or FE1~’°emissions. This broadening, which is comparable to the intrinsic broadening of 0.09 meV deduced by Hammond and Silver9 at the temperature of interest here explains the absence of observed structure of the VETO band. The result of subtracting the FETA and the FELO profiles is the band labelled FETA — FE in the figure. Since the A~Aand ~ components are cancelled out by this sub— traction, the PETA — VELO profile is the A6 emission band. The error flags shown in the figure indicate the 95 percent confidence inter— 5
6
RESOLVED SPLITTING OF THE FREE EXCITON LUMINESCENCE BAND
‘‘
\
\i”~
\
FETO FE~~
j
Vol. 31, No. 1
LSLIT IIWIDTH
\~fETA_FEL0
—,
o I -0.50
I—~O.3~mW (+,9)
•‘..
+ 0.50
0
+ 10
+ 1.50
ENERGY (meV) Fig. 1:
The TO, LO and TA phonon assisted luminescence bands associated with the indirect free exciton in intrinsic silicon.
The bands have
been shifted to higher energy by the energy of the phonon assisting the radiative recombination.
The spectra have been normalized
for easier comparison. The signal strengths for the FETO, LO TA FE and FE peaks are 4872, 3668 and 335 counts/sec, respectively. As the absolute photon energy is not important for the present work, the extrapolation position of the low energy edge of the TA band is set equal to zero.
This position is identified with the A
7
band edge, as shown by the vertical line labelled A7.
As
explained in the text, the extrapolation of the lower energy edge of the difference spectrum FETA
—
FELO gives the splitting
energy AE.
vals for the data points, together with an esti— mate of the mnac8uracy in achieving a match of the FETA and FEL A7—peaks. Extrapolating the low energy edge of the difference band, we obtain AE 0.31 (+O.03,—0.06) rneV, with uncertainties determined by the above—mentioned confidence intervals. This analysis and, conse— quently, the determination of AE does not depend on precise knowledge of the sample temperature and is rather insensitive to the instrumental broadening provided it is small compared with AE and the same for both the TA and LO replicas, which is the case here. The width at half
maximum intensity of the FELO band appears si — nificantly greater than that of the FETA_FEL profile. This could be due to a small A6 exciton contribution to the FELO band or, more likely, due to the non—parabolicity of the density of states of the lower exciton band for energies near AE. Neither of these effects should affect the above determination of AE. In summary, we have presented for the first time luminescence spectra which directly exhibit the ground state splitting of the free exciton in intrinsic silicon. It was necessary to study the weak TA replica which, unlike the stronger
Vol. 31, No. I
RESOLVED SPLITTING OF THE FREE EXCITON LUMINESCENCE BAND
TO replica, is not significantly ened. The present results, AE —0.06) meV are in good agreement 8’9 and experimental measurements detailed theoretical estimate10.
phonon—broad— 0.31 (+0.03, with other the most
This work was supported by NSERC grant #67—6714. We thank L.S. Yaggy and E.L. Kern of the Hughes Aircraft Company,which who was supplied ultra high purity silicon, grown the under contract No. F336l5—75—C—5283 for the U.S. Army and Air Force.
Acknowledgement—We thank Drs. R. Barrie and M.L.W. Thewalt for very helpful suggestions. REFERENCES
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.
T.P. McLEAN and R.J. LOUDON, J. Phys. Chem. Solids 13, 1 (1960). R.B. HAMMOND, D.L. SMITH and T.C. McGILL, Phys. Rev. Lett. 35, 1535 (1975). M.L.W. THEWALT and R.R. PARSONS, Solid State Commun. 20, 97 (1976). D.L. SMITH, R.B. HAMMOND, M. CHEN, S.A. LYON and T.C. McGILL, Proc. 13th mt. Conf. Phys. Semicond. Rome 1976, p. 1077. North Holland, Amsterdam (1976). M. CAPIZZI, F. EVANGELISTI, A. FROVA and P. VALFRE, Proc. 13th mt. Conf. Phys. Semicond. Rome 1976, p. 857. I. BALSLEV, Solid State Commun. 23, 205 (1977). T. TIMUSK, H. NAVARRO, N.O. LIPARI and M. ALTARELLI, APS Bull. 22, 351 (1977). 04. CAPIZZI, J.C. MERLE, P. FIORINI and A. FROVA, Solid State Commun. 24, 451 (1977); J.C. MERLE, M. CAPIZZI, P. FIORINI and A. FROVA, Phys. Rev. Bl7, 4821 (1978). R.B. HAMMOND and R.N. SILVER, Solid State Commun. 28, 993 (1978). N.O. LIPARI and M. ALTARELLI, APS Bull. 23, 426 (1978). M.L.W. THEWALT, M.Sc. Thesis, the University of British Columbia (1975), (unpublished). D.L. SMITH and T.C. McGILL, Phys. Rev. 814, 2448 (1976). A 6A7 labels are the same as Ref. 9, opposite to many earlier papers.
7