- Email: [email protected]
Raman scattering by silicon
Solid State Communications,
Vol. 11, pp. 47-49, 1972. Pergamon P r e s s .
Printed in Great Britain
RAMAN SCATTERING BY SILICON Kunimitsu Uchinokura, Tomoyuki Sekine and Etsuyuki Matsuura Department of P h y s i c s , Tokyo University of Education, Bunkyo-ku, Tokyo, Japan ( R e c e i v e d 29 March 1972 by Y . T o y o z a w a )
Reflection Raman spectroscopy has been performed on silicon at room temperature. One-phonon fine structure, which has been predicted by Cowley and observed in part by Wright et al., is fully obtained. Two-phonon structure is also obtained, which includes the most intense broad band observed by Parker et al. and weak broad bands not observed by them. One- and two-phonon structures reported here are very similar in shape to the ones predicted by Cowley by considering the anharmonicity of the lattice forces.
LATTICE vibrations of silicon have been investigated experimentally and theoretically through neutron diffraction, infra-red absorption and Raman scattering by many authors. The experimental investigations by Raman scattering, however, do not seem to have been fully performed. In addition to the main peak, 1 - s only a weak one-phonon peak at 305 cm-lwas observed by Wright et al. 4 and the most intense two-phonon broad band was observed by Parker et al., 2 which was not well resolved. In contrast to experiments, Cowley s,e performed detailed calculation of Raman spectra and obtained in particular two-phonon structure and one-phonon structure with wavenumber shift less than that of the main one-phonon peak. Johnson et al. 7 made critical-point a n a l y s i s . The detailed experiments, which can be compared with the theories, have not been reported.
operating with approximately 700 roW. The observation is made by reflection. The sample plane (111) is oriented at about 1S ° from the incident laser beam, with [110] direction perpendicular to it and the scattered light is collected at 90 ° to the incident beam direction. The laser beam is multi-passed and focused on the sample. Raman spectra are detected by synchronous single photon counting method and recorded by a digital printer and monitored by a chart recorder (using D - A converter). The sample is pulled single crystal and doped with 6 × 10 TM cm -1 phosphorus.
In this letter, we will report the observation of the first- and the second-order Raman spectra of silicon which include one-phonon fine structure and two-phonon weak structure.
In reflection Raman spectroscopy, scattered light is very weak compared with usual right-angle Raman spectroscopy. Russel 1 estimated experimentally that the first-order Raman intensity is about 100 times less in silicon than in diamond at 6328,~. It may be the main reason why the Raman spectra have not been fully investigated in silicon. In order to determine that the observed spectra are real Raman spectra, we have performed the measurements by using both 4880 and 5145A of laser lines.
The Raman scattering measurements are performed at room temperature using Spex model 1401 double monochromator and an argon-ion laser
Figure 1 shows the Stokes component of the reflection Raman spectrum of silicon with wavenumber shift less than 1500cm -1. A line at about 47
48
RAMAN SCATTERING BY SILICON
Vol. 11, No. 1
.., .'-•'.
I0 -41--
,el
]
'. :.~~
:. r~
\ i
i
i
,
~
.
.
.
5O0 WAVENUMBER
.
r
,
lOGO
,
,
,
1500
z w
SHIFT ( c m " )
--'....
~
FIG. 1. Raman spectrum of silicon at room temperature. 0 520 cm -1 is the main one-phonon peak, which has been investigated extensively by several authors. 1-3 Between 200 and 520 cm -1 , weak structures are observed with Rayleigh tail. A peak at about 305 cm -~ has been observed by Wright et al. 4 We have revealed the fine structure completely. Although the positions of the peaks are somewhat displaced, they are just what Cowley has predicted, s,6 They arise from the structure in the inverse lifetime of the zone-center optical phonon. The lifetime is determined by anharmonic coupling between the normal modes in the harmonic approximation. Cowley has assumed appropriate parameter and obtained his results. The difference between the experimental and the theoretical results probably comes from somewhat inappropriate choice of these parameters and not from the model of the theory itself. If, in the estimation of the parameters, our experimental results are taken into account and the theoretical spectrum is recalculated, the agreement between the experiment and the theory may become much better. The detailed investigation of the fine structure will contribute much to the study of the anharmonicity. The two-phonon spectrum is observed between 600 cm-1 and 1045 c m - ' . It consists of the most
[ 900
I 950
I 1000
I 1050
WAVENUMSER SHIFT ( e r a " )
FIG. 2. The most intense second-order Raman spectrum measured with better resolution
(4 cm-'). intense broad band between 920 cm-' and 1045 cm-' and weak structure below it. The former has been observed by Parker et al. 2 Ln Fig. 2, this band is shown with better resolution. Apparently the tail of this band, which vanishes at about 1045 c m - ' , corresponds to the two-phonon overtone of the r -point optical phonon, and a singularity at about 980 cm-' to the two-phonon overtone of the L-p~int TO phonon. The latter is first observed in this report and consists of broad bands with the maxima at about 620, 665 and 825cm-'. The observed second-order spectrum agrees qualitatively well with the Cowley's theoretical one (cf. D of Fig. 5 of reference5), but the present crystal orientation prevents us from performing a detailed comparison. A line corresponding to E of Fig. 5 of reference 5 was not observed. The experiment on the sample with (100) orientation and with polarization analysis is presently being done, and more thorough comparison between the experiment and the theory will be published separately.
REFERENCES 1.
RUSSEL J . P . , Appl. Phys. Lett. 6, 223 (1965).
2.
PARKER JR J.H., FELDMAN D.W. and ASHKIN M., Phys. Rev. 155, 712 (1967).
3.
HART T.R., AGGARWAL R.L. and LAX B., Phys. Rev. B], 638(1970).
Vol. 11, No. 1
RAMAN SCATTERING BY SILICON
4.
WRIGHT G.B. and MOORADIAN A., Phys. Rev. Lett. 18, 608 (1967).
5.
COWLEY R.A., J. Phys. (Paris) 26, 659 (1965).
6.
DOLLING G. and COWLEY R.A., Proc. Phys. Soc. 88, 463 (1966).
7.
JOHNSON F.A. and LOUDON R., Proc. R. Soc. (London) A28|, 274 (1964).
Wir berichten fiber Messungen der Rarnan-Streuung an Si bei Zimmertemperatur. Wir beobachteten die Ein-Phonon Feinstruktur vSIIig, die Cowley vorhersagte und Wright u.a. teilweise beobachteten. Wit beobachteten auch die Zwei-Phonon Struktur, die ein weites Band, das yon Parker u.a. berichtet wurde, und schw~chere weite B~nder, die noch nicht beobachtet women sind, enth~Ite. Die l>~obachtete Ein- und Zwei-Phononen Strukturen haben eine auffallende Ahnlichkeit mit den Strukturen, die Cowley mit 0berlegung yon anharmonischem Terrne der Kraft des Gitters erhaltete.
49
Vol. 11, pp. 47-49, 1972. Pergamon P r e s s .
Printed in Great Britain
RAMAN SCATTERING BY SILICON Kunimitsu Uchinokura, Tomoyuki Sekine and Etsuyuki Matsuura Department of P h y s i c s , Tokyo University of Education, Bunkyo-ku, Tokyo, Japan ( R e c e i v e d 29 March 1972 by Y . T o y o z a w a )
Reflection Raman spectroscopy has been performed on silicon at room temperature. One-phonon fine structure, which has been predicted by Cowley and observed in part by Wright et al., is fully obtained. Two-phonon structure is also obtained, which includes the most intense broad band observed by Parker et al. and weak broad bands not observed by them. One- and two-phonon structures reported here are very similar in shape to the ones predicted by Cowley by considering the anharmonicity of the lattice forces.
LATTICE vibrations of silicon have been investigated experimentally and theoretically through neutron diffraction, infra-red absorption and Raman scattering by many authors. The experimental investigations by Raman scattering, however, do not seem to have been fully performed. In addition to the main peak, 1 - s only a weak one-phonon peak at 305 cm-lwas observed by Wright et al. 4 and the most intense two-phonon broad band was observed by Parker et al., 2 which was not well resolved. In contrast to experiments, Cowley s,e performed detailed calculation of Raman spectra and obtained in particular two-phonon structure and one-phonon structure with wavenumber shift less than that of the main one-phonon peak. Johnson et al. 7 made critical-point a n a l y s i s . The detailed experiments, which can be compared with the theories, have not been reported.
operating with approximately 700 roW. The observation is made by reflection. The sample plane (111) is oriented at about 1S ° from the incident laser beam, with [110] direction perpendicular to it and the scattered light is collected at 90 ° to the incident beam direction. The laser beam is multi-passed and focused on the sample. Raman spectra are detected by synchronous single photon counting method and recorded by a digital printer and monitored by a chart recorder (using D - A converter). The sample is pulled single crystal and doped with 6 × 10 TM cm -1 phosphorus.
In this letter, we will report the observation of the first- and the second-order Raman spectra of silicon which include one-phonon fine structure and two-phonon weak structure.
In reflection Raman spectroscopy, scattered light is very weak compared with usual right-angle Raman spectroscopy. Russel 1 estimated experimentally that the first-order Raman intensity is about 100 times less in silicon than in diamond at 6328,~. It may be the main reason why the Raman spectra have not been fully investigated in silicon. In order to determine that the observed spectra are real Raman spectra, we have performed the measurements by using both 4880 and 5145A of laser lines.
The Raman scattering measurements are performed at room temperature using Spex model 1401 double monochromator and an argon-ion laser
Figure 1 shows the Stokes component of the reflection Raman spectrum of silicon with wavenumber shift less than 1500cm -1. A line at about 47
48
RAMAN SCATTERING BY SILICON
Vol. 11, No. 1
.., .'-•'.
I0 -41--
,el
]
'. :.~~
:. r~
\ i
i
i
,
~
.
.
.
5O0 WAVENUMBER
.
r
,
lOGO
,
,
,
1500
z w
SHIFT ( c m " )
--'....
~
FIG. 1. Raman spectrum of silicon at room temperature. 0 520 cm -1 is the main one-phonon peak, which has been investigated extensively by several authors. 1-3 Between 200 and 520 cm -1 , weak structures are observed with Rayleigh tail. A peak at about 305 cm -~ has been observed by Wright et al. 4 We have revealed the fine structure completely. Although the positions of the peaks are somewhat displaced, they are just what Cowley has predicted, s,6 They arise from the structure in the inverse lifetime of the zone-center optical phonon. The lifetime is determined by anharmonic coupling between the normal modes in the harmonic approximation. Cowley has assumed appropriate parameter and obtained his results. The difference between the experimental and the theoretical results probably comes from somewhat inappropriate choice of these parameters and not from the model of the theory itself. If, in the estimation of the parameters, our experimental results are taken into account and the theoretical spectrum is recalculated, the agreement between the experiment and the theory may become much better. The detailed investigation of the fine structure will contribute much to the study of the anharmonicity. The two-phonon spectrum is observed between 600 cm-1 and 1045 c m - ' . It consists of the most
[ 900
I 950
I 1000
I 1050
WAVENUMSER SHIFT ( e r a " )
FIG. 2. The most intense second-order Raman spectrum measured with better resolution
(4 cm-'). intense broad band between 920 cm-' and 1045 cm-' and weak structure below it. The former has been observed by Parker et al. 2 Ln Fig. 2, this band is shown with better resolution. Apparently the tail of this band, which vanishes at about 1045 c m - ' , corresponds to the two-phonon overtone of the r -point optical phonon, and a singularity at about 980 cm-' to the two-phonon overtone of the L-p~int TO phonon. The latter is first observed in this report and consists of broad bands with the maxima at about 620, 665 and 825cm-'. The observed second-order spectrum agrees qualitatively well with the Cowley's theoretical one (cf. D of Fig. 5 of reference5), but the present crystal orientation prevents us from performing a detailed comparison. A line corresponding to E of Fig. 5 of reference 5 was not observed. The experiment on the sample with (100) orientation and with polarization analysis is presently being done, and more thorough comparison between the experiment and the theory will be published separately.
REFERENCES 1.
RUSSEL J . P . , Appl. Phys. Lett. 6, 223 (1965).
2.
PARKER JR J.H., FELDMAN D.W. and ASHKIN M., Phys. Rev. 155, 712 (1967).
3.
HART T.R., AGGARWAL R.L. and LAX B., Phys. Rev. B], 638(1970).
Vol. 11, No. 1
RAMAN SCATTERING BY SILICON
4.
WRIGHT G.B. and MOORADIAN A., Phys. Rev. Lett. 18, 608 (1967).
5.
COWLEY R.A., J. Phys. (Paris) 26, 659 (1965).
6.
DOLLING G. and COWLEY R.A., Proc. Phys. Soc. 88, 463 (1966).
7.
JOHNSON F.A. and LOUDON R., Proc. R. Soc. (London) A28|, 274 (1964).
Wir berichten fiber Messungen der Rarnan-Streuung an Si bei Zimmertemperatur. Wir beobachteten die Ein-Phonon Feinstruktur vSIIig, die Cowley vorhersagte und Wright u.a. teilweise beobachteten. Wit beobachteten auch die Zwei-Phonon Struktur, die ein weites Band, das yon Parker u.a. berichtet wurde, und schw~chere weite B~nder, die noch nicht beobachtet women sind, enth~Ite. Die l>~obachtete Ein- und Zwei-Phononen Strukturen haben eine auffallende Ahnlichkeit mit den Strukturen, die Cowley mit 0berlegung yon anharmonischem Terrne der Kraft des Gitters erhaltete.
49