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Surface magnetoplasmon-optic phonon modes in InSb
PHYSICS LETTERS
Volume 45A, number 2
10 September 1973
SURFACE MAGNETOPLASMON-OPTIC PHONON MODES IN InSb E.D. PALIK, R. KAPLAN, R.W. GAMMON*‘, II. KAPLAN*2, J.J. QUINN*3 and R.F. WALLIS* Naval Research Laboratory, Washington, D.C. 20375, USA Received 24 April 1973 Surface magnetoplasmon-optic phonon modes have been measured in n-InSb in the geometry with magnetic field parallel to the surface-mode wave vector.
The properties of surface plasmon-optic phonon modes in InSb have been measured [ 1,2] and found in substantial agreement with classical theory [3]. Theory of these modes in an applied magnetic field has been done for magnetoplasmons [4,5] and magnetoplasmon-optic phonons [6-81. We present experimental results for the geometry with magnetic field H parallel to wave vector k of the surface mode [6,8]. The dispersion curves for surface polaritons are given by k&g
2000
’ 1+E’
c2
(1)
where the dielectric constant
E=e,
I
1+
- surface ----bulk modes
cd+
G
ok.+ - ti2 -irw
is 2 OP
-
w(o+iy)
1 (2) .
The parameters used are TO phonon frequency C+ = 18 1 cm-l, LO phonon frequency wL = 192 cm-‘, background dielectric constant E, = 16, effective mass ratio m */m = 0.022, phonon damping constant F = 2 cm-l, electron damping constant 7 = 10 cm-‘, carrier density N= 1 .O X 1017 cmT3 and plasma frequency w2 = 4nNe2/e,m *. The tw’o dispersion curves are shownPas heavy solid curves in fig. 1. The two bulk polariton modes are indicated by dashed lines. The vacuum and the evanescent (13= 35”) light lines are the light solid curves. An applied magnetic field splits each bulk mode inPermanent address: *l Univ. of Maryland, College Park, Md. *2 Syracuse Univ., Syracuse, N.Y. *3 Brown Univ., Providence, R.I. *4 Univ. of California, Irvine, Calif.
_
4cOO k (cm-‘)
Fig. 1. Dispersion curves for surface and bulk polariton modes in n-InSb. The insert indicates the arrangement of coupling prism, vacuum gap, and sample.
to two modes described by two Faraday dielectric constants. The two modes which move down in frequency push against the surface modes shifting them down slightly near the bend of the curves, and finally cross the surface modes. This leads to a region of pseudo-surface waves between the crossover points of the bulk modes. These pseudo-surface waves have both an attenuating and an oscillatory component normal to the surface. They should influence the attenuated-total-reflection (ATR) spectrum in a way similar to surface waves, and we expect no abrupt changes in line position, shape, or intensity when a bulk mode crosses a surface mode. We used a light-pipe with a Michelson interferometer to measure the room-temperature ATR spectrum. A Si prism provided an internal angle of incidence 8 = 35’. Incident light was polarized Eip. The three-layer system of Si prism, gap and InSb fitted into a 1,9 cm diameter light pipe as shown in fig. 1. 143
Volume 45A, number 2
I_
PHYSICS LETTERS
.
204: Y-WL ‘-UT T 5
3
160-
.:
.
l
1200
50
100
H tkG) Fig. 2. Observed magnetic-field dependence of surface polariton modes.
10 September 1973
terminate at the cyclotron frequency we. The observed lines, indicating the crossover of the 35” light line and the actual dispersion curves, do not terminate. However, this crossover frequency is very nearly equal to the asymptotic frequency. Preliminary ATR calculations indicate polarization effects, since both Eip and Eis produce Erp and E,, spectra. We have not yet analyzed the ATR light. Another feature is the appearance of a third surface mode when oc exceeds UT at - 43 kG. This weak, sharp line had a width of - 3 cm-l for a spectral resolution of 1 cm-l, in rough agreement with the value of f’. The computed field dependence of the asymptotic frequency of this third mode [6,8] is in agreement with experiment. This mode is confined between UT and wL and reaches a limiting value at high field, equal to the asymptotic surface-optic-phonon frequency.
For H=O, we observed surface-mode lines at the frequencies shown in fig. 2. For a gap of - 6pm between prism and sample, the ATR at the resonant frequencies was - 0.7. While line position is in agreement with the calculation of fig. 1, line width is a factor of two larger than calculated ATR spectra indicate [2]. The full width at half maximum is shown by vertical bars. Calculated dispersion curves with H # 0 indicate no appreciable shift of the surface modes at the 35’ light line [8], as borne out by experiment in fig. 2. However, the upper mode gains intensity slightly, broadens gradually to higher frequency, and then looses intensity above 40 kG. The line width is indicated at 50 kG. The lower mode also broadens somewhat. The field at which pseudo-surface waves would appear is - 12 kG for the lower mode and - 52 kG for the upper mode. No abrupt changes in intensity or line shape were observed here. The solid lines are the calculated asymptotic (large k) frequencies [6] which
144
We thank Prof. E. Burstein and A. Hartstein fruitful discussions.
for
References [l] N. Marshall, B. Fisher and H.J. Queisser, Phys. Rev. Lett. 27 (1971) 95. [2] V.V. Bryskin, Y.M. Gerbshtein and D.N. Mirlin, Sol. State Commun. 11 (1972) 695. [3] R.F. Wallis and J.J. Brion, Sol. State Commun. 9 (1971) 2099. [4] J.J. Brion, R.F. Wallis, A. Hartstein and E. Burstein, Phys. Rev. Lett. 28 (1972) 1455. [5] K.W. Chiu and J.J. Quinn, Phys. Rev. B5 (1972) 4707. [6] J.J. Brion et al., Surface Sci. 34 (1973) 73. [7] K.W. Chiu and J.J. Quinn, Phys. Rev. Lett. 29 (1972) 600. [8] K.W. Chiu and J.J. Quinn, Taormina Res. Conf. on the Structure of Matter - Polaritons 1972, in press.
Volume 45A, number 2
10 September 1973
SURFACE MAGNETOPLASMON-OPTIC PHONON MODES IN InSb E.D. PALIK, R. KAPLAN, R.W. GAMMON*‘, II. KAPLAN*2, J.J. QUINN*3 and R.F. WALLIS* Naval Research Laboratory, Washington, D.C. 20375, USA Received 24 April 1973 Surface magnetoplasmon-optic phonon modes have been measured in n-InSb in the geometry with magnetic field parallel to the surface-mode wave vector.
The properties of surface plasmon-optic phonon modes in InSb have been measured [ 1,2] and found in substantial agreement with classical theory [3]. Theory of these modes in an applied magnetic field has been done for magnetoplasmons [4,5] and magnetoplasmon-optic phonons [6-81. We present experimental results for the geometry with magnetic field H parallel to wave vector k of the surface mode [6,8]. The dispersion curves for surface polaritons are given by k&g
2000
’ 1+E’
c2
(1)
where the dielectric constant
E=e,
I
1+
- surface ----bulk modes
cd+
G
ok.+ - ti2 -irw
is 2 OP
-
w(o+iy)
1 (2) .
The parameters used are TO phonon frequency C+ = 18 1 cm-l, LO phonon frequency wL = 192 cm-‘, background dielectric constant E, = 16, effective mass ratio m */m = 0.022, phonon damping constant F = 2 cm-l, electron damping constant 7 = 10 cm-‘, carrier density N= 1 .O X 1017 cmT3 and plasma frequency w2 = 4nNe2/e,m *. The tw’o dispersion curves are shownPas heavy solid curves in fig. 1. The two bulk polariton modes are indicated by dashed lines. The vacuum and the evanescent (13= 35”) light lines are the light solid curves. An applied magnetic field splits each bulk mode inPermanent address: *l Univ. of Maryland, College Park, Md. *2 Syracuse Univ., Syracuse, N.Y. *3 Brown Univ., Providence, R.I. *4 Univ. of California, Irvine, Calif.
_
4cOO k (cm-‘)
Fig. 1. Dispersion curves for surface and bulk polariton modes in n-InSb. The insert indicates the arrangement of coupling prism, vacuum gap, and sample.
to two modes described by two Faraday dielectric constants. The two modes which move down in frequency push against the surface modes shifting them down slightly near the bend of the curves, and finally cross the surface modes. This leads to a region of pseudo-surface waves between the crossover points of the bulk modes. These pseudo-surface waves have both an attenuating and an oscillatory component normal to the surface. They should influence the attenuated-total-reflection (ATR) spectrum in a way similar to surface waves, and we expect no abrupt changes in line position, shape, or intensity when a bulk mode crosses a surface mode. We used a light-pipe with a Michelson interferometer to measure the room-temperature ATR spectrum. A Si prism provided an internal angle of incidence 8 = 35’. Incident light was polarized Eip. The three-layer system of Si prism, gap and InSb fitted into a 1,9 cm diameter light pipe as shown in fig. 1. 143
Volume 45A, number 2
I_
PHYSICS LETTERS
.
204: Y-WL ‘-UT T 5
3
160-
.:
.
l
1200
50
100
H tkG) Fig. 2. Observed magnetic-field dependence of surface polariton modes.
10 September 1973
terminate at the cyclotron frequency we. The observed lines, indicating the crossover of the 35” light line and the actual dispersion curves, do not terminate. However, this crossover frequency is very nearly equal to the asymptotic frequency. Preliminary ATR calculations indicate polarization effects, since both Eip and Eis produce Erp and E,, spectra. We have not yet analyzed the ATR light. Another feature is the appearance of a third surface mode when oc exceeds UT at - 43 kG. This weak, sharp line had a width of - 3 cm-l for a spectral resolution of 1 cm-l, in rough agreement with the value of f’. The computed field dependence of the asymptotic frequency of this third mode [6,8] is in agreement with experiment. This mode is confined between UT and wL and reaches a limiting value at high field, equal to the asymptotic surface-optic-phonon frequency.
For H=O, we observed surface-mode lines at the frequencies shown in fig. 2. For a gap of - 6pm between prism and sample, the ATR at the resonant frequencies was - 0.7. While line position is in agreement with the calculation of fig. 1, line width is a factor of two larger than calculated ATR spectra indicate [2]. The full width at half maximum is shown by vertical bars. Calculated dispersion curves with H # 0 indicate no appreciable shift of the surface modes at the 35’ light line [8], as borne out by experiment in fig. 2. However, the upper mode gains intensity slightly, broadens gradually to higher frequency, and then looses intensity above 40 kG. The line width is indicated at 50 kG. The lower mode also broadens somewhat. The field at which pseudo-surface waves would appear is - 12 kG for the lower mode and - 52 kG for the upper mode. No abrupt changes in intensity or line shape were observed here. The solid lines are the calculated asymptotic (large k) frequencies [6] which
144
We thank Prof. E. Burstein and A. Hartstein fruitful discussions.
for
References [l] N. Marshall, B. Fisher and H.J. Queisser, Phys. Rev. Lett. 27 (1971) 95. [2] V.V. Bryskin, Y.M. Gerbshtein and D.N. Mirlin, Sol. State Commun. 11 (1972) 695. [3] R.F. Wallis and J.J. Brion, Sol. State Commun. 9 (1971) 2099. [4] J.J. Brion, R.F. Wallis, A. Hartstein and E. Burstein, Phys. Rev. Lett. 28 (1972) 1455. [5] K.W. Chiu and J.J. Quinn, Phys. Rev. B5 (1972) 4707. [6] J.J. Brion et al., Surface Sci. 34 (1973) 73. [7] K.W. Chiu and J.J. Quinn, Phys. Rev. Lett. 29 (1972) 600. [8] K.W. Chiu and J.J. Quinn, Taormina Res. Conf. on the Structure of Matter - Polaritons 1972, in press.