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Photo hall measurements of band-tail absorption and recombination times in indium antimonide
Volume 63, number
2
OPTICS
COMMUNICATIONS
15 July 1987
PHOTO HALL MEASUREMENTS OF BAND-TAIL ABSORPTION AND RECOMBINATION TIMES IN INDIUM ANTIMONIDE H.A. MACKENZIE, Department Received
ofPhysics.
I7 February
G.R. ALLAN, J.J. HUNTER, Heriot- Watt University, Riccarton,
D.C. HUTCHINGS
and B.S. WHERRETT
EH14 4AS, UK
1987
Photo Hall measurements are reported for a n-type InSb sample at 77 K. A bulk recombination time of 350 ns and an effective surface recombination time of 20 ns, corresponding to a surface recombination velocity of 2.8 x lo5 cm s-i, has been estimated from an analysis of the frequency dependence of the photocarrier generation. The measurements yield interband absorption coefftcients in the band-tail which are systematically lower than the previous optical measurements, being up to an order of magnitude lower at 100 cm- ’ below the band edge. The form ofthe band-tail is qualitatively described in terms of the convolution of an exponential edge and an acceptor impurity resonance.
1. Introduction
dependent parameters by conventional optical measurements. In this paper we report a novel application of the photo-Hall technique [ 41 which provides data on the photo-generated carrier population in n-type InSb at 77 K as a function of both laser frequency and power. The photo-Hall voltage represents the photo-induced change in the conduction band free carrier population and, in our experiment, this change was achieved by illuminating the sample with band-gap-resonant radiation from a cw CO laser. Initial results are presented for low incident powers ( < 5 mW) which is a region where the absorption was found to be linear. This regime is comparable with the experimental conditions used to obtain the previously published data on optical interband absorption coefficients [ 2,3]. Optical transmission measurements are the most direct method of obtaining optical absorption coefficients, but such measurements include a free carrier contribution and the range of sample thicknesses required imposes limits on accuracy, particularly for absorption coefficients that are less than 1 cm- ‘. Small changes in the interband absorption can be measured by photoconduction techniques [ 41 but the measurement is affected by simultaneous changes in both mobility and carrier population which tend to complicate the interpretation of results. The photoHall effect monitors only the changes in the pho-
The photo-excitation of electron-hole pairs in the direct-gap semiconductor InSb by near resonant radiation from a cw CO laser is a complex process due to an inter-dependence of the photogenerated band populations, the optical absorption coefficient and the carrier recombination time. For the linear absorption case the number of carriers per unit volume, N, generated at irradiance, I, is given by N= aI~,Ifiw ,
(1)
where o is the absorption coefftcient; w is the radiation frequency and r, is the carrier recombination time. The detailed microscopic process involved in the creation of the optical nonlinearity in InSb have been discussed extensively [ 1 ] and it is now well established that the irradiance-dependence of the absorption (and inter alia the dispersion) associated with a dynamic Burstein-Moss shift of the Fermi level as the carrier population is increased by photogeneration. The roles of gap renormalisation processes, impurity states and free carrier absorption have not been fully clarified. The optical absorption band-tail of InSb [ 2,3] as shown in fig. 1 has thus far not been satisfactorily explained as it is extremely difficult to obtain unambiguous data on the above inter0 030-40 18/87/$03.50 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)
3.v.
73
Volume 63, number
2
OPTICS
COMMUNICATIONS
1
15 July 1987 RECORDING SYSTEM
CO LASER TRANSMITTED POWER
CONSTANT CURRENT SOURCE
HELMHOLTZ COILS
INCIDENT POWER
CHOPPER
I__
]
SPATIAL /FILTER AND ATTENUATOR
ZnSe BEAM SPLITTER
MONOCHROMATOR
4
-i
Fig. 2. Experimental
layout for photo-Hall
measurements.
Fig. 1. The frequency dependence of the optical absorption coefficient for n-type InSb at 77 K (Miller et al. [2], and Prise [3]).
toexcited population attributable to the interband component of the optical absorption coefficient and, for n-type material is independent of hole concentration due to~the lpw holemobility [ 5 1. IJsing this technique we have obtained new data for the shape and structure of the interband absorption band-tail. We have also evaluated both bulk recombination times and effective surface recombination times for InSb and from this data, the surface recombination velocity was estimated.
2. Experimental The experimental system is shown in fig. 2. This layout allows for simultaneous monitoring of the incident and transmitted optical powers, Hall and photo-Hall voltages and the photoconductive signal. The sample was a wafer of n-type InSb, 468 urn thick 74
with a net carier concentration of 2.67x lOI cmA3 and a mobility of 5.9x lo5 cm2 V’ s-’ at 77 K. The sample was mounted on a ZnSe disc in good thermal contact with a variable temperature cryostat tail. The photo-Hall signal wasgenerated from a cw CO laser beam, mechanically chopped and focussed to a spot diameter of 600 urn on the sample. All windows and sample surfaces were anti-reflection coated for 5.6 pm operation. To minimise any thermal effects a duty cycle of 1:25 was used and the photogenerated change in the Hall voltage was monitored using standard boxcar techniques. The magnetic field was typically 0.0 1 T. The incident and transmitted powers were measured by calibrated pyroelectric detectors. This system can measure a minimum photoinduced change of 10’ in the total free carrier population, corresponding, for our geometry, to a carrier concentration change of lo9 cmP3 in the band-tail. This degree of sensitivity enables interband absorption coefficients to be evaluated with significantly
Volume 63, number
2
OPTICS
Fig. 3. The number of photogenerated carriers for a fixed incident power (2 mW) plotted as a function of frequency (cm-‘).
greater accuracy than was previously conventional optical methods.
possible
by
3. Experimental results and analysis The basic experimental procedure was to record the photogenerated carrier population as a function of incident laser power for a range of laser lines. The output signal was linearly dependent on the magnetic field which was operated in the range 0.005 to 0.02 T, and was also relatively insensitive to spot size and positioning of the laser beam between the Hall probes in the central part of the sample. The photo induced-carrier concentration AN is calculated from AN=mN(I/,,/V,--l),
15 July 1987
COMMUNICATIONS
(2)
where N is the intrinsic carrier concentration, VPH and VD are the values for the photo-Hall voltage and ‘dark’ Hall voltage respectively; m takes into account the fractional illumination of the sample and is the ratio of the volume of sample enclosed by the Hall contacts and the illuminated volume. The factor m exhibits a frequency dependence which is inversely proportional to the absorption depth but for frequencies below 1850 cm- !, m is constant, (typically -80). From the accumulated results of experimental runs on some 50 different laser lines the number of photogenerated carriers as a function of frequency was plotted in fig. 3 for a fixed incident power. This graph
shows a pronounced peak at 1850 cm- ‘. The rise to this peak from the low frequency values can be partially explained from the shape of the band edge absorption curve of InSb, shown in fig. 1. The rapid fall in the generation curve on the high frequency side of the peak can be analysed by considering the sample dimensions relative to the optical absorption depth at the relevant frequencies. The optical absorption depth is considered as the distance over which the intensity falls to l/e of the initial value. Thus the carrier generation curve may be interpreted in terms of the absorption depth varying from the low absorption condition, where the laser beam propagates through the sample with low carrier generation, to the high absorption condition where the carrier generation is predominantly within a diffusion length (60 urn, see ref. [ 61) of the front surface. Here the dynamic population is again low because of rapid surface recombination. The peak corresponds to the absorption depth being equal to the sample thickness, which occurs at a frequency of 1850 cm- ‘. The value of optical absorption shown in fig. 1 may be used to estimate the appropriate recombination times for the achieved photocarrier population measured by the photo-Hall method. With low incident intensities there are no interband absorption saturation effects and, assuming an exponential decay in the internal intensity, through the example, we can write from equations (1) and (2) the recombination time r, as
“=
AoAN PO [ 1 -exp( --al)]
’
(3)
POis the incident power, 1 is the sample thickness and AN is the number of photo generated carriers. The effective recombination times thus calculated are shown in fig. 4. At frequencies below 1850 cm-’ the absorption depth is greater than the sample thickness, and bulk recombination dominates. From our data, this corresponds to a recombination time of 350 ns. Surface recombination is influential in reducing the carrier concentration in a volume extending approximately one diffusion length from any surface. The generation of carriers is almost entirely in this surface region for excitation frequencies above 1870 cm-‘. The recombination time was found to be 20 ns in this case. The effectiveness of the surface for scattering free carriers may be measured by the’sur75
Volume 63, number
2
OPTICS
COMMUNICATIONS
15 July 1987 100
10
moo
1a!xl
1900
1950 10
WAVENUMBER
(cme’)
Fig. 4. Photocarrier recombination time (ns) plotted against laser frequency (cm- ‘). This plot shows a value of _ 350 ns corresponding to bulk recombination below 1840 cm- ’ and a value of 20 ns at higher frequencies where surface recombination is dominant. 01
face recombination velocity, s. This is a phenomenological velocity which is dependent on the surface preparation. From the theoretical work of Frank et al. [ 71, which for our case, where 1,> 1, > 1la, then s=(I,lT)(Tlt-1)
)
1800 WAVENUMBER
km-‘1
Fig. 5. The interband absorption coefficient for n-type InSb at 77 K as a function of laser frequency. The dashed curve is the previous measurement of Miller [ 21 and Prise [ 31.
(5)
where ID is the free carrier diffusion length, T is the bulk recombination time and t is the appropriate surface dominated recombination time. Typically s can take values between 10 and 1O4m s- ‘. We report a value for s of 2.8~ lo3 m s-l. If the bulk recombination time is assumed at a constant carrier population for excitation frequencies below 1830 cm-’ then the photo-Hall data for frequencies in this region can be used to calculate the corresponding interband absorption. The band-tail thus generated, for a photogenerated carrier population of lo9 (N lOI cme3), is shown in fig. 5, for excitation frequencies in the range 1850-l 690 cm- I. At higher frequencies the photo-Hall results are consistent with the previous optical measurements. In a supplementary experiment, optical absorption measurements were made in the region between 1750-l 850 cm- ’ and were found to be in agreement with the previous authors results [ 2,3]. However, the curve diverges progressively towards lower frequencies until at 1700 cm-’ the interband contribution to the absorption is an order of magnitude smaller than the total absorption measured by Miller et al. [ 21 and Prise [ 31. We have also carried out photo76
1700
Hall experiments at a constant incident ii-radiance of 1 W cme2 which also yield decreased band-tail absorptions. The photo-Hall interband absorption data for excitation frequencies above 1850 cm- ’ has the form of a simple exponential absorption edge as found in many semiconductors and ionic materials [ 81. At lower frequencies the absorption characteristic departs from the exponential form and also shows a distinct feature at N 1790 cm- ‘. This absorption feature corresponds to the presences of an acceptor impurity state some 50 cm- ’ above the valence band. This has been previously observed in n-type InSb by several authors; in absorption [ 2,3,9], four-wavemixing [ 61, and Faraday rotation [ lo]. The lineshape of an acceptor absorption has been considered theoretically by Eagles [ 121, and may be expressed as f(x)=x”Z
(1+x)-4
)
where, X= (WtelWt,)(fiW-Es
+Ei)IE,
)
and m,, m, are the effective mass for the conduction
Volume 63, number
2
OPTICS
COMMUNICATIONS
and valence band respectively. Es and Ei are the fundamental band-gap and impurity state energy values. The absorption lineshape is asymmetric in form with a steeply rising edge on the low frequency side of the acceptor absorption peak but exhibits a more gradual decrease on the high frequency side. The predicted acceptor absorption lineshape accounts for the shape of the absorption feature at 1790 cm- ’ but does not fully explain the deviation from the exponential band-edge to the observed band-tail, which may be due, in part, to the integrated effect of all the ionised impurities. With the impurity concentrations in the sample used, it may be estimated that the impurity atoms are separated by, on average, 2-3 Bohr radii. The fluctuation in potential experienced by the conduction and valence band due to the randomly distributed electric microfields associated with these ionised impurities may lead to a broadening in the interband and acceptor impurity absorption [ 81. This aspect will be investigated further with samples of differing impurity content. The optical absorption measurements displayed in fig. 1 are displaced from present results by a non-resonant factor of 1.4 cm-‘. This factor is considerably larger than possible contributions from free carrier effects and may be attributable to a discrepancy in the earlier conventional measurement of optical absorption coefficients in this region. From the new results presented here we are able to formulate a more accurate form of the absorption band-tail in InSb which at higher absorption is consistent with earlier observations [2,3,9-l 11. The precise form of the observed band-tail will allow more accurate theoretical modelling and will give a greater insight to the physical processes involved in the cre-
15 July 1987
ation of the band-tail. It will be of considerable fundamental interest to extend this study into a nonlinear regime so that the carrier dynamics involved in the generation of nonlinear optical properties can be studied in greater detail.
Acknowledgement The authors acknowledge funding from the Ministry of Defence through the Royal Signals and Radar Establishment, Malvern, United Kingdom. Two of us (JJH and DCH) acknowledge support from the Science and Engineering Research Council (SERC) of the United Kingdom.
References [ I] B.S. Wherrett and N.A. Higgins, Proc. Roy. Sot. Lond. A379 (1982) 67. [ 2 ] D.A.B. Miller, C.T. Seaton, M.E. Prise and S.D. Smith, Phys. Rev. Lett. 47 (1981) 197. [ 31 M.E. Prise, private communication. [ 41 C.L. Littler and D.G. Seiler, J. Appl. Phys. 60 (1986) 26 1. [ 51H.H. Wieder, Laboratory notes on Electrical and galvanomagnetic measurements (Elsevier Scientific Publishing co., 1979) 41. [ 61 D.J. Hagan, H.A. MacKenzie, H.A. Al Attar and W.J. Firth, Optics Lett. 10 (1985) 187. [7] D. Frank and B.S. Wherrett, J. Opt. Sot. Am. B4 (1987) [ 81 f.‘D. Dow and D. Redtield, Phys. Rev. B 5 (1971) 594. [9]E.J.JohnsonandH.Y.Fan,Phys.Rev. 139(1965)Al991. [ lo] H.A. MacKenzie, R.B. Dennis, D. Voge and S.D. Smith, Optics Comm. 34 (1980) 205. [ll]R.Kaplan,SolidStateComm. 12(1973) 191. [ 121 D.M. Eagles, J. Phys. Chem. Solids I6 (1960) 76.
77
2
OPTICS
COMMUNICATIONS
15 July 1987
PHOTO HALL MEASUREMENTS OF BAND-TAIL ABSORPTION AND RECOMBINATION TIMES IN INDIUM ANTIMONIDE H.A. MACKENZIE, Department Received
ofPhysics.
I7 February
G.R. ALLAN, J.J. HUNTER, Heriot- Watt University, Riccarton,
D.C. HUTCHINGS
and B.S. WHERRETT
EH14 4AS, UK
1987
Photo Hall measurements are reported for a n-type InSb sample at 77 K. A bulk recombination time of 350 ns and an effective surface recombination time of 20 ns, corresponding to a surface recombination velocity of 2.8 x lo5 cm s-i, has been estimated from an analysis of the frequency dependence of the photocarrier generation. The measurements yield interband absorption coefftcients in the band-tail which are systematically lower than the previous optical measurements, being up to an order of magnitude lower at 100 cm- ’ below the band edge. The form ofthe band-tail is qualitatively described in terms of the convolution of an exponential edge and an acceptor impurity resonance.
1. Introduction
dependent parameters by conventional optical measurements. In this paper we report a novel application of the photo-Hall technique [ 41 which provides data on the photo-generated carrier population in n-type InSb at 77 K as a function of both laser frequency and power. The photo-Hall voltage represents the photo-induced change in the conduction band free carrier population and, in our experiment, this change was achieved by illuminating the sample with band-gap-resonant radiation from a cw CO laser. Initial results are presented for low incident powers ( < 5 mW) which is a region where the absorption was found to be linear. This regime is comparable with the experimental conditions used to obtain the previously published data on optical interband absorption coefficients [ 2,3]. Optical transmission measurements are the most direct method of obtaining optical absorption coefficients, but such measurements include a free carrier contribution and the range of sample thicknesses required imposes limits on accuracy, particularly for absorption coefficients that are less than 1 cm- ‘. Small changes in the interband absorption can be measured by photoconduction techniques [ 41 but the measurement is affected by simultaneous changes in both mobility and carrier population which tend to complicate the interpretation of results. The photoHall effect monitors only the changes in the pho-
The photo-excitation of electron-hole pairs in the direct-gap semiconductor InSb by near resonant radiation from a cw CO laser is a complex process due to an inter-dependence of the photogenerated band populations, the optical absorption coefficient and the carrier recombination time. For the linear absorption case the number of carriers per unit volume, N, generated at irradiance, I, is given by N= aI~,Ifiw ,
(1)
where o is the absorption coefftcient; w is the radiation frequency and r, is the carrier recombination time. The detailed microscopic process involved in the creation of the optical nonlinearity in InSb have been discussed extensively [ 1 ] and it is now well established that the irradiance-dependence of the absorption (and inter alia the dispersion) associated with a dynamic Burstein-Moss shift of the Fermi level as the carrier population is increased by photogeneration. The roles of gap renormalisation processes, impurity states and free carrier absorption have not been fully clarified. The optical absorption band-tail of InSb [ 2,3] as shown in fig. 1 has thus far not been satisfactorily explained as it is extremely difficult to obtain unambiguous data on the above inter0 030-40 18/87/$03.50 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)
3.v.
73
Volume 63, number
2
OPTICS
COMMUNICATIONS
1
15 July 1987 RECORDING SYSTEM
CO LASER TRANSMITTED POWER
CONSTANT CURRENT SOURCE
HELMHOLTZ COILS
INCIDENT POWER
CHOPPER
I__
]
SPATIAL /FILTER AND ATTENUATOR
ZnSe BEAM SPLITTER
MONOCHROMATOR
4
-i
Fig. 2. Experimental
layout for photo-Hall
measurements.
Fig. 1. The frequency dependence of the optical absorption coefficient for n-type InSb at 77 K (Miller et al. [2], and Prise [3]).
toexcited population attributable to the interband component of the optical absorption coefficient and, for n-type material is independent of hole concentration due to~the lpw holemobility [ 5 1. IJsing this technique we have obtained new data for the shape and structure of the interband absorption band-tail. We have also evaluated both bulk recombination times and effective surface recombination times for InSb and from this data, the surface recombination velocity was estimated.
2. Experimental The experimental system is shown in fig. 2. This layout allows for simultaneous monitoring of the incident and transmitted optical powers, Hall and photo-Hall voltages and the photoconductive signal. The sample was a wafer of n-type InSb, 468 urn thick 74
with a net carier concentration of 2.67x lOI cmA3 and a mobility of 5.9x lo5 cm2 V’ s-’ at 77 K. The sample was mounted on a ZnSe disc in good thermal contact with a variable temperature cryostat tail. The photo-Hall signal wasgenerated from a cw CO laser beam, mechanically chopped and focussed to a spot diameter of 600 urn on the sample. All windows and sample surfaces were anti-reflection coated for 5.6 pm operation. To minimise any thermal effects a duty cycle of 1:25 was used and the photogenerated change in the Hall voltage was monitored using standard boxcar techniques. The magnetic field was typically 0.0 1 T. The incident and transmitted powers were measured by calibrated pyroelectric detectors. This system can measure a minimum photoinduced change of 10’ in the total free carrier population, corresponding, for our geometry, to a carrier concentration change of lo9 cmP3 in the band-tail. This degree of sensitivity enables interband absorption coefficients to be evaluated with significantly
Volume 63, number
2
OPTICS
Fig. 3. The number of photogenerated carriers for a fixed incident power (2 mW) plotted as a function of frequency (cm-‘).
greater accuracy than was previously conventional optical methods.
possible
by
3. Experimental results and analysis The basic experimental procedure was to record the photogenerated carrier population as a function of incident laser power for a range of laser lines. The output signal was linearly dependent on the magnetic field which was operated in the range 0.005 to 0.02 T, and was also relatively insensitive to spot size and positioning of the laser beam between the Hall probes in the central part of the sample. The photo induced-carrier concentration AN is calculated from AN=mN(I/,,/V,--l),
15 July 1987
COMMUNICATIONS
(2)
where N is the intrinsic carrier concentration, VPH and VD are the values for the photo-Hall voltage and ‘dark’ Hall voltage respectively; m takes into account the fractional illumination of the sample and is the ratio of the volume of sample enclosed by the Hall contacts and the illuminated volume. The factor m exhibits a frequency dependence which is inversely proportional to the absorption depth but for frequencies below 1850 cm- !, m is constant, (typically -80). From the accumulated results of experimental runs on some 50 different laser lines the number of photogenerated carriers as a function of frequency was plotted in fig. 3 for a fixed incident power. This graph
shows a pronounced peak at 1850 cm- ‘. The rise to this peak from the low frequency values can be partially explained from the shape of the band edge absorption curve of InSb, shown in fig. 1. The rapid fall in the generation curve on the high frequency side of the peak can be analysed by considering the sample dimensions relative to the optical absorption depth at the relevant frequencies. The optical absorption depth is considered as the distance over which the intensity falls to l/e of the initial value. Thus the carrier generation curve may be interpreted in terms of the absorption depth varying from the low absorption condition, where the laser beam propagates through the sample with low carrier generation, to the high absorption condition where the carrier generation is predominantly within a diffusion length (60 urn, see ref. [ 61) of the front surface. Here the dynamic population is again low because of rapid surface recombination. The peak corresponds to the absorption depth being equal to the sample thickness, which occurs at a frequency of 1850 cm- ‘. The value of optical absorption shown in fig. 1 may be used to estimate the appropriate recombination times for the achieved photocarrier population measured by the photo-Hall method. With low incident intensities there are no interband absorption saturation effects and, assuming an exponential decay in the internal intensity, through the example, we can write from equations (1) and (2) the recombination time r, as
“=
AoAN PO [ 1 -exp( --al)]
’
(3)
POis the incident power, 1 is the sample thickness and AN is the number of photo generated carriers. The effective recombination times thus calculated are shown in fig. 4. At frequencies below 1850 cm-’ the absorption depth is greater than the sample thickness, and bulk recombination dominates. From our data, this corresponds to a recombination time of 350 ns. Surface recombination is influential in reducing the carrier concentration in a volume extending approximately one diffusion length from any surface. The generation of carriers is almost entirely in this surface region for excitation frequencies above 1870 cm-‘. The recombination time was found to be 20 ns in this case. The effectiveness of the surface for scattering free carriers may be measured by the’sur75
Volume 63, number
2
OPTICS
COMMUNICATIONS
15 July 1987 100
10
moo
1a!xl
1900
1950 10
WAVENUMBER
(cme’)
Fig. 4. Photocarrier recombination time (ns) plotted against laser frequency (cm- ‘). This plot shows a value of _ 350 ns corresponding to bulk recombination below 1840 cm- ’ and a value of 20 ns at higher frequencies where surface recombination is dominant. 01
face recombination velocity, s. This is a phenomenological velocity which is dependent on the surface preparation. From the theoretical work of Frank et al. [ 71, which for our case, where 1,> 1, > 1la, then s=(I,lT)(Tlt-1)
)
1800 WAVENUMBER
km-‘1
Fig. 5. The interband absorption coefficient for n-type InSb at 77 K as a function of laser frequency. The dashed curve is the previous measurement of Miller [ 21 and Prise [ 31.
(5)
where ID is the free carrier diffusion length, T is the bulk recombination time and t is the appropriate surface dominated recombination time. Typically s can take values between 10 and 1O4m s- ‘. We report a value for s of 2.8~ lo3 m s-l. If the bulk recombination time is assumed at a constant carrier population for excitation frequencies below 1830 cm-’ then the photo-Hall data for frequencies in this region can be used to calculate the corresponding interband absorption. The band-tail thus generated, for a photogenerated carrier population of lo9 (N lOI cme3), is shown in fig. 5, for excitation frequencies in the range 1850-l 690 cm- I. At higher frequencies the photo-Hall results are consistent with the previous optical measurements. In a supplementary experiment, optical absorption measurements were made in the region between 1750-l 850 cm- ’ and were found to be in agreement with the previous authors results [ 2,3]. However, the curve diverges progressively towards lower frequencies until at 1700 cm-’ the interband contribution to the absorption is an order of magnitude smaller than the total absorption measured by Miller et al. [ 21 and Prise [ 31. We have also carried out photo76
1700
Hall experiments at a constant incident ii-radiance of 1 W cme2 which also yield decreased band-tail absorptions. The photo-Hall interband absorption data for excitation frequencies above 1850 cm- ’ has the form of a simple exponential absorption edge as found in many semiconductors and ionic materials [ 81. At lower frequencies the absorption characteristic departs from the exponential form and also shows a distinct feature at N 1790 cm- ‘. This absorption feature corresponds to the presences of an acceptor impurity state some 50 cm- ’ above the valence band. This has been previously observed in n-type InSb by several authors; in absorption [ 2,3,9], four-wavemixing [ 61, and Faraday rotation [ lo]. The lineshape of an acceptor absorption has been considered theoretically by Eagles [ 121, and may be expressed as f(x)=x”Z
(1+x)-4
)
where, X= (WtelWt,)(fiW-Es
+Ei)IE,
)
and m,, m, are the effective mass for the conduction
Volume 63, number
2
OPTICS
COMMUNICATIONS
and valence band respectively. Es and Ei are the fundamental band-gap and impurity state energy values. The absorption lineshape is asymmetric in form with a steeply rising edge on the low frequency side of the acceptor absorption peak but exhibits a more gradual decrease on the high frequency side. The predicted acceptor absorption lineshape accounts for the shape of the absorption feature at 1790 cm- ’ but does not fully explain the deviation from the exponential band-edge to the observed band-tail, which may be due, in part, to the integrated effect of all the ionised impurities. With the impurity concentrations in the sample used, it may be estimated that the impurity atoms are separated by, on average, 2-3 Bohr radii. The fluctuation in potential experienced by the conduction and valence band due to the randomly distributed electric microfields associated with these ionised impurities may lead to a broadening in the interband and acceptor impurity absorption [ 81. This aspect will be investigated further with samples of differing impurity content. The optical absorption measurements displayed in fig. 1 are displaced from present results by a non-resonant factor of 1.4 cm-‘. This factor is considerably larger than possible contributions from free carrier effects and may be attributable to a discrepancy in the earlier conventional measurement of optical absorption coefficients in this region. From the new results presented here we are able to formulate a more accurate form of the absorption band-tail in InSb which at higher absorption is consistent with earlier observations [2,3,9-l 11. The precise form of the observed band-tail will allow more accurate theoretical modelling and will give a greater insight to the physical processes involved in the cre-
15 July 1987
ation of the band-tail. It will be of considerable fundamental interest to extend this study into a nonlinear regime so that the carrier dynamics involved in the generation of nonlinear optical properties can be studied in greater detail.
Acknowledgement The authors acknowledge funding from the Ministry of Defence through the Royal Signals and Radar Establishment, Malvern, United Kingdom. Two of us (JJH and DCH) acknowledge support from the Science and Engineering Research Council (SERC) of the United Kingdom.
References [ I] B.S. Wherrett and N.A. Higgins, Proc. Roy. Sot. Lond. A379 (1982) 67. [ 2 ] D.A.B. Miller, C.T. Seaton, M.E. Prise and S.D. Smith, Phys. Rev. Lett. 47 (1981) 197. [ 31 M.E. Prise, private communication. [ 41 C.L. Littler and D.G. Seiler, J. Appl. Phys. 60 (1986) 26 1. [ 51H.H. Wieder, Laboratory notes on Electrical and galvanomagnetic measurements (Elsevier Scientific Publishing co., 1979) 41. [ 61 D.J. Hagan, H.A. MacKenzie, H.A. Al Attar and W.J. Firth, Optics Lett. 10 (1985) 187. [7] D. Frank and B.S. Wherrett, J. Opt. Sot. Am. B4 (1987) [ 81 f.‘D. Dow and D. Redtield, Phys. Rev. B 5 (1971) 594. [9]E.J.JohnsonandH.Y.Fan,Phys.Rev. 139(1965)Al991. [ lo] H.A. MacKenzie, R.B. Dennis, D. Voge and S.D. Smith, Optics Comm. 34 (1980) 205. [ll]R.Kaplan,SolidStateComm. 12(1973) 191. [ 121 D.M. Eagles, J. Phys. Chem. Solids I6 (1960) 76.
77