- Email: [email protected]
Optical and photoelectric behaviour of PbS-Sb2S3 semiconductors
OPTICAL AND PHOTOELECTRIC BEHAVIOUR OF PbS-Sb& SEMICONDUCTORS S. C. KATYALand K. L. BHATAtt Department
of Physics, Maharshi Dayanand University,
Rohtak-124
(Received 16 April 1979; accepted in revised form 16 November
001, India 1979)
Atwbxt-Crystalline PbS-Sb& compounds are low symmetry semiconductors having some prpperties resembling those of vitreous semiconductors. To learn more about their physical properties a study of PbS.Sb&, 2PbS.SbrS3 and 5PbS.2SbrS3 semiconductors has been undertaken. Their far IR transmission has been observed in the spectral region 50-650 cm - I for the first time. The spectra show two optic mode behaviour and reflects the galena-like (PbS) and stibinite-like (St&) structure of the compounds. Results of photoconductivity and electrical conductibity measurements are also reported. Interpretation of the results indicates the presence of a continuous distribution of localised trap states in the band Rap of the semiconductors.
I. tNmtODucTlON
It has been reported [l] that there may not be an abrupt transition from crystalline to amorphous behaviour and that there exists a group of crystalline semiconductors having Glassy
properties
some of which
are similar
to those of
semiconductors.
Crystalline boron, PbS.Sb& and 5PbS.2Sb& are examples of such compounds. Their temperature dependent magnetic susceptibility has behaviour similar to that of semiconducting glasses [ I, 21 This behaviour has been explained due to their low lattice symmetry. 5PbS.2Sb2SJ has 80 molecules[3],and boron has more than 100atoms in their respective unit cells [l]. To learn more about their physical properties we have undertaken a study of some Pb-Sb-S compounds. There has not been any earlier study of these materials by far-IR spectroscopy. Although some photoelectric properties of PbS.Sb& have been reported in the literature[4], there has not been any earlier study of the electronic properties of various Pb-SU compounds. In this paper we present far-IR spectra, and results of photoconductivity and electrical conductivity measurements on the compounds 5PbS.2Sb5S’, PbS.Sb& and 2PbS.Sb&. 2. -AL
The compositions of interest in the ternary system were prepared from the corresponding high purity (99.999%) elements. In each case the mixture was heated in a sealed evacuated silica glass tube. The reactants were first heated for 2-3 hrs at 300°C the temperature was raised to looo”c and the system was kept at this temperature for about 20hr. The melt was continuously rotated to ensure homogenization and allowed to cool slowly inside the furnace for abour I2 hr. For structural chara&risation, X-ray powder d&action patterns were
recorded in each case. The d values of the prominent powder patterns were determined and compared with those for the constituent elements reported in literature 151.No trace of the constituent elements could be found. Differential thermal analysis was carried out using a Stanton Redcroft Model DTA 673-l apparatus. The heating rate was kept at 15°Cmin. in each case. SPbS.2Sb#, and 2PbS.Sb& indicated the presence of a single phase with melting temperatures 585°C and 641°C respectively. PbS.Sb&& showed closely spaced melting peaks at 472°C 486°C and 535°C. Far-IR transmission measurements were made in the spectral range 50-65Ocm-’ at room temperature in vacuum with a Polytech Fourier Spectrophotometer model FIR30 using the polyethylene pellet method. The resolution during measurements was 6cm-’ and 8 cm-’ in the spectral regions 50-450 cm-’ and 450-650 cm-‘, respectively. The various peaks observed in the spectrum were reproducible. The photoconductivity and electrical conductivity of the samples were measured from 100 to about 400°K in coplanar geometry using aquadag electrodes. An ECIL vibrating condenser electrometer or Philips d.c. microvoltmeter was used for current measurements. The decay of the photocurrent was observed at room temperature using a Servoscribe Model 572.2 potentiometric chart recorder. 3. IR TRANsMIssHlN
Results of transmission measurements in the spectral region 5MlO cm-’ are given in Fii. 1. Corresponding spectra for Sb& and PbS are also plotted for comparison. The positions of the various lattice bands and their approximate relative strengths, are given in Table 1. Sb& has an orthorhombic lattice. Its structure consists of zig7ag chains S&Mboriented along the c-axis. Within each chain the atoms are covalently bonded. The chains are bound to each other by weak van der Waals forces [6]. The higher frequency lattice bands (245, 275 and 335 cm-‘) should correspond to bond stretching vibrations, and the lower frequency bands can
tPresent address: Alexaodervon Humboldt-Stifttmg Fellow, Max-Plank-lrtstihrt fttr Festk&perforschung, Heisenbergstrasse I, fMOOO !%uttgM 80, West Germany, Reprint requests may be sent at this address. 821
822
S. C. KATYAL and K.
L. BHATIA
Table I. Position of lattice bands (in cm-‘) observed for various compositions studied. Approximate relative strenght of bands is shown in brackets (A) PbS . Sb&
65(w) 95 (w) 170(bs) 245 (w) 275 (w) 335 (w)
(B) 2PbS.Sl&
(C) 5PbS. 2Sb&
65(9 95 (sr) 170(bsr) 245 (wr) 275 (w) 335 (wr)
65 (ST) 95 (sr) 170(bsr) 245 (wr) 215 (w) 335 (wr)
(0 PbS
W S&S3
165(vs)
56 (vs) 110(s) 140(s) 170(s) 245 (vs) 275 (s) 335 (vs)
w = weak, WT= weaker, vw = very weak, s = strong, sr = stronger, vs = very strong, bs = broad and strong, bsr = broad and stronger.
be associated with bond bending vibrations of the chains.
I
I
I
PbS has a rock salt type structure in whcih the PM bond is ionic, and gives a strong reststrahlen lattice band around 165cm-‘. It has been found that SPbS.2Sb& and PbS.Sb& have complex galena-like (PbS) and stibinite-like (Sb&) structure (4,7). -Sb-!L% chains are oriented parallel to the crystallographic c-axis. At right angles to the c-axis, the structure is dominated by Pb atoms. This complex structure is reflected in the IR spectra reported here. There is a two optic mode behaviour for the Lattice vibrational modes of all the three compositions studied. In the mixed crystal system, two phonon frequencies for each of the allowed optic modes of the pure crystal are observed to occur at frequencies close to those of the end members. The two mode behatiour can be attributed to the large mass difference between Pb and Sb atoms, and to the different force constants of Pb-S and Sb-S bonds, which result from the different co-ordination numbers of the Pb and Sb atoms. Such a two optic mode behaviour has also been Fii. 2. Photocurrent vs intensity of incident light (llfi in low and high intensity regions for compositions (A) PbS.Sb& (B) ZPbS.Sb& and (C) SPbS.2Sb& at 29PK. Slopes of the curves are marked in the diagram.
observed in amorphous Pb-As-S and Pb-Ge-S compounds [8,91. It appears as if this feature is common in PbS based compounds.
Fii I. Room temp. IR transmission of PL+Sb-S compositions; (A) PbS.Sb&, (B) 2PbS.Sb&, (C) SPbS.2Sl&, (D) PbS, and (E) Sb& Ordinate scale for various compositions is displaced for clarity.
Figure 2 shows the dependence of the photocurrent on the intensity of incident white light for the three compositions: (A) PbS. Sb& (B) 2PbS.Sb$a and (C) 5PbS. 2Sb&. The dependence of the log&hm of photocurrent on reciprocal temperature is given in Fig. 3. EIectrical conductivity vs l/T is depicted in Fii 4. Results in Fii. 2 show an approxiemtely linear (slope 0.75-1.00) and sublinau (slope 0.17-0.37) behavi0W for the photocurrent in the low Iiit intensity and high light intensity regions, respectively. Such a’behaviola in photoconductivity has been explained by invoking a model involving recombination centres and also one type of trappingcentreN,inthebandgapoftbesemicoaductor (lo]. The experimental observation of a variaGon of photocurrent (IJ with the power of the tight intensity
@tical and photoekcti behaviourof PbS-Sb$, semicondu&rs I
I
’
1
’
1
Fig. 3. Temperature dependence of photoconductivity from room temp. lo about 110°Cin the compositions(A) PbS. Sb&, (B) 2PbS.Sb& and (C) SPbS.ZSb&. Cn between l/2 and 1 can be described by assuming an exponential (nonuniform) distribution of traps in the band gap. Taking electrons as majority carriers the trap density [lo] is
ME)=Aew
Ec - E, t
kT,
>
where E, and E, represent the conduction band edge and trap energies, respectively. T, is a parameter that can be
Fk 4. Plots of ek&ical conductivity (coplaner geometry) vs l/T for (A) PbS.Sb&,(B) 2PbS.Sb& and (0 JPb!X!S&.
823
adjusted to make the density of states vary more or less rapidly with energy. First we take T, 3 T, where T is the ambient temperature. The density of photoexcited carriers is [IO]
where S,, is the capture cross section for electron traps and u is the thermal velocity. The exponent T,(T+ TJ lies between 0.5 and unity for I’, z T. As the distribution approaches a more nearly uniform one which is constant in energy, the characteristic temperature i”,+m, and n varies more nearly linearly with light intensity. Thus, in the range of light intensities for which the density of free carriers is less than the density of trapped carriers, the simple model provides a description of I,, varying with the power of f between 0.5 and 1.0, and recombination exists in this region. For high light intensities (T, < 7’), such that the density of free carriers is greater than the density of trapped carriers, bimolecular recombination will predominate, and f,, will vary as f” (n =Z 0.5). The appearance of odd exponents between 0.5 and unity is evidence for a continuous distribution of states in the band gap of the semiconductors. The simple model described above can be used to make a fit to the present experimental data. The expression Z’,/(T+ TI) is equated to the low intensity experimental values of the exponent: 0.75 and 0.84 for the samples C and B. respectively. The corresponding values of TI are 900 and 15,600. In the data for sample A, the exponent is 1.0 and corresponds to the situation T, +m. Since the experimental values of the parameter S,, v and N, in eqn (2) are not known for the semiconductors uilder study, values of the quantities involved have been taken as N, = lOI cm3 for a carrier effective mass equal to the free electron mass at T = 3WK, S,, = 10-20cm2 and v = 10’cmlsec for n %p. By adjusting the value of the parameter A in eqn (l), a straight line relation between the photocurrent and intensity of the incident light in the low intensity region with the observed slope is obtained. In applying the model in the present case, constancy of the mobility and capture cross section, and homogeneity of the photoconductor has been assumed. Appearance of the odd exponent between 0.5 and unity suggests the presence of a continuous distribution of the states in the band gap of the semiconductors. The absence of super-linearity in the photocurrent vs intensity relation indicates the presence of one class of distribution of states having the same capture cross section. The temperature dependence of the photocurrent shows a slower variation at lower temperature and an almost exponential rise at higher temperature. Such a temperature variation of the photoconductivity also indicates a nonuniform distribution of the trap states in the band gap of the semiconductors. The photoconductivity in the sample 2Pbs. Sb$, shows saturation at higher temperatures. The photoconductivity activation energies in the higher temperature regions in the samples A, B and C are 0.21,0.27 and 0.23 eV, respectively, which gives estimated values for the trap depth. Figures 5 and 6 show
S. C.
824
KATYAL and K. L. BHA~A
TIME (scc.s)
Fa. 3. Rise and decay of photoamzfit in PbS.Sb& al room temp. (29PK)withthreeexcitationintensities;(A) I, (B) fll0 and (C) llloo. the steady state photoresponse of samples A and C, respectively, to a continuous white light source. After an initial rapid rise, a steady state photocurrent is attained. On cessation of the photoexcitation, the photocurrent first decays rapidly and then rehues to the dark conductivity value after a long time. This behaviour of the photoresponse is governed by the carrier relaxation in the presence of a set of fast and slow trapping centres. The initial rapid drop in the photocurrent on cessation of the exciting radiation corresponds to the recombination and empty& of comparatively shallow trap states. Dezay of the deeper trap states is represented by the slowly decreasing part of the decay curve. The present data for the
I
’
I
’
I
photocurrent decay gives information about the long term reltiation of the photoconductivity. The rise of photocurrent is more like an exponential one, whereas the decay is more complicated. This may be connected with the fact that the rise time is determined by the shallowest of the active levels, whereas the decay is the result of the total contribution of all the active levels. This would lead to a more complicated type of decay. The effect of intensity of the exciting radiation on the photoresponse of the semiconductor was also observed at different incident intensities. The variation of intensity was produced by placing neutral density filters over the source to avoid altering the numerical aperture of the optical system. This is shown in Figs. 5 and 6. The rise and decay times of the photocurrent shorten as the intensity is increased, which indicates a recombination limited growth process. The persistance of some portion of the photocurrent for a long time suggests that the distribution of trapping levels is continuous rather than discrete. The photoresponse decay curve of SPbS.tSb& has a slower rate than that of PbS.Sb& This feature indicates the presence of more non-uniformity in the distribution of the trap states. Similar behaviour is indicated in the intensity dependence of the photoresponse, as discussed before where the photocurrent vs intensity curve shows a smaller slope of 0.75 at lower excitation intensity. The variation of the photoconductivity and dark conductivity with the applied electric field (up to almost IO V/cm) in each case was almost ohmic as shown in Fig. 7. The temperature dependence of electrical conductivity shown in Fig. 4 exhibits both extrinsic and intrinsic carrier conduction processes. In the data for samples A and C there is a slowly varying region of conductivity which
’ IO
IQ. 7. Photocurrentand dark current vs appliedelectricMd at room temp. (29pK) for (A) PM. Sb& @) 2PbS.Sb& and (C) slopw of the curve Fs 6. Rise oad decay of photocvmntin SE%!%!%& at room 5PMU!?b& Full Iii is for photocUrrent. aremarkcdiacachcasc. temp.(29pK) with twu excitation intensities;(A) I ad (B)I/10.
Opticaland photoelectricbehaviourof PM-Sb& semiconductors
corresponds to the onset of extrinsic conduction at low temperature. Conduction should take place by a hopping process in this region. An exponential behaviour of the conductivity at higher temperatures is observed a=u,exp
E” -i;~
( )
and the activation energies for the samplesA and C are 0.54and 0.578eV, respectively. SpecimenB exhibits two activation energies 0.58 and 0.I6 eV, and there is no tlat part in the curve in the temperature region studied.In the higher temperature region the activation energies (OX0.578eV). indicate the thermal energy gaps of semiconductors to be 1.08, 1.16 and l.l4eV, respectively. At lower temperaturesthe almost flat portions of the curves indicate conduction by phonon-assisted tunneling through the spatially distributed localized electronic states in the band gap.
5. coNcLusxoN
A study of the optical and photoelectric properties of the low symmetry semiconductorsPbS-St& has been made. The IR lattice vibrationalspectra of the semiconductors exhibits two optic mode behaviour and reflects the gal&like (PbS) and &iii&e-like (Sb&) structure of the compounds. Results of photoconductivity and electrical conductivity measurements support the presence of continuouslydistributedlocalizedtrap states in the band gap of the semiconductors.Such features are somewhatsimilarto those in amorphoussemiconductors [ll, 121.
82s
Acknowkdgnnmls-The authors are grateful to Dr. Vcaugopalan for his help in measuringthe far-IRtransmissionspectraat the Raman Research Institute, Bangalore.They are indebted to Prof. E. S. R. Gopalof the Indian Institute of Science, Bangalore, for his assistance in obtainingthe X-ray powder di5action patterns.and for the use of low tempcralurefacilities in his laboratory. Financial assistance from Dqxutmeat of Atomic Energyand Departmentof Science and Technologyis gratefully acknowledged.ant of us (S. C. Katyal) is grateful to CSIR for the award of a research fellowship. One of the authors (K. L. Bhatiawishes to thankProf. K. Dransfeld,Ix. S. Hm aad the Humboldtfoundationfor hospitalityduringprepamb of the revised manuscript. -cEs
1. Matyas M. and FrumarM., Phys. Stutru Solidi (a) 13, K137 (1972). 2. Matyas M., Czech 1. Phys. BU, 413 (1973). 3. Wilson A. J. C., (General Editor) Pb-Sb-S minds (Struthual Data) Strudun Rep. (N. V. A. Oosthoek’s Uitgevers MIJUtrecht)Vol. 8, p. 173. 4. DmytrivA. Yu., Koval’skiiP. N. and MakarenkoV. V., SOD. Phys. Semicond. I, 1493(1974). 5. Swanson H. E. ef al., Standanf X-my di#racGonPowder Patterns (National Bureau of Standardscircular No. 539) (1960). 6. Abrikosov N. Kh., Bankina V. F., Poetskaya L. V., Shelimova L. E., and Skudnova, suniconducling II-VI, IV-VI and V-VI compounds,Plenum Press, New York, Chaps. 2 and 3, (1%9). 7. Born L. and Hellner,Am. Miner,45, 1266(MO). 8. Bhal P. K. and Bhatia K. L., Solid State Comnum.22,789 (1977). 9. BhatiaK. L.. KatyalS. C. and VcnugopalanS., 1. Non-Cryst. Solids 31,333 (1979). IO. Rose A., Concepts in Phokxondnctivity and Allied Problems, Chap.3. Wiley-Interscience.New York (1963). Il. Bhat P. K., Bhatia K. L., and Katyal S. C., /. Non-crysl. Solids 27,399 (1978). 12. Bhatia K. L., Katyal S. C., Phys. Statu.~Solidi (b) communicated(1980).
of Physics, Maharshi Dayanand University,
Rohtak-124
(Received 16 April 1979; accepted in revised form 16 November
001, India 1979)
Atwbxt-Crystalline PbS-Sb& compounds are low symmetry semiconductors having some prpperties resembling those of vitreous semiconductors. To learn more about their physical properties a study of PbS.Sb&, 2PbS.SbrS3 and 5PbS.2SbrS3 semiconductors has been undertaken. Their far IR transmission has been observed in the spectral region 50-650 cm - I for the first time. The spectra show two optic mode behaviour and reflects the galena-like (PbS) and stibinite-like (St&) structure of the compounds. Results of photoconductivity and electrical conductibity measurements are also reported. Interpretation of the results indicates the presence of a continuous distribution of localised trap states in the band Rap of the semiconductors.
I. tNmtODucTlON
It has been reported [l] that there may not be an abrupt transition from crystalline to amorphous behaviour and that there exists a group of crystalline semiconductors having Glassy
properties
some of which
are similar
to those of
semiconductors.
Crystalline boron, PbS.Sb& and 5PbS.2Sb& are examples of such compounds. Their temperature dependent magnetic susceptibility has behaviour similar to that of semiconducting glasses [ I, 21 This behaviour has been explained due to their low lattice symmetry. 5PbS.2Sb2SJ has 80 molecules[3],and boron has more than 100atoms in their respective unit cells [l]. To learn more about their physical properties we have undertaken a study of some Pb-Sb-S compounds. There has not been any earlier study of these materials by far-IR spectroscopy. Although some photoelectric properties of PbS.Sb& have been reported in the literature[4], there has not been any earlier study of the electronic properties of various Pb-SU compounds. In this paper we present far-IR spectra, and results of photoconductivity and electrical conductivity measurements on the compounds 5PbS.2Sb5S’, PbS.Sb& and 2PbS.Sb&. 2. -AL
The compositions of interest in the ternary system were prepared from the corresponding high purity (99.999%) elements. In each case the mixture was heated in a sealed evacuated silica glass tube. The reactants were first heated for 2-3 hrs at 300°C the temperature was raised to looo”c and the system was kept at this temperature for about 20hr. The melt was continuously rotated to ensure homogenization and allowed to cool slowly inside the furnace for abour I2 hr. For structural chara&risation, X-ray powder d&action patterns were
recorded in each case. The d values of the prominent powder patterns were determined and compared with those for the constituent elements reported in literature 151.No trace of the constituent elements could be found. Differential thermal analysis was carried out using a Stanton Redcroft Model DTA 673-l apparatus. The heating rate was kept at 15°Cmin. in each case. SPbS.2Sb#, and 2PbS.Sb& indicated the presence of a single phase with melting temperatures 585°C and 641°C respectively. PbS.Sb&& showed closely spaced melting peaks at 472°C 486°C and 535°C. Far-IR transmission measurements were made in the spectral range 50-65Ocm-’ at room temperature in vacuum with a Polytech Fourier Spectrophotometer model FIR30 using the polyethylene pellet method. The resolution during measurements was 6cm-’ and 8 cm-’ in the spectral regions 50-450 cm-’ and 450-650 cm-‘, respectively. The various peaks observed in the spectrum were reproducible. The photoconductivity and electrical conductivity of the samples were measured from 100 to about 400°K in coplanar geometry using aquadag electrodes. An ECIL vibrating condenser electrometer or Philips d.c. microvoltmeter was used for current measurements. The decay of the photocurrent was observed at room temperature using a Servoscribe Model 572.2 potentiometric chart recorder. 3. IR TRANsMIssHlN
Results of transmission measurements in the spectral region 5MlO cm-’ are given in Fii. 1. Corresponding spectra for Sb& and PbS are also plotted for comparison. The positions of the various lattice bands and their approximate relative strengths, are given in Table 1. Sb& has an orthorhombic lattice. Its structure consists of zig7ag chains S&Mboriented along the c-axis. Within each chain the atoms are covalently bonded. The chains are bound to each other by weak van der Waals forces [6]. The higher frequency lattice bands (245, 275 and 335 cm-‘) should correspond to bond stretching vibrations, and the lower frequency bands can
tPresent address: Alexaodervon Humboldt-Stifttmg Fellow, Max-Plank-lrtstihrt fttr Festk&perforschung, Heisenbergstrasse I, fMOOO !%uttgM 80, West Germany, Reprint requests may be sent at this address. 821
822
S. C. KATYAL and K.
L. BHATIA
Table I. Position of lattice bands (in cm-‘) observed for various compositions studied. Approximate relative strenght of bands is shown in brackets (A) PbS . Sb&
65(w) 95 (w) 170(bs) 245 (w) 275 (w) 335 (w)
(B) 2PbS.Sl&
(C) 5PbS. 2Sb&
65(9 95 (sr) 170(bsr) 245 (wr) 275 (w) 335 (wr)
65 (ST) 95 (sr) 170(bsr) 245 (wr) 215 (w) 335 (wr)
(0 PbS
W S&S3
165(vs)
56 (vs) 110(s) 140(s) 170(s) 245 (vs) 275 (s) 335 (vs)
w = weak, WT= weaker, vw = very weak, s = strong, sr = stronger, vs = very strong, bs = broad and strong, bsr = broad and stronger.
be associated with bond bending vibrations of the chains.
I
I
I
PbS has a rock salt type structure in whcih the PM bond is ionic, and gives a strong reststrahlen lattice band around 165cm-‘. It has been found that SPbS.2Sb& and PbS.Sb& have complex galena-like (PbS) and stibinite-like (Sb&) structure (4,7). -Sb-!L% chains are oriented parallel to the crystallographic c-axis. At right angles to the c-axis, the structure is dominated by Pb atoms. This complex structure is reflected in the IR spectra reported here. There is a two optic mode behaviour for the Lattice vibrational modes of all the three compositions studied. In the mixed crystal system, two phonon frequencies for each of the allowed optic modes of the pure crystal are observed to occur at frequencies close to those of the end members. The two mode behatiour can be attributed to the large mass difference between Pb and Sb atoms, and to the different force constants of Pb-S and Sb-S bonds, which result from the different co-ordination numbers of the Pb and Sb atoms. Such a two optic mode behaviour has also been Fii. 2. Photocurrent vs intensity of incident light (llfi in low and high intensity regions for compositions (A) PbS.Sb& (B) ZPbS.Sb& and (C) SPbS.2Sb& at 29PK. Slopes of the curves are marked in the diagram.
observed in amorphous Pb-As-S and Pb-Ge-S compounds [8,91. It appears as if this feature is common in PbS based compounds.
Fii I. Room temp. IR transmission of PL+Sb-S compositions; (A) PbS.Sb&, (B) 2PbS.Sb&, (C) SPbS.2Sl&, (D) PbS, and (E) Sb& Ordinate scale for various compositions is displaced for clarity.
Figure 2 shows the dependence of the photocurrent on the intensity of incident white light for the three compositions: (A) PbS. Sb& (B) 2PbS.Sb$a and (C) 5PbS. 2Sb&. The dependence of the log&hm of photocurrent on reciprocal temperature is given in Fig. 3. EIectrical conductivity vs l/T is depicted in Fii 4. Results in Fii. 2 show an approxiemtely linear (slope 0.75-1.00) and sublinau (slope 0.17-0.37) behavi0W for the photocurrent in the low Iiit intensity and high light intensity regions, respectively. Such a’behaviola in photoconductivity has been explained by invoking a model involving recombination centres and also one type of trappingcentreN,inthebandgapoftbesemicoaductor (lo]. The experimental observation of a variaGon of photocurrent (IJ with the power of the tight intensity
@tical and photoekcti behaviourof PbS-Sb$, semicondu&rs I
I
’
1
’
1
Fig. 3. Temperature dependence of photoconductivity from room temp. lo about 110°Cin the compositions(A) PbS. Sb&, (B) 2PbS.Sb& and (C) SPbS.ZSb&. Cn between l/2 and 1 can be described by assuming an exponential (nonuniform) distribution of traps in the band gap. Taking electrons as majority carriers the trap density [lo] is
ME)=Aew
Ec - E, t
kT,
>
where E, and E, represent the conduction band edge and trap energies, respectively. T, is a parameter that can be
Fk 4. Plots of ek&ical conductivity (coplaner geometry) vs l/T for (A) PbS.Sb&,(B) 2PbS.Sb& and (0 JPb!X!S&.
823
adjusted to make the density of states vary more or less rapidly with energy. First we take T, 3 T, where T is the ambient temperature. The density of photoexcited carriers is [IO]
where S,, is the capture cross section for electron traps and u is the thermal velocity. The exponent T,(T+ TJ lies between 0.5 and unity for I’, z T. As the distribution approaches a more nearly uniform one which is constant in energy, the characteristic temperature i”,+m, and n varies more nearly linearly with light intensity. Thus, in the range of light intensities for which the density of free carriers is less than the density of trapped carriers, the simple model provides a description of I,, varying with the power of f between 0.5 and 1.0, and recombination exists in this region. For high light intensities (T, < 7’), such that the density of free carriers is greater than the density of trapped carriers, bimolecular recombination will predominate, and f,, will vary as f” (n =Z 0.5). The appearance of odd exponents between 0.5 and unity is evidence for a continuous distribution of states in the band gap of the semiconductors. The simple model described above can be used to make a fit to the present experimental data. The expression Z’,/(T+ TI) is equated to the low intensity experimental values of the exponent: 0.75 and 0.84 for the samples C and B. respectively. The corresponding values of TI are 900 and 15,600. In the data for sample A, the exponent is 1.0 and corresponds to the situation T, +m. Since the experimental values of the parameter S,, v and N, in eqn (2) are not known for the semiconductors uilder study, values of the quantities involved have been taken as N, = lOI cm3 for a carrier effective mass equal to the free electron mass at T = 3WK, S,, = 10-20cm2 and v = 10’cmlsec for n %p. By adjusting the value of the parameter A in eqn (l), a straight line relation between the photocurrent and intensity of the incident light in the low intensity region with the observed slope is obtained. In applying the model in the present case, constancy of the mobility and capture cross section, and homogeneity of the photoconductor has been assumed. Appearance of the odd exponent between 0.5 and unity suggests the presence of a continuous distribution of the states in the band gap of the semiconductors. The absence of super-linearity in the photocurrent vs intensity relation indicates the presence of one class of distribution of states having the same capture cross section. The temperature dependence of the photocurrent shows a slower variation at lower temperature and an almost exponential rise at higher temperature. Such a temperature variation of the photoconductivity also indicates a nonuniform distribution of the trap states in the band gap of the semiconductors. The photoconductivity in the sample 2Pbs. Sb$, shows saturation at higher temperatures. The photoconductivity activation energies in the higher temperature regions in the samples A, B and C are 0.21,0.27 and 0.23 eV, respectively, which gives estimated values for the trap depth. Figures 5 and 6 show
S. C.
824
KATYAL and K. L. BHA~A
TIME (scc.s)
Fa. 3. Rise and decay of photoamzfit in PbS.Sb& al room temp. (29PK)withthreeexcitationintensities;(A) I, (B) fll0 and (C) llloo. the steady state photoresponse of samples A and C, respectively, to a continuous white light source. After an initial rapid rise, a steady state photocurrent is attained. On cessation of the photoexcitation, the photocurrent first decays rapidly and then rehues to the dark conductivity value after a long time. This behaviour of the photoresponse is governed by the carrier relaxation in the presence of a set of fast and slow trapping centres. The initial rapid drop in the photocurrent on cessation of the exciting radiation corresponds to the recombination and empty& of comparatively shallow trap states. Dezay of the deeper trap states is represented by the slowly decreasing part of the decay curve. The present data for the
I
’
I
’
I
photocurrent decay gives information about the long term reltiation of the photoconductivity. The rise of photocurrent is more like an exponential one, whereas the decay is more complicated. This may be connected with the fact that the rise time is determined by the shallowest of the active levels, whereas the decay is the result of the total contribution of all the active levels. This would lead to a more complicated type of decay. The effect of intensity of the exciting radiation on the photoresponse of the semiconductor was also observed at different incident intensities. The variation of intensity was produced by placing neutral density filters over the source to avoid altering the numerical aperture of the optical system. This is shown in Figs. 5 and 6. The rise and decay times of the photocurrent shorten as the intensity is increased, which indicates a recombination limited growth process. The persistance of some portion of the photocurrent for a long time suggests that the distribution of trapping levels is continuous rather than discrete. The photoresponse decay curve of SPbS.tSb& has a slower rate than that of PbS.Sb& This feature indicates the presence of more non-uniformity in the distribution of the trap states. Similar behaviour is indicated in the intensity dependence of the photoresponse, as discussed before where the photocurrent vs intensity curve shows a smaller slope of 0.75 at lower excitation intensity. The variation of the photoconductivity and dark conductivity with the applied electric field (up to almost IO V/cm) in each case was almost ohmic as shown in Fig. 7. The temperature dependence of electrical conductivity shown in Fig. 4 exhibits both extrinsic and intrinsic carrier conduction processes. In the data for samples A and C there is a slowly varying region of conductivity which
’ IO
IQ. 7. Photocurrentand dark current vs appliedelectricMd at room temp. (29pK) for (A) PM. Sb& @) 2PbS.Sb& and (C) slopw of the curve Fs 6. Rise oad decay of photocvmntin SE%!%!%& at room 5PMU!?b& Full Iii is for photocUrrent. aremarkcdiacachcasc. temp.(29pK) with twu excitation intensities;(A) I ad (B)I/10.
Opticaland photoelectricbehaviourof PM-Sb& semiconductors
corresponds to the onset of extrinsic conduction at low temperature. Conduction should take place by a hopping process in this region. An exponential behaviour of the conductivity at higher temperatures is observed a=u,exp
E” -i;~
( )
and the activation energies for the samplesA and C are 0.54and 0.578eV, respectively. SpecimenB exhibits two activation energies 0.58 and 0.I6 eV, and there is no tlat part in the curve in the temperature region studied.In the higher temperature region the activation energies (OX0.578eV). indicate the thermal energy gaps of semiconductors to be 1.08, 1.16 and l.l4eV, respectively. At lower temperaturesthe almost flat portions of the curves indicate conduction by phonon-assisted tunneling through the spatially distributed localized electronic states in the band gap.
5. coNcLusxoN
A study of the optical and photoelectric properties of the low symmetry semiconductorsPbS-St& has been made. The IR lattice vibrationalspectra of the semiconductors exhibits two optic mode behaviour and reflects the gal&like (PbS) and &iii&e-like (Sb&) structure of the compounds. Results of photoconductivity and electrical conductivity measurements support the presence of continuouslydistributedlocalizedtrap states in the band gap of the semiconductors.Such features are somewhatsimilarto those in amorphoussemiconductors [ll, 121.
82s
Acknowkdgnnmls-The authors are grateful to Dr. Vcaugopalan for his help in measuringthe far-IRtransmissionspectraat the Raman Research Institute, Bangalore.They are indebted to Prof. E. S. R. Gopalof the Indian Institute of Science, Bangalore, for his assistance in obtainingthe X-ray powder di5action patterns.and for the use of low tempcralurefacilities in his laboratory. Financial assistance from Dqxutmeat of Atomic Energyand Departmentof Science and Technologyis gratefully acknowledged.ant of us (S. C. Katyal) is grateful to CSIR for the award of a research fellowship. One of the authors (K. L. Bhatiawishes to thankProf. K. Dransfeld,Ix. S. Hm aad the Humboldtfoundationfor hospitalityduringprepamb of the revised manuscript. -cEs
1. Matyas M. and FrumarM., Phys. Stutru Solidi (a) 13, K137 (1972). 2. Matyas M., Czech 1. Phys. BU, 413 (1973). 3. Wilson A. J. C., (General Editor) Pb-Sb-S minds (Struthual Data) Strudun Rep. (N. V. A. Oosthoek’s Uitgevers MIJUtrecht)Vol. 8, p. 173. 4. DmytrivA. Yu., Koval’skiiP. N. and MakarenkoV. V., SOD. Phys. Semicond. I, 1493(1974). 5. Swanson H. E. ef al., Standanf X-my di#racGonPowder Patterns (National Bureau of Standardscircular No. 539) (1960). 6. Abrikosov N. Kh., Bankina V. F., Poetskaya L. V., Shelimova L. E., and Skudnova, suniconducling II-VI, IV-VI and V-VI compounds,Plenum Press, New York, Chaps. 2 and 3, (1%9). 7. Born L. and Hellner,Am. Miner,45, 1266(MO). 8. Bhal P. K. and Bhatia K. L., Solid State Comnum.22,789 (1977). 9. BhatiaK. L.. KatyalS. C. and VcnugopalanS., 1. Non-Cryst. Solids 31,333 (1979). IO. Rose A., Concepts in Phokxondnctivity and Allied Problems, Chap.3. Wiley-Interscience.New York (1963). Il. Bhat P. K., Bhatia K. L., and Katyal S. C., /. Non-crysl. Solids 27,399 (1978). 12. Bhatia K. L., Katyal S. C., Phys. Statu.~Solidi (b) communicated(1980).