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Photoconduction of natural cinnabar (α-HgS)
1. Phys. Chem. Solids, Vol. 42. pp. 567-571, 1981 Printed in Great Britain.
0022%3697/81/070567-05$02.00/0 Pergamon Press Ltd.
PHOTOCONDUCTION OF NATURAL CINNABAR(a-HgS) J. P. LEYRIS,H. CARLostand J. P. AICARDI Laboratoirede Physiquedu Solide, Universitt! de Perpignan, avenue de Villeneuve, 66025 Perpignan Cedex, France (Received 15 July 1980; accep.ted in revised form 5 November
1980)
Abstract-The photoconductivity measurements presented in this paper permit us to reveal a sensitizing process in mercury sulakipe (a-HgS) which is common to a number of II-VI compounds. The excitation spectra of the photocurrent as well as the results obtained in terms of excitation density and temperature allow us to locate the slow recombination center at I65 meV from the valence band. The ratio of capture cross sections for holes and electronsfor this center is around l@. Experiments on photoresponse to a cut off of the excitation show that, in the temperature range corresponding to the quenching of the photocurrent, the recombination process of free carriers is close to the bimolecular. However, the influence on our results of an electron trap located at 50meV from the conduction band is pointed out.
The electric contacts are carried out by an eutectic indium-gallium alloy (15.7”C) with 24.5% of indium in weight[ll]. The polarisation was fixed at 20V d.c. (injection measurements showed us that, at this voltage, the behavior of the specimen followed ad ohmic law). The crystal is placed on a slab of beryllium oxide (which makes it possible to isolate the sample electrically and at the same time to ensure a good thermal contact), stuck onto the copper tail of a cryostat for sensitive heat recovery, linked to a temperature regulator. The latter is measured by a cryogenic linear temperature sensor. The optical excitation is provided either by means of a grating monochromator (1200 lines/mm; resolution: 1 nm; focal length: 50cm; blaze: $0.0 nm) associated with a xenon light source, or by a hydrogen lamp and interference filters. The currents are detected either by a logarithmic picoammeter (10-4-10~‘2A) or by a linear one (lo-‘lo-l5 A). Figure 1 shows the excitation spectrum of the photoconductivity for temperatures ranging from liquid helium to liquid nitrogen. We observe three peaks. (1) The high energy one is located at 2.287 eV (at liquid helium temperature). It corresponds to the gap value found by different optical methods[6,20]. It disappears very quickly when temperature increases (Fig. 1). For this wavelength, corresponding to a strong absorption coefficient, the photocurrent is generated only near the surface. As the recombination speeds due to surface states become great when temperature increases, the recombination probability of photoexcited carriers becomes important. This explains the disappearance of 2. EXPERIMENTAL RESULTS this peak[21,22] at temperatures above SOK. We took our measurements on several natural crystals, (2) The second one is located at 2.222 eV, i.e. a with no notable difference in the results. We shall give here difference of 65 meV from the gap value. It corresponds the ones obtained with the sample previously used in our to the photoionisation of a localized center, whose exisT.S.C. experiments [16,17] (natural from Almadentence has been revealed by cathodoluminescence and Spain; dimension 3 x 3 x 0.7 mm’). photoluminescence experiments[lS, 231. This center’s emission is of the vibronic type. The photoluminescence thermal quenching measurements and the lifetime variatPresent address: Laboratoire de Physique de la Make CondensCe, Ecole Polytechnique, Route de Saclay, 91128 tions according to temperature allowed to situate the Palaiseau Cedex, France. ground state at 65 meV from the valence band[15]. 1. INTRODUCTlON
Cinnabar (cu-HgS) is a II-VI semiconductor compound with wide bandgap (2.1 eV at room temperature) wluch crystallises in the trigonal system. This substance has been very little studied owing to the difficulties of its crystallogenesis. Recently Doni et a/.[11 carried out the first theoretical work on its band structure. Studies have shown that both natural and synthetic crystals of cinnabar were highly resistant (p > 10” 0 x cm). Its conductivity has been determin as being of n-type by measurements of Hall-effect [2], photo-Hall effect[3] and drift mobility[4]. Moreover, the strong anisotropy revealed by optical experiments of absorption[S, 61 and luminescence[7], was found again by electric ones. The photo-Hall effect measurements showed that the mobility varies by a factor of 3 according to the polarisation (~II~= 30 cm* x V-’ x s-l; PlC = 10 cm* X V-’ X s-’ at room temperature). Our Laboratory has for some years now taken a keen interest in the study of cinnabar: crystallogenesis[8], obtaining of thin solid films by transport in a vapour zone and evaporation in a vacuum[9, lo], IR[ll], Halleffect [3], luminescence [ 12-151, thermally stimulated conductivity (T.S.C.)[16,17], space charges limited conductivity (S.C.L.C.)[17]. The photoconductivity of a-HgS has been studied by Roberts and Zallen[ 181and Roberts et al. [19] between 77 and 180K. We complete their measurements by various techniques, which enables us to improve their results and to explain more fully the photoconductivity mechanism of cinnabar, particularly by comparison with our T.S.C. experiments [ 16,171.
567
J. P.
I 1
LEYRIS et 01
I-
I+,(A)
o((Cm-1) 1o-4
I 4500
-400
ho0 I -1200
10-6
1o-9 t
; 100
~ 1
Fig. 1. Photoconductivity of cinnabar as a function of wavelength for different temoeratures. ---: absorution curve at liquid.helium[5]. 1
(3) The last peak appearing on the excitation spectrum of the photoconductivity is located at 2.122 eV, in other words a difference of 165meV from the gap width. The gap, determined by optical measurements[Q and the peak located at 2.222eV come under the same law for temperatures above 120K; the energy difference between the two curves is constant and equal to 80 meV. The value of the temperature coefficient obtained is of similar size to those provided by literature [5,19]: 6.65 X IO-“ eV X K-‘. In view of these first results, it would seem that, above 120K the excitation of the localized center is responsible for the photoconductivity observed. At these temperatures the ground state is ionised and radiative recombination no longer takes place. We then set the excitation wavelength at 577.0nm (yellow line of the hydrogen light source spectrum). This energy lower than the gap allows us to have an excitation of the sample homogeneous in volume and corresponds to the maximum photocurrent gain. Figure 2 shows the curves according to temperature for different excitation fluxes between 8 and 200K. We observe, for the maximum excitation density (d = (log Z,/Z]= 0, where I0 is the incident light intensity and I the same quantity measured after the neutral density filter), a photocurrent quenching region stretching from approx. 50 to 15OK. For the weakest excitations (d = 3 and d = 4) we discern shoulders for temperatures corresponding to those for the emptying of the traps revealed bythermally stimulated conductivity[lh, 171. The last experiments we made dealt with the response of the sample to a luminous pulse. Given the high values of the time constants, we used a simple mechanical
‘I
lo-‘(
I:
10-l’
50
100
150
200
250
T(K)
Fig. 2. Photocurrent in terms of temperature for different excitation densities (A,, = 577.0nm).
device (shutter) to cut off the light flow. The measurements were taken between liquid helium temperature and 120K at several excitation fluxes. We also recorded the photoresponse to some excitation densities for a temperature of 185K, which corresponds to the emptying zone of the trap at depth 300 meV revealed by our S.C.L.C.[17] and T.S.C.[16,17] measurements. 3. INTERPRETATION OF OUR RESULTS
Study of the photoconductivity quenching shows that the desensitizing process happens in a temperature range between 50 and 150K. This kind of behavior is often to be found in II-VI compounds such as CdS, ZnS, CdSe, , [24-271. The model proposed by Rose[28] and Bube[29] and developed since by a number of authors [30-331is made up of two types of recombination centers (called center I and center II by Rose). This is the only scheme which can explain such a large fall in the photocurrent when temperature increases. Center I (slow recombination center) has a much smaller capture cross section for electrons than for holes; center II (fast recombination center) has a much bigger capture cross section for free electrons than the slow recombination one. It is the position of the demarcation line of the holes (corresponding to the slow center) in relation to these two centers which explains the desensitizing process of the semiconductor (the demarcation line of the holes is defined in the following way: when a hole is located at this level, it has an equal probability of recombining with a free electron and of being thermally ejected into the valence band). At low temperature (or at high excitation) this demarcation level is located between the center I and the valence band. The lifetime of the free carriers in the conduction band is
569
Photoconduction of natural cinnabar (cr-HgS)
great. When the temperature increases (or when the excitation decreases), the demarcation line of the holes crosses the slow recombination center. The trapped holes are released into the valence band and captured by the fast recombination centers. There is a transfer of the electron recombination traffic from the slow towards the fast centers. The lifetime of the carriers in the conduction band decreases, which explains the sharp decay of the photocurrent. The detailed balance equations system, which governs the rates of variation of the different densities of carriers in the transport bands (n and p) as well as on the three levels introduced (n, and nz: density of electrons on the recombination centers I and II respectively; n3: density of electrons on the trap level), has been resolved by Bube [29]. In particular, when the demarcation line of the holes related to the center I is situated on this center, we may write the relation:
Figure 3 shows EFn = f( T), EFn being calculated at the breakpoint (which corresponds to the beginning of the quenching of photocurrent on Fig. 2 for the different variations fluxes) from the value of n at that point. From the slope and the ordinate at the origin we extract:
by taking N, and N, calculated from the effective mass[5,6] (m$ = 0.17m0 and rnt = 0.32mo, m. being the mass of the free electron). Figure 4 shows the Lux-Ampere Characteristic (L.A.C.), i.e. the variation of the photocurrent-excitation curve slope (in logarithmic coordinates) according to l/T. This shows that at very low temperatures the slope is around 0.5. When we reach the photocurrent quenching zone, the curve goes through a maximum close to 1. We
(1)
s”,u,,n(NI-nl)=(N,-N,)P*
(N,: density of states in level I; snI: capture cross section of the same center for an electron; Pr: probability per unit time for thermal ejection of a hole on level I’mto the valence band; uth: thermal velocity of the electrons in the conduction band) which can be written in the form:
(2) (No: effective density of states in the valence band; s,,: capture cross section of the center I for holes; El: depth of the center I from the valance band; k: Boltzmann constant). Using the equation defining the quasi-Fermi level of the electrons (EFn = kT ln(NJn) where N, is the effective density of states in the conduction band), we obtain: E
(3)
F”
I
I
60
55
,\ 65
T(K)
Fig. 3. Temperature dependence of the quasi-Fermi level of electrons (A, = 577.0nm).
BlDqI,h
A ‘ogI,,,
i
I
I
1
I
5
10
15
20
103!(K,
Fig. 4. Lux-Ampere Characteristic (L.A.C.): variation of the photocurrent I, vs the excitation I.., curve slope (m logarithmic coordinates) according to l/T (A,, = 577.0nm).
570
J. P.
LEYRIS et al.
are unable, in any temperature or excitation flux range, to reveal a supralinear region. However, Bube[34] points out that, when the trap level is located near the conduction band and remains in thermal contact with the latter, supralinearity does not occur. We go then from a zone with slope 0.5 to a one with slope 1 for the L.A.C. It is probable that the shallow trap (& = 60-70 meV from the conduction band revealed by T. S. C. between liquid helium and liquid nitrogen temperatures [16, I71 explains why we observe no supralinearity. This trap indeed predominates on our curves. It is in thermal equilibrium with the conduction band from very low temperatures and its influence is found through out all our measurements. We plotted (Fig. 5) In (co/a) = f(ln t) between liquid helium and 120K (G-, is the maximum conductivity at time origin and u the conductivity at time t during decay). We see that the photocurrent decay comes under a law in the form[35]:
bh=(I + &?)”
(4)
where R is the recombination rate of electrons in the center and no and lo are the number of electrons and the current at t = 0. This expression shows that the photocurrent variation does not follow a monomolecular process (for which we would have an exponential law) and (Y# 2 signifies that the process is not purely bimolecular because of the influence of the trapping. In Table 1 we give the parameters a and (noR)-’ according to T. we note that, when temperature increases, (n&-r (which has the dimensions of a time) decreases. In order to confirm this hypothesis, we varied the excitation density at T = 1lOK. We note that the time constant increases when the excitation density decreases; indeed the latter is linked to the lifetime T,, of the free carrier, which, in the case of a bimolecular process, depends on the excitation density. This lifetime is dependent upon the number of free carriers and at the
4
/
5
1+ i
L
I
2
3
4
5
6
‘l”(I)
Fig. 5. In (Q/U) = f(ln I) curves between 9 and 120K (0s: maximum conductivity at time origin; u: conductivity during decay at time t) (A,,, = 577.0nm).
same time upon the number of holes on the recombination center. On the contrary, in the case of a linear recombination (monomolecular process), the lifetime r, is constant. The Table 1. Evolution of (I and (n$)-’ according to temperature between liquid helium and 12OK
T, K a
(naR))‘, set
9
30
40
go
1.55 1.7 1.8 2 3.63 3.2 0.7 0.4
90
120
2 0.35
2 0.26
Fig. 6. Photoconductivity decay curves at different excitation densities (T = 185K; A,,, = 577.0nm).
Photoconduction of nat!ural cinnabar (a-HgS)
571
time constant of the sample should not therefore be dependent upon the excitation density. At 185K the decay curves (Fig. 6) show a fast decay zone and a slow one. The electronics of our detection system does not allow us to observe the first of these, i.e. the one which corresponds to the recombination on the fast centers. For long times, characteristic of de-trapping, the photocurrent follows a law in the form [35]:
whose capture cross sections for electrons are very different, is often found in II-VI compounds (Cd& ZnS, CdSe , . . . ,). However, chemical impurities or lattice defects introduce electron trap levels which upset any comparisons we might make with these compounds (lengthening of time constants of the sample, broadening of trap levels,. . .).
Zph= lo exp (- do).
1. Doni E., Resca L., Rodriguez S. and Becker W. M., Phys. Reo. b20(4), 1663(1979). 2. Verolini C. and Diamond H., L Apppl.Phys. 36, 1971(1965). 3. Butti C., Raymond A. and Bombre F., Phys. Sfatus Solidi
REFERENCES
(5)
The measurements in terms of excitation (Fig. 6) show that the time constant T is constant. This behavior (T= constant and exponential decay of the current) is characteristic of a monomolecular process of recombination of relaxed carriers. We find a value for 7 of around 1000sec. 4.CONCLUSION
Study of the photoconducitivity curves of cinnabar shows that the recombination process of free carriers is dependent upon temperature. Between 8 and 50K, it occurs on a slow recombination center; the lifetime of the electrons is long: the sample is sensitized. The L.A.C. in this range is slightly below 0.5. Exploitation of T.S.C.[16,17] shows for these temperatures the existence of a trap level in thermal contact with the conduction band, which plays a leading part in recombination processes (radiative as well as non-radiative). It explains in particular why we never observe a supralinear region in the L.A.C. Between 50 and 150K, we are in the photocurrent decay zone. The holes located on the slow recombination centers are freed into the valence band and captured by one or several faster non-radiative centers. By studying the evolution of the breakpoint corresponding to the beginning of decay in terms of temperature and excitation density, we determine the depth of the slow recombination center (170 meV from the valence band) and the ratio of capture cross sections for holes and electrons (s,/s. = I@). In this temperature range, called densensitizing zone of the sample, the L.A.C. goes through a maximum close to 1. As the carrier recombination traffic is carried out through fast recombination centers, lifetime decreases. The time constant of the sample in terms of temperature and excitation density shows that at these temperatures recombination is not monomolecular. The T.S.C. peak which appears at 104K[16,17] and which we attributed to a level with a depth of 120meV cannot therefore follow a simple monomolecular process. Beyond 15OK the slow recombination center is completely ionised. The lifetime of carriers in the conduction band is short. The time constant no longer varies, for long times, according to excitation density, The level revealed by T.S.C. at 165K[16,17] is therefore of monomolecular type. The behavior of the photoconductivity of cinnabar, which involves two types of recombination centers
(a)36,133 (1976). 4. Tabak M. D. and Roberts G. G., 1 Apppl Phys. 39, 4873 (1%8). 5. Langlois H., These de Troisieme Cycle. Paris (1973). 6. Lecoca-Maver M. C.. These de Troisieme Cvcle. Paris (1975)’ I 7. Noblanc J. P., Loudette J. and Duraffourg G., So/id Stute Commun. 5,803 (1%7). 8. Butti C. and BombrC F., C. R. Hebd. Sian. Acad. Sci B279, 623 (1974). 9. Debiais G., Barcelo J., Aicardi J. P., Masse G. and Bombre F., Thin Solid Films 7, 11 (1971).
10. Masse G., Aicardi J. P., Barcelo J., BombrC F. and Debiais G., Thin Solid Films 8. 397 (1971). 11. Barcelo J., Galtier M. ‘and Montaner A., C. R. Hebd. Sian. Acad. Sci. B274, 1410(1972). 12. Aicardi J. P.. These d’Etat. Pernienan (1977). 13. Masse G., These d’Etat. Perpighai (1977). 14. Poure A., These de Docteur-Ingenieur. Toulouse (1980). 15. Aguero-Soler G., These de Docteur-Ingenieur. Perpignan (1980). 16. Leyris J. P., Carlos H. and Aicardi J. P., /. Phys. 41, 305 (1980). 17. Carlos H., These de Troisieme Cycle. Perpignan (1980). 18. Roberts G. G. and Zallen R., .r. Phys. C. 4, 1890 (1971). 19. Roberts G. G., Lind E. L. and Davis E. A., .r. Phys. Chem.
Solids 30,833 (1%9). 20. Zallen R., Proc. of the II-VI Semicond., ht. Conf. New York (1967). 21. De Vore H. B., Phys. Rev. 102(l), 86 (1956). 22. El-Gabaly M., Wakim F. G. and Sawan Y., J. App/. Phys. 50(2), 933 (1979). 23. Aicardi J. P., Masse G. and EgCe M., Phys. Stutus Solidi (a)32,701 (1975). 24. Shionoya S., Era K. and Katayama H., J. Phys. Chem. So/ids 26,697 (1%5). 25. Maeda K., J. Phys. Chem. Solids 26, 1419(1965). 26. Blazhko N. A., Khostov V. A. and Salkov E. A., Phys. Status So/idi (a124 K63 (1974). 27. Bobyl A. V., Pekar G. S.‘and Sheinkman M. K., Phys. Status SoLdi (a)48,249 (1978). 28. Rose A., Concepts in Photoconductivity and Allied Prob/ems. Wiley, New York (1963). 29. Bube R. H., Photoconductivity in Solids. Wiley, New York
(l%O). 30. Sheinkman M. K. and Lyubchenko A. V., Sou. Phys. Lbkiudy M(4), 317 (l%6). 31. Ermolovich I. B., Luk’yanchikova N. V. and Sheinkman M. K., Sou. Phys. So/id State 9(10), 2280 (1%8). 32. Abdullaev G. B., Agaev V. G., Antonov V. B., Nani R. Kh. and Salaev E. Yu., Sou. Phys. Semicond. 6(9), 1492 (1973). 33. Kydd P. F. and Bryant F. J., Phys. Status Sosolidi(a)U, K49 (1974). 34. Bube R. H., J. Phys. Chem. Solids 1, 234 (1957). 35. Ryvkin S. hf., Photoelectric Efects in Semiconductors.
sultants Bureau Enterprises, New York (1%4).
Con-
0022%3697/81/070567-05$02.00/0 Pergamon Press Ltd.
PHOTOCONDUCTION OF NATURAL CINNABAR(a-HgS) J. P. LEYRIS,H. CARLostand J. P. AICARDI Laboratoirede Physiquedu Solide, Universitt! de Perpignan, avenue de Villeneuve, 66025 Perpignan Cedex, France (Received 15 July 1980; accep.ted in revised form 5 November
1980)
Abstract-The photoconductivity measurements presented in this paper permit us to reveal a sensitizing process in mercury sulakipe (a-HgS) which is common to a number of II-VI compounds. The excitation spectra of the photocurrent as well as the results obtained in terms of excitation density and temperature allow us to locate the slow recombination center at I65 meV from the valence band. The ratio of capture cross sections for holes and electronsfor this center is around l@. Experiments on photoresponse to a cut off of the excitation show that, in the temperature range corresponding to the quenching of the photocurrent, the recombination process of free carriers is close to the bimolecular. However, the influence on our results of an electron trap located at 50meV from the conduction band is pointed out.
The electric contacts are carried out by an eutectic indium-gallium alloy (15.7”C) with 24.5% of indium in weight[ll]. The polarisation was fixed at 20V d.c. (injection measurements showed us that, at this voltage, the behavior of the specimen followed ad ohmic law). The crystal is placed on a slab of beryllium oxide (which makes it possible to isolate the sample electrically and at the same time to ensure a good thermal contact), stuck onto the copper tail of a cryostat for sensitive heat recovery, linked to a temperature regulator. The latter is measured by a cryogenic linear temperature sensor. The optical excitation is provided either by means of a grating monochromator (1200 lines/mm; resolution: 1 nm; focal length: 50cm; blaze: $0.0 nm) associated with a xenon light source, or by a hydrogen lamp and interference filters. The currents are detected either by a logarithmic picoammeter (10-4-10~‘2A) or by a linear one (lo-‘lo-l5 A). Figure 1 shows the excitation spectrum of the photoconductivity for temperatures ranging from liquid helium to liquid nitrogen. We observe three peaks. (1) The high energy one is located at 2.287 eV (at liquid helium temperature). It corresponds to the gap value found by different optical methods[6,20]. It disappears very quickly when temperature increases (Fig. 1). For this wavelength, corresponding to a strong absorption coefficient, the photocurrent is generated only near the surface. As the recombination speeds due to surface states become great when temperature increases, the recombination probability of photoexcited carriers becomes important. This explains the disappearance of 2. EXPERIMENTAL RESULTS this peak[21,22] at temperatures above SOK. We took our measurements on several natural crystals, (2) The second one is located at 2.222 eV, i.e. a with no notable difference in the results. We shall give here difference of 65 meV from the gap value. It corresponds the ones obtained with the sample previously used in our to the photoionisation of a localized center, whose exisT.S.C. experiments [16,17] (natural from Almadentence has been revealed by cathodoluminescence and Spain; dimension 3 x 3 x 0.7 mm’). photoluminescence experiments[lS, 231. This center’s emission is of the vibronic type. The photoluminescence thermal quenching measurements and the lifetime variatPresent address: Laboratoire de Physique de la Make CondensCe, Ecole Polytechnique, Route de Saclay, 91128 tions according to temperature allowed to situate the Palaiseau Cedex, France. ground state at 65 meV from the valence band[15]. 1. INTRODUCTlON
Cinnabar (cu-HgS) is a II-VI semiconductor compound with wide bandgap (2.1 eV at room temperature) wluch crystallises in the trigonal system. This substance has been very little studied owing to the difficulties of its crystallogenesis. Recently Doni et a/.[11 carried out the first theoretical work on its band structure. Studies have shown that both natural and synthetic crystals of cinnabar were highly resistant (p > 10” 0 x cm). Its conductivity has been determin as being of n-type by measurements of Hall-effect [2], photo-Hall effect[3] and drift mobility[4]. Moreover, the strong anisotropy revealed by optical experiments of absorption[S, 61 and luminescence[7], was found again by electric ones. The photo-Hall effect measurements showed that the mobility varies by a factor of 3 according to the polarisation (~II~= 30 cm* x V-’ x s-l; PlC = 10 cm* X V-’ X s-’ at room temperature). Our Laboratory has for some years now taken a keen interest in the study of cinnabar: crystallogenesis[8], obtaining of thin solid films by transport in a vapour zone and evaporation in a vacuum[9, lo], IR[ll], Halleffect [3], luminescence [ 12-151, thermally stimulated conductivity (T.S.C.)[16,17], space charges limited conductivity (S.C.L.C.)[17]. The photoconductivity of a-HgS has been studied by Roberts and Zallen[ 181and Roberts et al. [19] between 77 and 180K. We complete their measurements by various techniques, which enables us to improve their results and to explain more fully the photoconductivity mechanism of cinnabar, particularly by comparison with our T.S.C. experiments [ 16,171.
567
J. P.
I 1
LEYRIS et 01
I-
I+,(A)
o((Cm-1) 1o-4
I 4500
-400
ho0 I -1200
10-6
1o-9 t
; 100
~ 1
Fig. 1. Photoconductivity of cinnabar as a function of wavelength for different temoeratures. ---: absorution curve at liquid.helium[5]. 1
(3) The last peak appearing on the excitation spectrum of the photoconductivity is located at 2.122 eV, in other words a difference of 165meV from the gap width. The gap, determined by optical measurements[Q and the peak located at 2.222eV come under the same law for temperatures above 120K; the energy difference between the two curves is constant and equal to 80 meV. The value of the temperature coefficient obtained is of similar size to those provided by literature [5,19]: 6.65 X IO-“ eV X K-‘. In view of these first results, it would seem that, above 120K the excitation of the localized center is responsible for the photoconductivity observed. At these temperatures the ground state is ionised and radiative recombination no longer takes place. We then set the excitation wavelength at 577.0nm (yellow line of the hydrogen light source spectrum). This energy lower than the gap allows us to have an excitation of the sample homogeneous in volume and corresponds to the maximum photocurrent gain. Figure 2 shows the curves according to temperature for different excitation fluxes between 8 and 200K. We observe, for the maximum excitation density (d = (log Z,/Z]= 0, where I0 is the incident light intensity and I the same quantity measured after the neutral density filter), a photocurrent quenching region stretching from approx. 50 to 15OK. For the weakest excitations (d = 3 and d = 4) we discern shoulders for temperatures corresponding to those for the emptying of the traps revealed bythermally stimulated conductivity[lh, 171. The last experiments we made dealt with the response of the sample to a luminous pulse. Given the high values of the time constants, we used a simple mechanical
‘I
lo-‘(
I:
10-l’
50
100
150
200
250
T(K)
Fig. 2. Photocurrent in terms of temperature for different excitation densities (A,, = 577.0nm).
device (shutter) to cut off the light flow. The measurements were taken between liquid helium temperature and 120K at several excitation fluxes. We also recorded the photoresponse to some excitation densities for a temperature of 185K, which corresponds to the emptying zone of the trap at depth 300 meV revealed by our S.C.L.C.[17] and T.S.C.[16,17] measurements. 3. INTERPRETATION OF OUR RESULTS
Study of the photoconductivity quenching shows that the desensitizing process happens in a temperature range between 50 and 150K. This kind of behavior is often to be found in II-VI compounds such as CdS, ZnS, CdSe, , [24-271. The model proposed by Rose[28] and Bube[29] and developed since by a number of authors [30-331is made up of two types of recombination centers (called center I and center II by Rose). This is the only scheme which can explain such a large fall in the photocurrent when temperature increases. Center I (slow recombination center) has a much smaller capture cross section for electrons than for holes; center II (fast recombination center) has a much bigger capture cross section for free electrons than the slow recombination one. It is the position of the demarcation line of the holes (corresponding to the slow center) in relation to these two centers which explains the desensitizing process of the semiconductor (the demarcation line of the holes is defined in the following way: when a hole is located at this level, it has an equal probability of recombining with a free electron and of being thermally ejected into the valence band). At low temperature (or at high excitation) this demarcation level is located between the center I and the valence band. The lifetime of the free carriers in the conduction band is
569
Photoconduction of natural cinnabar (cr-HgS)
great. When the temperature increases (or when the excitation decreases), the demarcation line of the holes crosses the slow recombination center. The trapped holes are released into the valence band and captured by the fast recombination centers. There is a transfer of the electron recombination traffic from the slow towards the fast centers. The lifetime of the carriers in the conduction band decreases, which explains the sharp decay of the photocurrent. The detailed balance equations system, which governs the rates of variation of the different densities of carriers in the transport bands (n and p) as well as on the three levels introduced (n, and nz: density of electrons on the recombination centers I and II respectively; n3: density of electrons on the trap level), has been resolved by Bube [29]. In particular, when the demarcation line of the holes related to the center I is situated on this center, we may write the relation:
Figure 3 shows EFn = f( T), EFn being calculated at the breakpoint (which corresponds to the beginning of the quenching of photocurrent on Fig. 2 for the different variations fluxes) from the value of n at that point. From the slope and the ordinate at the origin we extract:
by taking N, and N, calculated from the effective mass[5,6] (m$ = 0.17m0 and rnt = 0.32mo, m. being the mass of the free electron). Figure 4 shows the Lux-Ampere Characteristic (L.A.C.), i.e. the variation of the photocurrent-excitation curve slope (in logarithmic coordinates) according to l/T. This shows that at very low temperatures the slope is around 0.5. When we reach the photocurrent quenching zone, the curve goes through a maximum close to 1. We
(1)
s”,u,,n(NI-nl)=(N,-N,)P*
(N,: density of states in level I; snI: capture cross section of the same center for an electron; Pr: probability per unit time for thermal ejection of a hole on level I’mto the valence band; uth: thermal velocity of the electrons in the conduction band) which can be written in the form:
(2) (No: effective density of states in the valence band; s,,: capture cross section of the center I for holes; El: depth of the center I from the valance band; k: Boltzmann constant). Using the equation defining the quasi-Fermi level of the electrons (EFn = kT ln(NJn) where N, is the effective density of states in the conduction band), we obtain: E
(3)
F”
I
I
60
55
,\ 65
T(K)
Fig. 3. Temperature dependence of the quasi-Fermi level of electrons (A, = 577.0nm).
BlDqI,h
A ‘ogI,,,
i
I
I
1
I
5
10
15
20
103!(K,
Fig. 4. Lux-Ampere Characteristic (L.A.C.): variation of the photocurrent I, vs the excitation I.., curve slope (m logarithmic coordinates) according to l/T (A,, = 577.0nm).
570
J. P.
LEYRIS et al.
are unable, in any temperature or excitation flux range, to reveal a supralinear region. However, Bube[34] points out that, when the trap level is located near the conduction band and remains in thermal contact with the latter, supralinearity does not occur. We go then from a zone with slope 0.5 to a one with slope 1 for the L.A.C. It is probable that the shallow trap (& = 60-70 meV from the conduction band revealed by T. S. C. between liquid helium and liquid nitrogen temperatures [16, I71 explains why we observe no supralinearity. This trap indeed predominates on our curves. It is in thermal equilibrium with the conduction band from very low temperatures and its influence is found through out all our measurements. We plotted (Fig. 5) In (co/a) = f(ln t) between liquid helium and 120K (G-, is the maximum conductivity at time origin and u the conductivity at time t during decay). We see that the photocurrent decay comes under a law in the form[35]:
bh=(I + &?)”
(4)
where R is the recombination rate of electrons in the center and no and lo are the number of electrons and the current at t = 0. This expression shows that the photocurrent variation does not follow a monomolecular process (for which we would have an exponential law) and (Y# 2 signifies that the process is not purely bimolecular because of the influence of the trapping. In Table 1 we give the parameters a and (noR)-’ according to T. we note that, when temperature increases, (n&-r (which has the dimensions of a time) decreases. In order to confirm this hypothesis, we varied the excitation density at T = 1lOK. We note that the time constant increases when the excitation density decreases; indeed the latter is linked to the lifetime T,, of the free carrier, which, in the case of a bimolecular process, depends on the excitation density. This lifetime is dependent upon the number of free carriers and at the
4
/
5
1+ i
L
I
2
3
4
5
6
‘l”(I)
Fig. 5. In (Q/U) = f(ln I) curves between 9 and 120K (0s: maximum conductivity at time origin; u: conductivity during decay at time t) (A,,, = 577.0nm).
same time upon the number of holes on the recombination center. On the contrary, in the case of a linear recombination (monomolecular process), the lifetime r, is constant. The Table 1. Evolution of (I and (n$)-’ according to temperature between liquid helium and 12OK
T, K a
(naR))‘, set
9
30
40
go
1.55 1.7 1.8 2 3.63 3.2 0.7 0.4
90
120
2 0.35
2 0.26
Fig. 6. Photoconductivity decay curves at different excitation densities (T = 185K; A,,, = 577.0nm).
Photoconduction of nat!ural cinnabar (a-HgS)
571
time constant of the sample should not therefore be dependent upon the excitation density. At 185K the decay curves (Fig. 6) show a fast decay zone and a slow one. The electronics of our detection system does not allow us to observe the first of these, i.e. the one which corresponds to the recombination on the fast centers. For long times, characteristic of de-trapping, the photocurrent follows a law in the form [35]:
whose capture cross sections for electrons are very different, is often found in II-VI compounds (Cd& ZnS, CdSe , . . . ,). However, chemical impurities or lattice defects introduce electron trap levels which upset any comparisons we might make with these compounds (lengthening of time constants of the sample, broadening of trap levels,. . .).
Zph= lo exp (- do).
1. Doni E., Resca L., Rodriguez S. and Becker W. M., Phys. Reo. b20(4), 1663(1979). 2. Verolini C. and Diamond H., L Apppl.Phys. 36, 1971(1965). 3. Butti C., Raymond A. and Bombre F., Phys. Sfatus Solidi
REFERENCES
(5)
The measurements in terms of excitation (Fig. 6) show that the time constant T is constant. This behavior (T= constant and exponential decay of the current) is characteristic of a monomolecular process of recombination of relaxed carriers. We find a value for 7 of around 1000sec. 4.CONCLUSION
Study of the photoconducitivity curves of cinnabar shows that the recombination process of free carriers is dependent upon temperature. Between 8 and 50K, it occurs on a slow recombination center; the lifetime of the electrons is long: the sample is sensitized. The L.A.C. in this range is slightly below 0.5. Exploitation of T.S.C.[16,17] shows for these temperatures the existence of a trap level in thermal contact with the conduction band, which plays a leading part in recombination processes (radiative as well as non-radiative). It explains in particular why we never observe a supralinear region in the L.A.C. Between 50 and 150K, we are in the photocurrent decay zone. The holes located on the slow recombination centers are freed into the valence band and captured by one or several faster non-radiative centers. By studying the evolution of the breakpoint corresponding to the beginning of decay in terms of temperature and excitation density, we determine the depth of the slow recombination center (170 meV from the valence band) and the ratio of capture cross sections for holes and electrons (s,/s. = I@). In this temperature range, called densensitizing zone of the sample, the L.A.C. goes through a maximum close to 1. As the carrier recombination traffic is carried out through fast recombination centers, lifetime decreases. The time constant of the sample in terms of temperature and excitation density shows that at these temperatures recombination is not monomolecular. The T.S.C. peak which appears at 104K[16,17] and which we attributed to a level with a depth of 120meV cannot therefore follow a simple monomolecular process. Beyond 15OK the slow recombination center is completely ionised. The lifetime of carriers in the conduction band is short. The time constant no longer varies, for long times, according to excitation density, The level revealed by T.S.C. at 165K[16,17] is therefore of monomolecular type. The behavior of the photoconductivity of cinnabar, which involves two types of recombination centers
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sultants Bureau Enterprises, New York (1%4).
Con-