J . Phys. Chem. 1989, 93, 5895-5899
5895
Electronic Processes in Semiconductor Materials Studied by Nanosecond lime-Resolved Microwave Conductivity. 1. Cadmium Sulfide Macroscopic Crystal John M. Warman,* Matthijs P. de Haas, Stephan W. F. M. van Hovel1 tot Westerflier, Johannes J. M. Binsma, and Zvonimir I. Kolar Interfaculty Reactor Institute, Delft University of Technology, Mekelweg 15, 2600 G A Delft, The Netherlands (Received: November 9, 1988; In Final Form: February 1 , 1989)
The transient conductivity resulting from pulsed irradiation (with 3-MeV electrons) of a single, high-resistivity (4 X lo7 Q m) crystal of CdS has been studied by nanosecond time-resolved microwave conductivity. The ratio of the electron-hole pair mobility to the pair formation energy is determined to be 42 f 6 X lo4 m2 V-I s-’/eV. For end-of-pulse pair concentrations less than ca. I O l 9 m-3, the half-life of electrons toward localization was 25 ns. With increasing pair concentration above this value, the lifetime was found to become longer. This effect is attributed to trap saturation with the trap concentration m3 s-] (6.6 X lOI4 M-I s-l). estimated to be 3 X 10” m-3 ( 5 X lo-* M) with a rate constant toward trapping of 1.1 X The main trapping site is thought to be the singly ionized sulfur vacancy. No evidence was found for the Occurrence of direct electron-hole recombination, and an upper limit of 3 X m3 s-I (ca. 2 X 10’) M-I S-I) could be placed on the second-order rate constant for this process.
Introduction In recent years, the electronic properties of cadmium sulfide have become of considerable interest within chemistry because of the potential use of this semiconductor material in the photoelectrolytic and photocatalytic storage of solar energy.] While most attention in this context has been paid to processes occurring at the surface of the material, it is generally accepted that bulk properties, such as the diffusion coefficients of electrons and holes and their localization and recombination dynamics, may play a decisive role in determining the overall efficiency of solar energy conversion. In the present paper, we have applied the technique of pulse radiolysis with nanosecond time-resolved microwave conductivity (TRMC) to a study of the electronic properties of a high-resistivity single crystal of CdS. This work was carried out in order to provide a basis of comparison for concurrent studies of CdS in particle form, either as powder or in suspension, which will be the subject of subsequent publications. Experimental Section The CdS crystal used in the present work was grown by sublimation, according to the Piper-Polich method.610 The starting material was CdS powder from Aldrich Chemical Co. (Gold Label: 99.999%), which according to the manufacturer contained a 2.93% stoichiometric excess of cadmium. Since during crystal growth it is important to maintain a stoichiometric balance in the vapor phase,” the powder was pretreated to remove excess cadmium by heating at 900 OC for 4 h in a stream of hydrogen sulfide vapor. (1 ) Energy Resources Through Photochemistry and Catalysis; Gratzel, M., Ed.; Academic: New York, 1983. (2) Warman, J. M. In The Study of Fast Processes and Transient Species by Electron Pulse Radiolysis; Baxendale, J. H., Busi, F., Eds.; Reidel: Dordrecht, The Netherlands, 1982; p 129. (3) Infelta, P. P.; de Haas, M. P.; Warman, J. M. Radiat. Phys. Chem. 1977, 10, 353. (4) Warman, J. M.; de Haas, M. P. In Pulse Radiolysis of Irradiated Systems; Tabata, Y . , Ed.; CRC Press; in press. ( 5 ) de Haas, M. P. Ph.D. Thesis, University of Leiden, Delft University Press, 1977. (6) Piper, W. W.; Polich, S. J. J . Appl. Phys. 1961, 32, 1278. (7) Kaldis, E. J. Cryst. Growrh, 1968, 5, 376. (8) Ballentyne, D. W. B.; Wetwetana, S.; White, E. A. P. J. Cryst. Growth 1970, 7, 79. (9) Ballentyne, D. W. G . Prog. Cryst. Growth Characr. 1983, 6, 163. (IO) Kuwamoto, H.; Gunning, W. J. J . Appl. Phys. 1985, 57, 5542. ( I 1) Kumar, V.; Kroger, F. A. J . Solid State Chem. 1971, 3, 387.
0022-3654/89/2093-5895$01 .50/0
Approximately 5 g of treated powder was placed in an ampule that consisted of a 2-cm-diameter, 15-cm-length, quartz cylinder with one end drawn out to a cone. The ampule was cleaned prior to use, following the treatment described by Kaldis.’ It was then attached to a vacuum line and baked at 350 “ C until a pressure of 10” Torr was registered on a vacuum gauge close to the sample. At that point, the ampule was sealed. The ampule was then placed in a horizontal, cylindrical furnace in which the temperature in the center was held at 1100 “C. Prior to crystal growth, the tip of the cone was held at a temperature 100 OC higher than the section containing the powder for 4 h in order to clean the former. The ampule was then situated in the furnace such that the powder was at a temperature of 1100 “ C and the conical tip at a temperature 15-17 OC lower. An undercooling of approximately 15 OC has been found to be critical for uniform crystal g r o ~ t h . ~After - ~ 4 days, the temperature of the furnace was gradually lowered to room temperature over a period of 12 h and the ampule was removed. All of the starting material was found to have sublimed to the tip of the ampule to form a highly transparent, yellow-orange, conically shaped crystal with a cone axis of 7 mm and a diameter of 14 mm. The growing surface was smooth and slightly convex. X-ray diffraction measurements taken on different regions of the sample showed it to be a single crystal of hexagonal CdS. From linear current-voltage plots made on a thin slice of the crystal fitted with ohmic, indium contacts, the resistivity in the dark was determined to be 4 X lo7 !J m. Resistivities in excess of lo8 !J m have been reportedlo for CdS grown in this way. Since conduction-band electrons in CdS have a mobility of 300 X lo4 m2/V.s,12-15the background resistivity of the present sample corresponds to an equilibrium electron concentration of approximately 5 X loi2electrons/m3 (ca. M). For the microwave experiments, a rectangular block, of dimensions 3.4 X 3.4 X 7.0 mm, was cut from the crystal, with a diamond saw such that the c-axis of the crystal was perpendicular to the long axis and to one set of 3.4 X 7.0 mm faces. The inner dimensions of the wave guide used were 3.56 X 7.1 1 mm. The crystal was placed against a metal short-circuiting plate at the end of the wave guide, resulting in a sample length in the direction of microwave propagation of 3.4 mm. The crystal could be turned through 90” to investigate possible anisotropy in the radiationinduced conductivity, depending on whether the c-axis was parallel (12) Landolt BBrnstein, 111; Springer-Verlag: Berlin; 17b, p 189. (13) Spear, W. E.; Mort, J. Proc. Phys. SOC.,London 1963, 81, 130. (14) Woodbury, H. H. Phys. Rev. 1974, B9, 5188. (15) Boone, J. L.; Cantwell, G. J . Appl. Phys. 1985, 57, 1171.
0 1989 American Chemical Society
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The Journal of Physical Chemistry, Vol. 93, No. 15, 1989
or perpendicular to the electric field vector of the microwaves. The sample was irradiated with single pulses of 3-MeV electrons from a Van de Graaff accelerator with a pulse duration of 400 ps and a maximum beam current of 5 A. The upper wall of the wave guide was reduced to 0.4 mm to allow almost unattenuated transmission of the electron beam. The dose within the cell was monitored with gaseous CO, as a dosimeter.16 The dose per nanocoulomb beam charge was determined to be 1.15 Gy in the gas phase, which corresponds to an energy deposition of 4.38 X IO3 J/m3 per nC in the CdS sample (electron density 3.80 times that of water) a t the top of the cell. The penetration depth of 3-MeV electrons in bulk C d S in approximately 3 mm with approximately a cosine form of the dose-depth dependence. On correction for the attenuation of the beam in the sample, the average dose was determined to be 2.3 X lo3 J/m3 per nC. The beam charge was monitored throughout the measurements by a 5 0 4 coaxial collector and was varied between and 10-1nC for the electron radiolysis. The pulse-to-pulse reproducibility was within 2%. The Gaussian half-width of the beam was greater than 1 cm, thus entering close to uniform irradiation of the sample in the plane perpendicular to the beam. Experiments were also carried out with hard X-rays obtained by interposing a platinum target between the electron accelerator and the sample. The overall dose per beam charge was reduced in this way by a factor of approximately IO3. The depth distribution of dose in the sample under these irradiation conditions could be taken to be completely uniform. Even when X-rays are used, which have a much greater penetration depth than the initial 3-MeV electrons, energy deposition results mainly from the interaction between high-energy primary and secondary electrons with the bound electrons of the medium. Because of the low LET (linear energy transfer) of high-energy electrons (a few hundredths of an electronvolt per angstrom), kinetic complication due to dense tracks of ionization events will be negligible. This is particularly true for a medium such as CdS for which the electron-scattering length at close to thermal energies (ca. 100 A) is larger than the Onsager escape distance, r,, which for a dielectric constant of 9.5 is approximately 65 h;. The thermalization distance of electrons, involving many collisions, will therefore be considerably greater than r,, and even if recombination on close encounter was efficient, the majority of electron-hole pairs would escape each others' mutual Coulombic attraction and become homogeneously distributed within the bulk. The characteristic time scale on which the processes of geminate escape and recombination occur is given by TG = r:/D where D is the sum of the charge-carrier diffusion coefficients and is related to the mobility by D = p k s T / e . On substitution for rc and p = 300 X 10-4 m2/V.s, iGis found to be less than 1O-I3 S . This is much shorter than the time resolution of the present experiments. Kinetic complications due to this source could therefore not play a role on the nanosecond time scales applicable in the present work. If any rapid recombination were to occur and result in exciton formation, then this would not be observed by the present technique, which is only sensitive to the presence of mobile charged species. It is perhaps worth pointing out that such species would also not contribute in the determination of the average energy expended per electron-hole pair, E , (ev), used to derive the mobility from the present results since such species could not be dissociated by the relatively small electrical fields applied in those measurements. A question that frequently arises when solid-state systems are subjected to high-energy radiation is how much of the effects observed could possibly be attributed to the creation of lattice defects by the radiation itself. Because of the relatively much smaller mass of the electron compared with the atomic species forming, the lattice knock-on processes required for Frenkel defect formation are very inefficient for high-energy electrons and very large doses, usually on the order of many kilograys, are required to produce observable effects due to defect formation. In the present work, the dose used in the pulse in the initial experiments ( 1 6 ) Warman, J . M.; de Haas, M . P.Radiat. Phys. Chem. 1988, 32. 31,
Warman et al.
0
50
IO0
I50
Time ( n s )
Figure 1. Transient changes in microwave power on pulsed irradiation of the CdS crystal normalized to the dose in the pulse. A 400-ps pulse of 3-MeV electrons was used with doses of 0.0025 (0),0.0055 ( O ) ,0.012 (a), and 0.024 (B) Gy corresponding to end-of-pulse electron-hole pair concentrations of 5.4, 11.8, 25.7, and 51.5 X 10l8pairs/m3 respectively. It should be noted that the lifetime of the transient conductivity actually increases with increasing dose in the pulse, which is the opposite to expectations if electron-hole recombination were responsible for the decay.
was less than 30 mGy and only single pulses per trace were applied. Even in later work, when repetitive pulsing was used, the total accumulated dose rarely exceeded a few hundred rads. The only dose dependence found in the present experiments was in fact an increase in lifetime of electrons with increasing dose in the pulse, which is the opposite effect to that expected if additional trapping centers were being formed by the radiation. NO permanent changes in the decay kinetics could be found after the complete series of measurements reported. The transient change in microwave power reflected by the sample on pulsed irradiation was measured with microwave circuitry that has been described fully in previous article^.^-^ The time response of detection was approximately 1 ns. In the absence of irradiation, the sample was found to have no measurable microwave loss, in agreement with the insulating properties found in the dc measurements. The microwave power level incident on the sample was approximately 50 m W over the frequency band of 27-38 GHz used. The magnitude of the reduction in microwave power at the end of the pulse was measured over the full frequency band. The method of calculation required to determine the change in the conductivity of the sample from the observed change in reflected power has been described fully in separate publication^.^-^
Results and Discussion Pulsed irradiation of the CdS single crystal gave readily measurable changes in the microwave power reflected by the Cy, corresponding to a sample even for doses as low as concentration of electron-hole pairs formed in the pulse of only approximately 2 X IO1* m-3 (3 nM). The signal developed within the 1-11s rise time of the detection circuitry and resulted in an end-of-pulse level that was linearly dependent on t h e dose in the pulse. The resulting constancy of the dose-normalized end-of-pulse signal height is illustrated by the data shown in Figures 1 and 2. Subsequent decay of the signal took place on a time scale of tens to hundreds of nanoseconds and was markedly dependent on the dose conditions, as can be seen in Figures 1 and 2. It is convenient to divide the detailed presentation and discussion of the results into two parts: one dealing with the magnitude of the signal, which yields information on the yield and mobility of the carriers, and a second dealing with the decay kinetics, which is related to the presence of intrinsic and/or radiation-produced localization and recombination centers. Initial Conductivity. In Figure 3 is shown the variation of the end-of-pulse signal height with microwave frequency over the range available, from 27 to 38.0 GHz. In no case did the fractional
The Journal of Physical Chemistry, Vol. 93, No. 15, 1989 5897
Electronic Processes in Semiconductor Materials
was determined to be 42 f 6 X m2 !X1J-I. The rather large scatter in the individual points, which results in the estimated uncertainty of f15% in the final value of ( A u / D ) ~is, probably a result of the fact that the sample was not a perfect ”contact” fit to the wave guide. The data points shown in Figure 3 are for the c-axis of the crsytal parallel to the electric field vector of the microwaves. Within the uncertainty of the measurements, no change could be found in the conductivity when the c-axis was perpendicular rather than parallel to the electric field vector. The initial, Le., in the absence of charge-carrier decay, radiation-induced conductivity per unit dose. (Aa/D),, is directly related to the mobility of the charge carriers formed, p(-) and MU(+), and the average energy required to form one electron-hole pair, E , (ev), by
1.5 -
(Acr/D)o =
-
-
M-) + d + ) l / E p
(2)
For CdS, values of 6.317 and 7.2 eV18 have been determined for E, from high-energy radiation. Taking the average value of 6.7 and the measured value of (Au/D),, given above, we find for the m2 sum of the electron and hole mobilities a value of 280 X V-l SKI.This is within the range of values previously determined at room temperature by a variety of methods.I2-l5 The hole mobility has been found to have a value of approximately 15 X m2 V-l s-I,I3 indicating conduction-band electrons to be the major charge carriers in CdS. The agreement between the present microwave measurements of the charge-carrier mobilities and those determined by dc methods is to be expected, at room temperature at least, since the electron collision frequency in CdS is much larger than the radian microwave frequency used.4 From the value of E, and the absolute dosimetry, it is possible to calculate the initial concentration of pairs formed within a given pulse, Np(0),from the relationship
Np(0)= D/eE,
(3)
where e is the electronic charge (1.60 X C). The range of pair concentrations applicable to the data given in Figure 1 varies for example from approximately 5 X 10l8to 50 X 10I8m-3 (9-90 nM). Even the lowest of these concentrations is considerably larger than the equilibrium concentration of conduction-band electrons, of only 5 X 10l2 m-3, estimated to be intrinsically present on the basis of the background conductivity of the sample. The fact that substantially more excess electrons are produced by irradiation in the present experiments compared with the background level is important for further discussion of the kinetics and the mechanism of electron localization and recombination. This condition may also be responsible for the differences that we have found in the behavior of the present sample of CdS from those of commercial powders for which many orders of magnitude larger background conductivitiesare found, indicating the presence of a background electron concentration comparable to or even larger than that formed by the pulse. Clearly, such differences in the starting conditions should be taken into account when different materials are compared. Relaxation Kinetics. A particularly unexpected aspect of the present results was the finding that, for the lowest radiation doses (initial electron-hole pair concentrations), the first half-life of conduction band electrons was only approximately 20 ns and that it actually became longer when the dose was increased. This “inverse” effect of dose is illustrated by the data in Figure 1. The effect was observed whether the crystal was irradiated with 3-MeV electrons or X-rays, as shown by the first half-life data in Table I, and could therefore not be attributed to nonuniform irradiation of the sample or space charge effects due to stopping of the high-energy electrons within the crystal. In addition, it was found that when the sample was subjected to repetitive pulses at a rate of 50 Hz, the decay time was even longer, as is shown by the data in Figures 2 and 4 and in Table I. When conditions were returned to the single-pulse mode after repetitive pulsing, the lifetime (17) Eichinger, P.; Kallmann, H. Appl. Phys. Lett, 1974, 25, 676. (18) van Heerden, P. J.; Phys. Reu. 1957, 106, 468.
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The Journal of Physical Chemistry, Vol. 93, No. 15, 1989
Warman et al.
TABLE I: First Half-Lives, t l p of the Conductivity Transients in Single-Crystal CdS for Different Radiation Conditions and End-of-Pulse Electron-Hole Pair Concentrations, [e-h+] radiation 3-MeV electrons
pulse conditions 0.4 ns, single
[e-h*] X 5.4 12.0 26.0 51.0 89.0 120.0 120.0 4.3 20.0 100.0 100.0
0.4 ns, 50 Hz 2 ns, single
X-rays
I O ns, single 10 ns, 50 Hz
m-3
1.0
t , ns
21 24 35 70 102 145 1450 21 31 80 360
05 2-
t ?
10
05
0
0
50
I00
TIME
f
IO-^^
IU
I o-8
IO-^
lo-6
IO-^
Time ( 5 )
Figure 4. Log-log representation of the decay of the microwave conductivity following pulsed irradiation of the CdS crystal with X-rays with either with a single pulse ( 0 )or on repetitive pulsing at 50 Hz (O), the latter points taken for the 100th pulse in a pulse train.
returned to the original value found prior to repetitive pulsing. In other words, there was no substantial lasting effect of irradiation on the low-dose kinetics. If anything, one would normally expect the lifetime of charge carriers to decrease with increasing dose in the pulse because of the increased concentration of secondary products that can result in an increased rate of second-order back-reactions such as charge recombination. The inverse dose effect actually observed can be explained if the decay of the conduction band electrons is due to localization at intrinsic trapping sites in the matrix, which are present at a concentration of the same order of magnitude as the concentration of electron-hole pairs formed during the pulse. Thus, as the dose is increased, the electron concentration begins to exceed the trap concentration and the decay kinetics eventually become controlled by the rate at which the trapping centers are regenerated. The effect could, in other words, be due to "trap saturation". This effect can be represented in its simplest form by the following reaction scheme M
-
e-
+T
h+
+ T--
e-
+ h+
ks
kc
,150
.
0
(nr)
50
I00
I50
TIME (ns)
Figure 5. Dashed lines in A are taken from smooth lines drawn through the experimental data shown in Figure 1. The curves shown in B-D are calculated decay curves for conduction band electrons in a medium containing donor, D, and acceptor, A, point defects according to a reaction scheme given by reactions A and I-L in the text. The equilibrium, prepulse concentrations were taken to be given by [e-]
