Semiconductors, Vol. 34, No. 10, 2000, pp. 1157–1160. Translated from Fizika i Tekhnika Poluprovodnikov, Vol. 34, No. 10, 2000, pp. 1208–1211.Original Russian Text Copyright © 2000 by Belyaev, Rubets, Nuzhdin.

ELECTRONIC AND OPTICAL PROPERTIESOF SEMICONDUCTORS

Evolution of the Density of States during Phase Transitionsin Films of Cadmium Sulfotellurides Synthesized

under Profoundly Nonequilibrium ConditionsA. P. Belyaev, V. P. Rubets, and M. Yu. Nuzhdin

St. Petersburg Institute of Technology, Zagorodnyœ pr. 49, St. Petersburg, 198013 RussiaSubmitted April 11, 2000; accepted for publication April 19, 2000

Abstract—The results of structural, electrical, and photoelectric investigations of phase transitions in layers ofcadmium-sulfide and cadmium-telluride solid solutions synthesized under profoundly nonequilibrium condi-tions are reported. As a model process, the thermally activated decomposition of a CdSxTe1 – x single-phasesolution containing the α1 (x1 = 0.4–0.6) phase was chosen. Increasing the temperature was shown to result inthe formation a heterophase system with two phases α2 (x2 = 0.1–0.2) and α3 (x3 = 0.78–0.99). The electrondiffraction patterns, the photoelectric-current spectrum, and the temperature dependences of the dark electricalconductivity in the course of and after phase transitions are reported. The results of electrical and photoelectricinvestigations are compared with the results of structural investigations. Changes in the dark conductivity in thecourse of phase transitions are shown to simultaneously account for the evolution of the density of states nearthe Fermi level. © 2000 MAIK “Nauka/Interperiodica”.

1. INTRODUCTIONElectrical properties are known to be extremely sen-

sitive to changes in structure. Therefore, it seems prom-ising to use investigations of these properties to analyzephase-transition processes. Consequently, we reportbelow the results of investigations of the electrical andphotoelectric properties during the thermally activateddecomposition of films of a cadmium-sulfotelluridesolid solution and analyze the possibilities of usingthem in investigating phase-transition processes.

2. INVESTIGATED SAMPLESAND EXPERIMENTAL PROCEDURE

We investigated the layers of CdSxTe1–x (0.4 < x <0.6) solid solutions prepared by thermal evaporationand condensation under profoundly nonequilibriumconditions [1]. The choice of the method was dictatedby the purpose of the investigation that implies a modelobject prone to phase transitions. As substrates, weused the laminas of potash mica. The film thickness forall the investigated samples did not exceed a few tenthsof µm. The layers were of polycrystalline structure withcrystallites of cubic modification both before and afterthe thermal treatment.

Prior to the electrical measurements, the sampleswere cut into several parts, and silver contacts weredeposited on some of them. The ohmic behavior of thecontacts was checked against initial portions of the cur-rent–voltage characteristics.

Structural investigations were carried out using anÉMR-100 electron diffractometer and a PZM-100 elec-tron microscope. Electrical measurements were carried

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out under the current operating conditions in vacuum(a residual gas pressure of 10–3 Pa) using a B7-30 elec-trometer and a special heat controller making it possi-ble either to maintain a constant temperature (with anaccuracy of 0.1 K) or to vary it linearly. The rate ofheating and cooling was varied within 0.05–0.2 K/s.

The possibility of measuring the electric field influ-encing phase transitions was checked by comparing theproperties of the samples that experienced phase transi-tions under the effect of an electric field with propertiesof the samples subjected to these transitions without afield.

The influence of temperature on the properties ofthe contacts was tested by comparing electrical proper-ties of samples with the contacts deposited beforeannealing with the similar properties of samples whosecontacts were deposited following thermal treatment.

3. EXPERIMENTAL RESULTS

We investigated the influence of temperature on thestructure, the phase composition, and the electrical andphotoelectric properties of the solid-solution layers ofcadmium sulfotelluride in relation to the temperature-field characteristics.

The main results of the experiment are shown inFigs. 1 and 2.

In Fig. 1, we display the typical electron-diffractionpatterns from an as-prepared solid-solution film and athermally treated film. In Fig. 1, curve 1 is indicative ofthe presence of only the α1 phase corresponding to thecomposition of the solid-solution with x1 = 0.5 in the

000 MAIK “Nauka/Interperiodica”

1158

BELYAEV

et al

.

as-prepared film. Curve 2 obtained for an annealedsample implies the appearance of two phases α2 and α3

in the bulk: the CdSxTe1–x solid solutions with compo-sitions of x2 = 0.15 and x3 = 0.85, respectively.

111 200 220311

222111

111

200 220311

200 220 311222

222

15 20 25 30 35 40θ, min

CdS0.5Te0.5

CdS0.15Te0.85

CdS0.85Te0.15

1

2

J, arb. units

1

2

3

4

10–3

10–5

10–7

10–91.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4

100

10–1

10–2

10–3

1.0 1.5 2.0 2.5 3.0

"ω, eV

i p/i p

max

σ, Ω

–1 c

m–1

103/T, K–1

Fig. 1. Electron diffraction patterns of the films of aCdS−CdTe system: curve 1 was recorded before annealing,and curve 2, after annealing.

Fig. 2. Variations in the conductivity σ during the phasetransitions in the CdS0.5Te0.5 layer: curves 1 and 3 corre-spond to heating with a rate v, curves 2 and 4 show the tem-perature dependences of the conductivity of the layer afterthe phase transitions. Curves 1 and 2 correspond to v =0.05 K/s; curves 3 and 4 correspond to v = 0.2 K/s (the con-ductivity scale is on the left, and the temperature scale is atthe bottom); curve 5 is the typical photoelectric-currentspectrum for the CdS0.5Te0.5 layer (the current scale is onthe right, and the photon-energy scale is at the top).

5

The phase inhomogeneity in the samples afterannealing was also detected from the optical transmis-sion spectrum [2]. The character of the electron-diffrac-tion patterns was independent of the sample-annealingmethods used in this study.

In Fig. 2, we show the typical behavior of the elec-trical conductivity σ of the films in the course ofannealing in relation to the heating rate of the samples.Curve 1 shows the dark conductivity for an as-preparedsample heated with a rate of 0.05 K/s. A constant acti-vation energy of about 0.5 eV corresponds to its initialsection. At the temperature T ≈ 360 K, the conductivity-increase rate first grew somewhat with temperature andthen decreased rapidly. After that, the temperaturedependence of the conductivity was described by a sim-ple exponential curve with an activation energy of0.72 eV. The indicated exponential temperature depen-dence was retained further within the entire tempera-ture range under investigation under the subsequentheating and cooling (curve 2). A simple exponentialtemperature dependence with the same activationenergy for the given sample was also successfully repro-duced after subjecting the sample to atmospheric air.

Curves 3 and 4 in Fig. 2 represent the changes in theelectrical conductivity of another area of the sameCdSxTe1–x layer, but heated with a rate of 0.2 K/s.Exposing the samples to the highest temperature ofheating for several hours leaves their conductivityunchanged at this temperature.

A cumulative result of the thermal treatment was amultifold decrease in the conductivity of layers (for thesamples, the results of the investigation of which aredisplayed in Figs. 1 and 2, this decrease amounts tothree orders of magnitude). Samples with similar prop-erties could be produced from the as-prepared layers by“shock” heating using an electron beam.

The influence of the heating rate on the properties ofthe samples was determined by investigating the photo-conductivity. The lower the heating rate, the larger thephotoconductivity increase which could be obtained fora sample. For example, part of the sample annealed at aheating rate of 0.5 K/s (Fig. 2, curves 1, 2) showed aphotoconductivity increase by three orders of magni-tude after annealing at room temperature, while a“shock”-heated part was virtually photoinsensitive(undergoing irradiation with a 90-W incandescentlamp). In the as-prepared samples, the increase in pho-toconductivity is only severalfold.

A typical photoconductivity spectrum of the sam-ples is shown in Fig. 2, curve 5. Annealing almost didnot affect the shape of the photoconductivity spectrumor the absorption spectrum of the samples. The temper-ature dependences of the photoelectric current had aform characteristic of the monomolecular mode ofrecombination, and their qualitative shape was invari-ant under the thermal treatment. The current–illumi-nance characteristics were linear for all the investigatedsamples.

SEMICONDUCTORS Vol. 34 No. 10 2000

EVOLUTION OF THE DENSITY OF STATES 1159

4. DISCUSSION OF THE RESULTS

As can be seen from Fig. 1, the as-prepared filmsrepresent homogeneous solid solutions containing onlythe α1 phase. For the sample whose electron diffractionpattern is shown in Fig. 1, the α1 phase is theCdS0.5Te0.5 solid solution. For other investigated sam-ples, this can be a solid solution with a composition inthe range of x1 = 0.4–0.6. According to the equilibriumphase diagram [3], such a composition corresponds tothe domain of a limited mutual solubility. Moreover, itcorresponds to the part of the domain, where, as mightbe expected, the absolute loss of solid-solution stabilityshould occur. Consequently, the as-prepared samplesrepresent the metastable systems maintained in thenonequilibrium state by internal potential barriers. Theannealing of such systems is found to induce thedecomposition of the original solid solution and theformation of a heterogeneous thin-film structure com-posed of two solid solutions: CdTe-based (α2) andCdS-based (α3). Their composition must correspond tothe mutual-solubility domains of their components inthe equilibrium phase diagram of the system.

The results obtained by us for the CdS–CdTe systemare completely consistent with the aforesaid. A mixtureof the α2 + α3 phases was detected in the annealed sam-ples by the electron-diffraction and optical methods.The composition of the α2 and α3 phases correspondsto the mutual-solubility domains (x2 = 0.1–0.2; x3 =0.78–0.99). The subsequent thermal treatments influ-ence neither the electron-diffraction pattern nor theelectrical and photoelectric properties. Thus, we canstate that, in this study, we actually investigated the pro-cess of phase transition of the system (a homogeneoussolid solution) from a metastable state to an equilib-rium state (a two-phase mixture of solid solutions).

As a rule, the system passes from a metastable stateto an equilibrium state due to fluctuations, i.e., bymeans of the formation and growth of new-phasenuclei. This process takes a certain amount of time. It isreasonable to assume that the conditions taking placeduring this time must influence both the phase-transi-tion kinetics and the properties of the newly formedphases. This explains the cause of the distinctionbetween the electrical and photoelectric properties ofthe solid-solution samples annealed at various heatingrates. This is related to distinctions in the structure,which cannot be detected by electron diffraction. Con-sequently, we attempt to analyze the kinetics of thethermally activated decomposition of a homogeneousmetastable solid solution on the basis of the electricalproperties of this compound.

The condensed solid-solution layers belong to dis-ordered systems [4]. The charge transport proceeds insuch systems at high temperatures over the mobility-gap edge and is described by the expression [5]

(1)σ σmin Ec EF–( )/kT–[ ] ,exp=

SEMICONDUCTORS Vol. 34 No. 10 2000

which is qualitatively consistent with our experimentaldata. Here, σmin is the minimum metallic conductivity,Ec is the mobility-edge, EF is the Fermi level, k is theBoltzmann constant, and T is the temperature. The factthat the charge transport takes place over the mobility-gap edge is also confirmed by the results of calcula-tions. According to Mott and Davis [5], a specific testfor conduction over the mobility-gap edge is the repre-sentation of the experimental conductivity in theform of

with the subsequent calculation of the parameter C. Forthe samples investigated both before and after anneal-ing, the value of the factor C was on the order of103 Ω−1 cm–1, which agrees closely with the resultsobtained by Mott and Davis and with a minimummetallic conductivity σmin in expression (1). Thus, wecan state that the charge transport over the mobility-gapedge takes place both during and after the phase transi-tion.

An appreciable change in the dark conductivity dur-ing the charge transport over the mobility-gap edgesimilar to that taking place on annealing the investi-gated samples is possible only owing to a change in theFermi-level position. There are two reasons for thisfact. The first is a change in the value of the mobilitygap; the second is a change in the density of states. Noexperimental facts supporting the former reason havebeen revealed. Moreover, investigations of photocon-ductivity indicate the opposite: neither the photocon-ductivity spectrum nor absorption spectrum vary onannealing. At the same time, a number of experimentalresults testify in favor of the latter reason. Theseinclude the shape of the photoconductivity spectrum(Fig. 2, curve 5), the linear current–illuminance charac-teristic, the dependence of the photoelectric current onannealing conditions, and the stability of the tempera-ture dependence of the photoelectric current withrespect to thermal treatments.

Actually, the first two facts imply that the photoelec-tric current in the investigated samples was monomo-lecular [5]; i.e.,

(2)

where e is the elementary charge, F is the electric-fieldstrength, µD is the drift mobility, G is the rate of gener-ation of nonequilibrium charge carriers, and τ is thelifetime of these carriers. In the experiment under dis-cussion, a substantial variation of µD is improbable,because the value of µD typically specifies the form ofthe photoelectric-current temperature dependence,which was stable here with respect to the thermal treat-ment. It only remains for us to consider the lifetime τ.This lifetime is very sensitive to the defect-level con-centration near the Fermi level. Consequently, variousphotoelectric properties of cadmium sulfotellurides are

σ C E/kT–( )exp=

ip eFµDGτ ,=

1160 BELYAEV et al.

governed precisely by the density of states near theFermi level.

Thus, we can state that the photosensitive propertiesacquired by the samples of cadmium-sulfotelluridesolid solutions in the course of their phase transitionsare caused by a change in the density of states near theFermi-level position. In turn, the density of states con-trols the Fermi-level position. As was shown above, theFermi-level position specifies the dark conductivity.Therefore, a change in the dark conductivity occurringin cadmium sulfotelluride on annealing (Fig. 2,curves 1, 3) also accounts simultaneously for the evolu-tion of the density of states near the Fermi level and thecharacter of variations in the Fermi-level position in thecourse of phase transitions.

In conclusion, we will make a remark concerningthe peak in the temperature dependence of the darkconductivity (Fig. 2, curve 1). As can be seen fromFig. 2, no peak is observed at high heating rates. Werelate this fact to the inertial behavior of our detectinginstrumentation. For high heating rates, the rate of for-mation of new-phase islands turns out to be very high,and is exponentially related to the temperature, whichrises fast at high heating rates. As to the time constantof our detecting instrumentation, it amounts to seconds.

5. CONCLUSION

From the results of the investigation carried out, wecan conclude the following.

(i) The phase transitions in metastable solid solu-tions of cadmium sulfotellurides are accompanied by adrastic changes in the density of states near the Fermilevel and its subsequent monotone relaxation to theequilibrium concentration.

(ii) The microstructure and the photosensitive prop-erties of the phases formed as a result of the thermallyactivated phase transition of a metastable solid solutionare specified by the temperature-rise rate.

(iii) Variations in the dark conductivity during thethermally activated decomposition of metastable solidsolutions simultaneously reflect the features of varia-tions in the Fermi-level position and the features ofvariations in the density of states during the indicatedphase transitions.

ACKNOWLEDGMENTS

This work was supported by the Russian Foundationfor Basic Research, project no. 99-03-32676.

REFERENCES

1. A. P. Belyaev, V. P. Rubets, and I. P. Kalinkin, Fiz. Tverd.Tela (St. Petersburg) 39, 382 (1997) [Phys. Solid State39, 333 (1997)].

2. A. P. Belyaev, V. P. Rubets, and I. P. Kalinkin, Fiz. Tekh.Poluprovodn. (St. Petersburg) 31, 635 (1997) [Semicon-ductors 31, 540 (1997)].

3. J. Saraie, H. Kato, N. Yamada, et al., Phys. Status SolidiA 39, 331 (1977).

4. A. P. Belyaev, V. P. Rubets, and I. P. Kalinkin, Fiz. Tekh.Poluprovodn. (St. Petersburg) 31, 966 (1997) [Semicon-ductors 31, 823 (1997)].

5. N. F. Mott and E. A. Davis, Electronic Processes in Non-Crystalline Materials (Clarendon, Oxford, 1979; Mir,Moscow, 1982).

Translated by V. Bukhanov

SEMICONDUCTORS Vol. 34 No. 10 2000