Formation of order in a system of localized charges in disordered layers of solid

solutions of cadmium telluride and cadmium sulfide

A. P. Belyaev, V. P. Rubets, and I. P. Kalinkin

St. Petersburg Technological Institute, 198013 St. Petersburg, Russia~Submitted February 19, 1996; accepted for publication April 24, 1996!Fiz. Tekh. Poluprovodn.31, 286–290~February 1997!

Relaxation processes stimulated in layers of the solid solutions CdTexS12x (x,0.2) by a changein an external electric field, temperature, and illumination have been studied. Polarizationeffects and maxima of the inversion current of photostimulated and thermally stimulatedpolarization were found. It is shown that all characteristic features of the relaxationprocesses can be explained in a quasidipole model, and the inversion maxima of the current canbe interpreted as being due to a photostimulated and thermally stimulated order–disordertransition. © 1997 American Institute of Physics.@S1063-7826~97!01702-X#

The observation of inversion maxima of the thermally 2. EXPERIMENTAL RESULTS

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stimulated current and polarization in disordered layerssolid solutions~SSs! of cadmium selenide and telluride wareported in Ref. 1. These effects were not explained propeLater we observed similar phenomena in layers of solidlutions of cadmium telluride and cadmium sulfide. In tpresent paper we attempt to describe in detail and expthese phenomena.

1. EXPERIMENTAL SAMPLES AND EXPERIMENTALPROCEDURE

We investigated CdTexS12x (x,0.2) layers, synthesizeon a mica substrate by the method of vacuum thermal vaization and condensation of a mechanical mixture fromreactor with a ‘‘thermal screen.’’ According to x-ray phaand electron-diffraction analysis the layers possess a pcrystalline structure with average crystallite size of 1022

mm. The layers were approximately 1mm thick. To stabilizethe electrical properties, before the measurements the lawere annealed in a 1023 Pa vacuum for 2 h. After annealing0.5-cm-wide silver contacts, separated by a distance ofcm, were deposited on the samples. The resistivity ofcontacts was checked on the initial sections of the currvoltage characteristic. X-Ray analysis was used to determthe composition of the solid solutions.

The electrical characteristics of the samples were msured in a current regime using a V7-30 electrometer.take into account the parasitic capacitances, prior to the msurements, the experimental stand was checked usingdards consisting of active resistances, whose values wclose to that of the experimental samples. A quantitativetimate of the magnitude of the relaxing charges was madeintegrating the corresponding currents in time.

All measurements of the electric and photoelectric chacteristics of the samples were made in a vacuum of 123

Pa. A special constant-temperature chamber was usemaintain the temperature of the samples within 0.1 K. Tphotoelectric parameters of the layers were investigatedder illumination with a 90-W incandescent lamp.

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The electric, photoelectric, photoluminescence, andlaxation properties were investigated. The electric and ptoluminescence measurements revealed the following cacteristics: high conduction activation energy~greater than0.7 eV! and high resistivity~101021011 V•cm at room tem-perature!, a complicated temperature dependence of the cductivity, presence of relaxations, and a large half-widththe photoluminescence bands~0.3–0.5 eV!, i.e., a combina-tion of properties which are characteristic of disordersemiconductors.2

The amplitude of the fluctuations of the potential of trandom field, estimated according to the photoluminescemeasurements, was equal to 0.3–0.5 eV. It increasedincreasing cadmium telluride content in the solid solution

The basic results of the investigations of the relaxatproperties are presented in Figs. 1–3. The curve of the reation of the current in the external circuit of the sample wthe external emf source switched on~at time t50) and off(t515 s) is represented qualitatively in Fig. 1~curve1!. It isevident from the figure that when the external fieldswitched on, decreasing current relaxations occurred. Aequilibrium was established, the samples became polariThe surface charge densityQp accumulated during polarization was equal to 102721025 C/cm2. The value of the sur-face polarization depended on the illumination of the samand the magnitude of the external field. It increased togewith these actions, but sublinearly.

The characteristic time for establishing a stationavalue of the polarization depended on the temperatureamplitude of the fluctuations of the random potential in tsample~Fig. 2!. An increase in the amplitude of the nonunformity of the potential caused, the characteristic timeincrease.

The sample was polarized only at relatively low temperatures. As the temperature increased~slightly above roomtemperature!, the polarization vanished. The vanishing of plarization changed the shape of the current relaxation cuAfter an external electric field was switched on, the curre

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increased monotonically up to a stationary value. The scific value of the temperature at which the polarizing of tsample ceased depended on the magnitude of the extfield. As the magnitude of the external field increased,limit shifted into a higher-temperature region.

Curve 2 in Fig. 1 represents qualitatively the currerelaxation under strong illumination (t50) and with darkscreening (t515 s) of the layers in an electric field. As oncan see from the figure, after the sample is screened,relaxation is characterized by the formation of an inversmaximum j in , which precedes a stationary value of therect current. Such maxima could be observed with raheating of the polarized sample~Fig. 3, curve1!. For com-parison, the behavior of the current when the heated sam

FIG. 1. Curves of current relaxation in a layer of the solid solutiCdTexS12x (x50.1) with the amplitude of the fluctuations of the potentenergy of the electronsg50.3 eV; T5300 K; with the external fieldswitched on~1! and with illumination switched on~2! at timet50 and withboth switched off att515 s.

FIG. 2. Temperature dependences of the characteristic polarization timlayers of the solid solutions CdTexS12x with the amplitude of the fluctua-tions of the potential energy of the electronsg, eV: 1 — 0.42 (x50.15),2— 0.1 (x50.1).

178 Semiconductors 31 (2), February 1997

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is cooled is also shown in the figure~curve2!. The currentj in depends on the heating rate. The inversion maximvanishes completely with slow heating.

The relaxation curves described above are compcurves. They could be represented by a simple exponeon the initial sections only in some cases. We took advantof this circumstance to determine the characteristic polartion time.

Without the action of an external electric field no polaization of the samples was observed.

3. DISCUSSION

The random potential in disordered systems basedII–VI solid solutions is mainly formed by composition fluctuations over the volume.3 Charged impurities together withthe majority carriers — electrons in the layers investiga— perform the function of screening. As follows from thlow conductivity of the samples, at the experimental teperatures most electrons are localized either in the tail ofdensity of states of the conduction band or in donor leveThey can move only by thermal activation on delocalizstates or by thermally activated hops along localized staTo distinguish electron motion along the conduction baand along donor levels, we call a free donor a hole acorrespondingly, we call electron motion along the impurband hole motion. As they move, electrons and holesdistributed according to states in such a way as to minimthe potential energy. The electron and hole densities canassumed, to a first approximation, to be identical andlayer of the solid solution can be represented as a voluwith a nonuniform electron-hole quasiplasma in a randfield formed by the composition fluctuations of the solid slution. In addition, the possible configuration states of tcharges in the quasiplasma are limited by the particularrangement of the impurities in the volume.

An external voltage applied to a nonuniform systemdistributed nonuniformly. According to Shklovski�,4 most ofthe voltage is applied across the regions where the poteenergy is close to the mobility edge. In CdTexS12x layers,these are regions depleted of free carriers and enrichedlocalized carriers. Such regions are separated from oneother by distances which are much greater than the avespatial size of the nonuniformities. Correspondingly, tvoltage drop across them is much larger than the averagea result, a high electric field capable of redistributing carri

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FIG. 3. Relaxation curves of the thermally stimulated polarization currena layer of the solid solution CdTexS12x with heating~1! and cooling~2! ofthe sample.

178Belyaev et al.

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weak external biases. As a result, the dynamic equilibribetween individual components of the quasiplasma isstroyed. Experimental observation of this phenomenon ifilm of II–VI solid solutions was reported in Ref. 5. A nonuniform quasiplasma in an external field must arrive in a nequilibrium state, which must necessarily be nonuniform

It can be assumed that this state contains regions oftially separated, localized charges of opposite sign — qudipoles. A necessary condition for the formation of quasipoles is that the thermal energy must be comparable tochange in the energy caused by the external electric fieldatypical4 regions~system must be driven out of equilibrium!.The fact that polarization effects in films of the solid soltions CdTexS12x appear only at low temperatures and ththe limiting temperature increases together with the extefield are evidence in support of the proposed model.

To make a systematic calculation of the conditionsformation of quasidipoles, it is necessary to solve simuneously the continuity and Poisson equations with boundconditions that do not admit solutions in terms of elementfunctions.6 However, calculations performed for simpler intial conditions ~neglecting the conduction current and tnonuniformity of the sample! revealed a distinguishing feature, due to quasidipoles, of the temperature dependencthe thermally stimulated polarization current. AccordingRefs. 7 and 8, current inversion should occur in an extecircuit of the sample heated by the voltage; we obsersuch a current inversion in the CdTexS12x layers.

In our view, the inversion maximum of the current in thexternal circuit containing a CdTexS12x sample is due to therelaxation of charge which accumulates on the electrodesbecomes excess charge by virtue of the temperature dientation of the quasidipoles. An order–disorder transitioncurs in the CdTexS12x layers under the influence of the temperature.

Another argument in support of the quasidipole modepolarization is the inversion maximum of the current whiarises as a result of intense screening of the layers~Fig. 1,curve 2!. It necessarily follows from the proposed modOnce light gives rise to polarization, switching off the ligshould result in the appearance of excess charge on thetrodes. This charge is induced by virtue of the low condtivity of the sample and relaxes mainly through the extercircuit.

The increase in polarizability of the sample under taction of the light is due to the increase in the charge ofquasidipoles, and the rapidity of the charge recombinaafter screening is due to the character of the potential barThe potential barrier in the CdTexS12x layers is formedmainly as a result of fluctuations of the composition of tsolid solution; in this case the potential wells for the hoand electrons of the main bands coincide spatially.

Qualitative agreement between the experiment andquasidipole model can be also seen in the field relaxationthe current~Fig. 1, curve1!. The decreasing current relaxations are explained by the increase in the opposing fielthe process of orientation of the quasidipoles; the expontial temperature dependence of the characteristic polariza

179 Semiconductors 31 (2), February 1997

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wheren is the frequency factor of the system, andW is theheight of the potential barrier, which a quasidipole muovercome in order to become oriented. The values ofW cal-culated on the basis of Fig. 2 to within hundredths of anagree with the estimates of the amplitudeg of the nonuni-formity potential of the corresponding CdTexS12x samplesfrom photoluminescence measurements. This agreemenbe interpreted as additional evidence for the formationoriented quasidipoles in the random field of the experimensamples.

We shall present some quantitative assessments ofmodel. First, let us determine whether or not the minimufield at which polarization was observed is indeed capabledriving the system of localized and free carriers out of eqlibrium. We observed polarization effect at room tempeture in an electric field of not less thatE.100 V/cm. Sincethe random field in the experimental solid solutions is dmainly to composition fluctuations of the solid solution aaccording to Ref. 10 the composition of a phase of the sosolution depends on the size of the region where this phasformed, it can be assumed that the external voltage fmainly on the interphase regions~different regions will pos-sess a different composition and therefore a different bgap! and according to Shklovski�4 mainly atypical regions.Since there are no other alternatives, let us assume thatof the hundreds of interphase regions is atypical. Then,an average size of the regions in the CdTexS12x layers equalto 1022 mm, we obtain the energy change produced byfield of the order of 100 V/cm to be 1022 eV, which iscomparable to the thermal energy and hence sufficiendestroy the dynamic equilibrium in the system of localizand free charges. Second, let us see how realistic the voldensity of polarizing charges required by the model is.

It is well known that

r52div•P, ~2!

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wherer is the charge density,P andPn are, respectively, thepolarization vector in the sample and its normal projectioand Qp is the surface charge density. Then, interpretdiv P as the increment toPn as a result of the displacemenof carriers from one electrode to another and using theperimental dataQp5102721025 C/cm2, we obtain thecharge densityr5101321015cm23. This value with impuritydensity 101721019 cm23 ~Ref. 3! is completely realistic.

In conclusion, we note that the appearance of polarition in layers has also been observed by other authors. Scifically, polarization of doped layers of II–VI compound

179Belyaev et al.

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4. CONCLUSIONS

The following conclusions can be drawn on the basisthe results presented above.

1. Under certain conditions order in the distributioncharges localized in a volume — quasidipoles — can appin inhomogeneous layers of cadmium telluride and cadmsulfide under the influence of an external field.

2. A decrease of the temperature and an increase oexternal field and illumination of the sample give rise to tformation of quasidipoles in the disordered systeCdTexS12x .

3. An external manifestation of order in the distributioof localized charge in the disordered system CdTexS12x ispolarization of the sample.

4. A sharp increase in temperature or illumination opolarized disordered system can result in the appearancan inversion maximum of the current as a result of an orddisorder transition in the system of localized charges.

5. The characteristic time for establishing order inexperiment depends on the temperature with activationergy determined by the amplitude of the fluctuations of

180 Semiconductors 31 (2), February 1997

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disordered system.This work was performed with the support of the Ru

sian Fund for Fundamental Research~Grant 96-02-19138!.

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Translated by M. E. Alferieff

180Belyaev et al.