Relaxation of the electrical properties of vacuum-deposited a-Se 1 − x As xphotoconductive films: Charge-carrier lifetimes and drift mobilitiesChris Allen, George Belev, Robert Johanson, and Safa Kasap Citation: Journal of Vacuum Science & Technology A 28, 1145 (2010); doi: 10.1116/1.3472623 View online: http://dx.doi.org/10.1116/1.3472623 View Table of Contents: http://scitation.aip.org/content/avs/journal/jvsta/28/5?ver=pdfcov Published by the AVS: Science & Technology of Materials, Interfaces, and Processing Articles you may be interested in Resonant coupling for contactless measurement of carrier lifetime J. Vac. Sci. Technol. B 31, 04D113 (2013); 10.1116/1.4813757 Combined isothermal and nonisothermal dc measurements to analyze space-charge behavior in dielectricmaterials J. Appl. Phys. 97, 044103 (2005); 10.1063/1.1847703 Highly resistive annealed low-temperature-grown InGaAs with sub- 500 fs carrier lifetimes Appl. Phys. Lett. 85, 4965 (2004); 10.1063/1.1824179 Relaxation processes of photoexcited carriers in GaAs/AlAs multiple quantum well structures grown by molecularbeam epitaxy at low temperatures J. Appl. Phys. 94, 3173 (2003); 10.1063/1.1595142 Dynamic charge-carrier-mobility-mediated holography in thin layers of photoconducting polymers Appl. Phys. Lett. 81, 3705 (2002); 10.1063/1.1512824

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Relaxation of the electrical properties of vacuum-deposited a-Se1−xAsxphotoconductive films: Charge-carrier lifetimes and drift mobilities

Chris Allen, George Belev, Robert Johanson, and Safa Kasapa�

Department of Electrical and Computer Engineering, University of Saskatchewan, Saskatoon,Saskatchewan S7N 5A9, Canada

�Received 8 March 2010; accepted 9 July 2010; published 2 September 2010�

The authors have examined the relaxation of the electrical properties of vacuum-deposited x-rayphotoconductor-type a-Se1−xAsx �x=0%–0.5%� films in terms of the time evaluation of the deeptrapping time �, i.e., carrier lifetime, and the drift mobility � from the time the samples werebrought to 23 °C after they had been annealed at 55 °C �above the glass-transition temperature Tg�for 30 min. The changes in the lifetime and drift mobility arise from structural-relaxationprocesses and have been modeled using a stretched exponential-relaxation process, i.e., �=��

+ ��o−���exp�−�t /�sr���, where �� is the lifetime when the sample is fully relaxed �the final“equilibrium” value�, �o is the initial lifetime, �sr is the characteristic structural-relaxation time thatcontrols the relaxation of the observed property, and � is the stretching factor. The authors haveexamined the relaxation of � and � as a function of composition. Within experimental errors, thestructural-relaxation time associated with electron and hole lifetimes were the same, indicating thatthe same structural changes must be influencing both electron and hole deep traps. �sr was 7–8 h forpure a-Se and increased linearly with the As content to about 40 h for a-Se:0.5%As. The stretchingfactor � was in the range 0.6–0.7 for all the samples. The relaxation of the electron-drift mobilitycould also be fitted to a stretched exponential as well, using the same structural-relaxation time asfor the relaxation of the electron lifetime. The increase in the carrier range ���� was used to estimatethe ratio of the final to initial hole and electron deep-trap concentrations. This ratio was about 0.5for both hole and electron deep traps for the present conditions that involved equilibration at 55 °C�above Tg� and relaxation at 23 °C. The significant increase in the carrier range duringstructural-relaxation leads to marked improvements in the performance of a-Se based x-raydetectors from the instant they are manufactured. As a corollary, one can conclude that the electricalproperties of a-Se photoconductors will always relax toward their equilibrium values, reachingstable �relaxed� equilibriumlike values within a few days at room temperature in the worst case.© 2010 American Vacuum Society. �DOI: 10.1116/1.3472623�

I. INTRODUCTION

At present, one of the most developed x-ray photoconduc-tors for use in recently commercialized direct-conversionflat-panel x-ray image detectors is stabilized amorphous se-lenium �a-Se�.1–3 Stabilized a-Se refers to amorphous sele-nium that has been alloyed with arsenic up to about 0.5% Asto suppress the tendency of pure selenium to crystallize. Sta-bilized a-Se based photoconductors, which were called pho-toreceptors, were extensively used in xerography until thelate 1980s when they were eventually replaced by organicphotoconductors. a-Se photoreceptors were also used in xe-roradiography, an x-ray imaging process that involves pho-tocopying a body part with x-rays and is less well knownthan its use in xerography. Although xeroradiography is nowobsolete, a-Se has found a new application in modern digitaldirect-conversion flat-panel x-ray image detectors in which athick layer �e.g., 200 �m� of a-Se is sandwiched betweenelectrodes and functions essentially as a conventional x-rayphotoconductor. Upon the absorption of x-rays in a-Se, elec-trons and holes are created, which then drift toward the elec-

trodes in the presence of an applied field and become col-lected as a charge signal. The principles of operation of suchflat-panel detectors and the properties of a-Se that render thismaterial as one of the best large area x-ray photoconductorsto date have been extensively reviewed.2,3

One of the most important electrical properties of an x-rayphotoconductor is the range of the charge carriers, the prod-uct �� of the drift mobility �, and the lifetime �deep trappingtime� �. Inasmuch as x-ray absorption occurs throughout thebulk of the photoconductor, we need to collect both electronsand holes. The x-ray sensitivity, therefore, depends on col-lecting both electrons and holes. Hence we need to considerboth electron and hole ranges, �e�e and �h�h, in the design ofa-Se flat-panel detectors.4–7 Even though much work hasbeen done, dating back to the 1960s, on the effects of howalloying and chemical modification affects �e�e and �h�h,very little systematic work has been reported on the relax-ation of these properties. That is, the time evolution of thecarrier lifetime, the drift-mobility, and range upon stepchanges in the temperature or right after the deposition of thea-Se film. There is only one recent short study8 in which thetime evolution of electron and hole lifetimes, �e and �h, re-spectively, in a-Se:0.2%As has been studied under two con-

a�Author to whom correspondence should be addressed; electronic mail:safa.kasap@usask.ca

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ditions: �i� relaxation right after vacuum fabrication once thesample has been cooled to 23 °C �room temperature� and �ii�relaxation after the sample had been annealed and equili-brated at 55 °C for 30 min and then cooled to room tempera-ture. Both electron and hole lifetimes have been observed torelax toward their final or equilibrium values following astretched exponential behavior, i.e., the carrier lifetime � attime t following a step change in temperature, as given by

� = �� + ��o − ���exp�− �t/�sr��� , �1�

where �� is the lifetime when the sample is fully relaxed �theso-called final “equilibrium” value�, �o is the initial lifetime,�sr is the characteristic structural-relaxation time �or con-stant� that controls the relaxation of the observed property,and � is the stretching factor. For this one composition,8 �sr

was found to be almost the same for hole and electron life-times: about 15–17 h and �=0.6–0.7. The duration t90 forthe carrier lifetime to reach 90% of its final value is given by

t90 = �2.303�1/��sr, �2�

which yields 2.5 days. That is, it will take 2.5 days for thephotoconductor to acquire reasonably stable charge-carrierproperties from the end of its fabrication.

In this work, we extend the above relaxation study todifferent compositions of a-Se1−xAsx alloys, including purea-Se, and examine the changes in the relaxation as the Ascontent is increased from x=0 to 0.5% over the useful rangeof compositions for x-ray photoconductor applications. Thepractical significance of the work can be understood by not-ing that the x-ray sensitivity measurements depend stronglyon the carrier ranges, and as �e�e and �h�h improve withtime due to structural-relaxation, so does the x-ray sensitiv-ity. We need to know the duration over which this improve-ment takes place and how this duration depends on the Ascontent up to 0.5%As. Further, as shown by recent studies,even the resolution of direct-conversion flat-panel detectorsis influenced by the carrier ranges.9 Moreover, the actuala-Se photoconductor in the detector is a triple layer10,11 �or adouble layer12� and the As content in the layers are not nec-essarily identical. This means that the full relaxation will bedetermined by the slowest process, that is, the layer with thelongest structural-relaxation time.

It is important to mention some of the past work onstructural-relaxation effects to put the work into perspective.Abkowitz13–15 was able to carry out a series of xerographicexperiments to show clearly that the deep traps that controlthe hole lifetime were thermodynamic in origin, that is, theyare structural defects and exhibit structural-relaxation effects.When an a-Se film was heated to a temperature close to theglass-transition temperature Tg, equilibrated by annealing fora long time at this temperature and then cooled to roomtemperature, the hole deep-trap concentration �and hence thehole lifetime� exhibited relaxation toward its equilibriumconcentration at room temperature. The functional depen-dence of the relaxation process has not been studied in anydetail except for one particular composition in one of ourrecent papers, as mentioned above. The relaxation effects in

the hole drift mobility have also been studied in the past, butthrough temperature-cycling experiments. It has been shownthat the shallow traps that control the drift mobility also ex-hibit structural relaxation.16,17 Therefore, there is clear evi-dence in the literature that structural-relaxation influences theelectrical properties of a-Se, which should not be surprisinggiven that a-Se is a typical polymerlike glass with a lowglass-transition temperature Tg.

The structural-relaxation effects in a-Se and Se-rich chal-cogenide glasses are, of course, well documented with a richliterature on its effects on various properties such as the en-thalpy, density, hardness, viscosity, elastic modulus, dielec-tric properties, electrical properties, optical properties, etc.�see, for example, Refs. 18–29�. Typically, the observed re-laxation phenomena at room temperature last for a few days;this time scale is due to the fact that a-Se’s Tg, typicallyabout 35–45 °C �depending on the measurement technique�,is close to room temperature. Consequently, the structural-relaxation time �sr at room temperature is such that the re-laxation effects can be easily monitored over a few days. Incontrast, in many Se-based chalcogenide glasses, which alsoexhibit relaxation effects, Tg is much higher, and the struc-tural relaxation at room temperature takes months to years.

The term relaxation as used here represents the changes ina property, such as the carrier lifetime or the deep-trap con-centration, at a given temperature toward its equilibriumvalue that would be expected from thermodynamic consider-ations. In the case of a typical glass at a temperature belowthe crystallization temperature, the equilibrium state wouldbe the supercooled liquid state, which is a metastable equi-librium state vis-à-vis the equilibrium crystalline phase.Clearly, the value of the observed property must have devi-ated from the expected equilibrium value due to the thermalhistory imposed on it. The property consequently “recovers”toward its equilibrium value, which is the relaxation processthat we investigate in this work. The terms aging or physicalaging have also been used, in particular, in polymer andglass sciences. We use the term relaxation throughout to de-scribe the recovery of a property toward its equilibriumlikevalue. Further, it is not unusual to use the term “annealingtime” to refer to the duration of time from the instant thesample is brought to the temperature at which the propertiesare monitored. In the latter sense, we are “annealing” thesample at 23 °C and measuring its properties as a functionof annealing time.

II. EXPERIMENT

Several different sample compositions were used through-out the course of this work. The source material, in the formof glass shots �quenched from the liquid�, for all samples wassupplied by Anrad �Montreal�. These samples were pure a-Seand Se-As alloys with 0.2%, 0.3%, and 0.5% As. Somesamples contained oxygen �O� and chlorine �Cl� in parts permillion �ppm� amounts, which are difficult to measure withprecision. Impurities in the ppm range were found not toaffect the kinetics of the structural-relaxation process, but toaffect only the absolute value of the deep trapping times. �A

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very small amount of Cl addition in the ppm range has beentraditionally used to compensate for the increase in hole trap-ping when a-Se is alloyed with As.30�

Photoconductor-type a-Se sample films were prepared us-ing vapor deposition in a conventional stainless steelvacuum-coating system as described elsewhere.31 The sourcewas a directly heated Mo boat whose temperature could becontrolled by a proportional-integral-derivative temperaturecontroller. The boat temperature was kept at 250 °C. Thea-Se films were deposited onto Al-coated Corning 7059 sub-strates. The Corning 7059 glass substrates were cleaned andthen coated with a thermally evaporated Al film. The sub-strate temperature during the deposition was also controlledand kept at about 55 °C, which is above the glass-transitiontemperature for all the alloys used in this work. The lattervalues were determined by conventional differential scan-ning calorimetry �DSC� measurements and are not reportedhere. The a-Se film thickness ranged from 100 to 150 �m.The thickness of the a-Se film was measured using a digitalmicrometer by taking several readings and averaging. Theerrors in thickness measurements, in the worst case, werewithin about 2%, and typically about 1.5% ��2 �m�. �Al-though capacitance measurements can also be used to calcu-late the thickness, one needs to know the dielectric constant,which also exhibits relaxation.� A small circular, semitrans-parent gold contact was sputtered on top of each sample toprovide a top electrode for time-of-flight �TOF� measure-ments.

For nearly all the samples, the relaxation was monitoredafter annealing the a-Se sample above Tg, and bringing it toroom temperature. The sample was heated from room tem-perature to 55 °C, which is above Tg, and was kept at thattemperature for a minimum of 30 min. This process allowedthe a-Se structure to equilibrate at 55 °C, that is, acquire thesupercooled liquidlike equilibrium state. Following the an-nealing step at 55 °C, the sample was rapidly cooled downto room temperature �23 °C� and was allowed to rest untilthe sample temperature was at room temperature �which tookabout 30 min�. Then measurements began. A typical tem-perature profile for an annealing experiment is given in Fig.1. For a few of the samples, we monitored the lifetime evo-

lution from the point of fabrication. For an experiment fromdeposition, once the sample was fabricated, the gold contactswere sputtered on as quickly as possible and measurementsbegan. Given that the substrate temperature during deposi-tion was above Tg, and at 55–60 °C, and the annealing tem-perature was 55 °C, the two thermal histories are expectedto be quite similar. Indeed, we have shown previously thatthe lifetime relaxation in the two cases, as expected, has thesame relaxation kinetics,8 which are about the same �sr and�. The reason for annealing the samples at 55 °C was tohave the annealing temperature roughly the same as the sub-strate temperature during the deposition of the samples sothat the measured changes represented what would be expe-rienced in practice when detectors are manufactured fromthese stabilized a-Se alloys.

TOF and interrupted-field time-of-flight �IFTOF� mea-surements were performed at 23�1 °C �henceforth referredto as room temperature� on the samples as they relaxed inorder to observe the relaxation fully. The IFTOF experimen-tal technique has been already described previously32 andwill not be repeated here. Typical IFTOF photocurrent wave-forms can also be found in Ref. 32. A light pulse of durationof 200 ns from a xenon flash tube, focused onto the samplethrough a blue filter �approximately 460 nm�, was used tophotogenerate charge carriers. The absorption depth underblue light was less than 0.2 �m. While conventional TOFmeasurements allow the drift mobility � to be measured,IFTOF experiments provide a clear measurement of the deeptrapping time � to be measured, provided that the photocur-rent is not trap limited and the transport is not dispersive.This is the case for the present a-Se1−xAsx alloys in whichx�0.01. Thus, the TOF/IFTOF combination measures � and� separately. The photoexcitation was kept well inside the Auelectrode and away from the electrode circumference toavoid having some of the carrier drift in the fringe field. BothTOF and IFTOF experiments used a pulsed bias and thephotoexcitation was triggered within a few milliseconds fol-lowing the application of the bias voltage. The use of apulsed bias, followed by photoexcitation after a short delay,prevents the buildup of space-charge in the sample throughthe injection of carriers from the electrodes.33

The interval between measurements was initially keptvery short ��1 h� since the relaxation was initially fast. Thismeasurement interval was slowly increased as the samplerelaxed. Between measurement sets, the samples were restedin the dark. All TOF/IFTOF measurements were performedover the course of eight days. Each set of relaxation mea-surements was fitted with a stretched exponential of the formin Eq. �1�. It is important to mention that the TOF and IFTOFexperiments themselves somewhat influence the measure-ments because some charge becomes trapped during themeasurement. That is, space charge builds up during thecourse of the experiment. Hole detrapping occurs over a timescale of minutes. Hence the space charge due to hole trap-

FIG. 1. Typical temperature curve for a sample during the annealingexperiment.

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ping is less of a concern than electron trapping, inasmuch asthe detrapping time of electrons is in the order of hours.34

The operational definition of the transit time is also im-portant in accurately determining the drift mobility �. Thework done during the sixties and seventies simply used the“knee” of the photocurrent on the oscilloscope screen for thetransit time tT—a convenient and inexpensive procedure. Theoperational transit time we have used corresponds to the timewhen the photocurrent has fallen to half its value just beforethe carriers have reached the collecting electrode. There isless uncertainty in this operational definition. Further, thetransit time represents the time involved in collecting abouthalf the carriers, rather than the transit time of the fastestcarriers �the transit time at the knee�. Once tT has been mea-sured, the drift mobility is determined by �=L2 / tTV, whereL is the thickness and V is the applied voltage. The errorsinvolved in the drift mobility measurements are about 4%.These errors stem mainly from the errors involved in thethickness measurement L and, of course, the error involvedin the transit time tT measurement. All hole-drift mobilityexperiments were done at an applied field of 1 V /�m andall electron-drift mobility experiments were performed at2 V /�m. Except at high fields, at room temperature the holedrift mobility exhibits no field dependence, whereas the elec-tron drift mobility has only a weak field dependence35 �andhence the reason for keeping the field the same in all themeasurements�.

The lifetime measurement involves interrupting the pho-tocurrent by suddenly removing the bias voltage at a certaintime during the drift of the photoinjected carriers across thesample, typically when the carriers are in the middle of thesample. The bias is removed for an interruption duration ti

and then reapplied. If the photocurrents before and after theinterruption are i1 and i2, respectively, then the fractionalrecovered photocurrent, i2 / i1, is a measure of the fraction ofthe carriers left after the interruption period and can be usedto extract the trapping time � inasmuch as i2 / i1=exp�−ti /��.A semilogarithmic plot of i2 / i2 versus ti and the reciprocal ofthe slope of the best straight line were used to find the life-time �. An example of a hole-lifetime measurement duringrelaxation studies is shown in Fig. 2, in which the hole life-time has been measured for a sample of a-Se:0.5% As whenthe sample had been relaxed �that is, aged or annealed� atroom temperature for 1 and 250 h. There is a clear and sig-nificant improvement in the hole lifetime during relaxation.It is important to ensure that the measurements themselvesdo not influence the determination of � as the sample relaxesand that sufficient time has been allowed between measure-ments. We maintained small signals and avoided too manymeasurements that were closely spaced. Control experimentsshowed that, provided the sample was rested for about atleast 5–7 min between measurements, i2 / i1 was reproducibleto within 5%. There would be about 15–20 lifetime measure-ment points during the relaxation of the sample over a fewhundred hours or over about 8 days.

III. RESULTS AND DISCUSSION

A. Relaxation of charge-carrier lifetimes: Relaxationof deep traps

The relaxation has a noticeable effect on the measuredTOF photocurrent waveforms. Figure 3 shows the relaxationeffects on the electron TOF waveform of a typical sample ofa-Se:0.3% As �doped with 5 ppm Cl�. Similar results werealso observed for the hole photocurrent. The sample wasannealed at 55 °C and brought down to room temperature. Itcan easily be seen that the photocurrent waveform exhibitsless decay, i.e., less trapping, as time progresses, indicatingthat the charge-transport properties of a-Se improve duringthe structural-relaxation process. Similar improvements inthe hole-lifetime �not shown� were also observed in which,as the sample relaxed, the hole photocurrent waveformevinced less decay.

The improvement in the charge-carrier lifetime that is ap-parent in Fig. 3 can be examined quantitatively by measuringthe lifetime � �as described in Sec. II� and plotting � againstthe time from the instant the sample was equilibrated at roomtemperature. The relaxation of the lifetimes of electrons andholes in different samples of composition a-Se:0.2% As areshown in Fig. 4. The solid and dashed curves are the best fitsusing Eq. �1�. The symbol �o in Eq. �1� is the initial lifetimeright after the sample was brought to room temperature fol-lowing annealing at 55 °C. The final equilibrium lifetimeafter extensive annealing �after relaxation� at room tempera-ture is ��. �o approached �� through the stretched exponen-tial behavior in Eq. �1�. For the electron lifetime in Fig. 4,�e�=179 �s, �eo=129 �s, �sr�14.6 h, and ��0.6 with thegoodness of fit given by R2=0.9881. For the holes, we find

FIG. 2. Hole IFTOF experiments at two different “aging times,” 1 h and 250h, at 23 °C. The fractional recovered photocurrent, i2 / i1, after the removalof the bias field has been plotted semilogarithmically so that the reciprocalof the slope is the lifetime �h. The two examples are for hole transport ina-Se:0.5% As that has been relaxed �i.e., aged or annealed at 23 °C� for 1and 250 h. There is marked improvement in the hole lifetime uponrelaxation.

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�h�=32.7 �s, �ho=18.2 �s, �sr�17.1 h, and ��0.7 withR2=0.9761. Although these fits are stated as “best fits,” simi-lar best fits can also be achieved with a slight variation in �sr

and �, as one would expect when one is fitting a multivari-able function to a set of experimental data. For electrons,comparable fit quality can be achieved with �sr=14–16.5 hand �=0.6–0.7; initial and final lifetimes in contrast do notchange more than a few percent. A comparison of the effectsof changing �sr and � on the goodness of the fit is shown inFig. 5. From the figure, it is apparent that changing �sr by �2

h does not have a significant effect on the fit quality. It wouldhave been better to have more experimental points, but thelatter significantly risks introducing experimental artifactsinto the data through space-charge effects.

The relaxation kinetics of the carrier lifetime, whether forholes or electrons, for a given sample was the same whetherthe relaxation was monitored after annealing at 55 °C orafter deposition and contacting, as shown in Fig. 6 fora-Se:0.2% As �sample B�, where we have monitored the

FIG. 3. Change in the electron TOF waveform as the relaxation experiment progresses in a sample of a-Se:0.3% As �5 ppm Cl�. The applied field was2 V /�m. The sample was annealed at 55 °C for 30 min. and then cooled to room temperature, 23 °C, where the measurements were taken on the sampleas it relaxed immediately after deposition.

FIG. 4. Relaxation of the lifetime of electrons and holes in samples ofa-Se:0.2% As. The solid and dashed lines are the best fit curves based on thestretched exponential relaxation.

FIG. 5. �Color online� Comparison of different fitting parameters. The ef-fects of changing �sr and � on the curve fits.

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electron lifetime as normalized electron lifetime, � /��, ver-sus time for the two cases to highlight the closeness of thetwo relaxation characteristics. �See Sec. II for these two ther-mal histories.� As expected, the relaxation kinetics are thesame within experimental errors. Similarly, the structural-relaxation times for holes and electrons for a given compo-sition are practically the same. In Fig. 4, for a-Se:0.2% As,holes had �sr=17.1�2 h and �=0.7, while the electrons had�sr=14.6�2 h and �=0.6. Figure 7 shows the relaxation ofholes and electrons in pure a-Se, where the holes have �sr

=7.5�2 h and �=0.7 and the electrons have �sr

=7.7�2 h and �=0.6. The fact that both the electron andhole lifetime relaxation kinetics are similar for a given com-position implies that the fundamental processes that controlthe relaxation of the deep traps must be similar in the twocases.

Figure 8 shows a bar chart of how the structural-relaxation time for both holes and electrons varies with thesample composition; the stretching factor � remained inde-pendent of the sample composition, remaining in the range�=0.6–0.7 for all compositions. �sr has been found to in-crease with the As content. Furthermore, the increase was thesame for both electron and hole lifetime relaxations. A list ofall sample compositions used, as well as the overall improve-ments in lifetime, is given in Table I. It is apparent that thereis an increase of 36%–54% for the electron lifetime over thecourse of the relaxation period. The increase for the holelifetime, 34%–167%, is also significant. It is important to putthese changes into perspective by discussing the origin of thelifetime relaxation and also how it relates to any previouswork.

The charge-carrier lifetime changes during relaxation aresubstantial, increase up to 167%, and are much more thanthose increases that have been reported for some of the bulkproperties of a-Se, such as 3% for the density,18 2%–3% forfilm thickness and refractive index,25 2%–3% for Tg,19,27 andless than 1% for the dielectric constant.36 �On the other hand,the hardness relaxes by almost 30%.18� The charge-carrierlifetime is controlled by two factors: the deep-trap concen-tration and the capture cross section. Furthermore, as men-tioned in Sec. I, the deep traps have been interpreted as ther-modynamic or structural defects. We expect the relaxation ofthe lifetime to be closely linked with the changes in theconcentration of deep traps, rather than their capture crosssection. In fact, xerographic measurements by Abkowitzshow that the position of the deep-hole trap concentrationdistribution in energy remains unchanged during relaxation,but the peak concentration decreases, as shown in Fig. 3 inRef. 13. The decrease in the peak density of deep traps fromthe latter work is from 6�1014 to 2�1014 cm−3 eV−1, thatis, roughly by 66% �Table II�. This is within the range of

FIG. 6. Plot of normalized electron lifetime �� /��� vs time for a-Se:0.2% As�Sample B� for two cases described in the text: annealing experiments�samples annealed at 55 °C and then brought to room temperature� anddeposition experiments �sample lifetime monitored immediately after depo-sition�. Individual best fits are listed in Table I. The best fit for the combineddata yields �sr�15 h and ��0.6.

FIG. 7. �Color online� Relaxation of the lifetime of electrons and holes insamples of pure a-Se.

FIG. 8. �Color online� Structural relaxation time �sr for the lifetimes of thesamples of various compositions measured in this work.

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changes we have been observing in this work. Thus, consis-tent with the explanation given in Ref. 13, the lifetime relax-ation is a direct manifestation of the relaxation in the deep-trap concentration. Excess deep traps generated duringannealing at 55 °C have to be removed until the trap con-centration Nd�T , t� decreases and reaches the thermal equilib-rium value at the temperature of the measurements, 23 °C.

It is also instructive to mention that the alloying of a-Sewith As significantly increases the structural-relaxation time�sr. That is, alloying significantly slows down the structural-relaxation rate. �sr is about 7–8 h for pure a-Se and about 40h for a-Se:0.5% As corresponding to t90 of about 25 h �1 day�for pure a-Se and 144 h �6 days� for a-Se:0.5% As. Theincrease in �sr with the As content for a-Se1−xAsx is almostlinear in x, as shown in Fig. 9. This is not unexpected, sincex is small and any functional dependence on x can be writtenas a series expansion that would approximate a linear termwhen x is small. Arsenic is trivalent and is well known tolink Se chains and, thereby, increase the viscosity and theglass-transition temperature. That is, As within the a-Se poly-meric structure is a crosslinker and hinders the relative mo-lecular conformations. Since the creation of defects or their

removal must include molecular rearrangements, one shouldnot be surprised that the structural-relaxation time is longerin the more rigid As alloyed structure.

B. Relaxation of the drift mobility and carrier ranges

We have also examined the time evolution of the driftmobility during structural relaxation. The results of mobilityrelaxation in a sample of a-Se:0.3% As �doped with 5 ppmCl� are shown in Fig. 10. The changes in the drift mobility,especially for holes, are very small and, hence, there is no-ticeable and unavoidable scatter in the data. As is apparentfrom Fig. 10, there is, nonetheless, quite a clear trend ofimprovement in the drift mobilities of both holes and elec-trons as the sample relaxes. However, the quality of the fit tothe stretched exponential is obviously not very good due tothe scatter in the data. The best fit to the electron mobility inFig. 10�a� had a reasonable R2 value of 0.8930, while thebest hole mobility fit in Fig. 10�b� only had R2=0.8024. Thefit parameters for electrons were determined to be �e�

=2.826�10−3 cm2 V−1 s−1, �oe=2.239�10−3 cm2 V−1 s−1,�sr�20 h, and ��0.54. The change in the electron mobility

TABLE I. Overall changes in lifetime for all samples used in this work and the best fit structural relaxation time�sr. �Asterisks � �� represent measurements from sample deposition, not annealing. See Sec. II.�

Material composition

Initiallifetime

��s�

Finallifetime

��s�

Structuralrelaxation

time�h�

Final to initiallifetime ratio

Changein lifetime

�%�

HolesHoles, pure a-Se 7.6 10.2 7.5 1.34 34.2Holes, a-Se �7 ppm O� 40.9 109 8.5 2.67 167Holes, a-Se:0.2% As �Sample A� 18.2 32.7 17.1 1.80 79.7Holes, a-Se:0.3% As �5 ppm Cl�* 49.9 77.6 27.3 1.56 55.5Holes, a-Se:0.5% As 12.7 23.8 39.7 1.87 87.4

ElectronsElectrons, pure a-Se 114 155 7.7 1.36 36.0Electrons, a-Se:0.2% As �Sample A� 363 559 20.6 1.54 54.0Electrons, a-Se:0.2% As �Sample B� 129 179 14.6 1.39 38.8Electrons, a-Se:0.2% As �Sample B�* 147 227 15.6 1.54 54.4Electrons, a-Se:0.3% As �5 ppm Cl� 238 342 30.6 1.44 43.7Electrons, a-Se:0.5% As 262 378 39.7 1.44 44.3

TABLE II. Stretched exponential fits to the relaxation of the electron-drift mobility. We could obtain good fits using �sr and � for the electron-lifetimerelaxation. The table shows we can also obtain good fits by keeping �=0.6 and finding the best �sr and setting �sr to the lifetime-relaxation time �Table I� andfinding the best �. As mentioned in the text, the best fit parameters are to within about 25%.

Material �sr � R2 �sr�best� � R2 �sr ��best� R2

Electrons, pure a-Se 7.7 0.60 0.9364 9.1 0.60 0.9377 7.7 0.521 0.9385Electrons, a-Se:0.2% As �Sample B�* 15.7 0.60 0.7737 21.8 0.60 0.7837 15.7 0.496 0.78342Electrons, a-Se:0.2% As �Sample B� 14.6 0.60 0.8366 22.0 0.60 0.8558 14.6 0.5196 0.8422Electrons, a-Se:0.2% As �Sample A� 20.6 0.60 0.8432 15.2 0.60 0.8501 20.6 0.5 0.8486Electrons, a-Se:0.3% As �5ppm Cl� 30.6 0.06 0.8911 20.3 0.60 0.8906 30.6 0.5008 0.8879Electrons, a-Se:0.5% As 39.7 0.60 0.9300 29.3 0.60 0.9345 39.7 0.521 0.9385

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upon relaxation was therefore 26%, which is quite signifi-cant. For holes, �h�=0.1246 cm2 V−1 s−1, �oh

=0.1151 cm2 V−1 s−1, �sr�30.5 h, and ��0.55. The relax-ation in the hole mobility is only 8.3%. While these fit pa-rameters correspond to the best fits, it is important to notethat there is a significant range in what can be considered as“best.” Figure 11 demonstrates the effects of changing the fitparameters on the quality of the fit. Changing �sr as much as5 h has very little effect on the fit quality. Notice, in particu-lar, that we can easily fit a stretched exponential with �sr

=20–30 h, that is, a variation of �5 h around a mean of 25h �i.e., �25%�. Notice further that �sr for the electron driftmobility, within experimental errors, is close to that for theelectron lifetime relaxation for the same composition�Se:0.3% As�. For example, the stretched exponential fit tothe drift mobility with �sr=30.6 h from the lifetime relax-

ation is shown in Fig. 11 and results in a good fit with �=0.5 and R2=0.8879. We would like to emphasize that wewere able to fit a stretched exponential to the relaxation be-havior of the electron-drift mobility for all the compositionsby using the same structural relaxation time �sr as for thelifetime relaxation and having �=0.5–0.6. These are sum-marized in Table II. On the other hand, the changes in thehole mobility are more difficult to fit to a stretched exponen-tial reliably given the scatter in the data, as apparent in Fig.10�b�; and we do not make any conclusions on whether thehole-drift mobility relaxes in the same manner as the corre-sponding lifetime.

One should also account for the changes in the thicknessas the sample relaxes, which has not been done in Fig. 10,during which the density increases and the thickness de-creases. Tan et al.26 have examined the changes in the opticalproperties and thickness of a-Se films by examining thechanges in the interference observed in the optical-transmission spectra as the a-Se films underwent structuralrelaxation. The change in the thickness due to structural re-laxation was only about 2%–3% and was due to changes inthe density. In the present study, it was not possible to moni-tor the changes in the thickness of the a-Se film during therelaxation process because it was not practical to monitor thethickness as the TOF and IFTOF experiments were beingdone. A 3% decrease in the thickness, by virtue of �=L2 /VtT, would imply a 6% less change than what had beenobserved, i.e., hole drift mobility increasing by only 2%, not8%, upon full relaxation. A simple calculation was used toincorporate a decreasing thickness into the observed drift-mobility results. Given that the thickness can decrease 3%from its initial value, taking Lo=L� /0.97 and assuming thethickness would relax following a stretched exponential ofthe same form as the mobility, we tried to refit the electron-mobility data with a stretched exponential with �sr=25.5 hand �=0.50, the mobility was recalculated and fitted with astretched exponential again. This new fit had �e�=2.864�10−3 cm2 V−1 s−1 �oe=2.389�10−3 cm2 V−1 s−1, �sr

�22 h, and ��0.5 in which R2=0.8087. The change in the

FIG. 9. Structural relaxation time �sr vs As content in percent.

FIG. 10. Typical results for the relaxation of the mobility of �a� electrons and�b� holes in samples of a-Se:0.3% As �doped with 5 ppm Cl�.

FIG. 11. �Color online� Comparison of changing the fitting parameters on theelectron drift mobility fit for a-Se:0.3% As+5 ppm Cl.

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electron mobility is then 20% instead of 26%. That is, asimple correction of 6% due to the thickness relaxation. Fur-thermore, �sr is within the uncertainty of the original fit; R2 isactually lower in this case.

Even though the relaxation of the mobility could not bereadily fit to a stretched exponential particularly well, in con-trast to the lifetime relaxation, it is still informative and use-ful to observe the overall increase in mobility over the courseof the relaxation, taking into account the change in the thick-ness as well. Table III lists the overall changes in electronand hole-drift mobilities for all the sample compositionsused in this work. We have not listed �sr and �, given thelarge range of fit in these values, to avoid clouding the dis-cussion. The same �sr as that for lifetime can be used for theelectron-mobility relaxation with �=0.5–0.6. Notice that re-laxational changes in the electron mobility are much largerthan changes in the hole mobility.

The x-ray detector sensitivity, detective quantum effi-ciency, and modulation transfer function depend on charge-carrier ranges, which are the �� products for electrons andholes. We have, therefore, calculated the initial and finalranges for all the samples, which are listed in Table IV. Themost striking conclusion from the table is the extent ofchanges in the carrier ranges. The changes in the electronranges are 62%–96%, whereas the changes in the hole rangeare 36%–173% for the present compositions. There is noapparent tendency in these changes that correlates with theAs content. The distinct improvement in the carrier ranges,by almost 100% or more in certain cases upon structuralrelaxation, shows the importance of this phenomenon in thisclass of glassy semiconductors.

The following further observations are noteworthy. Thechanges in the electron lifetime are more than the changes inthe drift mobility. For example, for a-Se: 0.2% As, sample A,

TABLE III. Initial and final drift mobilities and their ratio as a result of structural relaxations processes. The finalvalues have been corrected for the thickness change.

MaterialInitial mobility�cm2 V−1 s−1�

Final mobility�cm2 V−1 s−1�

Ratio of finalto initial mobility

HolesHoles, pure a-Se 0.1275 0.1290 1.01Holes, a-Se �7 ppm O� 0.1250 0.1359 1.02Holes, a-Se:0.2% As �Sample A� 0.1133 0.1162 1.03Holes, a-Se:0.3% As �5 ppm Cl�* 0.1147 0.1183 1.03Holes, a-Se:0.5% As 0.1126 0.1217 1.08

ElectronsElectrons, pure a-Se 3.5790�10−3 4.1071�10−3 1.15Electrons, a-Se:0.2% As �Sample B�* 2.6103�10−3 3.3217�10−3 1.27Electrons, a-Se:0.2% As �Sample B� 2.7681�10−3 3.2409�10−3 1.17Electrons, a-Se:0.2% As �Sample A� 2.5476�10−3 3.0488�10−3 1.20Electrons, a-Se:0.3% As �5 ppm Cl� 2.3706�10−3 2.8626�10−3 1.21Electrons, a-Se:0.5% As 1.5022�10−3 2.0264�10−3 1.35

TABLE IV. Overall improvements in the charge-carrier ranges.

MaterialInitial range�cm2 V−1�

Final range�cm2 V−1�

Change in range�%� Nd�final� /Nd�initial�

Holes �10−6 �10−6

Holes, pure a-Se 0.97 1.32 35.7 0.74Holes, a-Se �7 ppm O� 5.43 14.81 172.6 0.37Holes, a-Se:0.2% As �Sample A� 2.06 3.80 84.3 0.54Holes, a-Se:0.3% As �5 ppm Cl�* 5.72 9.18 60.4 0.62Holes, a-Se:0.5% As 1.43 2.90 102.5 0.49

Electrons �10−7 �10−7

Electrons, pure a-Se 4.08 6.37 56.0 0.64Electrons, a-Se:0.2% As �Sample B� 9.48 18.57 96.0 0.51Electrons, a-Se:0.2% As �Sample B�* 3.57 5.80 62.5 0.62Electrons, a-Se:0.2% As �Sample A� 3.74 6.92 84.8 0.54Electrons, a-Se:0.3% As �5 ppm Cl� 5.64 9.79 73.5 0.58Electrons, a-Se:0.5% As 3.94 7.66 94.6 0.51

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the electron mobility changes by 20%, but the lifetimechanges by 54%. The electron transport in a-Se is believed tobe shallow-trap controlled with a relatively well defined dis-tribution of shallow traps,37 which means that the measureddeep-trapping time � is given by38

� = �1

�� 1

CdNd , �3�

where Cd is the deep-trap capture coefficient, Nd is the inte-grated deep-trap concentration, and � is the mobility-reduction factor due to the presence of shallow traps. That is,�=�c / ��r+�c���c /�r, where �c is the capture time into theshallow traps and �r is the release time from these traps ��r

�c�. Furthermore, we can write �c as �c=1 /CsNs, in whichCs is the effective shallow-trap capture coefficient and Ns isthe integrated shallow-trap density. The measured drift mo-bility is the effective mobility. That is,

� = ��o ��c

�r�o =

1

�rCsNs�o, �4�

where �o is the microscopic mobility or band mobility. Thecarrier range is then

�� =�o

CdNd. �5�

Thus, improvements in �� by a factor of �2 �or more�upon relaxation imply that, during the structural-relaxationprocess, Nd must decrease by the same factor, since �o andCd are unlikely to change significantly. We can find the dropin Nd quite easily from Eq. �5�,

Nd�final�Nd�initial�

=�o�o

����

=Initial range

Final range, �6�

which has been also tabulated in Table IV. This ratio is,surprisingly, about the same, �0.5, for nearly all the samplesand for both hole and electron deep traps. The structural-relaxation process seems to change the electron and holedeep-trap populations roughly by the same factor.

We can also speculate on the nature of shallow traps thatcontrol the drift mobility. In the case of electrons, the mostimportant shallow traps are located at about 0.3 eV below Ec,which is due to a distinct peak in the density of states at thisenergy.39 Such peaks are usually associated with defects. Weknow that these defects are structural in origin.16 In fact,Lucovsky et al.40 proposed that the shallow traps may be dueto dihedral-angle distortions in the random structure of a-Sein which the lone pair orbitals on adjacent Se atoms ap-proach parallel alignment. During the structural-relaxationprocess, their concentration �Ns in Eq. �4�� will have to de-crease toward the thermodynamically allowed equilibriumvalue at room temperature. This results in the observed in-crease in the drift mobility.

The case for shallow hole traps is more difficult to ac-count for because the changes are less than a few percentafter the correction for the thickness change. That is, thechanges are very small and comparable to typical errors inTOF measurements. If these shallow traps are also structural

defects with a thermodynamic origin, then one would expecta large change, as in the case of electron shallow traps. If, onthe other hand, the hole drift mobility is controlled primarilyby localized tail states above Ev,41 such tail states are intrin-sic to the amorphous structure and would not exhibit suchlarge changes. Indeed, the changes in the optical propertiesof a-Se with relaxation are quite weak.25 The Tauc bandgapand the Urbach width remain relatively unaffected with re-laxation. There is also a very small change in the bandgap,defined in terms of the photon energy, at which the absorp-tion coefficient is 104 cm−1.25 Furthermore, if hole drift isindeed controlled by tail states, then we would also expectthe drift mobility to be quite reproducible for a given com-position, once the structure has relaxed. Hole-drift mobilityin a-Se is remarkably reproducible, whereas the electron-driftmobility tends to depend on the source, which changes thedefect concentration.35

We only have two temperature points, 55 °C �where an-nealing was done� and 23 °C �where the relaxation was ob-served�. Since the ratio of the two deep-trap concentrations atthese two temperatures is known from above �Eq. �6��, wecan estimate the defect creation/annihilation energy Ed that isinvolved in the defect-equilibration process. Writing thethermodynamic-equilibrium defect concentration as Nd

=No exp�−Ed /kT�, where k is the Boltzmann constant and No

is the atomic concentration �neglecting the small entropyterm�, we have Nd�final� /Nd�initial�=exp�−�Ed /k��Tfinal

−1

−Tinitial−1 ��. Substituting �0.5 for the ratio of the defect con-

centrations from Table IV, we find Ed�0.18 eV. This wouldbe the type of energy content that would be involved in con-formational motions of the molecules, rather than a primarybond rupture energy.

C. Further discussion

1. Relaxation kinetics and stretched exponential

As mentioned in Sec. I, structural-relaxation effects ina-Se and Se-rich chalcogenide glasses have been studied pre-viously, especially using thermal analysis. Many of thesestudies are difficult to compare, since they involve widelydifferent techniques. For example, in DSC, the sample isheated or cooled through Tg. In dielectric analysis, the fre-quency is scanned isothermally and the dielectric constant ismeasured. In modulated temperature differential-scanningcalorimetry, the sample temperature is modulated and theheat capacity is measured. In stress-relaxation measurements,the time evolution of the elastic modulus is measured. Thereis no reason to expect that the kinetics of relaxation associ-ated with one property will be the same as the kinetics ofrelaxation of another property, unless there is a close linkbetween the two properties. For example, we should not ex-pect that the kinetics of the charge-carrier relaxation process,which involves the equilibration of structural defects, with itsparticular �sr and �, to match exactly the kinetics of vis-coelastic relaxation in which bulk structural reorganizationtakes place, even though the latter would, to some extent,influence the former.

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The time scale of the carrier lifetime �electrical property�relaxation in a-Se �about 25 h for 90% recovery at 23 °C�, atfirst glance, seems to be of the same extent as the time scalesinvolved in the relaxation of various bulk properties, such asthe enthalpy �or the heat capacity�. The relaxation of en-thalpy in evaporated a-Se films has been studied by Stephensby DSC.21 Over the same duration, enthalpy only relaxes by45% or less at about the same temperature �Fig. 10 in Ref.21� and the relaxation time for the enthalpy and viscosity areof the order of �100 h at 23 °C �Fig. 8 in Ref. 21�. Clearlythe enthalpy relaxation occurs over a longer time scale thandeep-trap relaxation.

Furthermore, Böhmer and Angell23 studied the viscoelas-tic properties of a-Se and monitored the stress relaxation inpure a-Se. They have found the relaxation to be described bytwo stretched exponentials, labeled as short- and long-timeterm contributions. As the name implies, they accounted forthe relaxation over short and long times. If we extrapolatetheir short-time relaxation to 23–24 °C, we would find a �sr

that is 30–60 h. Since their � is about 0.6, the same as here,the stress relaxation seems to occur also over a longer timescale than deep-trap equilibration. While the relaxation timesseem to be different for the relaxation of charge-carrier life-times and the bulk properties, the stretching factor � seemsto be quite comparable. On an a-Se:0.5% As sample, weobserved the enthalpy relaxation to have a stretching factorof about 0.4.27 Most recently, Malek et al.28,29 have shownthat the volume and enthalpy relaxations can be described bysimilar relaxation times and have found the stretched expo-nential � to be 0.52–0.63 for volume relaxation and 0.60–0.70 for enthalpy relaxation. These values are quite close tothe � found in this work, given the play in �. It is instructiveto mention that a stretched exponential behavior has beenwidely observed in many chalcogenide glasses not only inthermodynamically driven relaxations but also in light drivenchanges, i.e., the so-called photoinduced changes �e.g., Ref.42�. The interpretation and the origin of stretched exponen-tial relaxation have been topical subjects in the literature. Inthe present case, we are monitoring the annihilation of extradefects that had been generated during the 30 min annealingabove Tg. There have been various discussions in the litera-ture on how defect creation and annihilation induced �ordriven� by light in amorphous semiconductors can lead to astretched exponential kinetics �e.g., Refs. 43 and 44�. Itwould not be farfetched to imagine an analog behavior inwhich thermodynamically �thermally� driven defect creationand annihilation processes in principle can also evincestretched exponential kinetics.

2. Effects of relaxation on the detector performance

It is informative to examine the effect of the relaxation onthe x-ray sensitivity of an a-Se detector. The following equa-tion was used to calculate the sensitivity of a photoconduc-tive detector:4,6

S =5.45 � 1013 � e

�air/�air�W��en

� � �xe�1 − e−1/��

+1

�/xe − 1�e−1/xe − e−1/�� + xh�1 − e−1/��

−1

�/xh + 1�1 − e−1/�−1/xh�� , �7�

where S is the sensitivity in C cm−2 R−1, e is the elementarycharge, air and �air are the energy-absorption coefficient andthe density of the air, respectively, W� is the electron-holepair creation energy, which depends on the electric field F,en and are the energy-absorption coefficient and the linearattenuation-coefficient of the photoconductor, respectively, �is the normalized attenuation depth, �=1 / �L�, and xe

=�e�eF and xh=�h�hF represent the electron and holeschubwegs per unit thickness, respectively. For a mammo-graphic detector,2 the thickness L=200 �m, average inci-dent x-ray energy Eph�20 keV, and operating bias field is10 V /�m. For a general radiographic detector, the thicknessL=1000 �m, incident x-ray energy Eph=50 keV, and oper-ating bias field is 10 V /�m. The sensitivity of a mammo-graphic detector under positive bias increases by 1%–3%,while under negative bias it increases by 4%–9%. While thisdoes not seem like a significant increase, mammographic de-tectors have very stringent requirements in sensitivity in or-der to generate high quality images. On the other hand, ageneral radiographic detector under positive bias has a sen-sitivity increase of 8%–17% under positive bias and an in-crease of 14%–26% under negative bias. This large increasein sensitivity would be noticeable in a detector’s perfor-mance.

IV. SUMMARY AND CONCLUSIONS

The relaxation of the charge-transport properties of a-Seand its alloys has been experimentally examined by carryingout conventional TOF and IFTOF measurements. We exam-ined the relaxation immediately after annealing above Tg andcooling the sample to room temperature, as well as immedi-ately after deposition in which the substrate temperature,55–60 °C, was kept above the glass-transition temperatureTg.

Electron and hole lifetimes were found to relax on astretched exponential with a similar structural-relaxationtime �sr for a given a-Se alloy. The structural-relaxation timeassociated with electron and hole lifetimes was the same,indicating that the same structural changes must be influenc-ing both electron and hole deep traps. �sr was 7–8 h for purea-Se and increased linearly with the As content to about 40 hfor a-Se:0.5% As. The stretching factor � was in the range of0.6–0.7 for all the samples. �sr was also found to increaselinearly as the concentration of As in the a-Se alloy in-creased, indicating that the alloys containing more As re-quired more time for their properties to reach steady-statevalues.

The extent of relaxation of the carrier lifetime was sub-stantial, for example, hole lifetime changes were 34%–167%

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and electron lifetime changes were 36%–54%. The changesin the hole drift mobility were small �less than 4%�, whereasthe changes in the electron drift mobility were 14–34%,quite significant.

The relaxation of the electron drift mobility could also befitted to a stretched exponential with the same structural-relaxation time as the electron lifetime and with �=0.5–0.6 although the fits were not as good as that for theelectron lifetime. Thus, the structural-relaxation mechanismsinvolved in the electron and lifetime relaxation are likely tobe the same. The relaxation in the charge-carrier ranges ��involved a factor of �2 improvement. The increase in therange was used to estimate the ratio of the final to initial holeand electron deep-trap concentrations. This ratio was about�0.5 for both hole and electron deep traps for the presentconditions that involved equilibration at 55 °C followed byrelaxation at 23 °C. The comparison of the present workwith relaxation effects observed in other properties of a-Seshows that the relaxations of the electrical properties seem tooccur over a shorter time scale than the relaxations involvedin the mechanical properties, volume, and enthalpy. The sig-nificant increases in the charge-carrier transport propertiesduring structural relaxations lead to marked improvements inthe performance of a-Se based x-ray detectors from the in-stant they are manufactured. We have estimated thesechanges in the x-ray sensitivity. The biggest changes in thex-ray sensitivity, as expected, occur in the general radiologydetector �a-Se is 1000 �m thick� in which the carrier rangesplay a key role in the performance of the detector.

ACKNOWLEDGMENTS

The authors thank the Natural Sciences and EngineeringResearch Council of Canada �NSERC� and Anrad for finan-cial support.

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