Photoconductivity and Relaxation Dynamics in Sonochemically

J. Phys. Chem. C 2011, 115, 37–46

37

Photoconductivity and Relaxation Dynamics in Sonochemically Synthesized Assemblies of AgBiS2 Quantum Dots Biljana Pejova,*,† Diana Nesheva,‡ Zdravka Aneva,‡ and Anna Petrova§ Institute of Chemistry, Faculty of Natural Sciences and Mathematics, Sts. Cyril and Methodius UniVersity, POB 162, 1000 Skopje, Macedonia, Institute of Solid State Physics, Bulgarian Academy of Sciences, 72 Tzarigradsko Chaussee BouleVard, 1784 Sofia, Bulgaria, and Space Research Institute, Bulgarian Academy of Sciences, P. O. Box 799, 1000 Sofia, Bulgaria ReceiVed: July 16, 2010; ReVised Manuscript ReceiVed: NoVember 3, 2010

The transport properties of nonequilibrium (photoexcited) charge carriers in sonochemically synthesized threedimensional (3D) assemblies of AgBiS2 quantum dots (QDs) deposited as thin films were studied. To characterize the photoconduction of quantum-confined nanocrystals close packed in thin film form, both stationary and time-resolved experiments were performed. Besides by interband electronic transitions in the bulklike part of the nanocrystals, the photoresponse of nanocrystalline films was found to be also affected to a greater extent by the crystal boundary barrier height modulation upon illumination. The surface and bulk recombination velocities were found to be comparable. Good agreement was obtained between the band gap energy determined by analysis of the photoconductivity data measured by the constant field and the constant photocurrent method (∼1.18 eV). This value is in agreement with the optical spectroscopy data. It is higher than the optical band gap of a bulk specimen of this semiconductor, due to 3D confinement effects on the charge carrier motions within individual QDs. The nonequilibrium conductivity was found to relax exponentially with a time constant of 1.67 ms, which corresponds to average lifetime of minority charge carriers (holes). 1. Introduction The focus on emerging nanoscience and nanotechnologies has made the physical chemistry of low-dimensional systems one of the most attractive areas of research in the last years.1-4 The fact that most of the relevant materials’ properties are size dependent (within a material-dependent size range) has created the possibility to control and actually tune these properties. Size dependence of optical and electronic structure-related properties has been found to be particularly remarkable in the case of lowdimensional semiconductor materials. Probably the most notable phenomenon reflecting the previous statement is the size-induced band gap variation which occurs when the “characteristic size” of semiconductor nanoparticles becomes comparable with the exitonic Bohr radius5-12 for the corresponding bulk sample. The band gap variation in low-dimensional semiconductors occurs due to the confinement of charge carriers in one, two, or three spatial dimensions. Of central importance for the current study is the case of three-dimensional (3D) confinement effects in zero-dimensional semiconductor nanostructures. In order to emphasize the quantum character of the confinement effects, along with the nanodimensions of a particle’s characteristic length, the term “quantum dot” (QD) has been coined.13-20 The extensive work in the field of low-dimensional semiconductor materials in the last period has led to a more comprehensive understanding of the physics governing many aspects of these materials, at least in a semiquantitative manner. However, a number of issues have remained only partly covered, and some aspects have not even been significantly addressed. For example, the number of studies devoted to internal photo* To whom correspondence should be addressed. Tel.: +389-3-117-055. Fax: +389-3-226-865. E-mail: [email protected]. † Sts. Cyril and Methodius University. ‡ Institute of Solid State Physics, Bulgarian Academy of Sciences. § Space Research Institute, Bulgarian Academy of Sciences.

electrical effect and, in general, photophysics of low-dimensional structures (especially the relaxation phenomena governing the nonequilibrium charge carriers’ recombination) seems to be much smaller.21-45 The last statement is particularly valid when one deals with 3D assemblies of semiconductor QDs. Actually, problems related to equilibrium and nonequilibrium conductivity of 3D nanoparticle assemblies and also of nanocrystalline films have been studied to a much lesser extent.20,21,28,30-33,35-45 Perhaps the most notable among these, at least in relation to our present study, are the studies of photophysical phenomena in nanostructured CdSe,17-21,37-40,42,44,45 nanostructured silicon,22,28,35,41,43 nanocrystalline GaN,26 as well as thin films of silicon nanocrystals,28 InP nanoparticle arrays,29 nanostructured InAs/ GaAs, 36 and PbSe nanocrystal arrays.30 Actually, the formations, built up by close packing of individual QDs (such as, e.g., the 3D assemblies of QDs), are in the very focus of contemporary physical chemistry due to the number of very significant and still only partly explained aspects related to collective physical phenomena which develop upon interaction of the proximal QDs constituting the 3D QD assemblies, while keeping certain individual characteristics of QDs. Specifically the unique properties characteristic of an individual QD on one hand and the cooperative effects in proximal QDs on the other hand make these novel types of superstructures very convenient media with great potential for application in optical and electronic devices. The terms “QD solid” or “colloidal crystal” have been used in some recent publications referring to 3D QD assemblies.13-20 Such terms have been used in order to emphasize that these superstructures built up of QDs correspond to a new form of organization of matter. As a continuation of our previous work in the field,34,46-49 in the present study we explore photoelectrical phenomena in 3D assemblies of AgBiS2 QDs deposited in thin film form by our

10.1021/jp106605t  2011 American Chemical Society Published on Web 12/15/2010

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recently developed sonochemical approach.46 We analyze both static and dynamic phenomena related to the charge carrier transport properties in thermal equilibrium and also under the conditions when internal photoelectrical effect is observed. The present study enabled us to get a deeper insight into certain photoelectrical and optical properties of the title material. Clarification of these aspects shed more light on the possibilities offered by the proposed synthetic route, which, as explained in our previous work,46 enables fine tuning of the optoelectrical properties of the studied material. 2. Experimental Details 2.1. Synthesis of 3D Assemblies of AgBiS2 QDs in Thin Film Form by Conventional Chemical and Sonochemical Routes. The investigated 3D assemblies of semiconducting AgBiS2 QDs were synthesized in thin film form by the conventional chemical and sonochemical methods which have recently been developed by our group.46 Regardless of the particular approach, the reaction system was composed of silver nitrate, bismuth nitrate, and sodium thiosulfate, where the first two substances serve as metal ions precursors, whereas the third one plays the role of complexing agent and sulfide ion precursor. Having in mind the pronounced tendency of Bi3+ cation toward hydrolysis, to avoid precipitation of BiONO3, bismuth(III) nitrate was initially dissolved in a solution of nitric acid (c(HNO3) ) 2 mol/dm3), and even afterward this component was added to the reactor. Experimental synthetic conditions in the conventional chemical approach were optimized in a classical way, having in mind the two main aims of the present work: (i) to produce material with pronounced low-dimensional structure and (ii) to achieve maximum photoresponse characteristics. Our investigations have shown that high-quality homogeneous films could be deposited within a relatively wide interval of initial and final concentrations of the reactant species in the reactors, as well as their molar ratios. However, best photoelectrical performances of the finally synthesized 3D QD assemblies in thin film form were achieved with initial concentrations of both AgNO3 and Bi(NO3)3 solutions of 0.1 mol dm-3 and initial concentration of Na2S2O3 solution of 1 mol dm-3, keeping the volume ratio of these three species at 1:1:1. When the sonochemical approach was applied, the reaction system was continuously irradiated with a high-intensity ultrasonic radiation (100 W/cm2) with a frequency of 20 kHz, keeping all other experimental conditions unchanged. The sonification of the reactor was performed using a direct immersion ultrasonic horn. Standard commercially available microscopic glasses were used as substrates. In order to improve the adhesion of prepared thin films with substrate’s surface, an appropriate predeposition treatment of microscopic glasses was performed, as described in details in ref 46. In this reference, also a thorough discussion concerning the chemistry of the deposition process can be found. The as-deposited films were further subjected to postdeposition thermal annealing treatment at 250 °C, in air atmosphere. 2.2. Sample Characterization. To characterize the asdeposited and annealed films, the Debye-Scherrer method50 of X-ray diffraction analysis was employed, using monochromatic Cu-KR radiation. X-ray diffractograms were recorded on a Philips PW 1710 diffractometer. The XRD data were used for estimation of the average crystal size and refinement of the unit cell parameters. Gravimetric or interferometric methods were employed to determine film thickness.46,49 The thickness of films which were investigated in the present study spanned the range from 50 to 200 nm. Surface morphology of the films prepared by sonochemical and chemical routes was studied by atomic force microscopy

Pejova et al. (AFM) technique. A scanning nanoindenter NanoScan (http:// www.nanoscan.info/eng/index.html), a device for surface properties investigations and measurements of hardness and elastic modulus of ultrahard materials and thin films, was used operating in contact dynamic (surface topography) mode. Arrays of 1000 × 1000 pixels were taken on a scanning area of 1.0 × 1.0 µm2. For all electrical and photoelectrical measurements carried out in this study, we have used either silver-paste or melted indium planar electrodes, applied on the film’s surface. The electrodes demonstrated ohmic-like behavior in the range of the electric fields applied (10-1000 V/cm). For measurements of dark electrical resistance of the films, besides the standard twopoint probe method, also the four-point probe van der Pauw approach and the constant field method were employed.34,46-49 The type of predominant charge carriers was determined by thermoelectrical (hot-point probe) measurements, which showed that AgBiS2 is an n-type semiconductor. Temperature dependences of the photocurrent were obtained in the temperature range from 77 to 390 K by a Keithley 6487 Picoammeter under illumination with white light (400-750 nm, ∼30 mW/cm2). Spectral photoelectrical measurements were carried out employing either the constant field method or the constant photocurrent method (CPM).34,46-49,51 The CPM method allows precise exploration of the absorption spectrum of thin films, and thus important conclusions about size-induced changes in the electronic structure of photoconductive nanocrystalline materials could be derived. The CPM measurements were carried out at room temperature. The samples were illuminated with chopped monochromatic light (2 Hz) from an MDR 2 diffraction grating monochromator with a resolution of 2 nm/mm. The photocurrent was kept constant by varying the lamp supply voltage. The intensity of the incident monochromatic light F(hν) was determined from the dependences of the light intensity vs the lamp supply voltage measured previously for all wavelengths. For the measurements of the stationary spectral photoresponse by the constant field method, a monochromator from spectrophotometer Beckman DU-2 was used as an external source of radiation (wavelength range from 400 to 1200 nm). Time-resolved experiments for investigation of photoexcited charge carriers’ relaxation dynamics were performed by the constant field method. Photoconductivity time decay was monitored by the constant field method, collecting the timedependent voltage data by oscilloscope.34,49 3. Results and Discussion 3.1. Basic Structural Properties of the 3D AgBiS2 QD Assemblies Synthesized in the Form of Continual Thin Films. Previous results from the XRD study of the investigated nanostructured films have shown46 that the synthesized material (by either sonochemical or conventional chemical method) is the cubic modification of bismuth(III) silver sulfide. Normally, at room temperature the most stable modification of this semiconductor is the hexagonal one, while the cubic modification is stable at temperatures higher than 200 °C but is metastable at room temperature. Our observation of stable cubic structure at room temperature can be related to the very small grain size. A similar result has been reported for nanocrystalline CdSe.52 On the basis of XRD investigations, it was also shown that the structure of the synthesized semiconductor does not change upon annealing treatment at 250 °C in air atmosphere. By analysis of the intrinsic broadening of the diffraction peaks in the recorded XRD patterns, the average radius of the

3D Assemblies of AgBiS2 QDs

J. Phys. Chem. C, Vol. 115, No. 1, 2011 39 indexes h, k, and l (dhkl), diffraction angle (θ), and wavelength of the used X-ray diffraction radiation (λ), could be rewritten in the following manner (n being an integer constant)

2dnh,nk,nl sin θhkl ) λ

(1)

dhkl ) dnh,nk,nl n

(2)

where

According to the previous equations, the higher-order reflections from planes with Miller indexes h, k, and l may be regarded as first-order reflections from planes with indexes nh, nk, and nl (h′, k′, and l′). On the other hand, the equation that gives the relation between interplanar distance (dhkl) and unit cell parameter (a) in the case of cubic crystal system has the following simple form:50

1 h2 + k2 + l2 ) 2 dhkl a2

(3)

The combination of Bragg’s diffraction law and the last equation leads to the following expression Figure 1. XRD patterns of 3D assemblies of AgBiS2 QDs close-packed in thin film form (standard, chemically and sonochemically synthesized, and annealed film).

nanocrystals which build up the films was also estimated, using the Debye-Scherrer method.50 The estimated average radius of the grains in as-deposited AgBiS2 thin films prepared by chemical route is 8.4 nm, and it increases to 27.1 nm upon thermal treatments of investigated samples at 250 °C for 1 h. This is attributed to coalescence and crystal growth processes occurring during the annealing treatment.46 The average crystal radius in the case of sonochemically prepared AgBiS2 samples was found to be twice as small as in the case of samples synthesized by conventional chemical deposition, i.e., 4.2 nm. Therefore, the sonification of the reaction system was proved to be a useful synthetic tool for preparation of low-dimensional structures of investigated material. It should be mentioned that the estimated average crystal radius of the obtained semiconductor is the same both in the thin film form and as a precipitate from the same reaction system, regardless of the employed synthetic method. This finding is in agreement with the results obtained on the basis of light-scattering experiments53 concerning the cluster mechanism of crystal growth.46 Taking into account the fact that nanometer-sized crystals could exhibit an intrinsic lattice strain, caused by a high fraction of surface atoms, in addition to previously discussed analysis, here the experimental XRD data (Figure 1) are exploited for refinement of unit cell parameters and for estimation of lattice strain. The refinement of unit cell parameters can be done on the basis of the expression which arises from combination of the Bragg’s diffraction law and the equation connecting the interplanar distances dhkl with the unit cell parameter in the case of cubic crystalline system to which the studied semiconductor belongs.50 The usual mathematical form of Bragg’s law, which connects the distance between planes described by the Miller’s

sin2 θhkl ) A(h2 + k2 + l2)

(4)

where A ) λ2/4a2. The constant A has been obtained by a linear regression analysis of sin2 θhkl vs (h2 + k2 + l2) dependence (as implied by expression 4). Afterward, on the basis of the obtained value of A and experimentally used wavelength, the unit cell parameter has been calculated. In the case of chemically and sonochemically deposited thin film samples, the estimated unit cell parameter values are a ) 5.6750 and 5.6740 Å, respectively, while in the case of annealed sample (at 250 °C for 1 h), a ) 5.6612 Å. The obtained values of the unit cell parameter are close to the value of this quantity in macrocrystalline (strainfree) sample. According to these results, it could be concluded that the lattice strain in the case of synthesized low-dimensional AgBiS2 thin films is negligible. This conclusion is in line with the appearance of recorded XRD patterns. As can be seen from Figure 1, the maxima of the XRD peaks are not shifted in comparison to those in the macrocrystalline (strain-free) sample. To characterize the surface morphology of the films, atomic force microscopy (AFM) studies were carried out. In Figure 2a and b, a three-dimensional image and a surface relief along an occasional line parallel to the x-axis in the case of a sonochemically deposited AgBiS2 thin film are shown, respectively. Largescale fluctuations are evident whose lateral size is ∼50 nm, but their vertical amplitude is below 10 nm. The root-mean-square (rms) roughness determined for samples with similar thickness does not significantly depend on the preparation route. Superimposed on the large-scale fluctuations, a fine structure is also seen, which indicates existence of very small grains. A rough estimation of their size gives values between 5 and 10 nm. A qualitative comparison of the surface relief for sonochemically and chemically deposited samples leads to the conclusion that the crystal size in the sonochemically deposited films is smaller than that in the chemically deposited ones. These findings give a further proof of the nanocrystalline structure of the films and are in line with the X-ray diffraction data.

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Pejova et al.

Figure 3. Typical photoconductivity response spectrum of a thin film composed of 3D assemblies of AgBiS2 QDs close-packed in thin film form, measured by the constant field method.

Figure 2. (a) Three-dimensional AFM image of the surface of a AgBiS2 as-deposited thin film prepared with the sonochemical route. (b) Surface relief along an occasional line parallel to the x-axis.

3.2. Photoelectrical Properties. 3.2.1. Stationary PhotoconductiWity Spectral Response of AgBiS2 3D QD Assemblies. From the aspect of fundamental physical sciences, studies of photoconductivity phenomena in solids are very valuable, as they can contribute significantly to gaining of new knowledge concerning the band structure of investigated material, the nature and density of gap states, etc. However, such studies are worthwhile from an applicative point of view as well, since semiconductor photoresponse properties determine the fields of its potential application. In the present study we deal with 3D assemblies of AgBiS2 QDs deposited in thin film form, and there are certain specificities related to the low-dimensional nature of the studied system which we take into account to get an indepth insight into the photoelectrical phenomena. In this section, we focus on the stationary photoconduction spectral response and on analyses thereof. In the next one, we deal with the timeresolved studies of photoconductivity relaxation. To the best of our knowledge, literature data concerning both the stationary photoconductivity spectral response for AgBiS2 and the transient photoconductivity as well as any analyses thereof are not available (regardless on the form of this material, either macrocrystalline, thin film, or nanocrystalline). Measurements of stationary photoconductivity spectral response of the investigated films were, as mentioned before, performed by two approaches: the constant photocurrent method and the constant field method. Concerning the basic parameters related to the band structure of the studied material, the results obtained by analysis of data from the two types of measurements are in excellent agreement. However, for some aspects particular measurements have certain advantages, and in such cases we will explicitly refer to the type of measurement. According to the results of our investigations, as-deposited 3D assemblies of AgBiS2 QDs prepared by the conventional chemical route manifest relatively low photoresponse at room temperature (Ip/Id ) 2-4), while it is significantly increased upon postdeposition thermal treatment at 250 °C. Nanostructured films deposited sonochemically are characterized by even smaller photoconductivity than the chemically deposited one. This behavior is analogous to what we have found in the cases of CdSe54,55 and Bi2S349 quantum dots deposited in thin film form. All these three types of films are highly nanocrystalline

before thermal treatment, and it is thus expected that the grain boundary effects should be strongly manifested. Postdeposition thermal annealing, which is accompanied by coalescence and crystal growth processes, leads to significant increase of the average crystal radii and therefore to weakening of grain boundary effects. Note that we have found an opposite behavior in the case of nanocrystalline SnSe films.34 The presently studied system belongs to the class of lowdimensional polycrystalline materials. Therefore, in addition to the increase of the free charge carrier concentrations due to internal photoelectric effect, also the photoinduced modulation of grain boundary barrier heights could be important in determining the overall dynamics of charge carrier transport through the films.56-61 The photomodulation of the intercrystalline boundary barriers in the presently studied n-type semiconductor is explained as follows. In the absence of photoexcitation by external light source, in n-type semiconductor with acceptor-type surface states, band bending on the surface occurs as a result of the spontaneous negative charge transfer from the bulk part of the semiconductor to the surface. This process proceeds until the surface and bulk Fermi energy levels equilibrate. Upon photoexcitation, trapping of minority charge carriers occurs in the barrier region, leading directly to decrease of the charge accumulation in the intercrystalline boundary area and, consequently, reducing the diffusion potential (i.e., barrier height). Figure 3 shows a typical stationary spectral photoresponse curve for annealed AgBiS2 film (the function ∆σst./ ∆σst.,max. ) f (hν), constructed from the constant field method measurements). The photoconductivity spectrum has been corrected for the spectral dependence of the intensity of the excitation light source. Maximal photoresponse of the investigated thin film is observed at ∼2.0 eV, while the red absorption edge is at about 0.90 eV. Comparison of the photoresponse spectrum with the optical absorption spectrum reveals that while the absorption of the films continuously increases upon increase of the incident photon energies in the studied spectral range, the photoresponse shows a marked decrease at incident photon energies higher than about 2.10 eV. In the strong absorption region (R g 105 cm-1, hν significantly larger than the optical band gap) and large layer thickness (>5 × 10-5 cm), the product Rl > 5 and the exciting light is absorbed close to the film surface. Then the total volume in which carrier excitation takes place decreases, which could cause a photocurrent decrease. However, the thickness of our layers is rather small (50-200 nm), and this mechanism could not be the reason for the observed strong photocurrent decrease at hν > 2.1 eV. As discussed quantitatively


J. Phys. Chem. C, Vol. 115, No. 1, 2011 41

by Devore,62 another possible reason for this observation can be the effect of surface recombination, which we consider in the next two paragraphs. Our previous results46 have indicated that the current flow through the nanocrystalline AgBiS2 films is actually modulated by the grain boundary barriers. The variable-range hopping (VRH) and the thermionic emission appeared to be the predominant charge transport mechanisms at room temperature. According to the model of Orton and Powell,63 the temperature range over which the VRH mechanism will predominate in the overall conductivity depends on the magnitude of the Debye length (LD) relative to the crystal size (i.e., crystal diameter D). The Debye length is defined by

LD )

(

εrε0kBT 2

eN

)

1/2

(5)

where εr is the static relative dielectric constant of the investigated material, N is the free carrier concentration, and all other symbols have their usual meanings. In order to be able to estimate the Debye’s length in the case of nanostructured AgBiS2 films, the value for εr of the studied material is required. Unfortunately, to the best of our knowledge, no data for this quantity exist in the literature. However, for the purpose of rough estimation, taking a value of 15 for εr, which is close to the values characteristic for other similar semiconductor compounds64 (for a usual doping concentration of 1017 cm-3), gives a value for LD close to 15 nm. This value is nearly twice as small as the average crystal diameter of thermally annealed films. Therefore, the studied nanocrystals are only partially depleted of charge carriers, and therefore the thermionic emission is predominant over the VRH process. On the other hand, the recombination process of the photogenerated charge carriers is hindered by recombination barriers which cause spatial separation of the photogenerated electron-hole pairs. To be able to understand the photoconduction of the studied nanocrystalline AgBiS2 films on a deeper level, one has to analyze the shape of the photoconductivity spectral response in both qualitative and quantitative manner. For that purpose, we adopt the following approach. We express the overall increase in conductivity upon illumination, modulated either by increase of the free carriers’ concentration (∆σn) or by decrease of the grain boundary barrier height (∆Eb), as a sum of the two basic contributions:

∆σ ) ∆σn + ∆σEb

(6)

As shown in more detail elsewhere, following basically the approach of Orton et al.,58 the following explicit form of expression describing the spectral dependence of ∆σst. could be derived:

( )

defect level energy, and the quantity η is given65 by η ) (kBT/ Eb)[1 - exp (-Eb/kBT)]. Equation 7 is, strictly speaking, valid for materials characterized by average crystal size larger than the Debye length (D > LD), which is fulfilled in the case of annealed AgBiS2 films. A significant assumption in the derivation of eq 7 is that the thin film thickness l is much larger than the carrier diffusion length. Only in such a case is the excess carrier concentration ∆n proportional to [1 - exp(-Rl)]. This condition is actually not fulfilled in our case, as the carrier diffusion length and film thickness are comparable.66-69 Therefore, the surface and bulk recombination velocities are also comparable. As shown quantitatively elsewhere,70 the expression for ∆n in such a case is very sophisticated; it contains other terms as well, which make the function ∆n ) f(R) go through a maximum and decrease for higher values of R. Such behavior of the function ∆n ) f(R) would lead to a maximum in the photoconductivity spectral response curve. This is exactly what was observed in our experiments. According to the model originally proposed by Devore, the following equation for the spectral dependence of photoconductivity has been derived:62 τI × 1 - R2(hν)Dτ [RSτ(1 + e-R(hν)l) + R2(hν)Dτ(1 - e-R(hν)l)] [1 - e-R(hν)l] τ 1/2 l 1+S coth D 2(Dτ)1/2

∆σ(hν) ∝ N )

{

[

()

]

}

(8)

In the last expression, N denotes the number of created carrier pairs upon interaction with the incident radiation, D is the carrier diffusion constant (governing the diffusion carrier current), S is the surface recombination velocity, τ is the volume recombination lifetime, and all other terms have the usual meanings. Introducing a set of conveniently chosen dimensionless parameters in eq 8, λ ) l/(Dτ)1/2, ξ ) S(τ/D)1/2, Z ) Rl, and R ) ∆σst./ ∆σst.,max., it can be easily shown that in case when surface recombination is large compared to the volume recombination, the relation 8 reduces to a simpler form, i.e.:

{

1 - e-Z R(Z) ) 1+ λ ξ coth 2

()

[

( 2λ ) - Z coth( Z2 )]

ξλ λ coth

λ2 - Z2

} (9)

In cases when surface recombination is negligible compared to the volume recombination (S , D/τ, i.e., ξ , 1), eq 9 becomes very simple:

R(Z) ∝ (1 - e-Z)

(10)

Also, in the case of small sample thickness

Eb eτµ ∆σst. ) + [1 - exp(-R(hν)l)]exp l kBT Et eβµ ηNNcD exp kBT Nt - DN kBT

( )

R(Z) ∝

λ (1 - e-Z) 2ξ

(11)

(7)

In eq 7, N is the doping concentration, Nc is the conduction band density of states, Nt is the density of surface defects at grain boundaries, µ is the charge carrier mobility, l is the film thickness, τ is the excess carrier lifetime, Et is the grain-boundary

In other words, the photoconductivity spectrum shows a wellexpressed maximum followed by a photocurrent decrease with increasing energy of the exciting light, which is obtained only when surface recombination is large compared to the volume recombinationseq 9, or if these two are comparablesin which case the full eq 8 holds.

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Pejova et al.

Aside from the complexity of the dependence of ∆n on R (discussed before), even within the approximations used to derive eq 7, the following conclusions could be derived for the presently studied materials on the basis of this expression. The first term in eq 7, corresponding to so-called ordinary photoconductivity, becomes proportional to R in the limit of low absorption. The second term in eq 7, on the other hand, corresponds to the modulated photoconductivity, which arises as a result of the modulation of Eb by the incident photon flux. It can be clearly seen from Figure 3 that small nonequilibrium conductivity is actually measured at incident photon energies below the Eg value which was found to be ∼1.2 eV in our previous study.46 This part of the photoconductivity response spectrum could be attributed to the reduced value of the grain boundary barrier Eb upon interaction with light. At high photon energies, ∆σst. should become independent of R according to eq 7. However, this behavior is not observed in the present case due to the comparable surface and bulk recombination velocities, as elaborated before. It has been demonstrated that the phenomenological approaches to determine the band gap energy of nanostructured films from the photoconductivity spectral response data are inefficient in both qualitative and quantitative sense (see, e.g., refs 34 and 46). For example, analyzing the current photoconductivity spectrum within the Moss approach71,72 leads to a value of the band gap energy of about 1.7 eV, which is unphysically high. Of course, no conclusions concerning the type of bandto-band transitions could be derived on the basis of this approach. However, in the limit of low absorption of the films (Rl < 1), the photoconductivity spectrum (∆σst./ ∆σst.,max. ) f(hν)) is directly proportional to the absorption spectrum (R ) f (hν)).49 Due to this proportionality, we could employ straightforwardly the Fermi’s golden rule for band-to-band transitions within the framework of parabolic approximation for the dispersion relation to determine the films’ band gap energy. In the expressions arising from Fermi’s golden rule, the function R(hν) is simply replaced by ∆σst.(hν) or ∆σst./∆σst.,max.(hν). To analyze carefully the possible types of interband electronic transitions, in the present study, the dependencies of ((∆σst./∆σst.,max.) × hν)n vs hν for various values of the exponent n were constructed (including n ) 1/2, which has been employed for highly disordered, e.g., amorphous, materials). Clearly manifested linear dependencies of ((∆σst./ ∆σst.,max.) × hν)n on hν were observed only for n ) 2. This suggests that direct band-to-band electronic transitions contribute to the internal photoelectrical effect in the presently studied thin films, which is in line with the conclusions about the band structure of AgBiS2 thin films derived on the basis of the optical spectroscopy data given in our previous paper,46 and also with the available literature data for this material.50,51,53-57 To quantitatively characterize the mentioned transitions, linear least-squares interpolations of the ((∆σst./ ∆σst.,max.) × hν)2 vs hν dependencies in the relevant energy range were carried out. Subsequently, ((∆σst./∆σst.,max.) × hν)2 vs hν dependences were extrapolated to ∆σ × hν ) 0, and the corresponding transition energies were afterward determined on the basis of previously derived correlation equation of the form

((∆σst. /∆σst.,max.) × hν)2 ) const(hν - Eg,dir.)

(12)

The determined value for Eg,dir. is 1.18 eV (Figure 4), which is in good agreement with the value determined from optical spectroscopy data of 1.00 eV. Both of these values are, however,

Figure 4. ((∆σst./∆σst.,max.)hν)2 ) f (hν) dependence for AgBiS2 thin film constituted by 3D QD assemblies of this material (annealed at 250 °C for 40 min), constructed from the photoconductivity response spectrum measured by the constant field method, together with the extrapolation to (∆σst./∆σst.,max.)hν ) 0.

larger than the value corresponding to bulk AgBiS2 specimen (0.90 eV), which is due to 3D quantum confinement effects. We note in this context that the usage of the direct band gap semiconductor absorption function to calculate the band gap energy of the films from the photoresponse data is justified (and such procedure has been often adopted in the literature: see, e.g., ref 34 and references therein) since the quantum confinement effects usually do not change the type of band gap. The discretized energy level structure in each individual quantum dot (nanocrystal) is actually a reminiscence of the original “bulk” band structure, and the essential characteristics of the “starting” bulk bands are retained. Besides, in the present study we deal with a 3D assembly of close-packed nanocrystals, where, due to the interdot coupling, significantly delocalized states arise again.13-20 The good agreement between the band gap energies calculated on the basis of optical spectroscopy and photoconductivity data further confirms the persistence of the quantum confinement effects even in annealed AgBiS2 films (with an average crystal size of 27 nm). This, on the other hand, implies a relatively large value of Bohr’s excitonic radius for this material.46 The ∆σst.(hν) or ∆σst./∆σst.,max.(hν) dependencies, discussed before, were constructed from the measurements of photoconductivity by the constant field method. This method is essentially based on keeping the electric field in the specimen constant, while varying the incident radiation wavelength.73 Certain advantages of this method were implied before, discussing the analysis of our photoconductivity data. An alternative approach to measure the stationary photoconductivity spectral response of a photoconductor is the constant



photocurrent method (CPM). It is based on illumination of the photoconductor with a monochromatic light, varying the incident photon energies, while adjusting the number of incident photons so that the photocurrent in the sample is kept constant.51 Generally, the spectral dependence of the sample’s absorption coefficient, if certain assumptions are fulfilled, is related to the other measured parameters by the equation74

R(hν) ) R0

(

F0 Ip(hν, F) F(hν) Ip,0

)

1/γ

(13)

In this equation, Ip(hv, F) denotes the photoconductivity spectrum, F is the light intensity expressed in number of photons per unit area of the sample, the subscripts “0” refer to some reference energy of the incident photons at which the absorption coefficient was measured by a direct method, and γ is the exponent in the dependence Ip ∼ Fγ. If the steady state concentration of the photogenerated electrons (or holes) is kept constant during the change of the photon energy, and assuming that there is no spectral dependence of the photogenerated electrons’ mobility, the spectral dependence of the “impurity” absorption coefficient is given by the equation

R(hν) )

const. F(hν)

Figure 5. (Rhν)2 ) f (hv) dependence for AgBiS2 thin film constituted by 3D QD assemblies of this material (annealed at 250 °C for 40 min), constructed from the photoconductivity response spectrum measured by the constant photocurrent method, together with the extrapolation to Rhν ) 0.

(14)

which allows obtaining the absorption coefficient R in arbitrary units. Equation 13 has been used in our case to obtain the absolute values of R. The reference value of the absorption coefficient was taken from the optical spectroscopy measurements performed in our previous study.46 For more detailed description of the constant field and the constant photocurrent method, their physical bases, and the working equations for analysis of experimental data, the reader is referred to original and reference works 51 and 73 and references therein. In this context, it is of certain physical significance to test the agreement between the two methodologies with respect to the derived conclusions concerning the band structure parameters of the investigated material. The first quantity with respect to which we make these comparisons is the band gap energy of the 3D QD assemblies. Figure 5 shows a plot of (Rhν)2 vs hν constructed on the basis of constant photocurrent data, together with the extrapolation to Rhν ) 0. The band gap energy, obtained by this procedure (1.13 eV), is in excellent agreement with the one obtained by analysis of the data collected by the constant field method. As can be seen from Figure 5, the (Rhν)2 vs hν dependence displays a very good linearity. This is a further strong indication that the (nano)grains constituting the film are of good crystalline structure, i.e., that the local crystalline structure has been preserved. We devote the last part of the present section to analysis of the temperature-dependent photoconductivity σF data. In Figure 6, the temperature dependences of photocurrent measured for annealed nanostructured AgBiS2 films are presented. Actually, ln(σFT1/2) is plotted vs 1/T for two different illumination intensities (F and F/1024). For analysis of these results, we focused on the data in the temperature range which is not too low, so that the temperature dependence of Ip (and therefore σF) is clearly pronounced, and at the same time not too high for other scattering mechanisms to become important. For a

Figure 6. Dependence of ln(σφT 0.5) on T-1 in the case of annealed films illuminated by flux intensities F/1024 (a) and F (b).

barrier-dominated charge transport under illumination, we can write

44


Pejova et al.

[ ]

σF(T) ∝ exp -

Eσ,F kBT

(15)

The conductivity activation energy under illumination (Eσ,F) is actually proportional to the grain boundary barrier height. Assuming that the leading term in the overall ∆σ is ∆σEb (eq 6), which is true for partially depleted grains, as in the present case, then measuring the temperature dependence of σF at different illumination intensities could give us an insight into the dependence of intercrystalline barrier height on the intensity of incident radiation. Measurements performed at two different values of F, chosen such as F2/F1 ) 1024 (Figure 6), have shown that an increase of flux intensity by a factor of 210 decreases the Eσ value by a factor of 2. 3.2.2. Relaxation Dynamics Phenomena of Nonequilibrium Charge Carriers. To analyze the transient photoconductivity experiments, we first relied on macroscopic kinetic description of the nonequilibrium charge-carriers decay after the light impulse photoexcitation has been switched off. Such decay process can be described by differential equation of the form34,49,54,73

d(∆n) ) -νrec. dt

(16)

In eq 16, ∆n is the concentration of photogenerated charge carriers, while νrec. is the corresponding recombination rate. In the case when the relation between νrec. and ∆n is linear (νrec. ∝ ∆n), the process is linear from a kinetic aspect (first-order kinetics), while in the case when νrec. ∝ (∆n)2, it is a quadratic one (second-order kinetics). The solutions of eq 16 for linear and quadratic recombination dynamics regimes with initial condition ∆n(t ) 0) ) ∆n0 can be written in the form73

∆n(t) ) ∆n0e-t/τ ;

∆n0 ) τβRF

(17)

and

∆n(t) ) ∆n0

1 t√RβγF + 1

;

∆n0 )

RβF γ

(18)

for the first- and second-order kinetics, correspondingly. In eq 17, the phenomenological parameter τ is usually called the photocarrier relaxation time. In eqs 17 and 18, on the other hand, F is the intensity of the incident light, R is the absorption coefficient of the material, β is the quantum yield, and γ is the exponent in the dependence Ip ∼ Fγ. The time decay of nonequilibrium conductivity ∆σ(t) in the mentioned two cases could be described by expressions analogous to eqs 17 and 18. Figure 7a shows a typical oscillogram recorded in the case of thermally annealed AgBiS2 thin film. The oscilloscopically obtained voltage values were first converted to functions of the form ∆σ/∆σmax) f(t). This was done using the formulas which arise from the constant field method;73 once the time-dependent voltage drop data have been acquired by the oscilloscope, at each time point, the voltage drop is converted to nonequilibrium conductivity ∆σ (t). They were further analyzed by interpolation with functions governing the time dependence of photocarrier’s concentration in the case of linear and quadratic recombination regimes. It could be shown from eqs 17 and 18 that such functions are of the form ln(∆σ) ) f(t) and 1/∆σ ) f(t) in the

Figure 7. (a) Typical oscillogram for nanostructured AgBiS2 thin film after switching off the interaction with an impulse of electromagnetic radiation. (b) Dependence of ln(∆σ) on t constructed on the basis of experimental oscillographic data for an AgBiS2 thin film composed of 3D QD assemblies of this material.

case of linear and quadratic recombination, respectively. Linear dependence in a wide t-interval was observed only in the first case (Figure 7b), which indicates that the nonequilibrium charge carrier recombination occurs according to linear relaxation mechanism. The value of the relaxation time, calculated from the slope of ln(∆σ) as a function of t (dln(∆σ)/dt ) -1/τ), was found to be 1.67 ms. This is (on an absolute scale) a relatively high value for the relaxation time of a 3D assembly of semiconductor QDs. From a technological viewpoint, such characteristics suggest that the studied thin film materials could have a potential application in solar cell engineering. Since the title material has not been studied in detail (especially in the low-dimensional or thin film form), to the best of our knowledge there are not any other literature data for τ to compare with. AgBiS2 is a direct band gap material, and the charge carrier recombination could in principle occur via direct band-to-band mechanism (i.e., there are no limitations related to momentum conservation), but its band gap energy is not so small. Therefore, especially accounting for the low-dimensional structure of the currently studied samples, it seems more probable that the dominant charge carrier recombination process occurs via defect states in the forbidden gap of the bulklike part of the grains or via trap states at the grain boundaries. To get a deeper insight into the physical significance of the measured relaxation time, we relied on the elaboration of the basic model of Shockley-Reed-Hall.7,11,73 According to this model, it could be concluded that, under low intensity of the exciting light, the net recombination rate is proportional to the excess concentration of the minority charge carriers. The overall



Shockley-Reed-Hall recombination rate (after light impulse switch-off) is given by the following expression:11

np - ni2 ) τ (n + n1,k) + τn,k(p + p1,k) k)1 p,k N

νrec.,SRH

∑

(19)

In the last equation, ni is the intrinsic carrier concentration, τp(n),k are the average lifetimes of the photogenerated holes (electrons), and n1,k ) Nc exp(Et,k - Ec/(kBT)) and p1,k ) Nν exp (Eν - Et,k/(kBT)); Et.k is the energy level of the kth trap state. It is of special importance for the present work that eq 19 is valid regardless of the exact character of the defect levels which take part in the recombination process (i.e., recombination centers in the bulklike part of the semiconductor or at the grain boundaries). If one assumes that a single defect level, situated deep in the band gap, takes the main part in the recombination of nonequilibrium charge carriers, it could be shown that under low-injection conditions, in the case of n-type semiconductor7,11,73 eq 19 reduces to

νrec,SRH )

p - p0 ∆p ) τp τp

(20)

Within the outlined analysis, the measured phenomenological parameter τ has a simple physical meaning. It is the average lifetime of the minority charge carriers (holes in the present case). Of course, the outlined relatively simple picture which describes the recombination processes could be further elaborated to include some peculiarities which are characteristic for the studied system. First of all, one should keep in mind that the experimentally observable photoconduction properties of a polycrystalline film are actually averaged values over a large number of crystallites. This is particularly important when one deals with thin films composed of nanocrystals. Concerning the photoconductivity relaxation phenomena, it has to be kept in mind that, as noted before, there are two potential barriers which play the dominant role in the overall recombination kinetics. It has been elaborated in detail in the works of Pal et al.57,75,76 that in the case when photoexcitation is achieved by weak illumination intensities (which do not alter essentially the grain boundary drift barriers) the ∆σ should decay exponentially with time. This should be true regardless of whether the drift and the recombination barriers coincide or not. On the other hand, when photoexcitation is achieved by moderate illumination intensities, ∆σ should depend linearly on ln(t). Such a dependence implies a much slower time-decay process. Reanalyzing our experimental oscilloscopic data by plotting the ∆σ vs ln(t) functions, it was found that these dependencies are not linear. This finding is in line with the ones discussed in our previous paper devoted to nanocrystalline SnSe films. 4. Conclusions In the present study, the behavior of photoexcited charge carriers in 3D assemblies of AgBiS2 QDs deposited in thin film form have been investigated. The main results of the study may be summarized as follows: • The stationary photoresponse properties of AgBiS2 nanocrystalline films with average grain size of ∼27 nm were found to be affected to a great extent by the crystal boundary barrier height modulation upon illumination,

besides by interband electronic transitions in the bulklike part of the nanocrystals. Surface and bulk charge carriers’ recombination velocities were found to be comparable. • The band gap energy of the nanostructured films, determined by analysis of the photoconductivity data measured by the constant field method (1.18 eV), was found to be in excellent agreement with the value determined from the constant photocurrent method data (∼1.13 eV). Both values are in agreement with previous optical spectroscopy data and are higher than that characteristic for a bulk specimen of this semiconductor. This was attributed to 3D confinement effects on the charge carrier motions within individual QDs. • In general, the constant photocurrent measurements indicated that the nanograins constituting the film are of good crystalline structure, i.e., with negligible lattice strain. This was confirmed by the structural investigations, too. • The transient photoconductivity of the 3D QD assemblies deposited as thin films was found to relax exponentially with a time constant of 1.67 ms. On the basis of physical argumentsderivedfromextensionsoftheSchokley-Reed-Hall model, the last value has been attributed to average lifetime of minority charge carriers (holes). Acknowledgment. The authors acknowledge the Macedonian Ministry of Education and Science and the Bulgarian Ministry of Education, Youth and Science for financial support (grant BM-1). References and Notes (1) Collier, C. P.; Vossmeyer, T.; Heath, J. R. Annu. ReV. Phys. Chem. 1998, 49, 371. (2) Yoffe, A. D. AdV. Phys. 2001, 50, 1. (3) Yoffe, A. D. AdV. Phys. 2002, 51, 799. (4) Landman, U.; Luedtke, W. D. Faraday Discuss. 2004, 125, 1. (5) Yu, P. Y.; Cardona, M. Fundamentals of Semiconductors; Springer: Berlin, 1999. (6) Seeger, K. Semiconductor Physics; Springer-Verlag: New York, 1997. (7) Dalven, R. Introduction to Applied Solid State Physics; Plenum Press: New York, 1990. (8) Callister, W. D. Materials Science and Engineering; Wiley: New York, 1997. (9) Marder, M. P. Condensed Matter Physics; John Wiley & Sons: New York, 2000. (10) West, A. R. Basic Solid State Chemistry; John Wiley & Sons: New York, 2000. (11) Sze, S. M. Semiconductor DeVices: Physics and Technology; Wiley: New York, 1985. (12) Klingshirin, C. F. Semiconductor Optics; Springer: Berlin, 1997. (13) Kagan, C. R.; Murray, C. B.; Nirmal, M.; Bawendi, M. G. Phys. ReV. Lett. 1996, 76, 1517. (14) Gindele, F.; Westpha¨ling, R.; Woggon, U.; Spanhel, L.; Ptatschek, V. Appl. Phys. Lett. 1997, 71, 2181. (15) Artemyev, M. V.; Bibik, A. I.; Gurinovich, L. I.; Gaponenko, S. V.; Woggon, U. Phys. ReV. B 1999, 60, 1504. (16) Kim, D. E.; Islam, M. A.; Avila, L.; Herman, I. P. J. Phys. Chem. B 2003, 107, 6318. (17) Darugar, Q.; Landes, C.; Link, S.; Schill, A.; El-Sayed, M. A. Chem. Phys. Lett. 2003, 373, 284. (18) Ginger, D. S.; Greenham, N. C. J. Appl. Phys. 2000, 87, 1361. (19) Ginger, D. S.; Dhoot, A. S.; Finlayson, C. E.; Greenham, N. C. Appl. Phys. Lett. 2000, 77, 2816. (20) Jarosz, M. V.; Porter, V. J.; Fisher, B. R.; Mastner, M. A.; Bawendi, M. G. Phys. ReV. B 2004, 70, 195327. (21) Leatherdale, C. A.; Kagan, C. R.; Morgan, N. Y.; Empedocles, S. A.; Kastner, M. A.; Bawendi, M. G. Phys. ReV. B 2000, 62, 2669. (22) Arce, R. D.; Koropecki, R. R.; Olmos, G.; Gennaro, A. M.; Schmidt, J. A. Thin Solid Films 2006, 510, 169. (23) Fedotov, V. A.; Woodford, M.; Jean, I.; Zheludev, N. I. Appl. Phys. Lett. 2002, 80, 1297. (24) Meaudre, M.; Gueunier-Farret, M. E.; Meaudre, R.; Kleider, J. P.; Vignoli, S.; Canut, B. J. Appl. Phys. 2005, 98, 033531. (25) Hla´vka, J. J. Appl. Phys. 1997, 81, 1404.

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