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Towards particle size regulation of chemically deposited lead sulfide (PbS)
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Journal of Crystal Growth 280 (2005) 300–308 www.elsevier.com/locate/jcrysgro
Towards particle size regulation of chemically deposited lead sulfide (PbS) A.A. Rempela,b,, N.S. Kozhevnikovab, A.J.G. Leenaersa, S. van den Berghea a SCK-CEN, Boeretang 200, Mol, B-2400, Belgium Institute of Solid State Chemistry, Russian Academy of Sciences, Pervomaiskaya 91, GSP-145, 620219 Yekaterinburg, Russian Federation
b
Received 18 August 2004; accepted 1 March 2005 Available online 26 April 2005 Communicated by J.M. Redwing
Abstract Powders and solid films of lead sulfides (PbS) were produced by chemical bath deposition from thiourea aqueous solutions at a temperature of 325 K. By a Rietveld-like analysis of the X-ray spectra, it was shown that nanocrystalline PbS has the same rock salt structure B1 (space group Fm-3m) as coarse grained or single crystalline PbS. Nevertheless, this B1 structure is a very distorted structure with root mean square displacements up to 0.011 nm and with a microstrain up to 0.3%. The particle sizes in the PbS powders and films measured by scanning electron microscopy (SEM) are found to be in agreement with those determined by Bragg–Brentano X-ray diffraction (XRD) on powders and by glancing incident diffraction (GID) on films. It was found that by changing the chemical affinity in the range from 31.4 to 38.7 kJ/mol, it is possible to regulate the particle size of the chemically deposited sulfide powders from 100 to 300 nm. r 2005 Elsevier B.V. All rights reserved. PACS: 81.20.K; 61.72.Dd; 61.46 Keywords: A1. Nanostructures; A2. Growth from solutions; A3. Chemical bath deposition processes; B1. Sulfides; B2. Semiconducting lead compounds
1. Introduction Corresponding author. Institute of Solid State Chemistry,
Russian Academy of Sciences, Pervomaiskaya 91, GSP-145, 620219 Yekaterinburg, Russian Federation. Tel.: +7343374 73 06; fax: +7343374 44 95. E-mail address: [email protected] (A.A. Rempel).
Lead sulfide (PbS) is an important semiconductor with a narrow band gap. Due to its unique photoconductive properties, PbS is applied as an infrared detector and for mid-infrared lasers [1]. PbS has promising photosensitive properties and is
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a good photocatalyst [2]. The nanoclusters based on sulfur compounds also have great potential as quantum dots. For these applications, PbS with different particle sizes is required. Particle diameters should vary from a few micrometers for infrared detector applications to several nanometers for quantum dots. For the fabrication of PbS, different methods are used at present, namely, chemical deposition, electrodeposition, and molecular beam epitaxy. Among these methods, chemical bath deposition from aqueous solutions has some advantages. Indeed, it permits the routine creation of semiconductor nanocrystals. The size of chemically deposited nanocrystals is also much smaller than what can be realized using molecular beam epitaxy and lithographic methods [3]. The development of the methods of colloid chemistry for quantum dots fabrication has led to practical applications of quantum confinement, such as in solution-processed solar cells, lasers and as biological labels [4]. Nucleation and growth in solution leads to nearly spherical crystals. The spherical shape of nanocrystals is very important, for example, for the energy level spectrum of quantum dots [5]. In contrast, deposition by molecular beam epitaxy and electrodeposition typically yields nonspherical structures. Nanocrystals could also be made by the inverse micelle method [6], but this method is not efficient for creating large crystals or continuous films. In addition, chemical bath deposition involves relatively low costs and is a relatively easy technique. Substrates of various sizes and shapes may be used and no toxic gaseous precursors are needed. Moreover, the chemical bath deposition method allows the production of large volumes of powders and films for industrial applications. So, from one side, the production of PbS by chemical bath deposition is very convenient and useful. From the other side, the mechanisms of chemical bath deposition of sulfides have not been studied sufficiently well. For example, it is still impossible to alter the particle size, i.e. to increase or to reduce it. In the present work, we have systematically studied the influence of a chemical deposition parameter such as the chemical affinity of the
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reaction of PbS formation (i) on the particles size, both in films and powders, (ii) on the particle agglomeration degree, and (iii) on the microstructure of powders and films. To find out whether a correlation exists, the PbS synthesis was performed at different values of chemical affinity. The particle size, agglomeration, and microstructure of PbS films and powders were studied by various techniques: X-ray diffraction (XRD), reflectivity, glancing incident diffraction (GID), and scanning electron microscopy (SEM).
2. Experimental procedure 2.1. Synthesis For the present studies, PbS films and PbS powders were synthesized by chemical bath deposition. The films were deposited on glass substrates. To obtain films with uniform thickness and low roughness, the glass substrate was tilted at 601 during deposition. The powders were collected from solution by the filtering of residues. The chemical bath deposition method is based on a chemical reaction between dissolved precursors in aqueous solutions and can be considered as a particular case of heterogeneous precipitation in solution. The PbS powders and films under investigation are produced from alkaline aqueous solutions of an organic sulfur compound (thiourea) as a sulfur source at a temperature of 325 K. To limit the hydrolysis of the metal ions and the formation of oxygen-containing compounds, chelating agents, such as OH-ions and C6H5O3 7 -ions (Cit3-ions), are used. PbS forms via the overall reaction PbðOHÞCit2 þ ðNH2 Þ2 CS þ OH ! PbS # þH2 NCN þ Cit3 þ 2H2 O: The possibility of sulfide formation is determined by the value of the chemical affinity [7]: A ¼ RT ln ðIP=K sp Þ, where IP is the ionic product, and K sp the solubility product. In the chemical reaction of precipitation, the state of supersaturation for the sulfide is compulsory, i.e. IP should exceed K sp .
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So, positive values of A indicate that the reaction of sulfide formation proceeds spontaneously. Primary concentrations of precursors were calculated by applying thermodynamic analysis based on the thiourea hydrolysis reaction in alkaline medium [8]. The baths were prepared from aqueous solutions of lead acetate Pb(CH3COO)2 (0.1 M), sodium citrate Na3C6H5O7 (1 M), alkaline NaOH (3.8 M) and thiourea (NH2)2CS (0.5 M). The primary concentration regions of precursors in the chemical bath were the following: Pb(CH3COO)2 (from 0.005 to 0.01 M), sodium citrate Na3C6H5O7 (0.025 M), alkaline NaOH (from 0.016 to 0.530 M) and thiourea (NH2)2CS (from 0.025 to 0.5 M), where M is mol/l. Such concentration regions allow depositing not only the residues on the bottom of the reactor but also the films on the substrates. In this work, all specimens of PbS films and powders have been synthesized until the concentrations of lead and sulfur ions in solution achieved the equilibrium concentrations, i.e. decreasing of IP during synthesis down to Ksp. The necessary duration of the deposition reaction was chosen according to the preliminary kinetic experiments. The kinetics of the deposition process follows a sigmoidal profile, similar to those observed for autocatalytic reactions. Description of the reaction profile by a formal kinetic expression allows calculation of the reaction rate and, consequently, the time needed to establish the equilibrium. Furthermore, preliminary studies have shown that the chemical affinity value could affect the number of nuclei (at the start of the deposition process) and finally (after the particle growth is stopped) the size of particles. 2.2. Annealing To study the temperature stability of synthesized PbS, one of the powders, which was deposited by reaction with a chemical affinity of 34.7 kJ/mol, was subjected to annealing. For this purpose, the powder was compacted by uniaxial pressing of 1 MPa into disk-shaped pellets. The specimen was subsequently placed in a quartz tube, which was evacuated to 104 Pa, and sealed off. Before use, the tubes were rinsed with water,
(642)B1
4000 1 - as deposited powder 2 - annealed powder 2 Number of counts
302
3000
2000 1 1000
0
146
148
150 152 154 2 (degree)
156
158
Fig. 1. Narrowing of X-ray spectra of as-deposited powder after annealing. The powder was obtained in reaction with chemical affinity of 34.7 kJ/mol. The spectra are shown in the vicinity of reflection (6 4 2)B1.
ethanol, and acetone and dried at 900–1100 K for 5 min in an oxygen–hydrogen flame. Annealing in evacuated quartz tubes was performed by slow heating at a rate of 10 K/h to temperatures up to 900 K. Before and after annealing, the powder was subjected to XRD analysis. The observed narrowing of the XRD lines (Fig. 1), almost down to the width of the resolution function, indicates that the recrystallization of the powder is completed. 2.3. X-ray diffraction Powders and films of PbS were studied by XRD in Bragg–Brentano geometry and in GID geometry on a Philips X’Pert diffractometer using CuKa1,2 radiation. To determine the position, width and intensity (area) of reflections, each of the a1;2 doublets was fitted using the sum of two Pseudo-Voigt functions: 1 ðy y0 Þ2 V ðyÞ ¼ ca 1 þ b2 ðy y0 Þ2 þ ð1 cÞa exp . ð1Þ 2b2 The position of the a2 reflection was constrained based on the position of the a1 reflection, according to the Wulff–Bragg law and X-ray wavelength values for CuKa1 (l1 ¼ 154:056 pm)
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and CuKa2 (l2 ¼ 154:439 pm). The CuKa2 reflection intensity in a doublet was equal to 0.497 of the CuKa1 reflection intensity. From the positions of the reflections y0 , the lattice constant of a B1 unit cell was determined. For an exact determination of the lattice constant, an extrapolation to 901 was performed, providing an accuracy of 0.1 pm. In order to determine the crystallite size-related broadening of the reflections the full-width at half-maximum (FWHM) of the resolution function (instrumental broadening), FWHMR ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi p utg2 y þ vtgy þ w was measured on lanthanum hexaboride LaB6 NIST Standart Reference Powder 660a with a cubic lattice constant of acubic ¼ 415:69162 0:00097 pm. From the broadening of the reflections, the mean size of the regions of coherent scattering in PbS powders and films was determined. 2.4. Bragg– Brentano Diffractograms were recorded in Bragg–Brentano geometry, using an automatic divergence and antiscatter slit to keep the illuminated area constant and obtain sufficient intensity at higher angles. The illuminated area is chosen at 5 10 mm. To reduce peak widths, a receiving slit size of 0.1 mm is adopted. The profiles were taken in the 2y interval from 101 to 1601 in steps of Dð2yÞ ¼ 0:021 with incident and secondary soller slits of 40 mrad. The parameters for the resolution function for deposited powders were u ¼ 0:0042, v ¼ 0:0022, w ¼ 0:0054 [2y]; for pressed pellets before and after annealing, the parameters were u ¼ 0:0035, v ¼ 0:0032, w ¼ 0:0058 [2y]. 2.5. Glancing incident diffraction For GID measurements, parallel beam geometry is chosen, using a parabolic mirror in the incident beam and a 0.181 collimator to limit the accepted divergence of the diffracted beam. Diffractograms were recorded from 201 to 681 [2y] in steps of 0.021 [2y] with soller slits of 20 mrad. The incident angle was fixed at 0.51. The parameters for the resolution function for deposited films were u ¼ 0:0299, v ¼ 0:0267, w ¼ 0:0630 [2y]. In Fig. 2, the diffraction profile of a
303
à) PbS film measured in GID geometry
(111) (200) (220)
(311) (222) (200) (111)
(400)
b) PbS powder measured in Bragg-Brentano geometry (220) (311) (222)
30
40
50
(400) 60
2(degree) Fig. 2. Comparison of X-ray spectra of PbS film and powder produced in reaction with the same chemical affinity of 32.5 kJ/mol. X-ray measurements on film were made in GID geometry and on powder in Bragg–Brentano geometry. The Miller’s indices for a B1 structure are shown additionally.
film obtained by GID is shown together with the profile obtained in Bragg–Brentano geometry on the residue from the same chemical bath deposition experiment.
2.6. Reflectivity For the study of the density and roughness of the films, the X-ray reflection technique was used. For reflectivity measurements, a y 2y measurement is performed in parallel beam geometry between y ¼ 01 and y ¼ 11. Before the measurements, the system was carefully aligned. The experimental profile (see Fig. 3) was modeled as described in Ref. [9]. The calculated critical angle of 0.351 [y] for the PbS film, with a density of 7.59 g/cm3, approximately coincides with the experimental critical angle of 0.401 [y]. The thickness has been found to be 60 nm. The root mean square roughness of the films is calculated to be about 4 nm. The roughness of a film is mainly caused by discontinuity of the films. Indeed, the films are not monocrystalline but consist of a set of separated spherical-shaped nanoparticles on a substrate.
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304
106
Experimental critical angle
20000
16000
105
14000
Calculated critical angle
Number of counts
18000
104 103
12000 10000 0.395
0.400
0.405
102 0.2
0.4
0.6 (degree)
0.8
1.0
Fig. 3. X-ray reflectivity measured on PbS film deposited at affinity of 34.9 kJ/mol. Points show experimental data, solid line shows simulated function, arrow shows calculated critical angle of 0.351[y] for PbS with density of 7.59 g/cm3. The inset shows that experimentally observed critical angle is equal to 0.401[y].
Fig. 4. Microstructure of PbS powder which was deposited at the value of chemical affinity of 32.5 kJ/mol. The mean size of single particles measured by SEM is about 120 nm.
2.7. Scanning electron microscopy The film and residue microstructures were studied with SEM using a Jeol JSM6310 microscope at an accelerating voltage of 15 keV, with an aperture of 50 mm, and at a working distance of 15 cm. For the best resolution, the secondary electron (SE) regime with low beam current was used. For observing the topology of the sample, a backscattered electron image (BEI) was recorded. Two examples of microstructures of residue and film produced in the same chemical bath deposition experiment as observed by SEM, are shown in Figs. 4 and 5 respectively.
3. Results and discussion For the present studies, a number of chemical deposition experiments with various chemical reaction affinities A in the range from 31.4 to 38.7 kJ/mol (see Table 1) were performed. Normally, in this A range, both PbS film and residue are formed during the chemical reaction. But in a few experiments (specimens No. 3 and 5, see Table 1), only residues were formed. According to Ref. [10], good-quality (adherent) metal sulfide films are only obtained from baths which are supersaturated with respect to the precipitation of
Fig. 5. Microstructure of PbS film chemically deposited on glass with chemical affinity of 32.5 kJ/mol. The mean size of isolated particles measured by SEM is about 200 nm.
metal hydroxide species, irrespective of the substrate used. Our experiments are proving this point of view. And in experiments No. 3 and 5 (see Table 1) films were not formed, because the thermodynamical requirements for lead hydroxide Pb(OH)2 formation were not fulfilled. In this work, each monocrystalline particle is suggested to grow from one nucleus. The size of the monocrystalline particle is supposed to be equal to the size of the coherent X-ray scattering region.
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Table 1 Comparison of the particle sizes in chemically bath-deposited PbS determined by X-ray diffraction and scanning electron microscopy techniques Specimen
Chemical affinity A (kJ/mol)
Mean PbS formation rate in solution (g/(l min))
Powder 1
Mean particle size hDi (nm)
X-ray diffraction
Scanning electron microscopy
Bragg– Brentano geometry
Single particle size
Agglomerate size
100
900–2000
100715 31.4
0.007
Film
70710
Powder 2
110715 32.5
0.011
34.7
0.016
34.9
0.017
37.5
0.017
38.7
0.017
Film 3
230720
Powder Powder
4
Powder 6 Film
bð2yÞ ¼
ðFWHMexper Þ2 ðFWHMR Þ2 was cacu-
lated after determination of the FWHM of all experimental reflections FWHMexper. It should be
120
500–1000 No agglomeration
200
600–800
160715
170
800–1200
90
No agglomeration
230720
250
800–1500
300720
300
1000–1300
300
No agglomeration
230720
For the determination of the size of the coherent X-ray scattering region, an analysis of angular dependence of X-ray peak broadening has been carried out using the Williamson–Hall method [11]. This method suggests that the experimentally estimated value of broadening bð2yÞ can be attributed to both small particle size bs and microstrain bd . Thus, bð2yÞ is a superposition of size broadening bs and strainqffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi broadening bd . ffi 2 2 According to Ref. [12], bð2yÞ ¼ bs þ bd . Particle size broadening obeys the Scherrer–Warren equation [13] D ¼ K hkl l= ðcos y bs ð2yÞÞ. The equation bd ð2yÞ ¼ 4 tan y reflects peak broadening due to the microstrain [11]. That microstrain ( ¼ Dd=d) is a result of a distribution of both tensile and compressive forces and causes variations of the interplanar spacings d q around the average. Line broadening ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi
No agglomeration
200
110710
Powder
80
180720
Film 5
Glancing incident diffraction
mentioned that bð2yÞ 2bðyÞ. The FWHM was calculated when the experimental reflection was fitted by the pseudo-Voigt function (1) using a representation of FWHM in the following form FWHM ¼ bð2:355 0:276c 0:079c2 Þ [14]. The shape factor of particle Khkl was calculated according to Ref. [15]. Small particle size alone gives a horizontal plot b ð2yÞ ¼ bð2yÞ cos y=l against the scattering vector s ¼ 2 sin y=l. In case this plot has a nonzero slope, the average crystallite size D corresponds to the value 1=b ð2yÞ at s ¼ 0. The fact that strain-caused diffraction peak broadening follows a tan y function whereas crystallite size broadening has a 1= cos y dependence allows to separate these two effects. The microstrain is equal to the slope of b ð2yÞ versus s. Calculations have shown that the produced PbS particles in powders vary in diameter from 100 to 300 nm (Table 1) and that the residual strain in the PbS under investigation varies from 0.3% to 0.2%. It is found that the microstrain is higher for smaller crystallites.
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In addition to particle size and residual strain, the full-profile analysis of X-ray powder spectra allows the determination of the lattice constant (accuracy of 0.1 pm) and the root mean square displacements of the lead atoms in PbS. It has been found that the reduction in crystallite size from 300 to 100 nm is followed by a lattice constant pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi aB1 ¼ d hkl h2 þ k2 þ l 2 increase from 593.7 to 594.0 pm. The increase of the lattice constant up to 0.3 pm is several times higher than the inaccuracy of the lattice constant measurements and therefore it can be successfully employed for the analysis of the defects while crystallite size reduces. In order to get further information, additional studies on point defects, nonstoichiometry, dislocations, impurities and microstrain are to be performed. The root mean square displacements of the lead qffiffiffiffiffiffiffi atoms u¯ 2Pb decreases from 11 pm for specimens with smaller particle size (D ¼ 100 nm) to 8 pm for specimens with larger particle size (D ¼ 300 nm). The fact that the root mean square displacements for small nanoparticles are larger than for big particles proves the nonequilibrium state of nanoparticles. The values of mean particle sizes (regions of coherent scattering) determined by XRD are shown in Table 1. The particle sizes in the PbS residues were determined by XRD in Bragg– Brentano geometry. It can be seen from Table 1 that the particle sizes increase from 100 to 300 nm with increasing chemical affinity from 31.4 to 38.7 kJ/mol. The correlation between particle size in the residue and chemical affinity of the deposition reaction has a linear behavior (Fig. 6). The found correlation is the most interesting result of the present work. The size of the particles composing the PbS films was determined by GID and is also shown in Table 1. A less-pronounced but analogous correlation between particle size and chemical affinity could be seen, also for the films. To determine the microstructure of the residues and films, SEM was used. Two examples are given in Figs. 4 and 5. In addition, SEM allowed to verify the particle sizes determined by XRD (see Table 1) and to establish if the regions of coherent scattering coincide with the particles or, in other
350 PbS
300 Particle size D (nm)
306
X-ray diffraction scanning electron microscopy
250 200 150 100 50 30
32
34 36 38 Chemical affinity A (kJ/mol)
40
Fig. 6. Linear approximation (solid line) of dependence of particle size (region of coherent scattering) D via chemical affinity A of reaction of deposition of PbS powders shows strong correlation between these two values.
words, whether the particles seen by microscopy are monocrystalline. The results of the SEM study have shown that particles forming residues are strongly agglomerated in contrast to the particles in the films. The resolution of the SEM was sufficient to see single particles in residue agglomerates (Fig. 4). Discussing the residues, it can be concluded that the maximum particle size corresponds to the size of the agglomerates and not to monocrystals (Table 1), and the minimum size is the single-crystal size coinciding with that determined by XRD. Furthermore, the agglomeration degree, i.e. the number of particles in an agglomerate, appears to increase while the chemical affinity decreases (see Table 1). The particles observed by SEM on films are isolated and have the same size as determined by XRD, so the observed particles on films (in contrast to residues) are monocrystalline. SEM also showed that the films with a small particle size (D ¼ 100 nm) are more solid and continuous than the films formed by larger particles (D ¼ 200 nm). In Fig. 5, it is seen that the film with particles of D ¼ 200 nm consists of regularly shaped, isolated single crystals. From the XRD data on the size of monocrystalline particles, it is possible to determine the number of monocrystals produced from one unit of volume of reaction bath Ndif. From the other
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side, the chemical method based on kinetics gave the information of the real number of nuclei arising in solution Nkin. Because both values estimated for powder PbS (specimen No. 1, see Table 1) by XRD (N dif ¼ 1:4 1015 ) and chemical [8] methods (N kin ¼ 2:4 1015 ) are approximately equal, it can be concluded that the PbS particles formed from one unit of reaction bath volume are single crystals. Thus, during the particle growth process from one nucleus, one single crystal appeared. Having calculated the number of nuclei arising in one unit of volume, the mean distance R between these nuclei may be estimated via R ¼ ð6 103 =pNÞ1=3 0:12 N 1=3 ðmÞ. Our calculations gave the following results: for powder with D ¼ 100 nm the distance R 1 mm, and for powder with D ¼ 300 nm the distance R 4 mm. So, judging by the results obtained, to reduce the particle size the number of nuclei has to be increased or the distance between nuclei appearing at the start of chemical (deposition) reaction has to be below 1 mm. According to the annealing experiment, the temperature of 900 K, which is about 0.6 of the melting temperature (1391 K) of PbS, allows a complete recrystallization of the powder (see Fig. 1). Therefore, the annealing experiment has proven the nanocrystalline state of the particles of the PbS powder. Indeed, it is known that for nanocrystalline materials the recrystallization temperature is about 0.5 of the melting temperature [16]. In contrast, for bulk materials it is equal to 0.8–0.9 of the melting temperature.
4. Summary By using the thermodynamic constants, the concentration regions of formation for both residues and thin films of PbS are calculated and proven experimentally. To be able to reach equilibrium during the deposition, kinetic studies are performed. By full profile XRD analysis, the size of monocrystalline particles was estimated. The correlation between the size of particles of PbS powders and the chemical affinity was established. The smallest particle sizes of the synthesized powder and film are measured to be
307
100 and 70 nm, respectively. To decrease the particle size further, it is necessary to increase the number of nuclei or to reduce the distance between nuclei appearing at the start of chemical (deposition) reaction. Also, it was found that the PbS powders are strongly agglomerated. In contrast to powders, the PbS films are formed by monocrystalline single particles, this is an important feature for quantum dot production. The technique of PbS production discussed in the present work can be applied for the production of nanocrystalline powders and thin solid films of individual sulfides of metals of groups 11–14 and their solid solutions.
Acknowledgments The authors are indebted for discussion with Prof. E. van Walle. Two first authors (AAR and NSK) thank the Russian Foundation for Basic Research (No. 05–03–32500 and 03–03–32033) for financial support.
References [1] G. Bauer, H. Clemens, Semicond. Sci. Technol. 5 (1990) S122. [2] D. Beydoun, R. Amal, G. Low, S.J. McEvoy, Nanopart. Res. 1 (1999) 439. [3] A.P. Alivisatos, Science 271 (1996) 933. [4] D.J. Milliron, S.M. Hughes, Y. Cui, L. Manna, J. Li, L.-W. Wang, A.P. Alivisatos, Nature 430 (2004) 190. [5] Z. Hens, D. Vanmaekelbergh, E.J.A.J. Stoffels, H. van Kempen, Phys. Rev. Lett. 88 (2002) 236803. [6] A.R. Kortan, R. Hull, R.L. Opila, M.G. Bawendi, M.L. Steigerwald, P.J. Carroll, L.E. Brus, J. Am. Chem. Soc. 112 (1990) 1327. [7] I. Prigogine, R. Defay, Chemical Thermodynamics, Longmans, London, 1962, p. 543. [8] N.S. Belova, A.A. Rempel, Russ. J. Inorg. Mater. 40 (2003) 7. [9] D.K.G. De Boer, A.J.G. Leenaers, W.W. Van Hoogenholf, X-ray Spectrom. 24 (1995) 91. [10] P. O’Brien, J. McAleese, J. Mater. Chem. 8 (1998) 2309. [11] G.K. Williamson, W.H. Hall, Acta Metall. 1 (1953) 22. [12] L. Pasquini, A.A. Rempel, R. Wu¨rschum, K. Reimann, M.A. Mu¨ller, B. Fultz, H.-E. Schaefer, Phys. Rev. B 63 (2001) 1.
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[13] B.E. Warren, X-ray Diffraction, Dower Publications, New York, 1990, p. 381. [14] N. Belova, A. Uritskaya, A. Kurlov, A. Rempel, Proceedings X APAM Topical Seminar and conference ‘‘Materials of Siberia’’ ‘‘Nanoscience and Technology’’, Novosibirsk, 2003, p. 396.
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Journal of Crystal Growth 280 (2005) 300–308 www.elsevier.com/locate/jcrysgro
Towards particle size regulation of chemically deposited lead sulfide (PbS) A.A. Rempela,b,, N.S. Kozhevnikovab, A.J.G. Leenaersa, S. van den Berghea a SCK-CEN, Boeretang 200, Mol, B-2400, Belgium Institute of Solid State Chemistry, Russian Academy of Sciences, Pervomaiskaya 91, GSP-145, 620219 Yekaterinburg, Russian Federation
b
Received 18 August 2004; accepted 1 March 2005 Available online 26 April 2005 Communicated by J.M. Redwing
Abstract Powders and solid films of lead sulfides (PbS) were produced by chemical bath deposition from thiourea aqueous solutions at a temperature of 325 K. By a Rietveld-like analysis of the X-ray spectra, it was shown that nanocrystalline PbS has the same rock salt structure B1 (space group Fm-3m) as coarse grained or single crystalline PbS. Nevertheless, this B1 structure is a very distorted structure with root mean square displacements up to 0.011 nm and with a microstrain up to 0.3%. The particle sizes in the PbS powders and films measured by scanning electron microscopy (SEM) are found to be in agreement with those determined by Bragg–Brentano X-ray diffraction (XRD) on powders and by glancing incident diffraction (GID) on films. It was found that by changing the chemical affinity in the range from 31.4 to 38.7 kJ/mol, it is possible to regulate the particle size of the chemically deposited sulfide powders from 100 to 300 nm. r 2005 Elsevier B.V. All rights reserved. PACS: 81.20.K; 61.72.Dd; 61.46 Keywords: A1. Nanostructures; A2. Growth from solutions; A3. Chemical bath deposition processes; B1. Sulfides; B2. Semiconducting lead compounds
1. Introduction Corresponding author. Institute of Solid State Chemistry,
Russian Academy of Sciences, Pervomaiskaya 91, GSP-145, 620219 Yekaterinburg, Russian Federation. Tel.: +7343374 73 06; fax: +7343374 44 95. E-mail address: [email protected] (A.A. Rempel).
Lead sulfide (PbS) is an important semiconductor with a narrow band gap. Due to its unique photoconductive properties, PbS is applied as an infrared detector and for mid-infrared lasers [1]. PbS has promising photosensitive properties and is
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a good photocatalyst [2]. The nanoclusters based on sulfur compounds also have great potential as quantum dots. For these applications, PbS with different particle sizes is required. Particle diameters should vary from a few micrometers for infrared detector applications to several nanometers for quantum dots. For the fabrication of PbS, different methods are used at present, namely, chemical deposition, electrodeposition, and molecular beam epitaxy. Among these methods, chemical bath deposition from aqueous solutions has some advantages. Indeed, it permits the routine creation of semiconductor nanocrystals. The size of chemically deposited nanocrystals is also much smaller than what can be realized using molecular beam epitaxy and lithographic methods [3]. The development of the methods of colloid chemistry for quantum dots fabrication has led to practical applications of quantum confinement, such as in solution-processed solar cells, lasers and as biological labels [4]. Nucleation and growth in solution leads to nearly spherical crystals. The spherical shape of nanocrystals is very important, for example, for the energy level spectrum of quantum dots [5]. In contrast, deposition by molecular beam epitaxy and electrodeposition typically yields nonspherical structures. Nanocrystals could also be made by the inverse micelle method [6], but this method is not efficient for creating large crystals or continuous films. In addition, chemical bath deposition involves relatively low costs and is a relatively easy technique. Substrates of various sizes and shapes may be used and no toxic gaseous precursors are needed. Moreover, the chemical bath deposition method allows the production of large volumes of powders and films for industrial applications. So, from one side, the production of PbS by chemical bath deposition is very convenient and useful. From the other side, the mechanisms of chemical bath deposition of sulfides have not been studied sufficiently well. For example, it is still impossible to alter the particle size, i.e. to increase or to reduce it. In the present work, we have systematically studied the influence of a chemical deposition parameter such as the chemical affinity of the
301
reaction of PbS formation (i) on the particles size, both in films and powders, (ii) on the particle agglomeration degree, and (iii) on the microstructure of powders and films. To find out whether a correlation exists, the PbS synthesis was performed at different values of chemical affinity. The particle size, agglomeration, and microstructure of PbS films and powders were studied by various techniques: X-ray diffraction (XRD), reflectivity, glancing incident diffraction (GID), and scanning electron microscopy (SEM).
2. Experimental procedure 2.1. Synthesis For the present studies, PbS films and PbS powders were synthesized by chemical bath deposition. The films were deposited on glass substrates. To obtain films with uniform thickness and low roughness, the glass substrate was tilted at 601 during deposition. The powders were collected from solution by the filtering of residues. The chemical bath deposition method is based on a chemical reaction between dissolved precursors in aqueous solutions and can be considered as a particular case of heterogeneous precipitation in solution. The PbS powders and films under investigation are produced from alkaline aqueous solutions of an organic sulfur compound (thiourea) as a sulfur source at a temperature of 325 K. To limit the hydrolysis of the metal ions and the formation of oxygen-containing compounds, chelating agents, such as OH-ions and C6H5O3 7 -ions (Cit3-ions), are used. PbS forms via the overall reaction PbðOHÞCit2 þ ðNH2 Þ2 CS þ OH ! PbS # þH2 NCN þ Cit3 þ 2H2 O: The possibility of sulfide formation is determined by the value of the chemical affinity [7]: A ¼ RT ln ðIP=K sp Þ, where IP is the ionic product, and K sp the solubility product. In the chemical reaction of precipitation, the state of supersaturation for the sulfide is compulsory, i.e. IP should exceed K sp .
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So, positive values of A indicate that the reaction of sulfide formation proceeds spontaneously. Primary concentrations of precursors were calculated by applying thermodynamic analysis based on the thiourea hydrolysis reaction in alkaline medium [8]. The baths were prepared from aqueous solutions of lead acetate Pb(CH3COO)2 (0.1 M), sodium citrate Na3C6H5O7 (1 M), alkaline NaOH (3.8 M) and thiourea (NH2)2CS (0.5 M). The primary concentration regions of precursors in the chemical bath were the following: Pb(CH3COO)2 (from 0.005 to 0.01 M), sodium citrate Na3C6H5O7 (0.025 M), alkaline NaOH (from 0.016 to 0.530 M) and thiourea (NH2)2CS (from 0.025 to 0.5 M), where M is mol/l. Such concentration regions allow depositing not only the residues on the bottom of the reactor but also the films on the substrates. In this work, all specimens of PbS films and powders have been synthesized until the concentrations of lead and sulfur ions in solution achieved the equilibrium concentrations, i.e. decreasing of IP during synthesis down to Ksp. The necessary duration of the deposition reaction was chosen according to the preliminary kinetic experiments. The kinetics of the deposition process follows a sigmoidal profile, similar to those observed for autocatalytic reactions. Description of the reaction profile by a formal kinetic expression allows calculation of the reaction rate and, consequently, the time needed to establish the equilibrium. Furthermore, preliminary studies have shown that the chemical affinity value could affect the number of nuclei (at the start of the deposition process) and finally (after the particle growth is stopped) the size of particles. 2.2. Annealing To study the temperature stability of synthesized PbS, one of the powders, which was deposited by reaction with a chemical affinity of 34.7 kJ/mol, was subjected to annealing. For this purpose, the powder was compacted by uniaxial pressing of 1 MPa into disk-shaped pellets. The specimen was subsequently placed in a quartz tube, which was evacuated to 104 Pa, and sealed off. Before use, the tubes were rinsed with water,
(642)B1
4000 1 - as deposited powder 2 - annealed powder 2 Number of counts
302
3000
2000 1 1000
0
146
148
150 152 154 2 (degree)
156
158
Fig. 1. Narrowing of X-ray spectra of as-deposited powder after annealing. The powder was obtained in reaction with chemical affinity of 34.7 kJ/mol. The spectra are shown in the vicinity of reflection (6 4 2)B1.
ethanol, and acetone and dried at 900–1100 K for 5 min in an oxygen–hydrogen flame. Annealing in evacuated quartz tubes was performed by slow heating at a rate of 10 K/h to temperatures up to 900 K. Before and after annealing, the powder was subjected to XRD analysis. The observed narrowing of the XRD lines (Fig. 1), almost down to the width of the resolution function, indicates that the recrystallization of the powder is completed. 2.3. X-ray diffraction Powders and films of PbS were studied by XRD in Bragg–Brentano geometry and in GID geometry on a Philips X’Pert diffractometer using CuKa1,2 radiation. To determine the position, width and intensity (area) of reflections, each of the a1;2 doublets was fitted using the sum of two Pseudo-Voigt functions: 1 ðy y0 Þ2 V ðyÞ ¼ ca 1 þ b2 ðy y0 Þ2 þ ð1 cÞa exp . ð1Þ 2b2 The position of the a2 reflection was constrained based on the position of the a1 reflection, according to the Wulff–Bragg law and X-ray wavelength values for CuKa1 (l1 ¼ 154:056 pm)
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and CuKa2 (l2 ¼ 154:439 pm). The CuKa2 reflection intensity in a doublet was equal to 0.497 of the CuKa1 reflection intensity. From the positions of the reflections y0 , the lattice constant of a B1 unit cell was determined. For an exact determination of the lattice constant, an extrapolation to 901 was performed, providing an accuracy of 0.1 pm. In order to determine the crystallite size-related broadening of the reflections the full-width at half-maximum (FWHM) of the resolution function (instrumental broadening), FWHMR ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi p utg2 y þ vtgy þ w was measured on lanthanum hexaboride LaB6 NIST Standart Reference Powder 660a with a cubic lattice constant of acubic ¼ 415:69162 0:00097 pm. From the broadening of the reflections, the mean size of the regions of coherent scattering in PbS powders and films was determined. 2.4. Bragg– Brentano Diffractograms were recorded in Bragg–Brentano geometry, using an automatic divergence and antiscatter slit to keep the illuminated area constant and obtain sufficient intensity at higher angles. The illuminated area is chosen at 5 10 mm. To reduce peak widths, a receiving slit size of 0.1 mm is adopted. The profiles were taken in the 2y interval from 101 to 1601 in steps of Dð2yÞ ¼ 0:021 with incident and secondary soller slits of 40 mrad. The parameters for the resolution function for deposited powders were u ¼ 0:0042, v ¼ 0:0022, w ¼ 0:0054 [2y]; for pressed pellets before and after annealing, the parameters were u ¼ 0:0035, v ¼ 0:0032, w ¼ 0:0058 [2y]. 2.5. Glancing incident diffraction For GID measurements, parallel beam geometry is chosen, using a parabolic mirror in the incident beam and a 0.181 collimator to limit the accepted divergence of the diffracted beam. Diffractograms were recorded from 201 to 681 [2y] in steps of 0.021 [2y] with soller slits of 20 mrad. The incident angle was fixed at 0.51. The parameters for the resolution function for deposited films were u ¼ 0:0299, v ¼ 0:0267, w ¼ 0:0630 [2y]. In Fig. 2, the diffraction profile of a
303
à) PbS film measured in GID geometry
(111) (200) (220)
(311) (222) (200) (111)
(400)
b) PbS powder measured in Bragg-Brentano geometry (220) (311) (222)
30
40
50
(400) 60
2(degree) Fig. 2. Comparison of X-ray spectra of PbS film and powder produced in reaction with the same chemical affinity of 32.5 kJ/mol. X-ray measurements on film were made in GID geometry and on powder in Bragg–Brentano geometry. The Miller’s indices for a B1 structure are shown additionally.
film obtained by GID is shown together with the profile obtained in Bragg–Brentano geometry on the residue from the same chemical bath deposition experiment.
2.6. Reflectivity For the study of the density and roughness of the films, the X-ray reflection technique was used. For reflectivity measurements, a y 2y measurement is performed in parallel beam geometry between y ¼ 01 and y ¼ 11. Before the measurements, the system was carefully aligned. The experimental profile (see Fig. 3) was modeled as described in Ref. [9]. The calculated critical angle of 0.351 [y] for the PbS film, with a density of 7.59 g/cm3, approximately coincides with the experimental critical angle of 0.401 [y]. The thickness has been found to be 60 nm. The root mean square roughness of the films is calculated to be about 4 nm. The roughness of a film is mainly caused by discontinuity of the films. Indeed, the films are not monocrystalline but consist of a set of separated spherical-shaped nanoparticles on a substrate.
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304
106
Experimental critical angle
20000
16000
105
14000
Calculated critical angle
Number of counts
18000
104 103
12000 10000 0.395
0.400
0.405
102 0.2
0.4
0.6 (degree)
0.8
1.0
Fig. 3. X-ray reflectivity measured on PbS film deposited at affinity of 34.9 kJ/mol. Points show experimental data, solid line shows simulated function, arrow shows calculated critical angle of 0.351[y] for PbS with density of 7.59 g/cm3. The inset shows that experimentally observed critical angle is equal to 0.401[y].
Fig. 4. Microstructure of PbS powder which was deposited at the value of chemical affinity of 32.5 kJ/mol. The mean size of single particles measured by SEM is about 120 nm.
2.7. Scanning electron microscopy The film and residue microstructures were studied with SEM using a Jeol JSM6310 microscope at an accelerating voltage of 15 keV, with an aperture of 50 mm, and at a working distance of 15 cm. For the best resolution, the secondary electron (SE) regime with low beam current was used. For observing the topology of the sample, a backscattered electron image (BEI) was recorded. Two examples of microstructures of residue and film produced in the same chemical bath deposition experiment as observed by SEM, are shown in Figs. 4 and 5 respectively.
3. Results and discussion For the present studies, a number of chemical deposition experiments with various chemical reaction affinities A in the range from 31.4 to 38.7 kJ/mol (see Table 1) were performed. Normally, in this A range, both PbS film and residue are formed during the chemical reaction. But in a few experiments (specimens No. 3 and 5, see Table 1), only residues were formed. According to Ref. [10], good-quality (adherent) metal sulfide films are only obtained from baths which are supersaturated with respect to the precipitation of
Fig. 5. Microstructure of PbS film chemically deposited on glass with chemical affinity of 32.5 kJ/mol. The mean size of isolated particles measured by SEM is about 200 nm.
metal hydroxide species, irrespective of the substrate used. Our experiments are proving this point of view. And in experiments No. 3 and 5 (see Table 1) films were not formed, because the thermodynamical requirements for lead hydroxide Pb(OH)2 formation were not fulfilled. In this work, each monocrystalline particle is suggested to grow from one nucleus. The size of the monocrystalline particle is supposed to be equal to the size of the coherent X-ray scattering region.
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Table 1 Comparison of the particle sizes in chemically bath-deposited PbS determined by X-ray diffraction and scanning electron microscopy techniques Specimen
Chemical affinity A (kJ/mol)
Mean PbS formation rate in solution (g/(l min))
Powder 1
Mean particle size hDi (nm)
X-ray diffraction
Scanning electron microscopy
Bragg– Brentano geometry
Single particle size
Agglomerate size
100
900–2000
100715 31.4
0.007
Film
70710
Powder 2
110715 32.5
0.011
34.7
0.016
34.9
0.017
37.5
0.017
38.7
0.017
Film 3
230720
Powder Powder
4
Powder 6 Film
bð2yÞ ¼
ðFWHMexper Þ2 ðFWHMR Þ2 was cacu-
lated after determination of the FWHM of all experimental reflections FWHMexper. It should be
120
500–1000 No agglomeration
200
600–800
160715
170
800–1200
90
No agglomeration
230720
250
800–1500
300720
300
1000–1300
300
No agglomeration
230720
For the determination of the size of the coherent X-ray scattering region, an analysis of angular dependence of X-ray peak broadening has been carried out using the Williamson–Hall method [11]. This method suggests that the experimentally estimated value of broadening bð2yÞ can be attributed to both small particle size bs and microstrain bd . Thus, bð2yÞ is a superposition of size broadening bs and strainqffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi broadening bd . ffi 2 2 According to Ref. [12], bð2yÞ ¼ bs þ bd . Particle size broadening obeys the Scherrer–Warren equation [13] D ¼ K hkl l= ðcos y bs ð2yÞÞ. The equation bd ð2yÞ ¼ 4 tan y reflects peak broadening due to the microstrain [11]. That microstrain ( ¼ Dd=d) is a result of a distribution of both tensile and compressive forces and causes variations of the interplanar spacings d q around the average. Line broadening ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi
No agglomeration
200
110710
Powder
80
180720
Film 5
Glancing incident diffraction
mentioned that bð2yÞ 2bðyÞ. The FWHM was calculated when the experimental reflection was fitted by the pseudo-Voigt function (1) using a representation of FWHM in the following form FWHM ¼ bð2:355 0:276c 0:079c2 Þ [14]. The shape factor of particle Khkl was calculated according to Ref. [15]. Small particle size alone gives a horizontal plot b ð2yÞ ¼ bð2yÞ cos y=l against the scattering vector s ¼ 2 sin y=l. In case this plot has a nonzero slope, the average crystallite size D corresponds to the value 1=b ð2yÞ at s ¼ 0. The fact that strain-caused diffraction peak broadening follows a tan y function whereas crystallite size broadening has a 1= cos y dependence allows to separate these two effects. The microstrain is equal to the slope of b ð2yÞ versus s. Calculations have shown that the produced PbS particles in powders vary in diameter from 100 to 300 nm (Table 1) and that the residual strain in the PbS under investigation varies from 0.3% to 0.2%. It is found that the microstrain is higher for smaller crystallites.
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In addition to particle size and residual strain, the full-profile analysis of X-ray powder spectra allows the determination of the lattice constant (accuracy of 0.1 pm) and the root mean square displacements of the lead atoms in PbS. It has been found that the reduction in crystallite size from 300 to 100 nm is followed by a lattice constant pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi aB1 ¼ d hkl h2 þ k2 þ l 2 increase from 593.7 to 594.0 pm. The increase of the lattice constant up to 0.3 pm is several times higher than the inaccuracy of the lattice constant measurements and therefore it can be successfully employed for the analysis of the defects while crystallite size reduces. In order to get further information, additional studies on point defects, nonstoichiometry, dislocations, impurities and microstrain are to be performed. The root mean square displacements of the lead qffiffiffiffiffiffiffi atoms u¯ 2Pb decreases from 11 pm for specimens with smaller particle size (D ¼ 100 nm) to 8 pm for specimens with larger particle size (D ¼ 300 nm). The fact that the root mean square displacements for small nanoparticles are larger than for big particles proves the nonequilibrium state of nanoparticles. The values of mean particle sizes (regions of coherent scattering) determined by XRD are shown in Table 1. The particle sizes in the PbS residues were determined by XRD in Bragg– Brentano geometry. It can be seen from Table 1 that the particle sizes increase from 100 to 300 nm with increasing chemical affinity from 31.4 to 38.7 kJ/mol. The correlation between particle size in the residue and chemical affinity of the deposition reaction has a linear behavior (Fig. 6). The found correlation is the most interesting result of the present work. The size of the particles composing the PbS films was determined by GID and is also shown in Table 1. A less-pronounced but analogous correlation between particle size and chemical affinity could be seen, also for the films. To determine the microstructure of the residues and films, SEM was used. Two examples are given in Figs. 4 and 5. In addition, SEM allowed to verify the particle sizes determined by XRD (see Table 1) and to establish if the regions of coherent scattering coincide with the particles or, in other
350 PbS
300 Particle size D (nm)
306
X-ray diffraction scanning electron microscopy
250 200 150 100 50 30
32
34 36 38 Chemical affinity A (kJ/mol)
40
Fig. 6. Linear approximation (solid line) of dependence of particle size (region of coherent scattering) D via chemical affinity A of reaction of deposition of PbS powders shows strong correlation between these two values.
words, whether the particles seen by microscopy are monocrystalline. The results of the SEM study have shown that particles forming residues are strongly agglomerated in contrast to the particles in the films. The resolution of the SEM was sufficient to see single particles in residue agglomerates (Fig. 4). Discussing the residues, it can be concluded that the maximum particle size corresponds to the size of the agglomerates and not to monocrystals (Table 1), and the minimum size is the single-crystal size coinciding with that determined by XRD. Furthermore, the agglomeration degree, i.e. the number of particles in an agglomerate, appears to increase while the chemical affinity decreases (see Table 1). The particles observed by SEM on films are isolated and have the same size as determined by XRD, so the observed particles on films (in contrast to residues) are monocrystalline. SEM also showed that the films with a small particle size (D ¼ 100 nm) are more solid and continuous than the films formed by larger particles (D ¼ 200 nm). In Fig. 5, it is seen that the film with particles of D ¼ 200 nm consists of regularly shaped, isolated single crystals. From the XRD data on the size of monocrystalline particles, it is possible to determine the number of monocrystals produced from one unit of volume of reaction bath Ndif. From the other
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side, the chemical method based on kinetics gave the information of the real number of nuclei arising in solution Nkin. Because both values estimated for powder PbS (specimen No. 1, see Table 1) by XRD (N dif ¼ 1:4 1015 ) and chemical [8] methods (N kin ¼ 2:4 1015 ) are approximately equal, it can be concluded that the PbS particles formed from one unit of reaction bath volume are single crystals. Thus, during the particle growth process from one nucleus, one single crystal appeared. Having calculated the number of nuclei arising in one unit of volume, the mean distance R between these nuclei may be estimated via R ¼ ð6 103 =pNÞ1=3 0:12 N 1=3 ðmÞ. Our calculations gave the following results: for powder with D ¼ 100 nm the distance R 1 mm, and for powder with D ¼ 300 nm the distance R 4 mm. So, judging by the results obtained, to reduce the particle size the number of nuclei has to be increased or the distance between nuclei appearing at the start of chemical (deposition) reaction has to be below 1 mm. According to the annealing experiment, the temperature of 900 K, which is about 0.6 of the melting temperature (1391 K) of PbS, allows a complete recrystallization of the powder (see Fig. 1). Therefore, the annealing experiment has proven the nanocrystalline state of the particles of the PbS powder. Indeed, it is known that for nanocrystalline materials the recrystallization temperature is about 0.5 of the melting temperature [16]. In contrast, for bulk materials it is equal to 0.8–0.9 of the melting temperature.
4. Summary By using the thermodynamic constants, the concentration regions of formation for both residues and thin films of PbS are calculated and proven experimentally. To be able to reach equilibrium during the deposition, kinetic studies are performed. By full profile XRD analysis, the size of monocrystalline particles was estimated. The correlation between the size of particles of PbS powders and the chemical affinity was established. The smallest particle sizes of the synthesized powder and film are measured to be
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100 and 70 nm, respectively. To decrease the particle size further, it is necessary to increase the number of nuclei or to reduce the distance between nuclei appearing at the start of chemical (deposition) reaction. Also, it was found that the PbS powders are strongly agglomerated. In contrast to powders, the PbS films are formed by monocrystalline single particles, this is an important feature for quantum dot production. The technique of PbS production discussed in the present work can be applied for the production of nanocrystalline powders and thin solid films of individual sulfides of metals of groups 11–14 and their solid solutions.
Acknowledgments The authors are indebted for discussion with Prof. E. van Walle. Two first authors (AAR and NSK) thank the Russian Foundation for Basic Research (No. 05–03–32500 and 03–03–32033) for financial support.
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