A PbSe thin film is formed when the ionic product of Pb2+
ions exceeds the solubility product of PbSe (≈10−38
at 300 K) [16
]. The deposition process is based on the slow release of Pb2+
ions in the solution. The complexing agent trisodium citrate controls the Pb2+
concentration and slowly releases Pb2+
ions into the solution. The proposed reaction mechanism for formation of PbSe thin films is as follows,
where A is trisodium citrate.
Typical XRD patterns obtained from films grown at different temperatures and at pH 11 are shown in . The observed “d” spacings and the respective prominent peaks correspond to reflections of the (111), (200), (220), (311), (222), (331), (420) and (422) planes and are in good agreement with the standard data (JCPDS No. 06-0354). Thus, the XRD pattern reveals the polycrystalline nature of the as-deposited PbSe thin films with cubic structure.
X-ray diffraction patterns of PbSe thin films prepared at different temperatures.
The most intense peak for each of the samples prepared at 328, 333, 338, and 343 K corresponds to (200), (111), (111) and (220), respectively. This indicates that the orientation of the grain growth for PbSe films prepared at different temperatures is along different directions. The XRD pattern of PbSe prepared at room temperature (303 K) shows peaks for (200), (220), (420) and (422) in addition to several other peaks, which are mainly due to impurity phases (such as Pb, Se, PbO, or other Pb compounds).
The average crystallite size of PbSe thin films prepared at different temperatures calculated using Scherrer’s formula [17
] was found to increase from 23 to 33 nm with an increase of temperature from 303 to 343 K, as shown in . The rate of the deposition reaction increases at higher temperature and the crystallites grow faster resulting in a larger size.
Variation of the average crystallite size of PbSe thin films with the deposition temperature.
The lattice parameter “a” for cubic structure was determined by using the relation
” is the spacing between the planes in the atomic lattice, and (hkl
) are the Miller indices. The lattice constant values are found to be slightly different for different orientations of the same film. The probable explanation for this was given by Mothura et al. [18
]. Therefore, corrected values of the lattice constants were determined from the intercept of the Nelson–Riley plots. The Nelson–Riley curve is plotted between the calculated “a
” for different planes and the error function [19
and the corrected value of “a” is obtained by extrapolating the plot to θ = 90°. A typical Nelson–Riley plot for a PbSe thin film is shown in .
Nelson–Riley plot for PbSe thin film prepared at 338 K.
The lattice parameter is observed to increase slightly from 6.112 to 6.129 Å with deposition temperature. All the values of lattice constant of the as-prepared PbSe thin films were found to be different from the values of the bulk material (6.124 Å, JCPDS 06-0354). The deviation in the values of the lattice constant of the as-prepared PbSe films from the bulk value indicates the presence of strain in the films. The strain in the prepared PbSe films may arise due to the change of lattice nature and concentration of native imperfections during the film formation.
Dislocation density (δ) and microstrain (ε)
The dislocation density (δ) was calculated from Williamson and Smallman’s formula [20
” is a factor, which when equal to unity gives the minimum dislocation density, and “D
” is the average crystallite size. The average microstrain (ε) developed in the as-prepared PbSe films was calculated by using the relation [21
where “β” is the full width at half maximum and θ is the Bragg angle.
It has been observed that the dislocation density and microstrain decrease with increase in crystallite size, as shown in , which indicates a lower number of lattice imperfections. This may be due to a decrease in the occurrence of grain boundaries because of an increase in the crystallite size of the film with increasing temperature.
Variation of (a) dislocation density and (b) microstrain with crystallite size of the PbSe thin films.
Scanning electron microscopy gives valuable information regarding the shape and size of the grains on the surface of the deposited thin films. shows the SEM image of PbSe thin films prepared at 303 K (room temperature), and reveals cube-like structures, which are aggregated. From the SEM image of PbSe prepared at 338 K () and 343 K (), it was observed that the PbSe thin films consisted of spherical grains and were homogenous, without any voids or cracks.
SEM micrograph of PbSe prepared at (a) 303 K (b) 338 K and (c) 343 K.
The crystallite size obtained by XRD is equivalent to the mean size of the domains that scatter X-rays coherently [22
]. The grain size measured from SEM images is the surface morphology of grains that are agglomerated crystallites, leading to larger values of grain size.
X-ray fluorescence (XRF) studies
shows the XRF spectra of PbSe thin films prepared at 333 K. The spectrum exhibits prominent peaks of the Pb Lβ, Pb Lα1, Pb Lα2 and Se Kα1 lines showing the presence of Pb and Se in the prepared films.
XRF spectra of PbSe prepared at 333 K.
The absorption spectra of PbSe thin films recorded at room temperature as a function of wavelength in the range 360–900 nm, is shown in . It shows that the optical absorption of PbSe thin films increases with the deposition temperature. This may be attributed to the increase in crystallite size and decrease in defects. The (αh
ν) plots of PbSe thin films are linear over a wide range of photon energies, as shown in . This indicates the presence of a direct optical band gap in the as-prepared PbSe thin films [23
]. The optical band gap of these films was obtained by extrapolating the linear portion of the curve to the energy axis.
(a) UV absorption spectra; (b) (αhν)2 vs (hν) plots of PbSe thin films.
The band gap so obtained was observed to decrease from 2.10 to 1.96 eV, as the deposition temperature was increased from 328 to 343 K. Typical variation of band gap with crystallite size in the nanocrystalline PbSe thin films is shown in , which indicates an increase in the band gap with a decrease in crystallite size (the structural parameters and band-gap energies are also summarized in ). Clearly, the observed values of E
are higher than the value of the bulk optical band gap of PbSe [0.27 eV] [1
] due to quantum confinement in the nanocrystalline PbSe thin films. Similar changes in the band gap energy “E
” for PbSe thin films with smaller crystallite sizes have been reported for chemically deposited PbSe thin films by Gorer et al. [24
]. The value of the band gap was found to vary from 0.55 to 1.55 eV, depending on the crystallites size, by Gorer et al.
Variation of the band gap with crystallite size of PbSe thin films.
Structural parameters and band-gap energies of PbSe thin films deposited at different temperatures.