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Raman spectroscopy of CdS nanocrystalline semiconductors
Physica B 262 (1999) 31—39
Raman spectroscopy of CdS nanocrystalline semiconductors K.K. Nanda , S.N. Sarangi , S.N. Sahu *, S.K. Deb, S.N. Behera Institute of Physics, Sachivalaya Marg, Bhubaneswar-751005, India Solid State Physics Division, Bhaba Atomic Research Center, Bombay-400 085, India Received 9 May 1997; received in revised form 30 January 1998; accepted 23 July 1998
Abstract Raman scattering measurements were performed on nanostructured II—VI semiconductor CdS prepared by a chemical route. The Raman spectrum shows a low-frequency wing at 295 cm\ besides the characteristic first-order longitudinal optical phonon (1LO) mode at 305 cm\ when excited with a laser of wavelength 457.9 nm. The observed variation of the Raman shifts, widths and intensities of these two lines with the size of the nanoparticles is consistent with the interpretation that the low-frequency peak is a surface phonon (SP) mode. Increasing the wavelength of the exciting laser lowers the intensity of the LO mode, while shifting the lower-frequency SP mode to the higher-frequency side and simultaneously increases its width. This anomalous behavior is attributed to the possible electron hole excitation by the SP due to the presence of a continuum of localized and acceptor states within CdS band gap. The effect of temperature, on these modes, is also studied and discussed. 1999 Elsevier Science B.V. All rights reserved. Keywords: Semiconductors; CdS; Optical properties; Electron—phonon interaction; Surface roughness
1. Introduction Resonant Raman scattering has emerged as a unique probe for the study of atomic clusters as well as cluster assembled [1] and nanostructured [2] materials. It is well known that in a crystalline insulator or semiconductor the observed Raman shifts usually correspond to the longitudinal optical phonons (LO) whereas other modes such as the transverse optic (TO) and the surface phonon (SP) modes are not observable because of symmetry restrictions and their low intensities, respectively. But in the case of nanostructured materials the
* Corresponding author. E-mail: [email protected].
quantum size effects [3] come into play besides the enhancement of the surface to volume ratio which makes it plausible for the observation of SP mode by Raman scattering [2]. The present work is devoted to a detailed study of Raman scattering observation of the SP mode in CdS nanocrystalline semiconductors. Some preliminary results of this study are reported elsewhere [4]. However, the observation of SP modes in nanostructured CdS particles of a single size prepared by the technique The Raman data reported in this paper was taken at the Laser Lab of BARC Mumbai and the AFM data by Dr. S. Tripathi, TIFR Mumbai on samples prepared at IOP, Bhubaneswar. The acknowledgement is inadvertently omitted in this paper.
0921-4526/99/$ — see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 8 ) 0 0 4 7 4 - 8
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K.K. Nanda et al. / Physica B 262 (1999) 31—39
of thiophenol capping has been reported earlier by Deb et al. [5]. It is of some interest to compare the results of Raman measurements on sample prepared by different techniques. Besides the results reported so far are preliminary and a better understanding of these systems requires a more detailed study. In [5] a low-frequency shoulder at 292 cm\ to the LO phonon peak at 305 cm\ was observed in the Raman spectra of the thiophenol capped CdS particles. The estimated size of the particles being 23 As , the observed low-frequency peak was identified as the SP mode. In contrast Raman scattering measurements on CdS-nanostructured particles of different sizes prepared by a chemical route was reported in Ref. [4], where the behavior of the observed LO peak at 305 cm\ and the low-frequency wing at 295 cm\ was studied as a function of the size of the particles. It was found that the Raman intensity and the full-width at half-maximum (FWHM) of both the LO peak as well as the low-frequency peak decreases on going from nanocrystalline to bulk samples. On the other hand, the ratio of the intensities of the lowfrequency peak to the LO mode decreases at first on increasing size of the particles but then it saturates. In contrast a surface phonon mode is expected to show the following characteristic behavior: (i) with decreasing crystalline size the surface to volume ratio increases, hence the peak intensity should increase, (ii) the FWHM of the peak should increase with decreasing crystalline size, because of increasing disorder, (iii) if the nanoparticle is embedded in a medium the peak should shift to lower frequency if the dielectric constant of the medium increases and (iv) the SP mode should be located between the bulk TO (transverse optic) and LO modes. Thus, the observed low-frequency wing in the Raman spectra of CdS while satisfying the last criteria partially fulfills the first two [4] lending credentials to its interpretation as the SP mode. But the observed saturation rather than vanishing of the intensity ratio with increasing size has raised doubts regarding this identification. Fortunately, the AFM measurements of the surface topography indicated that the surface roughness increases with increasing thickness of the nanoparticle-deposited film. This provided a satisfactory explanation of the saturation of the intensity ratio because with in-
creasing surface roughness the Raman intensity of the SP mode is expected to grow while with increasing size of nanoparticles it is expected to diminish, thus leading to a saturation of the ratio [4]. In this paper more Raman scattering studies of the CdS nanostructured films are reported which can throw light on the identification of the SP mode. These measurements are carried out on a sample of a given size using different wavelengths of laser excitation, which show strong dependence of the SP mode on the exciting frequency. The plan of the rest of the paper is as follows: Section 2 is devoted to a brief description of the salient features of the technique of sample preparation and their characterization. The Raman scattering data are presented and analyzed in Section 3. A plausible theoretical explanation for the anomalous behavior of the Raman data, is presented in Section 4. In Section 5 we conclude by summarizing the main results.
2. Preparation and characterization of nanostructured CdS films CdS semiconductor films of different crystalline sizes have been grown on glass substrates chemically by a precipitation technique. The chemicals used for CdS synthesis are CdSO , thiourea, and NH OH. The different crystalline size are obtained by controlling the reaction time period, temperature and pH of the solution. Details of the preparation procedure is published elsewhere [6,7]. The composition/thickness and impurity analysis were carried out by Rutherford backscattering (RBS) and proton induced X-ray emission (PIXE) measurements using the 3MV peletron accelerator at Institute of Physics (IOP). PIXE analysis identified no impurities at ppm level. Presence of Cd, S and surface oxygen could be detected by RBS analysis which gave Cd to S ratio as 1.01 for the sample in which the thickness of the film is 1.4 lm which corresponds to bulk CdS. This sample is designated as S1. Three other CdS samples of different crystalline sizes/thicknesses have been studied and those are designated as S2, S3 and S4, respectively. Samples S2 and S3 have Cd to S ratio of 1.07 and 1.26 and thicknesses of 75 and 50 nm, respectively.
K.K. Nanda et al. / Physica B 262 (1999) 31—39
The last sample S4 has a thickness of 35 nm and a Cd to S compositional ratio of 1.4. The thickness of the various samples as estimated here may not be accurate because of the difficulties with RBS studies on non-uniform samples. However the deviation from stoichiometry and increase in Cd content with decreasing thickness of the film is noteworthy. The RBS and AFM studies [4] besides giving the average thickness of the films, also indicate that their surface roughness increases with increasing thickness. On the other hand, the size of the crystalline nanoparticles in these deposited films are estimated from the change in band gaps [8] determined from the optical absorption data. Thus the sizes of the nanoparticles can be related to the band gaps through the quantum size effect using the hyperbolic band model [9]. The sample S1 has band gap of 2.405 eV which corresponds to a size of 75 nm for crystalline nanoparticles. Similarly, the samples S2 and S3 have band gaps of 2.65 and 2.85 eV, respectively, with the corresponding sizes of the nanoparticles being 7.5 and 5.5 nm.
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temperature (300 K) in the back scattering geometry using the Ar>-ion laser with excitation wavelengths of 457.9, 488 and 514.7 nms. Sample S4 was too thin to give any detectable Raman signal. Since CdS nanoparticles are deposited on a glass substrate, rather than embedded in glass as in Ref. [2], the surrounding medium in our case is air for all the samples. The laser power is adjusted to 40 mW to avoid laser heating and coalescence of the nanoparticles. The scattered intensities were analyzed using a double monochromator with a standard detection system. The data were analyzed by fitting the intensity of the peaks to Lorentzian functions. The frequency-dependent background intensity was fitted to a polynomial and subtracted out from the raw data. A typical example of background subtraction along with the Raman peaks for the sample S2 is shown in Fig. 1. The function form of the two Lorentzians which were then fitted
3. Raman measurements and analysis Resonant Raman (RR) scattering measurements were performed on all the samples S1—S4, at room
Fig. 1. Representative case of background fitting for the sample S2 (j "457.9 nm).
Fig. 2. Resonant Raman spectra of CdS samples (S1—S3) at 300° K. The excitation source is 457.9 nm Ar> laser. The samples parameters are described in the text.
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to the peak and the shoulder is given by I(u)" A uC A uC *- *# (1) (u!u)#(C u) (u !u)#(C u) **where A (A ), u (u ) and C (C ) are, respective *- * *ly, the oscillator strength, frequency and line width of the mode corresponding to the shoulder (LO phonon). The parameters A , u and **C were obtained by fitting two Lorentzian to the *experimental data points. The fitted curves are represented by the solid lines, whereas the dashed lines represent the peaks corresponding to the individual modes. The first-order Raman spectra of the three samples S1, S2 and S3 using the 457.9 nm excitation is shown in Fig. 2, which shows the characteristic LO phonon with a shoulder in the low-frequency wing identified as the SP mode. The spectra depicted in Fig. 2 show the expected size dependence and have been analyzed and interpreted in Ref. [4] as mentioned earlier in the introduction.
The observed Raman spectra for all the three samples (Fig. 2) show the LO phonon frequency at 305 cm\ along with a shoulder at 295 cm\ in the low-frequency wing which agrees well with the result reported [2,5,10]. The two prominent peaks at 305 and 295 cm\ are denoted P1 and P2, respectively in the figures. It is to be noted that the Raman intensities of the peaks P1 as well as P2 decreases as one goes from nanocrystalline to bulk samples. Similarly, the width (FWHM) of P1 decreases from 14.14 to 12.67 cm\ and that of P2 changes from 8.43 to 8.33 cm\ on increasing the size from nanocrystalline to bulk samples. These results are shown in Fig. 3 and the observations are in conformity with the interpretation of the observed shoulder in the low-frequency wing as the surface phonon (SP) mode [4]. It is to be noted that the excitation energy of 2.7 eV (wavelength 457.9 nm) while satisfying the resonance condition for samples S1 and S2 (band gaps 2.405 and 2.65 eV) falls short of 0.15 eV in the case of the samples S3 (band gap 2.85 eV). It is expected that at resonance, the
Fig. 3. (a) Raman intensity; (b) FWHM; (c) Raman frequency and (d) the intensity ratio (I /I ) as a function of thickness/crystalline . . size. The excitation wavelength is 457.9 nm. P1 and P2 are the respective Raman peaks as shown in Fig. 1.
K.K. Nanda et al. / Physica B 262 (1999) 31—39
Fig. 4. The Raman spectra of sample S2 with different excitation wavelength, j (a) j"457.9 nm; (b) j"488 and (c) j"514.5 nm. Note that the low-frequency wing P2 shifts to higher frequency as the excitation wavelength is increased.
Raman intensity of the LO mode will be enhanced which will mask the weak SP mode resulting in a broad LO peak. To test this hypothesis, the Raman spectra were recorded using two other laser excitation wavelengths of 488 and 514.5 nm on the single sample S2. The results are presented in Fig. 4. The spectra while clearly showing the enhancement of the intensity of the LO phonon at resonance depict very anomalous behavior of the shoulder corresponding to the SP mode. As the excitation energy gets off resonance the shoulder shows a predominant shift from the lower-frequency (&291 cm\) to the higher-frequency (&330 cm\) wing. The variation of the intensity, width, frequency shift and the ratio of the intensities of the two peaks P2 and P1 as a function of excitation wavelength are plotted in Fig. 5 a—d. The width of peak P2 decreases slightly with increasing excitation
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wavelength while that of the peak P1 shows slight broadening as shown in Fig. 5c. However there is a drastic reduction in intensity of both the peaks P1 and P2 when excited with the laser of wavelength 514.5 nms; compared to the spectra excited by the other two shorter wavelength photons. This can be the result of going off resonance in the scattering because this long wavelength excitation corresponds to an energy of &2.4 eV, which falls short off the band gap by about 0.25 eV. Therefore, one needs to understand the predominant shifting of the peak P2 to higher frequencies and its narrowing while the peak P1 softens and broadens when the excitation frequency of the laser is lowered to offresonance. The observed Raman peaks under off-resonance scattering conditions when excited by the laser of wavelength 514.5 nms, also exhibit a temperature dependence which is shown in Fig. 6. At low temperature (70 K) there is a loss of intensity of the peak P1 and an increase in that of P2. On the other hand, the frequency of P1 hardens and that of P2 softens while the width of P1 decreases and that of P2 increases. The decrease in intensity of the phonon Raman peaks at low temperatures is expected because of the availability of lesser number of phonons. Similarly the hardening and narrowing of the LO phonon peak P1 at low temperatures can be attributed to the decrease in anharmonicity. But the softening and widening of the P2 peak on lowering the temperature is indicative of an incipient change in the surface structure.
4. An interpretation of the anomalies: The size dependence of the intensity of the shoulder to the LO peaks observed in the Raman spectra as depicted in Fig. 2, together with the feature that its frequency lies in the gap between the TO and the LO modes qualifies it to be identified as the surface mode. However, the dramatic shift of this mode to the high-frequency wing on lowering the excitation frequency of the laser, seems to disqualify it to be a surface mode. Looking for an alternate interpretation, the natural suggestion that emerges is that it could be an impurity mode. As mentioned earlier the CdS nanoparticles have excess Cd, the
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K.K. Nanda et al. / Physica B 262 (1999) 31—39
Fig. 5. (a) Raman intensity; (b) FWHM; (c) Raman frequency and (d) intensity ratio I /I as a function of excitation wavelength. P1 . . and P2 are the respective Raman peaks as shown in Fig. 3.
amount of which increases on decreasing the size. If the observed mode is attributed to these Cd impurities one can understand the increase in intensity with decreasing size of these nanoparticles, but it is not possible to explain why the mode should shift to higher frequencies on decreasing the frequency of the exciting photons. The excess Cd in these systems will form interstitial defects. Hence, if these materials are to give rise to a mode, with a frequency lower than LO mode, which is like a resonant mode, it is essential that the force constant binding the interstitial to the neighbors must soften. But then the mode moves to the high-frequency wing when excited with lower-frequency photons; thus behaving like a localized mode necessitating the hardening of the force constants. Why such a change in the force constants will occur is simply not understandable. Besides the observed softening (Fig. 6) and broadening of the mode on lowering the temperature simply rules out its interpretation as an impurity mode. The only other alternative interpretation is to invoke a rather strong coupling of the mode to the charge carriers [11] in the system. As a consequence
of such a strong charge carrier—phonon interaction, the phonon can acquire a self-energy which will result in an increase in the frequency of the mode. In order to establish the feasibility of such a mechanism, it is necessary to examine qualitative feature of the electronic structure of the semiconductor nanoparticles. These nanoparticles have the crystalline structure of their bulk counter parts and hence are characterized by the fully occupied valence band and an empty conduction band separated by the energy gap (E ). However, the charge carriers in these bands e.g., the electrons in the conduction band and holes in the valence band experience an overall confining potential due to the finite size of these particles. As a result there will be size-dependent discrete states in the conduction and valence bands resulting in the effective enhancement of the band gap; the so-called quantum size effect. It has been argued that in these semiconductor nanoparticles the hyperbolic band model [9] gives a better fit to the observed quantum size effect as compared to the effective mass approximation. The present method of the preparation of the CdS nanoparticles described in Section 2 does not
K.K. Nanda et al. / Physica B 262 (1999) 31—39
Fig. 6. The Resonant Raman Spectra of sample S2 at (a) 300°K and (b) 70°K. The excitation wavelength is 514.7 nm.
produce size-selected particles. Hence, the nanoparticles have a size distribution around a mean size. This in turn will lead to a bunching of the localized quantum confined states in the conduc-
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tion and the valence bands. Over and above there is excess Cd in the CdS nanoparticles. It is known that excess Cd can produce acceptor states within the gap of CdS [8,12]. These states together with those originating from quantum size effect will form a continuum of localized states near the valence band edge. The experimental observation of two additional peaks in the photoluminescence spectra of these CdS nanoparticles [8], one lower in energy and the other of higher energy than the bulk peak further corroborates the qualitative picture of the electronic structure shown schematically in Fig. 7. In fact a similar model without the effect of size distribution of the nanoparticles was originally proposed [8] to explain the photoluminescence data. But we shall argue that it is the latter effect namely the bunching of localized states due to size distribution which is crucial in the proposed understanding of the observed shift to higher frequency of the Raman peak corresponding to the surface mode. Normally all these localized states in the valence band except the ones arising from the Cd-acceptor states are occupied by electrons. On shining these nanoparticles with the laser of frequency greater than the effective band gap the electrons are resonantly excited to the localized states in the conduction band and there is resonant Raman scattering due to recombination of the electrons and holes. The resonant scattering being an efficient process,
Fig. 7. Schematic band diagram of CdS (a) buk; (b) size-selected nanoparticles showing descrete states and (c) size distributed nanoparticles and the presence of Cd acceptor results in bunching of electronic states.
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K.K. Nanda et al. / Physica B 262 (1999) 31—39
cited to the conduction band across the gap, they are available for the phonons to interact with these charge carriers. Thus, the phonon acquires a selfenergy which shifts its frequency to higher values. The calculation of the self-energy involves the Lindhard function in the case of metals, whereas in the present case of semiconductor nanoparticles the energies of the localized states will enter the evaluation of the Lindhard function. What still remains a puzzle is why the surface phonon mode couples so strongly to the charge carriers while the LO mode does not. These questions and the details of the calculation will be the subject matter of a future work. 5. Conclusion
Fig. 8. (a) Resonant Raman scattering process for which the energy of the laser beam is greater than the band gap of the semiconductor. In this process electron—hole pairs are created by the absorption of photons. These electron/hole emit a phonon before they recombine to give back a photon. (b) non-resonant scattering process for which the energy of the laser beam is smaller than the band gap of the semiconductors. The energy is not sufficient to excite electron from the valence band to the conduction band. But states are available near the valence band edge for the phonons to interact as a result of which electron—hole pairs are created in the continuum of localized states. The phonon acquires a self-energy which shifts the frequency of SP mode to higher values. The Feynman diagram for the processes are also shown.
the observed Raman phonons have a higher intensity. The recombination lifetimes being much smaller than the phonon lifetime, the phonons do not interact with the charge carriers in the system in the resonant Raman scattering process. On the other hand, when the exciting photon has a frequency less than the effective band gap, the scattering is nonresonant, thereby, there is a suppression of the intensities of the Raman shifted phonons. This is observed in Fig. 3b and c. But then the phonons now can interact with the electrons in the valence band and excite electron-hole pair in the continuum of localized states, which recombine to re emit the phonon, as shown in Fig. 8. Since in the non-resonant process the electrons are not ex-
Raman scattering measurements were performed on CdS semiconductor films having different crystalline sizes with different excitations. Beside the 1LO phonon mode, a peak at the low-frequency wing has been observed with excitation of 457.9 nm. But the low-frequency peak shifts to higher frequency as the excitation energy is decreased. The variations of the Raman shifts, widths and intensities of both the peaks with the size of the nanoparticles is consistent with the interpretation of the low-frequency wing as a SP mode. The anomaly with different excitations is attributed to the off-resonance scattering as the energy of the laser beam is less than the band gap of the material. It is argued that in this case the phonon acquires a self-energy that shifts the frequency of the SP mode to higher values. Acknowledgements Partial financial support received from IFCPAR project No. 1508-4 is gratefully acknowledged. The authors acknowledge Prof. V.S. Ramamurthy for helpful discussions. References [1] P. Melinon et al., Int. J. Mod. Phys. B 9 (1995) 339. [2] A. Mlayah, A.M. Brugman, R. Carles, J.B. Renucci, M.Ya. Valakh, A.V. Pogorelov, Solid State Commun. 90 (1994) 567 and references therein.
K.K. Nanda et al. / Physica B 262 (1999) 31—39 [3] S. Hayashi, H. Sanda, M. Agata, K. Yamamoto, Phys. Rev. B 40 (1989) 5544. [4] K.K. Nanda, S.N. Sahu, Appl. Surf. Sci. 119 (1997) 50. [5] S.K. Deb, A.P. Roy, M. Kundu, A.A. Khosravi, S.K. Kulkarni, Solid State Physics Symp., India, 1995. [6] S.N. Sahu, J. Mater. Sci. Mater. Electron 6 (1995) 43. [7] S.N. Sahu, S. Chandra, Solar Cells 22 (1987) 163. [8] K.K. Nanda, S.N. Sarangi, S.N. Mohanty, S.N. Sahu, Thin Solid Films 322 (1998) 21.
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[9] Y. Wang, A. Suna, W. Mahler, R. Kasowski, J. Chem. Phys. 87 (1987) 7315. [10] R. Rosetti, S. Nakahara, L.E. Brus, J. Chem. Phys. 79 (1983) 1086. [11] M.C. Klein, F. Hache, D. Ricard, C. Flytzanis, Phys. Rev. B 42 (1990) 11123. [12] S.M. Sze, Semiconductor Devices: Physics and Technology, Wiley, New York, 1985.
Raman spectroscopy of CdS nanocrystalline semiconductors K.K. Nanda , S.N. Sarangi , S.N. Sahu *, S.K. Deb, S.N. Behera Institute of Physics, Sachivalaya Marg, Bhubaneswar-751005, India Solid State Physics Division, Bhaba Atomic Research Center, Bombay-400 085, India Received 9 May 1997; received in revised form 30 January 1998; accepted 23 July 1998
Abstract Raman scattering measurements were performed on nanostructured II—VI semiconductor CdS prepared by a chemical route. The Raman spectrum shows a low-frequency wing at 295 cm\ besides the characteristic first-order longitudinal optical phonon (1LO) mode at 305 cm\ when excited with a laser of wavelength 457.9 nm. The observed variation of the Raman shifts, widths and intensities of these two lines with the size of the nanoparticles is consistent with the interpretation that the low-frequency peak is a surface phonon (SP) mode. Increasing the wavelength of the exciting laser lowers the intensity of the LO mode, while shifting the lower-frequency SP mode to the higher-frequency side and simultaneously increases its width. This anomalous behavior is attributed to the possible electron hole excitation by the SP due to the presence of a continuum of localized and acceptor states within CdS band gap. The effect of temperature, on these modes, is also studied and discussed. 1999 Elsevier Science B.V. All rights reserved. Keywords: Semiconductors; CdS; Optical properties; Electron—phonon interaction; Surface roughness
1. Introduction Resonant Raman scattering has emerged as a unique probe for the study of atomic clusters as well as cluster assembled [1] and nanostructured [2] materials. It is well known that in a crystalline insulator or semiconductor the observed Raman shifts usually correspond to the longitudinal optical phonons (LO) whereas other modes such as the transverse optic (TO) and the surface phonon (SP) modes are not observable because of symmetry restrictions and their low intensities, respectively. But in the case of nanostructured materials the
* Corresponding author. E-mail: [email protected].
quantum size effects [3] come into play besides the enhancement of the surface to volume ratio which makes it plausible for the observation of SP mode by Raman scattering [2]. The present work is devoted to a detailed study of Raman scattering observation of the SP mode in CdS nanocrystalline semiconductors. Some preliminary results of this study are reported elsewhere [4]. However, the observation of SP modes in nanostructured CdS particles of a single size prepared by the technique The Raman data reported in this paper was taken at the Laser Lab of BARC Mumbai and the AFM data by Dr. S. Tripathi, TIFR Mumbai on samples prepared at IOP, Bhubaneswar. The acknowledgement is inadvertently omitted in this paper.
0921-4526/99/$ — see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 8 ) 0 0 4 7 4 - 8
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of thiophenol capping has been reported earlier by Deb et al. [5]. It is of some interest to compare the results of Raman measurements on sample prepared by different techniques. Besides the results reported so far are preliminary and a better understanding of these systems requires a more detailed study. In [5] a low-frequency shoulder at 292 cm\ to the LO phonon peak at 305 cm\ was observed in the Raman spectra of the thiophenol capped CdS particles. The estimated size of the particles being 23 As , the observed low-frequency peak was identified as the SP mode. In contrast Raman scattering measurements on CdS-nanostructured particles of different sizes prepared by a chemical route was reported in Ref. [4], where the behavior of the observed LO peak at 305 cm\ and the low-frequency wing at 295 cm\ was studied as a function of the size of the particles. It was found that the Raman intensity and the full-width at half-maximum (FWHM) of both the LO peak as well as the low-frequency peak decreases on going from nanocrystalline to bulk samples. On the other hand, the ratio of the intensities of the lowfrequency peak to the LO mode decreases at first on increasing size of the particles but then it saturates. In contrast a surface phonon mode is expected to show the following characteristic behavior: (i) with decreasing crystalline size the surface to volume ratio increases, hence the peak intensity should increase, (ii) the FWHM of the peak should increase with decreasing crystalline size, because of increasing disorder, (iii) if the nanoparticle is embedded in a medium the peak should shift to lower frequency if the dielectric constant of the medium increases and (iv) the SP mode should be located between the bulk TO (transverse optic) and LO modes. Thus, the observed low-frequency wing in the Raman spectra of CdS while satisfying the last criteria partially fulfills the first two [4] lending credentials to its interpretation as the SP mode. But the observed saturation rather than vanishing of the intensity ratio with increasing size has raised doubts regarding this identification. Fortunately, the AFM measurements of the surface topography indicated that the surface roughness increases with increasing thickness of the nanoparticle-deposited film. This provided a satisfactory explanation of the saturation of the intensity ratio because with in-
creasing surface roughness the Raman intensity of the SP mode is expected to grow while with increasing size of nanoparticles it is expected to diminish, thus leading to a saturation of the ratio [4]. In this paper more Raman scattering studies of the CdS nanostructured films are reported which can throw light on the identification of the SP mode. These measurements are carried out on a sample of a given size using different wavelengths of laser excitation, which show strong dependence of the SP mode on the exciting frequency. The plan of the rest of the paper is as follows: Section 2 is devoted to a brief description of the salient features of the technique of sample preparation and their characterization. The Raman scattering data are presented and analyzed in Section 3. A plausible theoretical explanation for the anomalous behavior of the Raman data, is presented in Section 4. In Section 5 we conclude by summarizing the main results.
2. Preparation and characterization of nanostructured CdS films CdS semiconductor films of different crystalline sizes have been grown on glass substrates chemically by a precipitation technique. The chemicals used for CdS synthesis are CdSO , thiourea, and NH OH. The different crystalline size are obtained by controlling the reaction time period, temperature and pH of the solution. Details of the preparation procedure is published elsewhere [6,7]. The composition/thickness and impurity analysis were carried out by Rutherford backscattering (RBS) and proton induced X-ray emission (PIXE) measurements using the 3MV peletron accelerator at Institute of Physics (IOP). PIXE analysis identified no impurities at ppm level. Presence of Cd, S and surface oxygen could be detected by RBS analysis which gave Cd to S ratio as 1.01 for the sample in which the thickness of the film is 1.4 lm which corresponds to bulk CdS. This sample is designated as S1. Three other CdS samples of different crystalline sizes/thicknesses have been studied and those are designated as S2, S3 and S4, respectively. Samples S2 and S3 have Cd to S ratio of 1.07 and 1.26 and thicknesses of 75 and 50 nm, respectively.
K.K. Nanda et al. / Physica B 262 (1999) 31—39
The last sample S4 has a thickness of 35 nm and a Cd to S compositional ratio of 1.4. The thickness of the various samples as estimated here may not be accurate because of the difficulties with RBS studies on non-uniform samples. However the deviation from stoichiometry and increase in Cd content with decreasing thickness of the film is noteworthy. The RBS and AFM studies [4] besides giving the average thickness of the films, also indicate that their surface roughness increases with increasing thickness. On the other hand, the size of the crystalline nanoparticles in these deposited films are estimated from the change in band gaps [8] determined from the optical absorption data. Thus the sizes of the nanoparticles can be related to the band gaps through the quantum size effect using the hyperbolic band model [9]. The sample S1 has band gap of 2.405 eV which corresponds to a size of 75 nm for crystalline nanoparticles. Similarly, the samples S2 and S3 have band gaps of 2.65 and 2.85 eV, respectively, with the corresponding sizes of the nanoparticles being 7.5 and 5.5 nm.
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temperature (300 K) in the back scattering geometry using the Ar>-ion laser with excitation wavelengths of 457.9, 488 and 514.7 nms. Sample S4 was too thin to give any detectable Raman signal. Since CdS nanoparticles are deposited on a glass substrate, rather than embedded in glass as in Ref. [2], the surrounding medium in our case is air for all the samples. The laser power is adjusted to 40 mW to avoid laser heating and coalescence of the nanoparticles. The scattered intensities were analyzed using a double monochromator with a standard detection system. The data were analyzed by fitting the intensity of the peaks to Lorentzian functions. The frequency-dependent background intensity was fitted to a polynomial and subtracted out from the raw data. A typical example of background subtraction along with the Raman peaks for the sample S2 is shown in Fig. 1. The function form of the two Lorentzians which were then fitted
3. Raman measurements and analysis Resonant Raman (RR) scattering measurements were performed on all the samples S1—S4, at room
Fig. 1. Representative case of background fitting for the sample S2 (j "457.9 nm).
Fig. 2. Resonant Raman spectra of CdS samples (S1—S3) at 300° K. The excitation source is 457.9 nm Ar> laser. The samples parameters are described in the text.
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to the peak and the shoulder is given by I(u)" A uC A uC *- *# (1) (u!u)#(C u) (u !u)#(C u) **where A (A ), u (u ) and C (C ) are, respective *- * *ly, the oscillator strength, frequency and line width of the mode corresponding to the shoulder (LO phonon). The parameters A , u and **C were obtained by fitting two Lorentzian to the *experimental data points. The fitted curves are represented by the solid lines, whereas the dashed lines represent the peaks corresponding to the individual modes. The first-order Raman spectra of the three samples S1, S2 and S3 using the 457.9 nm excitation is shown in Fig. 2, which shows the characteristic LO phonon with a shoulder in the low-frequency wing identified as the SP mode. The spectra depicted in Fig. 2 show the expected size dependence and have been analyzed and interpreted in Ref. [4] as mentioned earlier in the introduction.
The observed Raman spectra for all the three samples (Fig. 2) show the LO phonon frequency at 305 cm\ along with a shoulder at 295 cm\ in the low-frequency wing which agrees well with the result reported [2,5,10]. The two prominent peaks at 305 and 295 cm\ are denoted P1 and P2, respectively in the figures. It is to be noted that the Raman intensities of the peaks P1 as well as P2 decreases as one goes from nanocrystalline to bulk samples. Similarly, the width (FWHM) of P1 decreases from 14.14 to 12.67 cm\ and that of P2 changes from 8.43 to 8.33 cm\ on increasing the size from nanocrystalline to bulk samples. These results are shown in Fig. 3 and the observations are in conformity with the interpretation of the observed shoulder in the low-frequency wing as the surface phonon (SP) mode [4]. It is to be noted that the excitation energy of 2.7 eV (wavelength 457.9 nm) while satisfying the resonance condition for samples S1 and S2 (band gaps 2.405 and 2.65 eV) falls short of 0.15 eV in the case of the samples S3 (band gap 2.85 eV). It is expected that at resonance, the
Fig. 3. (a) Raman intensity; (b) FWHM; (c) Raman frequency and (d) the intensity ratio (I /I ) as a function of thickness/crystalline . . size. The excitation wavelength is 457.9 nm. P1 and P2 are the respective Raman peaks as shown in Fig. 1.
K.K. Nanda et al. / Physica B 262 (1999) 31—39
Fig. 4. The Raman spectra of sample S2 with different excitation wavelength, j (a) j"457.9 nm; (b) j"488 and (c) j"514.5 nm. Note that the low-frequency wing P2 shifts to higher frequency as the excitation wavelength is increased.
Raman intensity of the LO mode will be enhanced which will mask the weak SP mode resulting in a broad LO peak. To test this hypothesis, the Raman spectra were recorded using two other laser excitation wavelengths of 488 and 514.5 nm on the single sample S2. The results are presented in Fig. 4. The spectra while clearly showing the enhancement of the intensity of the LO phonon at resonance depict very anomalous behavior of the shoulder corresponding to the SP mode. As the excitation energy gets off resonance the shoulder shows a predominant shift from the lower-frequency (&291 cm\) to the higher-frequency (&330 cm\) wing. The variation of the intensity, width, frequency shift and the ratio of the intensities of the two peaks P2 and P1 as a function of excitation wavelength are plotted in Fig. 5 a—d. The width of peak P2 decreases slightly with increasing excitation
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wavelength while that of the peak P1 shows slight broadening as shown in Fig. 5c. However there is a drastic reduction in intensity of both the peaks P1 and P2 when excited with the laser of wavelength 514.5 nms; compared to the spectra excited by the other two shorter wavelength photons. This can be the result of going off resonance in the scattering because this long wavelength excitation corresponds to an energy of &2.4 eV, which falls short off the band gap by about 0.25 eV. Therefore, one needs to understand the predominant shifting of the peak P2 to higher frequencies and its narrowing while the peak P1 softens and broadens when the excitation frequency of the laser is lowered to offresonance. The observed Raman peaks under off-resonance scattering conditions when excited by the laser of wavelength 514.5 nms, also exhibit a temperature dependence which is shown in Fig. 6. At low temperature (70 K) there is a loss of intensity of the peak P1 and an increase in that of P2. On the other hand, the frequency of P1 hardens and that of P2 softens while the width of P1 decreases and that of P2 increases. The decrease in intensity of the phonon Raman peaks at low temperatures is expected because of the availability of lesser number of phonons. Similarly the hardening and narrowing of the LO phonon peak P1 at low temperatures can be attributed to the decrease in anharmonicity. But the softening and widening of the P2 peak on lowering the temperature is indicative of an incipient change in the surface structure.
4. An interpretation of the anomalies: The size dependence of the intensity of the shoulder to the LO peaks observed in the Raman spectra as depicted in Fig. 2, together with the feature that its frequency lies in the gap between the TO and the LO modes qualifies it to be identified as the surface mode. However, the dramatic shift of this mode to the high-frequency wing on lowering the excitation frequency of the laser, seems to disqualify it to be a surface mode. Looking for an alternate interpretation, the natural suggestion that emerges is that it could be an impurity mode. As mentioned earlier the CdS nanoparticles have excess Cd, the
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K.K. Nanda et al. / Physica B 262 (1999) 31—39
Fig. 5. (a) Raman intensity; (b) FWHM; (c) Raman frequency and (d) intensity ratio I /I as a function of excitation wavelength. P1 . . and P2 are the respective Raman peaks as shown in Fig. 3.
amount of which increases on decreasing the size. If the observed mode is attributed to these Cd impurities one can understand the increase in intensity with decreasing size of these nanoparticles, but it is not possible to explain why the mode should shift to higher frequencies on decreasing the frequency of the exciting photons. The excess Cd in these systems will form interstitial defects. Hence, if these materials are to give rise to a mode, with a frequency lower than LO mode, which is like a resonant mode, it is essential that the force constant binding the interstitial to the neighbors must soften. But then the mode moves to the high-frequency wing when excited with lower-frequency photons; thus behaving like a localized mode necessitating the hardening of the force constants. Why such a change in the force constants will occur is simply not understandable. Besides the observed softening (Fig. 6) and broadening of the mode on lowering the temperature simply rules out its interpretation as an impurity mode. The only other alternative interpretation is to invoke a rather strong coupling of the mode to the charge carriers [11] in the system. As a consequence
of such a strong charge carrier—phonon interaction, the phonon can acquire a self-energy which will result in an increase in the frequency of the mode. In order to establish the feasibility of such a mechanism, it is necessary to examine qualitative feature of the electronic structure of the semiconductor nanoparticles. These nanoparticles have the crystalline structure of their bulk counter parts and hence are characterized by the fully occupied valence band and an empty conduction band separated by the energy gap (E ). However, the charge carriers in these bands e.g., the electrons in the conduction band and holes in the valence band experience an overall confining potential due to the finite size of these particles. As a result there will be size-dependent discrete states in the conduction and valence bands resulting in the effective enhancement of the band gap; the so-called quantum size effect. It has been argued that in these semiconductor nanoparticles the hyperbolic band model [9] gives a better fit to the observed quantum size effect as compared to the effective mass approximation. The present method of the preparation of the CdS nanoparticles described in Section 2 does not
K.K. Nanda et al. / Physica B 262 (1999) 31—39
Fig. 6. The Resonant Raman Spectra of sample S2 at (a) 300°K and (b) 70°K. The excitation wavelength is 514.7 nm.
produce size-selected particles. Hence, the nanoparticles have a size distribution around a mean size. This in turn will lead to a bunching of the localized quantum confined states in the conduc-
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tion and the valence bands. Over and above there is excess Cd in the CdS nanoparticles. It is known that excess Cd can produce acceptor states within the gap of CdS [8,12]. These states together with those originating from quantum size effect will form a continuum of localized states near the valence band edge. The experimental observation of two additional peaks in the photoluminescence spectra of these CdS nanoparticles [8], one lower in energy and the other of higher energy than the bulk peak further corroborates the qualitative picture of the electronic structure shown schematically in Fig. 7. In fact a similar model without the effect of size distribution of the nanoparticles was originally proposed [8] to explain the photoluminescence data. But we shall argue that it is the latter effect namely the bunching of localized states due to size distribution which is crucial in the proposed understanding of the observed shift to higher frequency of the Raman peak corresponding to the surface mode. Normally all these localized states in the valence band except the ones arising from the Cd-acceptor states are occupied by electrons. On shining these nanoparticles with the laser of frequency greater than the effective band gap the electrons are resonantly excited to the localized states in the conduction band and there is resonant Raman scattering due to recombination of the electrons and holes. The resonant scattering being an efficient process,
Fig. 7. Schematic band diagram of CdS (a) buk; (b) size-selected nanoparticles showing descrete states and (c) size distributed nanoparticles and the presence of Cd acceptor results in bunching of electronic states.
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cited to the conduction band across the gap, they are available for the phonons to interact with these charge carriers. Thus, the phonon acquires a selfenergy which shifts its frequency to higher values. The calculation of the self-energy involves the Lindhard function in the case of metals, whereas in the present case of semiconductor nanoparticles the energies of the localized states will enter the evaluation of the Lindhard function. What still remains a puzzle is why the surface phonon mode couples so strongly to the charge carriers while the LO mode does not. These questions and the details of the calculation will be the subject matter of a future work. 5. Conclusion
Fig. 8. (a) Resonant Raman scattering process for which the energy of the laser beam is greater than the band gap of the semiconductor. In this process electron—hole pairs are created by the absorption of photons. These electron/hole emit a phonon before they recombine to give back a photon. (b) non-resonant scattering process for which the energy of the laser beam is smaller than the band gap of the semiconductors. The energy is not sufficient to excite electron from the valence band to the conduction band. But states are available near the valence band edge for the phonons to interact as a result of which electron—hole pairs are created in the continuum of localized states. The phonon acquires a self-energy which shifts the frequency of SP mode to higher values. The Feynman diagram for the processes are also shown.
the observed Raman phonons have a higher intensity. The recombination lifetimes being much smaller than the phonon lifetime, the phonons do not interact with the charge carriers in the system in the resonant Raman scattering process. On the other hand, when the exciting photon has a frequency less than the effective band gap, the scattering is nonresonant, thereby, there is a suppression of the intensities of the Raman shifted phonons. This is observed in Fig. 3b and c. But then the phonons now can interact with the electrons in the valence band and excite electron-hole pair in the continuum of localized states, which recombine to re emit the phonon, as shown in Fig. 8. Since in the non-resonant process the electrons are not ex-
Raman scattering measurements were performed on CdS semiconductor films having different crystalline sizes with different excitations. Beside the 1LO phonon mode, a peak at the low-frequency wing has been observed with excitation of 457.9 nm. But the low-frequency peak shifts to higher frequency as the excitation energy is decreased. The variations of the Raman shifts, widths and intensities of both the peaks with the size of the nanoparticles is consistent with the interpretation of the low-frequency wing as a SP mode. The anomaly with different excitations is attributed to the off-resonance scattering as the energy of the laser beam is less than the band gap of the material. It is argued that in this case the phonon acquires a self-energy that shifts the frequency of the SP mode to higher values. Acknowledgements Partial financial support received from IFCPAR project No. 1508-4 is gratefully acknowledged. The authors acknowledge Prof. V.S. Ramamurthy for helpful discussions. References [1] P. Melinon et al., Int. J. Mod. Phys. B 9 (1995) 339. [2] A. Mlayah, A.M. Brugman, R. Carles, J.B. Renucci, M.Ya. Valakh, A.V. Pogorelov, Solid State Commun. 90 (1994) 567 and references therein.
K.K. Nanda et al. / Physica B 262 (1999) 31—39 [3] S. Hayashi, H. Sanda, M. Agata, K. Yamamoto, Phys. Rev. B 40 (1989) 5544. [4] K.K. Nanda, S.N. Sahu, Appl. Surf. Sci. 119 (1997) 50. [5] S.K. Deb, A.P. Roy, M. Kundu, A.A. Khosravi, S.K. Kulkarni, Solid State Physics Symp., India, 1995. [6] S.N. Sahu, J. Mater. Sci. Mater. Electron 6 (1995) 43. [7] S.N. Sahu, S. Chandra, Solar Cells 22 (1987) 163. [8] K.K. Nanda, S.N. Sarangi, S.N. Mohanty, S.N. Sahu, Thin Solid Films 322 (1998) 21.
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[9] Y. Wang, A. Suna, W. Mahler, R. Kasowski, J. Chem. Phys. 87 (1987) 7315. [10] R. Rosetti, S. Nakahara, L.E. Brus, J. Chem. Phys. 79 (1983) 1086. [11] M.C. Klein, F. Hache, D. Ricard, C. Flytzanis, Phys. Rev. B 42 (1990) 11123. [12] S.M. Sze, Semiconductor Devices: Physics and Technology, Wiley, New York, 1985.