Optical Vibration Modes in (Cd, Pb, Zn)S Quantum Dots in the Langmuir Blodgett Matrix

Physics of the Solid State, Vol. 44, No. 0, 2002, pp. 976 980. Translated from Fizika Tverdogo Tela, Vol. 44, No. 0, 2002, pp. 884 887. Original Russian Text Copyright 2002 by Milekhin, Sveshnikova, Repinskiœ, Gutakovskiœ, Friedrich, Zahn. W-DIMENSIONAL SYSTEMS AND SURFACE PHYSICS Optical Vibration Modes in (Cd, Pb, Zn)S Quantum Dots in the Langmuir Blodgett Matrix A. G. Milekhin*, L. L. Sveshnikova*, S. M. Repinskiœ*, A. K. Gutakovskiœ*, M. Friedrich**, and D. R. T. Zahn** * Institute of Semiconductor Physics, Siberian Division, Russian Academy of Sciences, pr. Akademika Lavrent eva 3, Novosibirsk, 630090 Russia ** Institute of Physics, Technical University, Chemnitz, D-0907 Germany Received June 26, 200 Abstract The structures with,, and quantum dots produced using the Langmuir Blodgett method are investigated by infrared (IR) spectroscopy, Raman scattering, and ultraviolet (UV) spectroscopy. The quantum dot size estimated from the UV spectra and high-resolution transmission electron microscopy (HRTEM) falls in the range 2 6 nm. The longitudinal optical () phonons localized in quantum dots and the surface optical vibration modes are revealed in the IR reflection and Raman scattering spectra of the structures under investigation. The frequencies of the surface optical modes are adequately described with allowance made for the effect of localizing optical phonons in the quantum dots. 2002 MAIK Nauka/Interperiodica.. INTRODUCTION In the last decade, low-dimensional semiconductor structures (quantum wells, quantum wires, and quantum dots) have attracted growing interest due to their unusual optical and electronic properties as compared to bulk materials [, 2]. The optical properties of bulk crystals and thin films are well understood and explained. However, elucidation of the optical properties of low-dimensional structures calls for theoretical and experimental investigations. At present, quantum dots have been produced using a number of techniques, such as self-organization of quantum dots during molecular-beam epitaxy [3], preparation of quantum dots in solutions [4] and glasses [5], colloid chemistry [6], etc. This paper reports on the results of analyzing the vibrational spectra of,, and quantum dots formed in the Langmuir Blodgett matrix. 2. SAMPLE PREPARATION AND EXPERIMENTAL TECHNIQUE The standard Langmuir Blodgett technique provides a means of preparing perfect films of Cd, Zn, and Pb behenates. The interaction of metal behenate films with gaseous hydrogen sulfide results in the formation of microcrystals or quantum dots of Cd, Zn, and Pb sulfides [7, 8]. In the present work, films of cadmium, zinc, and lead behenates were deposited onto aluminumcoated silicon substrates. The aluminum layer served as a mirror for measuring the reflection spectra. The thickness of the Langmuir Blodgett films used in the experiments was 400 monolayers (.2 µm). The as-prepared Langmuir Blodgett films were treated with hydrogen sulfide for 3 h under a pressure ranging from 50 to 00 Torr. As a result, the,, and quantum dots were formed in the behenic acid matrix according to the reaction Me(C 2 H 43 COO) 2 + H 2 S = MeS + 2C 2 H 43 COOH, () where Me = Cd, Zn, or Pb. The infrared (IR) reflection spectra of the studied structures were recorded on Bruker-IFS66 and IFS3v IR Fourier spectrometers with a glancing angle of incidence (θ 75 ) in p-polarized light. The IR spectrum of an aluminum mirror deposited onto a silicon substrate served as a reference spectrum. The resolution was 2 cm over the entire spectral range. The number of scans was equal to 500. The experiments on Raman scattering were carried out using a Dilor XY800 spectrometer in a backscattering geometry with the excitation by Ar + and Kr + lasers in the wavelength range 54.5 457.9 nm (2.4 2.7 ev) with a power of 40 mw. The resolution was equal to 2.9 cm over the entire spectral range. The ultraviolet (UV) absorption spectra were recorded on a Specord M-40 UV spectrometer in the wavelength range 250 800 nm with a spectral resolution of 0 cm. The experiments on high-resolution transmission electron microscopy (HRTEM) were performed using a JEM-400EX (JEOL) electron microscope with an accelerating voltage of 400 kev. The point resolution was 0.65 nm. The experiment was described in detail earlier in [9]. 063-7834/02/440-976$22.00 2002 MAIK Nauka/Interperiodica

OPTICAL VIBRATION MODES IN (Cd, Pb, Zn)S QUANTUM DOTS 977 3. RESULTS AND DISCUSSION In order to estimate the quantum dot size, we measured the UV absorption spectra of the structures under investigation. The UV absorption spectra of the structures with,, and quantum dots are displayed in Fig.. These spectra exhibit specific features (indicated by arrows) at 390, 270, and 255 nm, respectively, due to the se sh band-to-band transitions in the quantum dots. The vertical lines correspond to the band gaps in bulk and. The band gap of is equal to 0.4 ev (not shown in Fig. ). Within a simple model based on the effective mass approximation, we can estimate the mean size of spherical quantum dots as a function of the energy of the se sh transitions [0]: 2η 2 π 2 E se sh = E g + -------------- D 2 ----- m e + ----- m h 3.56e 2 --------------. εd (2) Absorbance.0 0.5 QD bulk QD bulk QD 300 400 500 600 Wawelength, nm Here, D is the diameter of the quantum dot, E g is the band gap, ε is the permittivity, and m e and m h are the electron and hole effective masses in the bulk of the material forming the quantum dot, respectively. The calculated dependences are shown in Fig. 2. The hatched regions correspond to the se sh transition energies determined, to within the experimental error, from the UV absorption spectra. The mean size of,, and quantum dots, which was determined from the comparison of the experimental and calculated data, was equal to 2.8 ± 0.2, 3.2 ± 0., and 4.2 ± 0.2 nm, respectively. For comparison, the quantum dots were examined using high-resolution transmission electron microscopy. The HRTEM images of the studied samples are displayed in Fig. 3. The dark-field region corresponds to (Fig. 3a) and (Fig. 3b) quantum dots, and the bright-field region corresponds to the behenic acid matrix. It can be seen from Fig. 3 that the quantum dots have a nearly spherical shape. The mean size of and quantum dots is equal to (3 ± ) and (4 ± 2) nm, respectively. Thus, the data obtained from analyzing the UV absorption spectra and HRTEM images are in good agreement. Analysis of the interplanar spacings demonstrated that the quantum dots exhibit a cubic structure, whereas the quantum dots have a wurtzite-type hexagonal structure. We failed to observe a diffraction pattern of quantum dots. This can be explained by a small (less than 0.%) volume fraction of crystal particles. Moreover, the small particle size leads to a considerable broadening of the diffraction peaks attributed to quantum dots, which, in turn, makes their visualization against the background of the diffraction pattern of the amorphous matrix of the Langmuir Blodgett film rather difficult. The vibrational spectrum of the structures prepared was examined using Raman and IR spectroscopy. Since Energy, ev Fig.. Experimental UV absorption spectra of the structures with,, and quantum dots. Vertical solid lines correspond the band gaps of the materials forming quantum dots. The band gap in is 0.4 ev (not shown in the figure). Vertical dashed arrows indicate the se sh transition energies in the quantum dots. 6 5 4 3 2 0 2 4 6 8 0 Diameter, nm Fig. 2. Calculated energy of the se sh transitions in,, and quantum dots as a function of the quantum dot diameter. The hatched regions correspond to the se sh transition energies determined from the UV absorption spectra. the selection rules are different for Raman and IR spectroscopy, these methods of analyzing the vibrational spectrum complement each other. Figure 4 depicts the Raman spectra of the structures with quantum dots in the frequency range of crystal lat-

978 MILEKHIN et al. (a) (b) 5 nm Raman intensity, arb. units SO 5 SO 200 300 400 Raman shift, cm 5 nm Fig. 4. Experimental Raman scattering spectra of the studied structures with quantum dots in the frequency range of lattice vibrations of,, and materials forming the quantum dots. Vertical lines indicate the frequencies of the and phonons in the bulk materials. Fig. 3. HRTEM images of the studied samples. The darkfield region corresponds to (a) and (b) quantum dots. The bright-field region corresponds to the behenic acid matrix. tice vibrations of the materials forming the quantum dots. The vertical lines indicate the frequencies of the transverse optical () and longitudinal optical () phonons in the bulk crystals. It can be seen from Fig. 4 that the frequency positions of the experimental Raman lines differ from the frequencies of the optical phonons of the materials forming the quantum dots. Two effects can be responsible for this behavior. These are the effect of localization of optical phonons and Raman scattering by surface optical phonons in quantum dots. The frequencies of the observed Raman lines of the studied structures with and quantum dots differ from the frequencies of the phonons in the bulk materials and amount to 207 and 297 cm, respectively. These values exceed the frequency of the phonon in (205 cm ) [] and are less than that of the phonon in (303 cm ) [2]. The difference between the experimental phonon frequencies in the structures with quantum dots and the frequencies in the bulk materials can be explained by the effect of localizing optical phonons in the quantum dots. Under the assumption that the low-dimensional quantum dots have a spherical shape, the wave vector of the localized optical phonons is determined by the expression q = πm/d. Here, m is the quantum number of the localized mode and d is the diameter of the quantum dot. The dispersion of ω(q) of the phonons in is negative. Hence, the frequency of the first localized mode ( ) is less than that of the bulk material. A decrease in the frequency of the mode as compared to the frequency of the phonon in single-crystal is observed experimentally (Fig. 4). In addition to the intense line, the Raman spectrum exhibits a low-frequency shoulder due to scattering by phonons and surface optical (SO ) phonons of the quantum dots. Figure 4 also illustrates the decomposition of the Raman spectrum into three components, which are represented by Lorentzian curves. For spherical quantum dots, the surface modes should satisfy the following relationship [3]: Here, ε (ω), ε m = 2.4, and l are the dielectric function of the material of the quantum dot, the dielectric constant of the Langmuir Blodgett, and the number of the surface mode, respectively. The calculated frequency of the SO mode with due regard for the effect of localizε ( ω) ------------ = --. l ε m (3)

OPTICAL VIBRATION MODES IN (Cd, Pb, Zn)S QUANTUM DOTS 979 ing optical phonons in quantum dots [4] is equal to 272 cm. This value is in good agreement with the frequency determined from the decomposition of the Raman spectrum (269 cm ). The dispersion of phonons in the crystal is a nonmonotonic function. The dispersion is positive in the range of wave vectors q = (0 0.6)π/a 0, where a 0 is the lattice parameter of [5]. This behavior of the dispersion leads to the experimentally observed increase in frequency of the mode as compared to the frequency of the phonon in bulk. The asymmetric shape of the Raman line in the spectra of the studied structures with quantum dots can be caused by the contribution of higher-order localized modes (m > ) to Raman scattering. Reflection, arb. units 00 SO SO SO 200 300 400 Wavenumber, cm The Raman spectra of the structures with quantum dots contain a single line at a frequency of 320 cm, which differs significantly from the frequencies of the and phonons; hence, this line cannot be interpreted as a localized mode. Most likely, it is associated with the surface vibration modes. This assumption is confirmed by the fact that the calculated frequency of the SO mode (36 cm ) coincides with the experimental value. As in the case of quantum dots, the overestimated value of the calculated frequency of the SO mode can be a consequence of the effect of localizing optical phonons in the quantum dots. This effect was disregarded in our calculations, because data on the frequencies of the and phonons in quantum dots were not available. The Raman spectra of the structures with quantum dots do not exhibit lines associated with optical phonons. This confirms the inference made from electron microscopy that the quantum dots have small sizes. For small-sized quantum dots, the ratio of the surface atoms to the bulk atoms is relatively large. In the case when the number of surface atoms becomes comparable or even larger than that in the bulk of the quantum dots, the contribution of the surface layers to Raman scattering becomes significant. Moreover, no optical phonons were observed in the IR reflection spectra for all the studied structures. Figure 5 shows the IR reflection spectra in the frequency range of lattice eigenmodes for the materials forming quantum dots. It can be seen from Fig. 5 that the specific features associated with the surface optical modes are located in the range between the frequencies of the and phonons. The calculated frequencies of the SO modes are indicated by arrows in Fig. 5. These frequencies are in good agreement both with the reflectance minima found from the IR spectra and with the SO mode frequencies determined from the Raman spectra. The IR spectrum of the structure with quantum dots exhibits a reflectance minimum at a frequency of approximately 275 cm, which exceeds the frequency of any vibration of the crystal lattice. The former frequency is close to the sum of frequencies of the and phonons (67 + 205 cm ) in Fig. 5. Experimental IR reflection spectra of the studied structures with quantum dots. Vertical lines and arrows indicate the frequencies of the and phonons in the bulk materials and the SO modes in the quantum dots, respectively. the crystal. Therefore, this feature can be associated with two-phonon processes. 4. CONCLUSIONS Thus, we performed a systematic investigation into the optical properties of the structures with,, and quantum dots produced using the Langmuir Blodgett method. Analysis of the IR and Raman spectra revealed lines attributed to both the optical phonons localized in the quantum dots and surface optical phonons. It was shown that the surface optical phonons are adequately described within the model of electromagnetic surface modes in spherical microcrystals. The experiments on high-resolution electron microscopy demonstrated that the quantum dots have a nearly spherical shape; therefore, the model used is quite adequate. The quantum dot size was determined from the experimental data on electron microscopy and UV spectroscopy in combination with the appropriate calculations. ACKNOWLEDGMENTS This work was supported by the Russian Foundation for Basic Research, project no. 0-03-32796. REFERENCES. G. Bastard, Wave Mechanics Applied to Semiconductor Heterostructures (Halsted Press, New York, 988). 2. Science and Engineering of One- and Zero-Dimensional Semiconductors, Ed. by S. P. Beaumont and C. M. Sotomayor Torres (Plenum, New York, 990), NA ASI Ser., Ser. B: Phys., Vol. 24.

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