- Email: [email protected]
Determination of dispersive optical constants of nanocrystalline CdSe (nc-CdSe) thin films
Materials Research Bulletin 47 (2012) 1400–1406
Contents lists available at SciVerse ScienceDirect
Materials Research Bulletin journal homepage: www.elsevier.com/locate/matresbu
Determination of dispersive optical constants of nanocrystalline CdSe (nc-CdSe) thin films Kriti Sharma, Alaa S. Al-Kabbi, G.S.S. Saini, S.K. Tripathi * Centre of Advanced Study in Physics, Department of Physics, Panjab University, Chandigarh 160014, India
A R T I C L E I N F O
A B S T R A C T
Article history: Received 19 October 2011 Received in revised form 11 January 2012 Accepted 1 March 2012 Available online 10 March 2012
The nanocrystalline thin films of CdSe are prepared by thermal evaporation technique at room temperature. These thin films are characterized by transmission electron microscopy (TEM), scanning electron microscopy (SEM), energy dispersive X-ray analysis (EDX), X-ray diffraction (XRD) and photoluminescence spectroscopy (PL). The transmission spectra are recorded in the transmission range 400–3300 nm for nc-CdSe thin films. Transmittance measurements are used to calculate the refractive index (n) and absorption coefficient (a) using Swanepoel’s method. The optical band gap (Eopt g ) has been determined from the absorption coefficient values using Tauc’s procedure. The optical constants such as extinction coefficient (k), real (e1) and imaginary (e2) dielectric constants, dielectric loss (tan d), optical conductivity (sopt), Urbach energy (Eu) and steepness parameter (s) are also calculated for nc-CdSe thin films. The normal dispersion of refractive index is described using Wemple–DiDomenico single-oscillator model. Refractive index dispersion is further analysed to calculate lattice dielectric constant (eL). ß 2012 Elsevier Ltd. All rights reserved.
Keywords: A. Nanostructures A. Thin films B. Vapor deposition D. Optical properties
1. Introduction In recent years, the field of nanocrystalline semiconducting thin films is rapidly expanding. The increasing interest for these materials is due to the fact that these are characterized by properties which are substantially different from the corresponding ones for bulk semiconductors [1]. These phenomena are known as confinement effects or quantum size effects and are of special interest in nanotechnology. The nanodimensions of semiconducting crystals influence the band structure which allows the nanotechnologists to design a semiconductor with suitable optical and electrical properties (i.e. suitable band gap energy) for various technical applications by controlling the crystal size [2]. Thin films of II–VI semiconductors are of considerable interest for their excellent optical properties in the visible region [3–5]. CdSe is an important member of this group of binary compounds. It has a direct intrinsic band gap of 1.74 eV, which makes it an interesting material for various applications such as solar cells, photodetector, light emitting diodes and other optoelectronic devices [6–8]. Shreekanthan et al. [9] found that CdSe films deposited at room temperature are cadmium rich with segregated selenium globules, but a deposition at higher temperatures has been found to yield stochiometric and homogeneous films. CdSe
* Corresponding author. Tel.: +91 172 2534462; fax: +91 172 2783336. E-mail addresses: [email protected], [email protected] (S.K. Tripathi). 0025-5408/$ – see front matter ß 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.materresbull.2012.03.008
often possesses n-type conductivity in bulk as well as in thin films [10]. As it is well known that CdSe can be crystallized in zinc blende (cubic), wurtzite (hexagonal) or wurtzite–zinc blende mixed phases, the transformation in crystalline phases of CdSe has attracted much attention in the past [11]. Some researchers have observed the phase transformation by annealing [12] or mechanically grinding CdSe samples [13]. A variety of methods have been used to prepare CdSe thin films (including physical vapor deposition, sputtering, spray pyrolysis, electrodeposition, etc.) [14–17]. Physical vapor deposition (PVD) is often used because it offers many possibilities to modify the deposition parameters and to obtain films with desired structures and properties. Aneva et al. [18] have deposited the CdSe nanocrystalline thin films of different thicknesses by thermal evaporation technique and studied the influence of the depositions and film thickness on the microstructure and the electrical properties using different techniques. The decrease of dark conductivity and photoconductivity with the layer thickness reduction (and the grain size decrease) is related to the size-induced increase of interface defects and appearance of new faster recombination centres [18]. Creti et al. [19] have studied the role of defect states on the electrical and optical properties in CdSe nanorods thin films. They have observed that deposition techniques affect the films morphologies and the self assembling allows more ordered quantum rods and films with reduced roughness. Earlier, our group has reported the effect of annealing on electrical and optical properties of nc-CdSe thin films [20]. Previous reports on studies of these nc-CdSe thin films are mainly related to structural
K. Sharma et al. / Materials Research Bulletin 47 (2012) 1400–1406
characterization [21,22], transport properties [23] and to optical properties [21,23]. So, it is clear from the above discussion, that not much work has been reported on the optical properties (specially the dispersion parameters) of nc-CdSe thin films. In the present work, we have investigated optical dispersion properties of nc-CdSe thin films because this information will be helpful in research towards applying this material in optical communication and optical devices. The study of optical absorption, particularly the absorption edge has been proved to be very useful for elucidation of the optical properties and optical constants of nc-CdSe. The evaluation of optical dispersions and other optical constants are of considerable importance for applications in integrated optic devices such as switches, filters and modulators, etc., where the refractive index of a material is the key parameter for device design. The objective of this paper is to obtain detailed information of optical dispersive constants of nc-CdSe thin films. We have used high percentage of selenium in CdSe because of its unique properties including high photosensitivity [24] to electromagnetic radiation. We have deposited thin films of nc-CdSe by thermal evaporation technique using inert gas condensation (IGC) method as it offers large possibilities to modify the deposition conditions and to obtain films with determined structure and properties. 2. Experimental Melt quenching technique has been used for the preparation of CdSe material. Constituent elements (5 N pure) are weighed according to their atomic percentages and sealed in quartz ampoules in vacuum 2 105 mbar. The sealed ampoules are kept inside the furnace where the temperature is increased up to 1000 8C at a heating rate of 2–3 8C/min. The ampoules are frequently rocked for 24 h at the highest temperature of the constituent elements to make the melt homogeneous. The quenching is done in liquid N2. Thin films of the alloy are prepared by thermal evaporation technique using IGC method in the presence of Argon as inert gas at room temperature and base pressure of 2 105 mbar on well-degassed Corning 7059 glass substrates. The films are kept in deposition chamber in dark for 24 h before taking optical measurements to attain thermodynamic equilibrium. Films have also been deposited on TEM grid. Transmission electron microscopy (TEM) has been done using Hitachi H7500 electron microscope, operating at 80 kV. Crystallographic study is carried out on the nc-CdSe thin films using a Spinner 3064 XPERT-PRO X-ray diffractometer operating at 45 kV and 40 mA current using Cu Ka radiation in the 2u range from 108
1401
to 808. The microstructure of the nc-CdSe thin films on the glass substrate has been studied by using a Jeol Scanning Electron Microscope (JSM-6610 LV) attached with EDX analyser to measure quantitatively the sample stiochiometry. The nc-CdSe thin films are coated with a thin layer of gold (Au) using a SEM sputter coating unit JEOL JFC-1600 before taking SEM and EDX. Photoluminescence (PL) spectrum of nc-CdSe thin film is recorded in the visible region on a computer-controlled luminescence spectrophotometer LS-50 B (Perkin Elmer Instruments) with laccuracy = 1.0 nm. A pulsed Xe discharge lamp is used as an excitation source. The sample is excited at 390 nm and the spectrum is recorded in the range from 470 nm to 640 nm. The normal incidence transmission spectra of the substrate with and without nc-CdSe thin films have been measured by a UV/VIS/NIR computer controlled spectrophotometer Perkin Elmer LAMBDA 750 in the transmission range 400–3300 nm at room temperature (300 K). 3. Results and discussion 3.1. Structural characterization The TEM image for CdSe nanoparticles is shown in Fig. 1(a). The TEM micrograph reveals the spherical shape of CdSe nanoparticles. The inset of this image shows nanoparticles at very large magnification. From TEM micrograph, we obtain the diameters of the nanoparticles and average diameter of the particles is calculated from the peak of the size distribution plots as shown in Fig. 1(b). The average particle size is in the range of 40–45 nm. Scanning electron microscopy (SEM) is a convenient technique to study the microstructure of thin films. Fig. 2 shows the surface morphology of thin films of CdSe nanoparticles. From the micrographs, it is observed that films are homogenous, without cracks or holes and that they cover the glass substrate well. The composition of the nc-CdSe thin films has been studied by energy dispersive X-ray spectroscopy (EDX). The elemental analysis is carried out only for Cd and Se as shown in Fig. 3. The curve exhibits the presence of Cd and Se peaks with an average atomic percentage ratio of 35:65. The CdSe thin films may grow with either sphalerite cubic (zinc-blende type) or the hexagonal (wurtzite-type) structure. The hexagonal state is the stable phase of CdSe while sphalerite cubic modification is a metastable structural phase commonly occurring at low temperature. Fig. 4 shows the XRD pattern of nc-CdSe thin films. The figure shows the XRD peak at d = 3.79 A˚, 2u = 23.438 which corresponds to the (1 0 0) plane of the hexagonal (wurtzite) crystal structure. The comparison of the observed d value with
Fig. 1. (a) TEM image of nanoparticles of CdSe thus formed. Inset shows CdSe nanoparticles at higher magnification. (b) Size distribution of CdSe nanoparticles.
K. Sharma et al. / Materials Research Bulletin 47 (2012) 1400–1406
1402
350
nc-CdSe
300
(100)
Counts
250 200 150 100 50 0 0
10
20
30
40
2θ0
Fig. 2. SEM image of nc-CdSe thin film.
50
60
70
80
90
Fig. 4. XRD pattern of nc-CdSe thin film.
standard d value [25] clearly indicates the formation of hexagonal (wurtzite-type) phase. So the nc-CdSe thin films deposited on glass substrate using thermal evaporation method possess hexagonal structure, in present case agrees well with the reported data [26,27]. The broad hump in the background is either due to the amorphous glass substrate or possibly due to some amorphous phase present in the thin film [22]. The size of the crystallite is evaluated by making the Gaussian fit of the intense part of the peak (considering broad hump as base) of X-ray diffraction using the Scherrer formula [22]: d¼
0:9l b cos u
(1)
where b is the full width at half maximum in radians, l is the wavelength of X-rays used and u is the Bragg’s angle. The average crystallite size is found to be approximately 12 nm.
3.2. Optical characterization The PL spectrum of nc-CdSe thin film recorded at room temperature is shown in Fig. 5. This figure shows two bands in green region, an intense band at 531 nm and a relatively less intense one at 584 nm. Also, a weak band at 487 nm in blue region can also be seen in the spectrum. The band gap of nc-CdSe film is found to be 2.25 eV. The band at 584 nm can be assigned to excitonic emission. Of importance is the appearance of two deep level emission peaks at 487 nm and 531 nm. These may be attributed to the presence of one deep trapping site and electron– hole recombination via trap state or imperfection site [28]. Deep states in nanocrystalline materials are mainly associated with stochiometric defects, dangling bonds or external adatoms such as oxygen [29] and intrinsic lattice defects, in view of much larger surface to volume ratio in nanocrystalline materials [30]. Appearance of the bands at 487 nm and 531 nm in the PL spectrum of ncCdSe thin films deposited via chemical bath deposition has also been reported by Singh et al. [31]. The spectral dependence of the transmittance, T, of the nc-CdSe thin films has been measured in the wavelength range 400– 3300 nm. The data is illustrated in Fig. 6. The value of refractive index, n, has been calculated using Swanepoel’s method from the observed transmittance spectra. The model behind Swanepoel’s
240
nc-CdSe
220
531 584
Intensity (a.u.)
200
487
180 160 140 120 100 80 460
Fig. 3. Typical EDX pattern of nc-CdSe: (a) spectra and (b) EDX element composition table.
480
500
520
540
560
λ (nm)
580
600
Fig. 5. PL spectrum of nc-CdSe thin film.
620
640
660
K. Sharma et al. / Materials Research Bulletin 47 (2012) 1400–1406
H¼
Hþ
H
4s2 ðs2 þ 1ÞT
2
s2
s2 þ 1 2
6 5 4 3
(2)
2
(3)
1 0.35
nc-CdSe
0.30
The value of n is calculated using Eq. (2) and is plotted vs. l in Fig. 7. This decrease in the value of refractive index with wavelength attributes to the significant normal dispersion behaviour of the films. The extinction coefficient, k, is a measure of the fraction of light lost due to scattering and absorption per unit distance of the penetration medium. The extinction coefficient (k) can be calculated by using the relation: al l 1 ln ¼ (4) k¼ x 4p 4pd where a is the absorption coefficient, d is the thickness of the film and x is the absorbance. The value of k decreases with increase in wavelength as plotted in Fig. 7 and follows the same trend as that of n. This observation confirms the decrease in the loss of light due to scattering and absorbance with increase in l. The dielectric constant which is another important optical parameter can be defined as:
eðvÞ ¼ e1 ðvÞ þ ie2 ðvÞ
(5)
The real and imaginary parts of dielectric constant can be calculated with the help of n and k values [35]. The real dielectric constant (e1) can be calculated as:
e1 ¼ n2 k2
(6)
while the imaginary dielectric constant (e2) can be calculated as:
e2 ¼ 2nk
(7)
0.25 0.20 0.15 0.10 0.05 0.00 0
1000
1500
2000
2500
3000
3500
Fig. 7. Plot showing variation of refractive index (n) and extinction coefficient (k) with wavelength (l).
constant are more than the imaginary part. The variation of the dielectric constant with photon energy indicates that some interactions between photons and electrons are produced in this energy range. The dissipation factor (tan d) can be calculated using relation [36]: tan d ¼
e2 e1
(8)
Fig. 9 shows the plot of the dissipation factor (tan d) as a function of frequency. It is clear from the figure that dissipation factor increases with increase in frequency. From the transmission data, nearly at the fundamental absorption edge, the values of
24 22 20 18 16 14 12 10 8 6 4 2 0 3.5
nc-CdSe
ε1
1.0
500
λ (nm)
The variation of the real and imaginary dielectric constants with energy (hn) is shown in Fig. 8. It is clear from the figure that the real and imaginary parts of the dielectric constant show a similar behaviour. It is also clear that the values of the real part of dielectric
nc-CdSe
0.8 0.6
3.0
nc-CdSe
2.5
0.4
2.0
ε2
Transmittance
nc-CdSe
k
n¼
2
7
n
method [32,33] assumes that the sample is a thin film of nonuniform thickness deposited on a transparent substrate having a refractive index s. The film has a complex refractive index n* = n ik, where n is the refractive index and k is the extinction coefficient. According to this method, which is based on the approach of Manifacier et al. [34], the refractive index in the region where a 0 is calculated by the following equation: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1403
0.2
1.5 1.0 0.5
0.0
0.0
0
500
1000
1500
2000
λ (nm)
2500
3000
3500
Fig. 6. Optical transmission spectra of nc-CdSe at room temperature. Inset shows the variation of optical absorption coefficient (a) with photon energy (hn).
0.5
1.0
1.5 hν (eV )
2.0
2.5
Fig. 8. Plot of real (e1) and imaginary (e2) parts of dielectric constant vs. photon energy (hn).
K. Sharma et al. / Materials Research Bulletin 47 (2012) 1400–1406
1404
1.20E+011
0.11 nc-CdSe
nc-CdSe
1.00E+011
eV/cm2
0.10
0.08
2
0.07
(αhν)
tan δ
0.09
8.00E+010 6.00E+010 4.00E+010 2.00E+010
0.06 0.00E+000 0.05 4.50E+014 4.80E+014 5.10E+014 5.40E+014 5.70E+014
1.0
1.5
2.0
2.5
hν (eV)
3.0
3.5
Fig. 10. Plot of (ahn)2 vs. hn for nc-CdSe thin films deposited at room temperature.
freq (Hz) Fig. 9. Plot of dissipation factor (tan d) vs. frequency (f).
values have been calculated from the relation:
Inset of Fig. 6 shows the variation of a with photon energy (hn). Figure shows that a increases with increase in hn. The fundamental absorption, which corresponds to the transition from valence band to conduction band, can be used to determine the band gap of the material. It corresponds to higher values of absorption coefficient a 104 cm1. The relation between a and the incident photon energy (hn) from the power law behaviour of Tauc can be written as [37]: n
a¼
Aðhn Eg Þ hn
(10)
where A is a constant, Eg is the optical band gap of the material and the exponent n depends on the type of transition. The n may have values 1/2, 2, 3/2 and 3 corresponding to the allowed direct, allowed indirect, forbidden direct and forbidden indirect transitions, respectively. The value of Eg is calculated by extrapolating the straight line portion of (ahn)1/n vs. hn graph to hn axis taking n = 0.5. Fig. 10 shows the plot of (ahn)2 vs. hn for nc-CdSe films. From the plot of the figure, the value of Eg is found to be 2.25 eV which is more as compared to bulk CdSe (1.7 eV) due to quantum confinement effect. Kale et al. [22] have reported the band gap value to be 2.1 eV for nc-CdSe thin films prepared by successive ionic layer adsorption and reaction method. Singh et al. [38] have synthesized nc-CdSe thin films by chemical bath deposition (CBD) at the two volumes of capping agents and found the band gap values as 1.92 eV and 2.02 eV. The absorption coefficient (a) near the fundamental absorption edge depends exponentially on the incident photon energy. The spectral dependence of a has also been studied at photon energies less than the energy gap i.e. in the region of so-called Urbach spectral tail, where ln a varies as a function of hn. The Urbach energy can be calculated by following relation [39]: hn aðhnÞ ¼ ao exp (11) Eu where ao is a constant and Eu is the Urbach energy which refers to the width of exponential absorption edge. Plotting the dependence of ln a vs. hn as shown in Fig. 11 should give a straight line. The Eu
1 dðln aÞ dðhnÞ
(12)
In both crystalline and amorphous materials there is no known origin of the exponential dependence of absorption coefficient with energy. This dependence may arise from the random fluctuations of the internal fields associated with structural disorder in many materials. The dependence of the optical absorption coefficient with photon energy may arise from electronic transitions between localized states. The steepness parameter, s = kT/Eu characterizing the broadening of the optical absorption edge due to electron phonon or exciton–phonon interactions [40] has also been determined at room temperature. The calculated values of Urbach energy (Eu) and steepness parameter (s) are 210 meV and 0.12 respectively. Optical response is most conveniently studied in terms of optical conductivity. The absorption coefficient (a) can be used to calculate the optical conductivity (sopt) as follows [41]:
s opt ¼
anc 4p
(13)
where a is the absorption coefficient, n is the refractive index and c is the velocity of light. Fig. 12 shows the variation of sopt as a function of photon energy (hn) for nc-CdSe thin film. It is clear from
10.8 nc-CdSe
10.6 10.4
ln α
absorption coefficient (a), are calculated in the region of strong absorption using the relation: 1 1 a ¼ ln (9) d T
Eu ¼
10.2 10.0 9.8 9.6 1.35
1.40
1.45
h ν (eV)
1.50
Fig. 11. ln a vs. energy plot of films.
1.55
1.60
K. Sharma et al. / Materials Research Bulletin 47 (2012) 1400–1406
3.50E+015
nc-CdSe
3.00E+015 2.50E+015
σopt
2.00E+015 1.50E+015 1.00E+015 5.00E+014 0.00E+000 0.5
1.0
1.5
2.0
2.5
3.0
3.5
hν (eV ) Fig. 12. Plot between optical conductivity (sopt) and photon energy (hn).
the figure that the optical conductivity increases with increase in the photon energy, which may be either due to the high absorbance of nc-CdSe thin films or due to the electrons excited by photon energy. 3.3. Refractive index dispersion The refractive index n is found to decrease with the increase in wavelength of incident photon as observed from Fig. 7. The refractive index dispersion below the interband absorption edge can be fitted by Wemple–DiDomenico relationship. The result of refractive index dispersion below the interband absorption edge corresponds to the fundamental electronic excitation spectrum. Thus, the refractive index is related to photon energy through the relationship [42,43]: n2 ¼ 1 þ
Eo Ed
(14)
2
E2o ðhnÞ
The physical meaning of the single-oscillator energy, Eo, is that it simulates all the electronic excitation involved. Eo takes values near the main peak of the imaginary part of the dielectric constant spectrum. The so-called dispersion energy, Ed, is related to the average strength of the optical transitions. By plotting (n2 1)1 vs. (hn)2 and fitting the data, a straight line is obtained as shown in Fig. 13. Eo and Ed are determined directly from the gradient
1405
(n2 1)1 and the intercept on vertical axis [44]. The calculated values of Eo and Ed are 1.4 eV and 3.54 eV respectively. It is observed that the plots are linear over the energy range from 0.5 to approximately 0.71 eV. At low energies, deviation from linearity with a positive curvature is usually observed due to the negative contribution of lattice vibrations to the refractive index. At high energies, a negative curvature deviation is sometimes observed due to the proximity of the band edge or excitonic absorption [43]. This model describes the dielectric response of transitions below the optical gap. It plays an important role in determining the behaviour of refractive index. This results from the relationship between electronic properties of the material and its chemical bond [45]. The value of static refractive index, no, for nc-CdSe thin films has been calculated from Wemple–DiDomenico dispersion parameters Eo and Ed by using the following relation: sffiffiffiffiffiffiffiffiffiffiffiffiffiffi E no ¼ 1 þ d Eo
(15)
The value of no is calculated by extrapolating the Wemple– DiDomenico dispersion equation to hn ! 0 (Eq. (14)). The calculated value of no is 1.88. The obtained data of refractive index n can be analysed to obtain the lattice dielectric constant (high frequency dielectric constant) [46]. This procedure describes the contribution of free carriers and the lattice vibration modes of the dispersion. The following equation can be used to obtain the lattice dielectric constant [46]:
e1 ¼ eL Bl2 B¼
(16)
e2 N
(17)
pc2 m
where e1 is the real part of dielectric constant, eL is the lattice dielectric constant, l is the wavelength, N is the free charge carrier concentration, m* is the effective mass of the charge carrier and c is the velocity of light. The real part of the dielectric constant e1 = n2 has been calculated at different values of l and plotted as a function of l2 as shown in Fig. 14. From the figure, the linear dependence of e1 on l2 is observed at longer wavelengths. Extrapolating the linear part of this dependence to zero wavelength gives the value of eL as 5.96. From the slopes of these lines, value of N/m* for nc-CdSe has also been calculated as 5.62 1047/cm3. The obtained value of N/m* is in good agreement with the reported values in the literature [47,48].
0.30 nc-CdSe
18
0.29
nc-CdSe
16 14
(n2-1)-1
0.28
12 10
n2
0.27
8
0.26
6 4
0.25
2 0.50
0.55
0.60
0.65
0.70
(h ν)2 (eV )2 1
Fig. 13. Plot of ðn2 1Þ
against (hn)2 for nc-CdSe thin films.
0.75
0.00E+000 2.00E-008 4.00E-008 6.00E-008 8.00E-008 1.00E-007 1.20E-007
λ 2 (cm2 ) Fig. 14. Plot of e1 vs. l2 of nc-CdSe thin films.
1406
K. Sharma et al. / Materials Research Bulletin 47 (2012) 1400–1406
The carrier concentration (Nopt) for nc-CdSe thin films can be calculated according to Drude’s theory of dielectric using the formula [47]:
e1 ðhwÞ ¼ n2 k2 ¼ eopt
2
ð hwD Þ ð hwÞ
2
(18)
where eopt is the residual dielectric constant due to ion core, £w is the photon energy and £wD is the screened plasma energy. By plotting (n2 k2) vs. (£w)2, the optical dielectric constant eopt for nc-CdSe thin films has been found to be 6.05. The factors of eopt and £wD are related to plasma frequency wP which is defined as: hwD hwP ¼ pffiffiffiffiffiffiffiffi
eopt
(19)
The evaluated values of £wP and the value of plasma frequency are 0.35 eV and 5.33 1013 Hz respectively. The optical carrier concentration (Nopt) in the conduction band can be determined by the relation: N opt ¼
2 o opt me wP 2 e
ee
(20)
where eo is the permittivity of free space, e is the elementary charge and me is the effective mass of electrons with value of m* = 0.4 mo [49] while mo is the free electron mass. The obtained value of Nopt 8.84 1022 is in good agreement with the carrier concentration of semiconductors [37]. 4. Conclusions The optical constants (refractive index n, extinction coefficient k and dielectric constants e1 and e2) of nc-CdSe thin films have been determined from the transmittance spectra using Swanepoel’s method. The optical band gap is calculated using Tauc’s method and it turns out to be 2.25 eV in contrast to bulk 1.7 eV. Direct transitions are responsible for the optical absorption. The refractive index and the extinction coefficient decrease with the increase in wavelength. The decrease in refractive index with increase in wavelength indicates that ncCdSe shows normal dispersion behaviour. Values of real part of the dielectric constant are higher than the imaginary ones and their spectral dependence reveals that both increase with increase in photon energy. These results indicate that dissipation factor (tan d) shows an increase with increase in photon energy. The optical conductivity of nc-CdSe increases with increasing photon energy. The Urbach slope and steepness parameter have been calculated from the well known Urbach relation. Refractive index dispersion is discussed in terms of Wemple–DiDomenico model and dispersion parameters Eo and Ed have also been calculated. Further, analysis of refractive index dispersion data has been done to calculate eL and N/m*. The value of optical carrier concentration Nopt has also been calculated using Drude’s theory of dielectric for nc-CdSe thin films.
Acknowledgements This work is financially supported by Department of Science and Technology (Major Research Project), N. Delhi. Ms Kriti Sharma is thankful to UGC, N. Delhi for providing the fellowship. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42] [43] [44] [45] [46] [47] [48] [49]
M.C. Troparesky, J.R. Chelikowsky, J. Chem. Phys. 144 (2001) 943. G. Hodes, I.D.J. Howel, L.M. Peter, J. Electrochem. Soc. 139 (1992) 3136. P.K. Ghosh, S. Jana, S. Nandy, K.K. Chattopadhay, Mater. Res. Bull. 42 (2007) 505. M.M. El-Nahass, M.M. Sallam, M.A. Afifi, I.T. Zedan, Mater. Res. Bull. 42 (2007) 371. R.S. Sonawane, S.K. Apte, S.D. Naik, D.B. Raskar, B.B. Kale, Mater. Res. Bull. 43 (2008) 618. A.A. Yadav, M.A. Barote, E.U. Masumdar, Chalcogenide Lett. 6 (2009) 149. S.K. Tripathi, J. Mater. Sci. 20 (2010) 5468. A.S. Khomane, P.P. Hankare, J. Alloys Compd. 489 (2010) 605. K.N. Shreekanthan, B.V. Rajendra, V.B. Kasturi, G.K. Shivakumar, Cryst. Res. Technol. 38 (2003) 30. A.O. Oduor, R.D. Gould, Thin Solid Films 270 (1995) 387. Z.S. Ju, Y.M. Lu, J.Y. Zhang, X.J. Wu, K.W. Liu, D.X. Zhao, Z.Z. Zhang, B.H. Li, B. Yao, D.Z. Shen, J. Cryst. Growth 307 (2007) 26. P.P. Hankare, P.A. Chate, D.J. Sathe, A.A. Patil, J. Mater. Sci.: Mater. Electron. 20 (2009) 776. A.G. Lehmann, M. Bionducci, F. Buffa, Phys. Rev. B 58 (1998) 5275. C.M. Rouleau, D.H. Lowndes, Appl. Surf. Sci. 127 (1998) 418. M. Ohishi, M. Yoneta, H. Saito, H. Sawanda, S. Mori, J. Cryst. Growth 184 (1998) 57. H. Cachet, R. Cortes, M. Froment, A. Etcheberry, Thin Solid Films 361 (2000) 84. T. Gruszecki, B. Holmstro¨m, Sol. Energy Mater. Sol. C 31 (1993) 227. Z. Aneva, D. Nesheva, C. Main, S. Reynolds, A.G. Fitzgerald, Z. Vateva, Semicond. Sci. Technol. 23 (2008) 095002. A. Creti, G. Leo, A. Persano, A. Cola, L. Manna, M. Lomascolo, Physica E 40 (2008) 2063. J. Sharma, G.S.S. Saini, N. Goyal, S.K. Tripathi, J. Optoelectron. Adv. Mater. 9 (2007) 3194. K.D. Patel, M.S. Jain, V.M. Pathak, R. Srivastava, Chalcogenide Lett. 6 (2009) 279. R.B. Kale, C.D. Lokhande, Semicond. Sci. Technol. 20 (2005) 1. H.M. Ali, H.A. Abd El-Ghanny, J. Phys.: Condens. Matter 20 (2008) 155205. J.-C. Chou, S.-Y. Yang, Y.-S. Wang, Mater. Chem. Phys. 78 (2003) 666. JCPDS data file no 8-459. K.N. Shreekanthan, B.V. Rajendra, V.B. Kasturi, G.K. Shivakumar, Cryst. Res. Technol. 38 (2003) 30. C. Baban, G.I. Rusu, Appl. Surf. Sci. 211 (2003) 6. S. Chaure, N.B. Chaure, R.K. Pandey, Physica E 28 (2005) 439. A.S. Edelestein, R.C. Camarata, Nanomaterials: Synthesis, Properties and Application, Institute of Physics Publishing, 1998,, p. 214, 230, 235, 241. V. Babentsov, J. Reigler, J. Schneider, O. Ehlert, T. Nann, M. Fiederle, J. Cryst. Growth 280 (2005) 502. R.S. Singh, S. Bhushan, A.K. Singh, S.R. Deo, Dig. J. Nanomater. Biostruct. 6 (2011) 403. R. Swanepoel, J. Phys. E: Sci. Instrum. 16 (1983) 1214. R. Swanepoel, J. Phys. E: Sci. Instrum. 17 (1984) 896. J.C. Manifacier, J. Gasiot, J.P. Fillard, J. Phys. E: Sci. Instrum. 9 (1976) 1002. M.M. Wakkad, E.K. Shoker, S.H. Mohamed, J. Non-Cryst. Solids 157 (2000) 265. F. Yakuphanoglu, A. Cukurovali, I. Yilmaz, Physica B 351 (2004) 53. J.J. Pankove, Optical Properties in Semiconductors, Prentice-Hall, Englewood Cliffs, NJ, 1971. R.S. Singh, S. Bhushan, A.K. Singh, Chalcogenide Lett. 7 (2010) 375. J.M. Gonza´lez-Leal, E. Ma´rquez, A.M. Bernal-Oliva, J.J. Ruiz-Pe´rez, R. JimenezGaray, Thin Solid Films 317 (1998) 223. H. Mahz, Phys. Rev. 125 (1962) 1510. J.I. Pankove, Optical Processes in Semiconductors, Dover Publications, New York, 1975 . M. DiDomenico, S.H. Wemple, J. Appl. Phys. 40 (1969) 720. S.H. Wemple, M. DiDomenico, Phys. Rev. B 3 (1971) 1338. M. Caglar, M. Zor, S. Ilican, Y. Caglar, Czech. J. Phys. 56 (2006) 277. S.H. Wemple, Phys. Rev. B 7 (1972) 3767. J.N. Zemel, J.D. Jensen, R.B. Schoolar, Phys. Rev. A 140 (1965) 330. Alaa A. Akl, J. Phys. Chem. Solids 71 (2010) 223. M.G. Hutchins, O. Abu-Alkhair, M.M. El-Nahass, K. Abdel-Hady, Mater. Chem. Phys. 98 (2006) 401. Q. Shen, K. Katayama, T. Sawada, T. Toyoda, Thin Solid Films 516 (2008) 5927.
Contents lists available at SciVerse ScienceDirect
Materials Research Bulletin journal homepage: www.elsevier.com/locate/matresbu
Determination of dispersive optical constants of nanocrystalline CdSe (nc-CdSe) thin films Kriti Sharma, Alaa S. Al-Kabbi, G.S.S. Saini, S.K. Tripathi * Centre of Advanced Study in Physics, Department of Physics, Panjab University, Chandigarh 160014, India
A R T I C L E I N F O
A B S T R A C T
Article history: Received 19 October 2011 Received in revised form 11 January 2012 Accepted 1 March 2012 Available online 10 March 2012
The nanocrystalline thin films of CdSe are prepared by thermal evaporation technique at room temperature. These thin films are characterized by transmission electron microscopy (TEM), scanning electron microscopy (SEM), energy dispersive X-ray analysis (EDX), X-ray diffraction (XRD) and photoluminescence spectroscopy (PL). The transmission spectra are recorded in the transmission range 400–3300 nm for nc-CdSe thin films. Transmittance measurements are used to calculate the refractive index (n) and absorption coefficient (a) using Swanepoel’s method. The optical band gap (Eopt g ) has been determined from the absorption coefficient values using Tauc’s procedure. The optical constants such as extinction coefficient (k), real (e1) and imaginary (e2) dielectric constants, dielectric loss (tan d), optical conductivity (sopt), Urbach energy (Eu) and steepness parameter (s) are also calculated for nc-CdSe thin films. The normal dispersion of refractive index is described using Wemple–DiDomenico single-oscillator model. Refractive index dispersion is further analysed to calculate lattice dielectric constant (eL). ß 2012 Elsevier Ltd. All rights reserved.
Keywords: A. Nanostructures A. Thin films B. Vapor deposition D. Optical properties
1. Introduction In recent years, the field of nanocrystalline semiconducting thin films is rapidly expanding. The increasing interest for these materials is due to the fact that these are characterized by properties which are substantially different from the corresponding ones for bulk semiconductors [1]. These phenomena are known as confinement effects or quantum size effects and are of special interest in nanotechnology. The nanodimensions of semiconducting crystals influence the band structure which allows the nanotechnologists to design a semiconductor with suitable optical and electrical properties (i.e. suitable band gap energy) for various technical applications by controlling the crystal size [2]. Thin films of II–VI semiconductors are of considerable interest for their excellent optical properties in the visible region [3–5]. CdSe is an important member of this group of binary compounds. It has a direct intrinsic band gap of 1.74 eV, which makes it an interesting material for various applications such as solar cells, photodetector, light emitting diodes and other optoelectronic devices [6–8]. Shreekanthan et al. [9] found that CdSe films deposited at room temperature are cadmium rich with segregated selenium globules, but a deposition at higher temperatures has been found to yield stochiometric and homogeneous films. CdSe
* Corresponding author. Tel.: +91 172 2534462; fax: +91 172 2783336. E-mail addresses: [email protected], [email protected] (S.K. Tripathi). 0025-5408/$ – see front matter ß 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.materresbull.2012.03.008
often possesses n-type conductivity in bulk as well as in thin films [10]. As it is well known that CdSe can be crystallized in zinc blende (cubic), wurtzite (hexagonal) or wurtzite–zinc blende mixed phases, the transformation in crystalline phases of CdSe has attracted much attention in the past [11]. Some researchers have observed the phase transformation by annealing [12] or mechanically grinding CdSe samples [13]. A variety of methods have been used to prepare CdSe thin films (including physical vapor deposition, sputtering, spray pyrolysis, electrodeposition, etc.) [14–17]. Physical vapor deposition (PVD) is often used because it offers many possibilities to modify the deposition parameters and to obtain films with desired structures and properties. Aneva et al. [18] have deposited the CdSe nanocrystalline thin films of different thicknesses by thermal evaporation technique and studied the influence of the depositions and film thickness on the microstructure and the electrical properties using different techniques. The decrease of dark conductivity and photoconductivity with the layer thickness reduction (and the grain size decrease) is related to the size-induced increase of interface defects and appearance of new faster recombination centres [18]. Creti et al. [19] have studied the role of defect states on the electrical and optical properties in CdSe nanorods thin films. They have observed that deposition techniques affect the films morphologies and the self assembling allows more ordered quantum rods and films with reduced roughness. Earlier, our group has reported the effect of annealing on electrical and optical properties of nc-CdSe thin films [20]. Previous reports on studies of these nc-CdSe thin films are mainly related to structural
K. Sharma et al. / Materials Research Bulletin 47 (2012) 1400–1406
characterization [21,22], transport properties [23] and to optical properties [21,23]. So, it is clear from the above discussion, that not much work has been reported on the optical properties (specially the dispersion parameters) of nc-CdSe thin films. In the present work, we have investigated optical dispersion properties of nc-CdSe thin films because this information will be helpful in research towards applying this material in optical communication and optical devices. The study of optical absorption, particularly the absorption edge has been proved to be very useful for elucidation of the optical properties and optical constants of nc-CdSe. The evaluation of optical dispersions and other optical constants are of considerable importance for applications in integrated optic devices such as switches, filters and modulators, etc., where the refractive index of a material is the key parameter for device design. The objective of this paper is to obtain detailed information of optical dispersive constants of nc-CdSe thin films. We have used high percentage of selenium in CdSe because of its unique properties including high photosensitivity [24] to electromagnetic radiation. We have deposited thin films of nc-CdSe by thermal evaporation technique using inert gas condensation (IGC) method as it offers large possibilities to modify the deposition conditions and to obtain films with determined structure and properties. 2. Experimental Melt quenching technique has been used for the preparation of CdSe material. Constituent elements (5 N pure) are weighed according to their atomic percentages and sealed in quartz ampoules in vacuum 2 105 mbar. The sealed ampoules are kept inside the furnace where the temperature is increased up to 1000 8C at a heating rate of 2–3 8C/min. The ampoules are frequently rocked for 24 h at the highest temperature of the constituent elements to make the melt homogeneous. The quenching is done in liquid N2. Thin films of the alloy are prepared by thermal evaporation technique using IGC method in the presence of Argon as inert gas at room temperature and base pressure of 2 105 mbar on well-degassed Corning 7059 glass substrates. The films are kept in deposition chamber in dark for 24 h before taking optical measurements to attain thermodynamic equilibrium. Films have also been deposited on TEM grid. Transmission electron microscopy (TEM) has been done using Hitachi H7500 electron microscope, operating at 80 kV. Crystallographic study is carried out on the nc-CdSe thin films using a Spinner 3064 XPERT-PRO X-ray diffractometer operating at 45 kV and 40 mA current using Cu Ka radiation in the 2u range from 108
1401
to 808. The microstructure of the nc-CdSe thin films on the glass substrate has been studied by using a Jeol Scanning Electron Microscope (JSM-6610 LV) attached with EDX analyser to measure quantitatively the sample stiochiometry. The nc-CdSe thin films are coated with a thin layer of gold (Au) using a SEM sputter coating unit JEOL JFC-1600 before taking SEM and EDX. Photoluminescence (PL) spectrum of nc-CdSe thin film is recorded in the visible region on a computer-controlled luminescence spectrophotometer LS-50 B (Perkin Elmer Instruments) with laccuracy = 1.0 nm. A pulsed Xe discharge lamp is used as an excitation source. The sample is excited at 390 nm and the spectrum is recorded in the range from 470 nm to 640 nm. The normal incidence transmission spectra of the substrate with and without nc-CdSe thin films have been measured by a UV/VIS/NIR computer controlled spectrophotometer Perkin Elmer LAMBDA 750 in the transmission range 400–3300 nm at room temperature (300 K). 3. Results and discussion 3.1. Structural characterization The TEM image for CdSe nanoparticles is shown in Fig. 1(a). The TEM micrograph reveals the spherical shape of CdSe nanoparticles. The inset of this image shows nanoparticles at very large magnification. From TEM micrograph, we obtain the diameters of the nanoparticles and average diameter of the particles is calculated from the peak of the size distribution plots as shown in Fig. 1(b). The average particle size is in the range of 40–45 nm. Scanning electron microscopy (SEM) is a convenient technique to study the microstructure of thin films. Fig. 2 shows the surface morphology of thin films of CdSe nanoparticles. From the micrographs, it is observed that films are homogenous, without cracks or holes and that they cover the glass substrate well. The composition of the nc-CdSe thin films has been studied by energy dispersive X-ray spectroscopy (EDX). The elemental analysis is carried out only for Cd and Se as shown in Fig. 3. The curve exhibits the presence of Cd and Se peaks with an average atomic percentage ratio of 35:65. The CdSe thin films may grow with either sphalerite cubic (zinc-blende type) or the hexagonal (wurtzite-type) structure. The hexagonal state is the stable phase of CdSe while sphalerite cubic modification is a metastable structural phase commonly occurring at low temperature. Fig. 4 shows the XRD pattern of nc-CdSe thin films. The figure shows the XRD peak at d = 3.79 A˚, 2u = 23.438 which corresponds to the (1 0 0) plane of the hexagonal (wurtzite) crystal structure. The comparison of the observed d value with
Fig. 1. (a) TEM image of nanoparticles of CdSe thus formed. Inset shows CdSe nanoparticles at higher magnification. (b) Size distribution of CdSe nanoparticles.
K. Sharma et al. / Materials Research Bulletin 47 (2012) 1400–1406
1402
350
nc-CdSe
300
(100)
Counts
250 200 150 100 50 0 0
10
20
30
40
2θ0
Fig. 2. SEM image of nc-CdSe thin film.
50
60
70
80
90
Fig. 4. XRD pattern of nc-CdSe thin film.
standard d value [25] clearly indicates the formation of hexagonal (wurtzite-type) phase. So the nc-CdSe thin films deposited on glass substrate using thermal evaporation method possess hexagonal structure, in present case agrees well with the reported data [26,27]. The broad hump in the background is either due to the amorphous glass substrate or possibly due to some amorphous phase present in the thin film [22]. The size of the crystallite is evaluated by making the Gaussian fit of the intense part of the peak (considering broad hump as base) of X-ray diffraction using the Scherrer formula [22]: d¼
0:9l b cos u
(1)
where b is the full width at half maximum in radians, l is the wavelength of X-rays used and u is the Bragg’s angle. The average crystallite size is found to be approximately 12 nm.
3.2. Optical characterization The PL spectrum of nc-CdSe thin film recorded at room temperature is shown in Fig. 5. This figure shows two bands in green region, an intense band at 531 nm and a relatively less intense one at 584 nm. Also, a weak band at 487 nm in blue region can also be seen in the spectrum. The band gap of nc-CdSe film is found to be 2.25 eV. The band at 584 nm can be assigned to excitonic emission. Of importance is the appearance of two deep level emission peaks at 487 nm and 531 nm. These may be attributed to the presence of one deep trapping site and electron– hole recombination via trap state or imperfection site [28]. Deep states in nanocrystalline materials are mainly associated with stochiometric defects, dangling bonds or external adatoms such as oxygen [29] and intrinsic lattice defects, in view of much larger surface to volume ratio in nanocrystalline materials [30]. Appearance of the bands at 487 nm and 531 nm in the PL spectrum of ncCdSe thin films deposited via chemical bath deposition has also been reported by Singh et al. [31]. The spectral dependence of the transmittance, T, of the nc-CdSe thin films has been measured in the wavelength range 400– 3300 nm. The data is illustrated in Fig. 6. The value of refractive index, n, has been calculated using Swanepoel’s method from the observed transmittance spectra. The model behind Swanepoel’s
240
nc-CdSe
220
531 584
Intensity (a.u.)
200
487
180 160 140 120 100 80 460
Fig. 3. Typical EDX pattern of nc-CdSe: (a) spectra and (b) EDX element composition table.
480
500
520
540
560
λ (nm)
580
600
Fig. 5. PL spectrum of nc-CdSe thin film.
620
640
660
K. Sharma et al. / Materials Research Bulletin 47 (2012) 1400–1406
H¼
Hþ
H
4s2 ðs2 þ 1ÞT
2
s2
s2 þ 1 2
6 5 4 3
(2)
2
(3)
1 0.35
nc-CdSe
0.30
The value of n is calculated using Eq. (2) and is plotted vs. l in Fig. 7. This decrease in the value of refractive index with wavelength attributes to the significant normal dispersion behaviour of the films. The extinction coefficient, k, is a measure of the fraction of light lost due to scattering and absorption per unit distance of the penetration medium. The extinction coefficient (k) can be calculated by using the relation: al l 1 ln ¼ (4) k¼ x 4p 4pd where a is the absorption coefficient, d is the thickness of the film and x is the absorbance. The value of k decreases with increase in wavelength as plotted in Fig. 7 and follows the same trend as that of n. This observation confirms the decrease in the loss of light due to scattering and absorbance with increase in l. The dielectric constant which is another important optical parameter can be defined as:
eðvÞ ¼ e1 ðvÞ þ ie2 ðvÞ
(5)
The real and imaginary parts of dielectric constant can be calculated with the help of n and k values [35]. The real dielectric constant (e1) can be calculated as:
e1 ¼ n2 k2
(6)
while the imaginary dielectric constant (e2) can be calculated as:
e2 ¼ 2nk
(7)
0.25 0.20 0.15 0.10 0.05 0.00 0
1000
1500
2000
2500
3000
3500
Fig. 7. Plot showing variation of refractive index (n) and extinction coefficient (k) with wavelength (l).
constant are more than the imaginary part. The variation of the dielectric constant with photon energy indicates that some interactions between photons and electrons are produced in this energy range. The dissipation factor (tan d) can be calculated using relation [36]: tan d ¼
e2 e1
(8)
Fig. 9 shows the plot of the dissipation factor (tan d) as a function of frequency. It is clear from the figure that dissipation factor increases with increase in frequency. From the transmission data, nearly at the fundamental absorption edge, the values of
24 22 20 18 16 14 12 10 8 6 4 2 0 3.5
nc-CdSe
ε1
1.0
500
λ (nm)
The variation of the real and imaginary dielectric constants with energy (hn) is shown in Fig. 8. It is clear from the figure that the real and imaginary parts of the dielectric constant show a similar behaviour. It is also clear that the values of the real part of dielectric
nc-CdSe
0.8 0.6
3.0
nc-CdSe
2.5
0.4
2.0
ε2
Transmittance
nc-CdSe
k
n¼
2
7
n
method [32,33] assumes that the sample is a thin film of nonuniform thickness deposited on a transparent substrate having a refractive index s. The film has a complex refractive index n* = n ik, where n is the refractive index and k is the extinction coefficient. According to this method, which is based on the approach of Manifacier et al. [34], the refractive index in the region where a 0 is calculated by the following equation: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1403
0.2
1.5 1.0 0.5
0.0
0.0
0
500
1000
1500
2000
λ (nm)
2500
3000
3500
Fig. 6. Optical transmission spectra of nc-CdSe at room temperature. Inset shows the variation of optical absorption coefficient (a) with photon energy (hn).
0.5
1.0
1.5 hν (eV )
2.0
2.5
Fig. 8. Plot of real (e1) and imaginary (e2) parts of dielectric constant vs. photon energy (hn).
K. Sharma et al. / Materials Research Bulletin 47 (2012) 1400–1406
1404
1.20E+011
0.11 nc-CdSe
nc-CdSe
1.00E+011
eV/cm2
0.10
0.08
2
0.07
(αhν)
tan δ
0.09
8.00E+010 6.00E+010 4.00E+010 2.00E+010
0.06 0.00E+000 0.05 4.50E+014 4.80E+014 5.10E+014 5.40E+014 5.70E+014
1.0
1.5
2.0
2.5
hν (eV)
3.0
3.5
Fig. 10. Plot of (ahn)2 vs. hn for nc-CdSe thin films deposited at room temperature.
freq (Hz) Fig. 9. Plot of dissipation factor (tan d) vs. frequency (f).
values have been calculated from the relation:
Inset of Fig. 6 shows the variation of a with photon energy (hn). Figure shows that a increases with increase in hn. The fundamental absorption, which corresponds to the transition from valence band to conduction band, can be used to determine the band gap of the material. It corresponds to higher values of absorption coefficient a 104 cm1. The relation between a and the incident photon energy (hn) from the power law behaviour of Tauc can be written as [37]: n
a¼
Aðhn Eg Þ hn
(10)
where A is a constant, Eg is the optical band gap of the material and the exponent n depends on the type of transition. The n may have values 1/2, 2, 3/2 and 3 corresponding to the allowed direct, allowed indirect, forbidden direct and forbidden indirect transitions, respectively. The value of Eg is calculated by extrapolating the straight line portion of (ahn)1/n vs. hn graph to hn axis taking n = 0.5. Fig. 10 shows the plot of (ahn)2 vs. hn for nc-CdSe films. From the plot of the figure, the value of Eg is found to be 2.25 eV which is more as compared to bulk CdSe (1.7 eV) due to quantum confinement effect. Kale et al. [22] have reported the band gap value to be 2.1 eV for nc-CdSe thin films prepared by successive ionic layer adsorption and reaction method. Singh et al. [38] have synthesized nc-CdSe thin films by chemical bath deposition (CBD) at the two volumes of capping agents and found the band gap values as 1.92 eV and 2.02 eV. The absorption coefficient (a) near the fundamental absorption edge depends exponentially on the incident photon energy. The spectral dependence of a has also been studied at photon energies less than the energy gap i.e. in the region of so-called Urbach spectral tail, where ln a varies as a function of hn. The Urbach energy can be calculated by following relation [39]: hn aðhnÞ ¼ ao exp (11) Eu where ao is a constant and Eu is the Urbach energy which refers to the width of exponential absorption edge. Plotting the dependence of ln a vs. hn as shown in Fig. 11 should give a straight line. The Eu
1 dðln aÞ dðhnÞ
(12)
In both crystalline and amorphous materials there is no known origin of the exponential dependence of absorption coefficient with energy. This dependence may arise from the random fluctuations of the internal fields associated with structural disorder in many materials. The dependence of the optical absorption coefficient with photon energy may arise from electronic transitions between localized states. The steepness parameter, s = kT/Eu characterizing the broadening of the optical absorption edge due to electron phonon or exciton–phonon interactions [40] has also been determined at room temperature. The calculated values of Urbach energy (Eu) and steepness parameter (s) are 210 meV and 0.12 respectively. Optical response is most conveniently studied in terms of optical conductivity. The absorption coefficient (a) can be used to calculate the optical conductivity (sopt) as follows [41]:
s opt ¼
anc 4p
(13)
where a is the absorption coefficient, n is the refractive index and c is the velocity of light. Fig. 12 shows the variation of sopt as a function of photon energy (hn) for nc-CdSe thin film. It is clear from
10.8 nc-CdSe
10.6 10.4
ln α
absorption coefficient (a), are calculated in the region of strong absorption using the relation: 1 1 a ¼ ln (9) d T
Eu ¼
10.2 10.0 9.8 9.6 1.35
1.40
1.45
h ν (eV)
1.50
Fig. 11. ln a vs. energy plot of films.
1.55
1.60
K. Sharma et al. / Materials Research Bulletin 47 (2012) 1400–1406
3.50E+015
nc-CdSe
3.00E+015 2.50E+015
σopt
2.00E+015 1.50E+015 1.00E+015 5.00E+014 0.00E+000 0.5
1.0
1.5
2.0
2.5
3.0
3.5
hν (eV ) Fig. 12. Plot between optical conductivity (sopt) and photon energy (hn).
the figure that the optical conductivity increases with increase in the photon energy, which may be either due to the high absorbance of nc-CdSe thin films or due to the electrons excited by photon energy. 3.3. Refractive index dispersion The refractive index n is found to decrease with the increase in wavelength of incident photon as observed from Fig. 7. The refractive index dispersion below the interband absorption edge can be fitted by Wemple–DiDomenico relationship. The result of refractive index dispersion below the interband absorption edge corresponds to the fundamental electronic excitation spectrum. Thus, the refractive index is related to photon energy through the relationship [42,43]: n2 ¼ 1 þ
Eo Ed
(14)
2
E2o ðhnÞ
The physical meaning of the single-oscillator energy, Eo, is that it simulates all the electronic excitation involved. Eo takes values near the main peak of the imaginary part of the dielectric constant spectrum. The so-called dispersion energy, Ed, is related to the average strength of the optical transitions. By plotting (n2 1)1 vs. (hn)2 and fitting the data, a straight line is obtained as shown in Fig. 13. Eo and Ed are determined directly from the gradient
1405
(n2 1)1 and the intercept on vertical axis [44]. The calculated values of Eo and Ed are 1.4 eV and 3.54 eV respectively. It is observed that the plots are linear over the energy range from 0.5 to approximately 0.71 eV. At low energies, deviation from linearity with a positive curvature is usually observed due to the negative contribution of lattice vibrations to the refractive index. At high energies, a negative curvature deviation is sometimes observed due to the proximity of the band edge or excitonic absorption [43]. This model describes the dielectric response of transitions below the optical gap. It plays an important role in determining the behaviour of refractive index. This results from the relationship between electronic properties of the material and its chemical bond [45]. The value of static refractive index, no, for nc-CdSe thin films has been calculated from Wemple–DiDomenico dispersion parameters Eo and Ed by using the following relation: sffiffiffiffiffiffiffiffiffiffiffiffiffiffi E no ¼ 1 þ d Eo
(15)
The value of no is calculated by extrapolating the Wemple– DiDomenico dispersion equation to hn ! 0 (Eq. (14)). The calculated value of no is 1.88. The obtained data of refractive index n can be analysed to obtain the lattice dielectric constant (high frequency dielectric constant) [46]. This procedure describes the contribution of free carriers and the lattice vibration modes of the dispersion. The following equation can be used to obtain the lattice dielectric constant [46]:
e1 ¼ eL Bl2 B¼
(16)
e2 N
(17)
pc2 m
where e1 is the real part of dielectric constant, eL is the lattice dielectric constant, l is the wavelength, N is the free charge carrier concentration, m* is the effective mass of the charge carrier and c is the velocity of light. The real part of the dielectric constant e1 = n2 has been calculated at different values of l and plotted as a function of l2 as shown in Fig. 14. From the figure, the linear dependence of e1 on l2 is observed at longer wavelengths. Extrapolating the linear part of this dependence to zero wavelength gives the value of eL as 5.96. From the slopes of these lines, value of N/m* for nc-CdSe has also been calculated as 5.62 1047/cm3. The obtained value of N/m* is in good agreement with the reported values in the literature [47,48].
0.30 nc-CdSe
18
0.29
nc-CdSe
16 14
(n2-1)-1
0.28
12 10
n2
0.27
8
0.26
6 4
0.25
2 0.50
0.55
0.60
0.65
0.70
(h ν)2 (eV )2 1
Fig. 13. Plot of ðn2 1Þ
against (hn)2 for nc-CdSe thin films.
0.75
0.00E+000 2.00E-008 4.00E-008 6.00E-008 8.00E-008 1.00E-007 1.20E-007
λ 2 (cm2 ) Fig. 14. Plot of e1 vs. l2 of nc-CdSe thin films.
1406
K. Sharma et al. / Materials Research Bulletin 47 (2012) 1400–1406
The carrier concentration (Nopt) for nc-CdSe thin films can be calculated according to Drude’s theory of dielectric using the formula [47]:
e1 ðhwÞ ¼ n2 k2 ¼ eopt
2
ð hwD Þ ð hwÞ
2
(18)
where eopt is the residual dielectric constant due to ion core, £w is the photon energy and £wD is the screened plasma energy. By plotting (n2 k2) vs. (£w)2, the optical dielectric constant eopt for nc-CdSe thin films has been found to be 6.05. The factors of eopt and £wD are related to plasma frequency wP which is defined as: hwD hwP ¼ pffiffiffiffiffiffiffiffi
eopt
(19)
The evaluated values of £wP and the value of plasma frequency are 0.35 eV and 5.33 1013 Hz respectively. The optical carrier concentration (Nopt) in the conduction band can be determined by the relation: N opt ¼
2 o opt me wP 2 e
ee
(20)
where eo is the permittivity of free space, e is the elementary charge and me is the effective mass of electrons with value of m* = 0.4 mo [49] while mo is the free electron mass. The obtained value of Nopt 8.84 1022 is in good agreement with the carrier concentration of semiconductors [37]. 4. Conclusions The optical constants (refractive index n, extinction coefficient k and dielectric constants e1 and e2) of nc-CdSe thin films have been determined from the transmittance spectra using Swanepoel’s method. The optical band gap is calculated using Tauc’s method and it turns out to be 2.25 eV in contrast to bulk 1.7 eV. Direct transitions are responsible for the optical absorption. The refractive index and the extinction coefficient decrease with the increase in wavelength. The decrease in refractive index with increase in wavelength indicates that ncCdSe shows normal dispersion behaviour. Values of real part of the dielectric constant are higher than the imaginary ones and their spectral dependence reveals that both increase with increase in photon energy. These results indicate that dissipation factor (tan d) shows an increase with increase in photon energy. The optical conductivity of nc-CdSe increases with increasing photon energy. The Urbach slope and steepness parameter have been calculated from the well known Urbach relation. Refractive index dispersion is discussed in terms of Wemple–DiDomenico model and dispersion parameters Eo and Ed have also been calculated. Further, analysis of refractive index dispersion data has been done to calculate eL and N/m*. The value of optical carrier concentration Nopt has also been calculated using Drude’s theory of dielectric for nc-CdSe thin films.
Acknowledgements This work is financially supported by Department of Science and Technology (Major Research Project), N. Delhi. Ms Kriti Sharma is thankful to UGC, N. Delhi for providing the fellowship. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42] [43] [44] [45] [46] [47] [48] [49]
M.C. Troparesky, J.R. Chelikowsky, J. Chem. Phys. 144 (2001) 943. G. Hodes, I.D.J. Howel, L.M. Peter, J. Electrochem. Soc. 139 (1992) 3136. P.K. Ghosh, S. Jana, S. Nandy, K.K. Chattopadhay, Mater. Res. Bull. 42 (2007) 505. M.M. El-Nahass, M.M. Sallam, M.A. Afifi, I.T. Zedan, Mater. Res. Bull. 42 (2007) 371. R.S. Sonawane, S.K. Apte, S.D. Naik, D.B. Raskar, B.B. Kale, Mater. Res. Bull. 43 (2008) 618. A.A. Yadav, M.A. Barote, E.U. Masumdar, Chalcogenide Lett. 6 (2009) 149. S.K. Tripathi, J. Mater. Sci. 20 (2010) 5468. A.S. Khomane, P.P. Hankare, J. Alloys Compd. 489 (2010) 605. K.N. Shreekanthan, B.V. Rajendra, V.B. Kasturi, G.K. Shivakumar, Cryst. Res. Technol. 38 (2003) 30. A.O. Oduor, R.D. Gould, Thin Solid Films 270 (1995) 387. Z.S. Ju, Y.M. Lu, J.Y. Zhang, X.J. Wu, K.W. Liu, D.X. Zhao, Z.Z. Zhang, B.H. Li, B. Yao, D.Z. Shen, J. Cryst. Growth 307 (2007) 26. P.P. Hankare, P.A. Chate, D.J. Sathe, A.A. Patil, J. Mater. Sci.: Mater. Electron. 20 (2009) 776. A.G. Lehmann, M. Bionducci, F. Buffa, Phys. Rev. B 58 (1998) 5275. C.M. Rouleau, D.H. Lowndes, Appl. Surf. Sci. 127 (1998) 418. M. Ohishi, M. Yoneta, H. Saito, H. Sawanda, S. Mori, J. Cryst. Growth 184 (1998) 57. H. Cachet, R. Cortes, M. Froment, A. Etcheberry, Thin Solid Films 361 (2000) 84. T. Gruszecki, B. Holmstro¨m, Sol. Energy Mater. Sol. C 31 (1993) 227. Z. Aneva, D. Nesheva, C. Main, S. Reynolds, A.G. Fitzgerald, Z. Vateva, Semicond. Sci. Technol. 23 (2008) 095002. A. Creti, G. Leo, A. Persano, A. Cola, L. Manna, M. Lomascolo, Physica E 40 (2008) 2063. J. Sharma, G.S.S. Saini, N. Goyal, S.K. Tripathi, J. Optoelectron. Adv. Mater. 9 (2007) 3194. K.D. Patel, M.S. Jain, V.M. Pathak, R. Srivastava, Chalcogenide Lett. 6 (2009) 279. R.B. Kale, C.D. Lokhande, Semicond. Sci. Technol. 20 (2005) 1. H.M. Ali, H.A. Abd El-Ghanny, J. Phys.: Condens. Matter 20 (2008) 155205. J.-C. Chou, S.-Y. Yang, Y.-S. Wang, Mater. Chem. Phys. 78 (2003) 666. JCPDS data file no 8-459. K.N. Shreekanthan, B.V. Rajendra, V.B. Kasturi, G.K. Shivakumar, Cryst. Res. Technol. 38 (2003) 30. C. Baban, G.I. Rusu, Appl. Surf. Sci. 211 (2003) 6. S. Chaure, N.B. Chaure, R.K. Pandey, Physica E 28 (2005) 439. A.S. Edelestein, R.C. Camarata, Nanomaterials: Synthesis, Properties and Application, Institute of Physics Publishing, 1998,, p. 214, 230, 235, 241. V. Babentsov, J. Reigler, J. Schneider, O. Ehlert, T. Nann, M. Fiederle, J. Cryst. Growth 280 (2005) 502. R.S. Singh, S. Bhushan, A.K. Singh, S.R. Deo, Dig. J. Nanomater. Biostruct. 6 (2011) 403. R. Swanepoel, J. Phys. E: Sci. Instrum. 16 (1983) 1214. R. Swanepoel, J. Phys. E: Sci. Instrum. 17 (1984) 896. J.C. Manifacier, J. Gasiot, J.P. Fillard, J. Phys. E: Sci. Instrum. 9 (1976) 1002. M.M. Wakkad, E.K. Shoker, S.H. Mohamed, J. Non-Cryst. Solids 157 (2000) 265. F. Yakuphanoglu, A. Cukurovali, I. Yilmaz, Physica B 351 (2004) 53. J.J. Pankove, Optical Properties in Semiconductors, Prentice-Hall, Englewood Cliffs, NJ, 1971. R.S. Singh, S. Bhushan, A.K. Singh, Chalcogenide Lett. 7 (2010) 375. J.M. Gonza´lez-Leal, E. Ma´rquez, A.M. Bernal-Oliva, J.J. Ruiz-Pe´rez, R. JimenezGaray, Thin Solid Films 317 (1998) 223. H. Mahz, Phys. Rev. 125 (1962) 1510. J.I. Pankove, Optical Processes in Semiconductors, Dover Publications, New York, 1975 . M. DiDomenico, S.H. Wemple, J. Appl. Phys. 40 (1969) 720. S.H. Wemple, M. DiDomenico, Phys. Rev. B 3 (1971) 1338. M. Caglar, M. Zor, S. Ilican, Y. Caglar, Czech. J. Phys. 56 (2006) 277. S.H. Wemple, Phys. Rev. B 7 (1972) 3767. J.N. Zemel, J.D. Jensen, R.B. Schoolar, Phys. Rev. A 140 (1965) 330. Alaa A. Akl, J. Phys. Chem. Solids 71 (2010) 223. M.G. Hutchins, O. Abu-Alkhair, M.M. El-Nahass, K. Abdel-Hady, Mater. Chem. Phys. 98 (2006) 401. Q. Shen, K. Katayama, T. Sawada, T. Toyoda, Thin Solid Films 516 (2008) 5927.