Chapter 5 Investigation of optical properties of WSe 2, W 0.9 Se 2 and MoSe 2 single crystals

Transcription

1 111 Chapter 5 Investigation of optical properties of WSe 2, W 0.9 Se 2 and MoSe 2 single crystals

2 INTRODUCTION Optical properties of every semiconducting substance play a central role for their device applications. The optical band gap or energy gap (E g ) of semiconducting materials is one of the central characteristic of the semiconducting material. It has been established that for maximum solar energy transfer, optical band gap E g of any semiconducting single crystal solar cells should be in the region of 1.4 ev. The semiconducting materials having optical band gap value close to this most favorable value are therefore regarded as to be appropriate for photovoltaic applications. Hence, the investigation of optical band gap is precious for every semiconducting material [1]. To identify the character of semiconducting single crystal one have to think about what happen when identical atoms are bring together to shape a solid such as a semiconducting crystal. As two identical atoms move toward each other the wave functions of their electrons initiate to superimpose. The energy division of the states depends mainly on the interatomic space. It is the degree of the energy gap and the comparative accessibility of electrons that decide whether a solid is a metal, a semiconductor, or an insulator. In a semiconducting substance the energy gap typically ranges from 0.1eV to 3eV and the concentration of electrons in the higher energy states is typically less than cm -3 [2]. The optical energy band gap (E g ) is typically categorized in to direct allowed, direct forbidden, indirect allowed and indirect forbidden optical transition. Direct and indirect optical energy band gap (E g ) can be found out by the following methods [2]. Optical absorption method. Photoelectrochemical method. Conductivity measurement as a function of temperature. Photoemission spectrum method. Band structure calculation method.

3 113 Looking at the significance of optical energy band gap in TMDCs materials, author has carried out an in depth investigation of optical properties of the sample of WSe 2, W 0.9 Se 2 and MoSe 2 using optical absorption method. The results obtained using optical absorption procedure has been illustrated and discussed in this chapter. 5.2 OPTICAL INVESTIGATION The straightforward method to discover the energy band structure of semiconductor is the optical absorption technique. In the optical absorption technique a photon of a recognized energy is applied on the sample material. By absorbing this photon energy, excited electron experience transition from lower energy state to a higher energy state. Therefore with introducing a slab of semiconductor material at the output of a monochromatic light source and investigating the change in the transmitted radiation, one can find out all the probable transitions an electron can construct and investigate a good deal about the division of energy states [2]. The ratio of transmitted to incident radiation projected to depends on photon energy and the width of the sample under investigation [2]. If a photon beam of intensity I o passes through a slab of a thickness t, then beam of photons attenuates in agreement with the exponential rule, (5.1) Where, α = Absorption coefficient (cm -1 ) t = Thickness of sample This coefficient α can be found out normally by evaluating I 0 /I. where I 0 represent incident intensity and I represent emerging intensity from the samples.

4 Fundamental Absorption and Electron Transition The fundamental absorption refers to transition of an excited electron from valence band to conduction band. The fundamental absorption which apparent it self by a sudden increase in absorption can be exploited to discover the optical energy gap of the semiconductor single crystal. On the other hand the transitions are subject to certain selection rules, thus the judgment of an energy band gap from the absorption edge is not a straightforward procedure. Since the momentum of a photon (h/λ) is very minute contrast to the crystal momentum h/a (where a is the lattice constant), the photon absorption progression should conserve the momentum of an electron. Absorption coefficient α(hυ) for a recognized photon energy hυ is proportional to the probability function P if, concentration of initial state n i, and concentration of empty final state n f. This course of action ought to be assumed for all possible transitions among initial state and final state separated by an energy difference equal to hυ. Thus we can write following equation for the all possible transition between energy states [3]. α ( hυ ) = A pif nin f (5.2) Here, for ease we have hypothetical state that all the lower energy states are filled and all the upper energy states are unfilled, a clause which is correct for undoped semiconductor at the temperature of 0 K. The fundamental theory of the direct and indirect transition has been invented by moss.et.al. [1] and pankov.et.al. [2] Direct and Indirect Transitions The absorption procedure and electron transition procedure taking place in a semiconductor can be described as entirely quantum mechanical in nature. These electron transition procedures give rise to interband absorption in substance. Such an electron transition can be classified in to two category, direct transitions and indirect transitions.

5 Direct Transition The electron transitions among two direct valleys where every momentum conserving transitions are permissible and recognized as a direct transition. Such a phenomenon is shown in figure 5.1. Every initial state at E i is related with a final state at E f with the following equation [2]. E = hυ E (5.3) f i However in parabolic bands, E f 2 2 k E g = ħ (5.4) 2m * e and E i 2 2 k = ħ (5.5) 2 m * h Thus, 2 2 ħ k 1 1 hυ Eg = + * * 2 me mh (5.6) E E f E g hυ E i K Fig. 5.1 Theoretical diagram of direct transitions

6 116 The density of directly related states can be represented by the following equation, N ( hυ ) d ( hυ ) 2 8π k dk = (5.7) 3 (2 π ) ( 2 m ) N h d h h E d h 2π ħ 3 / 2 ( υ ) ( υ ) = r 1 / 2 ( υ ) 2 3 g ( υ ) (5.8) Where m r represents reduced mass, which can be given by = + * * m r m e m h Consequently the absorption coefficient can be represented by the following equation, α ( hυ ) A ( hυ E g ) * 1 / 2 = (5.9) Where A* is derived by bardeen et al. is given by the following equation [3], A * * * h e 2 * * m h + m e 2 * n c h m e 3 / 2 2 m m q (5.10) Indirect Transition When an electron transition needs a change in both energy and momentum, a two step method become compulsory since the photon cannot give a modification in momentum. Momentum is conserved via a phonon relation, which is demonstrated in figure 5.2. A wide spectrum of phonon is accessible and these are typically the longitudinal and the transverse acoustic phonon. Every phonon has a characteristic energy E p. Therefore to accomplish the

7 117 transition from E i to E f a phonon is either emitted or absorbed. These two procedures can be given by the following equation [3]. hυ = E E + E e f i p hυ = E E E a f i p (5.11) E g + E P E g - E P E k Fig. 5.2 Theoretical diagram of indirect electron transition At high temperature phonons are present and can contribute in the absorption procedure. Due to this reason electron transition takes place in two steps. Such an electron transition is recognized as non vertical or indirect transition. Such types of indirect transitions have huge significance in semiconductors material. Using the concept of indirect band gap one can determine the energy band gap between the top of the valence band and the bottom of the conduction band [3].

8 118 Optical absorption of DVT grown crystals of WSe 2, W 0.9 Se 2 and MoSe 2 were investigated using UV VIS NIR spectrophotometer in the wavelength series of nm at room temperature. In the optical absorption technique photons of preferred wavelengths are bombarded on the sample under investigation and their comparative absorption is carried out. The photons with energies larger than the band gap are absorbed at the same time photons with energies smaller than band gap are transmitted. Thus using this technique the optical energy band gap can be found accurately. 5.3 OPTICAL BAND GAP DETERMINATION For the direct transitions the relationship between possible transitions across the energy gap of semiconductor and the absorption coefficient α can be given by the following equation [2]. α hv = A( hv E ) r g (5.12) For the indirect transitions above relation can be given by the following equation [2]. α h v = B ( ) r j h v E g ± E p j (5.13) j Where, α = Absorption coefficient hυ = Energy of the incident photon E g = The energy gap for the direct transition E g = The energy gap for indirect transition E p j = The phonons supported energies at indirect transition. E p = Phonon energy.

9 119 A and B are parameter which are essentially depends on temperature, and phonon energies. Equations (5.12) and (5.13) are adequate for the investigation of the experimental results achieved at constant temperature and they are most often used while interpreting results on absorption spectra attained from semiconducting substance. The exponent r in the above equations depend on whether the transition is permitted or not and the constants A and B will suppose to have diverse values for the permitted and prohibited transitions. In support of indirect transitions the complete form of equation (5.13) can be given as [2], 2 B a i 1 r B ei 1 α i = ( E E ) i / T g k i E E i / T g k θ + θ + θ θ i i = 1 E e 1 E 1 e ( ) r (5.14) Where, E = Photon energy, E g = The indirect energy gap θ i = Phonon corresponding temperature B ai and B ei are coefficients associated with absorption and emission of i th phonon. θ i is define by the following equation [2], i P θ = (5.15) i E k Where, E pi is the energy of i th phonon. In these matter the concentration of energy state is a constant and is independent of the energy and the equation illustrating the dependence of α in terms of direct and indirect transitions can be rewritten for direct transition as [2],

10 120 = A ( hv E ) r α g (5.16) And for indirect transition above equation can be rewritten as [2], α = i i r ( E E kθ ) 2 1 r 1 B + + ai ( E E / g kθ i ) B θ T ei / T g i = i θ i 1 e 1 1 e (5.17) 5.4 EXPERIMENTAL SET UP AND PROCEDURE The main intend of work presented in this chapter is to make investigation of the optical absorption spectra obtained from the crystals of WSe 2, W 0.9 Se 2 and MoSe 2. The optical absorption spectra of above mentioned crystals were obtained by the use of UV-VIS-NIR spectrophotometer (Maker: Perkin Elmer, Model: Lambda 19) in the wavelength range from 200nm 2500nm at room temperature. As described earlier all samples of TMDCs were grown by direct vapour transport technique (DVT). The grown samples demonstrate P-type conductivity with hole concentration of to10 14 cm -3 at room temperature. The optical absorption experiments were carried out at SICART, Vallabh Vidhyanagar. Measurements were executed at room temperature with the incident light normal to crystal plane.

11 UV-VIS-NIR Spectrophotometer The UV-VIS-NIR Spectrophotometer is demonstrated in figure 5.3. The shown spectrometer was utilized for the present investigation. This spectrophotometer can in addition be utilized to establish the optical absorption of thin films, solids, liquids and a range of filters etc. Moreover this instrument is useful to investigate kinetic properties of chemical reaction with respect to time. In addition it can be utilized for the chemical reaction investigation of different biological samples. The UV-VIS-NIR spectrometer is a Double-beam, double monochromator with ratio recording supervised by personal computer. The whole system of spectrometer is controlled by the computer system attach with the instrument. Three different experiments were carried out for each samples mention in the pervious section. The computerized data of optical absorption were created after each experiment. To attain the absorption spectra employing UV-VIS-NIR spectrophotometer, slim chip of DVT grown crystals were utilized. These chips of the specimen are pasted on a thick black paper. A small cut is created on the paper so that it can be exposed to the incident light. The reference paper used as a replica of the black paper also has the cut at exactly the same position as the crystal chip. This design is essential since the crystal dimension is smaller than that of the sample section. Clean glass slides can also be utilized as replica. For reflectance measurement normal aluminum coated mirror can be utilized as reference [4]. Fig. 5.3 Perkin Elmer Lambda UV-VIS-NIR spectrometer

12 122 Specifications of UV-VIS-NIR spectrometer Facility : Double Beam, Double Monochromator, Ratio Recording Instrument Model : LAMBDA 19 UV/VIS/NIR Lamp : Deuterium (UV), Tungsten/Halogen (VIS-NIR) Detectors : Photomultiplier tube for UV-Visible Wavelength Range : 200 to 2500 nm Scan speed : nm/min Slit Width : nm Smooth Bandwidth : 8.00 nm Wavelength Accuracy : ±0.15 nm for UV-VIS Base line flatness : ± Å Ordinate Mode : Scan, Time Drive, Wavelength Programming Photometric Accuracy : ± Å or ± 0.08 %T Software utilized : PECOL Software for quantitative description of color

13 RESULTS AND DISCUSSION The absorption spectra of WSe 2, W 0.9 Se 2 and MoSe 2 single crystals are revealed in figure 5.4, 5.5 and 5.6. A cautious investigation of these spectra confirms the occurrence of absorption edges between the spectral range 800 nm to 900 nm. To investigate the results from these spectra in the surrounding area of the absorption edge on the basis of two as well as three dimensional model, values of absorption coefficients α were calculated at each period of 1 nm. In absorption plots a number of peaks were observed but the sharp peak was observed in the wavelength range of 800 nm to 900 nm. This sharp peak confirms the sudden increase of absorption of photon in the sample at a specific wavelength, and the weaker peaks are formed due to interference effects. The graphical illustration of absorption coefficient α in terms of direct and indirect transitions can be performed with the help of formulae 5.12 and 5.13 using values of r given in table WSe Absorbance wave length λ (nm) Fig. 5.4 Optical absorption spectra of WSe 2 single crystal

14 W 0.9 Se 2 Absorbance wave length λ (nm) Fig. 5.5 Optical absorption spectra of W 0.9 Se 2 single crystal MoSe Absorbance wave length λ (nm) Fig. 5.6 Optical absorption spectra of MoSe 2 single crystal

15 125 Direct optical transition takes place simply when the boundaries of the valence and conduction band in K space overlap. However in the case of their non-coincidence, these transitions do not take place, because the wave vector of the photon cannot compensate for the change in crystal momentum. The crystal momentum is though conserved by emission or absorption of phonons throughout the process of electron photon interactions. Both these kind of an optical induced transitions in WSe 2, W 0.9 Se 2 and MoSe 2 single crystals at room temperature are investigated in this section. Table 5.1 Values of exponent r for different types of transitions Type of Transition Direct Indirect 2D 3D 2D 3D Allowed 0 1\2 1 2 Forbidden 1 3\2 2 3 By plotting the diagrams of (αhν) 1/r versus hν for various values of r given in Table 5.1, it is possible to determine value of optical band gap for different kind of transitions. Exploration of the plots to zero absorption will give the appropriate value of the energy band gaps of WSe 2, W 0.9 Se 2 and MoSe 2 single crystals.

16 (αhυ) 1/2 {cm -1/2 ev 1/2 } WSe Photon energy hυ (ev) Fig. 5.7 The Spectral Variation of (αhν) 1/2 Vs. hυ of WSe 2 single crystal 20 (αhυ) 1/3 {cm -1/3 ev 1/3 } WSe Photon energy hv (ev) Fig. 5.8 The Spectral Variation of (αhν) 1/3 Vs. hυ of WSe 2 single crystal

17 E E+07 (αhυ) 2 {cm -2 ev 2 } 3.00E E E E E E WSe E Photon energy hυ (ev) Fig. 5.9 The Spectral Variation of (αhν) 2 Vs. hυ of WSe 2 single crystal (αhυ) 2/3 {cm -2/3 ev 2/3 } WSe Photon energy hυ (ev) Fig The Spectral Variation of (αhν) 2/3 Vs. hυ of WSe 2 single crystal

18 128 (αhυ) 1/2 (cm -1/2 ev 1/2 ) W 0.9 Se Photon energy hυ (ev) Fig The Spectral Variation of (αhν) 1/2 Vs. hυ of W 0.9 Se 2 single crystal 20 (αhυ) 1/3 (cm -1/3 ev 1/3 ) W 0.9 Se Photon energy hυ (ev) Fig The Spectral Variation of (αhν) 1/3 Vs. hυ of W 0.9 Se 2 single crystal

19 E E E+07 (αhυ) 2 (cm -2 ev 2 ) 2.50E E E E E W 0.9 Se E Photon energy hυ (ev) Fig The Spectral Variation of (αhν) 2 Vs. hυ of W 0.9 Se 2 single crystal (αhυ) 2/3 (cm -2/3 ev 2/3 ) W 0.9 Se Photon energy hυ (ev) Fig The Spectral Variation of (αhν) 2/3 Vs. hυ of W 0.9 Se 2 single crystal

20 (αhυ) 1/2 (cm -1/2 ev 1/2 ) MoSe Photon energy hυ (ev) Fig The Spectral Variation of (αhν) 1/2 Vs. hυ of MoSe 2 single crystal 20 (αhυ) 1/3 (cm -1/3 ev 1/3 ) MoSe Photon energy hυ (ev) Fig The Spectral Variation of (αhν) 1/3 Vs. hυ of MoSe 2 single crystal

21 E E+07 (αhυ) 2 (cm -2 ev 2 ) 3.00E E E E E E MoSe E Photon energy hυ (ev) Fig The Spectral Variation of (αhν) 2 Vs. hυ of MoSe 2 single crystal 350 (αhυ) 2/3 (cm -2/3 ev 2/3 ) MoSe Photon energy hυ (ev) Fig The Spectral Variation of (αhν) 2/3 Vs.. hυ of MoSe 2 single crystal

22 132 α {cm -1 } WSe Photon energy hυ (ev) Fig The Spectral Variation of (α) Vs. hυ of WSe 2 single crystal (α) 1/2 {cm -1/2 } WSe Photon energy hv (ev) Fig The Spectral Variation of (α) 1/2 Vs. hυ of WSe 2 single crystal

23 E E+07 α 2 {cm -2 } 2.00E E E E WSe E Photon energy hυ (ev) Fig The Spectral Variation of (α) 2 Vs. hυ of WSe 2 single crystal α (cm -1 ) W 0.9 Se Photon energy hυ (ev) Fig The Spectral Variation of (α) Vs. hυ of W 0.9 Se 2 single crystal

24 α 1/2 (cm -1/2 ) W 0.9 Se Photon energy hυ (ev) Fig The Spectral Variation of (α) 1/2 Vs. hυ of W 0.9 Se 2 single crystal 1.50E+07 α 2 (cm -2 ) 1.00E E W 0.9 Se E Photon energy hυ (ev) Fig The Spectral Variation of (α) 2 vs. hυ of W 0.9 Se 2 single crystal

25 α (cm -1 ) MoSe Photon energy hυ (ev) Fig The Spectral Variation of (α) vs. hυ of MoSe 2 single crystal α 1/2 (cm -1/2 ) MoSe Photon energy hυ (ev) Fig The Spectral Variation of (α) 1/2 Vs. hυ of MoSe 2 single crystal

26 136 α 2 (cm -2 ) 2.00E E E E E E E E E E MoSe E Photon energy hυ (ev) Fig The Spectral Variation of (α) 2 Vs. hυ of MoSe 2 single crystal To determine direct and indirect energy band gap E g, the variation of (αhυ) 1/r as a function of hυ were plotted for 3D model and the variation of (α) 1/r as a function of hυ were plotted for 2D model. The spectral variations of these plots are illustrated in fig. 5.7 to The energy band gap Eg can be obtained from the exploration of the straight line portion of the curve on energy axis for zero absorption. Using this technique energy band gap for all the possible transitions were carried out. The found value of direct energy band gap and indirect energy band gap for the sample of WSe 2, W 0.9 Se 2 and MoSe 2 single crystal are shown in Table 5.2. From the Table 5.2 it can be seen that optical energy band gap values varies between 1.2eV to 1.4eV for the two dimensional (2D) and three dimensional (3D) model for the sample of WSe 2, W 0.9 Se 2 and MoSe 2 single crystal. So at last we conclude that direct and indirect allowed transition gives a good account of the optical absorption edge in our DVT grown sample of WSe 2, W 0.9 Se 2 and MoSe 2 single crystals. The found values of optical energy band gap of the above mentioned sample are matches with the reported values [5, 6] for both 2D and 3D models.

27 137 Table 5.2 Optical energy band gap of WSe 2, W 0.9 Se 2 and MoSe 2 single crystals Type of Transition WSe 2 W 0.9 Se 2 MoSe 2 3D Model (Indirect transition) Allowed 1.28 ev 1.3 ev 1.26 ev Forbidden 1.22 ev 1.24 ev 1.22 ev 3D Model (Direct transition) Allowed 1.39eV 1.39 ev 1.4 ev Forbidden 1.3eV 1.34 ev 1.31 ev 2D Model (Indirect transition) Allowed 1.33 ev 1.36 ev 1.35 ev Forbidden 1.23 ev 1.28 ev 1.26 ev 2D Model (Direct transition) Allowed Forbidden 1.39 ev 1.4 ev 1.39 ev By employing absorption spectra, transmittance (T) and reflectance (R) have been analyzed using equations 5.18 and 5.19 [7]. A = - log (T) (5.18) R = 1 (T+A) (5.19) In the above equation symbols have their standard denotation. The relation among transmittance (T) and reflectance (R) in graphical appearance are demonstrated in Fig (a) to Fig. 5.30(b). From the plots it is clear that reflectance and absorbance display the same trend but the value of reflectance is slightly higher then the transmittance. As a result we conclude that the surfaces of the DVT grown crystals are shiny to some extend.

28 138 Moreover the reflectance, the extinction (optical) coefficient (k) and the refractive index (n) of crystals at definite stable wavelength are associated by the subsequent mathematical expression [7]. =/4 (5.20) = {( 1) } / {(+1) } (5.21) By utilizing these formulas values of extinction (optical) coefficient (k) and refractive index (n) have been carried out at various wavelengths. The spectral variation in the optical parameters is demonstrated graphically in Fig.5.31 (a) to Fig.5.33 (b). Er = n 2 K 2 (5.22) Ei = 2nK (5.23) Real and imaginary part of dielectric constant can be found out using the equations 5.22 and 5.23 [7]. Using these formulas values of Er and Ei have been carried out at various wavelengths. The spectral variation in these parameters is demonstrated graphically in Fig.5.34 (a) to Fig.5.36 (b).

29 139 Fig. 5.28(a) The spectral variation of reflectance (R) and transmittance (T) with wavelength of WSe 2 single crystal Fig. 5.28(b) The spectral variation of reflectance (R) and transmittance (T) with wavelength of WSe 2 single crystal

30 140 Fig. 5.29(a) The spectral variation of reflectance (R) and transmittance (T) with wavelength of W 0.9 Se 2 single crystal Fig. 5.29(b) The spectral variation of reflectance (R) and transmittance (T) with wavelength of W 0.9 Se 2 single crystal

31 141 Fig. 5.30(a) The spectral variation of reflectance (R) and transmittance (T) with wavelength of MoSe 2 single crystal Fig. 5.30(b) The spectral variation of reflectance (R) and transmittance (T) with wavelength of MoSe 2 single crystal

32 142 Fig. 5.31(a) The spectral variation of the extinction coefficient (k) and refractive index (n) with wavelength of WSe 2 single crystal Fig. 5.31(b) The spectral variation of the extinction coefficient (k) and refractive index (n) with wavelength of WSe 2 single crystal

33 143 Fig. 5.32(a) The spectral variation of the extinction coefficient (k) and refractive index (n) with wavelength of W 0.9 Se 2 single crystal Fig. 5.32(b) The spectral variation of the extinction coefficient (k) and refractive index (n) with wavelength of W 0.9 Se 2 single crystal

34 144 Fig. 5.33(a) The spectral variation of the extinction coefficient (k) and refractive index (n) with wavelength of MoSe 2 single crystal Fig. 5.33(b) The spectral variation of the extinction coefficient (k) and refractive index (n) with wavelength of MoSe 2 single crystal

35 145 Fig. 5.34(a) The spectral variation of the real part (Er) and imaginary part (Ei) of dielectric constant with wavelength of WSe 2 single crystal Fig. 5.34(b) The spectral variation of the real part (Er) and imaginary part (Ei) of dielectric constant with wavelength of WSe 2 single crystal

36 146 Fig. 5.35(a) The spectral variation of the real part (Er) and imaginary part (Ei) of dielectric constant with wavelength of W 0.9 Se 2 single crystal Fig. 5.35(b) The spectral variation of the real part (Er) and imaginary part (Ei) of dielectric constant with wavelength of W 0.9 Se 2 single crystal

37 147 Fig (a) The spectral variation of the real part (Er) and imaginary part (Ei) of dielectric constant with wavelength of MoSe 2 single crystal Fig. 5.36(b) The spectral variation of the real part (Er) and imaginary part (Ei) of dielectric constant with wavelength of MoSe 2 single crystal

38 148 The analysis of fig.5.28 (a) to fig.5.30 (b) reveal that there is a noticeable change in reflectance (R) and transmittance (T) in the wavelength range 800 nm to 900 nm for the sample of WSe 2, W 0.9 Se 2 and MoSe 2 single crystals. Absorbance spectra of all three samples display large hike in the same region. A maxima of solar power also falls in the same region. At various region of the spectrum, R exhibits a few sharp deviations demonstrating the existence of sharp absorption bands overlapping broad conduction band showing typical characteristics of semiconducting material [7]. The study of fig.5.31 (a) to fig.5.33 (b) shows that general trend of spectral variation in refractive index (n) and optical constant (k) is fairly the same for the sample of WSe 2, W 0.9 Se 2 and MoSe 2 single crystals. Refractive index (n) and optical constant (k) exhibit a noticeable change near 850nm.The refractive index (n) of all three samples decreases sharply around 850 nm. On the other hand, optical absorbance increases at the same region of wave length spectrum. After 1000nm refractive index almost remains constant through out the spectrum for the W 0.9 Se 2 sample while it shows a number of variations for the sample of WSe 2 and MoSe 2 single crystals. Fig.5.33 (a) to fig.5.36 (b) demonstrate spectral variation in the real and imaginary part of dielectric constant for the all samples under investigation. Real part (Er) and imaginary part (Ei) both experience subtle variation in the spectral range 800nm to 900nm. Er experience subtle variation in specific spectral regions while Ei increases gradually through out the spectrum for all the samples under investigation. Comparable conclusion and graphical presentation was also reported by undkat.et.al.[7] and nariya. et.al. [8] in their research work.

39 CONCLUSIONS In this chapter author observed that both direct as well as indirect allowed transitions give a good account of the optical absorption edge for the sample of WSe 2, W 0.9 Se 2 and MoSe 2 single crystals. In this perspective, author has come to subsequent conclusions: The optical energy band gap of the sample of WSe 2, W 0.9 Se 2 and MoSe 2 single crystals have been determined accurately using graphical analysis. The values of direct and indirect band gap determined in the present research work are in good agreement with the reported values. Several optical parameters such as transmittance (T), reflectance (R), refractive index (n), extinction coefficient (K) and real and imaginary part of dielectric constant could be determined from the measured values of absorbance.

40 150 REFERENCES [1] T. S. Moss, Optical process in semiconductors, Butterworths, London, (1959). [2] J. I. Pankov, Optical process in semiconductors, Butterworths, London, (1971). [3] J. Bardeen, F. J. Blatt and L. H. Hall., Proc. of Atlantic City Photoconductivity Conference, Atlantic City, (1954). [4] F. Lukes, P. Dub, J. Univerzita, Optical properties of GeS, GeSe, SnS and SnSe, (1988). [5] B. L. Joesten, F. C. Brown, Phys. Rev.,148 (1966) 919. [6] F. C. Brown, T. Masumi, J. Tippins., J. Phys. Chem. Solids, 22 (1962) 101. [7] Sandip R. Unadkat, Ph.D. Thesis,Sardar Patel University, (2012). [8] B.B.Nariya, A.K.Dasadiya and A.R.Jani, PRAJNA, J. P. Appl. Scie., 19 (2011) [9] D. A. Dholakiya, G. K. Solanki, S. G. Patel, M. K. Agarwal, Bull.Mater. Sci., 24(3) (2001) 291. [10] D. A. Dholakiya, G. K. Solanki, S. G. Patel, M. K Agarwal, Scientia Iraica, 10 (2003) 373. [11] J. D. Wiley, D. Thomas, E. Schonherr and A. Breitschwerdt, J. Phys. Chem. Solids., 41 (1980) 801. [12] R. Fivaz, E. Mooser, Phys. Rev.,136 (1967) A833. [13] G. G. Macfarlance, T. P. McLean,J. E. Quarrington, V. Robetrs., Phys. Rev.,111 (1958) [14] C. Marasca, U. M. Grassano, R. Capelleti, S. Prato, N. Zema., J. Phys. Condens. Matter., 638 (1994) 7813.

41 151 [15] M. R. Tubbs, J. Phys. Chem. Solids, 27 (1966) [16] A. E. Dugan and H. K. Henisch. J. Phys. Chem Solids, 28 (1967) 971. [17] G. Domingo, R. S. Itoga, G. R. Kanewarf, Phys.Rev., 143 (1966) 536. [18] A. M. Elkarashy., J. Phys. Condens. Matter, 2 (1990) [19] J. D. Wiley, A. Breitschwerdt and E. Schonherr., Solid State Commun.,17 (1975) 355. [20] E. Bassani, G. Parravicini., Nuovo Cim., 95 (1967) B50. [21] N. Narsimlu, D. Srinivasu and G. S. Sastry. Cryst.Res.Tech., 29 (1994) 577. [22] A.Grisel, F.Levy and T.J.Wieting, Physics B+C, 99 (1980) 365. [23] S.Jandl, C.Deville, and J.Y.Harbec, Solid State Commun., 31 (1979) 351. [24] A,Zwick and M.A.Renucei, Phys. Status Solidi (B), 96 (1979). [25] W.Schairer and M.W.Schafer, Status Solidi A, 17 (1973) 757. [26] M. A. Gaffar, A. Abu El-Fadl., J. Phys. Chem. Solids,60 (1999) [27] J. D. Wiley, E. Schonheer and A. Breitschwerdt. Solid State. Commun., 34 (1980) 891. [28] A. Scacco, C. Marasca, U.M.Grassano, R. Capelletti, J. Phys. Condens. Matter, 6 (1994) 7851.