Modelling of optical properties of amorphous selenium thin films

ARTICLE IN PRESS Physica B 405 (2010) 1101–1107

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Modelling of optical properties of amorphous selenium thin films A. Solieman ,1, A.A. Abu-Sehly 2 Physics Department, Faculty of Science, Taibah University, P O Box 344, Madina, Saudi Arabia

a r t i c l e in fo

abstract

Article history: Received 2 July 2009 Received in revised form 1 November 2009 Accepted 2 November 2009

The investigated amorphous selenium (a-Se) films of different thicknesses (100–385 nm) were deposited by vacuum evaporation technique in a base pressure of 7.5  10  6 torr at room temperature. The transmission spectra T(l) of the a-Se films were measured over a wide range of wavelengths from 200 to 2500 nm. The measured spectra were analyzed by applying O’Leary, Johnson, Lim (OJL) model. The photon energy dependence of the dielectric function, e = e1 +ie2, of the investigated a-Se films was obtained. The film thickness, absorption coefficient a, refractive index n, high frequency dielectric constant eN and optical band gap Eg have been deduced. Increasing the film thickness was found to increase the refractive index and optical band gap energy. & 2009 Elsevier B.V. All rights reserved.

Keywords: Amorphous selenium OJL model Dielectric function Bandgap energy Thickness

1. Introduction In the last three decades, much more attention has been paid for studying the most commercial important chalcogenide semiconductors, the amorphous selenium (a-Se) and its alloys. They have being used in a lot of important applications of modern technology, such as switching [1,2], electrophotography [3–7] and memory devices due to their various photoinduced phenomena, such as photocrystallization [8], photoinduced anisotropy [9] and photodarkening [10]. Currently, they are used as a Videocon photoconductor material, as a photoconductor in X-ray imaging, in large area X-ray sensitive vidicons for medical imaging, called the X-icon, in electro-photographic light-to-image converter imaging devices, optical storage, in high-sensitivity TV pickup or video tubes, called the HARPICON, IR fiber optics and optical recording of images [11–14]. As is well known [15], Se can be produced in three basic structures: (a) the most common and most stable phase hexagonal structure, which shows high electrical conductivity, (b) relatively high resistive semiconductor of monoclinic structure which can be synthesized by growth from chemical solution and may be transformed into the hexagonal structure by heating, and (c) the supercooled liquid amorphous structure, which may be easily obtained by rapidly cooling from the liquid phase so that crystallites do not form.

 Corresponding author. Tel.: + 966 507460143; fax: + 966 48454770.

E-mail address: [email protected] (A. Solieman). On leave from Physics Department, El-Azhar University, Assiut, Egypt 2 On leave from Physics Dept., Assiut University, Assiut, Egypt 1

0921-4526/$ - see front matter & 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2009.11.014

The design and analysis of optoelectronic devices that are made by using semiconductors require high accurate determination of optical constants of such semiconducting materials. Although, many research efforts have been carried out in the recent years for understanding and studying the optical and electrical properties of a-Se films, the available information of its optical constants is still less than adequate. In this work, the optical dielectric response of a-Se, e.g., dielectric functions e = e1 +ie2, as well as optical refractive index, N=n+ik, and the optical band gap (Eg) dependent on the absorption coefficient (a) will be determined. Thin a-Se films will be deposited by thermal evaporation technique with different thicknesses. OJL model will be implemented to describe the dielectric function for a-Se films by fitting the transmission spectrum only in the range of 0.2–2.5 mm.

2. Experimental Appropriate amounts of selenium powder with purity of 99.99% (from Sigma Aldrich Co.) were used to deposit a-Se films by thermal evaporation coating unit on microscopic slide substrates at room temperature. The slide substrates of thickness 1.1 mm were carefully cleaned ultrasonically in acetone, ethanol for 30 min, and then rinsed with deionized water. A desired weight of the material was evaporated from a tungsten boat which was heated by passing a high current (100 A) under a base vacuum of 7.5  10  6 torr. For maintaining the homogeneity and thickness uniformity of all the films, the substrate was kept under mechanical rotation during the deposition process. Thin a-Se films with different thicknesses (100, 110, 150, 170, 249, 272 and 393 nm) were obtained. The structure of deposited Se films was examined using a Shimadzu XRD-6000 X-ray diffract-ometer ˚ The surface morphology and using Cuka-radiation (l =1.5418 A).

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microstructure of the films were observed by AFM (Veeco CP-II) in contact mode and SEM (Shimadzu Superscan SSX-550), respectively. The film thicknesses were deduced from SEM and AFM measurements on the edge of the tilted film and also calculated with a film thickness program (Shimadzu UV-2501PC Film thickness). The transmittance, T(l), spectra of the films were measured at normal incidence in the spectral range of (200– 2500 nm) by using a double-beam spectrophotometer (Shimadzu 3150 UV–VIS–NIR) of 0.1 nm resolution.

3. Optical modelling The two most important optical constants are the absorption coefficient a, the real part (called refractive index n) and imaginary part (called extinction coefficient k) of the complex refractive index N. The extinction coefficient k is related to the absorption coefficient a through a = 2pk/l, where l is the wavelength of interest. The value of the absorption coefficient indicates how readily photons will be absorbed by the material while the refractive index value determines the amount of dispersion that is important in the engineering of optical waveguides. The optical properties of many semiconductor materials can be described, explained and/or predicted by using the density of states (DOS) diagram, i.e. the number of electron states per unit energy per unit volume at any energy level. DOS of the amorphous semiconductor might be similar to that of its crystalline phase because both shared the same basic electronic and optical properties [16]. However, the important difference between amorphous and crystalline semiconductors is the existence of localized states in the mobility gap which created mainly by the structural defects and/or loss of long range order of amorphous material. Several research works were done [17–24] to calculate DOS of a-Se from different measurements. Usually, the optical transmittance and/or reflectance spectra are used to find out the optical constant by using two methods of optical data fitting: (1) the dielectric function models and (2) solving the Maxwell equation for the coherent light in the layer and the substrate for each wavelength using the necessary boundary conditions [25]. Tauc-Lorentz [26] and OJL [27] models are used widely for modelling the optical properties of amorphous semiconductors based on the DOS function. Other models [28–30] including sum of classical oscillators for calculating the complex dielectric function of materials are used to interpret the features in the transmission and/or reflection spectra of semiconductor films. Jellison–Modine model [31] was used to analyze the spectroscopic ellipsometry data and calculate the optical constants of thick a-Se film [32]. Grdijn et al. [33] used OJL model only for fitting T and R spectra of thin microcrystalline silicon (mcSi:H) film deposited on corning 1737F glass substrates. To our knowledge, the present study is the first application of OJL model only to find out the optical constants and thickness of a-Se films from transmission spectra. OJL model describes very well the interband transition in amorphous semiconductors. It assumes the parabolic shape valance- conduction band of density of states (DOS) with tail states exponentially decaying into the band gap. The empirical equations of DOS functions were adapted to include the transition in each of the DOS functions between the band region and the tail region. That is 8 9 rffiffiffiffiffiffiffiffi     > 1 1 EV E 1 > > > > > E 4 E N g  g exp  exp V < Vo = gV 2 V 2 2 V NV ðEÞ ¼ > > ffiffiffiffiffiffiffiffiffiffiffiffi p 1 > > > E r EV  gV > : NVo EV E ; 2

and 8 pffiffiffiffiffiffiffiffiffiffiffiffi > > > < NCo EEC rffiffiffiffiffiffiffiffi     NC ðEÞ ¼ > > NCo 1g exp 1 exp EEC > : gC 2 C 2

9 1 > EZ EC þ gC > > 2 = 1 > > Eo EC þ gC > 2 ;

NVo and NCo denote the valence band and conduction band DOS prefactors, EC and EV are the conduction band and valence band edges, and gV and gC are the breadth of the valence band tail (VBT) and conduction band tail (CBT) states, respectively. The tail states are resulted as a consequence of the disorder present in amorphous semiconductor and the breadth of these tail states indicate the amount of disorder. The joint density of states (JDOS) derived from DOS is given by Jð‘ oÞ ¼

4 X dðEc Ev ‘ oÞ V 2 v;c

where ‘ o is the photon energy of incident light and V is the illuminated volume. This equation can be expressed as an integral over the valence band and conduction band DOS functions Z 1 NV ðEÞNC ðEþ ‘ oÞ dE Jð‘ oÞ ¼ 1

The spectral dependence of the imaginary part of the dielectric function can be determined by the product of the dipole operator matrix element (also known as the oscillator strength) and the JDOS:   X 2 2 2 e2 ð‘ oÞ ¼ ð2peÞ2 R ð‘ oÞ dðEc Ev ‘ oÞ rA V 3V v;c Thus

e2 ð‘ oÞ ¼ ðpeÞ2



 4 R2 ð‘ oÞJð‘ oÞ 3rA

And the absorption coefficient is given by

að‘ oÞ ¼ R2 ð‘ oÞJð‘ oÞ R2 ð‘ oÞ is defined as the normalized dipole matrix element squared average and rA denotes the atomic density of material. However, the imaginary part of the dielectric function increases to infinity with energy due to its strong dependence on the combined DOS. Therefore, the model was modified by multiplying its original expression by Exp½ðWavenumberE0 Þ=Decay, where the so called Decay factor is added to drag down the imaginary part to zero at high frequencies. Kramers–Kronig-Relation (KKR) that connects real and imaginary parts of susceptibilities was used to calculate the real and imaginary parts of the dielectric function. The real part of the dielectric constant e1(o) is interconnected with absorption coefficient (a) through the imaginary part of the dielectric constant e2(o), by the Kramers–Kronig dispersion relation:   Z 1 0 2 o e2 ðo0 Þ 0 P e1 ðoÞ ¼ 1 þ do p o0 2 o2 0

e2 ðoÞ ¼



2o

p

 Z P

1 0

e 1 ð o0 Þ d o0 o0 2 o2

where o is the frequency of interest, o0 is the integration variable and P represents the principal value of the integral, which ensures that the singularity at o = o0 is avoided.   Z 1 0 2 o kðo0 Þ 0 P do nðoÞ ¼ 1 þ 02 p o o2 0 and   Z 2 kðoÞ ¼  P

p

1 0

nðo0 Þ do0 o0 2 o2

ARTICLE IN PRESS A. Solieman, A.A. Abu-Sehly / Physica B 405 (2010) 1101–1107

The real and imaginary parts of refractive index and thickness of a-Se film were obtained by fitting the transmission spectra using OJL model implemented in the commercial software SCOUT program [34]. The fitting process of the optical spectra was carried out using SCOUT software through the following steps: (1) Input the formula of the chosen model for the dielectric functions, OJL model in our work. The background value of refractive index was added to calculate the real and imaginary parts of the refractive index as a function of energy. The thickness of the film was put as a free fitting parameter. (2) Insert the initial values of the model parameters (see above) and the film thickness. (3) Calculate the optical transmittance spectra T½nðli Þ; kðli Þ; d; li  from well-known formulas based on the Fresnel formalism. Compare the obtained data with the experimental values by calculating the deviation. The deviation is given by squaring the difference of the simulated P 2 and measured values, D ¼ m i ¼ 1 jTEXp ðli ÞT½nðli Þ; kðli Þ; d; li j . (4) The automatic fitting is used to minimize the deviation by varying the fit parameters (model parameters and film thickness). The downhill simplex method is applied until an optimal fit is obtained. (5) Find out the values of optical constants, and (6) Plot the calculated and measured optical data, print the dielectric function, the thickness, and model parameters (mass S, gap energy E0, gamma and decay constant).

4. Results and discussion Se is crystallized via formation of the spherulites having a lamellar structure, with the width of the lamellae much less than

the length of the extended Se chain [35]. The deposited Se films are formed of heterogeneous clusters embedded in glassy matrix, as shown in Fig. 1, indicating the amorphous state of the film. In addition, the surface morphology obtained by AFM confirms the amorphous state of the as-deposited Se films as shown in Fig. 2. It is clear that the film has very smooth surface with tiny grains of about 40.6 nm in size and very low roughness (  1.91 nm). The amorphoucity or non-crystallinity of the deposited films was confirmed by the absence of crystallization peaks in the XRD pattern as shown in Fig. 3. XRD patterns do not exhibit any difference among all deposited Se films with different thicknesses, i.e. all deposited films are amorphous. The optical transmission spectra of glass substrate and a-Se films with different thicknesses in the wavelength range of 200– 2500 nm are shown in Fig. 4. The curves show the typical features of a-Se films [36–38]. It is clear that the transmission spectrum is divided into two regions according to their transmittance values namely: the transparent region, where T(l) is greater or equal to 90% and the strong absorption region, where T(l) drops down to 0%. In the transparent region, very thin layers (100–110 nm) do not exhibit any interference features which appear with thick films ( Z150 nm). The dielectric functions of the microscopic glass substrates were first obtained by using a sum of Kim’s oscillators [39]. The measured and fitted transmittance spectra of the substrate were in excellent agreement and the obtained dielectric function of glass substrate was saved in database of the Scout 2 program. The transmittance spectra of all films were fitted very well by using OJL model only. The model parameters and film thickness are used as free fit parameters and their values are listed in Table 1. For all transmission spectra, the positions and amplitude of the interferences as well as the value and curvature of the band gap energy are very well fitted as shown in Fig. 5. The values of film thicknesses are in good agreement with each other indicating that this simple model is adequate to describe the properties of this coating. The values of Eg and eN are also in agreement with those reported in the literature. The relative percentage errors between the experimental points, Ti exp(l), and the calculated transmission Tcalc(l), Ei ¼

Fig. 1. SEM photograph of a-Se film.

1103

Tiexp Tcalc ðlÞ  100 Tiexp

were determined and found to be lower than 2% in the region of high transparency, and about 7% in the region of strong

Fig. 2. 3D (left) and 2D (right) 5 mm  5 mm AFM pictures of the surface of a-Se thin films.

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absorption. Also, the deviation of calculated from experimental data was found to be ranged from 0.65 to 2.77, as listed in Table 1. The real and imaginary parts of dielectric function spectra obtained from OJL model are shown in Fig. 6. The e2(E) spectrums showed a broad-peak structure which is the typical spectral features observed in amorphous semiconductors due to the breakdown of crystal periodicity in the amorphous state. The same feature was observed by Innami et al. [32] for a-Se film

deposited on Si substrate at room temperature by vacuum evaporation. The thicker film has the bigger peak indicating that the surface is very clean, there is a dielectric discontinuity between the samples and ambient, and the high accurate behavior of the dielectric function spectrum that is similar or close to that of the bulk material. This is deduced from the simple criterion ‘‘biggest is the best’’ [40] which is applicable both to crystalline and amorphous semiconductors.

Fig. 3. XRD pattern of a-Se film. Fig. 5. Measured and fitted transmittance spectra of a-Se films of different thicknesses.

Fig. 4. Transmission spectra of a-Se films of different thickness.

Fig. 6. The real and imaginary parts of the dielectric functions of a-Se films of different thickness.

Table 1 Film thickness (nm) Band gap energy

Fitted Measured E0 (eV) EgT (eV) Eopt (eV) g

eN Mass Deviation

100 97 1.21 1.22 1.48

110 112 1.249 1.24 1.505

150 148 1.824 1.83 1.96

170 173 1.851 1.86 1.98

249 250 1.99 1.92 2.0

272 274 2.013 1.93 2.02

385 389 2.11 2.0 2.07

4.0 0.7 0.95

4.5 1.2 0.87

5.1 4.7 1.06

5.17 4.8 0.65

5.25 9.8 1.02

5.35 10.3 0.86

5.4 18.3 2.77

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On the other hand, in tetrahedrally coordinated amorphous materials like a-Se, linear combinations of atomic orbitals simply lead to bonding and antibonding molecular states which then broaden into valence and conduction bands, respectively. Therefore, four absorption peaks are expected to be dominant in the short range-ordered selenium [41,42], related to transitions among four local bands; (1) UVB (upper valence band)–LCB (lower lying conduction band); (2) MVB (midvalence band)–UCB (upper conduction band); (3) UVB–UCB; and (4) MVB–UCB. As shown in Fig. 6, our obtained e2(E) spectra have a broad peak near E0 ( 2.0 eV) with highest point of this peak is at around 2.8 eV. Thus this single broad peak may be attributed to UVB–LCB transition. Such a broad peak has been obtained by Innami et al., at 2.0 eV and its maximum value at  4.5 eV, for 850 nm thickness of a-Se film and they attributed it to MVB–UCB transition. Jellison–Modine model [31] proposed an expression for the optical constants of amorphous tetrahedral semiconductors which provides a decrease in the optical density at higher energy and a single broad peak of e2 (E) spectrum at E E0. In e1(E) spectrum, the appearance of peak around 2.4 eV is in good agreement with those obtained by Innami et al. [32] around 2.2 eV using SE measurement and by Nagels et al. [43] from transmission spectrum. Also, the features of e1(E) and e2(E) spectra around 2.5 eV are in good agreement with that reported for amorphous Se [24]. To check the goodness of e values obtained from fitting the transmittance spectrum using OJL model only, we computed its corresponding refractive index. In the OJL model, the refractive index n as a function of energy is predominantly determined by the parameter ‘mass’ that determines the shape of the conduction and valence band DOS. The results are, shown in Fig. 7, in excellent agreement with those given in the literatures [32,43,44,45]. There are two distinct regimes, seen from the curvature shape of the refractive index (n); one for the group of 100–110 nm film thickness, and the other for group of 150– 385 nm. That is consistent with the absence and presentation of interference features of transmittance spectra of the two groups of film thicknesses, respectively. It is clear that the refractive index increases with increasing the thickness of the films. That may be attributed to loss of the long range order in thin films of about 100 nm and such order is growing with increasing the film thickness. At long wavelength, close to zero frequency, n increases

from 2.1 for 100 nm film thickness up to 2.4 for larger thick film of 385 nm. This is confirmed by increasing the value of mass parameter with film thickness, as listed in Table 1. However, its value is still in the amorphous value and is lower than that of crystalline Se film. Since, the refractive index at zero frequency, n0 of semiconductors, such as Ge, Si, and the III–V compounds, is typically a little bit larger in the amorphous state than in the crystalline state. However, an opposite and larger change is reported for Se. n0 (c-Se //)= 3.41, n0 (c-Se ?)= 2.64 and n0(aSe)= 2.50 where n0(c-Se //) is measured with the light polarization parallel to c-axis or the /0 0 1S direction of the hexagonal lattice of the trigonal crystalline Se and n0 (c-Se ?) is measured with the light polarization perpendicular to the c-axis or the /0 0 1S direction of the hexagonal lattice of the trigonal crystalline Se [45]. The imaginary part of refractive index or extinction coefficient (k) is plotted as a function of wavelength as shown in Fig. 8. The plotting of the absolute value of the real part of dielectric function |e1| versus the square of photon energy (E2) is shown in Fig. 9. The values of high frequency dielectric constant eN are obtained by extrapolating the linear parts. The value of eN increases as the film thickness increases. The largest value of eN (5.4) for 385 nm film thickness is lower than those reported by Innami (6.007) and Nagels (6.077) for film of 850 nm thickness. At higher photon energy, the absorption coefficient (a) is given r as a function of photon energy (hn) [45], by ahn ¼ AðhnEopt g Þ where A and r are some physical constants that depend on the is a parameter that has been called material properties, Eopt g optical band gap energy. It is found that r =2 for most of crystalline semiconductors and many amorphous semiconductors, r =3 for some complicated glasses and r = 1 for a relatively is defined as the Tauc simple glass, such as a-Se [44,46] and Eopt g optical gap (after herein referred to as EgT ). For a-Se, the optical absorption coefficient at around the fundamental absorption edge where a Z104 cm  1, was found to follow the relationship: opt ahn ¼ AðhnEopt g Þ, where Eg  2:05 eV is the optical bandgap at room temperature [47]. According to Tauc’s law:ahn ¼ AðhnEgT Þ2 , Addachi et al. [48] has found the optical band gap EgT  1:95 eV. This kind of behavior at higher photon energies has been attributed to a sharp rise in the density of states at the band edges. The absorption coefficient (a) of our a-Se films was deduced from transmission spectrum using the parameters of OJL model and EgT for through Kramers–Kronig analysis. The values of Eopt g

Fig. 7. The real part of the refractive index (n) of a-Se films of different thickness as a function of the wavelength.

Fig. 8. Extinction coefficient of a-Se films of different thickness as a function of the wavelength.

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our a-Se films with different thicknesses were obtained by plotting ðahnÞ and ðahnÞ1=2 versus hn, as shown in Figs. 10 and and EgT ) 11, respectively. Both values of the optical bandgap (Eopt g and that obtained as a fit parameter of OJL model (E0) are listed in Table 1. O’Leary has studied the optical absorption in GaAs and a-Si:H using model DOS functions and calculated the joint density of states (and hence the absorption coefficient) as a function of the photon energy [49,50]. He concluded that the optical bandgap determined from plotting of typical Tauc’s equation depends on the spread of the tail states. When the tail spread widely the value of EgT is lower than Ec Ev and only when the tail is absence EgT ¼ Ec Ev . From Table 1, the value of optical band gap (fit parameter E0) is close to the value of EgT for lower film thickness for more thick films (100–170 nm) and close to the value of Eopt g (250–385 nm). This indicates that increasing the film thickness decreases the tail state spread and thus increases the optical band gap. Also, it is observed that some correlation between E0 and mass OJL parameters. For higher E0 values, higher values for the mass are found. The same correlation was reported by Grdijn et al. [33] for mc-Si:H films.

Fig. 9. |e1| vs. E  2 of a-Se films, |e1| = eN at E  2 =0.

5. Conclusion A-Se films with different thicknesses (100–385 nm) were prepared by vacuum evaporation at pressure of 7.5  10  8 Pa on microscopic glass slides. AFM image suggested that the evaporated films is very smooth and flat (rms roughness of 1.91 nm) and XRD patterns confirmed that the films are amorphous. OJL model was used successfully to fit the transmission spectra of the evaporated a-Se films. The obtained dielectric function in the 0.45–4.0 eV photon energy range were in good agreement with those previously published data for a-Se film. At long wavelength, close to zero frequency, n increases from 2.1 for 100 nm film thickness up to 2.4 for larger thick film of 385 nm. For lower film thickness (100–170 nm) the optical band gap (OJL parameter E0) is for close to the indirect EgT while it is close to the value of Eopt g more thick films (250–385 nm). References Fig. 10. (ahn)1/2 vs. photon energy hn for a-Se films of different thickness.

[6]

150 nm

8.0x104

170 nm

[7]

249 nm 272 nm

[8] [9]

385 nm

(αhν)

6.0x10

[1] [2] [3] [4] [5]

4

[10] [11] [12]

4.0x104

[13] [14]

2.0x104

[15] [16]

0.0 1.8

1.9

2.0 hν (eV)

2.1

Fig. 11. (ahn) vs. photon energy hn for a-Se films of different thickness.

2.2

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