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Room temperature photoluminescence spectrum modeling of hydrogenated amorphous silicon carbide thin films by a joint density of tail states approach and its application to plasma deposited hydrogenated amorphous silicon carbide thin films
Thin Solid Films 520 (2012) 7062–7065
Contents lists available at SciVerse ScienceDirect
Thin Solid Films journal homepage: www.elsevier.com/locate/tsf
Room temperature photoluminescence spectrum modeling of hydrogenated amorphous silicon carbide thin films by a joint density of tail states approach and its application to plasma deposited hydrogenated amorphous silicon carbide thin films Kıvanç Sel ⁎, İbrahim Güneş Department of Physics, Çanakkale Onsekiz Mart University, 17100 Çanakkale, Turkey
a r t i c l e
i n f o
Article history: Received 13 October 2011 Received in revised form 26 July 2012 Accepted 26 July 2012 Available online 3 August 2012 Keywords: Photoluminescence Density of tail states Hydrogenated amorphous silicon carbide
a b s t r a c t Room temperature photoluminescence (PL) spectrum of hydrogenated amorphous silicon carbide (a-SiCx:H) thin films was modeled by a joint density of tail states approach. In the frame of these analyses, the density of tail states was defined in terms of empirical Gaussian functions for conduction and valance bands. The PL spectrum was represented in terms of an integral of joint density of states functions and Fermi distribution function. The analyses were performed for various values of energy band gap, Fermi energy and disorder parameter, which is a parameter that represents the width of the energy band tails. Finally, the model was applied to the measured room temperature PL spectra of a-SiCx:H thin films deposited by plasma enhanced chemical vapor deposition system, with various carbon contents, which were determined by X-ray photoelectron spectroscopy measurements. The energy band gap and disorder parameters of the conduction and valance band tails were determined and compared with the optical energies and Urbach energies, obtained by UV–Visible transmittance measurements. As a result of the analyses, it was observed that the proposed model sufficiently represents the room temperature PL spectra of a-SiCx:H thin films. © 2012 Elsevier B.V. All rights reserved.
1. Introduction The mechanism that determines the shape of photoluminescence (PL) spectrum of hydrogenated amorphous silicon (a-Si:H) and hydrogenated amorphous silicon carbide (a-SiCx:H) has been studied for many years, but it is still controversial [1–9]. It is mainly because of the features of energy band gap structure, such as tail states of conduction and valance bands. For large energy band gap (EGap) amorphous materials, such as a-SiCx:H, the density of the tail states could also be large, which results in thermalization of charge carriers towards deeper‐tail-energy states and recombines at various energy levels. In this respect, the PL spectrum broadens and it respectively becomes difficult to model the PL mechanism. In the literature, mainly for a-Si:H, the static-disorder model, which was proposed by Dunstan and Boulitrop [3–5], assigns the PL spectrum to the distribution of the carriers in the conduction and valence band tail states. While, the Stokes shift model, which was proposed by Street [8], associates the PL spectrum with strong electron–phonon coupling. Moreover, these two models could coexist. On the other hand, a joint density of states (JDOS) approach was applied
⁎ Corresponding author at: Çanakkale Onsekiz Mart Üniversitesi, Fizik Bölümü, Çanakkale, 17100, Turkey. Tel.: +90 286 218 0018. E-mail address: [email protected] (K. Sel). 0040-6090/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.tsf.2012.07.114
to model the optical transitions in amorphous semiconductors such as a-Si:H for zero-temperature by Orapunt and O'Leary [9]. In this model, four types of transitions; extended valence band to extended conduction band, extended valence band to conduction band tail, valence band tail to extended conduction band and valence band tail to conduction band tail, were analyzed in the frame of a JDOS function with energy dependence of square root in band regions and exponential in the tail regions. In this work, the room temperature PL spectrum was modeled by an approach of applying JDOS, where the density of states of the conduction and valance band tails were introduced by empirical Gaussian functions. This model was investigated numerically as a function of Fermi energy (EF), EGap and disorder parameters of conduction band tail (ECB0) and valence band tail (EVB0), which represents the width of the tail states distribution. Finally, the proposed model was applied to the measured room temperature PL spectra of a-SiCx:H thin films, deposited by plasma enhanced chemical vapor deposition system (PECVD), with various x values. Resultantly, EGap, ECB0 and EVB0 of the films were determined. The analyses were supported and compared with the optical energies and Urbach energies (EUrbach), which were obtained by UV–Visible transmittance measurements and carbon contents (x) obtained by X-ray photoelectron spectroscopy (XPS) measurements. In addition to these analyses, the optical and PL characteristics of the films were reported and the PL spectra were analyzed within the frame of the static disorder and Stokes shift models.
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2. Modeling of the room temperature PL spectrum The disordered structure of amorphous semiconductors, such as a-Si:H and a-SiCx:H, results in distribution of localized states at band edges and deep states at around Fermi level in the energy band gap structure. The density of tail states is critical for luminescence mechanisms, since the excited charge carriers first thermalize through these states towards the deeper energy levels in the band tail states. Then, they most probably recombine radiatively or non-radiatively with charge carriers at valence band tail states or deep states, respectively. As a result, in order to model the PL spectrum, the transitions from conduction band tail to valence band tail states should be studied. For the purpose of this analyses, the density of tail states of conduction band (NCB(E)) and valence band (NVB(E)) were empirically presented by a Gaussian function, assuming that the valence band edge energy (EVB) is equal to zero and conduction band edge energy (ECB) is greater than zero, respectively: 2 2 NCB ðEÞ ¼ NCB0 exp −ðE−ECB Þ =2ECB0
ð1Þ
2 2 NVB ðEÞ ¼ NVB0 exp −E =2EVB0
ð2Þ
where, NCB0 and NVB0 denote the density of tail states at conduction band edge and valence band edge, respectively. The resultant distributions of density of tail states functions presented in Fig. 1(a), as a function of energy for different values of NCB0 and NVB0, where we set N0 = NCB0 = NVB0, and in Fig. 1(b), as a function of ECB0 and EVB0. The JDOS function, as an interpretation of PL intensity (I(ℏω)), was expressed as an integral over the product of NCB(E) and NVB(E) [9]. Due to the occupancy considerations, Fermi distribution function was included in the integration for empty states as (1 − F(E)) and for occupied states as F(E). ECB −ℏω
IðℏωÞ∝
∫
NCB ðE þ ℏωÞFðE þ ℏωÞNVB ðEÞ½1−FðEÞdE
ð3Þ
EVB
Fig. 2. Room temperature, normalized PL spectrum calculated by the proposed model, as a function of various values of a) EGap = ECB − EVB, b) EF and c) ECB0 and EVB0, where EVB0 was assumed to be 1.5ECB0. In the calculations, for constant variables were taken as N0 = 1022 cm−3 eV−1, EGap = 2.0 eV, EF = 1.0 eV, ECB0 = 50 meV and EVB0 = 75 meV.
and 3) [8]. Figs. 2(a) and 3(a) represent that, the PL spectrum shifts towards higher energies as EGap increases. PL peak energies (EL) were observed to be smaller than EGap, satisfying that the carriers thermalize through the localized tail states and the radiative optical transitions occur between inter-band tail states. Figs. 2(b) and 3(b) represents that the shift of EF towards higher energies results in a decrease in the width of the PL spectrum and a shift of EL towards the smaller energies, which can be interpreted as the increase of the probability of the radiative optical transitions between deeper states of both conduction and valence band tails. Finally, in Figs. 2(c) and 3(c) the dependence of PL spectrum on the ECB0 and
where, ℏω denotes the energy of the excitation light. The room temperature IðℏωÞ was calculated for various values of EGap, which was assumed to be the difference between ECB and EVB = 0 eV, EF, ECB0 and EVB0, where EVB0 was set to 1.5ECB0 to demonstrate the difference in the width of the energy band tails, such as the case of a-Si:H (Figs. 2
Fig. 1. a) Variation of NCB(E) and NVB(E) as a function of energy for various values of NCB0 and NVB0 (N0 = NCB0 = NVB0), where EF = 1 eV, EGap = 2.0 eV, ECB0 = 50 meV and EVB0 = 75 meV were fixed. b) NCB(E) and NVB(E) as a function of energy for various values of ECB0 and EVB0, where EF = 1 eV, EGap = 2.0 eV and N0 = 1022 cm−3 eV−1 were fixed.
Fig. 3. Variation of a) EGap = ECB − EVB, b) EF and c) ECB0 and EVB0 of the room temperature normalized PL spectrum calculated by the proposed model as a function of EL. In the calculations, for constant variables were taken as N0 = 1022 cm−3 eV−1, EGap = 2.0 eV, EF = 1.0 eV, ECB0 = 50 meV and EVB0 = 75 meV.
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relatively on EVB0 was plotted. As the disorder increases, the PL spectra both increase its width and shift towards the smaller energies. 3. Application of the room temperature PL model 3.1. Experimental work a-SiCx:H thin films were deposited by PECVD (Plasmalab μP80), using radio frequency (13.56 MHz) power density of 30 mW/cm 2, at substrate temperature of 250 °C, on ordinary glass substrates. In the deposition process the source gases of silane (SiH4) and ethylene (C2H4) were used, under constant pressure of 66.7 Pa. The total flow rate of the source gases was set to 20 ccm, where additionally H2 was supplied for further hydrogenation with constant hydrogen flow rate of 200 ccm. x was modified by adjusting the source gas concentration (M = (C2H4/(C2H4 + SiH4)) to the values of 0.0, 0.2, 0.5 and 0.7. Resultantly, as a total, four different types of a-SiCx:H films were deposited. XPS measurements (SPECS ESCA (Germany)) were performed by non-monochromatic Al Kα radiation, with the analyzer mode set at constant analyzer energy of 144 eV. The X-ray source was run at 250 W and the electrons were collected at the take off angle of 90°. In order to remove the surface contaminants, the films were pre-cleaned using Ar ion sputtering at 5 keV for 15 min. After the cleaning, XPS was measured by several scans at the energy resolution of 0.2 eV. The charging effect was eliminated by referencing the binding energies with respect to C 1s core level at 284.5 eV. x was calculated from the ratio of relative intensities to the total intensity in the spectrum; ,X N I In x¼ n Sn S n n¼1
ð4Þ
where ‘In’ is the area under the peak of the element (Si and C) in the XPS and ‘Sn’ is the sensitivity factor, which were taken as 0.25 for C and 0.27 for Si, respectively [10]. x, which was reported in detail in our previous work [11], are presented in Table 1. The film thickness and the optical energies of the films were determined by UV–Visible transmittance measurements (Perkin Elmer Lambda 2) at normal incidence. These analyses were reported in detail in our previouspwork ffiffiffiffiffiffiffiffiffiffi [12]. Tauc energy (ETauc) was determined from the graph of hυα, where α is the absorption coefficient, as a function pffiffiffiffiffiffiffiffiffiof ffi hυ, where the extrapolation of the linear function fit to hυα = 0 gives ETauc. Additionally, E04, which is the energy corresponding to the absorption value at 10 4 cm −1, was determined. EUrbach was determined from the graph of lnα plotted as a function of hυ, where the inverse of the slope of lnα gives EUrbach. ETauc, E04 and EUrbach are presented in Table 1. The room temperature PL spectra of the films, which were obtained by using 457.9 nm line of Argon ion laser as excitation light source, were presented in Fig. 4. In Fig. 4, as x increases, the PL spectra of a-SiCx:H broaden and shift towards the higher energies [7,8,13–18].
Fig. 4. The normalized room temperature PL spectrum of the a-SiCx:H films with various x. The solid line is the normalized PL spectrum and the fitted Gaussian curve and the broken line is the curve of the room temperature PL model fit. In the fitting we set NCB0 = NVB0 = 1022 cm−3 eV−1 and EVB0 = 1.5ECB0.
3.2. Application of the model to the PL spectrum of a-SiCx:H The measured room temperature PL spectra of a-SiCx:H were normalized and then fitted to Gaussian curves and the full-width of hall maxima of the Gaussian curves (ΔEL) was determined. Next, the Gaussian curves were fitted to the model Eq. (3). In Fig. 4, the measured room temperature PL spectra, the fitted Gaussian curves and the fitted curves of the model were plotted together as a function of energy. The curves of the model and the Gaussian curves of the experimental PL spectra closely overlap with the data. Whereas, for the a-SiCx:H films with higher x values, high energy tails were observed on the PL spectra. With the increasing x, as a result of the increase
Table 1 M, film thickness, x, E04, ETauc and EUrbach of a-SiCx:H films, obtained from XPS and UV– Visible transmittance spectroscopy analyses [11,12]. (M = (C2H4/(C2H4 + SiH4))
0.0
0.2
0.5
0.7
x Film thickness (nm) E04 (eV) ETauc (eV) EUrbach (meV)
0.00 226.5 2.00 1.99 41.9
0.17 523.4 2.18 2.03 96.2
0.37⁎ 230.7 2.42 2.40 113.1
0.48 240.8 2.60 2.55 118.9
⁎ x of the M = 0.5 film, which could not be determined by XPS, was determined by a statistical approach, where the optical constants were compared with the relevant results in the literature, which were reported in detail in our previous work [12].
Fig. 5. a) Variation of E04, ETauc and EL, as a function of x for the a-SiCx:H films. b) Variation of EUrbach, EVB0 and ECB0, as a function of x for the a-SiCx:H films.
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space and depends exponentially on energy with a logarithmic slope of E0 and the separation between non-radiative and radiative recombination centers are constant and is about 12 nm [3–5]. The slope of best fit of ΔEL versus EUrbach graph, which was presented in Fig. 6(a), is calculated as 1.95 ± 0.50 for the films, which is in the limit of the theoretically proposed value of 2.45 [5,15,18]. Moreover, the zero intercept of about 20 meV justifies that electron–phonon coupling is small. On the other hand, from the slope of the best fit of (ΔEL) 2 versus (E04–EL) graph, which was presented in Fig. 6(b), E0 is calculated as 0.062 ± 0.020 eV [8]. This value is in the order of the approximate E0 and agrees with the prediction of the Stokes shift model. 4. Conclusion Fig. 6. a) Variation of ΔEL as a function of the EUrbach, and b) variation of (ΔEL)2 as a function of E04–EL.
in the carbon concentration, C\C bonds, which could form sp 2 hybridized π bonded graphite-like structures in addition to sp 3 hybridized σ bonded tetrahedral structures, start to occur besides Si\Si and S\C, σ bonds [13,14]. Resultantly, in addition to the σ-states and the increase in the disorder, π-states start to occur around the high energy regime of the tail states. This additional increase in the density of tail states could be the result of the high energy tails observed in the PL spectra of a-SiCx:H films with higher x values. Accordingly, it can be concluded that the proposed model is in agreement with the experimental data. In the frame of the proposed model, in order to further analyze the PL spectra of a-SiCx:H films, the fitted EL were plotted together with E04 and ETauc, as a function of x in Fig. 5(a), where a linearly correlated increase was observed for all of them. EL of the films were slightly under E04 and ETauc, which is in agreement with the assumption that the radiative transitions occur between conduction band tail states and valence band tail states. In Fig. 5(b), EUrbach, EVB0 and ECB0 were plotted as a function of x. It was observed that, EVB0 was very close to EUrbach (Note that EVB0 = 1.5ECB0). Since EUrbach, which could be interpreted as the convolution of density of tail states of conduction and valence bands, is actually dominated by the larger width of valence band tail. As a result, the observed values of EUrbach and EVB0 were reasonable [8,12–14]. PL mechanisms were also investigated within the frame of static disorder model and Stokes shift model [3–6,8]. If the static disorder mechanism is dominant, ΔEL is given as; 2 2 e–ph 2 ðΔEL Þ ¼ ð2:45Eu Þ þ ΔEL
ð5Þ
2 where ΔEe–ph represents the contribution of Stokes shift model L (electron–phonon coupling (e–ph)) to the full-width hall maximum of the PL spectrum. On the other hand, if Stokes shift model mechanism is dominant, ΔEL can be expressed as [8]; 2 stat 2 ðΔEL Þ ¼ 4 ln2ðE04 −EL −Eth ÞE0 þ ΔEL
ð6Þ
2 where Eth is thermalization energy, ΔEStat represents the contribuL tion of statistical disorder model to the full-width hall maximum of the PL spectrum and E0 is the typical phonon energy, which is about 60 meV, supposing that the tail states are distributed randomly in
We have defined empirically NCB(E) and NVB(E), in terms of Gaussian functions. NCB(E) and NVB(E) were presented for various N0, ECB, EVB, ECB0 and EVB0 values. Considering the occupancy of the tail states, the room temperature PL spectrum was expressed as an integral of JDOS function and Fermi distribution function. The resultant PL spectrum of the model was investigated with respect to various EGap, EF and ECB0 and EVB0 values. The model was fitted to the measured room temperature PL spectra of a-SiCx:H films with various x and a very close overlap were obtained for all of them. EL was compared with the optical energies, ETauc and E04. Additionally, ECB0 and EVB0 were compared with EUrbach. As a result of the analyses, it can be concluded that the proposed PL model sufficiently represents the room temperature PL spectrum of a-SiCx:H thin films. Acknowledgment This work was carried out with the financial support of Çanakkale Onsekiz Mart University (COMU-BDP/2011-010). Thanks to Assoc. Prof. Dr. Barış Akaoğlu and Prof. Dr. İsmail Atılgan for sharing their laboratory facilities. References [1] M.H. Brodsky, R.S. Title, K. Weiser, G.D. Petit, Phys. Rev. B 1 (1970) 2632. [2] G.D. Cody, in: J.I. Pankove (Ed.), Semiconductors and Semimetals, vol. 21B, Academic Press, New York, 1984, p. 11. [3] F. Boulitrop, D.J. Dunstan, Phys. Rev. B 28 (1983) 5923. [4] D.J. Dunstan, F. Boulitrop, Phys. Rev. B 30 (1984) 5945. [5] T.M. Searle, W.A. Jackson, Philos. Mag. B 60 (1989) 237. [6] L.R. Tessler, I. Solomon, Phys. Rev. B 52 (1995) 10962. [7] J. Bullot, M.P. Schmidt, Phys. Status Solidi B 143 (1987) 345. [8] R.A. Street, Hydrogenated Amorphous Silicon, Cambridge University Press, Cambridge, 1991. [9] F. Orapunt, S.K. O'Leary, J. Appl. Phys. 104 (2008) (073513-1-14). [10] D. Briggs, M.P. Seah, in: Auger and X-ray Photoelectron Spectroscopy, vol. 1, John Wiley and Sons, Chichester UK, 1990. [11] K. Sel, B. Akaoğlu, I. Atilgan, B. Katircioglu, Solid-State Electron. 57 (2011) 1. [12] B. Akaoglu, K. Sel, I. Atilgan, B. Katircioglu, Opt. Mater. 30 (2008) 1257. [13] J. Robertson, Adv. Phys. 35 (1986) 317. [14] J. Robertson, Philos. Mag. B 66 (1992) 615. [15] F. Giorgis, P. Mandracci, L. Dal Negro, C. Mazzoleni, L. Pavesi, J. Non-Cryst. Solids 266–269 (2000) 588. [16] J. Cui, S.F. Yoon Rusli, M.B. Yu, K. Chew, J. Ahn, Q. Zhang, E.J. Teo, T. Osipowicz, F. Watt, J. Appl. Phys. 89 (2001) 2699. [17] J. Cui, S.F. Yoon Rusli, E.J. Teo, M.B. Yu, K. Chew, J. Ahn, Q. Zhang, T. Osipowicz, F. Watt, J. Appl. Phys. 89 (2001) 6153. [18] C. Palsule, S. Gangopadhyay, D. Cronauer, B. Schroder, Phys. Rev. B 48 (1993) 10804.
Contents lists available at SciVerse ScienceDirect
Thin Solid Films journal homepage: www.elsevier.com/locate/tsf
Room temperature photoluminescence spectrum modeling of hydrogenated amorphous silicon carbide thin films by a joint density of tail states approach and its application to plasma deposited hydrogenated amorphous silicon carbide thin films Kıvanç Sel ⁎, İbrahim Güneş Department of Physics, Çanakkale Onsekiz Mart University, 17100 Çanakkale, Turkey
a r t i c l e
i n f o
Article history: Received 13 October 2011 Received in revised form 26 July 2012 Accepted 26 July 2012 Available online 3 August 2012 Keywords: Photoluminescence Density of tail states Hydrogenated amorphous silicon carbide
a b s t r a c t Room temperature photoluminescence (PL) spectrum of hydrogenated amorphous silicon carbide (a-SiCx:H) thin films was modeled by a joint density of tail states approach. In the frame of these analyses, the density of tail states was defined in terms of empirical Gaussian functions for conduction and valance bands. The PL spectrum was represented in terms of an integral of joint density of states functions and Fermi distribution function. The analyses were performed for various values of energy band gap, Fermi energy and disorder parameter, which is a parameter that represents the width of the energy band tails. Finally, the model was applied to the measured room temperature PL spectra of a-SiCx:H thin films deposited by plasma enhanced chemical vapor deposition system, with various carbon contents, which were determined by X-ray photoelectron spectroscopy measurements. The energy band gap and disorder parameters of the conduction and valance band tails were determined and compared with the optical energies and Urbach energies, obtained by UV–Visible transmittance measurements. As a result of the analyses, it was observed that the proposed model sufficiently represents the room temperature PL spectra of a-SiCx:H thin films. © 2012 Elsevier B.V. All rights reserved.
1. Introduction The mechanism that determines the shape of photoluminescence (PL) spectrum of hydrogenated amorphous silicon (a-Si:H) and hydrogenated amorphous silicon carbide (a-SiCx:H) has been studied for many years, but it is still controversial [1–9]. It is mainly because of the features of energy band gap structure, such as tail states of conduction and valance bands. For large energy band gap (EGap) amorphous materials, such as a-SiCx:H, the density of the tail states could also be large, which results in thermalization of charge carriers towards deeper‐tail-energy states and recombines at various energy levels. In this respect, the PL spectrum broadens and it respectively becomes difficult to model the PL mechanism. In the literature, mainly for a-Si:H, the static-disorder model, which was proposed by Dunstan and Boulitrop [3–5], assigns the PL spectrum to the distribution of the carriers in the conduction and valence band tail states. While, the Stokes shift model, which was proposed by Street [8], associates the PL spectrum with strong electron–phonon coupling. Moreover, these two models could coexist. On the other hand, a joint density of states (JDOS) approach was applied
⁎ Corresponding author at: Çanakkale Onsekiz Mart Üniversitesi, Fizik Bölümü, Çanakkale, 17100, Turkey. Tel.: +90 286 218 0018. E-mail address: [email protected] (K. Sel). 0040-6090/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.tsf.2012.07.114
to model the optical transitions in amorphous semiconductors such as a-Si:H for zero-temperature by Orapunt and O'Leary [9]. In this model, four types of transitions; extended valence band to extended conduction band, extended valence band to conduction band tail, valence band tail to extended conduction band and valence band tail to conduction band tail, were analyzed in the frame of a JDOS function with energy dependence of square root in band regions and exponential in the tail regions. In this work, the room temperature PL spectrum was modeled by an approach of applying JDOS, where the density of states of the conduction and valance band tails were introduced by empirical Gaussian functions. This model was investigated numerically as a function of Fermi energy (EF), EGap and disorder parameters of conduction band tail (ECB0) and valence band tail (EVB0), which represents the width of the tail states distribution. Finally, the proposed model was applied to the measured room temperature PL spectra of a-SiCx:H thin films, deposited by plasma enhanced chemical vapor deposition system (PECVD), with various x values. Resultantly, EGap, ECB0 and EVB0 of the films were determined. The analyses were supported and compared with the optical energies and Urbach energies (EUrbach), which were obtained by UV–Visible transmittance measurements and carbon contents (x) obtained by X-ray photoelectron spectroscopy (XPS) measurements. In addition to these analyses, the optical and PL characteristics of the films were reported and the PL spectra were analyzed within the frame of the static disorder and Stokes shift models.
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2. Modeling of the room temperature PL spectrum The disordered structure of amorphous semiconductors, such as a-Si:H and a-SiCx:H, results in distribution of localized states at band edges and deep states at around Fermi level in the energy band gap structure. The density of tail states is critical for luminescence mechanisms, since the excited charge carriers first thermalize through these states towards the deeper energy levels in the band tail states. Then, they most probably recombine radiatively or non-radiatively with charge carriers at valence band tail states or deep states, respectively. As a result, in order to model the PL spectrum, the transitions from conduction band tail to valence band tail states should be studied. For the purpose of this analyses, the density of tail states of conduction band (NCB(E)) and valence band (NVB(E)) were empirically presented by a Gaussian function, assuming that the valence band edge energy (EVB) is equal to zero and conduction band edge energy (ECB) is greater than zero, respectively: 2 2 NCB ðEÞ ¼ NCB0 exp −ðE−ECB Þ =2ECB0
ð1Þ
2 2 NVB ðEÞ ¼ NVB0 exp −E =2EVB0
ð2Þ
where, NCB0 and NVB0 denote the density of tail states at conduction band edge and valence band edge, respectively. The resultant distributions of density of tail states functions presented in Fig. 1(a), as a function of energy for different values of NCB0 and NVB0, where we set N0 = NCB0 = NVB0, and in Fig. 1(b), as a function of ECB0 and EVB0. The JDOS function, as an interpretation of PL intensity (I(ℏω)), was expressed as an integral over the product of NCB(E) and NVB(E) [9]. Due to the occupancy considerations, Fermi distribution function was included in the integration for empty states as (1 − F(E)) and for occupied states as F(E). ECB −ℏω
IðℏωÞ∝
∫
NCB ðE þ ℏωÞFðE þ ℏωÞNVB ðEÞ½1−FðEÞdE
ð3Þ
EVB
Fig. 2. Room temperature, normalized PL spectrum calculated by the proposed model, as a function of various values of a) EGap = ECB − EVB, b) EF and c) ECB0 and EVB0, where EVB0 was assumed to be 1.5ECB0. In the calculations, for constant variables were taken as N0 = 1022 cm−3 eV−1, EGap = 2.0 eV, EF = 1.0 eV, ECB0 = 50 meV and EVB0 = 75 meV.
and 3) [8]. Figs. 2(a) and 3(a) represent that, the PL spectrum shifts towards higher energies as EGap increases. PL peak energies (EL) were observed to be smaller than EGap, satisfying that the carriers thermalize through the localized tail states and the radiative optical transitions occur between inter-band tail states. Figs. 2(b) and 3(b) represents that the shift of EF towards higher energies results in a decrease in the width of the PL spectrum and a shift of EL towards the smaller energies, which can be interpreted as the increase of the probability of the radiative optical transitions between deeper states of both conduction and valence band tails. Finally, in Figs. 2(c) and 3(c) the dependence of PL spectrum on the ECB0 and
where, ℏω denotes the energy of the excitation light. The room temperature IðℏωÞ was calculated for various values of EGap, which was assumed to be the difference between ECB and EVB = 0 eV, EF, ECB0 and EVB0, where EVB0 was set to 1.5ECB0 to demonstrate the difference in the width of the energy band tails, such as the case of a-Si:H (Figs. 2
Fig. 1. a) Variation of NCB(E) and NVB(E) as a function of energy for various values of NCB0 and NVB0 (N0 = NCB0 = NVB0), where EF = 1 eV, EGap = 2.0 eV, ECB0 = 50 meV and EVB0 = 75 meV were fixed. b) NCB(E) and NVB(E) as a function of energy for various values of ECB0 and EVB0, where EF = 1 eV, EGap = 2.0 eV and N0 = 1022 cm−3 eV−1 were fixed.
Fig. 3. Variation of a) EGap = ECB − EVB, b) EF and c) ECB0 and EVB0 of the room temperature normalized PL spectrum calculated by the proposed model as a function of EL. In the calculations, for constant variables were taken as N0 = 1022 cm−3 eV−1, EGap = 2.0 eV, EF = 1.0 eV, ECB0 = 50 meV and EVB0 = 75 meV.
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relatively on EVB0 was plotted. As the disorder increases, the PL spectra both increase its width and shift towards the smaller energies. 3. Application of the room temperature PL model 3.1. Experimental work a-SiCx:H thin films were deposited by PECVD (Plasmalab μP80), using radio frequency (13.56 MHz) power density of 30 mW/cm 2, at substrate temperature of 250 °C, on ordinary glass substrates. In the deposition process the source gases of silane (SiH4) and ethylene (C2H4) were used, under constant pressure of 66.7 Pa. The total flow rate of the source gases was set to 20 ccm, where additionally H2 was supplied for further hydrogenation with constant hydrogen flow rate of 200 ccm. x was modified by adjusting the source gas concentration (M = (C2H4/(C2H4 + SiH4)) to the values of 0.0, 0.2, 0.5 and 0.7. Resultantly, as a total, four different types of a-SiCx:H films were deposited. XPS measurements (SPECS ESCA (Germany)) were performed by non-monochromatic Al Kα radiation, with the analyzer mode set at constant analyzer energy of 144 eV. The X-ray source was run at 250 W and the electrons were collected at the take off angle of 90°. In order to remove the surface contaminants, the films were pre-cleaned using Ar ion sputtering at 5 keV for 15 min. After the cleaning, XPS was measured by several scans at the energy resolution of 0.2 eV. The charging effect was eliminated by referencing the binding energies with respect to C 1s core level at 284.5 eV. x was calculated from the ratio of relative intensities to the total intensity in the spectrum; ,X N I In x¼ n Sn S n n¼1
ð4Þ
where ‘In’ is the area under the peak of the element (Si and C) in the XPS and ‘Sn’ is the sensitivity factor, which were taken as 0.25 for C and 0.27 for Si, respectively [10]. x, which was reported in detail in our previous work [11], are presented in Table 1. The film thickness and the optical energies of the films were determined by UV–Visible transmittance measurements (Perkin Elmer Lambda 2) at normal incidence. These analyses were reported in detail in our previouspwork ffiffiffiffiffiffiffiffiffiffi [12]. Tauc energy (ETauc) was determined from the graph of hυα, where α is the absorption coefficient, as a function pffiffiffiffiffiffiffiffiffiof ffi hυ, where the extrapolation of the linear function fit to hυα = 0 gives ETauc. Additionally, E04, which is the energy corresponding to the absorption value at 10 4 cm −1, was determined. EUrbach was determined from the graph of lnα plotted as a function of hυ, where the inverse of the slope of lnα gives EUrbach. ETauc, E04 and EUrbach are presented in Table 1. The room temperature PL spectra of the films, which were obtained by using 457.9 nm line of Argon ion laser as excitation light source, were presented in Fig. 4. In Fig. 4, as x increases, the PL spectra of a-SiCx:H broaden and shift towards the higher energies [7,8,13–18].
Fig. 4. The normalized room temperature PL spectrum of the a-SiCx:H films with various x. The solid line is the normalized PL spectrum and the fitted Gaussian curve and the broken line is the curve of the room temperature PL model fit. In the fitting we set NCB0 = NVB0 = 1022 cm−3 eV−1 and EVB0 = 1.5ECB0.
3.2. Application of the model to the PL spectrum of a-SiCx:H The measured room temperature PL spectra of a-SiCx:H were normalized and then fitted to Gaussian curves and the full-width of hall maxima of the Gaussian curves (ΔEL) was determined. Next, the Gaussian curves were fitted to the model Eq. (3). In Fig. 4, the measured room temperature PL spectra, the fitted Gaussian curves and the fitted curves of the model were plotted together as a function of energy. The curves of the model and the Gaussian curves of the experimental PL spectra closely overlap with the data. Whereas, for the a-SiCx:H films with higher x values, high energy tails were observed on the PL spectra. With the increasing x, as a result of the increase
Table 1 M, film thickness, x, E04, ETauc and EUrbach of a-SiCx:H films, obtained from XPS and UV– Visible transmittance spectroscopy analyses [11,12]. (M = (C2H4/(C2H4 + SiH4))
0.0
0.2
0.5
0.7
x Film thickness (nm) E04 (eV) ETauc (eV) EUrbach (meV)
0.00 226.5 2.00 1.99 41.9
0.17 523.4 2.18 2.03 96.2
0.37⁎ 230.7 2.42 2.40 113.1
0.48 240.8 2.60 2.55 118.9
⁎ x of the M = 0.5 film, which could not be determined by XPS, was determined by a statistical approach, where the optical constants were compared with the relevant results in the literature, which were reported in detail in our previous work [12].
Fig. 5. a) Variation of E04, ETauc and EL, as a function of x for the a-SiCx:H films. b) Variation of EUrbach, EVB0 and ECB0, as a function of x for the a-SiCx:H films.
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space and depends exponentially on energy with a logarithmic slope of E0 and the separation between non-radiative and radiative recombination centers are constant and is about 12 nm [3–5]. The slope of best fit of ΔEL versus EUrbach graph, which was presented in Fig. 6(a), is calculated as 1.95 ± 0.50 for the films, which is in the limit of the theoretically proposed value of 2.45 [5,15,18]. Moreover, the zero intercept of about 20 meV justifies that electron–phonon coupling is small. On the other hand, from the slope of the best fit of (ΔEL) 2 versus (E04–EL) graph, which was presented in Fig. 6(b), E0 is calculated as 0.062 ± 0.020 eV [8]. This value is in the order of the approximate E0 and agrees with the prediction of the Stokes shift model. 4. Conclusion Fig. 6. a) Variation of ΔEL as a function of the EUrbach, and b) variation of (ΔEL)2 as a function of E04–EL.
in the carbon concentration, C\C bonds, which could form sp 2 hybridized π bonded graphite-like structures in addition to sp 3 hybridized σ bonded tetrahedral structures, start to occur besides Si\Si and S\C, σ bonds [13,14]. Resultantly, in addition to the σ-states and the increase in the disorder, π-states start to occur around the high energy regime of the tail states. This additional increase in the density of tail states could be the result of the high energy tails observed in the PL spectra of a-SiCx:H films with higher x values. Accordingly, it can be concluded that the proposed model is in agreement with the experimental data. In the frame of the proposed model, in order to further analyze the PL spectra of a-SiCx:H films, the fitted EL were plotted together with E04 and ETauc, as a function of x in Fig. 5(a), where a linearly correlated increase was observed for all of them. EL of the films were slightly under E04 and ETauc, which is in agreement with the assumption that the radiative transitions occur between conduction band tail states and valence band tail states. In Fig. 5(b), EUrbach, EVB0 and ECB0 were plotted as a function of x. It was observed that, EVB0 was very close to EUrbach (Note that EVB0 = 1.5ECB0). Since EUrbach, which could be interpreted as the convolution of density of tail states of conduction and valence bands, is actually dominated by the larger width of valence band tail. As a result, the observed values of EUrbach and EVB0 were reasonable [8,12–14]. PL mechanisms were also investigated within the frame of static disorder model and Stokes shift model [3–6,8]. If the static disorder mechanism is dominant, ΔEL is given as; 2 2 e–ph 2 ðΔEL Þ ¼ ð2:45Eu Þ þ ΔEL
ð5Þ
2 where ΔEe–ph represents the contribution of Stokes shift model L (electron–phonon coupling (e–ph)) to the full-width hall maximum of the PL spectrum. On the other hand, if Stokes shift model mechanism is dominant, ΔEL can be expressed as [8]; 2 stat 2 ðΔEL Þ ¼ 4 ln2ðE04 −EL −Eth ÞE0 þ ΔEL
ð6Þ
2 where Eth is thermalization energy, ΔEStat represents the contribuL tion of statistical disorder model to the full-width hall maximum of the PL spectrum and E0 is the typical phonon energy, which is about 60 meV, supposing that the tail states are distributed randomly in
We have defined empirically NCB(E) and NVB(E), in terms of Gaussian functions. NCB(E) and NVB(E) were presented for various N0, ECB, EVB, ECB0 and EVB0 values. Considering the occupancy of the tail states, the room temperature PL spectrum was expressed as an integral of JDOS function and Fermi distribution function. The resultant PL spectrum of the model was investigated with respect to various EGap, EF and ECB0 and EVB0 values. The model was fitted to the measured room temperature PL spectra of a-SiCx:H films with various x and a very close overlap were obtained for all of them. EL was compared with the optical energies, ETauc and E04. Additionally, ECB0 and EVB0 were compared with EUrbach. As a result of the analyses, it can be concluded that the proposed PL model sufficiently represents the room temperature PL spectrum of a-SiCx:H thin films. Acknowledgment This work was carried out with the financial support of Çanakkale Onsekiz Mart University (COMU-BDP/2011-010). Thanks to Assoc. Prof. Dr. Barış Akaoğlu and Prof. Dr. İsmail Atılgan for sharing their laboratory facilities. References [1] M.H. Brodsky, R.S. Title, K. Weiser, G.D. Petit, Phys. Rev. B 1 (1970) 2632. [2] G.D. Cody, in: J.I. Pankove (Ed.), Semiconductors and Semimetals, vol. 21B, Academic Press, New York, 1984, p. 11. [3] F. Boulitrop, D.J. Dunstan, Phys. Rev. B 28 (1983) 5923. [4] D.J. Dunstan, F. Boulitrop, Phys. Rev. B 30 (1984) 5945. [5] T.M. Searle, W.A. Jackson, Philos. Mag. B 60 (1989) 237. [6] L.R. Tessler, I. Solomon, Phys. Rev. B 52 (1995) 10962. [7] J. Bullot, M.P. Schmidt, Phys. Status Solidi B 143 (1987) 345. [8] R.A. Street, Hydrogenated Amorphous Silicon, Cambridge University Press, Cambridge, 1991. [9] F. Orapunt, S.K. O'Leary, J. Appl. Phys. 104 (2008) (073513-1-14). [10] D. Briggs, M.P. Seah, in: Auger and X-ray Photoelectron Spectroscopy, vol. 1, John Wiley and Sons, Chichester UK, 1990. [11] K. Sel, B. Akaoğlu, I. Atilgan, B. Katircioglu, Solid-State Electron. 57 (2011) 1. [12] B. Akaoglu, K. Sel, I. Atilgan, B. Katircioglu, Opt. Mater. 30 (2008) 1257. [13] J. Robertson, Adv. Phys. 35 (1986) 317. [14] J. Robertson, Philos. Mag. B 66 (1992) 615. [15] F. Giorgis, P. Mandracci, L. Dal Negro, C. Mazzoleni, L. Pavesi, J. Non-Cryst. Solids 266–269 (2000) 588. [16] J. Cui, S.F. Yoon Rusli, M.B. Yu, K. Chew, J. Ahn, Q. Zhang, E.J. Teo, T. Osipowicz, F. Watt, J. Appl. Phys. 89 (2001) 2699. [17] J. Cui, S.F. Yoon Rusli, E.J. Teo, M.B. Yu, K. Chew, J. Ahn, Q. Zhang, T. Osipowicz, F. Watt, J. Appl. Phys. 89 (2001) 6153. [18] C. Palsule, S. Gangopadhyay, D. Cronauer, B. Schroder, Phys. Rev. B 48 (1993) 10804.