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An alternative procedure for the determination of the optical band gap and thickness of amorphous carbon nitride thin films
Applied Surface Science 254 (2007) 412–415 www.elsevier.com/locate/apsusc
An alternative procedure for the determination of the optical band gap and thickness of amorphous carbon nitride thin films L. Escobar-Alarco´n a,*, A. Arrieta a,b, E. Camps a, S. Muhl c, S. Rodil c, E. Vigueras-Santiago d a
Departamento de Fı´sica, Instituto Nacional de Investigaciones Nucleares, Apdo. Postal 18-1027, Me´xico, DF 11801, Mexico Departamento de Fı´sica, Universidad Auto´noma Metropolitana Iztapalapa Apdo. Postal 55-534, Me´xico, DF 09340, Mexico c Instituto de Investigaciones en Materiales, Universidad Nacional Auto´noma de Me´xico, Apdo. Postal 364, Me´xico, DF 01000, Mexico d Facultad de Quı´mica, Universidad Auto´noma del Estado de Me´xico, Paseo Colo´ny Tollocan, Toluca 50110, Mexico b
Available online 10 July 2007
Abstract In this work, we propose an alternative procedure to obtain the optical band gap and the thickness of amorphous carbon nitride thin films that requires only the measurement of the absorbance spectrum of the samples. The method is based on an absorbance spectrum fitting (ASF) procedure using the Tauc model, which is widely applied to the study of amorphous semiconductors. With the aim of evaluating the proposed method two sets of carbon nitride samples deposited on glass substrates were analyzed; one prepared by pulsed laser ablation (PLA) and the second by magnetron sputtering. The obtained results using different conventional methods were compared with the results of the ASF method and a good agreement between the values and the tendencies with the experimental conditions used to prepare the films were observed. # 2007 Elsevier B.V. All rights reserved. PACS : 78.40.Fy; 81.05.Hd; 81.15.Fg Keywords: Optical band gap; Carbon nitride; Laser ablation; DC sputtering
1. Introduction The determination of the band gap in amorphous materials is somewhat difficult because the edges of the valence and conduction bands are not abrupt and the tail states complicate the definition of the true optical gap. As a result various empirical approaches have been developed for the determination of the band gap of such materials [1–4]. The most common are based on measurements of the optical absorption coefficient that are then related to the band gap. Particularly, for amorphous carbon nitride the optical band gap usually has been characterized by means of the so-called ‘‘Tauc gap’’ (ET), or the ‘‘E04 gap’’. In order to obtain either of these, it is necessary to measure the absorption coefficient (a) of the material as a function of the photon energy and normally this is carried out by measurements of the film absorbance, the reflectance and the film thickness [5]. It is worth mentioning that in amorphous carbon nitride the determination of the band
* Corresponding author. Fax: +52 55 53297332. E-mail address: [email protected] (L. Escobar-Alarco´n). 0169-4332/$ – see front matter # 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.apsusc.2007.07.052
gap, or the tendency of the band gap values as a function of an experimental parameter, is useful because this can provide information about the variation of the sp2/sp3 ratio. Several methods have been proposed in order to determine the band gap and thickness in a rapid, accurate and nondestructive way. These methods are generally based on the optical analysis of the absorption spectrum [6,7]. The thickness determination has been performed by optical interference methods [8] and from the transmittance and reflectance spectra [6]. In this work we propose a procedure to obtain the band gap and film thickness when only measurements of the absorbance spectrum are available. To our knowledge the proposed procedure is different to the numerical techniques for the interpretation of experimental data of absorption spectra that have been reported previously. 2. Band gap determination In order to obtain the optical band gap by our procedure we start by considering the Tauc model in which the main assumption is that the edges of the conduction band and valence
L. Escobar-Alarco´n et al. / Applied Surface Science 254 (2007) 412–415
band are parabolic [9,10], and can be described by: pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi aðvÞ hv ¼ Bðhv ET Þ
(1)
where ET denotes the optical Tauc gap and B is assumed to be constant. Since the absorbance measurements (A) are usually performed as a function of the wavelength (l), Eq. (1) can be rewritten in terms of l, as: 2 1 1 a ¼ B2 hcl (2) l l0 where l0 is the wavelength corresponding to the band gap energy (ET), h is the Planck’s constant and c is the velocity of the light. The absorption coefficient, a, is defined by the Lambert–Beer law using the definition for the transmittance and is related to the absorbance, as a first approximation, by: a ¼ 2:3ðA=xÞ, where x is the film thickness and it is clear that to be able to determine the absorption coefficient it is necessary to know the film thickness. If a more precise determination of the absorption coefficient is required, it is necessary to carry out corrections to the absorption due to reflection and other dispersive effects that reduce the intensity of the transmitted light. In this case the absorption coefficient depends on the transmittance (T), the reflectance (R) and the thickness (x) of the thin film. In the particular case of thin films deposited on a transparent substrate, the reflectance (R) from the film-substrate interface can be calculated using the refractive index of the film (nf) and the substrate (ns) via the Fresnel coefficients [5], and a similar calculation can be performed for the film–air interface, however, this increases the difficulty of determining the absorption coefficient. Using the definition of a, it is possible to rewrite Eq. (2) in the form: 2 1 1 A ¼ C1 l þ C2 (3) l l0 where C 1 ¼ B2 ðhc=2:3Þx, and C2 is a constant which takes into account the fraction of the incident light lost, assuming that the fraction reflected or dispersed is small. As can be seen, Eq. (3) allows the evaluation of the optical band gap by an absorbance spectrum fitting (ASF) procedure, using C1, l0 and C2 as the fitting parameters. The value of the optical band gap, in eV, can be calculated from the parameter l0 using the equation EASF ¼ 1239:83=l0 . This procedure has the advantage that only requires the measurement of the absorbance spectrum and no additional information is needed, such as the film thickness or the refractive index. Additionally, from the fitting parameter C1 and its definition it is clear that if the constant B is known, it is possible to determine the film thickness using the following expression: x ¼ 2:3C 1 =B2 hc. The value of B can be obtained using the usual procedure for the Tauc gap determination, that is, by plotting p ffiffiffiffiffiffi aE versus E, and B is the slope of the linear part of the graph. It is important to point out that the band gap value determined in this way is most useful in studying the behavior or trend of this property as a function of some deposition parameter, rather than the absolute value. In fact, other authors have pointed out that changes in the optical gap of an
413
amorphous semiconductor are more easily determined than the absolute magnitude of the gap itself [11]. 3. Experimental In order to evaluate the proposed procedure, two sets of amorphous carbon nitride thin films were deposited using two different deposition techniques. The first set was deposited by the laser ablation technique. In this case, the ablation was performed using a Q-switched Nd:YAG laser with emission at the fundamental line (l = 1064 nm) with a 28 ns pulse duration at a repetition rate of 10 Hz. The laser beam was focused on a rotating target, at an incidence angle of 458. The target was a graphite disk, 99.99% purity, 25 mm diameter and 2 mm thick. The deposition chamber base pressure was of the order of 7.0 106 Torr and was backfilled with nitrogen (99.99% purity) up to the working pressure of 7.5 102 Torr. The energy density delivered on the target was varied from 6.1 to 39.6 J/cm2 by keeping the spot size constant on the target surface and adjusting the energy per pulse. In all the experiments the substrates were placed at 50 mm from the graphite target. The second set of films was obtained using a pure (99.999%) graphite target that was reactively sputtered in an Ar/N2 discharge by means of a balanced DC magnetron operated at a pressure of 6.0 102 Torr, and at various discharge powers between 40 and 280 W. Before film deposition, the vacuum chamber was evacuated to a base pressure of less than 5 106 Torr using a turbomolecular pump. Subsequently, the target was plasma cleaned for 10 min to remove any contamination layer. The substrates used in these experiments were glass microscope slides. Prior to deposition they were ultrasonically cleaned in acetone and ethyl alcohol. All the films were deposited at room temperature. The absorbance and reflectance measurements of the deposited films were carried out using an UV–vis–NIR spectrophotometer (Cary 5000) equipped with an integrating sphere. The integrating sphere allows the simultaneous collection of the reflected and the dispersed light. The measurements were carried out from 350 to 1200 nm to avoid errors due to the absorption of the glass. The thickness of the deposited films was measured using a profilometer (Sloan Dektak IIA). For the samples deposited by magnetron sputtering, the band gap (ESWE) and thickness (xSWE) were determined by phase modulated spectroscopy (ellipsometer Jobin Yvon) in the 1.5– 5.0 eV energy range. In this case, the optical properties were calculated by the parameterization of the dielectric function using a two-oscillator Tauc–Lorentz model. Additionally, the band gap (ET) was calculated from reflectance and transmittance measurements to determine the absorption coefficient, a, by an iterative method using the Fresnel coefficients [12]. 4. Results 4.1. The band gap determination In general terms good fits to the experimental curves were obtained for both sets of samples. As an example, the value of
414
L. Escobar-Alarco´n et al. / Applied Surface Science 254 (2007) 412–415
the optical band gap corresponding to the sample deposited at 13.5 J/cm2 was calculated from the parameter l0 (1112.95 nm) giving a value of 1.11 eV. The other fitting parameters had the following values: C1 = 2033.52 and C2 = 0.09. The low value for C2, might be considered to indicate that this film had a low reflectivity. In order to corroborate this, measurements of the reflectance spectra were performed and the obtained spectra reveals that the reflectance was low, approximately 8.0% at 600 nm. Fig. 1 shows the optical band gap values obtained by the proposed procedure (EASF), the E04 and the Tauc gap (ET) for the samples grown by laser ablation (Fig. 1a) and the EASF, ET and the gap determined from the spectroscopic ellipsometry measurements (ESWE) for the samples deposited by magnetron sputtering (Fig. 1b). In these figures two aspects should be emphasized; firstly, in general terms a good agreement can be seen between the values of the Tauc gap obtained following the standard procedures and those of the proposed procedure, in fact the average deviation is approximately 5%. Secondly, it can be observed that the variation of the band gap as a function of the experimental preparation parameters, laser fluence or the
plasma power, shows the same trend. This in part indicates the effect of the deposition parameters on the type of deposited material but also, demonstrates the usefulness of the proposed fast method for the estimation of the band gap. Evidently, the information extracted from any of the methods is, to a first approximation, the same. Additionally, it is worth mentioning that the obtained values are in good agreement with those reported in the literature for a-CNx thin films prepared under similar conditions [13]. Finally, it should be noted that for many amorphous semiconductors the absolute magnitude of the optical gap, as determined by the linear extrapolation, is quite sensitive to the range over which the extrapolation is taken [14], the proposed procedure avoids this problem since the complete spectrum is fitted.
Fig. 1. The optical band gap of a-CNx thin films deposited at: (a) different laser fluences and (b) different plasma powers; determined by means of the different methods described in the text.
Fig. 2. The calculated and measured thickness as a function of: (a) the laser fluence for samples grown by laser ablation and (b) plasma power for samples grown by magnetron sputtering.
4.2. The thickness determination The slopes of the Tauc linear extrapolations (B) were determined by a least squares fitting, a mean value of 263 25 was obtained for the samples grown by laser ablation. With this value and the equation: x ¼ 2:3C 1 =B2 hc,
L. Escobar-Alarco´n et al. / Applied Surface Science 254 (2007) 412–415
the thickness of the samples of the two sets was determined. Fig. 2a and b shows the results obtained, for the PLD and sputtered samples, respectively, together with the error bars due to the uncertain associated with the determination of B. It can be seen that the thickness values obtained using our procedure shows good agreement with the thickness measured using the profilometer, revealing the same trend as a function of the laser fluence (Fig. 2a) or the plasma power (Fig. 2b) used for deposition, again providing a good estimate of the deposition rate as a function of the deposition parameter. 5. Conclusions In this work an alternative procedure of absorbance spectrum fitting, ASF, is described to easily and rapidly obtain the optical band gap and the thickness of thin films of amorphous carbon nitride. The main advantage of the ASF procedure is that it only requires the measurement of the absorbance spectrum and no additional information is needed of the film thickness or the refractive index. In order to evaluate the method two sets of samples deposited by laser ablation and magnetron sputtering on glass substrates were analyzed. The values of the band gap obtained using the different analysis methods were compared and a good agreement between the values and similar tendencies with the deposition parameters used to prepare the films were observed. Additionally, the thickness values obtained using the ASF procedure showed good agreement with the thickness measured by profilometry.
415
The possibility of applying the ASF procedure to other types of materials is in progress. Acknowledgements Authors wish to thank CONACYT-Me´xico for its partial support under contract 46344. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]
[12] [13] [14]
S. Karrer, O. Leary, Appl. Phys. Lett. 72 (1998) 1332. J. Tauc, R. Grigorovici, A. Vancu, Phys. Stat. Sol. 15 (1966) 627. G.D. Cody, B.G. Brooks, A. Abeles, Solar Energy Mater 8 (1982) 231. A.P. Sokolov, A.P. Shebanin, O.A. Golikova, M.M. Mezdrogina, J. Phys. Cond. Matt. 3 (1991) 9887. O.S. Heavens, Optical Properties of Thin Solid Films, DOVER, London, 1965. F. Demichelis, G. Kaniadakis, A. Tagliaferro, E. Tresso, Appl. Opt. 26 (1987) 1737. A.K. Ray, C.A. Hogarth, J. Phys. D: Appl. Phys. 23 (1990) 458. A.M. Goodman, Appl. Opt. 17 (1978) 2779. N.F. Mott, E.A. Davis, Electronic properties in non-crystalline materials, Oxford University Press, London, 1971. N. Savvides, J. Appl. Phys. 59 (1986) 4133. G.D. Cody, Hydrogenated Amorphous Silicon, in: J.I. Pankove (Ed.), Semiconductors and Semimetals, 21B, Academic Press, New York, 1984, p. 11. S.E. Rodil, S. Muhl, S. Maca, A.C. Ferrari, Thin Solid Films 433 (2003) 119. S.E. Rodil, S. Muhl, Diamond Relat. Mater. 13 (2004) 1521. R.M. Dawson, Y.M. Li, M. Gunes, D. Heller, S. Nag, R.W. Collins, C.R. Wronski, M. Bennett, Y.M. Li, Mater. Res. Soc. Symp. Proc. 258 (1992) 595.
An alternative procedure for the determination of the optical band gap and thickness of amorphous carbon nitride thin films L. Escobar-Alarco´n a,*, A. Arrieta a,b, E. Camps a, S. Muhl c, S. Rodil c, E. Vigueras-Santiago d a
Departamento de Fı´sica, Instituto Nacional de Investigaciones Nucleares, Apdo. Postal 18-1027, Me´xico, DF 11801, Mexico Departamento de Fı´sica, Universidad Auto´noma Metropolitana Iztapalapa Apdo. Postal 55-534, Me´xico, DF 09340, Mexico c Instituto de Investigaciones en Materiales, Universidad Nacional Auto´noma de Me´xico, Apdo. Postal 364, Me´xico, DF 01000, Mexico d Facultad de Quı´mica, Universidad Auto´noma del Estado de Me´xico, Paseo Colo´ny Tollocan, Toluca 50110, Mexico b
Available online 10 July 2007
Abstract In this work, we propose an alternative procedure to obtain the optical band gap and the thickness of amorphous carbon nitride thin films that requires only the measurement of the absorbance spectrum of the samples. The method is based on an absorbance spectrum fitting (ASF) procedure using the Tauc model, which is widely applied to the study of amorphous semiconductors. With the aim of evaluating the proposed method two sets of carbon nitride samples deposited on glass substrates were analyzed; one prepared by pulsed laser ablation (PLA) and the second by magnetron sputtering. The obtained results using different conventional methods were compared with the results of the ASF method and a good agreement between the values and the tendencies with the experimental conditions used to prepare the films were observed. # 2007 Elsevier B.V. All rights reserved. PACS : 78.40.Fy; 81.05.Hd; 81.15.Fg Keywords: Optical band gap; Carbon nitride; Laser ablation; DC sputtering
1. Introduction The determination of the band gap in amorphous materials is somewhat difficult because the edges of the valence and conduction bands are not abrupt and the tail states complicate the definition of the true optical gap. As a result various empirical approaches have been developed for the determination of the band gap of such materials [1–4]. The most common are based on measurements of the optical absorption coefficient that are then related to the band gap. Particularly, for amorphous carbon nitride the optical band gap usually has been characterized by means of the so-called ‘‘Tauc gap’’ (ET), or the ‘‘E04 gap’’. In order to obtain either of these, it is necessary to measure the absorption coefficient (a) of the material as a function of the photon energy and normally this is carried out by measurements of the film absorbance, the reflectance and the film thickness [5]. It is worth mentioning that in amorphous carbon nitride the determination of the band
* Corresponding author. Fax: +52 55 53297332. E-mail address: [email protected] (L. Escobar-Alarco´n). 0169-4332/$ – see front matter # 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.apsusc.2007.07.052
gap, or the tendency of the band gap values as a function of an experimental parameter, is useful because this can provide information about the variation of the sp2/sp3 ratio. Several methods have been proposed in order to determine the band gap and thickness in a rapid, accurate and nondestructive way. These methods are generally based on the optical analysis of the absorption spectrum [6,7]. The thickness determination has been performed by optical interference methods [8] and from the transmittance and reflectance spectra [6]. In this work we propose a procedure to obtain the band gap and film thickness when only measurements of the absorbance spectrum are available. To our knowledge the proposed procedure is different to the numerical techniques for the interpretation of experimental data of absorption spectra that have been reported previously. 2. Band gap determination In order to obtain the optical band gap by our procedure we start by considering the Tauc model in which the main assumption is that the edges of the conduction band and valence
L. Escobar-Alarco´n et al. / Applied Surface Science 254 (2007) 412–415
band are parabolic [9,10], and can be described by: pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi aðvÞ hv ¼ Bðhv ET Þ
(1)
where ET denotes the optical Tauc gap and B is assumed to be constant. Since the absorbance measurements (A) are usually performed as a function of the wavelength (l), Eq. (1) can be rewritten in terms of l, as: 2 1 1 a ¼ B2 hcl (2) l l0 where l0 is the wavelength corresponding to the band gap energy (ET), h is the Planck’s constant and c is the velocity of the light. The absorption coefficient, a, is defined by the Lambert–Beer law using the definition for the transmittance and is related to the absorbance, as a first approximation, by: a ¼ 2:3ðA=xÞ, where x is the film thickness and it is clear that to be able to determine the absorption coefficient it is necessary to know the film thickness. If a more precise determination of the absorption coefficient is required, it is necessary to carry out corrections to the absorption due to reflection and other dispersive effects that reduce the intensity of the transmitted light. In this case the absorption coefficient depends on the transmittance (T), the reflectance (R) and the thickness (x) of the thin film. In the particular case of thin films deposited on a transparent substrate, the reflectance (R) from the film-substrate interface can be calculated using the refractive index of the film (nf) and the substrate (ns) via the Fresnel coefficients [5], and a similar calculation can be performed for the film–air interface, however, this increases the difficulty of determining the absorption coefficient. Using the definition of a, it is possible to rewrite Eq. (2) in the form: 2 1 1 A ¼ C1 l þ C2 (3) l l0 where C 1 ¼ B2 ðhc=2:3Þx, and C2 is a constant which takes into account the fraction of the incident light lost, assuming that the fraction reflected or dispersed is small. As can be seen, Eq. (3) allows the evaluation of the optical band gap by an absorbance spectrum fitting (ASF) procedure, using C1, l0 and C2 as the fitting parameters. The value of the optical band gap, in eV, can be calculated from the parameter l0 using the equation EASF ¼ 1239:83=l0 . This procedure has the advantage that only requires the measurement of the absorbance spectrum and no additional information is needed, such as the film thickness or the refractive index. Additionally, from the fitting parameter C1 and its definition it is clear that if the constant B is known, it is possible to determine the film thickness using the following expression: x ¼ 2:3C 1 =B2 hc. The value of B can be obtained using the usual procedure for the Tauc gap determination, that is, by plotting p ffiffiffiffiffiffi aE versus E, and B is the slope of the linear part of the graph. It is important to point out that the band gap value determined in this way is most useful in studying the behavior or trend of this property as a function of some deposition parameter, rather than the absolute value. In fact, other authors have pointed out that changes in the optical gap of an
413
amorphous semiconductor are more easily determined than the absolute magnitude of the gap itself [11]. 3. Experimental In order to evaluate the proposed procedure, two sets of amorphous carbon nitride thin films were deposited using two different deposition techniques. The first set was deposited by the laser ablation technique. In this case, the ablation was performed using a Q-switched Nd:YAG laser with emission at the fundamental line (l = 1064 nm) with a 28 ns pulse duration at a repetition rate of 10 Hz. The laser beam was focused on a rotating target, at an incidence angle of 458. The target was a graphite disk, 99.99% purity, 25 mm diameter and 2 mm thick. The deposition chamber base pressure was of the order of 7.0 106 Torr and was backfilled with nitrogen (99.99% purity) up to the working pressure of 7.5 102 Torr. The energy density delivered on the target was varied from 6.1 to 39.6 J/cm2 by keeping the spot size constant on the target surface and adjusting the energy per pulse. In all the experiments the substrates were placed at 50 mm from the graphite target. The second set of films was obtained using a pure (99.999%) graphite target that was reactively sputtered in an Ar/N2 discharge by means of a balanced DC magnetron operated at a pressure of 6.0 102 Torr, and at various discharge powers between 40 and 280 W. Before film deposition, the vacuum chamber was evacuated to a base pressure of less than 5 106 Torr using a turbomolecular pump. Subsequently, the target was plasma cleaned for 10 min to remove any contamination layer. The substrates used in these experiments were glass microscope slides. Prior to deposition they were ultrasonically cleaned in acetone and ethyl alcohol. All the films were deposited at room temperature. The absorbance and reflectance measurements of the deposited films were carried out using an UV–vis–NIR spectrophotometer (Cary 5000) equipped with an integrating sphere. The integrating sphere allows the simultaneous collection of the reflected and the dispersed light. The measurements were carried out from 350 to 1200 nm to avoid errors due to the absorption of the glass. The thickness of the deposited films was measured using a profilometer (Sloan Dektak IIA). For the samples deposited by magnetron sputtering, the band gap (ESWE) and thickness (xSWE) were determined by phase modulated spectroscopy (ellipsometer Jobin Yvon) in the 1.5– 5.0 eV energy range. In this case, the optical properties were calculated by the parameterization of the dielectric function using a two-oscillator Tauc–Lorentz model. Additionally, the band gap (ET) was calculated from reflectance and transmittance measurements to determine the absorption coefficient, a, by an iterative method using the Fresnel coefficients [12]. 4. Results 4.1. The band gap determination In general terms good fits to the experimental curves were obtained for both sets of samples. As an example, the value of
414
L. Escobar-Alarco´n et al. / Applied Surface Science 254 (2007) 412–415
the optical band gap corresponding to the sample deposited at 13.5 J/cm2 was calculated from the parameter l0 (1112.95 nm) giving a value of 1.11 eV. The other fitting parameters had the following values: C1 = 2033.52 and C2 = 0.09. The low value for C2, might be considered to indicate that this film had a low reflectivity. In order to corroborate this, measurements of the reflectance spectra were performed and the obtained spectra reveals that the reflectance was low, approximately 8.0% at 600 nm. Fig. 1 shows the optical band gap values obtained by the proposed procedure (EASF), the E04 and the Tauc gap (ET) for the samples grown by laser ablation (Fig. 1a) and the EASF, ET and the gap determined from the spectroscopic ellipsometry measurements (ESWE) for the samples deposited by magnetron sputtering (Fig. 1b). In these figures two aspects should be emphasized; firstly, in general terms a good agreement can be seen between the values of the Tauc gap obtained following the standard procedures and those of the proposed procedure, in fact the average deviation is approximately 5%. Secondly, it can be observed that the variation of the band gap as a function of the experimental preparation parameters, laser fluence or the
plasma power, shows the same trend. This in part indicates the effect of the deposition parameters on the type of deposited material but also, demonstrates the usefulness of the proposed fast method for the estimation of the band gap. Evidently, the information extracted from any of the methods is, to a first approximation, the same. Additionally, it is worth mentioning that the obtained values are in good agreement with those reported in the literature for a-CNx thin films prepared under similar conditions [13]. Finally, it should be noted that for many amorphous semiconductors the absolute magnitude of the optical gap, as determined by the linear extrapolation, is quite sensitive to the range over which the extrapolation is taken [14], the proposed procedure avoids this problem since the complete spectrum is fitted.
Fig. 1. The optical band gap of a-CNx thin films deposited at: (a) different laser fluences and (b) different plasma powers; determined by means of the different methods described in the text.
Fig. 2. The calculated and measured thickness as a function of: (a) the laser fluence for samples grown by laser ablation and (b) plasma power for samples grown by magnetron sputtering.
4.2. The thickness determination The slopes of the Tauc linear extrapolations (B) were determined by a least squares fitting, a mean value of 263 25 was obtained for the samples grown by laser ablation. With this value and the equation: x ¼ 2:3C 1 =B2 hc,
L. Escobar-Alarco´n et al. / Applied Surface Science 254 (2007) 412–415
the thickness of the samples of the two sets was determined. Fig. 2a and b shows the results obtained, for the PLD and sputtered samples, respectively, together with the error bars due to the uncertain associated with the determination of B. It can be seen that the thickness values obtained using our procedure shows good agreement with the thickness measured using the profilometer, revealing the same trend as a function of the laser fluence (Fig. 2a) or the plasma power (Fig. 2b) used for deposition, again providing a good estimate of the deposition rate as a function of the deposition parameter. 5. Conclusions In this work an alternative procedure of absorbance spectrum fitting, ASF, is described to easily and rapidly obtain the optical band gap and the thickness of thin films of amorphous carbon nitride. The main advantage of the ASF procedure is that it only requires the measurement of the absorbance spectrum and no additional information is needed of the film thickness or the refractive index. In order to evaluate the method two sets of samples deposited by laser ablation and magnetron sputtering on glass substrates were analyzed. The values of the band gap obtained using the different analysis methods were compared and a good agreement between the values and similar tendencies with the deposition parameters used to prepare the films were observed. Additionally, the thickness values obtained using the ASF procedure showed good agreement with the thickness measured by profilometry.
415
The possibility of applying the ASF procedure to other types of materials is in progress. Acknowledgements Authors wish to thank CONACYT-Me´xico for its partial support under contract 46344. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]
[12] [13] [14]
S. Karrer, O. Leary, Appl. Phys. Lett. 72 (1998) 1332. J. Tauc, R. Grigorovici, A. Vancu, Phys. Stat. Sol. 15 (1966) 627. G.D. Cody, B.G. Brooks, A. Abeles, Solar Energy Mater 8 (1982) 231. A.P. Sokolov, A.P. Shebanin, O.A. Golikova, M.M. Mezdrogina, J. Phys. Cond. Matt. 3 (1991) 9887. O.S. Heavens, Optical Properties of Thin Solid Films, DOVER, London, 1965. F. Demichelis, G. Kaniadakis, A. Tagliaferro, E. Tresso, Appl. Opt. 26 (1987) 1737. A.K. Ray, C.A. Hogarth, J. Phys. D: Appl. Phys. 23 (1990) 458. A.M. Goodman, Appl. Opt. 17 (1978) 2779. N.F. Mott, E.A. Davis, Electronic properties in non-crystalline materials, Oxford University Press, London, 1971. N. Savvides, J. Appl. Phys. 59 (1986) 4133. G.D. Cody, Hydrogenated Amorphous Silicon, in: J.I. Pankove (Ed.), Semiconductors and Semimetals, 21B, Academic Press, New York, 1984, p. 11. S.E. Rodil, S. Muhl, S. Maca, A.C. Ferrari, Thin Solid Films 433 (2003) 119. S.E. Rodil, S. Muhl, Diamond Relat. Mater. 13 (2004) 1521. R.M. Dawson, Y.M. Li, M. Gunes, D. Heller, S. Nag, R.W. Collins, C.R. Wronski, M. Bennett, Y.M. Li, Mater. Res. Soc. Symp. Proc. 258 (1992) 595.