Depth-profiles in compositionally-graded amorphous silicon alloy thin films analyzed by real time spectroscopic ellipsometry

Thin Solid Films 313]314 Ž1998. 474]478

Depth-profiles in compositionally-graded amorphous silicon alloy thin films analyzed by real time spectroscopic ellipsometry H. Fujiwara, Joohyun Koh, R.W. CollinsU Materials Research Laboratory and Department of Physics, The Pennsyl¨ania State Uni¨ersity, Uni¨ersity Park, PA 16802, USA

Abstract Real-time spectroscopic ellipsometry ŽRTSE. has been applied to characterize composition depth-profiles in compositionally-graded amorphous silicon]carbon alloy Ža-Si 1yx C x :H. thin films, prepared using continuous variations in the flow ratio z Ž t . s wCH 4 xrwSiH 4 x q wCH 4 x4 during r.f. plasma-enhanced chemical vapor deposition ŽPECVD.. In order to calculate the dielectric functions of a-Si 1yx C x :H alloys for any value of x, a new parameterization of the measured dielectric functions was established using the recently-derived Tauc]Lorentz ŽT-L. model. This model is found to provide improved fitting of the measured dielectric functions of a-Si 1yx C x :H over the analyzed energy region of 2.2- E - 4.2 eV, in comparison to previous parameterization schemes. Applying the T-L parameterization, the depth-profiles in the C-content were then analyzed using a virtual interface approximation. For several a-Si 1yx C x :H graded layers having triangular variations in the C-content ˚ thick layers, we found very good agreement between the analyzed depth-profiles and those Ž0 - x- 0.24. over 25]130 A ˚ ., Ž . predicted from z t based on individually-deposited samples. In the depth-profile of the thinnest C-graded layer Ž; 25 A monolayer depth resolution was evident with an average compositional uncertainty of " 0.009. Q 1998 Elsevier Science S.A. Keywords: functions

Amorphous silicon]carbon alloys; Spectroscopic ellipsometry; Graded layers; Parameterization of dielectric

1. Introduction Recently, significant research efforts have been devoted to bandgap-engineered designs in order to realize improved performance of solar cells based on hydrogenated amorphous silicon Ža-Si:H. and its alloys with carbon and germanium w1x. In particular, amorphous silicon]carbon alloys Ža-Si 1y x C x :H. have been used widely as C-graded layers introduced at the pri or irp interfaces in substraterp-i-n or substratern-i-p solar cell configurations, respectively w1]3x. The optimum near-interface bandgap or compositional profiles in these solar cells, however, have U

Corresponding author. Tel.: q1 814 865 3059; fax: q1 814 865 2326; e-mail: [email protected] 0040-6090r98r$19.00 Q 1998 Elsevier Science S.A. All rights reserved PII S0040-6090Ž97.00867-5

yet to be established in part owing to the absence of adequate characterization techniques for the rela˚ . graded layers applied in many tively thin Ž d- 100 A solar cell structures. Real-time ellipsometry during thin film preparation has become a promising technique for obtaining composition depth-profiles of the thin film, and this method has several advantages over conventional post-deposition characterization methods, such as secondary ion mass spectrometry ŽSIMS. and X-ray photoelectron spectroscopy ŽXPS.. The primary advantage is that ellipsometry is non-destructive; another advantage is the potentially higher resolution that results from measuring undisturbed surfaces, since the depth-resolution of the conventional methods are limited by ion beam-induced, near-surface atomic

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mixing. Until recently, however, ellipsometry has suffered from cumbersome data analysis procedures. The standard approach requires analysis of the graded layer in the form of a multilayer with repeated application of the Fresnel equations for discretized layer elements, which induces cumulative errors with increasing graded layer thickness w4x. A virtual interface approximation developed recently provides an excellent solution to the analysis problem for the graded layers w5]7x. This approach enables one to deduce the composition of the top few monolayers of the film Ži.e. the outer layer. without a detailed knowledge of the underlying film structure. The basic premise of this approach relies on the fact that the thickness and dielectric function of the outer layer can be derived from the first derivative of successive pseudo-dielectric functions as long as the thickness of the outer layer is ) 10 2 times smaller than the measurement wavelength. This approach allows one to avoid the problem of cumulative errors noted above and has been applied successfully to the real-time feedback control of the composition profiles ˚ thick Al 1y xGa x As parabolic quantum well in 200-A structures w5x. In previous reports, we have expanded the virtual interface approach, enabling the analysis of amorphous semiconductor films in which a surface roughness layer is now taken into account w8,9x. In the previous studies, the complex dielectric functions of the a-Si 1y x C x :H layers were parameterized using the Forouhi]Bloomer ŽF-B. model w10x, in order to incorporate the C-content x as a free parameter in the virtual interface analysis. This was done solely for mathematical convenience without regard for the physical inconsistencies inherent in the F-B model. Most recently, however, a new physically-consistent parameterization approach called the Tauc]Lorentz ŽT-L. model was derived by Jellison and Modine, which provides improved fitting of amorphous semiconductor dielectric functions over a wide energy region with five free parameters w11,12x. Thus, in this study, we have advanced the analysis procedure applied earlier by incorporating the new parameterization formula. In addition, in order to assess the validity of the overall analysis, large triangular variations in the C-content Ž0 - x- 0.24. within very thin layers ˚ in thickness. were introduced, rather than Ž25]130 A the moderate linear composition profiles Ž0.05- x˚ characterized in the 0.10. over thicknesses of 400 A previous study w9x. 2. Experimental details In the preparation of the C-graded a-Si 1y x C x :H by PECVD, the substrate temperature was 2008C, the r.f. power flux was 130 mWrcm2 , the H 2-dilution gas flow

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ratio wH 2 xrwSiH 4 x q wCH 4 x4 was 5, the partial pressure of the sources gases ŽSiH 4 q CH 4 . was 0.05 Torr and the total gas flow was 30 standard cm3rmin. The use of H 2 dilution led to higher density a-Si 1yx C x :H film structures with relatively smooth surfaces Ž10]20 ˚ surface roughness layer. w13x. The C-content of the A film was controlled simply by varying the source gas flow ratio zs wCH 4 xrwSiH 4 x q wCH 4 x4 from 0.0 to 0.8, corresponding to C-contents x ranging from 0 to 0.23. In order to obtain the dielectric functions of aSi 1y x C x :H films for the parameterization, we first ˚ thick a-Si 1y x C x :H films deposited a series of 2000 A on c-Si wafer substrates for different fixed z values ranging from 0.2 to 0.8. These films were measured by real-time spectroscopic ellipsometry ŽRTSE. using a rotating-polarizer multichannel instrument w14x. The acquisition time for full Ž c , D . spectra from 1.4 to 4.8 eV was 0.8 s and the repetition times ranged from 8 to 120 s. We applied the Ý s Ž t .-minimization procedure to the RTSE data for these films in order to extract the dielectric functions of the a-Si 1y x C x :H bulk layer using a two-layer model: ambientrŽsurfaceroughness.rŽbulk-layer.rsubstrate w15x. The resulting films having uniform C-contents throughout the thickness were analyzed by XPS to determine their compositions x. In the preparation of the undoped C-graded aSi 1y x C x :H layers incorporated at the top of the pure a-Si:H i-layers in the n-i-p solar cells, z was initially increased linearly from 0.2 to 0.8 and then was decreased linearly back to 0.4 Žrather than 0.2., so that the C-content of the graded layer at the irp interface matches the value used for the top a-Si 1y x C x :H p-layer Ž x; 0.05.. In this study, several n-i-p cell structures were fabricated for graded layer thicknesses ranging ˚ by changing the total time for the from 25 to 130 A variation of z Ž t . from 38.0 to 205.0 s. The acquisition times t a for the RTSE measurement of one pair of ellipsometric spectra Ž c , D . were varied from 1.2 to 2.4 s depending on the thickness of the graded layers. In these times, averages over 15 and 30 polarizer rotations were obtained, respectively. During the 1.7 ˚ . and Ž3.2, 1.4 and 3.0 s repetition times t r Ž1.8, 0.8 A ˚ . of Ža-Si 0.98 C 0.02 :H, a-Si 0.76 C 0.24 :H. are deposited, A respectively. The graded layer analysis is performed post-deposition using a virtual interface approximation and a four-medium optical model consisting of Ži. the ambient; Žii. a surface roughness layer; Žiii. an outer layer which contains the most-recently deposited material; and Živ. the pseudo-substrate which contains the past history of the deposition. The surface roughness layer is modeled using the Bruggeman effective medium theory as a 0.5r0.5 volume fraction mixture of the outer-layer material and void. The overall

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analysis approach is based on least-squares regression with the free parameters being the outer-layer composition x, the outer-layer growth rate r and the surface roughness layer thickness d s . These three parameters are determined from three successive ellipsometric spectra over the range from 2.5 to 4.0 eV collected in time periods from 5.1 to 9.0 s. The details of the fitting procedure are described in previous publications w8,9x. 3. Results and discussion 3.1. Parameterization by the Tauc]Lorentz model Fig. 1 shows the dielectric functions for a-Si 1y x C x :H at the substrate temperature of 2008C obtained from RTSE analyses of the films deposited individually at the different fixed z values Ž0.0F zF 0.8.. The C-contents of the films provided in Fig. 1 were determined in the XPS analyses. As the C-content of the films increase, the dielectric function gradually broadens and its amplitude decreases. In order to extract the five photon energy-independent parameters used in the T-L model, each of these dielectric functions were fitted by the T-L expression. In this model, e 2 is expressed as a product of the Tauc equation TŽ E . and the Lorentz oscillator equation LŽ E . which is defined mathematically by

e 2 Ž E . s L Ž E .TŽ E . s =

Ž Ey ET . 2 E2

s 0, EF ET

Fig. 1. Dielectric functions at 2008C for a-Si 1y x C x :H obtained from RTSE analyses of individually-deposited films at different fixed values of the wCH 4 xrwCH 4 x q wSiH 4 x4 flow ratio z Ž0.0F z F 0.8.. The values of the C-content of the films as determined by XPS are also included. The solid lines are the results calculated with the Tauc]Lorentz model using photon energy-independent parameters given by the second-order polynomials in the measured C-content shown in Fig. 2.

AE0 CE 2

Ž E 2 y E02 . q C 2 E 2 , E) ET Ž1.

where A, C, E0 and ET Žall in units of eV. represent the resonance amplitude, broadening parameter, oscillator resonance energy and Tauc optical gap w11,12x. The Tauc formula TŽ E . is based on the assumptions of parabolic densities of conduction and valence band states and a constant momentum transition matrix element w16x. The real part of the dielectric function e 1 is obtained by Kramers]Kronig integration of Eq. Ž1.. This introduces the fifth free parameter e 1Ž`., the constant contribution to e 1Ž E .. The five free parameters of the T-L model w A, C, E0 , ET , e 1Ž`.x can be extracted by least-squares regression fitting of each of the dielectric functions shown in Fig. 1. The best fits are given as the solid lines in Fig. 1 and the resulting three free parameters are plotted as functions of the C-content in Fig. 2. The energy range from 2.2 to 4.2 eV was used in the analyses. In a first five-parameter fitting attempt with the T-L model, the parameters E0 and e 1Ž`. were

found to be independent of x within the confidence limits. Thus, in a second attempt, E0 and e 1Ž`. were fixed at the average values of 3.70 eV and 1.058, respectively, and a three-parameter fit was performed. The solid lines in Fig. 2 are second-order polynomial fits to the deduced parameters and the corresponding polynomial equations are provided in the figures. With the polynomial equations of Fig. 2, the dielectric function of a-Si 1y x C x :H can be calculated for any value of x using the T-L formulas. In order to compare different parameterization approaches, we also fit the dielectric functions of Fig. 1 to the F-B model. We found that the T-L model provides an average ; 20% improvement in the mean-square deviation between the experimental and calculated dielectric functions for the different films in comparison with the F-B model. Further improvements over the T-L model for e 2 Ž E . at lower energies are to be expected by incorporating the assumption of a constant dipole matrix element for the lower energy transitions w17x.

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Fig. 2. Three photon energy-independent parameters w A, C, ET x in the Tauc]Lorentz formula obtained from best fits of the dielectric functions in Fig. 1, plotted as a function of the carbon content determined by XPS. In this parameterization, the oscillator resonance energy E0 and the dielectric constant e 1Ž`. were fixed at 3.70 eV and 1.058, respectively. The solid lines are second-order polynomials given as functions of x in each of the panels.

3.2. Graded layer analysis by the ¨irtual interface approximation Fig. 3 shows the depth profiles in the C-content for ˚. the different graded layer thicknesses Ž ds 25]130 A determined by the virtual interface analysis. In this figure, zero depth is defined as the irp interface and positive values extend into the i-layer of the substratern-i-p solar cell structure. In the virtual interface analysis of graded layers with intended thick˚ fixed surface roughness nesses of 25, 45 and 90 A, ˚ were layer thicknesses d s ranging from 15 to 17 A used for greater stability in determining the instantaneous growth rate in the analysis. The validity of this assumption is based on the fact that no significant variations were observed even when d s was incorporated as a free parameter. For the thickest sample ˚ ., however, d s was varied in this series Ž ds 130 A owing to an observed transient roughness increase near the peak in the C-content. During graded layer

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Fig. 3. Depth profiles in the carbon content for graded a-Si 1y x C x :H layers incorporated at the irp interfaces of substratern-i-p solar cell structures. The depth is measured from the irp interface into the i-layer. The solid lines in each case are the depth-profiles calculated from z Ž t . assuming an ideal flowmeter and instantaneous system response, applying data collected for individually-deposited films.

formation, the results of the RTSE analysis show a reproducibly faster growth rate during the decreasing ramp in z Žnearest the p-layer.. This effect was observed for all structures in Fig. 3, but the effect tended to be enhanced as the total graded layer thickness was decreased. A possible origin of this effect could be the higher transient growth rate of a C-poor alloy Ž x- 0.2. on a C-rich alloy Ž x; 0.24. surface due to a higher sticking coefficient of Si-based precursors on the C-rich surface. The details of the time evolution for the C-content, instantaneous deposition rate and roughness thickness are described in a recent article w18x. The depth-profiles shown in Fig. 3 were obtained by integrating over time the instantaneous growth rate as determined by the virtual interface analysis. The solid lines in Fig. 3 indicate the ideal depth-profiles estimated from the dependence of the composition x on

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flow ratio z for individually-deposited films, assuming that the response of the SiH 4 and CH 4 flowmeters to their control signals was ideal and that the response of the film properties to variations in z was instantaneous. The intended thicknesses of the graded layers in Fig. 3 were Žfrom top to bottom. 25, 45, 90 and 135 ˚ and these values agree quite well with the observed A ˚ The small peak shifts in the thicknesses within " 5 A. measured C-content in comparison with the calculations were caused by the faster growth rate during the second ramp as well as the non-zero residence time of the source gases in the deposition chamber Ž; 5 s.. The effects of the gas residence time in the chamber are most apparent for the thinnest graded structure in ˚ .. For this sample, the depth-profile Fig. 3 Ž ds 24.5 A in the C-content generated during the second ramp deviates significantly from the results calculated for an ideal system and remains near xs 0.16 at the irp interface, rather than dropping to the expected value of xs 0.05. It is surprising that even for the thinnest graded layer a high sensitivity and resolution for the C-content is retained. In this measurement, t r ˚ at is 1.7 s and the depth-resolution is ostensibly 2.5 A the peak in the C-content Ž xs 0.21., suggesting monolayer-level resolution in this analysis. Nevertheless, the role of the surface roughness layer in limiting the depth resolution needs further clarification. 4. Summary We have applied real-time spectroscopic ellipsometry ŽRTSE. to characterize compositionally-graded structures of a-Si 1y x C x :H grown by PECVD in which the alloy composition x is changed from 0.02 to 0.24 and back to 0.05 over thicknesses ranging from 25 to ˚ Such graded layers are obtained through 130 A. continuous variations in the flow ratio z Ž t . s wCH 4 xrwCH 4 x q wSiH 4 x4 . A parameterization of the a-Si 1y x C x :H dielectric functions by the Tauc]Lorentz ŽT-L. model shows distinct improvements over previous parameterization approaches apparently owing to the physical consistency inherent in the T-L model. Further improvements over the T-L model, incorporating the assumption of a constant dipole Žrather than momentum. matrix element over the lower energy range, are expected in the future. Depth-profiles

of the C-graded layers were obtained from an analysis of RTSE data using a virtual interface approach along with the T-L parameterization scheme. In this study, the resulting depth-profiles of the C-content deduced from the RTSE analysis exhibit monolayer-level reso˚ roughness layers. A recent lution in spite of 10]20 A detailed comparison between RTSE and SIMS results beyond the scope of the present study shows that the optical measurement provides a sensitivity and resolution in graded layer analysis far superior to that of conventional sputter-depth profiling methods. These results demonstrate the potential power of RTSE depth-profiling for the optimization of the composition and optical gap variations for high performance amorphous semiconductor devices. References w1x N. Bernhard, G.H. Bauer, W.H. Bloss, Prog. Photovoltaics Res. Appl. 3 Ž1995. 149. w2x K.S. Lim, M. Konagai, K. Takahashi, J. Appl. Phys. 56 Ž1984. 538. w3x R.E.I. Schropp, J.D. Ouwens, M.B. von der Linden, C.H.M. van der Werf, W.F. van der Weg, P.F.A. Alkemade, Mater. Res. Soc. Symp. Proc. 297 Ž1993. 797. w4x F. Hottier, G. Laurence, Appl. Phys. Lett. 38 Ž1981. 863. w5x D.E. Aspnes, W.E. Quinn, M.C. Tamargo, M.A.A. Pudensi, S.A. Schwarz, M.J.S.P. Brasil, R.E. Nahory, S. Gregory, Appl. Phys. Lett. 60 Ž1992. 1244. w6x D.E. Aspnes, J. Opt. Soc. Am. A 10 Ž1993. 974. w7x S.D. Murthy, I. Bhat, B. Johs, S. Pittal, P. He, J. Electron. Mater. 24 Ž1995. 1087. w8x S. Kim, R.W. Collins, Appl. Phys. Lett. 67 Ž1995. 3010. w9x S. Kim, J.S. Burnham, J. Koh, L. Jiao, C.R. Wronski, R.W. Collins, J. Appl. Phys. 80 Ž1996. 2420. w10x A.R. Forouhi, I. Bloomer, Phys. Rev. B 34 Ž1986. 7018. w11x G.E. Jellison, Jr., F.A. Modine, Appl. Phys. Lett. 69 Ž1996. 371. w12x G.E. Jellison, Jr., F.A. Modine, Appl. Phys. Lett. 69 Ž1996. 2137. w13x Y. Lu, I. An, M. Gunes, M. Wakagi, C.R. Wronski, R.W. Collins, Appl. Phys. Lett. 63 Ž1993. 2228. w14x R.W. Collins, Rev. Sci. Instrum. 61 Ž1990. 2029. w15x I. An, Y.M. Li, H.V. Nguyen, C.R. Wronski, R.W. Collins, Appl. Phys. Lett. 59 Ž1991. 2543. w16x R.W. Collins, K. Vedam, Encycl. Appl. Phys. 12 Ž1995. 285. w17x G.D. Cody, in: J.I. Pankove ŽEd.., Semiconductor and Semimetals vol. 21, Academic Press, 1984. w18x H. Fujiwara, J. Koh, C.R. Wronski, R.W. Collins, Appl. Phys. Lett. 70 Ž1997. 2150.