Spectroscopic ellipsometry studies of II-VI semiconductor materials and solar cells

Transcription

1 The University of Toledo The University of Toledo Digital Repository Theses and Dissertations 2010 Spectroscopic ellipsometry studies of II-VI semiconductor materials and solar cells Jie Chen The University of Toledo Follow this and additional works at: Recommended Citation Chen, Jie, "Spectroscopic ellipsometry studies of II-VI semiconductor materials and solar cells" (2010). Theses and Dissertations This Dissertation is brought to you for free and open access by The University of Toledo Digital Repository. It has been accepted for inclusion in Theses and Dissertations by an authorized administrator of The University of Toledo Digital Repository. For more information, please see the repository's About page.

2 A Dissertation entitled Spectroscopic Ellipsometry Studies of II-VI Semiconductor Materials and Solar Cells by Jie Chen Submitted to the Graduate Faculty as partial fulfillment of the requirements for the Doctor of Philosophy Degree in Physics Dr. Robert W. Collins, Committee Chair Dr. Patricia Komuniecki, Dean College of Graduate Studies The University of Toledo December 2010

3 Copyright 2010, Jie Chen This document is copyrighted material. Under copyright law, no parts of this document may be reproduced without the expressed permission of the author.

4 An Abstract of Spectroscopic Ellipsometry Studies of II-VI Semiconductor Materials and Solar Cells by Jie Chen Submitted to the Graduate Faculty as partial fulfillment of the requirements for the Doctor of Philosophy Degree in Physics The University of Toledo December 2010 The multilayer optical structure of thin film polycrystalline II-VI solar cells such as CdTe is of interest because it provides insights into the quantum efficiency as well as the optical losses that limit the short-circuit current. The optical structure may also correlate with preparation conditions, and such correlations may assist in process optimization. A powerful probe of optical structure is real time spectroscopic ellipsometry (SE) that can be performed during the deposition of each layer of the solar cell. In the CdCl 2 post-deposition treatment process used for thin film polycrystalline II-VI solar cells, the optical properties of each layer of the cell change during the process due to annealing as well as to the elevated temperature. In this case, ex-situ SE before and after treatment becomes a reasonable option to determine the optical structure of CdCl 2 -treated CdTe thin film solar cells. CdTe solar cells pose considerable challenges for analysis by ex-situ SE. First, the iii

5 relatively large thickness of the as-deposited CdTe layer leads to considerable surface roughness, and the CdCl 2 post-deposition treatment generates significant additional oxidation and surface inhomogeneity. Thus, ex-situ SE measurements in reflection from the free CdTe surface before and after treatment can be very difficult. Second, SE from the glass side of the cell is adversely affected by the top glass surface which generates a reflection that is incoherent with respect to the reflected beams from the thin film interfaces and consequently depolarization if collected along with these other beams. In this research, the first problem is solved through the use of a succession of Br 2 +methanol treatments that smoothens the CdTe free surface, and the second problem is solved through the use of a 60 prism optically-contacted to the top glass surface that eliminates the top surface reflection. In addition, the succession of a Br 2 +methanol treatment not only smoothens the CdTe surface but also enables CdTe etching in a layer-by-layer fashion. In this way, it has been possible to track the optical properties of the CdTe component layer as a function of depth from the surface toward the CdS/CdTe interface in order to gain a better understanding of the film structure. In this study, ex-situ spectroscopic ellipsometry was applied first to investigate the optical properties of the TEC-15 glass substrate, and then to extract the optical properties of thin film CdTe and CdS both as-deposited and CdCl 2 -treated. After obtaining all the optical properties of the solar cell component layer materials, a comprehensive ex-situ SE analysis has been applied to extract the optical structure of a single thin film of CdCl 2 -treated CdTe, and finally to obtain the optical structure of the CdCl 2 iv

6 post-deposition treated CdTe solar cell. Based on the fundamental studies in this thesis, various aspects of the solar cell structure after the complicated CdCl 2 treatment have been determined. In future work the role of the key parameters of CdCl 2 post-deposition treatment process will be explored including: the temperature and treatment time. As a result, a correlation will be established between solar cell performance and film structure. Finally, an understanding of how solar cell structure can be optimized to achieve the highest solar cell performance may be possible through improved control of the CdCl 2 post-treatment process. v

7 Table of Contents Abstract Table of Contents List of Tables List of Figures iii vi ix xii 1 Introduction to Spectroscopic Ellipsometry History Purpose Data measured by ellipsometry Mathematical derivation Spectroscopic ellipsometer used in the study Data analysis 12 2 Introduction to CdTe-based Solar Cells CdTe-based solar cell structures Deposition method and process steps Application of spectroscopic ellipsometry as an analysis technique Optical Properties of TEC-15 Glass Introduction..26 vi

8 3.2 Experimental details Data analysis and results Verification of the Chemical Etching Process for CdTe Depth Profiling Introduction Structural evolution of CdTe during etching: experimental details Structural evolution of CdTe during etching: results and analysis Detection of a-te on etched CdTe: experiment details Detection of a-te on etched CdTe: results and analysis Optical Properties of Thin Film CdTe and CdS before and after CdCl 2 Post-deposition Treatment Introduction Optical properties of as-deposited CdTe and CdS films deposited on c-si substrates Optical properties of CdCl 2 post-deposition treated CdTe and CdS Etch-back profiling of CdTe thin film structure after post-deposition treatments Optical Structure of As-deposited and CdCl 2 -treated CdTe Superstrate Solar Cells Introduction Experimental details Results and discussion: film side and prism side measurements vii

9 6.4 Results and discussion: through the glass measurements Summary RTSE Analysis of CdTe Solar Cell Structures in the Substrate Configuration Introduction Analysis of CdTe deposition on rough molybdenum Ex situ spectroscopic ellipsometry analysis of a CdTe solar cell in the substrate configuration Spectroscopic Ellipsometry Studies of II-VI Alloy Films Introduction Top cell material candidates: Cd 1-x Mn x Te and Cd 1-x Mg x Te Bottom cell material: Cd 1-x Hg x Te Summary and Future Directions Summary Future directions 183 References 196 Appendix A Dielectric functions 207 viii

10 List of Tables 4.1 Best fit parameters and confidence limits that define Eqs. (4.1) and (4.2) for the dielectric function of a-te Fitting results for single crystal and thin film polycrystalline CdTe using an analytical model consisting of four critical points and one T-L background oscillator Fitting results for single crystal and thin film polycrystalline CdS using an analytical model consisting of three critical points and one T-L background oscillator Best fit dielectric function parameters comparing single crystal, CdCl 2 -treated, and as-deposited CdTe samples Best fit dielectric function parameters for as-deposited CdS on a fused silica prism, CdCl 2 -treated CdS on the prism, and. as-deposited CdS on c-si ix

11 6.1 Dielectric function library used in spectroscopic ellipsometry data analyses for CdTe solar cells Best fitting parameters added step by step to improve the mean square error (MSE) in modeling through-the-glass SE measurements of a CdTe solar cell Multilayer stack thicknesses, non-uniformity, and compositions, the latter expressed in terms of volume fractions, along with parameter confidence limits for the best fit to SE data obtained through the glass CdTe bulk and surface roughness layer thicknesses for the top four CdTe bulk layers Five models used to evaluate the Mo overlayer thickness using reference dielectric functions from the literature Best fit critical point and Tauc-Lorentz oscillator parameters describing the inverted dielectric function of polycrystalline ZnTe:Cu. The exponents µ n are fixed at the single crystal values of Table x

12 7.4 Best fit critical point and Tauc-Lorentz oscillator parameters for single crystal ZnTe Best fitting parameters added step by step to improve the standard mean square error (MSE) in the ellipsometric analysis of a CdTe solar cell in the substrate configuration Deposition parameters used to prepare the Cd x Mg 1-x Te and Cd x Hg 1-x Te thin films Critical point parameters of transition energy and width obtained in the fits to the dielectric functions of Fig Critical point energies and E 0 broadening parameters for two as-deposited Cd 1-x Mg x Te alloys from spectroscopic ellipsometry. Also shown are corresponding results for as-deposited and CdCl 2 -treated CdTe Energy position and width of the critical point generating the strongest peak in ε 2 for as-deposited thin film Cd 1-x Hg x Te xi

13 List of Figures r r E(, t) 1-1 Schematic representation of the electric field vector trajectory 0 for an elliptically polarized light wave at a fixed position r 0 versus time. Q is the tilt angle between the ellipse major axis a and the p-axis, measured in counterclockwise-positive sense when facing the light source. χ is the ellipticity angle given by tan -1 (b/a) Reflection of a polarized light wave at an interface between two media Spectroscopic ellipsometer used in this research mounted in the ex-situ mode of operation Simplified flow chart of the data analysis procedure Optical model and physical structure of a c-si wafer used as a substrate The substrate structure for CdTe solar cells..19 xii

14 2-2 The superstrate structure for CdTe solar cells The multilayer structure of the TEC-15 glass substrate Simple model deduced from the analysis of the transmittance and ellipsometric (ψ, ) spectra of Figs for the soda lime glass substrate. The surface roughness is obtained in a best fit of the (ψ, ) spectra Best fit simulated and experimental normal incidence transmittance spectra T vs. photon energy for an uncoated soda lime glass substrate used in the fabrication of TEC glasses Best fit simulated and experimental ellipsometric angle ψ = tan 1 ( r p /r s ) vs. photon energy for an uncoated soda lime glass substrate used in the fabrication of TEC glasses. The angle of incidence is Best fit simulated and experimental ellipsometric angle = δ p δ s vs. photon energy for an uncoated soda lime glass substrate used in the fabrication of TEC glasses. The angle of incidence is Index of refraction (left) and extinction coefficient (right) vs. wavelength for the xiii

15 uncoated soda lime glass substrate. The index of refraction results are derived from the ellipsometric ψ spectrum whereas the extinction coefficient results are derived from the transmittance spectrum. The data values are tabulated in Appendix A Model with best fitting parameters obtained in the analysis of the transmittance and ellipsometric (ψ, ) spectra of Figs. 3.8 and 3.9 for the soda lime glass substrate coated with a single layer of undoped SnO Normal incidence transmittance T vs. photon energy for a soda lime glass substrate coated with a single layer of undoped SnO 2, the first layer in the fabrication of TEC glasses. Experimental data (broken line) and a best fit simulation (solid line) are shown Ellipsometric angles ψ and vs. photon energy for a soda lime glass substrate coated with a single layer of undoped SnO 2. Experimental data (broken lines) and best fit simulations (solid lines) for an angle of incidence of 60 are shown (a,b) Real and imaginary parts of the dielectric function ε 1 and ε 2 vs. photon energy for undoped SnO 2 that forms the first layer of TEC glasses; (c) analytical expression xiv

16 for the complex dielectric function of (a,b) along with the best-fit free parameters and their confidence limits Model adopted for the analysis of the transmittance and ellipsometric (ψ, ) spectra of Figs and 3.13 obtained on the soda lime glass substrate coated with a single layer of SiO Normal incidence transmittance T vs. photon energy for a soda lime glass substrate coated with a single layer of SiO 2, which is used as the second layer in the fabrication of TEC glasses; experimental data (broken line) and a best fit simulation (solid line) are shown Ellipsometric angles ψ and vs. photon energy for a soda lime glass substrate coated with a single layer of SiO 2, which is used as the second layer in the fabrication of TEC glasses; experimental data (broken lines) and a best fit simulation (solid lines) are shown (a) Real (solid line) and imaginary (broken line) parts of the dielectric function ε vs. photon energy for SiO 2 that forms the second layer of the TEC glasses. The imaginary part of the dielectric function vanishes; (b) mathematical expression for the dielectric function in (a) along with the best fitting parameters and their xv

17 confidence limits Real and imaginary parts of the dielectric function ε vs. photon energy for the SiO 2 that forms the second layer of the TEC glasses (solid lines) for comparison with the reference data of a thermally-grown SiO 2 on crystalline silicon Best fit sample structure for a soda lime glass substrate coated with a two layer stack of undoped SnO 2 and SiO 2, which are the first two layers used in the fabrication of TEC glasses Ellipsometric angles (ψ, ) at an angle of incidence of 60 and transmittance T at normal incidence plotted versus photon energy for a soda lime glass substrate coated with a two layer stack of undoped SnO 2 and SiO 2, which are the first two layers used in the fabrication of TEC glasses Best fit multilayer stack for a complete TEC-15 glass sample. The layered structure includes thin undoped SnO 2, thin SiO 2, and thick doped SnO 2 :F with surface roughness on top. The previously-determined dielectric functions were used for the soda lime glass and the two thin layers. 43 xvi

18 3-19 Normal incidence transmittance T vs. photon energy for a complete TEC-15 glass sample consisting of a soda lime glass substrate coated with layers of undoped SnO 2, SiO 2, and top-most doped SnO 2 :F. Experimental data (broken line) and a best fit simulation (solid line) are shown Ellipsometric angles ψ and at a 60 angle of incidence plotted vs. photon energy for a complete TEC-15 glass sample consisting of a soda lime glass substrate coated with layers of undoped SnO 2, SiO 2, and top-most doped SnO 2 :F. The broken lines indicate experimental spectra and the solid lines indicate the best fit simulation Real and imaginary parts of the dielectric function ε 1 and ε 2 vs. photon energy for doped SnO 2 :F that forms the top-most layer of TEC-15 glass. These results are obtained as a best fit analytical expression at low energies where the film is semitransparent and by an inversion of (ψ, ) data at high energies where the film is opaque (a) The analytical equation for the dielectric function of the top-most SnO 2 :F layer of TEC-15 that holds below 4.4 ev; also shown is (b) a table of the best fit parameters in the equation and their confidence limits Multilayer structure with best-fit parameters for a complete TEC-7 glass sample. xvii

19 The layered structure includes thin undoped SnO 2, thin SiO 2, and a thick layer of doped SnO 2 :F with surface roughness on top. The previously determined dielectric functions for TEC-15 glass were used here for this TEC-7 glass sample Multilayer structure with best-fit parameters for a complete TEC-8 glass sample. The layered structure includes thin undoped SnO 2, thin SiO 2, and a thick layer of doped SnO 2 :F with surface roughness on top. The previously determined dielectric functions for TEC-15 glass were used here for this TEC-8 glass sample Transmittance T vs. photon energy for a complete TEC-7 glass sample; experimental data (broken line) and simulated results based on the ellipsometric model (solid line) are shown (left). The difference between the two data sets is shown at the right Normal incidence transmittance T vs. photon energy for a complete TEC-8 glass sample; experimental data (broken line) and simulated results based on the ellipsometric model (solid line) are shown (left). The difference between the two data sets is shown at the right xviii

20 3-27 For TEC-7 glass, the normal incidence scattering results predicted by combining ellipsometry and normal incidence specular transmittance are shown in comparison with experimental normal incidence integrated scattering data from a diffuse transmission experiment. Different TEC-7 samples were used for the two different data sets For TEC-8 glass, the normal incidence scattering results predicted by combining ellipsometry and normal incidence specular transmittance are shown in comparison with experimental normal incidence integrated scattering data from a diffuse transmission experiment. Different TEC-8 samples were used for the two different data sets A schematic of optical models used to evaluate a CdTe film by optical depth profiling during both deposition and etching processes The evolution of void volume fraction within the top 100 Å of the bulk layer as a function of CdTe bulk layer thickness obtained during the deposition and etching processes Schematic of the sample structural changes that occur in the last three etching steps for a CdTe film on c-si. The starting thickness of this CdTe film is 3500 Å. xix

21 Ellipsometric spectra for a smoothened CdTe film on a c-si wafer measured at angle of incidence of 63. The broken lines represent data measured before the first additional Br 2 +methanol etching step, and the solid lines represent data measured after the 6 th additional Br 2 +methanol etching step. The total etching time between the two is 18 seconds. The starting CdTe thickness before any etching was 3 µm Ellipsometric spectra for a CdTe thin film on a crystalline Si substrate after the 36 th and 37 th etch steps for comparison. The starting CdTe film thickness was 3500 Å Ellipsometric spectra for a CdTe thin film on a crystalline Si substrate with a starting thickness of 3500 Å measured after the 37 th (left) and 36 th (right) etching steps (data points). Also shown are their best fits (broken lines) Model and best-fit parameters used for the analysis of the ellipsometric spectra of Fig. 4.6 (left panel) collected after the 37 th etching step applied to a CdTe film on a crystalline Si substrate. Because the CdTe film is completely removed, this xx

22 analysis provides the structure of the c-si substrate. MSE indicates the mean square error in the fit Model and best fit parameters used for the analysis of the ellipsometric spectra of Fig. 4.6 (right panel) collected after the 37 th etching step applied to a CdTe film on a crystalline Si substrate. This analysis yields the structure of the a-te layer on the c-si substrate. The void volume fraction in the a-te layer has been obtained by expressing the a-te layer in this study of polycrystalline CdTe as a mixture of the a-te obtained in a previous study of single crystal CdTe along with a void component Real and Imaginary parts of the dielectric function ε 1 and ε 2 vs. photon energy for a-te generated through Br 2 +methanol etching of a polycrystalline CdTe film A comparison of the a-te optical properties deduced in this study (see Fig. 4.9) with the literature reference optical properties of a-te from 1.5~6 ev, the latter obtained by etching single crystal CdTe Ellipsometric spectra for a CdTe thin film on a crystalline Si substrate with a starting thickness of 3500 Å measured after the 35 th etch step (left panel). Also shown is xxi

23 the best fit and associated model deduced in the analysis of the ellipsometric spectra in order to extract the a-te/cdte/c-si structural parameters (right panel) Experimental and best fit spectra (left panel) along with the best fit parameters and model (right panel) for comparison with the results of Fig. 4.11, but without introducing an a-te component into the model. Such a model leads to a higher MSE Ellipsometric spectra and the best fit (left panel) for a smoothened CdTe film with a starting thickness of 3 µm obtained before the first additional etch after smoothening. Also shown is the model and best fit parameters used in the analysis of the ellipsometric spectra over the energy range of 2 to 6 ev in order to deduce the a-te volume fraction in the surface roughness layer (right panel) Experimental and best fit spectra (left panel) along with the best fit model and parameters (right panel) for comparison with the results of Fig. 4.13, but without introducing an a-te component into the model. This ellipsometric analysis is associated with a 3 µm thick smoothened CdTe film before the first additional etch after smoothening..69 xxii

24 4-15 Ellipsometric spectra and the best fit (left panel) for a smoothened CdTe film with a starting thickness of 3 µm obtained after the 6 th additional etch after smoothening. Also shown is the model and best fit parameters used in the analysis of the ellipsometric spectra over the energy range of 2 to 6 ev in order to deduce the surface roughness thickness and the a-te volume fraction in the CdTe structure (right panel) Experimental and best fit spectra (left panel) along with the best fit model and parameters (right panel) for comparison with the results of Fig but without introducing an a-te component into the model. This ellipsometric analysis is associated with a 3 µm thick smoothened CdTe film after the 6 th additional etch The room temperature dielectric functions of single crystal CdTe (broken lines) and a CdTe film deposited at 188 C (solid lines). The downward arrows point to the energy values of the four critical point transitions E 0, E 1, E 1 + 1, and E Band structure of CdTe xxiii

25 5-3 The room temperature ordinary dielectric functions of single crystal (wurtzite) CdS (broken lines) in comparison with the polycrystalline thin film CdS deposited on c-si at 225 C (solid line). The three downward arrows point to the energy values of the critical point transitions (left) Best fit analytical models of the room temperature dielectric functions for two CdTe films of thickness approximately 1000 Å, obtained from the same deposition but with different post-deposition processing: as-deposited (no treatments; broken line) and CdCl 2 -treated for 5 min at 387 C (solid line); (right) a comparison between the CdCl 2 -treated CdTe film (solid line) and single crystal CdTe (broken line) A schematic of the sputtering chamber for CdTe/CdS deposition on a fused silica prism (left) Best fit analytical models for the room temperature dielectric functions of a CdS film as-deposited on a fused silica prism measured from the prism side and on a c-si wafer measured from the ambient side; (right) best fit analytical model for the room temperature dielectric functions of CdS measured from the prism side before and after a 30 min CdCl 2 treatment at 387 C xxiv

26 5-7 Resonance energies E n (upper panel) and linewidths Γ n (lower panel) for the critical point transitions in single crystal CdTe (broken lines) and in d b ~ 1000 Å thick CdTe films sputter-deposited at different temperatures (points), all measured at 15 C Critical point energies (upper panel) and widths (lower panel) as functions of CdTe bulk layer thickness during etching by Br 2 +methanol for co-deposited CdTe films processed in three different ways: (i) as-deposited, (ii) annealed in Ar for 30 min, and (iii) CdCl 2 treated for 5 min. The deviations at low thickness are due to the onset of semi-transparency at the E 1 critical point energy Relative void volume fractions as functions of CdTe bulk layer thickness during etching by Br 2 +methanol for co-deposited CdTe films processed in three different ways: (i) as-deposited, (ii) thermally annealed in Ar for 30 min, and (iii) CdCl 2 -treated for 5 min. For the as-deposited and annealed films, the void fraction is scaled relative to the observed highest density film. For the CdCl 2 -treated film, the void volume fraction is scaled relative to single crystal CdTe Energy of the E 1 transition (upper panel) and its width Γ E1 (lower panel) as functions of CdTe bulk layer thickness in successive Br 2 +methanol etching steps for xxv

27 ~3000 Å thick CdTe films. The two films were processed under identical conditions including fabrication on c-si wafer substrates and annealing in Ar at 387 C for 30 minutes. The data for experiment #1 are the same as those depicted in Fig Energy of the E 1 transition (upper panel) and its width Γ E1 (lower panel) as functions of CdTe bulk layer thickness in successive Br 2 -methanol etching steps for ~3000 Å thick CdTe films. The two films were processed under similar conditions including fabrication on c-si wafer substrates and CdCl 2 treatment for 5 minutes. The data for experiment #1 are the same as those depicted in Fig Void volume fraction as a function of CdTe bulk layer thickness in successive Br 2 -methanol etching steps for ~3000 Å thick CdTe films in a second experiment for comparison with the results in Fig Two different post-deposition processing procedures were used: (i) an anneal in Ar for 30 min, and (ii) a CdCl 2 -treatment for 5 min. For the Ar annealed films, the void fraction is scaled relative to the depth at which the highest density is observed. For the CdCl 2 -treated film, the void volume fraction is scaled relative to single crystal CdTe. The void structure for the film annealed in Ar is attributed to structure in the as-deposited film (as in Fig. 5.8). In contrast, the void structure for the CdCl 2 treated film is associated with extensive xxvi

28 near-surface roughness Evolution of the surface roughness thickness and a depth profile of the void volume fraction plotted versus bulk layer thickness obtained in successive Br 2 +methanol etching steps that reduce the bulk layer thickness of an as-deposited CdTe component of a solar cell (a, left) Evolution of the surface roughness thickness and a depth profile of the void volume fraction plotted versus bulk layer thickness obtained in successive Br 2 +methanol etching steps that reduce the bulk layer thickness of the CdCl 2 -treated CdTe component of a solar cell; (b, right) a schematic structure suggested from (a) (left) Depth profiles of the critical point energies of the E 1, E and E 2 transitions in the as-deposited CdTe layer of a solar cell, plotted versus bulk layer thickness obtained in successive Br 2 +methanol etching steps that reduce the bulk thickness; (right) depth profiles of the linewidths of the E 1, E and E 2 transitions obtained in the same experiment (a, top left) Depth profiles of the critical point energies of the E 1, E and E 2 transitions in the CdCl 2 -treated CdTe layer of a solar cell, plotted versus the bulk xxvii

29 layer thickness obtained in successive Br 2 +methanol etching steps that reduce the bulk thickness; (b, top right) depth profiles of the linewidths of the E 1, E and E 2 transitions obtained in the same experiment; (c, bottom) a schematic structure suggested from (b) Energies of the E 1, E 1 + 1, and E 2 transitions as functions of CdTe bulk layer thickness in successive etches of a CdCl 2 treated CdTe solar cell that reach within 0.1 µm of the CdS/CdTe interface Broadening parameters Γ E1, Γ E1+ 1, and Γ E2 as functions of CdTe bulk layer thickness in successive etches of a CdCl 2 treated CdTe solar cell that reach within 0.1 µm of the CdS/CdTe interface Experimental pseudo-dielectric function spectra for the CdTe solar cell of Figs. 6.2 and 6.4 after the 15 th etching step; also shown is the best fit using the structural model of Fig Structural model for the CdTe solar cell after the 15 th etch step that provides the best fit in Fig Ex situ SE spectra in (ψ, ) (symbols) (a) from the free CdTe surface after 8 xxviii

30 Br 2 +methanol etching steps and (b) from the prism/glass side without etching. The best fit results (solid lines) yield the structural parameters in Figs and 6.11, including the thicknesses of the CdTe roughness, CdTe bulk, CdTe/CdS interface, and CdS bulk layers, as well as the volume fractions of CdS/CdTe in the interface layer and void in the CdS bulk layer The best fit results from the free CdTe surface after 8 Br 2 +methanol etching steps yielding the thicknesses of the CdTe roughness, CdTe bulk, CdTe/CdS interface, and CdS bulk layers, as well as the volume fractions of CdS/CdTe in the interface layer and void in the CdS bulk layer The best fit results from the prism/glass side without etching yielding the thicknesses of the CdTe roughness, CdTe bulk, CdTe/CdS interface, and CdS bulk layers, as well as the volume fractions of CdS/CdTe in the interface layer and void in the CdS layer CdS and CdTe/CdS interface layer thicknesses deduced from spectra collected through the prism/glass (solid line) and from spectra collected from the CdTe surface in successive etches (points, dotted line extrema) Multilayer stack used to model the thicknesses and compositions of the individual xxix

31 layers of the CdTe solar cell. The SE beam enters through the glass, and the reflection from the top surface is blocked since it is incoherent with respect to the reflection from the glass/film interface Step-by-step MSE reduction by adding one fitting parameter at a time. Starting with the CdTe thickness as a variable, each additional parameter was subsequently fitted. It was found that fitting the SnO 2 :F thickness provided the greatest improvement in MSE among all 2-parameter attempts. Similar methodology was used for all 12 parameters. Circular points indicate the best n-parameter fit with n given at the top and the added parameter given in Table Ellipsometric spectra (points) in ψ (top) and (bottom) at an angle of incidence of 60 as measured through the glass at a single point on a 3 x 3 cm 2 CdTe solar cell sample. The solar cell was treated with CdCl 2 but no back contact processing was performed. Also shown is a best fit (lines) using the model structure of Fig with the parameters listed in Table Time evolution of (ψ, ) at 5 photon energies selected from 706-point spectra acquired during sputter deposition of CdTe on a Mo coated glass slide. The full spectral acquisition time was 2 s and the angle of incidence was xxx

32 7-2 Flow chart of the three-iteration <MSE> minimization procedure for CdTe film growth on a rough Mo film substrate The schematic structure describing the final optical model for deposition on rough Mo The schematic structures describing the interface filling (left) and bulk layer growth (right) models for the first interface layer (Left) MSE, which is a measure of the quality of the fit to RTSE data, for the complete CdTe deposition using optical models for the CdTe film consisting of one bulk layer (broken line) and four bulk layers (solid line). In both cases a one-layer model for surface roughness was employed; (right) the MSE for the model with four bulk layers is shown on an expanded scale Evolution of the surface roughness thickness versus deposition time determined using a four-layer model for CdTe film growth on rough Mo. The spikes in the surface roughness thickness result from the consideration of each bulk layer individually with an independent surface roughness layer. In this case, the surface roughness layer on the underlying layer is instantaneously transformed into an interface layer at the vertical broken lines upon initial growth of the overlying layer, whose roughness layer starts from zero thickness xxxi

33 7-7 Time evolution of the CdTe overlayer volume percent during interface filling of the underlying CdTe roughness layer for CdTe growth on Mo (Left) Evolution of the individual bulk layer thicknesses versus deposition time determined using a four-layer model for CdTe film growth on Mo; (right) evolution of effective thickness of CdTe, including all bulk, interface, and surface layer components Mo dielectric function at a nominal temperature of 200 C acquired by inversion assuming a Mo substrate roughness thickness of 79.6 Å (solid line). For the overlying CdTe, four bulk layers and a roughness layer are used to describe the best fit model. For the first bulk layer, the Mo/CdTe interface roughness, the CdTe bulk, and CdTe surface roughness layer thicknesses d i, d b, d s, respectively, are determined in a dynamic analysis, in which case the criterion is the minimum average MSE. The Mo/CdTe interface roughness thickness d i is taken to be the same as the Mo substrate film roughness thickness. Also shown is the Mo dielectric function at room temperature before heating to the deposition temperature as determined by inversion, again assuming a Mo surface roughness layer thickness of 79.6 Å (broken line) Real (top panel) and imaginary (bottom panel) parts of the dielectric functions of the xxxii

34 four layers [(a)-(d)] of a CdTe thin film deposited on rough Mo. These results are determined from inversion, after determining the CdTe roughness and bulk layer thicknesses through minimization of the average MSE obtained throughout the layer analysis; (e) also shown is a comparison of the first layer dielectric function of CdTe deduced in this study with that of CdTe deposited on a smooth c-si substrate at a nominal temperature of 200 C. In (b)-(d) comparisons are provided between the dielectric function of a given layer and that of the layer underneath it Comparison of the surface roughness thickness at the end of the deposition for a Å thick CdTe film on Mo as deduced by RTSE with the relative surface height distribution and rms roughness from AFM A comparison of measured pseudo-dielectric functions (solid lines) for Mo thin films deposited by sputtering (a) on glass and (b) on Kapton. Also shown are the fits (broken lines) using a reference dielectric function for dense Mo determined separately, and the multilayer models depicted in the insets Ellipsometric spectra (solid lines) and best fit (broken lines) using the structural model and best fit parameters shown in the inset. The dielectric function is determined simultaneously using a model assuming a sum of critical point structures. xxxiii

35 The resulting dielectric function is shown in Fig Dielectric function of thin film ZnTe:Cu prepared by magnetron sputtering with 1 wt.% Cu in the ZnTe target (solid lines). A model consisting of four critical points in the band structure has been used in this analysis. The data points are literature results for single crystal ZnTe Step-by-step MSE reduction by adding one fitting parameter at a time. Starting with the CdTe thickness as a variable, each additional parameter was subsequently fitted. It was found that fitting the CdS thickness provided the greatest improvement in MSE among all 2-parameter attempts. Similar methodology was used for all 14 parameters. Circles connected by the solid line indicate the best n-parameter fit with n given at the top and the added parameter given in Table Ellipsometric spectra for a CdTe solar cell deposited on Mo in the substrate configuration (points). The cell was exposed to a CdCl 2 treatment before this measurement. The top contact of the solar cell is not incorporated over the area probed, leading to the structure: ambient/cds/cdte/znte:cu/mo. The solid line depicts the optical model shown in Fig Optical model for a CdTe solar cell in the substrate configuration (excluding the top xxxiv

36 contact) deposited on a Mo film surface. This model and the best fit parameters provide the solid line results in Fig Current-voltage and normalized quantum efficiency spectra for a champion 16.5% efficient CdTe/CdS thin-film solar cell Two-terminal tandem cell based on Cd 1-x Mg x Te and Cd 1-x Hg x Te absorbers Real (a) and imaginary (b) parts of the pseudo-dielectric functions of RF sputtered CdTe (E g = 1.50 ev), Cd 1-x Mn x Te (E g = 1.63 ev) and Cd 1-x Mg x Te (E g = 1.61 ev) films all in the as-deposited state; (c) Pseudo-dielectric function of as deposited Cd 1-x Mn x Te samples after different storage times in laboratory ambient: (1) immediately after Br 2 /methanol etch; (2) 3 weeks after deposition; and (3) 1.5 years after deposition Best fit (lines) to the second derivative of the experimental pseudo-dielectric function (points) for the as-deposited Cd 1 x Mn x Te film of Fig. 8.3 (c: immediately after etch). The three CP transitions, E 1, E 1 + 1, and E 2, are indicated by arrows with best fit energies of 3.352, 3.884, and ev, respectively. The composition of x=0.06 can be estimated by the empirical relationship between E 1, the strongest CP in this xxxv

37 case, and the composition Variation of the pseudo-dielectric function of as deposited Cd 0.94 Mn 0.06 Te with time after Br 2 /methanol etching, measured in situ at room temperature during exposure to laboratory ambient Pseudo-dielectric functions of as-deposited and one-step and two-step CdCl 2 treated Cd 0.94 Mn 0.06 Te samples Index of refraction and extinction coefficient of amorphous TeO Pseudo-dielectric functions of as-deposited and CdCl 2 treated Cd 1-x Mg x Te samples Approximate dielectric functions, i.e., optical properties deduced with a best attempt to eliminate surface effects, for as-deposited films and CdCl 2 -treated films obtained by SE after Br 2 +methanol etching that improves the surface quality (points); (a) CdTe; (b) Cd 1-x Mn x Te; (c) Cd 1-x Mg x Te; the solid lines show the results of fits to extract critical point energies and widths. The result for the CdCl 2 -treated Cd 1-x Mn x Te could not be fit with a critical point parabolic band model xxxvi

38 8-10 Pseudo-dielectric function obtained directly from experimental (ψ, ) data using a single interface conversion formula for a Cd 1-x Mg x Te sample prepared from a target of CdTe (80 wt.%) + MgTe (20 wt.%) (CGT42). The solid line describes experimental data and the dashed line describes the best fit result. The deduced bulk and surface roughness layer thicknesses are shown Best fit analytical dielectric function obtained from an analysis of the experimental (ψ, ) data for the Cd 1-x Mg x Te sample of Fig prepared from a target of CdTe (80 wt.%) + MgTe (20 wt.%) (CGT42) Pseudo-dielectric function obtained directly from experimental (ψ, ) data using a single interface conversion formula for a Cd 1-x Mg x Te sample prepared from a target of CdTe (60 wt.%) + MgTe (40 wt.%) (CGT92). The solid line describes experimental data and the dashed line describes the best fit result. The deduced bulk and surface roughness layer thicknesses are shown Best fit analytical dielectric function obtained from an analysis of the experimental (ψ, ) data for the Cd 1-x Mg x Te sample of Fig prepared from a target of CdTe (60 wt.%) + MgTe (40 wt.%) (CGT92) xxxvii

39 8-14 Band gap of as-deposited thin film Cd 1-x Hg x Te as a function of the substrate temperatures over the range from 23 C to 153 C Dielectric functions from mathematical inversion and from the corresponding analytical model fit for as-deposited Cd 1-x Hg x Te films prepared with different substrate temperatures Comparison of the real (left) and imaginary (right) parts of the pseudo-dielectric function of as-deposited and CdCl 2 treated Cd x Hg 1-x Te films, including results (a) before and (b) after a single Br 2 /methanol etching step..177 xxxviii

40 Chapter One Introduction to Spectroscopic Ellipsometry 1.1 History The very first ellipsometric studies were performed by Professor Paul Drude (1863~ 1906), even though the term ellipsometry was not used at that time [1-1]. Drude was the first to derive the equations of ellipsometry, and was also the first to perform experimental studies on both absorbing and transparent solids. The optical properties determined in these ellipsometry studies were found to be quite accurate. In fact, when Palik compared Drude s results with those obtained 100 years later, the results were amazingly close [1-2]. Because of the absence of fast computation methods made possible by the modern computer, Drude obtained the optical properties of solids at only a few selected wavelengths [1-1]. After Paul Drude s tremendous impact on ellipsometry development, very little progress was reported in the succeeding 70 years. One exception was a 1945 article authored by Alexandre Rothen who described the half-shade method to detect the polarization state change of light upon reflection from a specular surface, and coined the term ellipsometry [1-3]. When laboratory computers became prevalent in the 1960s and 1

41 1970s, automated ellipsometers for diverse purposes were developed [1-4]. Among the different types of automated ellipsometers developed at that time, two major types are still widely used in the spectroscopic mode of operation: (i) the rotating element ellipsometer [1-5], and (ii) the phase modulation (PM) ellipsometer [1-6]. The photon energy range of spectroscopic ellipsometry has increased significantly over the years since D. E. Aspnes and A. A. Studna developed the first rotating analyzer spectroscopic ellipsometer covering the full (near-infrared)-to-(near-ultraviolet) range [1-7]. At the same time, the instrument development focus was also placed on increasing the speed of full spectroscopic measurement by incorporating a multichannel detection system in the ellipsometer in order to acquire the entire spectral range essentially simultaneously [1-8]. As a result of this effort, the technique of real time spectroscopic ellipsometry (RTSE) arose for analysis of thin film growth and materials processing. 1.2 Purpose Spectroscopic ellipsometry is used to obtain the optical properties of materials of interest in optical and electronic applications [1-9]. Once optical properties of materials are available, thin film thicknesses can be measured using optical models for single thin film and multilayer samples. Advanced data analysis often enables measurement of thickness and optical properties simultaneously [1-10, 1-11]. The measurable thickness range for ellipsometry varies from submonolayer to several microns. For spectroscopic ellipsometry measurements of thickness, a wide spectral range is important since the light must penetrate through the thin film, reflect from an underlying interface, return through 2

42 the film, and proceed to the detector. In studies of semiconductors, lower energy gap materials such as CuInSe 2 can be analyzed for thickness when the spectral range extends deeper into the infrared. For energies below the semiconductor band gap, the light remains unabsorbed and reflects from the bottom interface of the film, enabling wave superposition and phase shifts that allow thickness to be determined. This demonstrates the advantage of spectroscopic ellipsometers with an extended near-ir spectral range, even below the 1.1 ev band gap of the most common Si diode detectors used in ellipsometers. A similar advantage exists for spectroscopic ellipsometers with an extended ultraviolet spectral range when characterizing the thickness of metal thin films. In addition to thickness, other properties of a film can be determined through ellipsometric measurements performed in real time during the deposition process [1-12]. These include roughness thickness on the surface of the film and the optical properties of the film. From the latter, the film density deficit (represented by a volume fraction of voids in the layer), film crystalline quality (represented by a defect density or average grain size), alloy composition, and temperature may be determined. In fact, real time measurements may also provide a depth profile of the film structure and properties, and even area uniformity of the film. 1.3 Data measured by ellipsometry An ellipsometric measurement provides the angles (ψ, ), corresponding to the relative amplitude ratio (tanψ) and phase shift difference ( ) between the complex 3

43 amplitude reflection coefficients for E r p and E r s, the orthogonal linear electric field components of a polarized light wave [1-13]. These electric field components are parallel ( p E r ) and perpendicular ( E r ) to the plane of incidence. (The overline arrow denotes a s complex vector in which case each vector component has a real amplitude and phase.) The nature of E r p and E r s for a light wave will be further elucidated in the next section. Thus, the quantity measured by ellipsometry is the ratio ρ% of the complex amplitude reflection coefficients for the p-polarized field component ( R % ) to that for the s-polarized field component ( R % ): where s R% p i ρ% = = tanψ e ; (1-1) R% s ref E% p R% p = = R% inc p exp( iδ p ), (1-2) E% p ref E% s R% s = = R% inc s exp( iδ s ). (1-3) E% s p Here, the notational style of these equations will be summarized. Generally, the subscripts p and s identify the wave characteristics for vector components parallel and perpendicular to the plane of incidence, respectively. For example, δ p and δ s represent the phase shifts of each orthogonal electric field component upon reflection. On the other hand E % p( s) denotes the p (s) orthogonal component of the electric field amplitude. The superscripts ref and inc in Eqs. (1-2) and (1-3) refer to the electric field components of the reflected and incident light waves. 4

44 As a result, the angles ψ and are defined by: R% p tan ψ =, (1-4) R% p s = δ δ. (1-5) s R % p( s) are also called the complex Fresnel coefficients. As a complex variable, p( s) R % provides information on the amplitude change and phase shift of the p (s) field components of the wave upon its reflection from the sample. In fact, the complex Fresnel coefficients provide the reflected-to-incident amplitude ratio and the reflected-minus-incident phase shift for each orthogonal electric field component E r p (or E r s ) of the polarized light wave. 1.4 Mathematical derivation In order to understand the derivation of optical properties from the ellipsometric angles (ψ, ), it is necessary to understand first the mathematics of polarized light. When the most general state of elliptically polarized light wave transmits through or reflects from one or more interfaces between media at a non-normal angle of incidence, the polarization change can be defined in terms of a change in tilt angle and ellipticity angle of the general polarization ellipse. This change depends on the angle of incidence and the optical properties and thicknesses of the media. The elliptically polarized state of monochromatic light in any medium assumed to be isotropic can be described by decomposing the beam into two orthogonal components which are linear and parallel ( E r ) p 5

45 as well as linear and perpendicular ( E r ) to the plane of incidence. s Both components are plane waves and a superposition of such components is described by [1-14] : r r r r r E(, t) = E exp i( q ωt) ; (1-6) 0 [ ] where q r is the complex propagation vector, ω is the wave frequency, and E r 0 determines the polarization state of the wave. In this linear p-s basis, r r r i p i s E ˆ ˆ 0 E E E e γ γ = + = p + E e s. (1-7) p s p s For this general polarization state of the light wave, the endpoint of the vector E r 0 traces an ellipse as a function of time t during propagation at a fixed position rr 0. A complete cycle is made in a time phase velocity of 2π τ =. The plane wave also travels in space with a ω ω v =, and the endpoint of the field vector traverses one full Re( q% ) ellipse after a distance equal to the wavelength complex magnitude of the propagation vector: 2π λ =. Here is %q defined as the Re( %q ) r q = qq % ˆ. 6

46 s χ a b Q r r E(, t) 0 p r r = 0 Figure 1-1 Schematic representation of the electric field vector trajectory E( r0, t) for an elliptically polarized light wave at a fixed position r 0 versus time. Q is the tilt angle between the ellipse major axis a and the p-axis, measured in counterclockwise-positive sense when facing the light source. χ is the ellipticity angle given by tan -1 (b/a). r r In Equation 1-6, the wavevector q r defines the propagation direction. If one assumes q r is parallel to the z-axis, the wave becomes: where r E( r, t) = E exp i( qz ω t) ; (1-8) 0 [ % ] ω 4πσ r ω 2 q% = ε + = % r i N c ω c, (1-9) or ω %q = N%. c Here c is the speed of light in vacuum. At the light wave frequency ω, ε r and σ r denote the real dielectric function and real optical conductivity of the medium in which the wave 7

47 travels, and N % is its complex index of refraction, where [1-15] 4πσ r = + = ε r + N% n ik i. (1-10) ω Here n is the (real) index of refraction, and k is the extinction coefficient of the medium. ω c It should be noted that Re( %q ) = n, so the phase velocity of the wave is v = and the c n 2π c 2π wavelength is λ = = v as expected. Next %q and N % are substituted into nω ω Equation 1-8 to give r r r ωkz ωnz E(, t) = E0 exp exp i ωt. (1-11) c c In addition to the complex index of refraction N %, the complex dielectric function ε% is another commonly used quantity to describe the macroscopic optical properties of solids [1-15], where: 2 % 1 i 2 N, (1-12) ε = ε + ε = % 2 2 = ε =, (1-13) ε1 r n k 4πσ ε r 2 = = 2 nk. (1-14) ω Ellipsometry measures the change in polarization state of the incident light caused by reflection from one or more interfaces. When an incident linearly polarized light wave reflects from a single interface between two media (see Fig. 1.2), the state of polarization of the reflected beam can assume an elliptical state with the tilt and ellipticity angles depending on the optical properties of the sample. 8

48 incident wave reflected wave s p.. Medium 0 Medium 1 Plane of sample θ i θ i θ % t p s s p Plane of incidence s. p transmitted wave Figure 1-2 Reflection of a polarized light wave at an interface between two media. For the ideal situation of a perfectly planar interface on the atomic scale with no roughness, the optical properties of the reflecting medium can be derived from the ellipsometric angles (ψ, ) as long as the optical properties of the incident medium and the angle of incidence are known [1-13]. In the simplest case of reflection and transmission at the perfectly planar interface between two isotropic media (see Fig. 1.2), the ratio of the complex Fresnel reflection coefficients can be written: N% s cosθi na cos % θ t R% p na cos % θt + N% s cosθi ρ% = =, (1-15) R% s na cosθi N% s cos % θt na cosθi + N% s cos % θt where n a is the assumed real refractive index of Medium 0 (ambient, see Fig. 1.2), N % s is the complex index of refraction of Medium 1 (substrate, see Fig. 1.2), θ i is the angle of incidence and % θ t is the complex angle of refraction. cos % θ t can be obtained from sinθ i, 9

49 n a, and N % s by using a complex form of Snell s Law: cos % θ = ± t N% n N% sin s a i s θ. (1-16) Then, eliminating cosθ t from Equation 1-15 yields: R% ρ% = = ( N% s cosθi m na N% s na sin θi )( na cosθi ± N% s na sin θi ) ( s cosθi ± a s a sin θi )( a cosθi m s a sin θi ) p R% s N% n N% n n N% n a i i s a i, (1-17) na sin θi m cosθi N% s na sin θi ρ% =, (1-18) n sin θ ± cosθ N% n sin θ and solving for 2 N % s yields: N% 2 1 n sin θ 1 ρ % = + tan θ. (1-19) 1+ ρ% s a i i As a result, by using the dielectric function definition in Equation 1-12, ε% s can be obtained from ρ% 2 % ε = ε sin θ 1 + tan θ s a i. (1-21) 1+ ρ% i Therefore, if one knows (i) ε a the dielectric function of the ambient; (ii) θ i the angle of incidence, and (iii) (ψ, ) the measured ellipsometric angles, then one can determine the dielectric function of the reflecting medium. 1.5 Spectroscopic ellipsometer used in the study The spectroscopic ellipsometer used for the study described in this thesis was manufactured by J. A. Woollam Company [1-16]. The specific model used here was the M-2000DI, which is a rotating-compensator multichannel ellipsometer. This 10

50 ellipsometer covers the photon energy range from 0.74 to 6.50 ev. One complete set of spectra in the ellipsometric angles (ψ, ) (0.74~6.5 ev) can be collected as an average over a minimum of two optical cycles in a time of (30.7 Hz) -1 = 32 ms; thus, the single optical period is 16 ms. Here 30.7 Hz is the mechanical rotation frequency of the compensator. In the case of real time SE applications, specifically for monitoring the CdTe or CdS deposition process, acquisition times from 1 to 3 seconds were chosen. In the case of the ex-situ SE applications, the data acquisition time of 10 seconds was chosen to ensure a higher precision in the measured (ψ, ) spectra. As a result of the multichannel detection capability, this spectroscopic ellipsometer is ideal for in-situ process monitoring and quality control, and specifically for studies of the CdTe-based solar cells as described in this thesis. Figure 1-3 Spectroscopic ellipsometer used in this research mounted in the ex-situ mode of operation. The angle of incidence is adjustable for this ellipsometer. For ex-situ studies, the ellipsometer is set at angles of incidence ranging from 45 to 75 at 5 intervals. 11