Applications of real-time and mapping spectroscopic ellipsometry for process development and optimization in hydrogenated silicon thin-film photovoltaics technology

Solar Energy Materials & Solar Cells ∎ (∎∎∎∎) ∎∎∎–∎∎∎

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Applications of real-time and mapping spectroscopic ellipsometry for process development and optimization in hydrogenated silicon thin-film photovoltaics technology Lila Raj Dahal a,b,c, Jian Li a,b,d, Jason A. Stoke e, Zhiquan Huang a,b, Ambalanath Shan a,b, Andre S. Ferlauto a,b,f, Christopher R. Wronski g, Robert W. Collins a,b, Nikolas J. Podraza a,b,n a

Department of Physics and Astronomy, University of Toledo, Toledo, OH 43606, USA Center for Photovoltaics Innovation and Commercialization, University of Toledo, Toledo, OH 43606, USA NSG-Pilkington NA, Northwood, OH 43619 USA d National Renewable Energy Laboratory, Golden, CO 80401 USA e Physics Faculty, Rocky Mountain College, Billings, MT 59102 USA f Instituto de Ciências Exatas, Departamento de Física, Universidade Federal de Minas Gerais, BR-31270901 Belo Horizonte, MG, Brazil g Department of Electrical Engineering, The Pennsylvania State University, University Park, PA 16802 USA b c

art ic l e i nf o

Keywords: Hydrogenated amorphous silicon (a-Si:H), hydrogenated nanocrystalline silicon (nc-Si:H) Real time spectroscopic ellipsometry (RTSE) Mapping spectroscopic ellipsometry Roll-to-roll deposition Thin film Si solar cells

n

a b s t r a c t Four applications of real-time spectroscopic ellipsometry (RTSE) and ex-situ mapping spectroscopic ellipsometry (SE) in thin-film hydrogenated silicon (Si:H) photovoltaics (PV) technology are reviewed with the common theme being the development and application of SE-derived growth evolution diagrams. The goals of these applications are to understand and consequently further advance this technology. In the first application, fabrication of engineered thin films consisting of periodic arrays of silicon (Si) nanocrystallites in an amorphous Si:H (a-Si:H) host matrix has been guided by a growth evolution diagram developed by RTSE for radio-frequency plasma-enhanced chemical vapor deposition (PECVD) using SiH4 þH2 mixtures. Such precisely controlled microstructures are of interest as possible intrinsic-layer components of p–i–n and n–i–p thin-film PV devices, and RTSE is shown to be a key technique for guidance in fabrication and for structure verification. In the second application of growth evolution diagrams, very-high-frequency PECVD intrinsic a-Si:H, hydrogenated amorphous silicon– germanium alloys (a-Si1  xGex:H), and hydrogenated nanocrystalline silicon (nc-Si:H) have been investigated for use as the top, middle, and bottom-cell i-layer components, respectively, of triplejunction n–i–p solar cells. The growth evolution diagram for the bottom-cell i-layer, starting from an underlying mixed-phase amorphous þnanocrystalline silicon [(a þnc)-Si:H] n-layer, reveals a bifurcation at a critical H2-dilution flow ratio R (R ¼[H2]/[Si2H6], in this application) between mixed-to-amorphous phase evolution [(aþnc)-a] at low R and mixed-to-nanocrystalline phase evolution [(aþ nc)-nc] at high R. The highest performance single-step nc-Si:H solar cell is found at minimal R while remaining on the nanocrystalline side of the identified bifurcation where suitable grain boundary passivation can be assured. Because of the importance of the roll-to-roll flexible substrate configuration in such multijunction Si:H-based PV technology, RTSE has been demonstrated in a third application for monitoring PECVD of a-Si:H n–i–p solar cell structures on back-reflector-coated flexible roll-to-roll polymer substrates. RTSE has been used for probing along the center line of the moving substrate during deposition, and ex-situ mapping SE has been used over the full substrate area after deposition. Detailed studies of the top-most p-layer of the n–i–p solar cell have been performed, with the goal being to develop spatially-dependent (in contrast to R-dependent) growth evolution diagrams in order to evaluate uniformity across the width of the substrate and thus to enable optimization of the resulting a-Si:H PV modules. In this study, efficiency optimization occurs at the p-layer transition region in which a-Si:H nucleates from the i-layer surface, but evolves to predominantly nc-Si:H for improved contact to the top-most In2O3:Sn layer. In the fourth and final application reviewed here, the mapping-SE-deduced properties of the Si:H i and p-layers have been spatially correlated with device performance parameters from an array of n–i–p a-Si:H-based dot cells over a 13  13 cm2 substrate area. Analysis of the SE data acquired over the full area provides property maps of i-layer thickness and band gap, p-layer thickness and band gap, and p-layer surface roughness thickness for the n–i–p structure. The mapped values

Corresponding author. E-mail address: [email protected] (N.J. Podraza).

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adjacent to the PV devices have been correlated with the device performance parameters. When sufficient non-uniformity exists, these correlations enable optimization based on specific ranges of values that characterize the fundamental properties of the material and the film structure. & 2014 Elsevier B.V. All rights reserved.

1. Introduction and Overview Thin-film hydrogenated silicon (Si:H) based photovoltaic (PV) devices may incorporate amorphous silicon (a-Si:H), nanocrystalline silicon (nc-Si:H), and even mixed-phase (amorphous þnanocrystalline) silicon [(a þnc)-Si:H] intrinsic layers (i-layers) prepared by plasma-enhanced chemical vapor deposition (PECVD) as the optically absorbing components of n–i–p and p–i–n solar cells [1,2]. Alloys of these Si:H i-layer components with Ge are also of interest for lowering their band gaps, thus increasing the fraction of light absorbed and the current generated for a given thickness. It is widely known that optimization of all such devices is a challenge due to the dependence of the PECVD film structure and phase on the corresponding properties of the underlying layer (or the substrate). An associated challenge is generated by continuous changes of film structure and phase that can occur with accumulated thickness due to evolution from an initial substrate control of the structure and phase to a subsequent plasma control of these properties. Barriers to crystallite nucleation arise due to growth kinetics or film stress and also contribute to an evolution in the characteristics of the film. Addressing these challenges through in-depth characterization of Si:H-based materials, device structures, and their fabrication processes by advanced spectroscopic ellipsometry (SE) techniques establishes the overarching theme of this review. Optimum single-step a-Si:H i-layers, as evaluated by the product of the fill-factor (FF) and open-circuit voltage (Voc) of the resulting n–i–p or p–i–n single-junction PV devices, are produced by PECVD from SiH4 þH2 or Si2H6 þH2 at the maximum level of H2-dilution possible while avoiding the initial nucleation and consequent propagation of crystallites from the amorphous phase throughout the i-layer thickness [3–7]. H2-dilution ensures a well-ordered amorphous network that reaches its fully lightsoaked state after o 100 h under air-mass (AM) 1.5 illumination. The benefits of H2-dilution in a-Si:H i-layer deposition are wellknown and include enhanced passivation of the growth surface by atomic H and hence enhanced diffusion of film precursors on the surface during the growth process [8–10]. Atomic H also diffuses into the sub-surface of the a-Si:H where it can relax strained Si–Si bonds [11]. The latter effect, which has been termed “chemical annealing”, also promotes crystallite nucleation as elucidated in studies of Si–H bonding using real-time infrared spectroscopy [12,13]. In contrast, the corresponding single-step PECVD nc-Si:H i-layers for single-junction devices having optimum Voc-FF product are produced using minimum H2-dilution while ensuring continuous nanocrystal propagation from nanocrystallite growth surfaces [14,15]. In this case, it appears that the lower H2-dilution level leads to grain boundaries that are passivated with a thin amorphous phase, as opposed to void structures at grain boundaries that can occur at excessive H2-dilution levels. Quantitative analysis of the nanocrystalline and amorphous volume fractions within mixed-phase (aþ nc)-Si:H films is one of the key challenges in the characterization of these films for identification of processing–property correlations. Most often the nanocrystalline fraction is estimated on the basis of X-ray analysis or Raman spectroscopy, in which case device grade i-layer material incorporates a depth-averaged volume fraction of  0.3–0.7 [14,16,17]. Measurements of the Raman emission cross-section ratio used for determination of nanocrystalline volume fraction, however, yield values that

range over more than an order of magnitude leading to significant uncertainties in the result [18]. It is a greater challenge, however, to profile non-destructively versus film depth using these techniques due to the penetration depth of the probes, which can span the full i-layer thickness or at least a significant fraction of it. The challenge is even greater still for depth-profiling the phase composition of n and p-layers having thicknesses of 100–300 Å within the device structure. An alternative approach for analysis of the nanocrystalline and amorphous volume fractions involves real-time SE (RTSE) in conjunction with virtual-interface analysis (VIA), which serves as a probe of the very top surface of the film, within a typical outerlayer thickness of  3–30 Å [15]. In the general VIA methodology, a graded film is modeled as a four-medium structure with (i) a “pseudo-substrate“ that incorporates the history of the gradedlayer deposition, (ii) the thin outer-layer with a complex dielectric function deduced in the analysis, (iii) a surface roughness layer modeled as a 0.5/0.5 volume fraction mixture of outer-layer material and voids, and (iv) the ambient medium. The VIA approach is not without its own limitations, however. In the specific VIA used for mixed-phase Si:H, the outer-layer of the growing film is considered as a microscopic mixture of an initialstate material from which crystallites nucleate and a final-state material of presumably coalesced nanocrystals. If the final-state material is predominantly nc-Si:H, however, with a fraction of amorphous material and/or void present at the grain boundaries, then the nanocrystalline fraction in the VIA is measured relative to that of the coalesced final-state material. Only when the coalescence occurs fully and the final-state material is single-phase ncSi:H does the deduced nanocrystalline volume fraction serve as an absolute measure. Professor J. David Cohen, to whom our article in this tribute issue is dedicated, has made substantial progress in overcoming the above-described challenges of Si:H materials and device characterization by contributing to the current understanding of the electronic structure of optimum thin-film Si:H solar cells through a variety of powerful capacitance spectroscopies [19– 24]. In particular, Cohen and collaborators [5,17,25–27] have made significant contributions in characterizing the electronic properties of graded-layer materials in the highest efficiency nc-Si:H solar cells developed by Yan et al. [28]. In tribute to the exemplary research of Professor Cohen on electronic spectroscopy, the present article reviews complementary optical spectroscopy of Si:H materials and solar cell structures through SE based on high-speed multichannel detection. This review is presented in four sections with the intent to build from the foundations described in a previous extensive review published in 2003 [29]. The common theme throughout these sections is the development and application of SE-derived growth evolution diagrams as described in Ref. [29] to facilitate process design for nanostructured materials (Section 2), multijunction solar cells (Section 3), and large area PV structures on roll-to-roll flexible and rigid substrates (Sections 4 and 5) having additional capabilities of combinatorial optimization (Section 5). In the remainder of this section, an overview of the article will be given, including motivations, key outcomes, and future prospects of this research. Section 2 of the review describes the results of research motivated by the potential improvements in thin-film Si:H solar cell process design through a-Si:H and nc-Si:H i-layers fabricated

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with multi-step and profiled H2-dilution ratios [4,28]. For such complex i-layer processing, optimization principles have been facilitated by the growth evolution diagrams developed in previous studies by RTSE [15,29,30]. Improvements in the FF stability of a-Si:H based thin-film solar cells have been reported by incorporating into the device structure mixed-phase (a þnc)-Si:H i-layers having isolated nanocrystalline domains within the amorphous matrix [31–34]. Optimization and reproducible control of such nanostructures is a challenge, however, due to the strong substrate dependence and the rapid evolution of the nanocrystallites from their initial nuclei, and thus the difficulty of controlling both the volume fraction of isolated nanocrystallites for a constant depthaveraged value and the spatial uniformity for potential process scale up. Thus, effective approaches are required for monitoring and controlling nanocrystallite evolution, through both initiation and suppression of the nucleation mechanism. In Section 2 of this review, results of RTSE studies are described for process development and monitoring toward the fabrication of mixed-phase (a þnc)-Si:H i-layers by modulating the H2-dilution in order to generate a nanostructured film with a controlled distribution of crystallites [35]. Such thin films may have applications in top-most junctions of tandem and multijunction thin-film Si:H solar cells with high FF stability against light-induced degradation. Section 3 of this review is motivated by the recognition that in progressing from the highest Voc-FF performance to the highest efficiency thin-film Si:H-based solar cells, light collection must be optimized. Thus, the highest efficiency Si:H based solar cells historically have employed triple-junction n–i–p device structures [36–39]. Such structures may combine absorber i-layers of PECVD a-Si:H, amorphous silicon–germanium alloys (a-Si1 xGex:H), and nc-Si:H for use as the top, middle, and bottom-cell i-layer components, respectively. In the development of i-layer growth evolution diagrams for these highest efficiency configurations of multijunctions, one must adopt an underlying film having the same structure as the n-layer that is optimized for the particular junction of the multijunction. Such studies reviewed in Section 3 have reaffirmed that the highest performance, not only for a-Si:H top-cell materials, but also for aSi1 xGex:H middle-cell materials, is obtained for single-step i-layers when these layers are prepared under the previously-described maximal H2-dilution conditions [15,40]. In analogous studies reviewed in Section 3, the growth evolution diagram for the bottom nc-Si:H thin-film solar cell has revealed characteristics unique to this n–i structure. In particular, the structure employs an underlying mixed-phase n-layer consisting of (aþnc)-Si:H having estimated 0.6/0.4 a-Si:H/nc-Si:H volume fractions. The nc-Si:H i-layer growth evolution diagram then reveals a bifurcation at a critical R value that separates the ultimate phase evolution of (aþnc)-Si:H to a-Si:H [(aþnc)-a] at low R from the ultimate phase evolution of (aþnc)-Si:H to nc-Si:H [(aþ nc)-nc] at high R [15,40]. Considering such a diagram, the highest efficiency single-step nc-Si:H solar cell has been obtained at minimal R while remaining on the nanocrystalline side of the identified bifurcation apparently where suitable grain boundary passivation is assured. This work also suggests that the bifurcation defines the H2-dilution endpoint of graded layer processing. This is the lowest H2-dilution level employed for the top-most region of the nc-Si:H i-layer in n–i–p structures. Dropping below this level leads to a continuous increase in the volume fraction of any residual amorphous phase at the expense of the nanocrystalline phase. The starting H2-dilution level for grading, i.e., the highest H2-dilution used for initial nucleation of the nc-Si:H i-layer, depends sensitively on the underlying substrate film. This level is selected such that immediate nucleation of nanocrystals occurs from the substrate, while retaining an amorphous phase, rather than trapped voids, at the crystallite boundaries. The mixed-phase (a þ nc)-Si:H n-layer with 0.6/0.4 a-Si:H/nc-Si:H volume fractions as used in this

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research is found to assist in ensuring the desired initial i-layer structure [15,40]. The applications presented in Section 4 are motivated by the above-described sensitivity of the final Si:H-based thin-film solar cell performance to the process parameters for the optimum set of values, the most sensitive being the H2-dilution ratio. Thus, the development of real-time monitoring tools is of great interest in Si:H-based thinfilm PV technology. An effective such tool provides instantaneous information on material properties of relevance to solar cell performance, and also may enable tuning of the process parameters to obtain the specified product with higher yield and reduced downtime. Although RTSE has been used extensively to study the growth evolution of the component layers of thin-film Si:H solar cells at a fixed point on a stationary, rigid substrate during growth by PECVD [29], little such work has been done on moving, flexible substrates in the roll-to-roll configuration until recently. Thus, in Section 4, the focus is on a review of these recent RTSE measurements and analysis of a-Si:H n–i–p solar cell structures on a moving, back-reflector (BR) coated, flexible polymer substrate during growth by rf PECVD [41] in a roll-to-roll cassette deposition system [42]. In this case, RTSE has been applied along a single line at the center of the advancing roll, and ex-situ mapping SE has been applied over the full area of the roll's leading end, i.e., the initial roll length exposed to plasma ignition and shortly beyond that initial length into the regime of constant coating thickness. The first focus of Section 4 of this review is a recent investigation of a PECVD process for the i-layer simply as a demonstration of the RTSE capability in roll-to-roll deposition [41]. Because analysis of the topmost Si:H p-layer in the substrate/BR/n–i–p configuration is more demanding, the p-layer process is the second focus of Section 4 [43]. In thin-film Si:H PV technology, the need exists for careful control of the p-layer fabrication including the p-layer thickness – at  100 Å; its phase – initially protocrystalline evolving toward nanocrystalline; and its optical properties – an absorption onset as high in photon energy as possible. Such control is needed in order to optimize Voc and the blue response of the cell [44,45]. Thus, a goal of research reviewed in this second focus of Section 4 is to monitor the growth of the Si:H p-layer at high H2-dilution ratio along the center line of the leading end of the advancing roll as the progression occurs from p-layer plasma ignition through the a-Si:H, (aþnc)-Si:H, and nc-Si:H growth regimes versus thickness. Also reviewed in Section 4 are ex-situ mapping SE studies performed after p-layer deposition, in order to measure the leading end of the roll across its full width, and thus to characterize the p-layer uniformity before deposition of the In2O3:Sn (ITO) transparent conducting oxide top contact [43]. For the instrumentation used in such studies, the ellipsometer unit is translated over the substrate, probing sequentially point by point with autofocus capability for mm-scale resolution. From the leading end of the roll, the p-layer exhibits an approximately linear thickness gradient over the start-up length, i.e., the length of the PECVD zone, because increasing distances along the substrate from this end have spent a linearly increasing time duration within the plasma zone. Thus, using ex-situ mapping SE, the spatiallyresolved phase diagram of the p-layer can be plotted over the 15 cm width and 18 cm start-up length of the flexible substrate [43]. Such a spatial phase diagram identifies the locations at which the a-(aþ nc) and (aþnc)-nc transitions appear over the area of the flexible substrate/film structure. Superimposing the bulk layer thickness map onto the spatial phase diagram yields the spatially-dependent growth evolution diagram (in contrast to the typical R-dependent diagram) as described at the end of Section 4. This diagram is a first step in enabling design of the proper PECVD electrode and gas injection system, as well as the optimum deposition conditions and substrate speed to ensure a uniform, high-quality Si:H p-layer over the entire area of the substrate, as required for optimization of

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n–i–p module performance in the substrate/BR/n–i–p configuration. Spatially-resolved growth evolution diagrams for both the component i and p-layers, along with an evaluation of the thickness uniformity from mapping SE provide the insights necessary for reducing the difference between the small-area solar cell efficiency and the large-area module efficiency. Applications of mapping SE presented in Section 5 are motivated by the need to reproduce the optimum device performance achieved on the laboratory scale in large-area configurations when scaling up thin-film PV technologies. In these technologies – in particular for a-Si:H and nc-Si:H – significant differences exist between champion cells and modules [46]. One component of this difference relates to large-area deposition uniformity. For example in the research laboratory, optimum a-Si:H and nc-Si:H for the i-layers of solar cells are prepared within narrow regions of deposition parameter space [1,2]. Not only is the i-layer absorber for the a-Si:H solar cells prepared under narrow conditions defined by maximum H2-dilution, while avoiding nanocrystallite nucleation [3–7], the optimum p-layer conditions are similarly based on protocrystallinity concepts [44,45]. Optimum growth of nc-Si:H requires different conditions for nucleation and steadystate growth [15,28,40]. Rapid generation of the nanocrystalline phase from the underlying n-layer is possible at high R, depending on the nature of the n-layer; however, the R value must be reduced to a minimum while avoiding conversion to the amorphous phase during steady-state growth. It is a challenge to maintain such conditions over large areas, in particular in roll-to-roll deposition, and such challenges can account in part for the performance difference between laboratory cells and production modules. The results reviewed in Section 5 demonstrate the promise of methods that can map fundamental properties of thin-film PV materials over large areas, enabling local correlations between such properties and device performance. Such correlations can be useful for understanding the uniformity issues that may impact device performance. Mapping SE has been applied recently for property correlations with the performance of dot cells fabricated in a large-area array [47]. To this end, analysis of SE data has become increasingly advanced through the use of analytical expressions that reduce the number of free parameters needed in the analysis [48–51] so that even very rough surfaces, such as those in the actual PV devices, can be probed [51]. Not only can SE provide the starting-point information of thicknesses, optical band gaps, and spectroscopic optical properties in the form of the complex dielectric function (ε¼ε1 þ iε2) of component layers, but also it can access crystalline grain size, defect density, disorder, and stress through the deduced parameters describing ε [49,50]. This methodology has been performed initially on a-Si:H solar cells in order to demonstrate the concept, however, the approach is expected to be effective in the future for all thin-film PV technologies. A limitation of the studies reviewed in Sections 4 and 5 is that the mapping SE measurements were performed ex-situ and so were restricted to completed solar cell stacks. Recently, an advanced mapping SE instrument has been integrated into the deposition equipment as an in-situ tool so that the extensive substrate roll lengths can be mapped after each deposition step, without the need to remove the roll-to-roll cassette from the vacuum system [52,53]. Through such an in-situ mapping capability, guidance for future improvements in large area process optimization can be expected.

2. Controlled fabrication of mixed-phase hydrogenated silicon 2.1. Experimental methods Continuous H2-dilution profiling has been adopted for optimization of grain boundary passivation in nc-Si:H i-layer materials

throughout the thickness [25–28]. The similarly challenging optimization problem in modulating H2-dilution, however, has been less widely explored. Such modulation can be employed in order to generate (a þ nc)-Si:H with a specified volume fraction of embedded nanocrytallites. The work reviewed here demonstrates that (a þnc)-Si:H i-layers can be fabricated having a periodic array of crystallites within an amorphous matrix. By controlling the H2-dilution and by monitoring using RTSE, the average crystallite size as well as the in-plane and out-of-plane crystallite spacings of the film can be controlled independently. Each Si:H and (a+nc)-Si:H i-layer film studied here was deposited starting with a single-phase a-Si:H layer, which was prepared on a native-oxide-covered crystalline silicon (c-Si) wafer substrate from pure SiH4 using a single-chamber, radio-frequency (rf; 13.56 MHz) PECVD system. The key deposition variable for the overlying layers was the H2-dilution ratio, R ¼[H2]/[SiH4], where [H2] and [SiH4] indicate the gas flow rates. This R value was fixed for the development of a growth evolution diagram with singlestep i-layers, whereas R was modulated for the fabrication of an (a þnc)-Si:H i-layer film with controlled phase composition. All other deposition parameters were fixed for both the initial R¼0 layer and the overlying layers as follows: a calibrated substrate temperature of 200 1C, an rf plasma power of 0.08 W/cm2 (the minimum possible for a stable plasma in the PECVD system), and a low partial pressure of the SiH4 source gas of 0.06 Torr, yielding a low total pressure of o1.0 Torr. Substrate temperature calibration was performed by in-situ SE measurements using a nativeoxide-covered Si wafer substrate. The shift in the Si E1 and E2 critical point energies from their room temperature values yield the true surface temperature of the Si wafer, applying the wellknown temperature shifts of the critical point energies [54]. An initial series of single-step Si:H films was prepared at H2dilution ratios over the range 0 oR≤170 on top of the R¼0 a-Si:H layers. These single-step Si:H layers were studied for the development of a growth evolution diagram. The controlled mixedphase (a þnc)-Si:H film was prepared by modulating R between R¼0 and R¼ 40 during PECVD. The underlying R¼ 0 a-Si:H serves as the first half-cycle a-Si:H component of the (a þ nc)-Si:H film and also serves to erase the memory of the c-Si wafer substrate in growing the (a þnc)-Si:H film. The Si:H and (a þ nc)-Si:H deposition processes were investigated in real time using a rotatingcompensator multichannel ellipsometer with design specifications provided elsewhere [55]. The single-step Si:H films prepared at low H2-dilution remain in the amorphous growth regime throughout their thickness. For such films, the time evolution of the bulk and surface roughness layer thicknesses, as well as the spectroscopic ε of the bulk layer were extracted from the RTSE data set using a global Σs-minimization procedure, where s is the unweighted error function in least-squares regression analysis [56]. The concept underlying this analysis is that, with NT time points and NE energy points, a total of 2NTNE measured ellipsometric angles (ψ, Δ) are available. Assuming a model for the film consisting of time-dependent bulk and surface roughness layer thicknesses with a thickness-independent complex ε, there will be 2 (NE þ NT) unknowns in the data analysis problem. Since 2NTNE is inevitably much greater than 2(NE þNT), the data analysis problem can be solved by least-squares regression. In contrast, single-step Si:H films prepared with high H2dilution tend to develop in the amorphous or so called “protocrystalline“ phase for an initial period of growth, but subsequently nucleate isolated nanocrystallites from within the amorphous matrix at a well-defined thickness. These nuclei grow in the form of inverted cones, and eventually coalesce to form a nc-Si:H phase that is relatively stable structurally upon continued growth. Consequently, the final films exhibit an amorphous phase near the substrate interface and a nanocrystalline phase at the top of

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the film, each with its distinct ε. An intervening structurallygraded (a þ nc)-Si:H phase exists such that the nanocrystallite volume fraction measured relative to that in the top-most nc-Si:H increases with depth – starting from zero, where initial nucleation observed, and approaching unity, where complete coalescence is observed. The optical properties of thin laminar elements of the graded layer can be modeled using the Bruggeman effective medium approximation (EMA) as a mixture of a-Si:H and nc-Si:H components whose ε spectra are those of the clearly-identifiable underlying and overlying phases [57]. Thus, RTSE data collected during the growth of such a structurally-graded (a þnc)-Si:H film are conveniently interpreted using the VIA methodology described more generally in Section 1 [58,59]. This analysis utilizes a four-medium optical model consisting of (i) the pseudo-substrate incorporating the past history of the deposition; (ii) an outer-layer of the most recently deposited material; (iii) a surface roughness layer; and (iv) the ambient medium. The interface between the outer-layer and the pseudosubstrate is the virtual interface in the VIA. The surface roughness layer is modeled using the EMA as a 0.5/0.5 volume fraction mixture of the outer-layer material and void [57]. The VIA approach is also based on least-squares regression with free parameters as functions of time that include the volume fractions of Si:H nanocrystallites and voids in the outer-layer fnc and fv, the outer-layer growth rate r, and the surface roughness layer thickness ds. After this information is obtained, the bulk layer thickness db can be extracted in an integration of r(t). In addition, the areal density Nd of nanocrystallites in the amorphous matrix and the half-angle θ of the nanocrystalline inverted cones can be estimated using a geometric model to be described later in the next section [59].

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Fig. 1. (a) Surface roughness layer thickness and (b) nanocrystallite volume fraction in the near-surface region of the bulk layer plotted versus bulk layer thickness for an R¼ 40 film deposited on a c-Si wafer substrate coated with R¼ 0 a-Si:H. The evolution of the nanocrystallite fraction as predicted by a cone growth model is also shown (solid line); the inset shows parameterizations of the imaginary parts of the dielectric function spectra, ε2, for the fully amorphous (dotted line) and nanocrystalline (solid line) R¼ 40 Si:H materials. (Adapted with permission from Ref. [35]).

2.2. Results and discussion Fig. 1 shows the evolution of the surface roughness layer thickness and relative nanocrystallite volume fraction in the outer-layer (top 3 Å in this case) for an R¼ 40 Si:H film prepared on a native-oxide-covered c-Si substrate over-coated with R¼0 a-Si:H. Nanocrystallites first nucleate from the amorphous phase at a bulk layer thickness of db ¼ 160 Å, which is denoted as the amorphous-to-(mixed-phase) (amorphousþnanocrystalline) [a-(aþnc)] transition. This transition is identified by abrupt roughening starting from an otherwise stable or [as in Fig. 1(a)] smoothening surface. This roughening occurs due to the protrusion of nanocrystals above the surface [29]. At db ¼500 Å, the nanocrystallites coalesce to form an identifiable nc-Si:H thin-film phase which is referred to as the (mixed-phase)-to-nanocrystalline [(aþnc)-nc] transition, as described in Section 1. This transition is identified by a maximum in the surface roughness thickness which occurs when crystallites make contact in the coalescence process. The inset of Fig. 1(b) shows spectra in the imaginary part of the dielectric function, ε2, for the near-substrate amorphous and nearsurface nanocrystalline R ¼40 Si:H materials. The complex dielectric function for the amorphous phase was determined by exact inversion assuming bulk and surface roughness layer thicknesses obtained by Σs minimization, which was performed on data acquired in the first  150 Å of R ¼ 40 a-Si:H film growth on the R¼ 0 layer. The inverted ε was then fit to a band-gap-modified oscillator function based on the assumption of square-root densities of states versus energy and an energy-independent dipole matrix element, i.e., the Cody–Lorentz model [48]. The complex dielectric function ε for the nanocrystalline phase was determined using the VIA methodology and was fit to two oscillators simulating the E1 and E2 transitions of crystalline Si with a common indirect band gap based on the assumption of parabolic E(k) bands and an energy-independent momentum matrix element [50,60,61].

In order to obtain the growth evolution diagram shown in Fig. 2, results are plotted from a total of 10 depositions performed at different R values from R ¼15 to R¼ 170 on c-Si/native-oxide substrates coated with a-Si:H deposited at R¼ 0. In Fig. 2, the bulk layer thicknesses db that identify the a-(a þnc) and (a þ nc)-nc transitions are plotted as a function of R [29]. These transition thicknesses are obtained as shown in Fig. 1 for R ¼40. Films prepared at Ro15 do not exhibit the a-(a þnc) transition and remain amorphous throughout 4000 Å of growth. The films prepared with R ¼15 and 30 exhibit only the a-(a þnc) transition with the (a þnc)-nc transition occurring at thicknesses greater than the final thickness of the film (6500 and 900 Å for R ¼15 and 30, respectively). Thus, films prepared over the range 15≤R≤150 initially nucleate in the amorphous phase as protocrystalline Si:H, but undergo the a-(a þnc) transition at a bulk layer thickness that decreases with increasing R throughout the series. The (a þnc)-nc transition also occurs at a subsequent bulk layer thickness that also decreases with increasing R. It should be noted that for R≥170, the film initially nucleates as nc-Si:H directly on the amorphous R¼0 substrate without the formation of a protocrystalline Si:H layer. The growth evolution diagram shown in Fig. 2, in conjunction with nanocrystallite nucleation density studies (see Section 3) [40], have been used to guide the modulation of R during a single deposition in order to produce a film of (a þ nc)-Si:H with a controllable nanocrystallite component volume fraction with increasing thickness. The modulated Si:H structure was deposited onto a native-oxide-covered c-Si substrate while measuring by RTSE with the intention of fabricating a film with a constant volume average nanocrystalline fraction as a function of depth. The particular film described in detail here was designed to consist of low-dilution (R¼0) crystallite suppression regions deposited starting from the c-Si substrate, alternating with high-

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Fig. 2. Growth evolution diagram for Si:H films deposited by rf (13.56 MHz) PECVD onto an R¼ 0 a-Si:H film. The fixed deposition parameters include a standard intrinsic-layer substrate temperature, 200 1C; the minimum power for a stable plasma, 0.08 W/cm2; and a low total pressure, o 1 Torr. The variable parameter, serving as the abscissa of the diagram, is the H2-dilution ratio R ¼[H2]/[SiH4]. The ordinate axis represents the bulk layer thicknesses at the amorphous to mixedphase (amorphousþ nanocrystalline) transition [a-(a þnc); squares] and the mixed-phase to structurally-stable nanocrystalline transition [(a þ nc)-nc; circles]. (Adapted with permission from Ref. [35]).

dilution (R ¼40) crystallite nucleation regions in order to produce a controlled mixed-phase film with nanocrystallites spaced approximately 400 Å apart both in the film plane and out of the plane. Three pairs of R ¼0/R¼ 40 layers were deposited. Fig. 3 shows the surface roughness layer thickness and the nanocrystalline and void volume fractions in the outer-layer (3–20 Å thick for R¼ 40 to 0, respectively) as functions of the bulk layer thickness. Complex dielectric function spectra ε used in the analysis of Fig. 3 have been deduced from the previous R ¼0 and R¼40 Si:H depositions. Fig. 4(a) shows a dark-field cross-sectional transmission electron micrograph (TEM) of the structure of Fig. 3. The TEM image corroborates the thicknesses of the amorphous and mixedphase regions of the (a þ nc)-Si:H film as determined by the VIA. Both VIA and TEM results demonstrate that it is possible for the R¼ 0 deposition to suppress further nanocrystallite growth on the R¼ 40 mixed-phase material and thereby produce alternating amorphous and mixed-phase regions, the latter with a welldefined size and average spacing for the crystalline inclusions. The R¼ 0/40 cycles beyond the first one, however, show variations in the nanocrystallite evolution depending on the underlying structure. These variations provide additional insights into the well-known substrate dependence of the growth evolution diagrams [6,29]. The most obvious example of such variations is the additional voids that appear upon nanocrystallite nucleation for the second and third R¼40 layers. The voids are introduced in the VIA in order to maintain a fit quality that does not degrade with thickness during these second and third R¼40 cycles. The appearance of voids reflects a reduced amplitude dielectric function for the outerlayer as deduced in the VIA. In a previous review [29], a detailed discussion is presented on the application of the time or thickness evolution of the fit quality for identification of complexities in the models used for RTSE analysis. These complexities typically arise from thickness variations in the dielectric function as is the case in the second and third R¼ 40 cycles of the deposition of Fig. 3. For these R¼ 40 layers, the surface roughness layer thicknesses at the a-(a þnc) transition have increased from ds ¼10 Å for the first R ¼40 layer to ds ¼30 Å and 60 Å for the second and third layers, respectively. As the surface roughness thickness increases, the voids first appear in the mixed-phase layer (at ds ¼30 Å) and

Fig. 3. The bulk layer thickness evolution of (a) the surface roughness thickness, (b) the nanocrystalline volume fraction in the near-surface of the bulk layer, and (c) the void volume fraction all for a modulated film structure prepared by alternating Si:H layers fabricated using high (R¼ 40) and low (R¼ 0) H2-dilution ratios, as determined by virtual interface analysis (VIA) applied to RTSE data. (Adapted with permission from Ref. [35]).

Fig. 4. (a) Dark-field cross-sectional transmission electron microscopy image of the modulated Si:H film structure of Fig. 3 prepared by alternating Si:H layers fabricated using high (R ¼40) and low (R ¼0) H2-dilution ratios; (reproduced with permission from Ref. [35]); (b) a schematic that depicts the film structure and definitions of cone angle and nucleation density after the first cycle in (a).

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then stabilize in volume fraction throughout the mixed-phase regime (at ds ¼ 60 Å). This behavior can be attributed to the inability of the crystalline phase to cover rough surfaces conformally and the associated shadowing and failure of the amorphous phase to completely fill the interstices. A second example of the effect of roughness is a loss in the regularity of the nanocrystallite profile, which occurs for the third cycle in Figs. 3 and 4(a). It is also important to note in Fig. 3 that the a-(a þnc) transition of the R¼40 material shifts to lower bulk layer thickness with increasing cycle number, as indicated by bulk thickness db required to reach a given fnc value, e.g., if fnc ¼0.25, then db ¼ 320, 220, 140 Å for cycles 1, 2, and 3, respectively. This shift can be attributed to the increased structural order of the underlying R¼ 0 materials with increasing cycle number due to the influence of the (a þnc)-Si:H beneath these materials. The implication is that the underlying nanocrystals serve as templates for a more highly ordered R¼0 a-Si:H that covers their surfaces. In order to improve the periodicity of the modulated structures, thicker R ¼0 layers may be necessary with increasing cycle number; alternatively, the H2-dilution ratio of the high R layers could be reduced slightly with increasing cycle number. In either case, it should be clear that such variations in the thickness of the R ¼0 a-Si:H layers and in the H2-dilution of the high R (a þnc)-Si:H layers can be used to produce films with periodic arrays of nanocrystallites, adjusting for substrate dependences so as to achieve controllable separations both in the plane of the film and out of the plane. To conclude this section, the geometric aspects of the nucleation process associated with the growth evolution diagram will be considered. In Fig. 4(b), a schematic model is depicted for conical nanocrystal growth from an amorphous phase, including definitions for the cone half-angle θ and nucleation density Nd. The solid line in Fig. 1(b) is the result of a calculation using the cone growth model for the single R¼40 deposition assuming a fixed cone half-angle θ versus time. The fixed cone half-angle in the model is given by cos θ¼Δdb/ (Δdb þΔds), where Δdb is the bulk layer thickness that evolves between the (aþnc)-nc and a-(aþ nc) transitions and where Δds is the surface roughness thickness increase occurring over the bulk layer thickness range of Δdb [40]. The nanocrystallite nucleation 2 density can then be estimated as Nd snc ¼6.0  1010 cm  2, which is associated with an initial in-plane nanocrystallite spacing of snc ¼ 2Δdb tan θ¼ 400 Å. A detailed discussion of the structural transitions and associated cone growth characteristics observed in thin Si:H films is provided in a previous review [29].

3. Growth evolution diagrams of Si:H multijunction n–i–p solar cell components 3.1. Experimental methods Vhf PECVD growth evolution diagrams have been developed for the components of triple-junction thin-film Si:H-based solar cells in the n–i–p configuration. To construct these diagrams for Si:H top-cell and Si1  xGex:H middle-cell i-layers, vhf PECVD was performed from Si2H6 þH2 and Si2H6 þ GeH4 þH2 mixtures, respectively, on the surfaces of a-Si:H n-layers. For the growth evolution diagrams of bottom-cell nc-Si:H i-layers, vhf PECVD was performed from Si2H6 þH2 on the surfaces of mixed-phase (a þnc)-Si:H n-layers. A schematic of the multijunction solar cell configuration is shown in Fig. 5(a). The deposition conditions used for the top, middle, and bottom-cell i-layer materials are summarized in Table 1. These conditions have enabled comparison of the effect of a GeH4 addition to Si2H6 in vhf PECVD as well as the effect of Si2H6 depletion in vhf PECVD. Combining similarly-deposited i-layers in triple-junction n–i–p solar cells have led to 11% stabilized performance [37]. The growth evolution diagrams have

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Fig. 5. (a) Multijunction n–i–p Si:H structure with three stacked cells including the bottom cell with a nc-Si:H i-layer, middle-cell with an a-Si1  xGex: H i-layer, and top-cell with an a-Si:H i-layer. Single junction component cells of this stack were studied by RTSE using a mixed-phase (aþnc)-Si:H n-layer for the bottom-cell nc-Si:H and single-phase a-Si:H n-layers for the middle cell a-Si1 xGex: H and top cell a-Si:H; (b) configuration of samples for correlation of i-layer growth evolution diagrams from RTSE with solar cell performance parameters. The circle indicates the anode of the PECVD reactor.

been correlated with the performance of co-deposited singlejunction solar cells in order to further explore the applicability of the maximal and minimal H2-dilution concepts, particularly for the vhf a-Si1  xGex:H and nc-Si:H i-layers, respectively. Growth diagram development by RTSE for the top and middlecell i-layers of a-Si:H and a-Si1 xGex:H, respectively, was performed using multichamber vhf (70 MHz) PECVD with c-Si/(native-oxide)/ (n-type a-Si:H) substrates. For device performance studies, additional samples  2000 Å thick were co-deposited onto textured steel/Ag/ZnO/(n-type a-Si:H) structures in the device configuration along with the specular c-Si/(native-oxide)/(n-type a-Si:H) substrates for RTSE, as shown in Fig. 5(b). Deposition parameters included a vhf plasma power of 0.05 W/cm2 and a total gas pressure of  0.2 Torr. In order to obtain high-efficiency middle-junction cells, the substrate temperature of 107 1C used for the top-cell Si:H is increased to 170 1C, as determined by in-situ SE calibrations as described in Section 2.1 [54]. The flow ratio G¼[GeH4]/{[Si2H6]þ [GeH4]} was set at 0 for the top i-layers, resulting in growth rates ranging from  2.3 to  0.8 Å/s as R increases from 60 to 150. For the middle-cell i-layer, G was set to 0.286, resulting in growth rates ranging from  2.6 to  1.1 Å/s as R increases from 45 to 150.

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Table 1 Deposition conditions for the Si:H-based multijunction component i-layers used in the top, middle, and bottom cells fabricated by vhf PECVD. The multijunction structure is shown in Fig. 5(a). The RTSE-developed growth evolution diagrams for these i-layers were correlated with single-junction solar cell performance applying the deposition configuration of Fig. 5(b). Layer type

Deposition gas pressure (mTorr)

VHF (70 MHz) plasma power (W/cm2)

Calibrated substrate surface temperature (1C)

Gas flow ratios R ¼[H2]/{[SiH4] ( þ GeH4)} G ¼ [GeH4]/{[SiH4] þ[GeH4]}

Intended thickness (Å)

Deposition rate (Å/s)

Top-cell i-layer Middle-cell i-layer Bottom-cell i-layer

200 200 200

0.05 0.05 0.05

107 170 107

R ¼ 60, 70, 80, 100, 115, 120, 130, 140, 150; G ¼0 R ¼ 45, 60, 70, 80, 100, 120, 135, 150; G ¼ 0.286 R ¼ 40, 60, 80, 100, 105, 110, 115, 120, 140; G ¼0

2000 2000 5000

2.3  0.8 2.6  1.1 3.5  1.2

these layers. With the exception of the Si2H6 flow, the deposition conditions for the bottom-cell i-layer were the same as those of the top-cell i-layer. In particular, the substrate temperature for the bottom-cell i-layer was T ¼107 1C, rather than the standard optimum of  200 1C [37], in order to compare the growth evolution diagram to that of the similarly-prepared top-cell i-layer. The Si2H6 flow rate was 4 sccm for the bottom cell, as compared with 2 sccm for the top cell in order to evaluate the effect of reduced depletion on the growth evolution diagram. The Si:H growth rates at this higher Si2H6 flow ranges from 3.5 to 1.2 Å/s as R increases from 60 to 140. The RTSE analysis approaches have been described in greater detail in Section 2.1. RTSE data of this section were obtained using a rotating-compensator multichannel instrument [55,62], enabling determination of ε of the growing film as well as db(t) and ds(t) for films growing uniformly with thickness [63]. From db(t), the instantaneous deposition rate r(t) can be determined. The VIA technique is applied for films whose phase and optical properties are evolving continuously with thickness, yielding fnc(db) as in Fig. 1(b) [59]. The i-layer microstructure was also investigated through cross-sectional TEM images obtained using a JEOL-3011 HR-TEM which assisted in the corroboration of the RTSE analysis results. 3.2. Results and discussion

Fig. 6. (a) Real and (b) imaginary parts of the dielectric function (ε1, ε2) of the bulk component of a mixed-phase (aþ nc)-Si:H n-layer obtained from an exact inversion of RTSE data at the end of the deposition (points). The inset shows a schematic diagram of the substrate and (a þ nc)-Si:H n-layer on which the Si:H i-layer of the bottom cell is over-deposited; analysis was performed by RTSE. Also shown (solid line) is a best fit to the inversion results using the structure of the bulk layer depicted in the inset.

For the bottom cells, the growth evolution diagram for nc-Si:H i-layers was developed using similar substrate structures, the exception being underlying (a þnc)-Si:H n-layers having an 0.6/0.4 volume fraction mixture of a-Si:H/nc-Si:H. The deduced room temperature ε and structure of a typical n-layer are shown in Fig. 6. In fact, this dielectric function is characteristic of a film containing a significant nc-Si:H component, as indicated by a well defined peak in the imaginary part ε2 at 4.1 eV and a shoulder at 3.5 eV [50]. The physical thickness of this layer is  108 Å, which includes the bulk layer and surface roughness layer thicknesses. The importance of this investigation is that it directly correlates PECVD growth evolution diagrams for the  0.4–0.6 μm thick ncSi:H i-layers with the performance of n–i–p devices incorporating

Fig. 7(a) shows the contours of the growth evolution diagram for the top-cell i-layer deposited on the a-Si:H n-layer as described in the previous section. These results were obtained using the VIA technique designed in this case to extract the relative volume fraction of nc-Si:H in the top  10 Å of the bulk layer along with the bulk layer thickness from an integration of the instantaneous deposition rate. This diagram demonstrates that, under the vhf PECVD conditions used here, the Si:H films deposited on a-Si:H n-layers remain amorphous throughout at least 2000 Å of bulk layer growth for Rr80. The upward-pointing arrow on the a-(aþnc) transition data point for the R¼80 deposition in Fig. 7(a) indicates that this transition occurs at a thickness greater than  2000 Å. The 2000 Å thickness is of interest because that is the final thickness of the i-layer, and so is also the total i-layer thickness in the co-deposited devices. At higher R (100rRr150), the Si:H films initially nucleate as a-Si:H in the protocrystalline regime but undergo the a-(aþnc) transition starting from a thickness that decreases with increasing R. The surface roughening onset, which identifies the nominal a-(aþnc) transition given by the solid line in Fig. 7(a), provides sensitivity to this transition at a nanocrystalline volume fraction of o0.02 within the bulk layer near-surface. The difference in Fig. 7(a) compared to Fig. 2 is attributed to the use of Si2H6 which significantly increases the R values at which the phase transitions occur. Fig. 7(b) shows the growth evolution diagram for the middlecell Si1  xGex:H, demonstrating that the structural and phase evolution of the Si1  xGex:H exhibits behavior analogous to that of the Si:H in Fig. 7(a). This diagram shows that the Si1  xGex:H

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Fig. 8. Nanocrystalline volume fraction in the top 10 Å of the accumulating bulk layer, yielding a depth profile versus the bulk layer thickness for the (a) R¼ 100 and (b) R=115 Si:H films of the bottom-cell series, as determined from RTSE and VIA. The inset in (a) shows a TEM image of the bottom-cell R¼ 100 i-layer with a nc-Si:H cone terminating into the bulk due to the dominant growth of amorphous material from the amorphous component of the n-layer.

Fig. 7. A growth evolution diagram for (a) vhf PECVD top-cell Si:H i-layers and (b) middle-cell Si1  xGex:H i-layers with G ¼0.286 as deposited on a-Si:H n-layers. The diagram depicts the thicknesses of the a-(a þnc) transition (solid line, squares) and the (a þnc)-nc transition (dashed line, solid circles). Upward arrows extending from data points indicate that the transitions occur at thicknesses above the indicated values. Contour lines in the crystallite volume fraction fnc are also plotted. The optimum one-step process for a 2000 Å thick layer is shown. (Adapted with permission from Ref. [15]).

films remain amorphous throughout  2000 Å of bulk layer growth for Rr 70, as indicated by the upward-pointing arrow on the a-(a þnc) transition data point at R ¼70 in Fig. 7(b). At higher H2-dilution levels (80 rRr150), the films initially nucleate on the underlying n-layer as a-Si1  xGex:H but undergo the a-(a þnc) transition at a thickness that decreases with increasing R. Fig. 7(b) shows that although the a-(a þnc) transition obtained from the roughening onset (solid line) is sensitive to nanocrystalline volume fractions of o0.02 in the near-surface of the bulk layer at low R, sensitivity degrades at higher R as the a-(a þnc) transition shifts to lower thickness. The shallower contour slopes in fnc for Si1  xGex:H in Fig. 7(b) compared to those for Si:H in Fig. 7 (a) can be explained by a broader distribution of thicknesses at which the a-(a þnc) transition occurs for individual nuclei. Fig. 8 shows results for the evolution of the relative nc-Si:H volume fraction in the Si:H bottom-cell i-layers deposited with R¼ 100 and R ¼115. The underlying films are (a þnc)-Si:H n-layers whose typical structure appears in the inset of Fig. 6. In the early stages of growth, both films in Fig. 8 exhibit phase compositions similar to that of the underlying n-layer with 0.6/0.4 volume fractions of a-Si:H/nc-Si:H. For the film with R ¼115, nanocrystallites nucleate from the nanocrystalline phase of the underlying n-layer, grow preferentially, and ultimately coalesce to a nanocrystalline structure that is relatively stable upon continued

Fig. 9. A growth evolution diagram for vhf PECVD bottom-cell Si:H i-layers as deposited on mixed-phase (aþ nc)-Si:H n-layers. The contour lines in the nc-Si:H volume fraction fnc are depicted as well as the (a þnc)-a transition (squares) where fnc  0 and the (a þ nc)-nc transition (circles) where fnc  1. (Adapted with permission from Ref. [40]).

growth. At R¼ 100, however, the i-layer grows initially as mixedphase Si:H and evolves to pure a-Si:H with fnc ¼0 due to the preference for amorphous growth. Thus, the growth evolution diagram in Fig. 9 for the bottom-cell Si:H i-layers, deposited on the mixed-phase a-Si:H/nc-Si:H n-layers with 0.6/0.4 volume fractions, exhibits different behavior than that of the top-cell Si:H i-layers grown on a-Si:H n-layer surfaces, as shown in Fig. 7(a). In Fig. 9, the volume fraction of nc-Si:H in the initial stage of growth ( o150 Å) increases continuously with increasing R, with values of Ro105 suppressing the substrate-imposed crystallinity and R 4105 enhancing the substrate-imposed crystallinity. For example at db  100 Å, fnc increases from  0.1 to  0.4 and then to 1.0, a stable nanocrystalline structure, as R increases from 40 to 105 and then to 140. As the thickness is reduced, however, the structure is dominated by the substrate such that fnc remains constant at the substrate value of 0.4 with increasing R. Thus, initial-stage mixed-phase Si:H growth in Figs. 8 and 9 results from a template or memory effect imposed

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by the underlying (a þnc)-Si:H n-layer. At lower H2-dilution levels (R o105), the mixed-phase i-layers evolve to a-Si:H due to the preference for amorphous growth. This preferential amorphous growth is suggested by the TEM image in the inset of Fig. 8, whereby the dominantly growing phase is amorphous, resulting in the decay of nanocrystalline clusters that terminate  1000 Å into the bulk layer. Support for the SE and TEM interpretations come from the open-circuit voltage of the co-deposited devices, to be discussed later in this section. In the range of Ro105, the (a þnc)-a transition shifts to larger thickness with increasing R. At higher H2-dilution (R4105), the initial mixed-phase material rapidly evolves to nc-Si:H due to the preference for nanocrystalline growth. In this regime, the (a þnc)-nc transition shifts to lower thickness with increasing R as in the standard growth evolution diagrams of Figs. 2 and 7(a) and (b). The interesting feature of Fig. 9 is the bifurcation that occurs at a H2-dilution value of R¼105, which divides the ultimate phase of the film between amorphous and nanocrystalline – even though the film appears to nucleate as a common mixed-phase (aþ nc)-Si:H. In this region, the ultimate phase is likely to be influenced by perturbations in the deposition conditions and the nature of the substrate including its surface roughness. In addition, the phase is expected to be sensitive to position over the substrate surface due to even the slightest spatial variations in conditions, an aspect that will be addressed in Sections 4 and 5. By characterizing the phase evolution and quantifying the phase composition as in Figs. 7(a) and (b) and 9, it may be possible to select H2-dilution levels in order to maximize film quality for one-step, multi-step, or even graded layers. In the case of a 2000 Å thick a-Si:H i-layer for the top cell, the optimum one-step deposition process is predicted to occur on the basis of the growth evolution diagram at the maximal value of R¼80, i.e., the largest R value possible such that the i-layer remains amorphous throughout its thickness during growth. This expectation is borne out in device studies reported elsewhere [15,40]. These device studies reveal some basic correlations observed between the growth evolution diagram and (Voc, FF) of n–i–p solar cells. When the a-(a þnc) transition occurs within the i-layer such that mixedphase material appears at the i/p interface, then Voc is observed to decrease from values typical of an amorphous i-layer toward those typical of a nanocrystalline i-layer. Nanocrystalline cell Voc values, ranging from 0.4 to 0.6 eV are obtained when the (aþ nc)-nc transition occurs within the i-layer, leading to coalesced nanocrystals at the i/p interface. In general, the FF drops when the cone-like growth of either the nanocrystalline phase evolves from an amorphous phase or vice versa. The next paragraphs focus on the observation of similar such behavior for the a-Si1  xGex:H of the middle cell. Fig. 10 shows results for the open-circuit voltage and efficiency obtained for the a-Si1 xGex:H devices co-deposited with the i-layers studied by RTSE as shown in Fig. 7(b). For these devices, the one-step optimized i-layer process for a 2000 Å thickness is expected at R¼70 according to the same maximum H2-dilution principle that applies for the a-Si:H top-cell devices [15,40]. In fact, the optimum is revealed as predicted in the device performance of Fig. 10(b), but much less distinctly. Above R¼70, a detectable volume fraction of nanocrystalline Si1  xGex:H is present in the near-surface of the film ranging from fnc ¼0.05 at R¼80 to fnc ¼0.08 at R¼100, as obtained from the Fig. 7(b) growth evolution diagram. In contrast to the results for Si:H [15,40], the presence of a small volume fraction (o0.1) of nanocrystallites at the i/p interface of the Si1 xGex:H solar cells does not significantly decrease Voc and efficiency. The lack of a strong effect caused by the i/p interface crystallites in Si1 xGex:H may be due to the inhomogeneous nature of crystallite nucleation as indicated by the much flatter contour lines on the growth evolution diagram in Fig. 7(b). Thus, the range

Fig. 10. (a) Open-circuit voltage, Voc, and (b) efficiency, η, as functions of the H2dilution ratio R for vhf PECVD single-junction n–i–p solar cells incorporating middle-cell Si1  xGex:H i-layers. Underlying the i-layers in these cells, a-Si:H n-layers are used. The volume fractions of nc-Si:H within the top  10 Å of the i-layer of the solar cell are shown; the vertical line indicates the a-(aþ nc) transition for a 2000 Å thick i-layer. The vertical arrow indicates the optimum single-step i-layer deposition process (Adapted with permission from Ref. [15]).

Fig. 11. (a) Fill-factor, FF, and (b) open-circuit voltage, Voc, as functions of the H2dilution flow ratio R¼ [H2]/[Si2H6] for vhf PECVD single-junction solar cells incorporating bottom-cell Si:H i-layers. Mixed-phase (a þnc)-Si:H n-layers are used in these cells. The vertical line indicates the R¼ 105 bifurcation between a-Si:H growth at low R and nc-Si:H growth at high R – in the limit of large thickness. The arrow indicates the optimum single-step nc-Si:H i-layer deposition process. (Adapted with permission from Ref. [40]).

of 70oR≤100 in Fig. 10 is avoided in device fabrication due to irreproducibility and poor yield, including a strong dependence on the n-layer structure when mixed-phase (aþnc)-Si:H n-layers are generated by a template effect from the underlying nc-Si:H bottom cell. A much more significant drop in performance with a decrease in Voc to o0.6 V occurs for R¼120 which can be attributed to an abrupt increase in the volume fraction of crystallites at the i/p interface (to 0.44 for the co-deposited i-layer). In the case of 0.4–0.6 μm thick nc-Si: H bottom-cell i-layers, a comparison of the growth evolution diagram of Fig. 9 and the device performance of Fig. 11 shows that the optimum one-step deposition process is found to occur at the minimal value of R¼110, i.e., the smallest R value possible such that the i-layer evolves to a structurally-stable nc-Si:H film during its growth. At R¼100 the (a þnc)-a transition occurs at a thickness of 1500 Å, and it is clear from the Voc value of 0.95 V in Fig. 11(b) that the top of the film is a-Si:H. At R ¼120 the (a þnc)-nc transition occurs at

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a thickness of 2000 Å, and in this case, it is clear from Voc value of 0.46 V in Fig. 11(b) that the top of the film is nc-Si:H. The highest performance nc-Si:H i-layer from Fig. 11(a) is obtained at R ¼110, just before a more rapid drop in FF associated with the bifurcation region where an  0.5/0.5 mixture of a-Si:H/nc-Si:H propagates throughout the film bulk. The continued lower FF for the low R a-Si:H films in Fig. 11(a) is attributed to the nc-Si:H phase at the bottom of the i-layer (  400 Å thick for R¼ 60) transitioning to a-Si:H within the bulk of the i-layer. It should be noted that the overall bottom-cell performance at the optimum of R¼110 can be increased by using an elevated substrate temperature (i.e., 200 1C rather than 100 1C, calibrated values) [37]. Finally, the differences in the growth evolution diagrams of Figs. 7 (a) and 9 cannot be attributed solely to the substrate. For example, in Fig. 7(a) at R¼ 100, the film undergoes an a-(aþnc) transition at 600 Å, whereas in Figs. 8 and 9, the film undergoes the reverse (aþnc)-a transition at 1500 Å. The origin of the phase difference of the ultimate Si:H film lies in the lower Si2H6 flow of 2 sccm for the top-cell i-layer compared with the flow of 4 sccm for the bottom-cell i-layer. Lower flows of Si-containing gas promote depletion conditions and a tendency for nanocrystalline development at lower R values and thicknesses in the protocrystalline regime [64]. In order to gain a better understanding of the growth processes of mixed-phase Si:H and Si1 xGex:H thin-film materials, the nature of conical growth behavior as observed previously for Si:H [29,59] has been explored. The conical growth geometry was described previously and is depicted in Fig. 4(b). In the previous work, it was demonstrated that cone angles can be estimated from RTSE and that the results are in good agreement with TEM images [59]. In the present study, in addition to selected TEM measurements of cone angles, two methods based on RTSE have been employed. The first is a simplified version of that described in Ref. [59]. In this case, θ cos  1[Δdb/(Δds þΔdb)], as described in Section 2.2. This expression is based on assumption that in the nanocrystalline growth regime the nanocrystalline phase grows faster than the amorphous phase, leading to a spherically-shaped cap on each conical nanocrystalline structure [65]. The nucleation density can also be determined using the same transition information, also described in Section 2.2. The second RTSE method of cone angle determination derives directly from the deposition rates according to θ¼cos  1(ra/rnc),

Fig. 12. Estimations of (a) cone angle, θ, and (b) nucleation density, Nd, based on RTSE data and TEM. The cone angle and nucleation density were extracted from the changes in surface roughness and bulk layer thicknesses that occur from the a-(aþ nc) transition to the (aþ nc)-nc transition. The cone angle was also estimated from the ratio of deposition rates in the single-phase amorphous and the structurally-stable nanocrystalline growth regimes. (Adapted with permission from Ref. [40]).

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where ra and rnc are the rates for the amorphous and nanocrystalline phases. Fig. 12(a) presents accumulated cone angle data for the vhf PECVD top-cell Si:H and middle-cell Si1 xGex:H films of this study plotted versus the a-(aþ nc) transition thickness. The cone angle data were obtained from TEM and from the two RTSE methods, and the a-(aþ nc) transition thickness was obtained from RTSE as the roughening transition. Also shown are the nucleation densities. Agreement among the three methods for cone angle is reasonable, with the first RTSE method based on Δdb and Δds providing very clear trends in the cone angle and nucleation density (solid lines). The larger error bars for the cone angles from the deposition rate ratio arise from taking the ratio of two rates that are relatively close. For the R¼150 a-Si1 xGex:H film with a cone angle of  271, for example, the rates are ra ¼1.0470.025 Å/s and rnc ¼ 1.1770.025 Å/s, which gives rise to an error bar range on θ of  101. A reduction in cone angle with increasing a-(aþ nc) transition thickness is expected as the amorphous phase growth rate increases toward the nanocrystalline phase growth rate. The agreement in cone angles provides support for the model of cone growth kinetics in terms of a higher growth rate of one phase over the other [65]. Differences are highlighted in Fig. 12 between these vhf PECVD results using Si2H6 as the source and previous results using rf PECVD with SiH4 as the silicon source (dashed lines) [29,59]. The rf PECVD films exhibit a high nanocrystallite nucleation density, implying that once crystallites nucleate, there is a shorter range of bulk layer thickness before coalescence is observed. In addition, the cone angles for rf PECVD films appear to be smaller and less dependent on R. These differences are of continuing interest and require further investigation.

4. RTSE monitoring and off-line SE mapping of Si:H thin-films in roll-to-roll deposition 4.1. Experimental methods In the roll-to-roll fabrication and characterization of the n–i–p a-Si:H solar cell structures, sputtered Ag/ZnO:Al, PECVD a-Si:H n and i-layers, as well as a PECVD Si:H p-layer were all deposited onto Cr-coated flexible polyethylene naphthalate (PEN) polymer and studied by RTSE. From the RTSE monitoring and off-line SE mapping studies of this structure, only results for the i-layer and p-layer of the n–i–p solar cell are reviewed in this section, although such results have been obtained on the underlying layers as well. In fact, it was necessary to characterize the three deposition steps (Ag/ZnO:Al/n-layer) by RTSE before the absorber i-layer was analyzed by RTSE. First, the PEN roll was fully coated with Cr, which acts as an adhesion layer. Next an opaque Ag layer was deposited, followed by a ZnO:Al layer to form the Ag/ZnO:Al back-reflector structure. The Cr, Ag, and ZnO:Al depositions were performed by magnetron sputtering at room temperature, using an Ar sputtering gas pressure of 5 mTorr. For the ZnO:Al, the substrate speed was chosen to be 0.015 cm/s in order to obtain a final ZnO:Al thickness of  3000 Å. Next, a thin a-Si:H n-layer was deposited by PECVD under conditions including a calibrated substrate temperature of 110 1C, gas flows of 10 sccm for SiH4 and 1 sccm for the dopant gas (5% PH3 in H2, resulting in D ¼[PH3]/[SiH4] ¼0.005), a total gas pressure of 0.35 Torr, and an rf plasma power of 0.013 W/cm2. The substrate speed was chosen to be 0.13 cm/s so that the final n-layer thickness reached  200 Å. For the a-Si:H i-layer, the deposition conditions included the same substrate temperature of 110 1C, gas flow rates for SiH4 and H2 of 25 sccm each, yielding R¼1, a total gas pressure of 0.4 Torr, and an rf plasma power density of 0.019 W/cm2. Table 2 summarizes these deposition

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Table 2 Deposition conditions for the a-Si:H n–i–p solar cells deposited on flexible PEN polymer substrates in a cassette roll-to-roll system. Layer type

Deposition pressure (mTorr)

rf Plasma power (W/cm2)

Calibrated Substrate temp. (1C)

Gas flows (sccm) and ratios: R¼ [H2]/[SiH4]; D¼ [doping-gas]/[SiH4]

Roll-to-roll speed (cm/s)

Intended thickness (Å)

[Ar]¼ 10 [Ar]¼ 10 [Ar]¼ 10 [SiH4]¼ 10; {5 vol% [PH3] in H2} ¼1 R¼ 0.1, D ¼ 0.005 [H2]¼ 25; [SiH4] ¼25 R¼ 1 [H2]¼ 300; [SiH4]¼ 2; {5 vol% [B2H6] in H2} ¼0.5 R¼ 150; D ¼0.0125

0.02 0.02 0.015 0.13

1000 2000 3000 200

Normal: 0.012 Reduced: 0.0086 Slow: 0.015 Fast: 0.020

2000 2800 800 500

Cr Ag ZnO n-Layer

5 5 5 350

0.73 0.73 0.73 0.013

RT RT RT 110

i-Layer

400

0.019

110

p-Layer

1500

0.13

110

located at the very end of the deposition zone (at the “leading end“ of the substrate) at the time of plasma ignition. The simple result is def f ðxÞ ¼ Ro ðx  xo Þ=vp ;

Fig. 13. (a) Schematic multilayer n–i–p a-Si:H solar-cell structure fabricated in a cluster-tool deposition system with flexible substrates carried by a roll-to-roll cassette; (b) the monitoring configuration used for RTSE studies of thin-film a-Si:H i-layers and Si:H p-layers deposited by PECVD in the structure of (a). (Adapted with permission from Ref. [43]). The monitoring point is at the center of moving substrate 13 cm from the entrance to the 18 cm long plasma zone. The substrate is 15 cm wide.

conditions and Fig. 13(a) shows the resulting n–i–p solar cell structure. The substrate traveled at a constant linear speed during the plasma ignition and full deposition of the i-layer as shown in Fig. 13(b); RTSE was performed throughout the process. In reviewing the RTSE analysis results obtained in the roll-to-roll PECVD i-layer process, the focus is on the effective thickness deff, or the volume of i-layer material per unit substrate area. The components that determine deff include the n/i interface roughness layer with thickness di and variable i-layer volume fraction fi, in addition to the bulk and surface roughness layers of thicknesses db and ds, respectively. Thus, the resulting summation is deff ¼ fidi þdb þ0.5ds, with the four values on the right side obtained via in-situ SE and/ or RTSE analysis. The effective thickness is modeled assuming a constant deposition rate Ro within the deposition zone, yielding an expression given in terms of the distance x along the substrate length from a reference position xo. The substrate position xo is

xo r x r xo þ xp ;

ð1Þ

where vp is the adjustable speed of the substrate and xp ¼ 18 cm is the length of the PECVD zone. For values of x oxo, deff ¼ 0 since this region is outside the deposition zone and moves away from the zone with time. For values of x 4xo þxp, deff reaches its final value of deff ¼Roxp/vp, as this portion of the substrate has passed completely through the 18 cm of the deposition zone. Thus, the leading end of the substrate spans the range of x given by xo r xr xo þ xp, over which the thickness increases linearly with position x. In fact, this leading end of the substrate is generally discarded in the manufacturing process, but with RTSE monitoring it provides valuable information on the process and properties of the film. Both normal-speed (0.0120 cm/s) and reduced-speed (0.0086 cm/s) depositions of the i-layer were performed under identical deposition conditions. Normal speed refers to the substrate speed yielding the desired effective thickness in the device after a full traversal of the deposition zone, which is obtained for xZxo þxp; in this case deff ¼Roxp/vp  3000 Å. In contrast, a reduced speed refers to the substrate speed vp,r yielding the desired thickness deff ¼Roxp,r/vp,r  3000 Å at the fixed RTSE monitoring point, which is characterized by x¼xo þxp,r ¼xo þ13 cm in Eq. (1) based on the fact that the monitoring point is located 13 cm from the point at which the substrate enters the deposition zone and 5 cm from the point of exit. Thus, under conditions of constant deposition rate, the reduced speed is given simply by vp,r ¼(xp.r/xp) vp ¼ (13/18) vp ¼ 0.72 vp. Furthermore the reduced-speed effective thickness at a given location x (measured relative to xo) is given by deff,r(x)¼(vp/vp,r)deff(x), and so should be increased by a factor of 18/ 13¼ 1.40 relative to the normal-speed effective thickness. Deviations from these simple relationships have been observed and can be attributed to variations in Ro with time and thus, substrate position during deposition. Such variations can be attributed to initial plasma transients, to a-(aþnc) and (aþnc)-nc transitions during deposition, or to drifts in the deposition process. As the last rf PECVD Si:H step, the p-layer was deposited on the Ag/ZnO/n-layer/i-layer with the standard substrate temperature of 110 1C; gas flows of 2 sccm SiH4, 300 sccm H2, yielding R ¼150, and 0.5 sccm dopant gas (5% B2H6 in H2; resulting in D ¼[B2H6]/ [SiH4] ¼0.0125); a total pressure of 1.5 Torr; and a rf power density of 0.13 W/cm2. Two p-layer depositions were performed along different lengths of the substrate, at substrate speeds of 0.015 and 0.020 cm/s. For these depositions, the final effective p-layer thicknesses reached  800 Å and  500 Å, respectively, after the substrate passed through the 18 cm deposition zone, as determined by ex-situ mapping SE. Thicker p-layers than those used in the devices were studied in this case in order to observe clearly the a-(a þ nc) transitions. Because the RTSE monitoring point is

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located 13 cm from the substrate entrance to the deposition zone and 5 cm from the substrate exit, RTSE provides information on a fraction of 13/18  0.72 of the total effective thickness development, respectively. Thus for 800 Å and 500 Å thick p-layers, only the first  580 Å and 360 Å can be observed. The deficits from 800 Å and 500 Å are due to the deposition that occurs over the 5 cm length beyond the monitoring point [see Fig. 13(b)]. RTSE during the i-layer and p-layer depositions was performed using a commercially-available single rotating-compensator multichannel instrument (J.A. Woollam Co., M2000-XI) that can provide (ψ, Δ) spectra from 0.75 to 5.8 eV. Rotating-compensator instrument designs and operational principles are described in the literature [55,62]. To improve precision, pairs of (ψ, Δ) spectra were collected within a time of  1 s, as averages over a number of optical cycles. During the acquisition time for one pair of (ψ, Δ) spectra,  1–2 Å and 0.4–0.7 Å in the effective thickness of the respective a-Si:H i-layer and p-layer materials accumulate on top of a stationary film stack. Thus, in roll-to-roll deposition, the coated substrate moves  0.08–0.2 mm during this acquisition time. Analyses of all spectra involve numerical inversion, leastsquares regression, and VIA algorithms as described in Section 2.1 [56,59,63]. The angle of incidence for all SE measurements during depositions was fixed at a value within the range of 70.01 70.61. The studies of the roll-to-roll processes of the i-layer and p-layer are divided into two parts, one focusing on RTSE analysis of the deposition process along the center line of the advancing roll-to-roll PEN polymer substrate, and the other focusing on ex-situ mapping SE of the resulting layers. Thus, to complement the RTSE, the thickness uniformity of the i-layers and p-layers across the width of the substrate was evaluated by ex-situ mapping SE using a commercially-available instrument (AccuMap-SE, J.A. Woollam Co.). The (ψ, Δ) spectra for ex-situ mapping were collected from 0.75 to 6.5 eV. In order to improve the signalto-noise ratio in mapping, data acquisition was performed with a 10 s optical cycle averaging time. The grid size in mapping was 1 cm2 and the angle of incidence was fixed at 65.01. At this angle, the ellipsometer beam forms an elliptical spot on the surface with a 1.5 mm major axis. 4.2. Results and discussion Analysis of the PECVD process of the i-layer film on (Ag/ZnO/nlayer)-coated PEN polymer required characterization of the underlying layers. The individual layer optical properties required to obtain the thickness evolution of each film were obtained in-situ from single spectra taken after depositing each layer in succession. The Ag and ZnO optical properties were generated by fitting the (ψ, Δ) spectra using Drude behavior for the free electrons in the low-photon-energy near-IR region and one or more critical point resonances for the bound electrons in the high-photon-energy UV region [50]. The amorphous n-layer optical properties were generated from best-fit parameters obtained using the Cody– Lorentz oscillator expression, which is a band-gap-modified Lorentz oscillator with an assumed constant dipole matrix element as described in Section 2.1. In this case due to the thinness of the n-layer, however, all oscillator parameters were coupled to the deduced band gap through the same relations for i-layers given elsewhere [48]. The i-layer complex dielectric function ε was determined from the RTSE data at a thickness of  200 Å applying the Σs-minimization method described in Section 2.1, over a range of time points during which the i-layer thickness varied by  50 Å. It should be noted that the n/i interface roughness layer thickness is selected as the roughness layer thickness on the underlying n-layer, determined through in-situ SE analysis of the n-layer. The resulting i-layer ε obtained by

13

Fig. 14. (a) Real and (b) imaginary parts of the a-Si:H i-layer dielectric function obtained by inversion (open points) from a deposition at normal substrate speed (0.012 cm/s), yielding the desired thickness at the end of the deposition zone. Also shown are the results of a model obtained by applying a Kramers–Kronigconsistent, band-gap-modified Lorentz oscillator (Cody–Lorentz model; lines). (Adapted with permission from Ref. [41]).

inversion was fit using the analytical Cody–Lorentz oscillator expression for smoothing [48]. Both the inverted and smoothed dielectric functions of the i-layer are presented in Fig. 14. The parameters obtained here are consistent with those reported previously for a-Si: H i-layers measured at room temperature, after accounting for linear adjustments according to the elevated temperature of measurement (110 1C) [66]. Fig. 15(a) shows the evolution of i-layer effective thickness as obtained using the time-independent analytical ε spectra shown in Fig. 14. Returning to the expression deff ¼ fidi þdb þ0.5ds, Fig. 15(b)–(d) shows the thin-film components from which deff is calculated including db, ds, and fi, respectively. The deduced effective thickness is relevant for the monitoring point and a normal substrate speed of 0.012 cm/s was used. The initial i-layer growth is modeled by considering an interface filling mechanism starting from n-layer surface roughness [67]. This is simplified by the fact that in this analysis the underlying Ag is deposited at room temperature, yielding a specular film. So in this specular case for n/i interface formation, the 38 Å thick surface roughness on the n-layer is assumed to consist of 0.5/0.5 vol. fraction n-layer/void before i-layer deposition. After the onset of i-layer deposition, the void component is filled in by the i-layer material in about 30 s as shown in Fig. 15(d). During this time, the i-layer surface roughness increases to  50 Å, indicating nearly conformal coverage of the n-layer by the i-layer. During bulk i-layer growth, however, the surface roughness on the i-layer decreases and stabilizes at  25 Å, which is thinner than the starting roughness on the n-layer thereby indicating a smoothening effect of i-layer deposition on the amorphous n-layer. In Fig. 15(a), good agreement is observed between the measured and simulated thickness assuming a constant deposition rate. The measured effective thickness is slightly higher in the

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Fig. 16. Evolution of the effective i-layer thickness during reduced-speed roll-toroll deposition (0.0086 cm/s) on a (Cr/Ag/ZnO:Al/n-layer)-coated polymer substrate, yielding the desired final thickness at the monitoring point (circles), followed by normal-speed deposition (0.012 cm/s), yielding the desired final thickness at the end of the deposition zone (triangles). The thickness evolution entirely at normal substrate speed is also included (squares). A comparison of the broken and solid lines at the end of the two depositions is a measure of deposition reproducibility upon stopping and restarting the plasma for reduced speed followed by normal speed deposition. The deviation from the prediction of ideal deposition in the transition from steady-state reduced speed to steady-state normal speed results from striking the plasma at higher power and pressure levels. (Adapted with permission from Ref. [41]).

Fig. 15. Evolution of (a) the i-layer effective thickness during normal-speed (0.012 cm/s) roll-to-roll deposition on a (Cr/Ag/ZnO:Al/n-layer)-coated polymer substrate; the inset shows the thickness stability. Evolution of (b) the i-layer bulk thickness; (c) the i-layer surface roughness thickness; and (d) the i-layer volume fraction within the n/i interface roughness layer; the inset in (d) shows the latter volume fraction on an expanded time scale during interface filling. The effective thickness in (a) is given as a sum of the interface roughness, bulk, and surface roughness components according to deff ¼ fidi þ db þ 0.5ds, where fi is the interface i-layer volume fraction and di is the interface roughness thickness, fixed at di ¼ 37.9 Å. (Adapted with permission from Ref. [41]).

region of linear increase due to the higher deposition rate during plasma ignition, which is performed in this experiment at higher rf power and pressure than the steady-state values. Once the substrate length exposed to plasma ignition passes by the monitoring point, the measured effective thickness stabilizes, and thus the simulation better matches the experimental results. In subsequent studies, the deviation from linear behavior has been reduced by depositing the i-layer at the operating rf power and pressure by igniting the plasma using a heated filament. The inset focuses on the stability of the steady-state thickness value, which varies by no more than  20 Å as 10 cm of the polymer substrate passes after thickness stabilization. Similar behavior as that of Fig. 15(a) is observed for an i-layer deposition at the reduced substrate speed of 0.0086 cm/s as shown in Fig. 16 (upper data set, x o18 cm). This deposition at reduced substrate speed enables one to observe the final target thickness at the RTSE monitoring point (see Fig. 16; upper data set, 13o xo18 cm). In fact at the 18 cm point, the final reduced-speed thickness has been deposited on the trailing end of the substrate

exiting the plasma zone. After this 18 cm substrate length has passed through the deposition zone, the plasma is terminated and the substrate motion is stopped simultaneously. In a second deposition on this same substrate, the motion is re-started under the normal-speed conditions and the plasma is re-ignited essentially simultaneously. This normal-speed deposition that follows the reduced-speed one without loss of continuity (see Fig. 16; upper data set, 18 ox o31 cm), however, deviates substantially from the simulated result assuming a constant deposition rate. This effect is due to the re-starting of the plasma, and also the higher sensitivity to the plasma ignition transient in this process. In addition, re-igniting the plasma under the same conditions, yielding the same steady state plasma power as the first normalspeed deposition, leads to a final effective thickness rate that is somewhat different from that during the first normal-speed deposition (see Fig. 16; lower data set). The final thickness after a complete pass through the deposition zone for the reduced/ normal speed deposition is 6.5% less (1940 Å) than the final thickness observed at the end of the first normal-speed deposition (horizontal broken line at 2076 Å). This demonstrates the ability of the RTSE method to identify property irreproducibility due to process variability (such as power coupling into the plasma) on an initial leading end of the substrate, which is then cut off in the manufacturing process for possible further ex-situ study. The leading end of the roll-to-roll-deposited i-layer on (Ag/ ZnO:Al/n-layer)-coated PEN polymer moving at normal speed, was analyzed ex-situ by mapping SE. From the leading end of a roll-toroll substrate, mapping essentially provides the same information as an RTSE experiment, as one can measure film properties versus accumulated thickness in the process. The additional complexity of an ex-situ mapping measurement results from post-oxidation of the surface. The benefit of mapping compared to RTSE, however, is the ability to characterize the film thickness evolution at different locations across the substrate width. In Fig. 17, the mapping results of the i-layer show that the thickness variation is linear with substrate position. This observation supports the assumption of a constant deposition rate within the plasma zone. The difference in deposited thickness over a span of 13 cm (2076 Å in Fig. 16 versus  1800 Å in Fig. 17), however, is attributed to the higher deposition rate in the plasma striking. In

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Fig. 17. Map of the effective thickness for normal-speed deposition (0.012 cm/s) of the a-Si:H i-layer, with its leading edge at the left. The horizontal axis is the direction of substrate advance during deposition whereas the vertical axis scale defines the width of the substrate.

addition, the larger i-layer final thickness (  2650 Å) in Fig. 17 compared to the final thickness observed in real time (2076 Å in Fig. 16) is due to additional deposition occurring from the monitoring point to the end of the deposition zone. It should be recalled that the stable thickness in the RTSE process is obtained after the time required for the substrate to traverse the 13 cm length from the plasma zone entrance to the monitoring point. The data along the vertical axis in Fig. 17, from which the edge-toedge uniformity of the deposition can be evaluated, shows that the i-layer is thicker in the central portion than the edges. This may be due to a slight sagging of the flexible polymer substrate, when it moves through the deposition zone. The mapping results are of interest because they can identify sources of non-uniformity across the width of the substrate. Fig. 18 shows the evolution of the p-layer effective thickness (or film volume/area), which consists of individual interface roughness, bulk, and surface roughness layer thickness components as described earlier in this section. The plasma was ignited with a heated filament and the substrate speed for this deposition was 0.015 cm/s. Also shown is a prediction based on assumptions of (i) a time-independent deposition rate starting from plasma ignition, and also (ii) a position-independent rate along the center line in the first 13 cm of the deposition zone. Deviations from this prediction can be understood by considering the time evolution of the three components as shown in Fig. 19. Before p-layer deposition, a 28 Å thick microscopic roughness layer exists on the i-layer surface, as a 0.5/0.5 volume fraction mixture of i-layer/void. The relatively smooth i-layer surface is due to use of a specular Ag deposition process. The initial p-layer growth is modeled by considering a transition from i/p interface filling to bulk p-layer growth on the resulting i/p interface roughness layer [67]. At the onset of p-layer deposition, the void volume is filled by the p-layer material in a time of  1 min. During this time, the surface roughness on the p-layer increases to  28 Å, the same value as the i-layer surface roughness thickness, indicating conformal coverage of the i-layer by the thin p-layer. The bulk layer and surface roughness layer thickness evolution for the p-layer, as shown in Fig. 19(a) and (b), suggests that the p-layer grows initially in the amorphous phase. The layer undergoes an a-(a þnc) transition at  8 min, after  155 Å of bulk p-layer deposition when the surface roughness abruptly increases. Thus, the acceleration of the p-layer effective thickness in Fig. 18 may be attributed to a higher growth rate for the nc-Si:H phase relative to

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Fig. 18. Evolution of the effective thickness as measured by RTSE during roll-to-roll deposition of a thin Si:H p-layer at a substrate speed of 0.015 cm/s on an underlying a-Si:H i-layer; also shown is a prediction assuming a time and position-independent deposition rate Ro throughout the plasma zone. The assumed rate of Ro ¼0.51 Å/s is that associated with the amorphous phase as measured in the early stages of growth. (Adapted with permission from Ref. [43]).

the amorphous (or protocrystalline) Si:H phase [15,40]; this appears in the bulk layer thickness evolution in Fig. 19(a), as well. After the mixed-phase growth regime, the p-layer undergoes the (a þnc)-nc transition at  13 min when the surface roughness reaches its maximum and begins to decrease. This transition occurs after  320 Å bulk p-layer thickness. The decrease in surface roughness is attributed to the coalescence of the inverted conical crystallites that protrude above the surface; the result is a stable-phase nc-Si:H [59]. The bulk layer thickness saturates at 17 min, at which time the leading end of the substrate has fully crossed the deposition zone. For later times, all film characteristics should stabilize at the values obtained at 17 min; however, the continued decrease in surface roughness suggests temporal variation such that crystallite nucleation and coalescence are favored with increasing time after plasma ignition. This may occur if the plasma composition drifts due to a number of possible causes including powder formation, SiH4 depletion, and conditioning of internal chamber surfaces by the high-R plasma [68]. These a-(a þnc) and (a þnc)-nc transitions can be seen more clearly in the surface roughness evolution as a function of bulk p-layer thickness on a logarithmic scale, as shown in Fig. 20. Here Fig. 20(a) corresponds to the results in Fig. 19(b) whereas Fig. 20 (b) depicts the results for a higher p-layer substrate speed of 0.020 cm/s. From Fig. 20(b), it is clear that the p-layer deposited at 0.020 cm/s undergoes an a-(a þ nc) transition at 130 Å bulk p-layer thickness, but there is no clear transition to stable phase nc-Si:H even after a bulk p-layer thickness of 380 Å, in fact, beyond the transition thickness for the 0.015 cm/s deposition. At 380 Å, the bulk layer thickness saturates, indicating that the leading end of the roll has been fully coated. This comparison provides further support for the suggestion that the conditions within the deposition zone vary over time with a greater tendency for nanocrystallite development and coalescence with increasing time. At a higher substrate speed, the p-layer deposition is completed in a shorter time which suppresses this tendency. The ex-situ SE mapping results for the p-layer deposited at 0.015 cm/s are shown in Fig. 21. Here, the surface roughness evolution along the center line in Fig. 21(a) is in good agreement with that of the RTSE result shown in Fig. 20(a). The mapping results also demonstrate that the p-layer film initially grows in the a-Si:H (or protocrystalline) phase, transitions to mixed-phase (a þnc)-Si:H, and finally coalesces into a stable-phase nc-Si:H.

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Fig. 19. Evolution of (a) p-layer bulk thickness, (b) p-layer surface roughness layer thickness, and (c) p-layer volume fraction in the i/p interface layer during roll-toroll PECVD of a thin-film Si:H p-layer at a substrate speed of 0.015 cm/s on an underlying a-Si:H i-layer. In (c), a transition from i-layer surface roughness to i/p interface roughness at a fixed interface thickness of 28 Å occurs when the p-layer volume fraction reaches 0.5. (Adapted with permission from Ref. [43]).

Fig. 21. Maps of (a) the surface roughness layer thickness and (b) the bulk layer thickness for a p-layer deposited on (Cr/Ag/ZnO/n/i-layer)-coated PEN polymer at a substrate speed of 0.015 cm/s. The left side broken lines indicate the locations at which the a-(a þnc) transition occurs at the surface of the deposited p-layer. The right side broken lines indicate the locations at which the (aþ nc)-nc transition occurs at the surface of the p-layer. (Adapted with permission from Ref. [43]).

Fig. 20. Surface roughness evolution as measured by RTSE for p-layers deposited at substrate speeds of (a) 0.015 cm/s and (b) 0.020 cm/s. The results in (a) show an a(aþ nc) transition at the rapid rise in roughness where db  155 Å; the (a þ nc)- nc transition is observed as the roughness reaches its maximum where db  320 Å. The results in (b) show only an a-(a þnc) transition at db  130 Å. (Adapted with permission from Ref. [43]).

The mixed-phase roughening transition occurs when the surface roughness layer thickness is  30 Å. Above that transition, there is a continuous increase in the roughness layer thickness to  100 Å, as also indicated in the RTSE result of Fig. 20(a). Thus, the a(a þnc) transition line is drawn on the surface roughness thickness map where this abrupt increase is observed (left broken line).

Similarly, the (a þnc)-nc transition occurs where the surface roughness thickness reaches a maximum (right broken line). These two lines identify a spatially-resolved phase diagram, defining the locations of single-phase amorphous, stable-phase nanocrystalline, and mixed-phase p-layers at the top surface of the leading end of the substrate. By superimposing the phase boundaries onto the bulk layer thickness map, a spatially-resolved growth evolution diagram is obtained. This diagram relates the bulk layer thickness at which the transitions occur, not to the traditional variable R, but rather to the position on the substrate. On the p-layer diagram, the a(a þnc) transition is observed to occur at bulk layer thicknesses ranging from 30 Å to 200 Å and the (a þ nc)-nc transition is observed to occur at bulk layer thicknesses ranging from 300 to 600 Å, depending on the location on the substrate in both cases. The thickness maps in Fig. 21 enable one to evaluate the deposition uniformity across the width of the flexible substrate. From the contours in Fig. 21(b), it is clear that the bulk p-layer thickness is greater in the central region than at the edges. The effect appears to be enhanced in the nc-Si:H growth regime, in part due to the higher growth rate of the nc-Si:H phase coupled with the apparent lower nanocrystal nucleation density near the

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the spatial dependence of the bulk p-layer thickness at the transition can be estimated, thus generating the spatiallyresolved growth evolution diagram. The diagram of Fig. 22(b) shows that crystallite nucleation leading to the a-(aþnc) transition thickness occurs over a bulk p-layer thickness range from 70 to 140 Å. Lower transition thicknesses occur near the top edge of the substrate. As described earlier, the deposition clearly saturates at the top and center of the substrate before the p-layer undergoes the (aþnc)-nc transition. The hint of such a transition may be observed in the lower right edge of the map where the bulk layer thickness is largest. Across the width, once again, the bulk p-layer thickness within the central region is larger than that of the edges, indicating that the deposition rate peaks in the center and decreases toward the edges. Since the substrate speed determines the time during which the substrate resides within the deposition zone, the desired final thickness can be obtained by choosing the substrate speed accordingly. This is possible in a cassette roll-to-roll deposition system [42], but the substrate speed is constrained in continuous roll-toroll deposition. By optimizing the deposition parameters, in particular the gas flows, their ratios, and patterns, and ensuring that the flexible substrate is uniformly flat by maintaining constant tension across the width, a uniform p-layer can be obtained with the desired final thickness after passing through the deposition zone. A similar process can also be applied for studies of the i-layer used in the thin-film a-Si:H solar cells, in terms of the uniformity of thickness, phase, and optical properties; however, since this is an intermediate PECVD step prior to key junction formation, exposure of the i-layer to atmosphere is not desirable. Thus, an in-situ mapping SE tool would be most beneficial. Instrumentation meeting this need will be addressed in Section 5.3.

5. Property–performance correlations in solar cells for evaluations of non-uniformity Fig. 22. Maps of (a) the p-layer surface roughness thickness and (b) the p-layer bulk thickness deposited on (Cr/Ag/ZnO/n/i-layer)-coated PEN polymer at a substrate speed of 0.020 cm/s. The broken lines indicate the locations at which the a(a þnc) transition occurs at the surface of the deposited p-layer. (Adapted with permission from Ref. [43]).

substrate edges. A thicker layer at the center may also occur if the substrate is sagging slightly such that the central portion of the substrate is closer to the cathode plate than the edges. A third possible reason may be that the plasma is more intense in the central region than at the edges. Below the transition to stablephase nc-Si:H in Fig. 21, the surface roughness layer tends to be larger near the center of the substrate; however, near and above this transition, the situation is reversed. The net effect of the observed behavior is that near the edge of the substrate, nucleation occurs at a lower thickness and the density of these nuclei appear to be lower since the coalescence occurs at a somewhat greater bulk layer thickness. The roughness evolution of the p-layer deposited at 0.020 cm/s substrate speed along the center line in Fig. 22(a) shows the a(a þnc) transition at  100 Å. Once again, the surface roughness evolution along the center line given by ex-situ mapping is in reasonable agreement with RTSE results. Consistent with the RTSE observations, there is no clear (a þnc)-nc transition along this line. In order to understand the non-uniformities for this p-layer deposition, the a-(a þnc) transition line is first drawn on the surface roughness map of Fig. 22(a), where the abrupt increase in roughness thickness is observed. The same line is then superimposed onto the bulk p-layer thickness map of Fig. 22(b) so that

5.1. Experimental methods In this section, a review of property–performance correlations will be presented for completed a-Si:H n–i–p thin-film solar cells. Singlejunction solar cell stacks have been fabricated onto 15.2  15.2 cm2 borosilicate glass in the Cr/Ag/ZnO/n/i/p/[In2O3:Sn (ITO)] configuration. As described in Section 4, PECVD has been used for the Si:H layers and magnetron sputtering has been used for the remaining components: the Ag, ZnO, and ITO layers. Thus, these device studies differ from those of Sections 3 and 4 in that a rigid rather than flexible substrate is used. This eliminates complications in interpretation of the results due to the moving roll-to-roll substrate, and also enables a higher substrate temperature for the i-layer relative to that used in the study reviewed in Section 4. For the i-layer, the calibrated substrate temperature and H2-dilution ratio were 200 1C and R¼[H2]/[SiH4]¼15, respectively. For the p-layer, the corresponding values were 100 1C and R¼250. For the target i-layer thickness of  3000 Å used in the device, the a-(aþ nc) transition occurred near the R value selected in the deposition process, whereas for the p-layer thickness of  100 Å, the (aþnc)-nc transition occurred near the selected R value. These selections of R, near the transition lines of the growth evolution diagrams, provide an opportunity to employ the expected thickness non-uniformity in the deposition process to generate i and p-layer films with different nanocrystalline volume fractions at the surface. In other words, for these R values, thickness non-uniformity is expected to translate to non-uniformity in the surface nanocrystallinity according to the growth evolution deposition diagrams. As a result, one can exploit these nanocrystallite fraction variations at the surfaces of the i-layer and p-layer in order to identify the specific i/p and p/ITO interface

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Fig. 23. Maps of a-Si:H n–i–p solar cell parameters of (a) open-circuit voltage, Voc; (b) short-circuit current, Jsc; (c) fill-factor, FF; and (d) efficiency as measured under AM1.5 illumination from 246 operating 0.25 cm2 dot cells covering a 13  13 cm2 area. The substrate is glass coated with a specular Cr/Ag/ZnO back-reflector/electrical-contact. (Reproduced with permission from Ref. [47]).

properties that yield optimum device parameters in a combinatorial fashion. Depositions were performed in a multichamber load-locked system without vacuum breaks, with the exception of the final ITO deposition. For the ITO top contact, a shadow mask was inserted to deposit a periodic 16  16 array of 0.25 cm2 dots. The Ag was deposited under smooth surface conditions in order to correlate mapping SE and device performance results in this initial study with minimal additional complications. One goal is to correlate basic properties with device performance, and another goal is to understand the origin of non-uniformities over the deposition area and how they affect device performance. As a result, the device performance and structural parameters deduced in this study are relevant for specular devices not optimized for light trapping. SE was performed over a grid pattern covering the deposition area. The mapping points avoided the ITO dots, so that the surface layer in the measurement was the Si:H p-layer. These measurements were conducted using the commercially-available system described in Section 4.1 (AccuMap-SE, J.A. Woollam Co.). Thus, in each measurement, non-uniformities on sub-mm scales are averaged whereas non-uniformities on larger scales can be probed. 5.2. Results and discussion Fig. 23(a–d) shows maps of a-Si:H solar cell performance parameters over the  13  13 cm2 area having the glass/Cr/Ag/n–i–p structure. The clearest spatial patterns are observed in Voc and shortcircuit current density (Jsc). Fig. 24(a–d) shows maps of the SE-deduced i and p-layer thicknesses as well as the p-layer surface roughness

thickness and p-layer optical absorption onset energy over the same 13  13 cm2 area as the solar cell stack. The p-layer roughness thickness provides information pertaining to nanocrystallite content. In fact, the nucleation, growth, and coalescence of nanocrystals under these high H2-dilution conditions (R 250) lead to crystallites protruding from the surface that contribute to the roughness variations. The map of the optical absorption onset energy for the Si:H p-layer shown in Fig. 24(d) was obtained by a band-gap-modified Lorentz oscillator parameterization [50,60,61]. In the case of the very thin players with small nanocrystalline grains, a higher energy absorption onset and higher apparent optical band gap is generated when the crystallite content in the p-layer increases. This can be observed in the inset of Fig. 1(b) where the ε2 spectrum of the nc-Si:H is seen to be lower than that of a-Si:H in the photon energy range above 2.25 eV but below the lowest direct transition of c-Si near 3.5 eV. Different non-uniformity patterns are observed in the property maps of Fig. 24. The a-Si:H i-layer thickness pattern reflects the power coupling into the plasma and associated effects due to field fringing at the electrode edges. The Si:H p-layer thickness pattern is apparently due at least in part to the gas flow pattern in the chamber. A thicker bulk p-layer on the right side of the substrate appears correlated with a smaller surface roughness thickness, indicative of a more compact film on the right side as compared to the left. Because the gas flow is from left to right, this compact material is interpreted as more highly coalesced (i.e., smoother) nc-Si:H since SiH4 depletion is likely to occur as the gas flows from left to right, in effect leading to a locally increasing R value in this direction. In contrast, on the left, contacted – but not fully coalesced – nanocrystallites exist within a film with a rougher surface and a larger volume percentage of a-Si:H. The p-layer behavior in Fig. 24(b and c) may also result from the possibility that a

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Fig. 24. Maps of the (a) a-Si:H i-layer bulk thickness; (b) Si:H p-layer bulk thickness; (c) Si:H p-layer surface roughness thickness; and (d) p-layer absorption onset energy over a 13  13 cm2 area of an n–i–p solar cell structure. These results were obtained by ex-situ mapping SE. (Adapted with permission from Ref. [47]).

thicker i-layer on the right side may itself exhibit near-surface nuclei that promote p-layer nanocrystal nucleation preferentially on that side. The larger absorption onset energy for the p-layer material on the right side may arise from the blue shift in near band edge absorption onset ( 2.25–3.0 eV) when the layer increases in nanocrystallinity toward the right, as described in the previous paragraph [50]. The circular patterns on all maps at the locations x¼ 74.2 cm, result from the holes in the cathode that allow optical access by RTSE. The holes can be closed when uniform depositions are desired; however, in combinatorial studies that rely on thickness non-uniformities, potentially useful information can be extracted. The range in thicknesses in these regions can yield a range of near-surface nanocrystallite fractions in accordance with growth evolution diagrams. The focus of the present discussion involves the correlations in Figs. 25–27 between the device results in Fig. 23 for 246 operating dot cells deposited over the substrate area and those in Fig. 24 for the material properties as determined by mapping SE. Before discussing the results, the wide scatter in the solar cell performance data in Figs. 25–27 will be discussed. There are two origins of this scatter. Of the 256 cells fabricated over this area,  10 or 4% of the total are completely shunted and are not shown on the figure. Another  15 cells or  6% of the total exhibit low shunt resistance and give rise to the cells with  5% efficiency and lower. These tend to be the cells with thinner i-layers prepared near the edges of the electrode where particulates may occur. For larger area mini-modules, these shunts can be repaired by electrochemical passivation processes, as described elsewhere [69]. The second source of scatter,  2% absolute in efficiency, arises due to the selections of R and thickness near the transitions on the growth evolution diagram where significant non-uniformity can

be observed. The scatter then arises due to the fact that for a given property parameter on the plot, other parameters are varying that lead to the wide distribution in efficiency. In spite of the scatter, there exist well-defined maximum envelopes in cell performance as a function of each property parameter (solid lines as guides to the eye) with maxima in the envelope observable for most parameters. The maxima versus i-layer properties occur because the i-layer thickness just below the a-(a þnc) transition for the given H2-dilution ratio lies within the thickness range of the non-uniformity. Similarly one must conclude that the maxima versus p-layer properties occur because the p-layer thickness very near to the (a þnc)-nc transition for the given H2-dilution ratio is the optimum process condition, and this thickness also lies within the range of the non-uniformity. In Fig. 25, the maximum in the efficiency envelope at an i-layer thickness near 2800 Å results from a rapid rise followed by a saturation in Jsc with thickness on the low i-layer thickness side, in conjunction with a decrease in FF on the high i-layer thickness side – both of which are generally expected trends [1,2]. The increase in Jsc with increasing thickness is due to an increase in absorbance of the layer at the lower thicknesses. The decrease in FF may be due to a reduction in collection and electric field strength within thicker i-layers; however, the observed effect is relatively large considering the narrow range of thickness. Unexpected behavior contributing to the optimum position, as well, is the decrease in Voc with increasing i-layer thickness above 2800 Å. This effect may be due to the fact that for larger i-layer thicknesses at R ¼15, there may be improved ordering or small crystallites near the i-layer surface that promote immediate crystallite nucleation in the overlying p-layer, thus leading to a reduced Voc. This may also

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Fig. 25. Solar cell parameters of (a) open-circuit voltage, Voc; (b) fill-factor, FF; (c) short-circuit current, Jsc; and (d) efficiency measured under AM1.5 illumination from 246 operating 0.25 cm2 dot cells covering a 13  13 cm2 area. These results are correlated with the i-layer thickness determined by ex-situ mapping SE for the closest location. The vertical broken lines indicate the range of i-layer thickness over which the ten best solar cells are obtained with efficiencies between 7.0 and 7.5%. The lines are guides for the eye describing the maximum envelope versus i-layer thickness. (Adapted with permission from Ref. [47]).

Fig. 26. Solar cell parameters of Voc and efficiency measured under AM1.5 illumination from 246 operating 0.25 cm2 dot cells covering a 13  13 cm2 area. These results are correlated with (a,c) the p-layer bulk thickness and (b,d) p-layer surface roughness thickness determined by ex-situ mapping SE for the closest location to the solar cell. The vertical broken lines indicate the ranges of p-layer bulk and surface roughness thicknesses over which the ten best solar cells are obtained with efficiencies between 7.0 and 7.5%. The lines are guides for the eye describing the maximum envelope versus the p-layer thicknesses. (Adapted with permission from Ref. [47]).

lead to a premature reduction in FF, greater than expectations based on an increase in i-layer thickness alone. The envelopes in Fig. 26 suggest that the cell performance is strongly affected by p-layer crystallinity, as may be expected given the high H2-dilution of R 250. The decrease in Voc with p-layer bulk thickness and its associated increase with p-layer roughness thickness suggests that the p-layer is predominantly nanocrystalline, is evolving

beyond the crystallite contact point where maximum roughness occurs, and is undergoing smoothening with increasing thickness. Under these conditions, a-Si:H intergrain material is present before complete coalescence, the latter identified by the completion of surface smoothening. The observed behavior suggests that the optimum p-layer starts as protocrystalline Si:H at the i/p interface but evolves a dominant fraction of crystallites (but with a-Si:H at the

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Fig. 27. Solar cell parameters of (a) Voc and (b) efficiency measured under AM1.5 illumination from 246 operating 0.25 cm2 dot cells covering a 13  13 cm2 area. These results are correlated with the p-layer optical absorption onset energy determined by ex-situ mapping SE for the closest location to the solar cell. The vertical broken lines indicate the range of onset energy over which the ten best solar cells are obtained with efficiencies between 7.0 and 7.5%. The lines are guides for the eye describing the maximum envelope versus p-layer absorption onset energy. (Adapted with permission from Ref. [47]).

boundaries) that may yield improved contact to the ITO. The highest Voc in Fig. 23(a) occurs in the upper left where the surface roughness in Fig. 24(c) is a maximum, implying the lowest volume fraction of crystallinity over the area. In this situation, the near-surface contacting crystallites may be providing improved contact with the ITO, whereas protocrystalline Si:H underneath produces the best i/p interface. This interpretation is consistent with previous observations comparing Voc with nanocrystallite fraction [45]. Finally, Fig. 27 shows a broad maximum in the efficiency envelope function at a p-layer absorption onset energy of 1.84–1.85 eV. This maximum is defined as expected by an increase in Jsc with increasing absorption onset energy at low values and a decrease in Voc with increasing onset energy at high values due to the increase in crystallite content. In each of Figs. 25–27, horizontal lines are added to the efficiency plots at 7.0 to 7.5%. The 10 cells between these two efficiencies occur within well-defined ranges of the basic property values, and no scatter is observed outside those ranges. These best cells occur in Fig. 25 for i-layer thicknesses of 2850 750 Å and in Fig. 26 for p-layer bulk thicknesses of 111 76 Å and p-layer surface roughness thicknesses of 10775 Å. In addition, the best cells occur in Fig. 27 for p-layer optical absorption onset energies of 1.848 70.008 eV, which is a value characteristic of the nc-Si:H material in the coalescence regime of the nanocrystallites. The best performing cell with an efficiency of 7.5% lies within the optimum range of parameters, but at the edges of the p-layer thickness and absorption onset ranges. The fact that only 10 cells exist with the optimum combination of processes attests to the non-uniformity of the deposition process when performed near the growth evolution boundaries of both i and p-layers. Identifying the physical location of the optimum cells in Fig. 23 suggests that the optimum condition combines a moderate level of SiH4 depletion with a lower plasma density associated with the side of the cathode with the monitoring ports. The methodology of exploiting spatial non-uniformities for optimization as described here is expected to have a wide variety of applications in thin-film PV technologies. 5.3. Future directions in process–property–performance correlations The primary limitation of the optimization methodology using property–performance correlations arises due to the ex-situ nature of the SE mapping measurement. As a result, mapping SE analysis is challenging since it must be performed on the completed solar cell structure, which will have at least 11 individual layers for the case of the triple-junction solar cell. Even for a single-junction device, the mapping SE analysis is challenging and has been facilitated by the single-spot RTSE measurement and

analysis. In order to overcome this problem and reduce the need for RTSE measurements, an in-situ mapping SE system for the cassette roll-to-roll fabrication would be desirable, which can also serve as an in-line system for continuous roll-to-roll fabrication. Such an in-situ mapping tool based on an expanded-beam spectroscopic ellipsometer has been installed recently on the deposition system used in the studies of Sections 4 and 5, as shown in Fig. 28. This system provides the capability of mapping any layer in-situ under vacuum immediately after fabrication. The details of the construction and operation of this system are presented elsewhere [52,53]; here a brief description will be provided due to the potential importance of the capability in thin-film PV. In the in-situ mapping SE instrument, an expanded beam of polarized light from a broad-band source illuminates the moving coated substrate surface. A rectangular aperture immediately after the source is designed to define the expanded beam in order to illuminate an  1 cm (along the length)  12 cm (across the width) area of the coated substrate. A polarizer and compensator placed after the aperture generate ellipticallypolarized rays, and a focusing mirror directs these rays to illuminate the substrate. After reflection from the substrate, the rays converge through a second polarizer (or analyzer) onto a pin-hole. The incidence angle describing the reflection from the coated substrate depends on location across its width. Angle of incidence selection, or equivalently imaging of the illuminated surface, is performed by the pin-hole. The transmitted image of the coated substrate surface appears length-wise along the slit of an imaging spectrograph so that the image can be dispersed by a grating onto a CCD. Thus, the instrument produces spatial information along one index of the CCD array simultaneously with spectroscopic information along the orthogonal index, as indicated in Fig. 28. The same structure studied in Section 4 was explored in the first applications of the instrument. A Cr/Ag/ZnO-coated PEN structure was investigated using a two-layer model consisting of ZnO bulk and surface roughness layers of thicknesses, db and ds, respectively, on the opaque Ag. The ε1 and ε2 spectra of ZnO were simulated using a complex function that includes both a Sellmeier term in the real part ε1 and a critical point oscillator in both real and imaginary parts, ε1 and ε2 [50]. In Fig. 28, at the bottom, a map of the ZnO bulk layer thickness is shown on a start up stretch of the substrate. In addition, because this analysis involves a simpler (opaque Ag)/ZnO structure, details of the ZnO optical properties and plasmonic absorption at the Ag/ZnO interface are accessible [53]. Simplification in the modeling as a result of the in-situ capability will also be beneficial in the transition to analysis of textured back-reflectors.

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Fig. 28. Schematic of the expanded beam spectroscopic ellipsometer system for in-situ roll-to-roll mapping of solar cell stacks on flexible substrates. The CCD output schematic at center depicts data acquisition with the two-dimensional charge-coupled device (CCD); spectroscopy (300–1000 nm) is performed along one dimension, and line imaging width-wise across the substrate (0–12 cm) is performed along the second dimension. A map is generated when the substrate roll is translated parallel to its length. A map is shown at lower right for the ZnO bulk layer thickness obtained from a (Cr/Ag/ZnO)-coated polyimide substrate over an  9 cm x 36 cm area.

6. Summary In this article, we have been reviewed novel optical characterization methodologies designed for addressing challenges in thinfilm hydrogenated silicon photovoltaics technology. In-depth characterization of Si:H-based materials, device structures, and their fabrication processes by spectroscopic ellipsometry (SE) techniques yields growth evolution diagrams, providing guidance in materials and device design and optimization. Four specific applications of these techniques have been highlighted in this review. RTSE with virtual interface analysis (VIA) has been applied to study and control the growth of mixed-phase (aþnc)-Si:H thin films so as to maintain a constant average nanocrystalline volume fraction with accumulated thickness. RTSE studies have been used to determine the thickness and substrate dependence of the structure, summarized via the growth evolution diagrams, and thereby identify the required H2-dilution ratios and bulk layer thicknesses of components in engineered Si:H films that can result in specific isotropic or anisotropic distributions of nanocrystallites. It is found that nanocrystallite nucleation can be stopped and restarted with well-defined conical crystallite

decay and growth behaviors via the use of alternating low and high H2-dilution layers, respectively. The observed protocrystalline layers decrease in thickness, however, with increasing cycle number due to the increase in ordering of the underlying layers with increasing thickness. As a result, in order to obtain periodic arrays of crystallites, the H2-dilution ratio, R¼ [H2]/[SiH4], of the high dilution layers must be decreased with increasing cycle number. Similarly RTSE has been applied to develop growth evolution diagrams for vhf PECVD using Si2H6 þ H2 to obtain thin-film Si:H and Si2H6 þ GeH4 þH2 to obtain its alloys with Ge. These diagrams have been augmented relative to previous versions by including contour lines that represent the relative crystalline volume fraction in the top  3–30 Å of the i-layer at a given bulk layer thickness as determined through VIA. As a result, general principles have been established that enable understanding and thus predicting the optimum one-step i-layer deposition processes for the individual top, middle, and bottom cells of a triple-junction device. The performance of the component single-junction devices are consistent with these predictions. For growth on mixed-phase (a þnc)-Si:H n-layers, a bifurcation in the growth evolution diagram is observed versus R such that a-Si:H is the ultimate phase at

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R values lower than the bifurcation and a structurally-stable nc-Si: H film is the ultimate phase at higher R values. The growth evolution diagrams in conjunction with cell performance enable design of multi-step and graded-layer vhf PECVD processes for improvements in device performance. Roll-to-roll fabrication is a key process technology for such thin-film multijunction Si:H solar cells if flexible substrates are desired. In the first application of RTSE in roll-to-roll fabrication, PECVD a-Si:H i-layers have been characterized during growth on (Ag/ZnO:Al/n-layer)-coated polymer substrates moving at a constant linear speed in a roll-to-roll cassette configuration. Ex-situ SE mapping performed on the transient leading edge of the coated polymer substrate supported the RTSE results obtained along the center line of the substrate, but also provided information on the evolution of the deposition and the uniformity across the width of the substrate. For example, it was found that in mapping across the substrate width, the i-layer in the central portion of the substrate is thicker than at the edges possibly due to the sagging of the polymer when it is moving during deposition. The successful acquisition of the RTSE data and the consistent analysis results for the a-Si:H i-layer implies that RTSE can be used as an effective process monitoring tool for roll-to-roll thin-film a-Si:H solar cell fabrication and may be extended to other thin-film PV technologies, as well. As a second, more detailed application of RTSE and ex-situ mapping SE in the roll-to-roll configuration, the evolution of the top-most thin-film Si:H p-layer has been studied for substrate-type a-Si:H n–i–p solar cells. In this study, two p-layers have been deposited at substrate speeds of 0.015 and 0.020 cm/s with all other process parameters unchanged. Both RTSE and ex-situ mapping SE results for the p-layer deposited at 0.015 cm/s show clear transitions from amorphous (protocrystalline) Si:H to mixed-phase (aþ nc)-Si:H and then finally to a structurally-stable nc-Si:H film with increasing bulk player thickness to 800 Å. A spatially-resolved phase diagram that maps the amorphous Si:H, mixed-phase (aþnc)-Si:H, and stable-phase ncSi:H regions at the top surface of the film has been identified on the basis of the surface roughness evolution. The transition boundaries are then superimposed onto the bulk p-layer thickness map in order to generate the spatially-resolved growth evolution diagram. The RTSE results for the p-layer deposited at 0.020 cm/s show only the transition from amorphous Si:H to mixed-phase (aþnc)-Si:H, as the deposition saturates before reaching the nanocrystallite coalescence thickness. Thus, the spatial phase diagram in this case exhibits only an amorphous to mixed-phase (aþ nc)-Si:H transition line. In general, such diagrams can be developed under different deposition conditions to provide insights into p-layer process optimization that yields high performance for large area thin-film Si:H solar cell modules. The ability to apply SE for mapping the basic multilayer properties enables direct correlation with a-Si:H device performance parameters for optimization. The ultimate goal of such research is to understand the origin and effects of deposition non-uniformity on cells and modules from both basic property and device standpoints. In this study, a 16  16 array of n–i–p cells 0.25 cm2 in size has been fabricated over a 13  13 cm2 substrate area, and this area has also been mapped at mm-scale resolution by SE. Analysis of the SE data over the full area has provided maps of basic properties including i-layer thickness and its band gap, p-layer thickness and its absorption onset energy, and p-layer surface roughness thickness in the n–i–p structure. The values of these properties adjacent to the small-area devices have been correlated with device performance parameters. By depositing the i-layer and p-layer at H2dilution ratios near the transition boundaries of the growth evolution diagram, optimum device performance can be identified. Consistent with current understanding, optimization occurs (i) at the maximum i-layer H2-dilution ratio while avoiding nanocrystal nucleation and (ii) at the p-layer transition region in which a-Si:H

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nucleates from the i-layer surface to form the i/p junction, but evolves such that contacting nanocrystallites with a-Si:H in the boundary regions yield improved ITO contact. Thus, observed optima in device performance have been understood in terms of basic properties, and the impact of property variations over the surface has been evaluated. Although this methodology has been applied for the first time to single-junction a-Si:H solar cells in a specular configuration, it will be more powerful when applied to fully textured devices, multijunctions, as well as to other thin-film PV technologies.

Acknowledgments This research was supported by the U.S. Army Research Office and U.S. Army Research Laboratory and was accomplished under Cooperative Agreement Number W911NF-0-2-0026. Support was also provided by NASA, Space Photovoltaics Division, Grant number NNC06GA04G, the Department of Energy University Processes and Products Development Support Program, Contract number DE-FG36-08GO18073, by the NIST ATP Program, and by the State of Ohio Wright Centers of Innovation Program. The authors acknowledge the assistance of X. Deng of University of Toledo and S. Cao of Xunlight Corp. in the work of Section 3, and M. Fried, G. Juhasz, C. Major, O. Polgar, A. Nemeth, and P. Petrik of the Institute for Technical Physics & Materials Science (MFA), Budapest, Hungary in the development of the expanded beam spectroscopic ellipsometer of Section 5.3.

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