IEEE JOURNAL OF PHOTOVOLTAICS, VOL. 8, NO. 3, MAY 2018 871 Analysis of Back-Contact Interface Recombination in Thin-Film Solar Cells Sanjoy Paul , Sachit Grover, Ingrid L. Repins , Brian M. Keyes, Miguel A. Contreras, Kannan Ramanathan, Rommel Noufi, Zhibo Zhao, Feng Liao, and Jian V. Li Abstract—The open-circuit voltage (VO C ) in a generic TCO/ buffer/absorber/back-contact thin-film solar cell device is a key parameter in the recombination analysis. In particular, VO C is sensitively influenced by the interface recombination at the buffer/absorber front interface and at the absorber/back-contact interface. This paper reports the temperature, excitation light intensity, and wavelength-dependent open-circuit voltage analysis to separate and quantify recombination rates in solar cells at the front and back interfaces, in the depletion regions, and in the quasi-neutral region. The wavelength-dependent VO C analysis is exploited to extract the absorber/back-contact recombination coefficient. The experimentally observed results are verified using SCAPS-1D (one dimensional—a solar cell capacitance simulator) simulation. Index Terms—Back-contact, interface, open-circuit voltage, photovoltaics, recombination, SCAPS-1D. I. INTRODUCTION HE interface recombination is critical in thin-film solar cell’s (TFSC’s) performance especially the open-circuit voltage (VOC ) –. Extraction of interface recombination rates enables more detailed analysis for material and device engineering to reduce interface recombination and improve VOC . VOC is a special operating point in the current–voltage T Manuscript received October 4, 2017; revised December 17, 2017 and March 6, 2018; accepted March 17, 2018. Date of current version April 19, 2018. This work was supported in part by Taiwan Ministry of Science and Technology grant number MOST 107-2218-E-006-022-MY3, in part by the U.S. Department of Energy under Contract DE-EE-0007541 with Texas State University and DEAC36-08GO28308 with the National Renewable Energy Laboratory (NREL), and in part by the collaborative research and development agreement between First Solar, Inc. and NREL. (Corresponding authors: Sanjoy Paul; Jian V. Li.) S. Paul is with the Department of Physics and Material Science, Engineering, and Commercialization Program, Texas State University, San Marcos, TX 78666 USA (e-mail:,[email protected]). S. Grover, Z. Zhao, and F. Liao are with First Solar, Inc., Perrysburg, OH 43551 USA (e-mail:,[email protected]; [email protected]; [email protected]). I. L. Repins, B. M. Keyes, and R. Noufi are with the National Renewable Energy Lab, Golden, CO 80401 USA (e-mail:, [email protected]; [email protected]; [email protected]). M. A. Contreras is with Ascent Solar Technologies, Inc., Thornton, CO 80241 USA (e-mail:,[email protected]). K. Ramanathan is with the Stion Corporation, San Jose, CA 95119 USA (e-mail:,[email protected]). J. V. Li is with the Department of Aeronautics and Astronautics, National Cheng Kung University, Tainan 70101, Taiwan, and also with the Department of Physics and Material Science, Engineering, and Commercialization Program, Texas State University, San Marcos, TX 78666 USA (e-mail:, [email protected] mail.ncku.edu.tw). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/JPHOTOV.2018.2819664 characteristics in analyzing recombination in solar cells because at this point all generated charge carriers recombine. The physics of recombination mechanism can be revealed from the experimental VOC analysis with the variation of different experimental conditions such as temperature (T) , , excitation light intensity (Ga , measured in suns) –, and excitation wavelength (λ) , . Previous investigation with combined T and Ga -dependent VOC has proven useful in identifying and quantifying Shockley–Read–Hall (SRH) recombination rates at different locations such as at the buffer/absorber (Ri,f ), in the depletion region (Rd ), and in the quasi-neutral (Rb ) region . However, this analysis did not consider the recombination at the absorber/back-contact interface Ri,b . Here, in this paper, we extend the previous analysis to resolve recombination rates in the complete absorber of a TFSC (from the buffer/absorber interface to absorber/back-contact interface) using excitation-wavelength-dependent VOC analysis. The mathematical formulation to include recombination at both buffer/absorber and absorber/back-contact interfaces is presented. We apply this methodology to two major types of solar cells with nonnegligible (CdTe) and negligible (Cu(In,Ga)Se2 ; CIGS) absorber/back-contact interfacial recombination. Additionally, our analysis provides suggestions to improve the interfaces and enhance the performance of the solar cells. II. EXPERIMENTAL AND SIMULATIONS Two major types of solar cells (CIGS and CdTe), which share the same device architecture TCO/buffer/absorber/back contact), were used in this analysis. The CIGS solar cells were fabricated using the three-stage coevaporation method . The layer structure of the CIGS device (bottom to top) is—soda lime glass substrate, 1 μm of bilayer Mo back contact, 2 μm CIGS absorber, CdS buffer layer, ZnO (TCO), and Ni–Al front-contact. The efficiency of this device is 19.5%. Detail material synthesis and device fabrication steps can be found in . The CdTe solar cell with the 19.6% efficiency was fabricated by First Solar Inc. . The temperature and intensity-dependent current–voltage (I–V) characteristics were measured using a standard AM1.5 light source (Newport 96000 solar simulator). A Keysight B2912A source measure unit was used in this experiment. The temperature of the samples was varied between 70 and 310 K. Neutral-density filters were used to vary the intensity of incident light on the solar cell between 1 × 10−6 and 1 sun. 2156-3381 © 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications standards/publications/rights/index.html for more information. 872 IEEE JOURNAL OF PHOTOVOLTAICS, VOL. 8, NO. 3, MAY 2018 particular interest in this paper and its inclusion provides a more accurate and complete recombination analysis in TFSCs. To probe the absorber/back-contact recombination, we introduce the wavelength-dependent VOC analysis. In analogy with the prior recombination formalism, we consider Ri,f , Rd , Rb , and Ri,b SRH recombination rates at the buffer/absorber interface, in the depletion region, in the quasi-neutral region, and at the absorber/back-contact interface. The temperature (T) and the bias (V)-dependent recombination rates were expressed as follows: qV Ri,f = R0i,f e k B T qV Rd = R0d e 2k B T qV Rb = R0b e k B T qV Ri,b = R0i,b e k B T Fig. 1. Energy band diagram of a generic TCO/buffer/absorber (p-type)/backcontact heterojunction solar cell with the front interface, the depletion region, quasi-neutral region, and the back-contact interface. Note, for VO C analysis using white light R i , f = R i , R i , b = 0, and S hf = S h . Different parameters are Ga the generation rate averaged over the absorber thickness W, e/h the electron/hole, q the electronic charge, E C /E V /E F the energy of conduction/valence-band/Fermi-level, E g the absorber bandgap, W d the depletion width, τ e the minority carrier lifetime in the quasi-neutral region, S hf /S eb the surface recombination velocity of hole/electron at front/back interface, ϕ b 0 the potential barrier for majority carrier at the interface, ξi the Fermi-energy separation from the minority band edge at the interface, ξb the bulk Fermi-energy separation from the valence band edge. Capacitance–voltage (CV) measurements were performed using an Agilent 4294A impedance analyzer at frequency of 10 kHz with applied bias voltage ranging from –1.0 to 0.5 V. For extraction of back-contact recombination in CdTe and CIGS solar cell structures, monochromatic LED light sources of different wavelengths (625, 780, and 940 nm) were used. Observed experimental results for CdTe and CIGS solar cells were verified via SCAPS-1D (one dimensional—a solar cell capacitance simulator) simulation –. All simulation parameters used in this paper are in the Appendix. The SCAPS-1D program was developed at ELIS (University of Gent, Belgium) to simulate CdTe, CIGS, and other solar cells –. where, kB is the Boltzmann constant. R0i,f , R0d , R0b , and R0i,b are bias-independent (V = 0) recombination coefficients at the buffer/absorber interface, in the depletion region, in the quasi-neutral region, and at the absorber/back-contact interface, in that order. These coefficients essentially account for the intrinsic properties of material or device and represent effectiveness of the corresponding recombination pathways. Note that the exponential functions in (1) describe the densities of carriers, which are characterized by respective diode ideality factors (2 for the recombination in the depletion region and 1 for the recombination in the quasi-neutral region and at the interfaces) . Utilizing the concept in  and from the energy band diagram (in Fig. 1), we present the mathematical formula for recombination coefficients (R0i,f , R0d , R0b , and R0i,b ) as follows: R0i,f = Shf NV e R0d = Wd ni τe + τh R0b = W n2i τ e NA R0i,b = Seb NC e III. MATHEMATICAL FORMULATION In the recombination formalism, we present the generic heterojunction solar cells structure (TCO/buffer/absorber/back contact) in Fig. 1 to show different regions and interfaces of interest. In the previous analysis , , quantitative extraction of recombination rates at different cell regions (at the buffer/absorber interface Ri , in the depletion region Rd , and in the quasi-neutral region Rb ) was performed using analytical approximation and SRH recombination statistics –. Extraction of surface recombination velocity (Sh ) at the interface (buffer/absorber) and minority carrier lifetime (τe ) were possible because of their dependency on recombination coefficients Ri and Rb , respectively . In the prior analysis, conspicuously, the recombination at the absorber/back-contact interface was missing which is of (1) qφb0 B T −k − ( E g −ξ b ) kB T . (2) The symbols in (2) have usual meanings (as noted in Fig. 1 caption). Interpretation of all recombination coefficients (R’s) using (1) and (2) is as follows. The recombination coefficient (Ri,f ) is proportional to the surface recombination velocity of holes at the buffer/absorber interface (Shf ) and the hole density at this interface. This expression assumes that the Fermi-level pinning occurs at the front interface which is applicable for high recombination velocity or low injection level. Recombination coefficients at the absorber/back contact (Ri,b ) is proportional to the surface recombination velocity of electron (Seb ) and the electron density at this interface. In the depletion region, the recombination coefficient (Rd ) is proportional to the space charge width (Wd ), intrinsic carrier concentration (ni ), and inverse sum of carrier lifetimes (i.e., τe + τe for electrons and holes). In the quasi-neutral region, the recombination coefficient (Rb ) is PAUL et al.: ANALYSIS OF BACK-CONTACT INTERFACE RECOMBINATION IN THIN-FILM SOLAR CELLS proportional to the absorber thickness, square of intrinsic carrier concentration (n2i ), inverse of minority carrier lifetime (τe ), and density of electrons (minority carriers). Now, focusing on the VOC (voltage at which all generated charge carriers recombines), total generation across the absorber Ga W equated with the total recombination ( R = Ri,f + Rd + Rb + Ri,b ) which leads to the following: qVOC qVOC R0i,f + R0b + R0i,b e k B T + R0d e 2k B T − Ga W = 0. (3) The solution of (3) which relates the VOC with the temperature (T), the average generation rate Ga , and all recombination rates (R0i,f , R0d , R0b , and R0i,b ) is given by the following: ⎡ VOC ⎜ ×⎜ ⎝ = 4Ga W R0i,f R0b + + d 2 R0 R0i,b Like the VOC analysis with white light illumination, there are two steps to extract all recombination coefficients R0i,f , R0d , R0b , and R0i,b . They are 1) intensity-dependent VOC analysis at fixed T (say 300 K), and 2) temperature-dependent VOC analysis at fixed intensity (1 sun). Intensity-dependent VOC analysis with blue light (with K1Blue ) enables one to extract R0d and R0i,f + R0b . Now with known R0d , the intensitydependent VOC analysis with red light (with K1Red ) helps to extract R0i,f + R0b + R0i,b and finally R0i,b (by subtracting K1Blue and K1Red ). Note that in this analysis, R0i,f and R0b are coupled and need a secondary relationship (temperature-dependent VOC analysis under 1 sun condition) to decouple them. In the limit 4W (R 0i +R 0b ) of K2 Ga = Ga 1, (4) reduces to the following: d 2 (R 0 ) 1 R0d 2kB T ⎢ n ⎢ = ⎣ i,f q 2 R + Rb + Ri,b 0 0 0 ⎛ VOC ⎞⎤ (4) Ea = where R0d 1 2 Ri,f + Rb + Ri,b 0 0 0 4W R0i,f + R0b + R0i,b . K2 = d 2 R0 K1 = (5) It is clear from (4) that VOC is a function of T and Ga (excitation light intensity) which enables the extraction of all recombination coefficients experimentally. The extraction of the interface recombination coefficients R0i,f and R0i,b required different experimental conditions beside temperature and intensitydependent VOC analysis based on white light illumination. The wavelength-dependent VOC analysis extends the analysis to the back contact with recombination coefficient R0i,b . For simplification, we denote the combined front and back interface recombination coefficient as R0i (prior analysis). For VOC analysis with monochromatic short-wavelength light source (blue), the photons energy is well above the absorber’s bandgap and hence the photogeneration is weighted toward the front interface, which make R0i = R0i,f . On the other hand, photogeneration with longwavelength light (red), whose photon energy is barely above the bandgap, makes near uniform generation profile across the absorber depth, rendering R0i = R0i,f + R0i,b . So, VOC analysis with monochromatic blue and red light sources, the coefficient K1 can be written as follows: R0d 1 = 2 Ri,f + Rb 0 0 K1Red = R0d 1 . 2 Ri,f + Rb + Ri,b 0 0 0 Ga W kB T n = . q R0i,f + R0b + R0i,b (7) It was experimentally observed that near room temperature, VOC is linear in T . So, with the condition K2 Ga 1, the activation energy of recombination Ea can be obtained using the formula VOC = Eqa + T ( dVdTO C ) and on simplification ⎟⎥ ⎥ + 1 − 1⎟ ⎠⎦ 2kB T n K1 Ga K2 + 1 − 1 q K1Blue 873 (6) R0i,f Eai,f + R0b Eab + R0i,b Eai,b R0i,f + R0b + R0i,b (8) where Eai,f , Eab , and Eai,b are the activation energies at the buffer/absorber interface, in the quasi-neutral region, and at the absorber/back-contact interface, respectively. So, recombination activation energy (Ea ) is the average activation energy of Eai,f , Eab , and Eai,b weighted by respective recombination rates (R0i,f , R0b , and R0i,b ) at V = 0. Experimentally, the value of Ea can be extracted by extrapolating the T-dependent VOC data to T = 0 K (i.e., at T = 0 K, Ea = VOC ) . With the knowledge (will be discussed in the result section) of the activation energies Eai,f , Eab , and Eai,b , one Ri,f can obtain R0 b which enables one to decouple R0i,f and R0b . 0 Now combining (3), (6), and (8), the four unknown recombination coefficients R0i,f , R0d , R0b , and R0i,b are readily solvable via the matrix method—with the transformation matrix ⎞ ⎛ qVOC qVOC qVOC qVOC e kB T e 2k B T e kB T e kB T ⎟ ⎜ ⎟ ⎜ 1 0 1 − 2K 1B l u e ⎟ ⎜ 1 ⎟ ⎜ ⎟ ⎜ ⎠ ⎝ 1 − 2K1R e d 1 1 1 i,f b i,b 0 Ea − Ea Ea − E a Ea − E a ⎛ i,f ⎞ ⎛ ⎞ R0 Ga W ⎜ Rd ⎟ ⎜ 0 ⎟ ⎜ ⎟ ⎟. × ⎜ 0b ⎟ = ⎜ (9) ⎝ 0 ⎠ ⎝ R0 ⎠ 0 Ri,b 0 With this recombination analysis, other parameters such as surface recombination velocity of holes at the buffer/absorber interface (Shf ), the surface recombination velocity of electron at the absorber/back contact (Seb ), and the electron lifetime (τe ) can be extracted using (2). In extracting Seb , ξb (the bulk Fermi level above valance) can be obtained from the equation 874 IEEE JOURNAL OF PHOTOVOLTAICS, VOL. 8, NO. 3, MAY 2018 fitting experimental data with (4) yield K1 = 6.18 × 105 and K2 = 1561.4 Sun−1 . Note that white light illumination does not include the back-contact recombination term in the expression of K1 and K2 . From the values of K1 and K2 , we obtain the = 3.7 × 108 cm−2 s−1 and using this R0d value of R0d = K2W 1K 2 value the values of R0i + R0b = 299.4 cm−2 s−1 . Note that here both R0i and R0b are coupled and need other experiments to decouple them. The temperature-dependent VOC analysis at 1 sun 4G W (R i +R b ) condition (with verified K2 Ga = a d 02 0 1) leads to (R 0 ) estimate activation energy of recombination Ea = 1.45 eV [see Fig. 3(b)]. With known value of ϕb0 = 1.17 V (from capacitance measurement—data not shown) and Eg = 1.5 eV, the estimated ration of R0i and R0b is 3 × 102 cm−2 s−1 and Fig. 2. Flow chart for the recombination analysis with the thin-film solar cell to extract various recombination coefficients, surface recombination velocities, and electron lifetime as mentioned in the formalism section. R 0i R 0b R 0i R 0b ≈ 0.18. Using R0i + R0b ≈ = 0.18, the estimated value of R0i = 45.8 cm−2 s−1 and R0b = 254.2 cm−2 s−1 . Considering VOC = qVOC 888 meV, the recombination coefficients are Ri = R0i e k B T = qVOC 4.1 × 1016 cm−2 s−1 , Rd = R0d e 2k B T = 1.1 × 1016 cm−2 s−1 , qVOC Fig. 3. (a) Dependence of V OC on excitation light intensity (G) at T 300 K. (b) Temperature (T)-dependent V OC at one Sun illumination. In both figures, the squares and dashed lines represent the experimental data and fitted lines, respectively. qϕb0 = qϕbi + ξb . The flow chart summary of extracting recombination coefficients along with various electronic parameters (surface recombination velocity and electron lifetime) using white light and monochromatic light illumination is represented in Fig. 2 for simplicity. Here onward, the experimental data analysis on CdTe and CIGS solar cells will be discussed which includes the extraction of recombination coefficients at the buffer/absorber interface, in the depletion region, in the quasi-neutral region, and at the absorber/back-contact interface. IV. RESULTS AND DISCUSSION A. Recombination Analysis With CdTe Solar Cells The dependence of VOC on illumination (white light) intensity at T 300 K and on T at 1 sun illumination is shown in Fig. 3(a) and (b), respectively. From Fig. 3(a), the and Rb = R0b e k B T = 2.3 × 1017 cm−2 s−1 . Using (2) (R0i,f = R0i , and Shf = Sh ) and considering ni = 9 × 105 cm−3 , NV = 1.8 × 1019 cm−3 , NA = 1 × 1015 cm−3 , and ϕb0 = 1.17 eV, we extract the values of Sh = 1.25 × 102 cm/s and τe = 1.59 ns. The summary of extracted recombination coefficients, surface recombination velocity at buffer/absorber interface, and the electron lifetime in this analysis is tabulated in Table I. In case of CdTe device, back-contact optimization is a known challenge , . The previous analysis with white light source fails to probe back-contact recombination. To extend the recombination at the back contact, the intensity (Ga )-dependent VOC at excitation wavelength λEx = 625 nm, and λEx = 780 nm are shown in Fig. 4(a). Now, from the fitting using (4), the estimated value of K1Blue = 8.64 × 105 , K1Red = 6.03 × 105 , K2Blue = 610.4 Sun−1 , and K2Red = 1134.4 Sun−1 , respectively. Utilizing (6), the transformation matrix in (9), and experimental results, one can easily estimate the recombination coefficients (at V = 0) from front- to back contact (R0i,f , R0d , R0b , and R0i,b ). With the relation K1Blue · K2Blue = 2W , one obtains Rd 0 the value of R0d = 3.7 × 108 cm−2 s−1 . With simplified equaR 0i , b R 0d 1 − 2K 1B l u e and R0d = 3.7 × 108 cm−2 s−1 , 2K 1R e d 1 we obtain R0i,b = 93 cm−2 s−1 . Using matrix equation (9), we estimate the R0i,f + R0b = 214 cm−2 s−1 and R0i,f + R0b + R0i,b = 307 cm−2 s−1 and finally R0i,b = 93 cm−2 s−1 (as ob- tion = served previously). Now with blue light excitation and using (8) and with known values [Ea = 1.45 eV, Eab = Eai,b = Eg = 1.5 eV, Eai,f = ϕb0 (front) = 1.17 V] we obtain the values of R0b = 167 cm−2 s−1 , and R0i,f = 47 cm−2 s−1 . At V = VOC , we estimate the recombination coefficients Ri,f = 3.4 × 1016 cm−2 s−1 , Rd = 1.0 × 1016 cm−2 s−1 , Rb = 1.1 × 1017 cm−2 s−1 , and Ri,b = 6.3 × 1016 cm−2 s−1 . By considering NV = 1.8 × 1019 cm−3 and ϕb0 = 1.17 eV, the observed front surface recombination velocity of hole (Shf ) PAUL et al.: ANALYSIS OF BACK-CONTACT INTERFACE RECOMBINATION IN THIN-FILM SOLAR CELLS 875 TABLE I EXTRACTED RECOMBINATION COEFFICIENTS, SURFACE RECOMBINATION VELOCITY, AND LIFETIME OF MINORITY CARRIER IN CDTE SOLAR CELL USING WHITE LIGHT SOURCE Fig. 4. (a) Illumination-dependent V OC (in CdTe cell) with a different excitation light source wavelength of λEx = 625 and 780 nm. (b) Dependence of V OC with excitation wavelength λEx = 600 and 800 nm generated using the SCAPS-1D program. and lifetime of electron were 1.25 × 102 cm/s and τe = 2.43 ns using (2). The surface recombination velocity at the back contact (Seb ) was extracted from a known value of NC = 8 × 1017 cm−3 and ϕbi = 0.92 V as 1.28 × 105 cm/s. All extracted recombination coefficients, surface recombination velocities, and electron lifetime are in Table II. It is important to note that the recombination rate in the quasi-neutral region Rb ≈ 1017 cm−2 s−1 is overestimated because it implicitly includes the back-contact recombination rate Ri,b . This results in a lower estimate of minority-carrier lifetime τe . To verify further, we simulated intensity-dependent VOC with monochromatic light of wavelength λEx = 600 and 800 nm in SCAPS-1D (using the baseline structure: Au (back contact)/CdTe (5 μm)/CdS (25 nm)/SnOx (0.5 μm)) as shown in Fig. 4(b). Intensity-dependent VOC data simulated by SCAPS -1D helps to understand our experimentally observed data. Here we did not try to match the simulated data with the experimental one and fit it with the discussed method. Dependency of VOC on too many semiconducting material and device parameters made this task difficult. The set of parameters used for the simulation is based on experimentally extracted device parameters (such as NA , Eg , τe , Shf , Seb ,W, etc.) while keeping other parameters (as available in SCAPS-1D for CdTe-baseline) unchanged. The errors associated with the experimentally observed material and devices parameters have impact on VOC which contribute to the difference between simulation and experiment. On the other hand, uniform distribution of traps at mid-gap was considered in this simulation. But in actual device nonuniform and complicated energetic distribution of traps is possible. Finally, while simulation provides consistent comparison with the experimental results but simulation using more realistic device parameters could be of particular interest in the future. Extraction of ϕbi in a device with very thin absorber is challenging compared with semi-infinite thick absorber. Due to this reason, for example, there is considerable difficulty in extracting ϕbi with CdTe device with thickness of about 3–5 μm, which could also be compounded by the presence of a non-ohmic back contact. The preceding (white light) analysis on the CdTe device was carried out using a ϕbi value of 0.92 V. Regretfully, this is an educated guess based on VOC value instead of an actual extraction ϕbi from the Mott–Schottky plot, which would have been 0.75 V. Therefore, further methodological improvement is necessary on this topic. Moreover, because the error in ϕbi directly translates to the same error in ϕb0 , the extraction of Sh is affected because of its exponential dependency on ϕb0 , . As an example, changing ϕbi to 1.02 V—and error of 0.1 V—would lead to a seemingly alarming change in Shf = 6.24 × 103 cm/s as compared with Sh = 1.25 × 102 cm/s (using ϕbi = 0.92 V) while keeping τe relatively unchanged at ∼ 1.5 ns. In this case, it is perhaps more informative to inspect the recombination coefficients and observed values are as follows: R0i = 58 cm−2 s−1 , R0d = 1.1 × 108 cm−2 s−1 , and R0b = 189 cm−2 s−1 at V = 0 and Ri = 5.1 × 1016 cm−2 s−1 , Rd = 3.4 × 1015 cm−2 s−1 , and Rb = 1.7 × 1017 cm−2 s−2 at V = VOC which does not deviate from the previous analysis (see Table I). Note the spatial distribution of excess carrier density in steady state depends on the absorption coefficient (generation), the diffusion length (transport and bulk recombination), and the surface recombination (boundary conditions) . If both l and 1/α are short compared with the absorber thickness, then the back-contact recombination does not play a significant role. The opposite is true if either or both l and 1/α is long compared with the absorber thickness. B. Recombination Analysis With CIGS Solar Cells The estimation of recombination coefficients at buffer/absorber interface, in the depletion region, and in the bulk of the absorber of CIGS devices have been investigated 876 IEEE JOURNAL OF PHOTOVOLTAICS, VOL. 8, NO. 3, MAY 2018 TABLE II EXTRACTED RECOMBINATION COEFFICIENTS, SURFACE RECOMBINATION VELOCITIES, AND ELECTRON LIFETIME IN CDTE SOLAR CELLS USING BLUE AND RED LIGHT SOURCE Intensity-dependent VOC data with a CIGS baseline structure [Mo (back contact)/p-CIGS (2 μm)/n-CdS (50 nm)/n-ZnO (50 nm)] were generated using SCAPS-1D with white light and different excitation wavelength (λEx = 600 and 900 nm) as shown in Fig. 5(b). In this simulation, we created the bandgap profile via a two-segment linear compositional grad[Ga] ) in CuIn1−x Gax Se2 . ing scheme with Ga content (x = [Ga]+[In] The bandgap in this structure linearly varies from 1.15 eV (at CdS/CIGS contact) to 1.05 eV at a depth of 0.5 μm in the CIGS absorber and then to 1.3 eV (at CIGS/back contact). The simulated data have qualitative consistency with the experimentally observed intensity-dependent VOC [see Fig. 5(a)]. Almost equal observed value of K1Blue and K1Red may be attributed to the bandgap grading. However, the actual cell may have complicated bandgap grading which compels further examination. V. CONCLUSION Fig. 5. (a) Intensity-dependent V OC data for CIGS solar cell with two different excitation wavelengths λEx = 625 and 940 nm as well as with white light. Here symbols are experimental data and dotted lined are fitted data. (b) SCAPS-1D simulated intensity-dependent V OC data with white light and three different available wavelengths λEx = 600 and 900 nm. and published elsewhere . Here, the wavelength-dependent VOC analysis on three-stage coevaporated CIGS devices has been performed to confirm that the absorber/back-contact recombination is indeed negligible. This result is presented in Fig. 5(a) which shows intensity-dependent VOC at two excitation laser light λEx = 625 and 940 nm. The fitting with (4) yield almost identical K1 values K1Blue = 20918.8 ± 605.7 versus K1Red = 21308.0 ± 2119 within experimental errors. This is due to the bandgap gradient of the CIGS absorber deposited by three-stage coevaporation. This bandgap gradient is manifested as more elevated conduction band toward the back contact and function as a back-surface field commonly observed a-Si/c-Si heterojunction device . This feature repels minority electrons away from the back contact and effectively reduces interface recombination rate. We have investigated the temperature, illumination intensity, and wavelength-dependent VOC analysis [VOC (T, I, λ) analysis] with generic TCO/buffer/absorber/back-contact solar cell (CdTe and CIGS) in order to separate and quantify the recombination coefficients at buffer/absorber interface (Ri,f ), in the depletion region (Rd ) and bulk of the absorber (Rb ), and at absorber/back contact (Ri,b ). The VOC (T, I) analysis with white light illumination can be used to extract the recombination rates Ri,f , Rd , and Rb while neglecting Ri,b . This analysis is valid under certain conditions such as the a-Si/c-Si heterojunction solar cells with a back-surface field/passivation and three-stage coevaporated CIGS solar cells due to the advantageous bandgap gradient. Ri,f depends on two main factors: 1) surface recombination velocity, and 2) the potential barrier height ϕb0 , the latter being constrained by the alignment of the conduction band of the TCO and the valence band of the absorber. The complete TCO/buffer/absorber structure of the CIGS device is analyzed to reveal the dependence of ϕb0 on bandgap, band offset, band bending, and inversion to devise strategies for reducing the absolute rate of interface recombination as well as the relative strength of interface recombination over bulk recombination. Furthermore, we improved upon the aforementioned method to extract Ri,b further via wavelength dependent VOC analysis and tested with CdTe solar cell in which the recombination at the back contact is nonnegligible. This characterization method will be useful in other heterojunction devices where the interface recombination is crucial, i.e., Cu2 O , CuZnSnS4 –, and even CIGS with high Ga content where bandgap gradient is not optimized . 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