The high performance of polycrystalline CdTe thin film solar cells is enabled by annealing in the presence of Cl. This process is typically carried out for tens of minutes resulting in reduction of defect states within the bandgap among other beneficial effects. In this work, we investigate laser annealing as a means of rapidly annealing CdTe using a continuous wave sub-bandgap 1064 nm laser. The partial transmission of the beam allows us to monitor the annealing process in-situ and in real time. We find that optoelectronic and structural changes occur through two distinct kinetic processes resulting in the removal of deep defects and twinned regions, respectively. A multilayer optical model including surface roughness is used to interpret both the in-situ transmission as well as ex-situ reflectivity measurements. These experiments demonstrate beneficial material changes resulting from sub-bandgap laser-driven CdCl2 treatment of CdTe in minutes, which is an important step towards accelerating the processing of the CdTe absorber layer.

CdTe-based photovoltaic (PV) modules currently have the lowest manufacturing cost compared to all other PV technologies, currently well under $0.60 /Wp although cost reductions in silicon PV manufacturing threaten to eclipse this mark.1 The largest cost driver in CdTe module manufacturing is the cost of the front and back glass (including transparent front contact). The second largest is the aggregate materials and processing costs of the CdS and CdTe deposition, Cl-treatment, and Cu diffusion steps.2 These multiple steps are performed in series, and tools for these combined steps are parallelized with respect to the rest of the production lines due to their slower combined throughput times. This leads to multiplicatively larger capital expenditures thus driving up manufacturing costs. As a result of these cost drivers, a great deal of research effort has been focused on alternative substrates,3–7 low-cost non-vacuum deposition techniques (see Ref. 8 and references therein), and subsequent rapid thermal processing.9–12 Non-glass substrates often necessitate alternate thermal processes due to limitations imposed by the less thermally robust substrates such as plastic or metal. Non-vacuum deposition techniques typically produce films of lower structural and optoelectronic quality meaning that a post-deposition method for improving material quality is required. In order to not negate the gains achieved by a faster or cheaper deposition technique, this processing should be rapid and cost effective.

Laser annealing (LA) is a promising means for rapidly improving PV absorber material quality that is capable of providing a local source of heat concentrated in the active semiconductor layers.13 This saves both time and energy by not heating the substrate, which has a comparatively much larger thermal mass. As an example, some of us have demonstrated that LA on the order of seconds for annealing electrodeposited CuInSe2 resulting in working solar cells.14 Other studies have shown that LA can improve the quality of thin-film PV absorbers such as CuInSe2 (Refs. 15 and 16) as well as CdTe.17–19 In this paper, we demonstrate the feasibility of using LA to improve initially low-quality, thin-film CdTe. In addition, we present a novel means to assess the annealing process and study the kinetics by in-situ monitoring of the transmitted LA light. This has the potential to provide valuable real-time feedback during the annealing process (whether driven by the laser or not) which can help to realize gains in manufacturing throughput and yield. We demonstrate this in-situ method for LA both with and without the presence of CdCl2.

The materials used for this study are superstrate CdTe solar cell device structures without a back contact (Glass/TCO/CdS/CdTe). The CdTe absorber layer was deposited via RF sputtering with the substrate held at room temperature to intentionally create low optoelectronic quality material. The samples were made following similar practices as described elsewhere.20,21 Continuous-wave (CW) laser annealing was carried out using a CW Nd:YAG laser operating at its fundamental wavelength of 1064 nm. The absorption in the CdTe layer at this laser energy (1.17 eV) occurs because of sub-bandgap defect levels, which are especially plentiful in these intentionally sub-optimal films. Davis et al. used photoluminescence experiments in conjunction with photothermal deflection spectroscopy (PDS) to show that the absorption in CdTe near 1.17 eV is due to localized defect states within the bandgap.22 A detailed description of the laser annealing optical arrangement can be found elsewhere23 with a brief explanation given here. The sample was illuminated through the glass substrate (inset Fig. 1(a)) with only the CdTe layer absorbing at this wavelength due to the significantly larger bandgaps of the other layers. The laser beam, which has a Gaussian spatial profile, was first expanded, then in some cases passed through cylindrical lenses to produce a line beam, and finally passed through appropriate apertures. In order to avoid large variations in illumination intensity over the annealed area, only about 50% of the initial beam power was allowed to pass through the aperture (thus blocking the wings of the Gaussian to result in less intensity variation on the sample). The apertures used were a 1 × 6 mm2 aperture used for line beam scans and a 1 mm diameter circular aperture for in-situ measurements. All anneals were performed in an air-tight chamber with infrared (IR) transmitting windows on both front and back surfaces which was evacuated and purged with argon 5 times before annealing.

FIG. 1.

Calculated maximum temperatures (a) reached in the CdTe layer during simulated CW exposures as a function of laser power density. The inset shows a diagram of the thin film stack and annealing configuration. The time dependence of the temperature for three power densities is shown in part (b).

FIG. 1.

Calculated maximum temperatures (a) reached in the CdTe layer during simulated CW exposures as a function of laser power density. The inset shows a diagram of the thin film stack and annealing configuration. The time dependence of the temperature for three power densities is shown in part (b).

Close modal

During single spot anneals, the transmitted intensity of the annealing light is monitored using a photodiode detector, which gave in-situ measurements of the annealing process. (The annealing laser light is only partially absorbed due to the relatively weaker nature of sub-bandgap absorption.) A reference signal was taken from a quartz beam splitter placed before the sample allowing for real-time calibration of fluctuations and drift of the laser intensity. The absence of a back contact allowed for post-annealing characterization of the absorber layer by PDS and X-ray diffraction (XRD) in the same condition as the in situ transmission experiments. Additionally, the absence of a back contact allowed for the later application of CdCl2 while keeping all other processing conditions the same and eliminating any effects of the back contact (reflection and interdiffusion) on the laser annealing process. Surface roughness measurements were made by optical profilometry collected on a Zygo NewView system with a 20× objective lens. XRD was performed using a Philips X'pert Bragg-Brentano X-ray powder diffractometer with Cu Kα1 radiation.

In order to estimate the temperature reached during LA, a finite element simulation of light absorption and heat flow was carried out. Optical and thermal properties of the film layers and substrate can be found in Ref. 24 and references therein with the exception of the absorption coefficient (α) for these particular CdTe layers, which was determined to be 1660 cm−1 at 1064 nm from the PDS measurements shown below. As in the real experiment, the laser light was modeled as incident to the glass superstrate with reflection at each interface calculated according to the Fresnel equations. Beer–Lambert absorption was treated only for the CdTe layer as it was the only film with an appreciable absorption coefficient, α, at 1064 nm (1660 cm−1). The heat generated from laser light absorption versus depth is calculated by taking the derivative of the light intensity with film depth;25 although for times above ∼30 s, only the total power absorption is important. The temperature distribution is then found by solving the time-dependent heat transport equation with the optical absorption as the source. COMSOL Multiphysics®26 was used for these simulations similar to our prior work using pulsed lasers.24 We consider thermal losses due to natural convection on all surfaces to ambient atmosphere at room temperature, as well as losses due to evaporation and infrared emission. The modeled temperatures are considered estimates as they do not consider the temperature dependencies of the physical constants, which are considered to be a small correction.

Fig. 1(a) shows the maximum simulated temperatures at the CdTe/air interface achieved during CW exposures, as well as a schematic of our samples. The temperatures plotted in part (a) for all power densities were taken after 40 s of exposure, which Fig. 1(b) shows was sufficient enough time for the samples to have reached equilibrium. Also, the temperature gradient at this point was less than 1 °C over the entire thickness of the CdTe layer.23 The “high-” and “low-power” regions refer to laser annealing regimes that result in specific material characteristics as will be explained shortly. The temperatures reached in these laser treatments are significantly below the melting threshold of CdTe (1092 °C).

The wavelength dependence of the absorption coefficient at and below the CdTe bandgap was measured by PDS,27,28 with experimental details on our arrangement found elsewhere.29 PDS is particularly adept at measuring very small levels of absorption in thin films and has been used by several other researchers for the study of processing conditions on CdTe films.22,30,31 The PDS data were calibrated by scaling such that the highly absorbing region matched data obtained from a spectrophotometer.29,32,33 The reflectivity (both specular and diffuse components) was measured in a PerkinElmer Lambda 950 UV/Vis/NIR spectrophotometer with a 150 mm integrating sphere. Analysis of the reflectivity measurements was performed within the framework of an optical model based on the Fresnel equations including surface roughness scattering parameters. This is outlined in the  Appendix.

Uniform areas of sufficient size for X-ray diffraction analysis were produced by scanning the laser as a line beam across a roughly 1 × 1 cm2. Samples were annealed at low power (62.4 W/cm2) with dwell times of 30, 100, and 250 seconds and at high power (140 W/cm2) with dwell times of 20, 40, and 100 seconds. Fig. 2 shows the key features of the data taken from these samples. The most likely explanation for the triplet of peaks appearing between 2θ = 21–27° near the position of the zinc blende (111) CdTe peak is that of symmetry lowering associated with twins or stacking faults producing local hexagonal symmetry (wurtzite stacking). The volume fraction of the defected regions is related to the relative areas under the two hexagonal satellite peaks marked by asterisks. Similar triplets indicating structural defects have been previously reported for nanostructured34 and thin film35 CdTe. Its presence does not necessarily reveal true polymorphism, but can also be the result of twinning35 and stacking faults.36 Pure zinc blende is desired for optimal electronic behavior and is the only phase typically seen in the device quality CdTe.36 Indeed, first-principles calculations reveal that a local wurtzite phase will act as a hole trap.35 CdCl2 treatment is associated with the passivation and, in some cases, elimination of 2D structural defects.37 

FIG. 2.

X-ray diffraction spectra from (a) low- and (b) high-power density laser annealed CdTe. Peaks from local wurtzite stacking are distinguished with an asterisk (*).

FIG. 2.

X-ray diffraction spectra from (a) low- and (b) high-power density laser annealed CdTe. Peaks from local wurtzite stacking are distinguished with an asterisk (*).

Close modal

Fig. 2(a) reveals that low-power annealing does not change the volume fraction of defected CdTe even for dwell times of 250 s. Fig. 2(b), on the other hand, shows a systematic reduction in the satellite peaks as a function of time for the higher power density. This is interpreted as a reduction in the density of stacking faults or twins which would imply an improvement in the electronic quality of CdTe absorber. Due to the overlap of the (002) wurtzite peak and the (111) zinc blende peak, it is not possible to unambiguously determine the coherence length of the zinc blende phase.

Figs. 3(a) and 3(b) show the absorption coefficient from the laser annealed samples measured by PDS. The conspicuous oscillations with energy separation ΔE0.1 eV are interference fringes related to the absorber film. This was confirmed by measuring the separation in minima or maxima, ΔE(eV), and calculating the thickness according to l(μm)=0.124/(2nΔE), where n is the real part of the index of refraction and l is in microns. This yielded a thickness value of 2.1 μm which was in good agreement with the expected thickness of 2.2 μm calculated from the deposition parameters. These oscillations lie on top of a very broad peak centered at 0.75 eV. This peak may either arise from a distribution of mid-gap defects or from interference fringes from the thinner layers in the cell stack. Efforts to resolve its origin were not successful; however, the feature does not appreciably change under any of the annealing conditions.

FIG. 3.

Photothermal deflection spectroscopy measurements of (a) low- and (b) high-power laser annealed samples. (c) Evolution of the Urbach energy with laser annealing.

FIG. 3.

Photothermal deflection spectroscopy measurements of (a) low- and (b) high-power laser annealed samples. (c) Evolution of the Urbach energy with laser annealing.

Close modal

At low power, there is a little change to the spectra except for a small drop in α below 1.4 eV, which represents the transitions involving rather shallow defects and band tails. When annealed with higher laser power (Fig. 3(b)), the reduction of α is much more apparent. The reduction of this signal with LA is a result of defects and disorder being annealed out of the film. Also seen in these spectra are changes to the Urbach edge, which spans the region between 1.3 and 1.5 eV, and is a convolution of the conduction and valence band tails. As such, a steepening Urbach edge signifies a decrease in the concentrations of shallow defects that cause band tailing. This tail is characterized by an Urbach energy, EU, which is found by fitting the region to an exponential of the form α=α0eE/EU, where α0 is a constant and E is the photon energy. The values of EU are plotted as a function of time in Fig. 3(c). At low power, an initial decrease in EU quickly saturates, whereas at high power the value is continuously reduced. This behavior suggests that there are two distinct defect annealing mechanisms.

Measurements of the total reflectivity using the spectrophotometer are shown in Fig. 4. The data were taken using an integrating sphere, meaning that they are a sum of specular and scattered reflections. However, it is only the specular component that gives rise to the interference oscillations. The samples annealed at low power (Fig. 4(a)) show no discernible change in reflection with laser annealing. The high power annealed samples (Fig. 4(b)), however, exhibit a continuous decline in the peak-to-peak intensity of the oscillations, while the average reflectivity values remain unchanged. This fact indicates an increase of non-specular scattering from the film. Indeed, previous SEM studies of these materials revealed dramatic changes to the surface morphology under high-power annealing conditions.23 

FIG. 4.

Total reflection spectra for (a) low- and (b) high-power laser annealed samples. The inset in (b) shows the change in reflection, ΔR, that occurs due to interference from the specular reflections.

FIG. 4.

Total reflection spectra for (a) low- and (b) high-power laser annealed samples. The inset in (b) shows the change in reflection, ΔR, that occurs due to interference from the specular reflections.

Close modal

Equations (A1)–(A14) in the  Appendix can be used to estimate the surface roughness of the laser annealed film from reflectivity measurements by measuring the difference between adjacent minima and maxima (ΔR in the inset in Fig. 4(b)) through the inclusion of the surface roughness scattering parameters given in Eqs. (A3) and (A4). The peaks chosen to calculate ΔR are those closest to 1064 nm (1.17 eV) ensuring that the surface roughness calculated is closest to the length scale of relevance to the in-situ transmission measurements (i.e., the maximum at 1.03 eV and minimum at 1.08 eV). ΔR is then calculated by taking the difference of equation (A14) determined at the maximum (1.03 eV) and minimum (1.08 eV). This gives ΔR as a function of surface roughness, which can be compared with the experimentally determined values of ΔR from Fig. 4. An underlying assumption in this calculation is that the scattered component of the reflectivity is constant between adjacent minimum and maximum. This was confirmed by using an integrating sphere to measure only the scattered component of light by removing the section of the sphere receiving the specularly scattered light from the sample. Over the range 1.03–1.08 eV, the scattered component varied only by 0.2% absolute for a given sample thus justifying the assumption. This method only considers changes in the reflectivity due to surface roughness changes at the CdTe surface as well as measured changes in α of the entire thin-film stack. We believe that these are dominated by the relatively much optically thicker CdTe layer, although we cannot explicitly rule out changes in the other layers or at the interfaces as well.

Fig. 5 plots the modeled variation in peak-to-peak intensity ΔR versus root mean square surface roughness (σRMS) of the free CdTe surface. ΔR decreases with increasing surface roughness as expected experimentally, since these peaks are caused by interfering specular reflections. The measured value of ΔR from Fig. 4 for the unannealed reference is 10.9%. This is the approximate value of the leftmost asymptotic value and is consistent with the measured value of σRMS from the optical profilometry of 10 nm. For the sample annealed the longest at high power, the decreased value of ΔR indicates a large increase in RMS surface roughness to 37 nm. We suspect that some grain growth or recrystallization at the high laser powers causes this increased roughness, which would be consistent with our XRD results. The estimates of σRMS from ΔR are average values over the entire area illuminated during the reflectivity measurements. Optical profilometry was attempted to measure the roughness directly; however, large spatial variations in surface roughness following annealing led to a very large variation in results. We have seen that lateral variation in temperature occurs during laser annealing when the beam intensity is non-uniform and the beam size is small compared to the lateral heat flow distance in the laser annealing of CISe thin films. It should be noted that the illumination spot during the optical profilometry measurements is considerably smaller (<1 mm2) than that of the reflectivity measurements, meaning that it cannot average these spatial variations as effectively.

FIG. 5.

Calculated values of ΔR from Eq. (A14) plotted as a function of the surface roughness of the CdTe film. The table shows the experimental values of ΔR from the high-power annealed samples with the corresponding calculated values of σRMS. These are also shown on the plot with red markers.

FIG. 5.

Calculated values of ΔR from Eq. (A14) plotted as a function of the surface roughness of the CdTe film. The table shows the experimental values of ΔR from the high-power annealed samples with the corresponding calculated values of σRMS. These are also shown on the plot with red markers.

Close modal

The use of sub-bandgap light for LA means that a portion of the light is transmitted through the sample. The measurement of this transmission during the annealing process (without CdCl2) is shown in Fig. 6. At the lowest power densities, there is a slow rise in transmission that saturates after 100 s of exposure. At high power densities, there is only a decrease. Intermediate power densities show a mixed behavior in which the initial rising transmission rolls over and then decreases vs time with the exposure of time. This behavior is clearly driven by two distinct processes that are occurring during the LA process, and therefore, understanding these transmission transients will reveal information about the kinetics of the LA process in real-time.

FIG. 6.

In-situ measurements of the transmitted portion of the annealing laser beam.

FIG. 6.

In-situ measurements of the transmitted portion of the annealing laser beam.

Close modal

The optical modeling framework developed in the  Appendix can also be used to understand the transmission transients. The PDS and reflectivity data have revealed that both the absorption coefficient and the surface roughness change during the sub-bandgap LA. Presumably, similar processes would also occur during conventional annealing and could thus be monitored using the sub-bandgap light transmission or reflection methods such as we describe herein. We use the data from Figs. 3 and 4 to extract the surface roughness and absorption coefficient for the particular annealing times listed. Equation (A15) is then used to calculate the transmission of the film stack at 1064 nm, which is plotted in Fig. 7 as a function of surface roughness, simulating the effects of low and high power annealed samples (62.4 W/cm2 and 140 W/cm2, respectively). These curves are plotted normalized to the unannealed transmission value (T0) calculated from the initial surface roughness (10 nm) and the initial absorption coefficient value (1660 cm−1) from the PDS measurements. The initial condition before the laser is turned on is given by the black dot. Annealing at low power for 250 s amounts to a purely vertical movement from this position (red square) as there is no measured change to surface roughness, and is due to a decrease in the absorption coefficient to 1500 cm−1 (Fig. 3(a)). This calculation predicts a 3% increase in transmission from the initial value, which is very similar to the measured value from the in-situ monitoring. Annealing with high power for 100 s reveals a much larger drop in absorption coefficient to 1280 cm−1 (Fig. 3(b)) and an increase in σRMS to 37 nm determined from Fig. 5. These combined effects predict an overall decrease in transmission of about 6%, shown by the red X along the curve. This is slightly higher than the 4% drop seen in the in-situ data after 100 s, but is still in reasonable agreement.

FIG. 7.

Calculated transmission of the thin film stack following laser annealing normalized to the initial transmission plotted versus the CdTe surface roughness. The black circle represents the unannealed films with a measured value of σRMS of 10 nm. The red square shows the asymptotic transmission of the lowest power anneal where σRMS was observed not to change, which predicts a rise in the transmission with LA. The red X shows the combined effects of increasing surface roughness and decreasing absorption coefficient, which predicts an overall drop in the transmission.

FIG. 7.

Calculated transmission of the thin film stack following laser annealing normalized to the initial transmission plotted versus the CdTe surface roughness. The black circle represents the unannealed films with a measured value of σRMS of 10 nm. The red square shows the asymptotic transmission of the lowest power anneal where σRMS was observed not to change, which predicts a rise in the transmission with LA. The red X shows the combined effects of increasing surface roughness and decreasing absorption coefficient, which predicts an overall drop in the transmission.

Close modal

This analysis shows that the general features of the in-situ transmission can be used to reveal the material property changes that occur during annealing. Specifically, the transmission rise at low power indicates electronic defect annealing, and the decrease with high power combines defect annealing with surface roughness increases. We have also shown that at high power, there is a decrease in the presence of local stacking faults, although it is unclear if this is related. The exact cause of these surface changes is presently unknown, and we speculate that it is related to the grain growth that has been shown previously with laser annealing.17 This analysis also shows that there are two distinct kinetic processes that drive each behavior and that only by annealing at high power can both be activated.

The transmission monitoring technique presented in Sec. III C was extended to study the in-situ annealing data from CdTe in the presence of CdCl2. The Cl activation step is vital in CdTe PV devices in order to achieve the highest quality material. Samples were prepared similarly as before with the addition of CdCl2 on the surface of the CdTe film. The CdCl2 was applied in a methanol solution that was allowed to dry, leaving a thin film. The sample was not otherwise heat treated, so that all the observed effects are from the LA. The in-situ transmission data during laser annealing are shown in Fig. 8, where the CdCl2 treated data are shown compared to the non-CdCl2 treated material laser annealed at the same power density. These data show much larger initial increases in the transmission when Cl is present, even at higher powers where no increase was seen without Cl. This shows that there is an even larger reduction in α at 1064 nm resulting from increased defect annealing in the presence of Cl. At the highest powers, the transmission eventually drops below that of the non-Cl treated samples, which could signify greater grain growth and stacking fault elimination, both of which have been shown to occur with the presence of Cl in CdTe (Refs. 8 and 38) (especially for films deposited at low substrate temperature such as these). This also serves as a first demonstration of laser induced Cl-activation for CdTe thin films.

FIG. 8.

Normalized in-situ transmission data of both Cl and non-Cl treated CdTe during laser annealing.

FIG. 8.

Normalized in-situ transmission data of both Cl and non-Cl treated CdTe during laser annealing.

Close modal

In this research, we have shown the utility of sub-bandgap laser light to anneal structural and electronic defects in thin film CdTe. XRD measurements revealed the removal of structural defects such as twins and stacking faults, while optical measurements showed that sub-bandgap defects were also reduced by LA. In addition, an optical model was presented that can be used in conjunction with in-situ measurements of the transmitted annealing laser light to reveal information of these changes in real-time. This represents a simple, yet informative, monitoring method that could lead to increased product yield in a manufacturing setting. Finally, the analysis developed for in-situ monitoring was applied to the effects of LA of CdTe in the presence of CdCl2. The results clearly show enhancements in the degree of roughness increase and removal of sub-bandgap defects compared to laser annealing without CdCl2.

This work was fully supported by the Department of Energy through the Bay Area Photovoltaic Consortium under Award No. DE-EE0004946.

To interpret the measured optical properties, the reflection and transmission coefficients for a multilayer stack were calculated. These calculations also accounted for surface roughness of the CdTe free surface. The Fresnel coefficients for a single interface which scatters non-specularly between layers l and m having complex indices of refraction, ñn+ik, at normal incidence are

rlm=slmr(ñlñmñl+ñm),
(A1)
tlm=slmt(2ñlñl+ñm),
(A2)

where sij are the scattering parameters defined by39 

slmr=exp{12[2π(nlnm)σlmλ]2},
(A3)
sijt=exp{12[2πniσijλ]2}.
(A4)

Equations (A3) and (A4) amount to a scale factor that is determined by the surface roughness at the interface of films l and m(σlm), the real part of the index of refraction (nl,m), and the wavelength (λ). The Fresnel coefficients for a stack of films can then be calculated by Airy summation of the reflected and transmitted components through each film. For a three film stack (CdTe/CdS/TCO) on a glass substrate free standing in air, this eventually leads to

rtotal=r12345+t12345r51t54321e2iδ51r54321r51e2iδ5,
(A5)
ttotal=t12345t51eiδ51r51r54321e2iδ5,
(A6)

with the nested coefficients being

r123=r12+t12r23t21e2iδ21r21r23e2iδ2,
(A7)
t123=t12t23eiδ21r23r21e2iδ2,
(A8)
r1234=r123+t123r34t321e2iδ31r21r23e2iδ3,
(A9)
t1234=t123t34eiδ31r34r321e2iδ3,
(A10)
r12345=r1234+t1234r45t4321e2iδ41r4321r45e2iδ4,
(A11)
t12345=t1234t45eiδ41r45r4321e2iδ4.
(A12)

The subscript 1 refers to an air layer from which the light is incident. The physical representation of the other numbers depends on whether the light is incident on the CdTe side or through the glass. For example, during the reflection measurements, light is incident on the CdTe, meaning that 2 is CdTe, 3 is CdS, etc. The phase factors δm are

δm=(2πnmdmλ)+iαmdm2,
(A13)

where αm is the absorption coefficient of the material in layer m. In this case, the reflectance can be calculated by the method prescribed in Ref. 40 by considering the reflectance of an optically thick glass substrate that incoherently scatters light and then simply adding additional films on top. This leads to

R=|r12345|2+|t12345|2|r51|2|t54321|2exp(2αd)1|r54321|2|r51|2exp(2αd),
(A14)

where α and d are the absorption coefficient and thickness of the substrate, respectively. The situation for calculating the transmittance is, in principle, the same. However, in practice, it is much more difficult to calculate since in the in-situ transmission measurements used in this study the light is incident on the glass substrate. This means that one cannot start by calculating the transmission coefficient of an incoherently scattering substrate and add the films as in Ref. 40. Instead, one must first calculate the transmission according to

T=|ttotal|2
(A15)

and then integrate with respect to the real part of the phase factor δm of the optically thick medium (glass) over all possible phases. This onerous calculation can be avoided by realizing that in our transmission experiment, we are only interested in relative changes to the transmission. Therefore, any oscillations that appear due to coherent scattering in the glass will be completely canceled out as long as the index and thickness of the glass do not change. Therefore, Eq. (A15) is sufficient for us to calculate the relative changes in transmission.

1.
A.
Goodrich
,
P.
Hacke
,
Q.
Wang
,
B.
Sopori
,
R.
Margolis
,
T. L.
James
, and
M.
Woodhouse
,
Sol. Energy Mater. Sol. Cells
114
,
110
(
2013
).
2.
M.
Woodhouse
,
A.
Goodrich
,
M.
Redlinger
,
M.
Lokanc
, and
R.
Eggert
,
The Present, Mid-Term, and Long-Term Supply Curves for Tellurium; and Updates in the Results from NREL's CdTe PV Module Manufacturing Cost Model
(
NREL/PR-6A20-60430, Golden, CO
,
USA
,
2013
).
3.
W. L.
Rance
,
J. M.
Burst
,
D. M.
Meysing
,
C. A.
Wolden
,
M. O.
Reese
,
T. A.
Gessert
,
W. K.
Metzger
,
S.
Garner
,
P.
Cimo
, and
T. M.
Barnes
,
Appl. Phys. Lett.
104
,
143903
(
2014
).
4.
L.
Kranz
,
C.
Gretener
,
J.
Perrenoud
,
R.
Schmitt
,
F.
Pianezzi
,
F.
La Mattina
,
P.
Blösch
,
E.
Cheah
,
A.
Chirilă
,
C. M.
Fella
,
H.
Hagendorfer
,
T.
Jäger
,
S.
Nishiwaki
,
A. R.
Uhl
,
S.
Buecheler
, and
A. N.
Tiwari
,
Nat. Commun.
4
,
2306
(
2013
).
5.
X.
Mathew
,
J. P.
Enriquez
,
A.
Romeo
, and
A. N.
Tiwari
,
Sol. Energy
77
,
831
(
2004
).
6.
A.
Romeo
,
G.
Khrypunov
,
F.
Kurdesau
,
M.
Arnold
,
D. L.
Bätzner
,
H.
Zogg
, and
A. N.
Tiwari
,
Sol. Energy Mater. Sol. Cells
90
,
3407
(
2006
).
7.
A. N.
Tiwari
,
A.
Romeo
,
D.
Baetzner
, and
H.
Zogg
,
Prog. Photovoltaics Res. Appl.
9
,
211
(
2001
).
8.
B. E.
McCandless
and
J. R.
Sites
, in
Handbook of Photovoltaics Science and Engineering
, 2nd ed., edited by
A.
Luque
and
S. S.
Hegedus
(
John Wiley & Sons, Ltd
,
West Sussex, England
,
2011
), pp.
600
640
.
9.
R.
Chakrabarti
,
S.
Ghosh
,
S.
Chaudhuri
, and
A. K.
Pal
,
J. Phys. D: Appl. Phys.
32
,
1258
(
1999
).
10.
R.
Dharmadasa
,
O. K.
Echendu
,
I. M.
Dharadasa
, and
T.
Druffel
,
ECS Trans.
58
,
67
(
2013
).
11.
J.
Li
,
D. R.
Diercks
,
T. R.
Ohno
,
C. W.
Warren
,
M. C.
Lonergan
,
J. D.
Beach
, and
C. A.
Wolden
,
Sol. Energy Mater. Sol. Cells
133
,
208
(
2015
).
12.
K. M.
Rickey
,
Q.
Nian
,
G.
Zhang
,
L.
Chen
,
S. V.
Bhat
,
Y.
Wu
,
G.
Cheng
, and
X.
Ruan
,
Proc. SPIE
8465
,
846505
(
2012
).
13.
B. J.
Simonds
,
H. J.
Meadows
,
S.
Misra
,
C.
Ferekides
,
P. J.
Dale
, and
M. A.
Scarpulla
,
J. Photonics Energy
5
,
050999
(
2015
).
14.
H. J.
Meadows
,
A.
Bhatia
,
V.
Depredurand
,
J.
Guillot
,
D.
Regesch
,
A.
Malyeyev
,
D.
Colombara
,
M. A.
Scarpulla
,
S.
Siebentritt
, and
P. J.
Dale
,
J. Phys. Chem. C
118
,
1451
(
2014
).
15.
A.
Bhatia
,
H.
Meadows
,
W. M.
Hlaing Oo
,
P. J.
Dale
, and
M. A.
Scarpulla
,
Thin Solid Films
531
,
566
(
2013
).
16.
H. J.
Meadows
,
D.
Regesch
,
M.
Thevenin
,
J.
Sendler
,
T.
Schuler
,
S.
Misra
,
B. J.
Simonds
,
M. A.
Scarpulla
,
V.
Gerliz
,
L.
Guetay
,
J.
Guillot
, and
P. J.
Dale
,
Thin Solid Films
582
,
23
26
(
2015
).
17.
A. L.
Dawar
,
C.
Jagadish
,
K. V.
Ferdinand
,
A.
Kumar
, and
P. C.
Mathur
,
Appl. Surf. Sci.
22/23
,
846
(
1985
).
18.
D. J.
As
and
L.
Palmetshofer
,
J. Cryst. Growth
72
,
246
(
1985
).
19.
N.-H.
Kim
,
C.
Il Park
, and
J.
Park
,
J. Korean Phys. Soc.
62
,
502
(
2013
).
20.
N. R.
Paudel
and
Y.
Yan
,
Appl. Phys. Lett.
104
,
143507
(
2014
).
21.
N.
Paudel
,
K. A.
Wieland
, and
A. D.
Compaan
,
Sol. Energy Mater. Sol. Cells
105
,
109
(
2012
).
22.
C. B.
Davis
,
D. D.
Allred
,
A.
Reyes-Mena
,
J.
Gonzalez-Hernandez
,
O.
Gonzalez
,
B. C.
Hess
, and
W. P.
Allred
,
Phys. Rev. B
47
,
13363
(
1993
).
23.
B. J.
Simonds
,
S.
Misra
,
N.
Paudel
,
K.
Vandewal
,
A.
Salleo
,
C.
Ferekides
, and
M. A.
Scarpulla
,
Proc. SPIE
9180
,
91800
F (
2014
).
24.
B. J.
Simonds
,
V.
Palekis
,
M. I.
Khan
,
C. S.
Ferekides
, and
M. A.
Scarpulla
,
Proc. SPIE
8826
,
882607
(
2013
).
25.
B. S.
Yilbas
,
Laser Heating Applications: Analytical Modeling
(
Elsevier
,
2012
).
26.
COMSOL Multiphysics, Version 4.3 (
2012
).
27.
A. C.
Boccara
,
D.
Fournier
,
W.
Jackson
, and
N. M.
Amer
,
Opt. Lett.
6
,
51
(
1981
).
28.
W. B.
Jackson
,
N. M.
Amer
,
A. C.
Boccara
, and
D.
Fournier
,
Applied Optics
20
,
1333
(
1981
).
29.
K.
Vandewal
,
S.
Albrecht
,
E. T.
Hoke
,
K. R.
Graham
,
J.
Widmer
,
J. D.
Douglas
,
M.
Schubert
,
W. R.
Mateker
,
J. T.
Bloking
,
G. F.
Burkhard
,
A.
Sellinger
,
J. M.
Frechet
,
A.
Amassian
,
M. K.
Riede
,
M. D.
McGehee
,
D.
Neher
, and
A.
Salleo
,
Nat. Mater.
13
,
63
(
2014
).
30.
J. G.
Mendoza-Alvarez
,
B. S. H.
Royce
,
F.
Sanchez-Sinencio
,
O.
Zelaya-Angel
,
C.
Menezes
, and
R.
Triboulet
,
Thin Solid Films
102
,
259
(
1983
).
31.
A.
Bezryadina
,
C.
France
,
R.
Graham
,
L.
Yang
,
S. A.
Carter
, and
G. B.
Alers
,
Appl. Phys. Lett.
100
,
013508
(
2012
).
32.
N. M.
Amer
and
W. B.
Jackson
,
Hydrogenated Amorphous Silicon-Optical Properties
(
Elsevier
,
1984
).
33.
E.
Buchaca-Domingo
,
K.
Vandewal
,
Z.
Fei
,
S. E.
Watkins
,
F. H.
Scholes
,
J. H.
Bannock
,
J. C.
De Mello
,
L. J.
Richter
,
D. M.
DeLongchamp
,
A.
Amassian
,
M.
Heeney
,
A.
Salleo
, and
N.
Stingelin
,
J. Am. Chem. Soc.
137
,
5256
(
2015
).
34.
Y.
Ma
,
J.
Jian
,
R.
Wu
,
Y.
Sun
, and
J.
Li
,
Powder Diffr.
26
,
S47
(
2011
).
35.
Y.
Yan
,
M. M.
Al-Jassim
,
K. M.
Jones
,
S.-H.
Wei
, and
S. B.
Zhang
,
Appl. Phys. Lett.
77
,
1461
(
2000
).
36.
K.
Durose
, in
CdTe and Related Copmounds; Physics, Defects, Hetero- and Nano-Structures, Crystal Growth, Surfaces and Applications
, edited by
R.
Triboulet
and
P.
Siffert
(
Elsevier, Ltd.
,
Amsterdam, The Netherlands
,
2010
), pp.
171
227
.
37.
C.
Uzan
,
R.
Legros
,
Y.
Marfaing
, and
R.
Triboulet
,
Appl. Phys. Lett.
45
,
879
(
1984
).
38.
S.
Yoo
,
K. T.
Butler
,
A.
Soon
,
A.
Abbas
,
J. M.
Walls
, and
A.
Walsh
,
Appl. Phys. Lett.
105
,
062104
(
2014
).
39.
I.
Filinski
,
Phys. Status Solidi
49
,
577
(
1972
).
40.
O.
Stenzel
,
The Physics of Thin Film Optical Spectra
(
Springer
,
Berlin
,
2005
).