Abstract
High-throughput experimentation provides efficient mapping of composition–property relationships, and its implementation for the discovery of optical materials enables advancements in solar energy and other technologies. In a high throughput pipeline, automated data processing algorithms are often required to match experimental throughput, and we present an automated Tauc analysis algorithm for estimating band gap energies from optical spectroscopy data. The algorithm mimics the judgment of an expert scientist, which is demonstrated through its application to a variety of high throughput spectroscopy data, including the identification of indirect or direct band gaps in Fe2O3, Cu2V2O7, and BiVO4. The applicability of the algorithm to estimate a range of band gap energies for various materials is demonstrated by a comparison of direct-allowed band gaps estimated by expert scientists and by automated algorithm for 60 optical spectra.
Introduction
Modern technologies, such as photovoltaics, solar fuels, electrochromic devices, window coatings, and pigments, require materials with specific optical properties. High-throughput (HiTp) and combinatorial materials science approaches have been successfully applied for the discovery of high-performance optical materials.(1) Efficient synthesis techniques employing HiTp approaches provide access to high-order, for example, ternary and quaternary, composition spaces, which have been sparsely explored for the discovery of functional materials. Applying HiTp optical characterization on such material libraries produces vast quantities of spectral data; and some optical parameters, such as average reflectivity over the visible range, can be readily calculated.(2) Other performance metrics are model-dependent and are traditionally extracted through manual analysis. In this article, we focus on the data analytic aspects of estimating band gap energies from HiTp transmission and reflection responses of combinatorial material libraries under ultraviolet–visible (UV–vis) illumination. We demonstrate our approach in the context of HiTp screening of composition libraries for the discovery of light absorbers for solar energy applications.
While the optimal band gap of a light absorber for photovoltaic or solar fuels applications varies with device design, the identification of new semiconductors with band gap energies in the visible to near-ultraviolet range is important for advancing these technologies.(3) The band gap energy is the primary performance metric for qualifying a material as a candidate for solar energy applications, motivating rapid measurement of band gap energy for accelerating the discovery of solar absorber materials. In particular, the HiTp methods must readily identify the band gap energy of light absorber phases in a composition library and any systematic variation in band gap energy with respect to composition, a common manifestation of composition alloying within a light absorber phase.(4)
High-throughput optical property measurements typically rely on estimation of properties from transmission and reflectance responses of materials under illumination. We recently described an on-the-fly high-throughput spectroscopy instrument capable of measuring the transmission and total reflection responses (TR instrument) at a throughput better than 1 sample per second(5) and have also adapted this technique for diffuse reflectance measurements (DR instrument). Estimation of band gap energy from these high throughput measurements is an arduous task when using traditional manual analysis by an expert scientist, limiting the efficacy of high-throughput data acquisition. In this article, we present a constrained piecewise linear fitting based algorithm that allows rapid estimation of band gap energy (typically, <0.5 s per spectrum on an Intel Core i7-3770 CPU @ 3.4 GHz, 16 GB RAM, 64-bit Windows 7 OS). We build intuitive parameters into the algorithm to mimic an expert scientist’s judgment so that absorption spectra that do not conclusively identify a band gap are flagged, and the band gap energy is calculated for the remaining samples. We demonstrate this approach by applying the algorithm to the characterization of various metal oxides using both the TR and DR measurement techniques.
Tauc Analysis and Existing Algorithms
In both automated and manual estimation of the band gap energy from an optical absorption spectrum, researchers typically employ the Tauc relationship:(6)
( 1) where h is the Planck’s constant, ν is the frequency of light, and Eg is the band gap energy. The value of the exponent n is related to the electronic nature of the band gap, with values of 3, 2, 3/2, and 1/2 corresponding to indirect forbidden (IF), indirect allowed (IA), direct forbidden (DF), and direct allowed (DA) transitions, respectively. This approximate relationship between photon energy and absorption is particularly relevant when the absorption coefficient (α) exceeds 104 cm–1 for photon energies approximately 1 eV above the band gap energy.(6) This condition essentially requires the semiconductor under investigation to be a strong absorber, and for the purpose of identifying materials for solar absorption applications, materials that do not meet the strong absorber criterion are not of primary interest.
The band gap energy, Eg, is typically determined through inspection of (αhν)1/n vs hν plots (also called Tauc plots),(7) where the linear trend given by eq 1 is modeled as the tangent of the Tauc plot near the point of maximum slope if the Tauc plot contains a sufficiently linear region.(8) This linear tangent is then extrapolated to the point where (αhν)1/n is 0 or a small value provided by modeling the baseline signal.
It is important to note that although the Tauc approach was derived using the parabolic band representation of localized energy states for amorphous materials, it typically remains valid for polycrystalline materials using parabolic band approximation based on Maxwell–Boltzmann statistics.(9) However, in case of defective or degenerate semiconductors, the band gap observed in optical absorption measurements (apparent band gap) could differ from the fundamental band gap of the semiconductor due to effects such as Burstein–Moss shifts,(10) band gap renormalization due to electron–electron and electron–ion interactions,(11) and formation of dopant levels within the band gap. While empirical estimation of the fundamental band gap from optical spectra of degenerate semiconductors is an active area of research,(9) the intentional modification of optical absorption by tailoring defect chemistry is also a promising strategy,(12) and for the purposes of semiconductor discovery for solar absorption, the apparent band gap is a suitable property to map in high throughput studies. Given the high throughput implementation of Tauc analysis in the present work, each reported band gap is understood to be the apparent band gap of the material in its thin film (and likely defective) form.
Since manual inspection of Tauc plots to identify the point of maximum slope is prohibitive for rapid estimation of band gaps, several semiautomated algorithms for Tauc analysis of absorption spectra have been reported. Anderson et al.(13) provide composition-band gap mapping by providing user-specified ranges of the photon-energy and Tauc-value ((αhν)1/n) to define a portion of the Tauc plot for linear regression. The extrapolation of the fitted Tauc line to the (αhν)1/n = 0 line provides the estimate of Eg. Ghobadi et al.(14) use a similar approach to determine band gap as a function of particle size in CdSe nanostructured thin films. Such algorithms are not amenable to automated analysis on material libraries in which the band gap energy may span a wide energy range. To overcome the need for user-specified partitions of the Tauc plot, the maxima in the first-derivative of (αhν)1/n vs hν may be used to identify data points whose tangents represent the Tauc line. However, this approach is sensitive to noise and local optical features, as demonstrated and discussed by Escobedo Morales et al.(8)
It is also important to recognize that absorption spectra may contain small contributions from nonlinear effects (e.g., plasmonic scattering) and subgap absorption tails due to defect states or intraband absorption.(15) For IA, IF, and DF gaps, the large value of n in eq 1 amplifies the importance of these contributions to the absorption signal, possibly resulting in a skewed band gap energy upon extrapolation of the fitted Tauc line to (αhν)1/n = 0. To address these issues, we developed an analysis algorithm that partitions the Tauc plot into a series of linear segments and then identifies the linear segment most representative of the Tauc relationship based on the energy ranges, Tauc value ranges, and Tauc slopes of the line segments. The algorithm also identifies a line segment to model the subgap absorption baseline, and the intersection of the two lines provides the estimation of Eg. We have encoded this process into an automated algorithm, and below we demonstrate its ability to interpret Tauc spectra from (a) 49 duplicate α-Fe2O3 samples using TR data, (b) α-Cu2V2O7 using TR data, (c) monoclinic-BiVO4 using DR data, and (d) a biphasic sample using DR data.
Some limitations of high throughput band gap mapping and opportunities for enhancing high throughput materials discovery are also discussed. The algorithm contains several free parameters whose values have been chosen through manual consideration of thousands of Tauc spectra. The ability of the algorithm to mimic expert judgment is demonstrated by comparing its analysis of various oxide and sulfide thin films to that of expert scientists. This automated extraction of band gap energy is an enabling technology for light absorber discovery and more generally for combinatorial materials science, as demonstrated in part 2 of this manuscript series.
Algorithm and Discussion
Generation of Tauc Property Spectra
In this section, we describe processing of optical data to generate the Tauc spectra (eq 1) on which the band gap estimation algorithm is applied. For the TR instrument, the measured transmission and reflection spectra are scaled by a reference transmission spectrum obtained on a bare substrate and a Spectralon white cube, respectively. The resulting fractional transmission (T) and fractional reflection (R) spectra are processed for outlier removal and noise filtering using a fourth-degree polynomial Savitzky–Golay filter and photon energy filtering window of 45 nm.(16) The absorption coefficient of the sample and the transmission are related according to the Beer–Lambert equation (αL = −ln T).(17) With an approximation that the fractional intensity of light that has the opportunity to be absorbed by the sample is given by 1 – R, the Beer–Lambert equation is modified(18) as follows:
( 2) where α is the absorption coefficient and L is the optical path length through the sample thickness.
For the DR instrument, a Spectralon white reference is used to calculate the fractional diffuse reflection (DR) spectra, which is then smoothed using Savitzky–Golay filtering. The absorption coefficient (α) can be expressed in terms of DR according to the Kubelka–Munk radiative transfer model:(19)
( 3) where s is the spectral scattering factor. We adopt the common assumption that s is a constant.(20) This approximation is a practical necessity for HiTp analysis and introduces the possibility of systematic errors in the extracted band gap from DR data, which can be addressed for representative samples using detailed optical characterization techniques such as spectroscopic ellipsometry.(21)
With this data processing, both TR and DR instruments yield optical spectra that are proportional to α, leading to an instrument-specific definition of the quantity β, which is defined as αL (eq 2) for the TR instrument and α/s (eq 3) for DR instrument. To apply eq 1, we define the family of Tauc property spectra as
( 4) where n is the Tauc exponent used in eq 1, which in the present work is limited to IA (n = 2) and DA (n = 1/2) band gaps. The corresponding Tauc property spectra are referred to as TPIA and TPDA, respectively, which are interpreted to ascertain the respective band gap energies, EgIA and EgDA. Each Tauc spectrum is scaled by its maximum value (see eq 4), making the proportionality constants in eqs 2 and 3 inconsequential and enabling the parameters for the band gap estimation algorithm to be generalized for all types of TP. We note that this scaling makes the TP spectrum unitless, and since TP is analyzed as a function of hν, slopes of this spectrum have units of eV–1.
Constrained Piecewise Linear Fitting
TP spectra are fit with k + 1 linear segments using k nonterminal nodes, and the value of k is chosen so that the piecewise linear regression model routinely fits the data with a coefficient of determination in excess of 0.99, and we choose k = 6 upon examination of several TP spectra. The linear fit is optimized by minimizing the loss function, which is defined as normalized sum of squared errors, that is, ∑((TP – TPfit)/TP)2. The division by TP in this objective function promotes a better fit for the baseline absorption and mitigates sensitivity to noise in the higher absorption region of TP. In particular, this normalization has an important consequence for fitting the nonlinear onset of absorption near the band gap energy. With a typical least-squares objective function, this nonlinear region can be fit by a single line with little penalty since TP is small at the onset of absorption. Our modification to the traditional objective function amplifies the importance of this absorption onset region such that it is usually modeled with multiple linear segments, which promotes the identification of baseline signals that mimic those identified by expert scientists. During the segmented linear fitting procedure, the energy offset between successive nodes is constrained to be greater than p1 = 0.05 eV, which discourages overfitting of local features (typically noise). Additionally, noise in TP at lower and higher energy limits of the instrument can cause the first and last linear segments to misrepresent the data. Therefore, these segments are retained for further analysis only if their energy range is greater than a certain minimum, which we chose to be twice the minimum offset between nodes (p2 = 2p1 = 0.1 eV).
As discussed below, the band gap estimation algorithm can be sensitive to an excess of line segments in the fitting model, and while k = 6 is often necessary, some TP spectra require fewer line segments. While an iterative fitting routine with different values of k could be used to identify the requisite number of line segments, we have developed an alternate strategy that focuses on removing the primary artifact of overfitting, that is, dissecting the linear Tauc region into multiple line segments. If a region of TP is nearly linear and would be considered by an expert analyst to be the linear Tauc region, that entire region should be modeled as a single line segment in the fitting result. This performance can be achieved by starting with an overfit line segment model followed by merging of neighboring line segments that are sufficiently similar. We implement this strategy by merging neighboring line segments that meet the following criterion:
( 5) where Δ(TP)i and Δ(TP)i+1 are the extent of TP values traversed by the ith and (i + 1)th linear segments, respectively. The quantity δi,merge is the maximum difference in TP between this pair of neighboring line segments and the line segment created by merging these line segments into a single line segment that connects their extreme end points. This quantity is illustrated in Figure 1, which demonstrates that a merged line segment sufficiently represents a pair of neighboring line segments if δi,merge is small. This merging step is repeated iteratively until no neighboring line segments meet the above criterion, and we find that the resulting line segment model of TP closely mimics the judgment of experts, particularly with the parameter p3 = 0.1. Since the number of line segments may be lower than k after this merging procedure, we define the postmerge number of line segments as ns.
Thin-Film Interference Effects
Thin film interference is a well-known phenomenon in which light reflected at the film–air and film–substrate interfaces of a thin film interfere to generate oscillations in the reflection and transmission spectra. In the case of optical spectra obtained from the TR instrument, the term T/(1 – R) in eq 2 provides interference-free determination of optical absorption coefficient.(22) For DR spectra, the application of Kubelka–Munk radiative transfer model (eq 3) assumes that a vanishingly small fraction of incident light is diffusely reflected from the film–substrate interface; and consequently the model is not applicable to DR spectra exhibiting interference oscillations. For the present purpose of solar light absorber discovery, we identify and disregard such spectra because thin-film interference oscillations are generally observed in weakly absorbing samples. Prior to application of our band gap estimation algorithm, we filter out samples whose optical spectra have significant contributions from interference patterns using a minimum allowed slope (MAS) criterion (eq 6):
( 6) where Si is the slope of the ith line segment. TP spectra that fail this criterion are excluded from further analysis, and we observe that p4 = −2 eV–1 provides robust identification of spectra with significant thin-film interference effects. While alternate methods for identifying interference fringes can be employed, the MAS criterion for the piecewise fit linear segments provides interference detection with less sensitivity to noise than, for example, peak identification methods.
Band Gap Estimation
With a line segment model of TP in hand, the algorithm proceeds by identifying both the line segment that best represents the above-gap linear Tauc region (the “Tauc line segment”, see eq 1) and the line segment that best represents the below-gap baseline. Given a Tauc line segment and baseline segment, the abscissa of the intersection of these lines represents the corresponding band gap energy. It is worth noting that multiple pairs of absorption onset and baseline linear segments could be found in a single TP spectrum, for example, in the case of a multiphase system. The algorithm is thus generalized to permit the identification of an arbitrary number of band gaps, although this number is practically limited to 2 or 3 when the algorithm is seeded with k = 6 nonterminal nodes.
We proceed by defining and describing the set of inequalities for evaluating whether a given line segment (index τ) from the fitting model is a Tauc line segment with a well-defined baseline. A primary criterion set (C1) is used to evaluate each nonterminal line segment (τ ∈ [2,ns – 1]) by comparing its properties to those of the preceding (lower photon energy, index τ – 1) and succeeding (higher photon energy, index τ + 1) line segments. A second, modified criterion set (C2) is used to evaluate the last line segment (τ = ns).
Tauc Line Segment Identification
Criterion set 1 (C1): To mimic an expert’s estimation of the Tauc line as the tangent of TP at the point of maximum slope, the slope of Tauc line segment τ must exceed that of its preceding and succeeding line segments. To elucidate the prudence of these criteria, we consider the relationship of the Tauc line segment with the lower-energy absorption edge, which is typically manifested as an exponential tail.(6) As a result, TP has positive curvature for photon energies just below the linear Tauc region. Attributing a region within this absorption tail to a Tauc line segment can lead to significant underestimation of the band gap. By requiring that the slope of the Tauc line segment is greater than those of the preceding and succeeding line segments, the identified Tauc line will not be in the absorption tail, providing the best estimate of the band gap energy. Since the line segment preceding the Tauc line segment is part of the absorption tail, it should have a positive or approximately zero slope, leading to an additional criterion that the slope of the preceding line segment exceed a minimum value of p5 = −0.05 eV–1. In addition, line segment τ should capture at-least a minimum TP difference of p6 = 0.1 to ensure that the Tauc line segment region represents a substantial portion of the normalized TP. Compared to the alternate strategy of identifying the maximum slope point in TP and constructing the Tauc line from the corresponding tangent, we find that combining the line segment merging strategy with the following set of inequalities provides an algorithm that is less susceptible to noise and more consistent with an expert’s analysis:
( 7a) 
( 7b) 
( 7c) 
( 7d)
Criterion Set 2 (C2): Evaluating the terminal line segment as a Tauc line segment is necessary for detecting a band gap near the upper limit of the photon energy measurement range. Since a subsequent line segment is not available for evaluation of the inequalities in eq 7, the applicable subset of criteria are adopted and the Δ(TP) criterion is made more restrictive. An additional criterion that the photon energy range (ΔEns) spanned by the line segment is sufficiently large is added to eliminate artifacts from sharp transients in the absorption signal that can arise due to poor signal-to-noise at the highest photon energies, where the lamp intensity is weak. The resulting set of inequalities for τ = ns are summarized as
( 8a) 
( 8b) 
( 8c) 
( 8d)
Baseline Segment Identification
For a Tauc line segment (line segment index τ), the corresponding baseline segment (line segment index B) is defined as the lowest energy linear segment that precedes the Tauc line segment and has a slope that is sufficiently less than the Tauc line segment but above the minimum value defined in C1. Further, a constraint that slope of the linear segments monotonically increases from baseline segment up to the Tauc line segment is added, as is expected for the absorption onset.
( 9a) 
( 9b) 
( 9c) 
( 9d) where Ei is the high energy terminal value for line segment i, and p7 = 0.2 eV–1.
This criteria set promotes identification of a baseline that precedes the nonlinear absorption tail described above, for using this tail as a baseline would result in overestimation of the band gap energy. If a baseline segment cannot be identified for a given Tauc line segment, the Tauc line segment is not used for band gap estimation. When multiple Tauc line segments are identified in a single TP, the baseline line segment for a given Tauc line segment must succeed any lower-energy Tauc line segments.
These criteria complete the band gap estimation algorithm;, and a summary of the analysis flow and parameters involved in each process are provided in Figure 2 and Table 1, respectively. In the following section, we discuss the application of this algorithm to a wide range of light absorbers.
Figure 2. Flowchart of the automated band gap estimation algorithm. The steps employing user-defined parameters are noted, and the dashed line encloses the subroutine for identifying the Tauc line segment(s).
Table 1. Details of the Parameters Involved in the Automated Band-Gap Estimation Algorithm
| parameter | description | value | reasoning |
|---|---|---|---|
| p1 | minimum offset between successive nodes of piecewise linear fits. | 0.05 eV | discourage overfitting of local features by separating linear segment nodes along the energy axis. |
| p2 | minimum energy span for first and last linear segments. | 0.1 eV | similar to p1 with increased value to avoid overfitting of transients at extremes of the spectra. |
| p3 | fraction of TP value traversed by neighboring line segments to determine if they should be merged. | 0.1 | mimic the level of linear smoothing that is visually performed by an expert analyst, which scales with the slope of the TP in the surrounding region. |
| p4 | determines the minimum allowed slope of the line segments. | –2 eV–1 | provides robust identification of spectra with significant thin-film interference effects. |
| p5 | minimum slope for a line segment preceding the Tauc line segment up to and including the corresponding baseline segment. | –0.05 eV–1 | encodes the physical requirement that a Tauc line segment is preceded by line segments that are either part of an absorption tail or a baseline and should have a shallow or positive slope. |
| p6 | minimum Δ(TP) captured by a Tauc line segment | 0.1 | encourages the identification of linear features that describe a significant fraction of the TP signal. |
| p7 | minimum difference in slope between a Tauc line segment and its corresponding baseline segment | 0.2 eV–1 | requires band gap transition to yield a substantial increase in TP slope and discourages false band gap identification from subgap absorption, for example, from defect states or intraband transitions. |
Results and Discussions
To demonstrate the algorithm and verify the estimation of band gap energy, we apply the algorithm to the characterization of phase-pure metal oxides. As a first example, we apply the algorithm described above to optical spectra obtained using TR instrument on 49 duplicate 1 mm2 Fe2O3 thin film samples synthesized on a FTO coated glass substrate via inkjet printing.(5) Figure 3 depicts the initial data processing for a representative sample where the fraction T and R spectra (Figure 3a) were used to calculate β, the absorption coefficient up to a factor of the film thickness (eq 2, Figure 3b). To investigate the presence of both a direct (DA) and an indirect (IA) band gap, the respective TP spectra were calculated using eq 4 (Figure 3c).
Figure 3. (a) Fractional transmission (T) and reflection (R) spectra for a representative Fe2O3 sample; (b) spectrum proportional to absorption coefficient, as derived from T,R using eq 2; (c) direct-allowed (DA) and indirect-allowed (IA) TP spectra. Each TP spectrum is analyzed using the constrained piecewise linear fitting algorithm to identify the band gap energy.
The TP spectra for IA and DA were analyzed using the automated algorithm, resulting in positive detection of a single DA band gap and a single IA band gap for each of the 49 duplicate samples; and the corresponding band gap energies are shown using false color scale representation in Figure 4a,b, respectively. The mean DA band gap energy (EgDA) is 2.372 eV, and the mean IA band gap energy (EgIA) is 2.062 eV with standard deviations of 0.018 and 0.002 eV, respectively. Out of the set of 49 samples, the TP spectra corresponding to the smallest and largest estimates of DA and IA gaps are shown in Figure 4c,d. These figures demonstrate that the small variations in the calculated DA and IA band gap energies are a result of variations in the experimental data rather than the performance of the algorithm. In particular, while the different shapes of the TPDA spectra in Figure 4c result in substantially different linear segmentations, the extracted band gap energy is consistent due to the judicious selection of the Tauc and baseline line segments. The 49 independent measurements with automated band gap calculations consistently produced DA and IA band gap energies that are in excellent agreement with previously reported optical characterization of α-Fe2O3 (EgDA approximatley 2.2 eV and EgIA in the range 1.8–2.0 eV).(23)
Figure 4. False color mapping of (a) EgDA and (b) EgIA for 49 duplicate Fe2O3 samples. The 1 mm2 samples were organized as a 7 × 7 square grid with a 2 mm pitch, and the calculated band gap energies are plotted according to this physical layout. The TP spectra for samples exhibiting the smallest and largest estimates of (c) EgDA and (d) EgIA are also shown. For each plot, the end points of the piecewise linear fit are highlighted as red circles. The Tauc line segment (dotted magenta), baseline segment (dotted black), and their intersection (whose abscissa is the estimate of the band gap) illustrate the band gap estimation procedure.
As a second example of band gap estimation from TP spectra obtained from the TR instrument, we apply our algorithm to a sputtered thin film sample of α-Cu2V2O7, a recently reported indirect-gap photoelectrocatalyst.(24) Figure 5 demonstrates the estimation of the DA and IA band gap energies as 2.43 and 2.06 eV, respectively. The Tauc analysis of the IA gap in Figure 5 provides an illuminating example of the importance of using a slightly negative value for the minimum baseline slope parameter p5 in eq 9c. For the TPIA signal, an expert analyst would likely draw a zero-slope line that extends from the minimum value of the TPIA. The linear segment that best simulates such a baseline was correctly selected by the automated algorithm, and this line segment happens to have a slightly negative slope. The resulting estimation of band gap energy is in excellent agreement with that of an expert analyst.
Figure 5. Direct-allowed (DA) and indirect-allowed (IA) TP spectra for α-Cu2V2O7. End points of the piecewise linear fit (red circles), Tauc line segments (dotted magenta), and baseline segments (dotted black) and the estimates of EgDA and EgIA are shown.
To demonstrate band gap estimation on data obtained from the DR instrument, we apply our algorithm to TPDA spectra of representative samples from a sputter-deposited composition library.(25) This library will be discussed further in future work, and for the present purposes, we select representative samples, starting with two samples identified through X-ray diffraction measurements to have the monoclinic BiVO4 structure. As shown in Figure 6, we observe very precise estimation of the DA gap, in excellent agreement with the literature value of 2.49 eV.(26)
Figure 6. Direct-allowed (DA) TP spectra for two monoclinic BiVO4 samples characterized using the diffuse reflectance (DR) technique. For each sample, end points of the piecewise linear fit (red circles), Tauc line segments (dotted magenta), baseline segments (dotted black), and the estimate of EgDA are shown.
Another illustrative example from the (Bi–V–Fe)Ox library is shown in Figure 7. This sample is more Bi-rich and contains two phases, including the same BiVO4 phase as the samples in Figure 5. As noted in the algorithm, the linear segmentation of a given TP can be analyzed for the presence of multiple band gaps. For this biphasic sample, the BiVO4 direct band gap is successfully identified, and a second DA band gap near 3.0 eV is also identified. The simultaneous measurement of two band gap energies cannot be as robust as the individual measurement of two phase-pure samples, but for combinatorial band gap mapping, the ability to identify multiple band gaps is useful for studying composition–property relationships. Since the identification of two band gaps indicates that the given sample is not phase-pure, this result has implications for the underlying phase diagram, which is generally not known for a combinatorial material library. Algorithms for interpreting composition–band gap trends is the subject of ongoing research, and the automated Tauc analysis described in the present work provides a crucial capability for enabling high throughput materials discovery.
Figure 7. Direct-allowed (DA) TP spectra for a biphasic sample in which two DA gaps are identified. Both Tauc line segments (dotted magenta) and baseline segments (dotted black) are shown.
It is worth noting that the automated analysis of the BiVO4 samples also identifies an indirect-allowed (IA) gap at 2.44 eV (see Figure S1) that we disregard due to its proximity to the direct-allowed transition, which typically generates much stronger absorption. That is, an IA band gap can only be reliably identified using Tauc analysis when the corresponding Tauc line segment does not strongly overlap with the onset of DA absorption. The materials and data of Figures 4 and 5 exhibit energy differential values (EgDA – EgIA) of approximately 0.3 and 0.4 eV, respectively. These examples provide an important rule of thumb that an IA band gap can only be detected by absorption spectroscopy and automated Tauc analysis if the IA band gap energy is separated from the lowest DA transition by approximately 0.3 eV or more. For discovery of photoabsorbers, IA transitions are of primary interest when the direct band gap is at substantially higher energy, in which case the significantly lower indirect-allowed band gap can provide insight into composition-dependent phenomena such as band gap tuning.(27) Thus, for the purpose of photoabsorber discovery, Figures 4–7 provide excellent demonstration of the precise identification of DA and IA band gaps using the automated Tauc analysis algorithm.
To demonstrate the algorithm’s ability to estimate a range of band gap energies for various materials whose optical properties are not known, we compare the algorithm-generated band gaps with those estimated by three expert scientists. We generated a representative data set of 60 TPDA spectra (see Figure S2) from our UV–vis characterization database. The corresponding 60 composition samples included metal oxides and metal sulfides with a total of 11 cation elements represented and up to four cations present in each sample. The data set consisted of 50 TPDA spectra for which the algorithm identified a single band DA band gap via the C1 criteria and 10 spectra for which a DA band gap was not identified. For each spectrum, the ground truth for the presence/absence of a DA band gap was established by majority consensus of the three expert scientists. The performance of the automated algorithm in mimicking the expert judgment is shown in Figure 8a, revealing excellent true-positive (98%) and true-negative (82%) rates for spectra with ground-truth presence and absence of a DA band gap, respectively. The algorithm and parameter values (Table 1) were intentionally chosen to minimize the false-negative rate at the expense of the false-positive rate, as desired for material discovery applications. The false-positive rate can be lowered if so desired by tuning parameters to make the Tauc and baseline identification criteria more restrictive. Indeed, the extent to which a given TP exceeds or fails inequalities in the criteria sets could be used to ascertain a confidence level in the positive or negative band gap detection, respectively. The goodness of fit of the linear segment model, as quantified by the loss function used in the fitting routine (or similar metrics), could also be used to ascertain uncertainty (or lack of confidence), although in the spirit of mimicking expert judgment, we consider the difference in slope Sτ – SB to be the most straightforward indicator of confidence in the presence of a band gap. While the comparison to expert results included only two false-positive cases, Figure S3 shows the automated Tauc construction for these spectra corresponded to relatively small values of Sτ – SB, which supports the use of this metric as an indicator of confidence in the band gap identification.
Figure 8. (a) True-positive, true-negative, false-positive, and false-negative percentages for the automated algorithm’s ability to identify a band gap given the presence/absence of a band gap as per the majority consensus of three expert scientists as ground truth. (b) Comparison of band gap energies estimated by expert scientists and by the automated algorithm for the 48 true-positive samples. The range of values (for each sample) reported by the three expert scientists is denoted by a vertical line with the median value denoted by a blue marker. A solid black line representing ideal match and dashed black lines representing a mismatch of 0.1 eV are also shown.
For the true-positive samples, Figure 8b shows a comparison of the band gap energies estimated by the expert scientists and by the automated algorithm, demonstrating that the discrepancies are typically within 0.1 eV, with an R2 value of 0.89 between the mean of expert scientist estimated band gaps and algorithm estimated band gap. For several TPDA spectra with band gap energy near 1.8 eV, we observe that modeling of the baseline signal is unusually subjective since the transient in TPDA extends beyond the lower energy limit of the spectra (1.3 eV), resulting in more significant discrepancies in this region of Figure 8b. This provides an important guide for experiment design that the lower and higher energy limit of the spectra should extend at least 0.5 eV beyond the band gap energy range of interest. Figure 8b also contains two outlier data points, which upon subsequent inspection appear to be the result of unusually subjective analysis due to the convolution of multiple overlapping DA transitions in each TPDA spectrum (see plots 14 and 33 in Figure S2).
While these results demonstrate the successful automation of band gap extraction, we also note that the algorithm is based on parameters that are intuitive to an expert scientist, facilitating adaption of the algorithm for different instruments or particular research purposes. We also find that the algorithm enables quality control and exploration of various optical properties through monitoring the following algorithm outputs: slope of the Tauc line segment, slope of the background line segment, criterion set used for identifying the Tauc line segment, number of band gaps identified, and the area under the Tauc line segment. Finally, deployment of this algorithm in high throughput experiments will provide training data for machine learning algorithms to infer and predict composition–structure–property relationships.
Summary
High-throughput mapping of optical properties is of significant importance for rapid discovery of materials for a variety of applications, especially solar energy technologies. In this article, we develop an analysis methodology that allows us to rapidly estimate band gap energy and demonstrate the utility of the algorithm by estimating band gap energies for α-Fe2O3, α-Cu2V2O7, and monoclinic-BiVO4 phases. While the algorithm has several free parameters, we used expert researchers to train the values of these parameters and demonstrate that the presented values yield an algorithm with excellent reproducibility and ability to estimate band gap energies from both diffuse reflectance and transmission–reflection measurements. The intuitive nature of the free parameters allows further fine-tuning of the accuracy and tailoring to specific experiments when necessary.
Supporting Information
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acscombsci.6b00053.
TPDA plots for 60 samples used for expert–automated algorithm comparison, identification of false positives using descriptors obtained from the automated algorithm, and guidelines used by expert scientists for band gap estimation (PDF)
Data used to generate figures and source code for Python 2.7 implementation of the algorithm (ZIP)
The authors declare no competing financial interest.
Acknowledgment
This work is performed by the Joint Center for Artificial Photosynthesis, a DOE Energy Innovation Hub, supported through the Office of Science of the U.S. Department of Energy under Award Number DE-SC0004993. The authors thank Earl Cornell and Slobodan Mitrovic for assistance with instrument hardware and initial efforts in data processing, Thomas F. Jaramillo for providing insight into the rigors of band gap estimation using Tauc plots, Meyer Pesenson for helpful discussions with data processing, and Lan Zhou for assistance with sample preparation.
References
This article references 27 other publications.
- 1.(a) Perkins
, J. D.; Paudel, T. R.; Zakutayev, A.; Ndione, P. F.; Parilla, P. A.; Young, D. L.; Lany, S.; Ginley, D. S.; Zunger, A.; Perry, N. H.; Tang, Y.; Grayson, M.; Mason, T. O.; Bettinger, J. S.; Shi, Y.; Toney, M. F.Inverse design approach to hole doping in ternary oxides: Enhancing p-type conductivity in cobalt oxide spinels Phys. Rev. B: Condens. Matter Mater. Phys. 2011, 84 ( 20) 205207, DOI: 10.1103/PhysRevB.84.205207[CrossRef], [CAS]1a.https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3MXhsFKltLjJ&md5=e370bfe6f374ca75bd61ca4a5f4d4d2cPerkins, J. D.; Paudel, T. R.; Zakutayev, A.; Ndione, P. F.; Parilla, P. A.; Young, D. L.; Lany, S.; Ginley, D. S.; Zunger, A.; Perry, N. H.; Tang, Y.; Grayson, M.; Mason, T. O.; Bettinger, J. S.; Shi, Y.; Toney, M. F.Physical Review B: Condensed Matter and Materials Physics (2011),Holes can be readily doped into small-gap semiconductors such as Si or GaAs, but corresponding p-type doping in wide-gap insulators, while maintaining transparency, has proven difficult. Here, by utilizing design principles distd. from theory with systematic measurements in the prototype A2BO4 spinel Co2ZnO4, we formulate and test practical design rules for effective hole doping. Using these, we demonstrate a 20-fold increase in the hole d. in Co2ZnO4 due to extrinsic (Mg) doping and, ultimately, a factor of 104 increase for the inverse spinel Co2NiO4, the x = 1 end point of Ni-doped Co2Zn1-xNixO4.(b) Barron, S. C.; Gorham, J. M.; Green, M. L.Thermochromic Phase Transitions in VO2-Based Thin Films for Energy-Saving Applications ECS Trans. 2014, 61 ( 2) 387– 393, DOI: 10.1149/06102.0387ecst[CrossRef], [CAS]1b.https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28Xhs1yqurrE&md5=92b0d3e8a74a44a54661dc7efb729e67Barron, S. C.; Gorham, J. M.; Green, M. L.ECS Transactions (2014),The thermochromic transition in vanadium dioxide (VO2) has potential application as a smart energy-saving window coating, but the temp. of the transition must be depressed from 68 °C to Earth ambient temps. by the incorporation of transition metal impurities. In this paper, we describe a high throughput combinatorial expt. to characterize the V1-xMxO2 phase space, in which M is another metal, for thermochromic transitions. Thin film combinatorial libraries were prepd. by pulsed laser deposition on hot silicon substrates, and the M impurities were found to substitute into the VO2 cryst. lattice on the V-site. For M = Ta, Nb, and W, the thermochromic transition temp. was depressed with increasing M concn. Doping with multiple M atoms is also easily accomplished by combinatorial synthesis and was found to have unexpected effects on the thermochromic transition.(c) Kirby, S. D.; van Dover, R. B.Improved conductivity of ZnO through codoping with In and Al Thin Solid Films 2009, 517, 1958– 1960, DOI: 10.1016/j.tsf.2008.10.066[CrossRef], [CAS]1c.https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD1MXktlaruw%253D%253D&md5=7eef5b0736a4fe776646e77a4c9b480dKirby, S. D.; van Dover, R. B.Thin Solid Films (2009),We have studied the effect of codoping ZnO with Al and In using compn. spreads prepd. by off-axis r.f. sputtering. We find a large improvement in the elec. cond. of doped ZnO and attribute this to size compensation, as inferred by measuring the vol. of the unit cell as a function of compn. Adding a small amt. of In to Al-doped ZnO results in an increase in the fraction of Al dopant atoms that are activated, and the mobility remains high as well. Codoping allows for a higher cond. than single-doping in films deposited at a modest temp. with no post-annealing. - 2.Perkins
, J. D.; Teplin, C. W.; van Hest, M. F.; Alleman, J. L.; Li, X.; Dabney, M. S.; Keyes, B. M.; Gedvilas, L. M.; Ginley, D. S.; Lin, Y.; Lu, Y.Optical analysis of thin film combinatorial libraries Appl. Surf. Sci. 2004, 223 ( 1–3) 124– 132, DOI: 10.1016/S0169-4332(03)00917-6[CrossRef], [CAS]2.https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2cXitlyqug%253D%253D&md5=7a282863e2f70fdc3848f0dee5b19b04Perkins, J. D.; Teplin, C. W.; van Hest, M. F. A. M.; Alleman, J. L.; Li, X.; Dabney, M. S.; Keyes, B. M.; Gedvilas, L. M.; Ginley, D. S.; Lin, Y.; Lu, Y.Applied Surface Science (2004),The authors have developed, and are using, optical reflection and transmission mapping as a characterization tool for analyzing compositionally graded thin film combinatorial libraries. Measurements cover 200 nm-25 μm. For the UV-visible-NIR region, a multichannel fiber optically coupled CCD array-based spectrometer is used for simultaneous reflection and transmission mapping. For the IR, a FTIR spectrometer is used for sequential reflection and transmission maps. Depending upon the type of library being analyzed, the measured spectra can, with appropriate modeling, be analyzed for the optical band gap, film thickness, index of refraction, plasma frequency, cond., carrier scattering time and color, in addn. to simple reflectance and transmittance. These techniques are discussed using examples taken from the work on both transparent conducting oxides and metal nitrides for optical coatings. - 3.Hu
, S.; Xiang, C.; Haussener, S.; Berger, A. D.; Lewis, N. S.An analysis of the optimal band gaps of light absorbers in integrated tandem photoelectrochemical water-splitting systems Energy Environ. Sci. 2013, 6 ( 10) 2984, DOI: 10.1039/c3ee40453f[CrossRef], [CAS]3.https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3sXhsV2it7fE&md5=cd660988f30bdee6369817f75f6e5de3Hu, Shu; Xiang, Chengxiang; Haussener, Sophia; Berger, Alan D.; Lewis, Nathan S.Energy & Environmental Science (2013),The solar-to-hydrogen (STH) efficiency limits, along with the max. efficiency values and the corresponding optimal band gap combinations, have been evaluated for various combinations of light absorbers arranged in a tandem configuration in realistic, operational water-splitting prototypes. To perform the evaluation, a current-voltage model was employed, with the light absorbers, electrocatalysts, soln. electrolyte, and membranes coupled in series, and with the directions of optical absorption, carrier transport, electron transfer and ionic transport in parallel. The c.d. vs. voltage characteristics of the light absorbers were detd. by detailed-balance calcns. that accounted for the Shockley-Queisser limit on the photovoltage of each absorber. The max. STH efficiency for an integrated photoelectrochem. system was found to be ∼31.1% at 1 Sun (=1 kW m-2, air mass 1.5), fundamentally limited by a matching photocurrent d. of 25.3 mA cm-2 produced by the light absorbers. Choices of electrocatalysts, as well as the fill factors of the light absorbers and the Ohmic resistance of the soln. electrolyte also play key roles in detg. the max. STH efficiency and the corresponding optimal tandem band gap combination. Pairing 1.6-1.8 eV band gap semiconductors with Si in a tandem structure produces promising light absorbers for water splitting, with theor. STH efficiency limits of >25%. - 4.Yin
, Z.; Tang, X.A review of energy bandgap engineering in III–V semiconductor alloys for mid-infrared laser applications Solid-State Electron. 2007, 51 ( 1) 6– 15, DOI: 10.1016/j.sse.2006.12.005[CrossRef], [CAS]4.https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2sXht1Oqsbg%253D&md5=d7eaca80ae5d2956775c1a9dae29518aYin, Zongyou; Tang, XiaohongSolid-State Electronics (2007),A review. Semiconductor lasers emitting in mid-IR range, 2-5 μm, have many important applications in semiconductor industries, military, environmental protection, telecommunications, mol. spectroscopy, biomedical surgery and researches. Different designs of the reactive regions in mid-IR laser structures were studied for achieving high performance devices. Semiconductor mid-IR lasers with double heterostructure, quantum well, quantum cascade, quantum wire, quantum dash and quantum dot active regions were reviewed. The performance of the lasers with these different active regions and the development of the newly emerging III-V-N materials for mid-IR applications were discussed in details. - 5.Mitrovic
, S.; Cornell, E. W.; Marcin, M. R.; Jones, R. J.; Newhouse, P. F.; Suram, S. K.; Jin, J.; Gregoire, J. M.High-throughput on-the-fly scanning ultraviolet-visible dual-sphere spectrometer Rev. Sci. Instrum. 2015, 86 ( 1) 013904, DOI: 10.1063/1.4905365[CrossRef], [CAS]5.https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2MXovFSksA%253D%253D&md5=fb329f3f16e133a5f0155c395df30c15Mitrovic, Slobodan; Cornell, Earl W.; Marcin, Martin R.; Jones, Ryan J. R.; Newhouse, Paul F.; Suram, Santosh K.; Jin, Jian; Gregoire, John M.Review of Scientific Instruments (2015),The authors have developed an on-the-fly scanning spectrometer operating in the UV-visible and near-IR that can simultaneously perform transmission and total reflectance measurements at the rate better than 1 sample/s. High throughput optical characterization is important for screening functional materials for a variety of new applications. The authors demonstrate the utility of the instrument for screening new light absorber materials by measuring the spectral absorbance, which is subsequently used for deriving band gap information through Tauc plot anal. (c) 2015 American Institute of Physics. - 6.(a) Wood
, D.; Tauc, J.Weak Absorption Tails in Amorphous Semiconductors Phys. Rev. B 1972, 5, 3144– 3151, DOI: 10.1103/PhysRevB.5.3144(b) Davis, E. A.; Mott, N. F.Conduction in non-crystalline systems V. Conductivity, optical absorption and photoconductivity in amorphous semiconductors Philos. Mag. 1970, 22, 0903– 0922, DOI: 10.1080/14786437008221061[CrossRef], [CAS]6b.https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaE3cXltlGhsrc%253D&md5=a1316ac69b4ca2a51974521c58620523Davis, Edward A.; Mott, Nevill F.Philosophical Magazine (1970),The exptl. evidence concerning the d. of states in amorphous semiconductors and the ranges of energy in which states are localized is reviewed; this includes d.c. and a.c. cond., drift mobility, and optical absorption. There is evidence that for some chalcogenide semiconductors the model proposed by Cohen, Fritzsche, and Ovshinsky (1969) should be modified by introducing a band of localized states, near the center of the gap. The values of C, when the d.c. cond. is expressed as C exp (-E/kT), are considered. The behavior of the optical absorption coeff. near the absorption edge and its relation to exciton formation are discussed. Finally, an interpretation of some results on photocond. is offered. - 7.(a) Tauc
, J.; Grigorovici, R.; Vancu, A.Optical Properties and Electronic Structure of Amorphous Germanium Phys. Status Solidi B 1966, 15, 627– 637, DOI: 10.1002/pssb.19660150224[CrossRef], [CAS]7a.https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaF28XktlGit7Y%253D&md5=d99a61c902bd1b30c6c704a31df83b48Tauc, J.; Grigorovici, R.; Vancu, A.Physica Status Solidi (1966),The optical consts. of amorphous Ge are detd. for photon energies 0.08-1.6 ev. From 0.08 to 0.5 ev., the absorption is due to k-conserving transitions of holes between the valence bands as in p-type crystals; the spin-orbit splitting is 0.20 and 0.21 ev. in nonannealed and annealed samples, resp. The effective masses of the holes in the 3 bands are 0.49 m (0.43 m), 0.04 m, and 0.08 m. An absorption band is observed below the main absorption edge (at 300°K. the max. of this band is at 0.86 ev.); the absorption in this band increases with increasing temp. This band is due to excitons bound to neutral acceptors, and these are presumably the same ones that play a decisive role in the transport properties, which are considered to be assocd. with vacancies. The absorption edge has the form ω2ε2 ∼ (ℏω - Eg)2 (Eg = 0.88 ev. at 300°K.). This suggests that the optical transitions conserve energy but not k vector, and that the ds. of states near the band extrema have the same energy dependence as in cryst. Ge. A simple theory describing this situation is proposed, and comparison of it with the exptl. results leads to an estimate of the localization of the conduction-band wave functions. 24 references.(b) Tauc, J.; Menth, A.; Wood, D. L.Optical and Magnetic Investigations of the Localized States in Semiconducting Glasses Phys. Rev. Lett. 1970, 25 ( 11) 749– 752, DOI: 10.1103/PhysRevLett.25.749[CrossRef], [CAS]7b.https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaE3cXltFCntbs%253D&md5=795da3ab06d7c98cf41a671a5052b6beTauc, Jan; Menth, A.; Wood, Darwin LewisPhysical Review Letters (1970),Optical absorption and magnetic susceptibility of amorphous As2S3 were measured as functions of temp. An exponential variation of absorption coeff., α, with photon energy was found at 0.09 < α < 0.5 cm-1. A Curie term in the susceptibility was characteristic of disorder in the vitreous material. A model relating the weak absorption tail to the susceptibility requires highly localized states having an exponential energy distribution in the gap. - 8.Escobedo Morales
, A.; Sanchez Mora, E.; Pal, U.Use of diffuse reflectance spectroscopy for optical characterization of un-supported nanostructures Rev. Mex. Fis. 2007, 53 ( 5) 18– 22There is no corresponding record for this reference. - 9.Dolgonos
, A.; Mason, T. O.; Poeppelmeier, K. R.Direct optical band gap measurement in polycrystalline semiconductors: A critical look at the Tauc method J. Solid State Chem. 2016, 240, 43– 48, DOI: 10.1016/j.jssc.2016.05.010[CrossRef], [CAS]9.https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28XotlGjsr8%253D&md5=deec178f169ae04a7ef299b50f6fbf9aDolgonos, Alex; Mason, Thomas O.; Poeppelmeier, Kenneth R.Journal of Solid State Chemistry (2016),The direct optical band gap of semiconductors is traditionally measured by extrapolating the linear region of the square of the absorption curve to the x-axis, and a variation of this method, developed by Tauc, has also been widely used. The application of the Tauc method to cryst. materials is rooted in misconception-and traditional linear extrapolation methods are inappropriate for use on degenerate semiconductors, where the occupation of conduction band energy states cannot be ignored. A new method is proposed for extg. a direct optical band gap from absorption spectra of degenerately-doped bulk semiconductors. This method was applied to pseudo-absorption spectra of Sn-doped In2O3 (ITO)-converted from diffuse-reflectance measurements on bulk specimens. The results of this anal. were corroborated by room-temp. photoluminescence excitation measurements, which yielded values of optical band gap and Burstein-Moss shift that are consistent with previous studies on In2O3 single crystals and thin films. - 10.(a) Moss
, T. S.Theory of the Spectral Distribution of Recombination Radiation from InSb Proc. Phys. Soc., London, Sect. B 1957, 70 ( 2) 247– 250, DOI: 10.1088/0370-1301/70/2/414(b) Burstein, E.Anomalous Optical Absorption Limit in InSb Phys. Rev. 1954, 93 ( 3) 632– 633, DOI: 10.1103/PhysRev.93.632[CrossRef], [CAS]10b.https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaG2cXjvVartA%253D%253D&md5=e633bd928cdcb7e7f8da8a28a446305fBurstein, EliasPhysical Review (1954),Tanenbaum and Briggs (C.A. 48, 448d) report that the room-temp. optical absorption limit of InSb is 7.0 μ; of a rather impure sample, 3.2 μ. This anomalous effect is confirmed. It is shown to be due to the small effective mass of the electrons in InSb rather than to a specific impurity effect. - 11.Berggren
, K. F.; Sernelius, B. E.Band-gap narrowing in heavily doped many-valley semiconductors Phys. Rev. B: Condens. Matter Mater. Phys. 1981, 24 ( 4) 1971– 1986, DOI: 10.1103/PhysRevB.24.1971[CrossRef], [CAS]11.https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaL3MXlsVaqsLc%253D&md5=02813b3a2746a221c287c95cae155707Berggren, K. F.; Sernelius, B. E.Physical Review B: Condensed Matter and Materials Physics (1981),Band-gap shrinkage in impure n-Si and Ge as a function of impurity concn. is studied theor. at T = 0 K. Above the Mott crit. d. it is assumed that electrons occupy the host conduction band in the form of an electron gas. Interactions among the free carriers and with the ionized point impurities give rise to a downward shift of the conduction band. Interband matrix elements are explicitly includedfor the valence bands. As a consequence, the 2 valence bands at the center of the zone are shifted upwards by the same amt. Correlation and impurity scattering both give corrections to the band gap, which are of the same order of magnitude. The band gap depends rather sensitively on the arrangement of donor ions. The choice of dielec. screening is investigated, and comparison with previous calcns. is made. Present theor. results and exptl. ests. of the band-gap narrowing show an order-of-magnitude agreement, although there is considerable scatter in the exptl. data. Shortcomings of the present theory are briefly discussed. - 12.(a) Asahi
, R.; Morikawa, T.; Ohwaki, T.; Aoki, K.; Taga, Y.Visible-light photocatalysis in nitrogen-doped titanium oxides Science 2001, 293 ( 5528) 269– 271, DOI: 10.1126/science.1061051[CrossRef], [PubMed], [CAS]12a.https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD3MXlt1yitbc%253D&md5=db2b823b547b5c3bb17ab314d215660aAsahi, R.; Morikawa, T.; Ohwaki, T.; Aoki, K.; Taga, Y.Science (Washington, DC, United States) (2001),To use solar irradn. or interior lighting efficiently, the authors sought a photocatalyst with high reactivity under visible tight. Films and powders of TiO2-xNx have revealed an improvement over titanium dioxide (TiO2) under visible light (wavelength < 500 nm) in optical absorption and photocatalytic activity such as photodegrdns. of Methylene blue and gaseous acetaldehyde and hydrophilicity of the film surface. Nitrogen doped into substitutional sites of TiO2 has proven to be indispensable for band-gap narrowing and photocatalytic activity, as assessed by first-principles calcns. and x-ray photoemission spectroscopy.(b) Loiudice, A.; Ma, J.; Drisdell, W. S.; Mattox, T. M.; Cooper, J. K.; Thao, T.; Giannini, C.; Yano, J.; Wang, L. W.; Sharp, I. D.; Buonsanti, R.Bandgap Tunability in Sb-Alloyed BiVO4 Quaternary Oxides as Visible Light Absorbers for Solar Fuel Applications Adv. Mater. 2015, 27 ( 42) 6733– 40, DOI: 10.1002/adma.201502361[CrossRef], [PubMed], [CAS]12b.https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2MXhsFyqsrjO&md5=5c56b654ba561d3b46573303f382227eLoiudice, Anna; Ma, Jie; Drisdell, Walter S.; Mattox, Tracy M.; Cooper, Jason K.; Thao, Timothy; Giannini, Cinzia; Yano, Junko; Wang, Lin-Wang; Sharp, Ian D.; Buonsanti, RaffaellaAdvanced Materials (Weinheim, Germany) (2015),One approach to reducing the bandgap is the utilization of ternary and quaternary oxides, which have been receiving increased attention as light absorbers that, critically, also supply the potential needed to drive multi-electron oxidn. reactions. In this work, we report the discovery of antimony-alloyed bismuth vanadate (Sb-BiVO4). Through a combination of theor. predication and exptl. validation, we show that this novel photoanode material possesses a bandgap that linearly decreases below 2.4 eV with increasing Sb content. This work is enabled by the development of a novel two-step synthesis process that will broadly aid new materials discovery by providing synthetic access to a wide range of compositionally complex oxides. - 13.Anderson
, A. Y.; Bouhadana, Y.; Barad, H.-N.; Kupfer, B.; Rosh-Hodesh, E.; Aviv, H.; Tischler, Y. R.; Rühle, S.; Zaban, A.Quantum efficiency and bandgap analysis for combinatorial photovoltaics: sorting activity of Cu-O compounds in all-oxide device libraries ACS Comb. Sci. 2014, 16, 53– 65, DOI: 10.1021/co3001583[ACS Full Text
], [CAS]13.https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2cXotVemsQ%253D%253D&md5=5f06307f2456d0f9c50fd7398f54599bAnderson, Assaf Y.; Bouhadana, Yaniv; Barad, Hannah-Noa; Kupfer, Benjamin; Rosh-Hodesh, Eli; Aviv, Hagit; Tischler, Yaakov R.; Ruhle, Sven; Zaban, ArieACS Combinatorial Science (2014),All-oxide-based photovoltaics (PVs) encompass the potential for extremely low cost solar cells, provided they can obtain an order of magnitude improvement in their power conversion efficiencies. To achieve this goal, we perform a combinatorial materials study of metal oxide based light absorbers, charge transporters, junctions between them, and PV devices. Here we report the development of a combinatorial internal quantum efficiency (IQE) method. IQE measures the efficiency assocd. with the charge sepn. and collection processes, and thus is a proxy for PV activity of materials once placed into devices, discarding optical properties that cause uncontrolled light harvesting. The IQE is supported by high-throughput techniques for bandgap fitting, compn. anal., and thickness mapping, which are also crucial parameters for the combinatorial investigation cycle of photovoltaics. As a model system we use a library of 169 solar cells with a varying thickness of sprayed titanium dioxide (TiO2) as the window layer, and covarying thickness and compn. of binary compds. of copper oxides (Cu-O) as the light absorber, fabricated by Pulsed Laser Deposition (PLD). The anal. on the combinatorial devices shows the correlation between compns. and bandgap, and their effect on PV activity within several device configurations. The anal. suggests that the presence of Cu4O3 plays a significant role in the PV activity of binary Cu-O compds. - 14.Ghobadi
, N.Band gap determination using absorption spectrum fitting procedure Int. Nano Lett. 2013, 3, 2, DOI: 10.1186/2228-5326-3-2[CrossRef], [CAS]14.https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2cXhtFyhurY%253D&md5=616e13ba679e8d91bbb18c8ad37f3972Ghobadi, NaderInternational Nano Letters (2013),In this article, using the Tauc model, the absorption spectrum fitting method was applied to est. the optical band gap and width of the band tail of the CdSe nanostructural films that requires only the measurement of the absorbance spectrum, and no addnl. information such as the film thickness or reflectance spectra is needed. Samples are prepd. by chem. bath deposition method. Fabricated nanostructural thin films are thick but are composed from nanoparticles. - 15.(a) Drobny
, V. F.; Pulfrey, L.Properties of reactively-sputtered copper oxide thin films Thin Solid Films 1979, 61 ( 1) 89– 98, DOI: 10.1016/0040-6090(79)90504-2[CrossRef], [CAS]15a.https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaE1MXls1KqurY%253D&md5=9fd138214bf7d2795bfb9925879716dbDrobny, V. F.; Pulfrey, D. L.Thin Solid Films (1979),Reactive sputtering in O-Ar mixts. was used to produce thin Cu oxide films with a range of properties that can be controlled easily by varying the partial pressure of O in the discharge. The phase compn., resistivity and optical consts. were investigated. The phases Cu + Cu2O, Cu2O, Cu2O + CuO, CuO were identified and each phase exhibited characteristic values of resistivity and optical consts.(b) Rakhshani, A. E.; Varghese, J.Optical absorption coefficient and thickness measurement of electrodeposited films of Cu2O Phys. Status Solidi A 1987, 101 ( 2) 479– 486, DOI: 10.1002/pssa.2211010220[CrossRef], [CAS]15b.https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaL2sXls1Chtr8%253D&md5=b6b9222fd05001c3d5932f9c95394d25Rakhshani, A. E.; Varghese, J.Physica Status Solidi A: Applied Research (1987),The disadvantage of electrodeposited Cu2O films on opaque substrates regarding the measurement of their transmittance and optical absorption coeff. is overcome by a successful and reliable procedure of transferring the films onto glass slides. The method can be applied to other electrodeposited films. An accurate method for measuring the film thickness, required for the evaluation of absorption coeffs., is described. Transmittance and reflectance interferometry which are used for this purpose det. a d. of (5.6 ± 0.6) g cm-3 for the films. This value can be used to evaluate the films thickness by a weighing method. The existing model for the evaluation of absorption coeff. is discussed in detail and developed further for the purpose aspired. The film absorption coeffs. were measured at 0.5-1.0 μm. The measured values after correction for the effect of an electronically inactive absorption tail, resembled those for bulk Cu2O. An optical bandgap in the range of 1.9 to 2.0 eV was obtained for the films.(c) Roberts, S.Optical Properties of Copper Phys. Rev. 1960, 118 ( 6) 1509– 1518, DOI: 10.1103/PhysRev.118.1509[CrossRef], [CAS]15c.https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaF3cXht1GjsLg%253D&md5=49bb771eb252d45c66c713065d10e1bfRoberts, S.Physical Review (1960),Optical properties of solid Cu have been measured in a wave-length range from 0.365 to 2.5 μ and at temps. 90°, 300°, and 500°K. Annealed and electropolished specimens were used. Measurements were made in vacuo of about 2 × 10-5 mm. (Hg); it was observed that the oxide film which normally forms on Cu upon exposure to air could be removed by heating in vacuo to a temp. of 500°K. In the wave-length range below 0.6 μ the data confirm the well-known facts relating to a threshold for interband electronic transitions. At longer wave lengths the optical properties are detd. almost entirely by free electrons. Deviations from simple theory are partly explained by the anomalous skin effect; it is concluded that the electronic collisions at the metal surface are diffuse. However,the anomalous skin effect is not sufficient to explain the observed deviations and a more complete interpretation ought to consider the non-spherical nature of the Fermi surface and variation of the relaxation time over this surface. - 16.Savitzky
, A.; Golay, M. J. E.Smoothing and Differentiation of Data by Simplified Least Squares Procedures Anal. Chem. 1964, 36 ( 8) 1627– 1639, DOI: 10.1021/ac60214a047[ACS Full Text], [CAS]16.https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaF2cXksVCjur8%253D&md5=8406f1500e608f8f89eada4d7949ed77Savitzky, Abraham; Golay, Marcel J. E.(1964),The operation may be carried out on a computer by convolution of the data. Two examples are presented as subroutines in the FORTRAN language. - 17.Swinehart
, D. F.The Beer-Lambert Law J. Chem. Educ. 1962, 39 ( 7) 333, DOI: 10.1021/ed039p333[ACS Full Text], [CAS]17.https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaF38Xkt1KhtLc%253D&md5=7aa1fad287b487355014dd0622b2e9ceSwinehart, D. F.Journal of Chemical Education (1962),There is no expanded citation for this reference. - 18.Peng
, H.; Ndione, P. F.; Ginley, D. S.; Zakutayev, A.; Lany, S.Design of Semiconducting TetrahedralMn1–xZnxOAlloys and Their Application to Solar Water Splitting Phys. Rev. X 2015, 5 ( 2) 021016, DOI: 10.1103/PhysRevX.5.021016[CrossRef], [CAS]18.https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2MXpvF2hu74%253D&md5=abccef45eb43383a2724e5146d8bb6bbPeng, Haowei; Ndione, Paul F.; Ginley, David S.; Zakutayev, Andriy; Lany, StephanPhysical Review X (2015),Transition metal oxides play important roles as contact and electrode materials, but their use as active layers in solar energy conversion requires achieving semiconducting properties akin to those of conventional semiconductors like Si or GaAs. In particular, efficient bipolar carrier transport is a challenge in these materials. Based on the prediction that a tetrahedral polymorph of MnO should have such desirable semiconducting properties, and the possibility to overcome thermodn. soly. limits by nonequil. thin-film growth, we exploit both structure-property and compn.-structure relationships to design and realize novel wurtzite-structure Mn1-xZnxO alloys. At Zn compns. above x ≈ 0.3, thin films of these alloys assume the tetrahedral wurtzite structure instead of the octahedral rocksalt structure of MnO, thereby enabling semiconductor properties that are unique among transition metal oxides, i.e., a band gap within the visible spectrum, a band-transport mechanism for both electron and hole carriers, electron doping, and a band lineup suitable for solar hydrogen generation. A proof of principle is provided by initial photo-electrocatalytic device measurements, corroborating, in particular, the predicted favorable hole-transport properties of these alloys. - 19.Kubelka
, P.New Contributions to the Optics of Intensely Light-Scattering Materials. Part I J. Opt. Soc. Am. 1948, 38 ( 5) 448– 457, DOI: 10.1364/JOSA.38.000448[CrossRef], [PubMed], [CAS]19.https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A280%3ADyaH1c%252FmtVKgug%253D%253D&md5=1bfe837bfc7f2fb868e165ee748212d1KUBELKA PJournal of the Optical Society of America (1948),There is no expanded citation for this reference. - 20.(a) Murphy
, A. B.Band-gap determination from diffuse reflectance measurements of semiconductor films, and application to photoelectrochemical water-splitting Sol. Energy Mater. Sol. Cells 2007, 91, 1326– 1337, DOI: 10.1016/j.solmat.2007.05.005[CrossRef], [CAS]20a.https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2sXntFartbs%253D&md5=9e5b0e74adc3f9d739846481025bbae7Murphy, A. B.Solar Energy Materials & Solar Cells (2007),Measurements of the diffuse reflectance of TiO2 semiconductor coatings, such as are used for H2O splitting, are analyzed using the Kubelka-Munk radiative transfer model. The widely used practice of detg. the band gap of the coating directly from the diffuse reflectance is inaccurate, since the diffuse reflectance depends on parameters such as the thickness, refractive index and surface roughness of the coating. However, the absorption coeff. can be derived from the diffuse reflectance using an inversion method; the band gap can then be obtained from the absorption coeff. Finally, the diffuse reflectance of C-doped TiO2 presented by Khan et al. [Science 297(2002) 2243-2245] is analyzed; while the band-gap wavelength is extended into the visible region, it is overestimated. Also, light at visible wavelengths is only very weakly absorbed, and is expected to make only a minor contribution to the H2O-splitting efficiency.(b) Murphy, A. B.Optical properties of an optically rough coating from inversion of diffuse reflectance measurements Appl. Opt. 2007, 46, 3133– 43, DOI: 10.1364/AO.46.003133[CrossRef], [PubMed], [CAS]20b.https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2sXmvVKgtbg%253D&md5=8e7d4e88cb381810d2ddfeccb23a7bf8Murphy, Anthony B.Applied Optics (2007),A method is developed for detg. the optical properties of an optically rough coating on an opaque substrate from reflectance measurements. A modified Kubelka-Munk two-flux model is used to calc. the reflectance of the coating as a function of the refractive index, absorption coeff., scattering coeff., and thickness. The calcd. reflectance is then fitted to measurements using a spectral projected gradient algorithm, allowing the optical properties to be obtained. The technique is applied to titanium dioxide coatings on a titanium substrate. Realistic values of refractive index and absorption coeffs. are generally obtained. Quantities that are useful for solar water-splitting applications are calcd., including the depth profile of absorption and the proportion of the incident photon flux absorbed in the coating under solar illumination. - 22.Hishikawa
, Y.; Nakamura, N.; Tsuda, S.; Nakano, S.; Kishi, Y.; Kuwano, Y.Interference-Free Determination of the Optical Absorption Coefficient and the Optical Gap of Amorphous Silicon Thin Films Jpn. J. Appl. Phys. 1991, 30 ( Part 1, No. 5) 1008– 1014, DOI: 10.1143/JJAP.30.1008[CrossRef], [CAS]22.https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK3MXktFOks7s%253D&md5=5fd735638c3b9d8127470feaf699b122Hishikawa, Yoshihiro; Nakamura, Noboru; Tsuda, Shinya; Nakano, Shoichi; Kishi, Yasuo; Kuwano, YukinoriJapanese Journal of Applied Physics, Part 1: Regular Papers, Short Notes & Review Papers (1991),A new method to det. the optical absorption coeff. (α) of thin films is presented. The α of hydrogenated amorphous silicon (a-Si:H) based alloys can be accurately detd. from transmittance (T) and reflectance (R) by using T/(1-R), which almost completely eliminates disturbances from the optical interference effect. The method is applicable to any thin films, as long as the film is a single layer. Based on the interference-free α, various methods to det. the optical gap (EOPT) of a-Si:H, a-SiGe:H films are discussed. The (nαhν)1/3 plot and the (αhν)1/3 plot are most suitable for characterizing these films. The well-known (αhν)1/2 plot is less suited for detailed discussion of the EOPT than the cube root plot, because the plot includes a large ambiguity in the EOPT. The effect of the optical interference effect on the detn. of the EOPT is also discussed. - 23.Al-Kuhaili
, M. F.; Saleem, M.; Durrani, S. M. A.Optical properties of iron oxide (α-Fe2O3) thin films deposited by the reactive evaporation of iron J. Alloys Compd. 2012, 521, 178– 182, DOI: 10.1016/j.jallcom.2012.01.115[CrossRef], [CAS]23.https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC38XivVCksbk%253D&md5=ae0fd22f5f5e736e5a1031980a2fe787Al-Kuhaili, M. F.; Saleem, M.; Durrani, S. M. A.Journal of Alloys and Compounds (2012),Thin films of hematite (α-Fe2O3) were deposited by the reactive evapn. of Fe in an O atm. The films were deposited on unheated and heated substrates. Structural anal., using x-ray diffraction, verified the phase of the films and revealed that the films had a polycryst. structure composed of nano-crystallites. Atomic force microscopy indicated that the films had smooth surfaces, with a lateral grain size that increased substantially by substrate heating. The optical properties of the films, including the refractive index, extinction coeff., absorption coeff., and band gap were detd. from spectrophotometric measurements. In the wavelength range 600-2000 nm, the refractive indexes were 1.7-2.2 for the films deposited on unheated substrates, and 2.3-2.9 for the films deposited on heated substrates. The films had direct and indirect band gaps. The direct band gap was 2.18 eV, and the indirect band gap was 1.82-1.96 eV, depending on the substrate temp. - 24.Zhou
, L.; Yan, Q.; Shinde, A.; Guevarra, D.; Newhouse, P. F.; Becerra-Stasiewicz, N.; Chatman, S. M.; Haber, J. A.; Neaton, J. B.; Gregoire, J. M.High Throughput Discovery of Solar Fuels Photoanodes in the CuO–V2O5 System Adv. Energy Mater. 2015, 5, 1500968, DOI: 10.1002/aenm.201500968 - 25.Suram
, S. K.; Zhou, L.; Becerra-Stasiewicz, N.; Kan, K.; Jones, R. J. R.; Kendrick, B. M.; Gregoire, J. M.Combinatorial thin film composition mapping using three dimensional deposition profiles Rev. Sci. Instrum. 2015, 86 ( 3) 033904– 033904, DOI: 10.1063/1.4914466[CrossRef], [CAS]25.https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2MXksFWrs7w%253D&md5=97137b256009bb639de6f5c310ad9f3eSuram, Santosh K.; Zhou, Lan; Becerra-Stasiewicz, Natalie; Kan, Kevin; Jones, Ryan J. R.; Kendrick, Brian M.; Gregoire, John M.Review of Scientific Instruments (2015),Many next-generation technologies are limited by material performance, leading to increased interest in the discovery of advanced materials using combinatorial synthesis, characterization, and screening. Several combinatorial synthesis techniques, such as soln. based methods, advanced manufg., and phys. vapor deposition, are currently being employed for various applications. In particular, combinatorial magnetron sputtering is a versatile technique that provides synthesis of high-quality thin film compn. libraries. Spatially addressing the compn. of these thin films generally requires elemental quantification measurements using techniques such as energy-dispersive X-ray spectroscopy or X-ray fluorescence spectroscopy. Since these measurements are performed ex-situ and post-deposition, they are unable to provide real-time design of expts., a capability that is required for rapid synthesis of a specific compn. library. By using three quartz crystal monitors attached to a stage with translational and rotational degrees of freedom, we measure three-dimensional deposition profiles of deposition sources whose tilt with respect to the substrate is robotically controlled. We exhibit the utility of deposition profiles and tilt control to optimize the deposition geometry for specific combinatorial synthesis expts. (c) 2015 American Institute of Physics. - 26.Payne
, D. J.; Robinson, M. D. M.; Egdell, R. G.; Walsh, A.; McNulty, J.; Smith, K. E.; Piper, L. F. J.The nature of electron lone pairs in BiVO4 Appl. Phys. Lett. 2011, 98 ( 21) 212110, DOI: 10.1063/1.3593012[CrossRef], [CAS]26.https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3MXms1Slu74%253D&md5=28f6b119702e6c08d983de3ec80e77a2Payne, D. J.; Robinson, M. D. M.; Egdell, R. G.; Walsh, A.; McNulty, J.; Smith, K. E.; Piper, L. F. J.Applied Physics Letters (2011),The electronic structure of BiVO4 was studied by x-ray photoelectron, x-ray absorption, and x-ray emission spectroscopies, in comparison with d. functional theory calcns. Results confirm both the direct band gap of 2.48 eV and that the Bi 6s electrons hybridize with O 2p to form antibonding lone pair states at the top of the valence band. The results highlight the suitability of combining s2 and d0 cations to produce photoactive ternary oxides. (c) 2011 American Institute of Physics. - 27.Copple
, A.; Ralston, N.; Peng, X.Engineering direct-indirect band gap transition in wurtzite GaAs nanowires through size and uniaxial strain Appl. Phys. Lett. 2012, 100 ( 19) 193108, DOI: 10.1063/1.4718026[CrossRef], [CAS]27.https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC38XmslKksLo%253D&md5=56b1018ae26d8c5d2af7793d981f166aCopple, Andrew; Ralston, Nathaniel; Peng, XihongApplied Physics Letters (2012),Electronic structures of wurtzite GaAs nanowires in the 0001 direction were studied using first-principles calcns. It was found that the band gap of GaAs nanowires experiences a direct-to-indirect transition when the diam. of the nanowires is smaller than ∼28 Å. For those thin GaAs nanowires with an indirect band gap, it was found that the gap can be tuned to be direct if a moderate external uniaxial strain is applied. Both tensile and compressive strain can trigger the indirect-to-direct gap transition. The crit. strains for the gap-transition are detd. by the energy crossover of two states in conduction bands. (c) 2012 American Institute of Physics.
