Evaluating photoluminescent response of sample

Abstract

A method includes illuminating a surface of a sample with a first light having a first wavelength (λ1) and detecting first intensities of a first photoluminescence induced within the sample by absorption of the first light by the sample. The method also includes illuminating the surface of the sample with a second light having a second wavelength (λ2) that is different from the first wavelength and detecting second intensities of a second photoluminescence induced within the sample by absorption of the second light by the sample. The method also includes generating an output representing the first intensities and the second intensities.

Description

Evaluating Photoluminescent Response of Sample CROSS-REFERENCE TO RELATED APPLICATION

[0001] This application claims priority to U.S. Provisional Patent Application No. 63 / 567,905, filed on March 20, 2024, the entire contents of which are incorporated by reference herein. STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

[0002] This invention was made with government support under Grant No. N00014-20-1- 2587, awarded by the Office of Naval Research (ONR). The government has certain rights in the invention. BACKGROUND

[0003] Mapping recombination-inducing defects and their distributions within semiconductor materials can be useful in improving processes for manufacturing semiconductor materials and devices. For example, surface recombination velocity (SRV) can be used to quantify recombination losses at surfaces and interfaces in semiconductors, and SRV can vary with changes in crystal growth, orientation, environmental exposure, processing, surface passivation, and interface formation during device fabrication. Current methods for quantifying SRV involve fabricating and examining samples of different thicknesses and can be time consuming. SUMMARY

[0004] A first example is a method comprising: illuminating a surface of a sample with afirst light having a first wavelength ( 1); detecting first intensities of a firstphotoluminescence induced within the sample by absorption of the first light by the sample;illuminating the surface of the sample with a second light having a second wavelength ( 2)that is different from the first wavelength; detecting second intensities of a second photoluminescence induced within the sample by absorption of the second light by the sample; and generating an output representing the first intensities and the second intensities.

[0005] A second example is a non-transitory computer readable medium storing instructions that, when executed by one or more processors of a diagnostic device, cause the diagnostic device to perform the method of the first example.

[0006] A third example is a diagnostic device comprising: one or more processors; a light source; a light detector; and a computer readable medium storing instructions that, whenexecuted by the one or more processors, cause the diagnostic device to perform the method of the first example.

[0007] When the term “substantially” or “about” is used herein, it is meant that the recited characteristic, parameter, or value need not be achieved exactly, but that deviations or variations, including, for example, tolerances, measurement error, measurement accuracy limitations, and other factors known to those of skill in the art may occur in amounts that do not preclude the effect the characteristic was intended to provide. In some examples disclosed herein, “substantially” or “about” means within + / - 0-5% of the recited value.

[0008] The following publications are hereby incorporated by reference herein: (1) Interpreting Halide Perovskite Semiconductor Photoluminescence Kinetics, Margherita Taddei, Sarthak Jariwala, Robert J. E. Westbrook, Shaun Gallagher, Aaron C. Weaver, Justin Pothoof, Mark E. Ziffer, Henry J. Snaith, and David S. Ginger, ACS Energy Lett.2024, 9,2508 2516, available at https: / / pubs.acs.org / doi / abs / 10.1021 / acsenergylett.4c00614#; (2)Supplementary Information: Interpreting Halide Perovskite Semiconductor Photoluminescence Kinetics; Margherita Taddei, Sarthak Jariwala, Robert J. E. Westbrook, Shaun Gallagher, Aaron C. Weaver, Justin Pothoof, Mark E. Ziffer, Henry J. Snaith, and David S. Ginger, available at

[0009] These, as well as other aspects, advantages, and alternatives will become apparent to those of ordinary skill in the art by reading the following detailed description, with reference where appropriate to the accompanying drawings. Further, it should be understood that this summary and other descriptions and figures provided herein are intended to illustrate by way of example only and, as such, that numerous variations are possible. BRIEF DESCRIPTION OF THE DRAWINGS

[0010] Figure 1 is a block diagram of a diagnostic device, according to an example.

[0011] Figure 2 is a schematic side view of a sample, according to an example.

[0012] Figure 3 is a schematic top view of a sample, according to an example.

[0013] Figure 4 is a schematic side view of a sample, according to an example.

[0014] Figure 5 is a schematic top view of a sample, according to an example.

[0015] Figure 6 shows a combined diffusion and rate equation for minor carrier electrons within a sample, according to an example.

[0016] Figure 7 shows an equation defining the depth distribution of the generation of minor carrier electrons within a sample as an exponential function, according to an example.

[0017] Figure 8 shows an equation defining the absorptivity of a sample as a function of illumination wavelength, according to an example.

[0018] Figure 9 shows equations defining surface recombination velocity boundary conditions at layer boundaries of a sample, according to an example.

[0019] Figure 10 shows an equation defining photoluminescent intensity of a sample, according to an example.

[0020] Figure 11 shows an equation defining carrier lifetime distribution within a sample in the form of a stretched exponential function, according to an example.

[0021] Figure 12 is a plot of photoluminescent decay within a sample, according to an example.

[0022] Figure 13 is a plot of photoluminescent decay within a sample, according to an example.

[0023] Figure 14 shows fitting parameters for stretched exponential functions, according to an example.

[0024] Figure 15 show the parameters for fitting the diffusion and rate equations, according to an example.

[0025] Figure 16 show the parameters for fitting the diffusion and rate equations, according to an example.

[0026] Figure 17 is a block diagram of a method, according to an example. DETAILED DESCRIPTION

[0027] An improved method for evaluating and characterizing the depth dependence of the photoluminescent response of a material sample is needed. Photoluminescence is the process by which a material emits light in response to photoexcitation. Light incident on the material is absorbed and generates free electrons and holes (i.e., charge carriers) within the material, which eventually recombine to emit light. The intensity of the photoluminescent response of the material can represent how efficiently the material generates charge carriers that recombine to emit light. Both the intensity and the rate of decay of the intensity of the photoluminescent response can represent how quickly the generated charge carriers recombine, for example, at material boundaries or at defect locations within the material.

[0028] Some methods for evaluating the depth dependence of a sample’s photoluminescent response involve fabricating multi-layer semiconductor structures that have the same arrangement of material layers but different layer depths. The variations in the photoluminescent intensity or decay rate for samples having different material layer depths can be compared to what would be expected based on only the variation in layer depths.Adding thickness to a material layer that is less than three nominal penetration depths for the material at the illumination wavelength will generally result in absorption of noticeably more incident photons and more photoluminescence, but a non-uniform distribution of defect centers within the material can cause deviations from the otherwise expected photoluminescence profile. A method that helps evaluate and characterize the depth dependence of the photoluminescent response of a sample via examination of only that sample would be useful.

[0029] Accordingly, a method includes illuminating a surface of a sample with a firstlight having a first wavelength ( 1). As an example, the sample could be a Perovskitesemiconductor layer on a semi-transparent electrode layer made of indium tin oxide. Thus, the illuminated surface could be the semiconductor layer or the electrode layer in various examples. The first wavelength could be within the range of 440 nm to 500 nm, for example, and is generally shorter than the bandgap wavelength of the material under test. The method also includes detecting first intensities of a first photoluminescence induced within the sample by absorption of the first light by the sample. This generally involves capturing multiple images of the surface over time after the illumination of the sample via the first light has ended. The pixel intensities (e.g., pixel brightnesses) of the images represent photoluminescent intensity at the corresponding locations of the sample. The first photoluminescence will typically have a wavelength defined by the bandgap of the material within the sample. The camera that captures the images can use filters that are tuned to pass the bandgap wavelength of the material and block the first wavelength, to avoid capturing illumination backscatter. The method also includes illuminating the surface of the samplewith a second light having a second wavelength ( 2) that is different from the firstwavelength. The second wavelength could be within the range of 620 nm to 750 nm, and is generally shorter than the bandgap wavelength of the material under test. The method also includes detecting second intensities of a second photoluminescence induced within the sample by absorption of the second light by the sample. This generally involves capturing multiple images of the surface over time after the illumination of the sample via the second light has ended. The camera that captures the images can use filters that are tuned to pass the bandgap wavelength of the material and block the second wavelength, to avoid capturing illumination backscatter. The method also includes generating an output representing the first intensities and the second intensities, such as saving data tables or displaying images.

[0030] In some examples, the method also includes evaluating a depth dependence of a photoluminescent response of the sample by using the first intensities and the secondintensities. In the case of the first wavelength being absorbed more strongly than the second wavelength, typically being shorter than the second wavelength, the first photoluminescence is generally more representative of carrier recombination at shallower depths below the surface and the second photoluminescence is generally more representative of carrier recombination at deeper depths below the surface. This is because the probability of a first wavelength photon being absorbed by the material is generally greater than the probability of the second wavelength photon being absorbed by the material. In many examples, the photoluminescent response of the sample can be detected for more than two wavelengths of light to develop a more complete picture of the depth dependence of the photoluminescent response of the sample, which can lead to better information about the spatial distribution of recombination centers within the material.

[0031] Figure 1 is a block diagram of a diagnostic device 10. The diagnostic device 10 includes a computing device 100, a light source 120, and a light detector 122.

[0032] The computing device 100 includes one or more processors 102, a non-transitory computer readable medium 104, a communication interface 106, and a user interface 108. Components of the computing device 100 are linked together by a system bus, network, or other connection mechanism 112.

[0033] The one or more processors 102 may be any type of processor(s), such as a microprocessor, a field programmable gate array, a digital signal processor, a multicore processor, etc., coupled to the non-transitory computer readable medium 104.

[0034] The non-transitory computer readable medium 104 may be any type of memory, such as volatile memory like random access memory (RAM), dynamic random access memory (DRAM), static random access memory (SRAM), or non-volatile memory like read- only memory (ROM), flash memory, magnetic or optical disks, or compact-disc read-only memory (CD-ROM), among other devices used to store data or programs on a temporary or permanent basis.

[0035] Additionally, the non-transitory computer readable medium 104 may store instructions 111. The instructions 111 are executable by the one or more processors 102 to cause the computing device 100 to perform any of the functions or methods described herein.

[0036] The communication interface 106 may include hardware to enable communication within the computing device 100 and / or between the computing device 100 and one or more other devices. The hardware can include any type of input and / or output interfaces, a universal serial bus (USB), PCI Express, transmitters, receivers, and antennas, for example.

[0037] The communication interface 106 may be configured to facilitate communication with one or more other devices, in accordance with one or more wired or wireless communication protocols. For example, the communication interface 106 may be configured to facilitate wireless data communication for the computing device 100 according to one or more wireless communication standards, such as one or more Institute of Electrical and Electronics Engineers (IEEE) 801.11 standards, ZigBee standards, Bluetooth standards, etc. As another example, the communication interface 106 can be configured to facilitate wired data communication with one or more other devices. The communication interface 106 may also include analog-to-digital converters (ADCs) or digital-to-analog converters (DACs) that the computing device 100 can use to control various components of the computing device 100 or external devices.

[0038] The user interface 108 may include any type of display component configured to display data. As one example, the user interface 108 can include a touchscreen display. As another example, the user interface 108 can include a flat-panel display, such as a liquid- crystal display (LCD) or a light-emitting diode (LED) display. The user interface 108 can include one or more pieces of hardware used to provide data and control signals to the computing device 100. For instance, the user interface 108 can include a mouse or a pointing device, a keyboard or a keypad, a microphone, a touchpad, or a touchscreen, among other possible types of user input devices. Generally, the user interface 108 can enable an operator to interact with a graphical user interface (GUI) provided by the computing device 100 (e.g., displayed by the user interface 108).

[0039] The light source 120 can take the form of one or more lasers or one or more light emitting diodes (LEDs) that are collectively configured to emit light having a tunable wavelength and power spectral density. The light source 120 is generally configured to generate any power spectral density of light within the ultraviolet, visible, and infrared spectra.

[0040] The light detector 122 typically takes the form of an image sensor, such as a charge-coupled device (CCD), a complementary metal oxide semiconductor (CMOS) pixel sensor, one or more photodiodes, one or more photoresistors, or one or more phototransistors. Other examples are possible.

[0041] Figure 2 is a schematic side view of a sample 304. As shown, the sample 304 includes a semiconductor layer 310 (e.g., a Perovskite layer) on a semi-transparent electrode layer 312 (e.g., indium tin oxide). The semiconductor layer 310 includes a surface 302A that faces away from a surface 302B of the semi-transparent electrode layer 312.

[0042] Figure 3 is a schematic top view of the sample 304. The diagnostic device 10 uses the light source 120 to illuminate the surface 302A with a light 306A (e.g., one or more pulses of light) having a first wavelength 1. In other examples, the light source 120 can illuminate the surface 302B with the light 306A. In some examples, the first wavelength 1 is less than 500 nm. Typically, at least 95% of a power spectral density of the light 306A is within a rangeof 0.95 1 to 1.05 1.

[0043] The diagnostic device 10 also uses the light detector 122 to detect first intensities of a photoluminescence 308A induced within the sample 304 by absorption of the light 306A by the sample 304. The first wavelength1is generally chosen to be shorter than the bandgap wavelengthBGof material under test. The bandgap wavelengthBGis also the wavelength of the photoluminescence 308A. The light detector 122 is typically used to capture one or more images of the surface 302A to detect the first intensities of the photoluminescence 308A. More specifically, the light detector 122 can capture multiple images of the surface 302A over time, for example, while the light source 120 is no longer illuminating the surface 302A with the light 306A. The intensity or brightness of the pixels of the captured images represent intensities of the photoluminescence 308A at corresponding locations of the sample 304. In some examples, the light detector 122 is used to capture images of the surface 302B instead. The diagnostic device 10 can generate an output representing the first intensities of the photoluminescence 308A by displaying the one or more images of the surface 302A or the surface 302B using the user interface 108 or by saving the one or more images of the surface 302A or the surface 302B to the computer readable medium 104.

[0044] Figure 4 is a schematic side view of the sample 304.

[0045] Figure 5 is a schematic top view of the sample 304. The diagnostic device 10 also uses the light source 120 to illuminate the surface 302A with a light 306B (e.g., one or more pulses of light) having a second wavelength2. In other examples, the light source 120 can illuminate the surface 302B with the light 306B. In some examples, the second wavelength2is greater than 620 nm and less than 750 nm. Typically, at least 95% of a power spectraldensity of the light 306B is within a range of 0.95 2 to 1.05 2.

[0046] The diagnostic device 10 also uses the light detector 122 to detect second intensities of a photoluminescence 308B induced within the sample 304 by absorption of the light 306B by the sample 304. The second wavelength 2 is generally chosen to be less than the bandgap wavelength BG of the photoluminescence 308B. The light detector 122 is typically used to capture one or more images of the surface 302A to detect the second intensities of the photoluminescence 308B. More specifically, the light detector 122 cancapture multiple images of the surface 302A over time, for example, while the light source 120 is no longer illuminating the surface 302A with the light 306B. The intensity or brightness of the pixels of the captured images represent intensities of the photoluminescence 308B at corresponding locations of the sample 304. In some examples, the light detector 122 is used to capture images of the surface 302B instead. The diagnostic device 10 can generate an output representing the second intensities of the photoluminescence 308B by displaying the one or more images of the surface 302A or the surface 302B using the user interface 108 or by saving the one or more images of the surface 302A or the surface 302B to the computer readable medium 104.

[0047] The first intensities of the photoluminescence 308A and the second intensities of the photoluminescence 308B can be compared or otherwise used to evaluate or characterize a depth dependence of a photoluminescent response of the sample 304. The desired result is generally a quantitative or qualitative model for the depth dependence of the photoluminescent response of the sample 304, which can be used as a proxy for the spatial distribution of recombination centers within the sample 304. In some examples, a manual inspection of the first intensities and the second intensities (i.e., the images representing the first intensities and the second intensities) can be sufficient to make useful inferences about the distribution of recombination centers within the sample 304 as a function of depth. For example, if the first intensities of the photoluminescence 308A exhibit faster decay than the second intensities of the photoluminescence 308B, it can be inferred that there are more recombination centers near the illuminated surface than deeper in the sample.

[0048] In other examples, the distribution of recombination centers within the sample 304 as a function of depth is characterized by a mathematical model. The first intensities of the photoluminescence 308A can be expressed as a function of two spatial dimensions (y,z) that define the surface 302A and the time (t) after illumination with the light 306A is ceased: PL1(t,y,z). For example, an image of the surface 302A captured at t=0 includes an array of pixel values that define the intensity of the photoluminescence 308A at corresponding locations of the sample 304 as PL1(t=0,y,z). Images captured at t=1 s, t=2 s, t=3 s, etc. can be characterized as PL1(t=1 s, y,z), PL1(t=2 s, y,z), and PL1(t=3 s, y,z), respectively.

[0049] The second intensities of the photoluminescence 308B can be expressed as a function of the two spatial dimensions (y,z) that define the surface 302A and the time (t) after illumination with the light 306B is ceased: PL2(t,y,z). For example, an image of the surface 302A captured at t=0 includes an array of pixel values that define the intensity of the photoluminescence 308B at corresponding locations of the sample 304 as PL2(t=0,y,z).Images captured at t=1 s, t=2 s, t=3 s, and so on can be characterized as PL2(t=1 s, y,z), PL2(t=2 s, y,z), and PL2(t=3 s, y,z), respectively.

[0050] In some examples, more than two wavelengths, steady state or pulsed illumination, and / or various intensity levels of illumination are used to detect more than two time series of photoluminescent intensities. Using additional wavelengths, illumination waveforms, and intensities of illumination to cause and then detect photoluminescence allows for an easier model fitting process and a better model fit.

[0051] Accordingly, minority carrier diffusion and rate equations are used along with estimated boundary conditions to create an initial version of a model that characterizes the photoluminescent response as a function of time and depth within the sample. The parameters of the model are then (e.g., iteratively) adjusted to improve the fit of the model to the acquired intensity data. The equations that are solved are shown in Figures 6-11.

[0052] Figure 6 shows a combined diffusion and rate equation for minor carrier electrons within the sample 304.

[0053] Figure 7 shows an equation defining the depth distribution of generation of minor carrier electrons within the sample 304 as an exponential function.

[0054] Figure 8 shows an equation defining the absorption of the sample 304 as a function of illumination wavelength.

[0055] Figure 9 shows equations defining surface recombination velocity boundary conditions at layer boundaries of the sample 304.

[0056] Figure 10 shows an equation defining photoluminescent intensity of the sample 304.

[0057] Figure 11 shows an equation defining carrier lifetime distribution within the sample 304 in the form of a stretched exponential function.

[0058] Referring to Figure 9 as an example, generating the model can include using the first intensities of the photoluminescence 308A and the second intensities of the photoluminescence 308B to determine boundary conditions for the model in the form of a first surface recombination velocity at the surface 302A, a second surface recombination velocity at the surface 302B, and / or a third surface recombination velocity at the surface 302C, which is the interface between the semiconductor layer 310 and the semi-transparent electrode layer 312.

[0059] Generating the model can also include iteratively adjusting one or more parameters of the model to improve a fit of the model to the first intensities of the photoluminescence 308A and the second intensities of the photoluminescence 308B (and / orto other photoluminescent intensities detected in association with additional illuminationwavelengths). As shown in Figures 6-10, such parameters include the absorptivity ( ) of thesample 304, the illumination intensity I, the initial hole concentration P0 of the sample 304, the initial electron concentration N0 of the sample 304, the diffusion constant D of the sample 304, the non-radiative recombination constant knrof the sample 304, the radiative recombination constant kradof the sample 304, the Auger recombination constant kAugof the sample 304, the surface recombination velocity SRV1n(0) at the surface 302A, the surface recombination velocity SRV2n(d) at the surface 302C, and the surface recombination velocity SRV3n(0) at the surface 302B.

[0060] In some examples, generating the model includes generating the model using anexperimentally determined or estimated wavelength-dependent absorption function ( ) forthe sample 304, an initial charge carrier concentration N0 that is estimated based on intensities of the light 306A and the light 306B, an estimated non-radiative recombination constant knr for the sample 304, a known or estimated radiative recombination constant krad for the sample 304, a known or estimated Auger recombination constant kAug for the sample 304, a diffusion parameter D for the sample 304, a shallow trap density for the sample 304, or a charge back-transfer rate associated with an electrode. Generating the model also generally involves (e.g., iteratively) adjusting one or more of the aforementioned parameters to improve a fit of the model to the first intensities of the photoluminescence 308A and the second intensities of the photoluminescence 308B (and / or to other photoluminescent intensities detected in association with additional illumination wavelengths).

[0061] In some examples, the equation of Figure 11 is used to characterize the spatial heterogeneity of carrier lifetime within the sample 304 in directions parallel to the surface 302A. For example, the computing device 100 can determine a first stretching factor1for a first stretched exponential function using the first intensities of the photoluminescence 308A. The first stretched exponential function models the first intensities of the photoluminescence 308A within a heterogeneous region of the sample 304. The computing device 100 can also determine a second stretching factor 2 for a second stretched exponential function using the second intensities of the photoluminescence 308B. The second stretched exponential function models the second intensities of the photoluminescence 308B within a heterogeneous region of the sample 304. The first stretched exponential function and the second stretched exponential function can be used as a basis for determining parameters of the model.

[0062] Some examples involve generating the model using an estimated diffusion coefficient D for minority carriers and / or an estimated surface recombination velocity SRVfor the minority carriers. In this context, generating the model can include using the model to perform a first simulation of photoluminescent decay within the sample 304 that is induced by illumination of the surface of the sample with the light 306A and using the model to perform a second simulation of photoluminescent decay within the sample 304 that is induced by illumination of the surface of the sample with the light 306B. The model can be improved by adjusting the estimated diffusion coefficient D or the estimated surface recombination velocity SRV such that the model better predicts the first intensities of the photoluminescence 308A and the second intensities of the photoluminescence 308B. The aforementioned steps can be performed iteratively (e.g., via optimization algorithms such as a least-square method, or a machine learning model such as a nearest neighbor classifier) to improve the model fit.

[0063] In some examples, illumination of the sample 304 with the light 306A can be performed by adjusting or sweeping the intensity of the light 306A and illumination of the sample 304 with the light 306B can be performed by adjusting or sweeping the intensity of the light 306B. Thus, the diagnostic device 10 can illuminate the surface 302A with the light 306A such that the light 306A has a third intensity and illuminate the surface 302A with the light 306A such that the light 306A has a fourth intensity that is different from the third intensity. Accordingly, the first intensities of the photoluminescence 308A that were induced by the third intensity of the light 306A are associated with the third intensity and the first intensities of the photoluminescence 308A that were induced by the fourth intensity of the light 306A are associated with the fourth intensity. Likewise, the diagnostic device 10 can illuminate the surface 302A with the light 306B such that the light 306B has a fifth intensity and illuminate the surface 302A with the light 306B such that the light 306A has a sixth intensity that is different from the fifth intensity. Accordingly, the second intensities of the photoluminescence 308B that were induced by the fifth intensity of the light 306B are associated with the fifth intensity and the second intensities of the photoluminescence 308B that were induced by the sixth intensity of the light 306B are associated with the sixth intensity. This information can be used to refine the model to account for variations in carrier generation and recombination that are based on illumination intensity.

[0064] Figure 12 is a plot of photoluminescent decay within a sample such as the sample 304. More specifically, Figure 12 shows time resolved photoluminescent decay of a FA0.83Cs0.17Pb(I 0.75Br0.25)3 film excited at 640 nm with a frequency of 0.5 MHz and fluence of17 nJ / cm2 (5.25 × 1010 photons / pulse / cm2, N0 = 9.3 × 1014 cm 3) (red) and 470 nm with afrequency of 0.5 MHz and fluence of 6 nJ / cm2 (1.38 × 1010 photons / pulse / cm2, N0 = 2.74 ×1014 cm 3) (blue). The inset of Figure 12 shows the first 80 ns of the decay. The decay is fitwith a stretched exponential function (dashed line). The thickness of the film is about 500 nm.

[0065] Figure 13 is a plot of photoluminescent decay within a sample such as the sample 304. More specifically, Figure 13 shows time resolved photoluminescent decay of a perovskite treated with 3-aminopropyltrimethoxysilane (APTMS), excited at 640 nm, 0.25 MHz, 17 nJ / cm2 / pulse (red) and 470 nm, 0.25 MHz, 6 nJ / cm2 / pulse (blue). The inset of Figure 13 shows the first 80 ns of the decay. The decay is fit with a stretched exponential function (dashed line). The thickness of the film is about 500 nm.

[0066] Figure 14 shows the fitting parameters for the stretched exponential functions shown in Figure 12 and Figure 13.

[0067] Figure 15 and Figure 16 show the parameters for fitting the diffusion and rate equations to the data shown in Figure 12 and Figure 13.

[0068] Figure 17 is a block diagram of a method 200. As shown in Figure 17, the method 200 includes one or more operations, functions, or actions as illustrated by blocks 202, 204, 206, 208, and 210. Although the blocks are illustrated in a sequential order, these blocks may also be performed in parallel, and / or in a different order than those described herein. Also, the various blocks may be combined into fewer blocks, divided into additional blocks, and / or removed based upon the desired implementation.

[0069] At block 202, the method 200 includes the diagnostic device 10 illuminating the surface 302A or the surface 302B of the sample 304 with the light 306A having the firstwavelength ( 1). Functionality related to block 202 is described above with reference toFigures 2-16.

[0070] At block 204, the method 200 includes the diagnostic device 10 detecting the first intensities of the photoluminescence 308A induced within the sample 304 by absorption of the light 306A by the sample 304. Functionality related to block 204 is described above with reference to Figures 2-16.

[0071] At block 206, the method 200 includes the diagnostic device 10 illuminating the surface 302A or the surface 302B of the sample 304 with the light 306B having the secondwavelength ( 2) that is different from the first wavelength. Functionality related to block 206is described above with reference to Figures 2-16.

[0072] At block 208, the method 200 includes the diagnostic device 10 detecting the second intensities of the photoluminescence 308B induced within the sample 304 by absorption of the light 306B by the sample 304. Functionality related to block 208 is described above with reference to Figures 2-16.

[0073] At block 210, the method 200 includes the diagnostic device 10 generating an output representing the first intensities and the second intensities. Functionality related to block 210 is described above with reference to Figures 2-16.

[0074] ENUMERATED EXAMPLE EMBODIMENTS (EEEs)

[0075] EEE 1 is a method comprising: illuminating a surface of a sample with a first lighthaving a first wavelength ( 1); detecting first intensities of a first photoluminescence inducedwithin the sample by absorption of the first light by the sample; illuminating the surface ofthe sample with a second light having a second wavelength ( 2) that is different from the firstwavelength; detecting second intensities of a second photoluminescence induced within the sample by absorption of the second light by the sample; and generating an output representing the first intensities and the second intensities.

[0076] EEE 2 is the method of EEE 1, wherein the sample comprises a semiconductor layer having a bandgap wavelength that is longer than the first wavelength.

[0077] EEE 3 is the method of EEE 2, wherein the bandgap wavelength is longer than the second wavelength.

[0078] EEE 4 is the method of any one of EEEs 2-3, wherein the semiconductor layer is a Perovskite layer.

[0079] EEE 5 is the method of any one of EEEs 2-4, wherein the surface is a surface of the semiconductor layer.

[0080] EEE 6 is the method of any one of EEEs 2-5, wherein the sample comprises a semi-transparent electrode layer in contact with the semiconductor layer.

[0081] EEE 7 is the method of EEE 6, wherein the surface is a surface of the semi- transparent electrode layer

[0082] EEE 8 is the method of any one of EEEs 1-7, wherein the first wavelength is less than 500 nm.

[0083] EEE 9 is the method of any one of EEEs 1-8, wherein the second wavelength is greater than 620 nm and less than 750 nm.

[0084] EEE 10 is the method of any one of EEEs 1-9, wherein at least 95% of a powerspectral density of the first light is within a range of 0.95 1 to 1.05 1.

[0085] EEE 11 is the method of any one of EEEs 1-10, wherein at least 95% of a powerspectral density of the second light is within a range of 0.95 2 to 1.05 2.

[0086] EEE 12 is the method of any one of EEEs 1-11, wherein illuminating the surface with the first light comprises illuminating the surface with a pulse of light.

[0087] EEE 13 is the method of any one of EEEs 1-12, wherein illuminating the surface with the second light comprises illuminating the surface with a pulse of light.

[0088] EEE 14 is the method of any one of EEEs 1-13, wherein detecting the first intensities comprises capturing an image of the surface.

[0089] EEE 15 is the method of any one of EEEs 1-14, wherein detecting the first intensities comprises capturing images of the surface over time while no longer illuminating the surface with the first light.

[0090] EEE 16 is the method of any one of EEEs 1-15, wherein detecting the second intensities comprises capturing an image of the surface.

[0091] EEE 17 is the method of any one of EEEs 1-16, wherein detecting the second intensities comprises capturing images of the surface over time while no longer illuminating the surface with the second light.

[0092] EEE 18 is the method of any one of EEEs 1-17, further comprising evaluating or characterizing a depth dependence of a photoluminescent response of the sample by using the first intensities and the second intensities.

[0093] EEE 19 is the method of EEE 18, wherein evaluating the depth dependence comprises performing a manual comparison of the first intensities and the second intensities.

[0094] EEE 20 is the method of any one of EEEs 18-19, wherein evaluating the depth dependence comprises generating a model characterizing the photoluminescent response as a function of time and depth within the sample.

[0095] EEE 21 is the method of EEE 20, wherein the surface is a first surface of the sample, wherein generating the model comprises using the first intensities and the second intensities to determine boundary conditions for the model in the form of a first surface recombination velocity at the first surface and a second surface recombination velocity at a second surface of the sample that is opposite the first surface.

[0096] EEE 22 is the method of any one of EEEs 20-21, wherein generating the model comprises iteratively adjusting one or more parameters of the model to improve a fit of the model to the first intensities and the second intensities.

[0097] EEE 23 is the method of any one of EEEs 20-22, wherein generating the model comprises generating the model using an experimentally determined or estimatedwavelength-dependent absorption function for the sample, an initial charge carrier concentration that is estimated based on an intensity of the first light and the second light, an estimated non-radiative recombination constant for the sample, a known or estimated radiative recombination constant for the sample, a known or estimated Auger recombination constant for the sample, a diffusion parameter for the sample, a shallow trap density for the sample, or a charge back-transfer rate associated with an electrode.

[0098] EEE 24 is the method of EEE 23, wherein generating the model comprises adjusting one or more of the estimated non-radiative recombination constant, the known radiative recombination constant, the known Auger recombination constant, or the diffusion parameter to improve a fit of the model to the first intensities and the second intensities.

[0099] EEE 25 is the method of any one of EEEs 20-24, further comprising: determining a first stretching factor for a first stretched exponential function using the first intensities, wherein the first stretched exponential function models the first intensities within a heterogeneous region of the sample; and determining a second stretching factor for a second stretched exponential function using the second intensities, wherein the second stretched exponential function models the second intensities within the heterogeneous region of the sample, wherein generating the model comprises generating the model using the first stretching factor and the second stretching factor as a basis for determining parameters of the model.

[0100] EEE 26 is the method of EEE 25, wherein the parameters of the model comprise an estimated diffusion coefficient for minority carriers and / or an estimated surface recombination velocity for the minority carriers, wherein generating the model further comprises: using the model to perform a first simulation of photoluminescent decay within the sample that is induced by illumination of the surface of the sample with the first light; using the model to perform a second simulation of photoluminescent decay within the sample that is induced by illumination of the surface of the sample with the second light; and adjusting the estimated diffusion coefficient or the estimated surface recombination velocity such that the model better predicts the first intensities and the second intensities.

[0101] EEE 27 is the method of EEE 26, wherein steps (a), (b), and (c) are performed iteratively.

[0102] EEE 28 is the method of EEE 27, wherein the iterative performance of steps (a), (b), and (c) are performed using a machine learning algorithm.

[0103] EEE 29 is the method of any one of EEEs 1-28, wherein illuminating the surface with the first light comprises illuminating the surface with the first light such that the firstlight has a third intensity and illuminating the surface with the first light such that the first light has a fourth intensity that is different from the third intensity, the method further comprising: associating the first intensities of the first photoluminescence respectively with the third intensity and the fourth intensity, wherein illuminating the surface with the second light comprises illuminating the surface with the second light such that the second light has a fifth intensity and illuminating the surface with the second light such that the second light has a sixth intensity that is different from the fifth intensity, the method further comprising: associating the second intensities of the second photoluminescence respectively with the fifth intensity and the sixth intensity.

[0104] EEE 30 is the method of any one of EEEs 1-29, wherein generating the output comprises displaying one or more images representing the first intensities and the second intensities.

[0105] EEE 31 is the method of any one of EEEs 1-30, wherein generating the output comprises saving data representing the first intensities and the second intensities.

[0106] EEE 32 is a non-transitory computer readable medium storing instructions that, when executed by one or more processors of a diagnostic device, cause the diagnostic device to perform the method of any one of EEEs 1-31.

[0107] EEE 33 is a diagnostic device comprising: one or more processors; a light source; a light detector; and a computer readable medium storing instructions that, when executed by the one or more processors, cause the diagnostic device to perform the method of any one of EEEs 1-31.

[0108] While various example aspects and example embodiments have been disclosed herein, other aspects and embodiments will be apparent to those skilled in the art. The various example aspects and example embodiments disclosed herein are for purposes of illustration and are not intended to be limiting, with the true scope and spirit being indicated by the following claims.

Claims

CLAIMS What is claimed is:

1. A method comprising: illuminating a surface of a sample with a first light having a first wavelength ( 1);detecting first intensities of a first photoluminescence induced within the sample by absorption of the first light by the sample; illuminating the surface of the sample with a second light having a second wavelength( 2) that is different from the first wavelength;detecting second intensities of a second photoluminescence induced within the sample by absorption of the second light by the sample; and generating an output representing the first intensities and the second intensities.

2. The method of claim 1, wherein the sample comprises a semiconductor layer having a bandgap wavelength that is longer than the first wavelength.

3. The method of claim 2, wherein the bandgap wavelength is longer than the second wavelength.

4. The method of claim 2, wherein the semiconductor layer is a Perovskite layer.

5. The method of claim 2, wherein the surface is a surface of the semiconductor layer.

6. The method of claim 2, wherein the sample comprises a semi-transparent electrode layer in contact with the semiconductor layer.

7. The method of claim 6, wherein the surface is a surface of the semi- transparent electrode layer.

8. The method of claim 1, wherein the first wavelength is less than 500 nm.

9. The method of claim 1, wherein the second wavelength is greater than 620 nm and less than 750 nm.

10. The method of claim 1, wherein at least 95% of a power spectral density of thefirst light is within a range of 0.95 1 to 1.05 1.

11. The method of claim 1, wherein at least 95% of a power spectral density of thesecond light is within a range of 0.95 2 to 1.05 2.

12. The method of claim 1, wherein illuminating the surface with the first light comprises illuminating the surface with a pulse of light.

13. The method of claim 1, wherein illuminating the surface with the second light comprises illuminating the surface with a pulse of light.

14. The method of claim 1, wherein detecting the first intensities comprises capturing an image of the surface.

15. The method of claim 1, wherein detecting the first intensities comprises capturing images of the surface over time while no longer illuminating the surface with the first light.

16. The method of claim 1, wherein detecting the second intensities comprises capturing an image of the surface.

17. The method of claim 1, wherein detecting the second intensities comprises capturing images of the surface over time while no longer illuminating the surface with the second light.

18. The method of claim 1, further comprising evaluating or characterizing a depth dependence of a photoluminescent response of the sample by using the first intensities and the second intensities.

19. The method of claim 18, wherein evaluating or characterizing the depth dependence comprises performing a manual comparison of the first intensities and the second intensities.

20. The method of claim 18, wherein evaluating or characterizing the depth dependence comprises generating a model characterizing the photoluminescent response as a function of time and depth within the sample.

21. The method of claim 20, wherein the surface is a first surface of the sample, wherein generating the model comprises using the first intensities and the second intensities to determine boundary conditions for the model in the form of a first surface recombination velocity at the first surface and a second surface recombination velocity at a second surface of the sample that is opposite the first surface.

22. The method of claim 20, wherein generating the model comprises iteratively adjusting one or more parameters of the model to improve a fit of the model to the first intensities and the second intensities.

23. The method of claim 20, wherein generating the model comprises generating the model using an experimentally determined or estimated wavelength-dependent absorption function for the sample, an initial charge carrier concentration that is estimated based on an intensity of the first light and the second light, an estimated non-radiative recombination constant for the sample, a known or estimated radiative recombination constant for the sample, a known or estimated Auger recombination constant for the sample, a diffusion parameter for the sample, a shallow trap density for the sample, or a charge back-transfer rate associated with an electrode.

24. The method of claim 23, wherein generating the model comprises adjusting one or more of the estimated non-radiative recombination constant, the known radiative recombination constant, the known Auger recombination constant, or the diffusion parameter to improve a fit of the model to the first intensities and the second intensities.

25. The method of claim 20, further comprising: determining a first stretching factor for a first stretched exponential function using the first intensities, wherein the first stretched exponential function models the first intensities within a heterogeneous region of the sample; and determining a second stretching factor for a second stretched exponential functionusing the second intensities, wherein the second stretched exponential function models the second intensities within the heterogeneous region of the sample, wherein generating the model comprises generating the model using the first stretching factor and the second stretching factor as a basis for determining parameters of the model.

26. The method of claim 25, wherein the parameters of the model comprise an estimated diffusion coefficient for minority carriers and / or an estimated surface recombination velocity for the minority carriers, wherein generating the model further comprises: (a) using the model to perform a first simulation of photoluminescent decay within the sample that is induced by illumination of the surface of the sample with the first light; (b) using the model to perform a second simulation of photoluminescent decay within the sample that is induced by illumination of the surface of the sample with the second light; and (c) adjusting the estimated diffusion coefficient or the estimated surface recombination velocity such that the model better predicts the first intensities and the second intensities.

27. The method of claim 26, wherein steps (a), (b), and (c) are performed iteratively.

28. The method of claim 27, wherein the iterative performance of steps (a), (b), and (c) are performed using a machine learning algorithm.

29. The method of claim 1, wherein illuminating the surface with the first light comprises illuminating the surface with the first light such that the first light has a third intensity and illuminating the surface with the first light such that the first light has a fourth intensity that is different from the third intensity, the method further comprising: associating the first intensities of the first photoluminescence respectively with the third intensity and the fourth intensity, wherein illuminating the surface with the second light comprises illuminating the surface with the second light such that the second light has a fifth intensity and illuminatingthe surface with the second light such that the second light has a sixth intensity that is different from the fifth intensity, the method further comprising: associating the second intensities of the second photoluminescence respectively with the fifth intensity and the sixth intensity.

30. The method of claim 1, wherein generating the output comprises displaying one or more images representing the first intensities and the second intensities.

31. The method of claim 1, wherein generating the output comprises saving data representing the first intensities and the second intensities.

32. A non-transitory computer readable medium storing instructions that, when executed by one or more processors of a diagnostic device, cause the diagnostic device to perform the method of claim 1.

33. A diagnostic device comprising: one or more processors; a light source; a light detector; and a computer readable medium storing instructions that, when executed by the one or more processors, cause the diagnostic device to perform the method of claim 1.

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