System and method of semiconductor characterization

Abstract

A system for characterizing a semiconductor sample is disclosed. The system comprises a measurement subsystem, a data analysis subsystem, and a statistical analysis subsystem coupled to each other via an interconnection. The measurement subsystem excites a semiconductor sample by shining light on one or more points in the semiconductor sample to generate electron hole pairs, which creates a change in conductivity of the semiconductor sample. The measurement subsystem measures one or more voltage decay curves corresponding to the one or more points in the semiconductor sample based on the changes in conductivity, and transmits the measured voltage decay curves to the data analysis subsystem. The data analysis subsystem extracts one or more normalized decay curves from the transmitted measured voltage decay curves, which the data analysis subsystem then transmits to the statistical analysis subsystem. The statistical analysis subsystem analyzes the transmitted normalized decay curves.

Description

1 2 SYSTEM AND METHOD OF SEMICONDUCTOR CHARACTERIZATION 3 4 FIELD OF THE INVENTION 5

[0001] The present disclosure relates to characterization of semiconductors. 6 7 BRIEF SUMMARY 8

[0002] A system for characterizing a semiconductor sample comprising: a measurement 9 subsystem, a data analysis subsystem, and a statistical analysis subsystem coupled to each other 10 via an interconnection, wherein the measurement subsystem excites a semiconductor sample, said 11 excitation comprising passing a current through the semiconductor sample to create a voltage 12 across said sample, shining light on one or more points in the semiconductor sample to generate 13 electron hole pairs at the one or more points, wherein said generation of electron hole pairs creates 14 a change in conductivity of said semiconductor sample; the measurement subsystem measures one 15 or more voltage decay curves corresponding to the one or more points in said semiconductor 16 sample based on the changes in conductivity; the measurement subsystem transmits the one or 17 more measured voltage decay curves via the interconnection to the data analysis subsystem; the 18 data analysis subsystem extracts one or more normalized decay curves corresponding to the 19 transmitted one or more measured voltage decay curves, wherein the one or more normalized 20 decay curves correspond to one or more discrete estimates of survival functions; the data analysis 21 subsystem transmits the extracted one or more normalized decay curves via the interconnection to 22 the statistical analysis subsystem; the statistical analysis subsystem analyzes the transmitted one 23 or more normalized decay curves, said analyzing comprising obtaining one or more discrete 24 estimates of a probability of recombination corresponding to the one or more normalized decay 25 curves, and computing one or more summary statistics corresponding to each of said obtained one 26 or more discrete estimates of the probability of recombination. 27

[0003] A system for characterizing a semiconductor sample using transient 28 photoconductive decay measurements comprising: a transient photoconductive decay 29 measurement subsystem, a data analysis subsystem, and a statistical analysis subsystem coupled 30 to each other via an interconnection, wherein the transient photoconductive decay measurement 31 subsystem excites a semiconductor sample, said excitation comprising passing a current through 32 the semiconductor sample to create a voltage across said sample, shining light on one or more CA 3085115 Date reçue / Received date 2026-01-08 2 points in the semiconductor sample to generate electron hole pairs at the one 1 or more points, 2 wherein said generation of electron hole pairs changes a conductivity of said semiconductor 3 sample; the transient photoconductive decay measurement subsystem measures one or more 4 voltage decay curves corresponding to the one or more points in said semiconductor sample based 5 on the changes in conductivity; the transient photoconductive decay measurement subsystem 6 transmits the one or more measured voltage decay curves via the interconnection to the data 7 analysis subsystem; the data analysis subsystem extracts one or more normalized decay curves 8 corresponding to the transmitted one or more measured voltage decay curves, wherein the one or 9 more normalized decay curves correspond to one or more discrete estimates of survival functions; 10 the data analysis subsystem transmits the extracted one or more normalized decay curves via the 11 interconnection to the statistical analysis subsystem; and the statistical analysis subsystem analyzes 12 the transmitted one or more normalized decay curves, said analyzing comprising obtaining one or 13 more discrete estimates of a probability of recombination corresponding to the one or more 14 normalized decay curves, and computing one or more summary statistics corresponding to each of 15 said obtained one or more discrete estimates of the probability of recombination. 16

[0004] A system for characterizing a plurality of semiconductor samples using transient 17 photoconductive decay measurements comprising: a transient photoconductive decay 18 measurement subsystem, a data analysis subsystem, and a statistical analysis subsystem coupled 19 to each other via an interconnection, wherein the transient photoconductive decay measurement 20 subsystem excites the plurality of semiconductor samples, said excitation comprising passing a 21 current through each of the plurality of semiconductor samples to create a voltage across each of 22 the plurality of semiconductor samples, and shining light on one or more points in each of the 23 plurality of semiconductor samples to generate electron hole pairs at the one or more points, 24 wherein for each of the one or more points said generation of electron hole pairs changes the 25 voltage across the corresponding semiconductor sample; the transient photoconductive decay 26 measurement subsystem measures one or more voltage decay curves created based on the changes 27 in the voltage across each of the plurality of semiconductor samples; the transient photoconductive 28 decay measurement subsystem transmits the one or more measured voltage decay curves via the 29 interconnection to the data analysis subsystem; the data analysis subsystem extracts one or more 30 intermediate voltage decay curves corresponding to the transmitted one or more measured voltage 31 decay curves; the data analysis subsystem transmits the extracted one or more intermediate voltage CA 3085115 Date reçue / Received date 2026-01-08 3 decay curves via the interconnection to the statistical analysis subsystem; and 1 the statistical 2 analysis subsystem analyzes the transmitted one or more intermediate voltage decay curves, said 3 analysis comprising converting the transmitted one or more intermediate voltage decay curves to 4 one or more minority carrier population decay curves, and performing one or more comparisons 5 of survival behavior using the one or more minority carrier population decay curves . 6

[0005] The foregoing and additional aspects and embodiments of the present disclosure 7 will be apparent to those of ordinary skill in the art in view of the detailed description of various 8 embodiments and / or aspects, which is made with reference to the drawings, a brief description of 9 which is provided next. 10 11 BRIEF DESCRIPTION OF THE DRAWINGS 12

[0006] The foregoing and other advantages of the disclosure will become apparent upon 13 reading the following detailed description and upon reference to the drawings. 14

[0007] FIG. 1 shows the steps used in the prior art analysis approaches 15

[0008] FIG. 2 shows an example analysis setup. 16

[0009] FIG. 3 shows a sample voltage decay curve 300. 17

[0010] FIG. 4 shows a grid of points for mapping spatial nonuniformities across a 18 semiconductor sample. 19

[0011] FIG. 5A shows one embodiment of an analysis performed on a voltage decay curve. 20

[0012] FIG. 5B shows an example of extracting readings to form an intermediate voltage 21 decay curve V(t). 22

[0013] FIG. 6 shows one embodiment of step 504. 23

[0014] FIG. 7 shows an embodiment of a process to perform comparison between two or 24 more samples, or two or more locations within the same sample. 25

[0015] FIG. 8 shows an example flowchart to calculate and compare summary statistics. 26

[0016] FIG. 9 shows a process to estimate an upper bound twin to calculate the proportion 27 of recombination events taking place within a localized region of interest compared to the number 28 of recombination events taking place within the entire semiconductor sample. 29

[0017] FIG. 10 shows a process to estimate an upper bound twin to calculate the proportion 30 of minority carriers within the localized area as compared to the entire semiconductor sample. 31

[0018] FIG. 11 demonstrates an example embodiment of an integrated testing procedure. CA 3085115 Date reçue / Received date 2026-01-08 4

[0019] FIG. 12A demonstrates another example embodiment of an 1 integrated testing 2 procedure. 3

[0020] FIG. 12B demonstrates an example embodiment of further actions which are 4 performed as part of integrated testing. 5

[0021] While the present disclosure is susceptible to various modifications and alternative 6 forms, specific embodiments or implementations have been shown by way of example in the 7 drawings and will be described in detail herein. It should be understood, however, that the 8 disclosure is not intended to be limited to the particular forms disclosed. Rather, the disclosure is 9 to cover all modifications, equivalents, and alternatives falling within the spirit and scope of an 10 invention as defined by the appended claims. 11 12 DETAILED DESCRIPTION 13

[0022] While the description here focuses on analysis of results obtained using the transient 14 photoconductive decay technique, it is equally applicable to the analysis of results obtained using 15 other similar techniques, that is, where a population is generated, and a measurable output related 16 to the survival of the generated population is measured. 17

[0023] Similarly while many of the examples here are discussed in relation to mercury 18 cadmium telluride (HgCdTe), the analyses are equally applicable to any semiconductor material. 19 Introduction 20

[0024] In the transient photoconductive decay technique, in one embodiment a current is 21 passed through a sample which is to be measured. As a result, a voltage is created across the 22 sample. The voltage is proportional to the resistance of the sample, which in turn is proportional 23 to the resistivity and hence inversely proportional to the conductivity of the sample. 24

[0025] Then, light is shone upon the sample to generate electron hole pairs. Depending on 25 whether the sample is p-type or n-type, either electrons or holes are the minority carriers. As a 26 result, the conductivity of the sample increases, leading to a drop in the resistance of the sample. 27 As a consequence of the resistance drop, the voltage across the sample will also drop. 28

[0026] The generated minority carriers drift under the influence of the bias field created by 29 the voltage and diffuse throughout the sample due to the concentration gradient. Over time, these 30 minority carriers will also recombine within the sample. As a consequence of the recombination 31 of the minority carriers, the conductivity will decay to its value before the light was shone upon CA 3085115 Date reçue / Received date 2026-01-08 5 the sample. As the conductivity decays so does the resistance, and consequently 1 the voltage across 2 the sample will also increase. 3

[0027] The aim of the transient photoconductive decay technique is to analyse the decay 4 of the induced transient increase in conductivity by measuring the change in voltage across the 5 sample. The sample can be characterized using this technique. 6

[0028] A variation of the transient photoconductive decay technique is spatial mapping. In 7 this variation, light is shone on different locations of the sample, and the resultant transient 8 photoconductive decay curves are measured. By doing so, spatial variations across a sample can 9 be characterized. 10 Material Parameters 11

[0029] In previous works, several parameters of interest have been characterized using the 12 transient photoconductive decay technique. 13

[0030] Two parameters of interest which have been characterized in previous works are 14 the bulk minority carrier lifetime and the surface recombination velocity. 15

[0031] The bulk minority carrier lifetime τb is the average time a minority carrier identified 16 at a particular instant and location within the bulk of a semiconductor will exist until 17 recombination. It is defined by: τ􀭠 = p − p􀭭 R 18 19 where p is the total minority carrier density 20 po is the equilibrium minority carrier density 21 R is the minority carrier recombination rate 22

[0032] The bulk minority carrier lifetime τb is highly dependent upon the nature of the 23 recombination mechanisms within the bulk of the semiconductor. 24

[0033] The surface recombination velocity s is a measure of the recombination rate of 25 minority carriers at the surface of a semiconductor. It is defined for excess holes in an n-type 26 semiconductor with a surface at x = 0 by: s = D􀭟 ∂p ∂x 1 p 􀸬 􀭶􀭀􀬴 27 28 where Da is the ambipolar diffusion coefficient 29 p is the excess hole concentration 30

[0034] For excess electronics in a p-type semiconductor with a surface at x = 0: CA 3085115 Date reçue / Received date 2026-01-08 6 s = D􀭟 ∂n ∂x 1 n 􀸬 􀭶􀭀􀬴 1 2 where Da is the ambipolar diffusion coefficient 3 n is the excess hole concentration 4

[0035] Physically, the surface recombination velocity can be understood as follows: A 5 current of holes or electrons of density p or n drift with an average velocity equal to the surface 6 recombination velocity s into the surface and the holes or electrons are then removed. Thus, as 7 the surface recombination velocity increases, the excess hole or electron concentration at the 8 surface decreases. 9 Recombination Mechanisms 10

[0036] A detailed explanation of examples of various bulk recombination mechanisms in, 11 for example, HgCdTe is given in Sections 2.2.1 to 2.2.3 of R. Rajaduray, “Investigation of Spatial 12 Characterisation Techniques in Semiconductors,” Honours Thesis 1998, University of Western 13 Australia. 14

[0037] For example, with reference to HgCdTe three important bulk recombination 15 mechanisms are Auger, radiative and Shockley-Read-Hall (SRH) recombination. Auger and 16 radiative recombination are strongly dependent upon the carrier concentrations and energy gap. 17 SRH recombination is associated with the presence of defect states within the bandgap, known as 18 traps. 19

[0038] There may be other bulk recombination mechanisms present in other 20 semiconductor materials. 21

[0039] Similarly, an explanation of surface recombination mechanisms in HgCdTe is 22 given in section 2.3 of R. Rajaduray, “Investigation of Spatial Characterisation Techniques in 23 Semiconductors,” Honours Thesis 1998, University of Western Australia. 24

[0040] Three surface recombination mechanisms in HgCdTe are: 25 - Thermal transitions through Shockley-Read-Hall centres in the depletion region: This 26 process is similar to the SRH bulk recombination mechanism. 27 - Thermal transitions via fast surface states. 28 - Tunnel transitions through the Shockley-Read-Hall centres in the depletion region 29

[0041] There may be other surface recombination mechanisms present in other 30 semiconductor materials. CA 3085115 Date reçue / Received date 2026-01-08 7 Previous Analysis 1 Approaches 2

[0042] Many of the existing analysis approaches are based on parametric techniques. FIG 3 1 shows the steps involved in the prior art analysis approaches: 4 101: Creating a model based on one or more assumptions 5 102: Setting up one or more differential equations with boundary conditions based on the 6 assumptions 7 103: Solving the differential equations to obtain a solution with one or more parameters 8 which shows the expected behavior of the decay of the minority carrier population over 9 time, and 10 104: Fitting experimental results to the obtained solution using, for example, least squares 11 fitting to extract the one or more solution parameters. 12

[0043] Two examples of steps 101–103 are explained below. The first example uses the 13 approach detailed in W. Van Roosbroeck, "Injected Current Carrier Transport in a Semi‐Infinite 14 Semiconductor and the Determination of Lifetimes and Surface Recombination Velocities." 15 Journal of Applied Physics 26.4 (1955): 380-391. The solution is given as: 16 p(U) = p(0)exp[U(S􀬶 − 1)]erfc􀵣S√U􀵧 17 (1) 18 where U is time t normalized with respect to τb 19 τb is the bulk minority carrier lifetime 20 p(U) is the minority carrier population at normalized time U or at time t = U × τb 21 p(0) is the minority carrier at normalized time U = 0 or equivalently t = 0 22 S is the normalized surface recombination velocity. S is further given by: S = sτ􀭠 L 23 24 where s is the surface recombination velocity 25 L is the minority carrier diffusion length, given by √(Da × τb) 26

[0044] The second example of steps 101–103 provides a solution for a finite rectangular 27 sample of dimensions 2A, 2B and 2C and uses the approach detailed in J. S. Blakemore, 28 Semiconductor Statistics, Oxford Pergamon 1962. The solution is given as a series of 29 eigenfunctions for different modes (i,j,k) and is given by: CA 3085115 Date reçue / Received date 2026-01-08 8 p(t) = p(0) ABC 􀷍 K􀭧􀭨􀭩 × exp􀵣−t􀵫ν􀭠 + ν􀭧􀭨􀭩􀵯􀵧 􀭧􀭨􀭩 1 2 (2) 3 where p(t) is the minority carrier population at time t 4 p(0) is the minority carrier at time t = 0 5 Kijk is the constant for mode (i, j, k) 6 υijk is the inverse of the time constant for mode (i, j, k) 7 υb is the inverse of the bulk minority carrier lifetime τb 8

[0045] Then, once a solution such as in equations (1) and (2) above have been provided, 9 experimentally obtained decay curves can be fitted to these curves using, for example, least squares 10 regression. The parameters used to obtain the best fit are extracted and recorded. For example, 11 using the Van Roosbroeck model, the surface recombination velocity s and bulk minority carrier 12 lifetime τb to obtain the best fit are extracted. 13

[0046] There are other analysis approaches which are variations of these 2 approaches. 14 Usually, these variations employ slightly different assumptions to create a model. However many 15 of these approaches are flawed for several reasons. 16

[0047] Many of the existing approaches use models which employ unrealistic assumptions 17 and then set up differential equations and boundary conditions based on these unrealistic 18 conditions. 19

[0048] For example, firstly many of the models assume that recombination parameters 20 such as the bulk minority carrier lifetime and the surface recombination velocity are spatially and 21 temporally constant within the analyzed semiconductor sample. This has clearly been shown not 22 to be the case. Studies such as those performed by V. C. Lopes et al “Characterization of 23 (Hg,Cd)Te by the Photoconductive Decay Technique,” J. Vac Sci, vol. 8, no. 2, pp. 1167–1170, 24 Mar / Apr 1990; and R. G. Pratt et al “Minority carrier lifetime in n-type Bridgman grown Hg1- 25 xCdxTe,” J. Appl. Physics vol 54, no. 9 pp. 5152–5157, 1983; showed spatial nonuniformity of 26 bulk lifetime across semiconductor samples. Furthermore, as shown in Chapter 6 of Ramesh 27 Rajaduray, “Investigation of Spatial Characterisation Techniques in Semiconductors,” Honours 28 Thesis 1998, University of Western Australia, the extracted parameters clearly exhibited temporal 29 nonuniformity, that is, when segments of a voltage decay curve with differing temporal extents 30 were fitted to equation (1), the values of the extracted parameters were non-uniform. CA 3085115 Date reçue / Received date 2026-01-08 9

[0049] Secondly, many of the models assume that the dominant recombination 1 mechanism 2 is independent of the minority carrier density. This is also unrealistic, when it has been shown in 3 that in certain situations, minority carrier concentration dependent recombination mechanisms 4 such as Auger recombination will dominate in materials such as HgCdTe. As an example, in pages 5 53 and 54 of Ramesh Rajaduray, “Investigation of Spatial Characterisation Techniques in 6 Semiconductors,” Honours Thesis 1998, University of Western Australia, it was shown that at 7 time t = 0, a population of minority carriers equivalent to 19% of the total number of minority 8 carriers is generated within a small area. It was shown in, for example, G. Nimtz, et al. "Transient 9 carrier decay and transport properties in Hg1-xCdxTe." Phys. Rev. BIO p 3302 (1974); and F. 10 Bartoli et al. "Auger‐limited carrier lifetimes in HgCdTe at high excess carrier concentrations." 11 Journal of Applied Physics vol. 45 no. 5 pp. 2150-2154 (1974); that under such conditions Auger 12 recombination is likely to dominate over radiative and Shockley-Read-Hall mechanisms. 13

[0050] Furthermore, as was pointed out by D. A. Redfern et al "On the transient 14 photoconductive decay technique for lifetime extraction in HgCdTe" in Optoelectronic and 15 Microelectronic Materials Devices, 1998. Proceedings. 1998 Conference on, pp. 275-278. IEEE, 16 1999, “none of the current models unambiguously [explained] experimental results and that 17 detailed lifetime extraction by photoconductive decay is still not a quantitative technique.” 18

[0051] In addition, the generation and recombination of minority carriers which occur 19 within a semiconductor sample each time light is incident on the sample, are random processes. 20 As a consequence, carrier concentrations at particular points within a semiconductor sample are 21 also likely to vary randomly as well. This means that diffusion based movements, which are highly 22 dependent on concentration gradients, are also likely to be random in nature. As a consequence, 23 this further intensifies the random behavior of the carrier concentration at a particular point within 24 a semiconductor sample. If carrier concentration dependent recombination mechanisms dominate, 25 then the random behavior is even further intensified. However many of the differential equations 26 set up in steps 101-104 of FIG. 1 above are assumed to be deterministic in nature. 27

[0052] As a consequence of the above, many of the previously proposed models employ 28 unrealistic assumptions which lead to an incorrect understanding of the evolution of the population 29 of generated minority carriers over time within a semiconductor sample. 30

[0053] As a further consequence, analysis approaches which use such models to perform 31 spatial mapping of recombination parameters, such as, for example, spatial bulk minority carrier CA 3085115 Date reçue / Received date 2026-01-08 10 lifetime mapping are inherently flawed. Not only is the understanding of the 1 evolution of the 2 population over time wrong, but the incorrect behavior is then used to detect parameter variations 3 which is fundamentally opposite to the assumptions employed. 4

[0054] Therefore, there is a need for analysis approaches which are less reliant on using 5 models with inherently unrealistic assumptions to perform parametric-based analysis, or worse 6 still: Using models built on certain assumptions with the aim of detecting properties which are in 7 direct opposition to these assumptions. 8 New Analysis Approaches 9

[0055] This section demonstrates several analysis approaches which overcome the 10 problems due to the parametric analysis approaches used previously. 11

[0056] An example analysis setup is shown in FIG. 2. Transient photoconductive decay 12 measurement subsystem 201 is used to obtain voltage decay curves for a semiconductor sample. 13 Example embodiments of transient photoconductive decay measurement subsystem 201 are 14 known to those of ordinary skill in the art. In one embodiment, as shown in FIG. 3, an obtained 15 voltage decay curve 300 denoted as Vme(t) comprises a plurality of measurements comprising 16 measurements 305, 306 and 307 of the voltage across the sample at corresponding times 301, 303, 17 and 304. The time instant corresponding to each measurement within the plurality is separated 18 from the time instant corresponding to the preceding measurement by a time interval Δt (302), 19 such as shown in FIG 3. 20

[0057] Statistical analysis subsystem 204 performs statistical analyses which will be 21 described later. In one embodiment, the statistical analysis subsystem 204 is implemented in 22 hardware. In one embodiment, the statistical analysis subsystem 204 is implemented in software. 23 In yet another embodiment, statistical analysis subsystem 204 is implemented in a combination of 24 hardware and software. Different programming languages and systems can be used to implement 25 statistical analysis subsystem 204, including, for example, SPSS, S, R, STATA, MATLABTM, 26 SAS®, MICROSOFTTM, EXCELTM, SQL and C++. 27

[0058] Data analysis subsystem 203 performs various functions, including preparing data 28 for statistical analysis subsystem 204, collating the results of analysis performed by statistical 29 analysis subsystem 204, performing further analysis of the results from statistical analysis 30 subsystem 204 and presenting the results of these analyses. In one embodiment, the data analysis 31 subsystem 203 is implemented in hardware. In one embodiment, the data analysis subsystem 203 CA 3085115 Date reçue / Received date 2026-01-08 11 is implemented in software. In yet another embodiment, data analysis 1 subsystem 203 is 2 implemented in a combination of hardware and software. Different programming languages and 3 systems can be used to implement data analysis subsystem 203, including, for example, SPSS, S, 4 R, STATA, MATLABTM, SASTM, MICROSOFTTM, EXCELTM, SQL and C++. 5

[0059] Database 205 is used to store voltage decay curve data obtained from transient 6 photoconductive decay subsystem 201, and data for intermediate processing performed by 7 statistical analysis subsystem 204 and data analysis subsystem 203. Different programming 8 languages and systems can be used to implement database 205, including, for example, SQL and 9 MICROSOFTTM ACCESSTM. 10

[0060] Interconnection 202 is used to connect the different subsystems together. These 11 could include, for example, local area networks (LAN), campus area network (CAN), wide area 12 networks (WAN). Interconnection 202 could encompass one or more subnetworks. 13 Interconnection 202 could be implemented using various media including wireless, wired, optical 14 network, and could encompass various technologies including Ethernet and IP-based networks. 15

[0061] In one embodiment, the system illustrated in FIG. 2 is used to compare one or more 16 semiconductor samples. Then, for each of the one or more semiconductor samples, one or more 17 voltage decay curves such as voltage decay curve 300 in FIG. 3, is measured using, for example, 18 transient photoconductive decay measurement subsystem 201. 19

[0062] In another embodiment, the system illustrated in FIG. 2 is used to map spatial non20 uniformities across a single semiconductor sample. In this embodiment, using transient 21 photoconductive decay measurement subsystem 201, light is shone at different points across a 22 semiconductor sample, and for each point a voltage decay curve is obtained. For example, in one 23 embodiment, light is shone at each point, for example points 401, 402 and 403 within a grid of 24 points 404 such as shown in FIG. 4 for sample 400 is created. Voltage decay curves such as 25 voltage decay curve 300 of FIG. 3 as shown above are then obtained for each point. 26

[0063] As explained previously, the generation, movement and recombination of minority 27 carriers which occurs within a semiconductor sample each time light is incident on a spot on the 28 semiconductor sample using the transient photoconductive decay measurement subsystem 201 are 29 random sub-processes which are part of a single overall random or stochastic process. 30 Consequently, each obtained voltage decay curve represents the evolution of the population of 31 minority carriers with time for one realization of this overall random process. CA 3085115 Date reçue / Received date 2026-01-08 12

[0064] In one embodiment, in order to remove the impact of noise, light 1 is shone on the 2 same spot on the semiconductor sample a plurality of times. Then, each time light is shone on the 3 spot, a corresponding voltage decay curve is obtained. 4

[0065] In one embodiment, the following analysis is applied to each obtained voltage 5 decay curve as shown in FIG. 5A. 6

[0066] In step 501, using for example, data analysis subsystem 203, the segment of the 7 measured voltage decay curve with times greater than the time corresponding to the peak of the 8 voltage decay curve is extracted to form an intermediate voltage decay curve V(t). An example is 9 shown in FIG. 5B. The time 5A-01 corresponds to the peak (5A-02) of the obtained voltage decay 10 curve 5A-00. Then, the segment 5A-03 of the voltage decay curve 5A-00 for all times greater than 11 time 5A-01 is extracted, to form intermediate voltage decay curve 5A-04. Each time instant on 12 intermediate voltage decay curve 5A-04 is separated from the next time measurement by Δt (5A- 13 08), such as, for example, time instants 5A-05, 5A-06 and 5A-07. The intermediate voltage decay 14 curve 5A-04 can be represented as V(nΔt), n = 0, 1, 2 … N where nΔt are the time instants. 15

[0067] In the embodiment where light is shone on the same spot a plurality of times and a 16 corresponding measured voltage decay curve is obtained for each time, a plurality of 17 corresponding intermediate voltage decay curves Vk(nΔt) are obtained, k = 1, 2, 3 … K. The 18 corresponding intermediate voltage decay curves are then averaged out to provide a smoothed 19 intermediate voltage decay curve Vs(nΔt), that is: V􀭱(nΔt) = Σ V􀭩(nΔt) 􀭏􀭩 􀭀􀬵 K 20 21 This is performed for n = 0, 1, 2 … N. 22

[0068] In optional step 502, using for example, data analysis subsystem 203, the 23 intermediate voltage decay curve V(nΔt) or smoothed intermediate voltage decay curve Vs(nΔt) 24 obtained in step 501 is converted to a minority carrier population decay curve p(t). Various 25 approaches to perform this conversion are known to those of skill in the art and will not be 26 explained further within this specification. 27

[0069] In step 503, in one embodiment, using for example, data analysis subsystem 203 28 the intermediate voltage decay curve V(nΔt) or smoothed intermediate voltage decay curve 29 Vs(nΔt) obtained in step 501 is normalized to the voltage at time t = 0 to obtain a normalized decay 30 curve Vno(nΔt). In an alternate embodiment, if optional step 502 is performed, the p(t) obtained CA 3085115 Date reçue / Received date 2026-01-08 13 in step 502 is normalized to the minority carrier population at time t = 0 to obtain 1 a normalized 2 decay curve pno(t). 3

[0070] The normalized decay curve represents a discrete estimate Se(nΔt), n = 0, 1, 2…N 4 of the continuous time survival function S(t) = P[τ > t]. S(t) is the probability that minority carriers 5 will survive, that is not recombine, until beyond time t. If, in step 501, a smoothed intermediate 6 voltage decay curve is provided as an output, then the obtained normalized smoothed decay curve 7 is a better discrete estimate Se(t) of S(t). 8

[0071] In step 504, Se(t) is analysed using, for example, statistical analysis subsystem 204. 9 One embodiment of step 504 is shown in FIG. 6. The cumulative distribution function CDF(t) = 10 P[τ ≤ t] is obtained by P[τ ≤ t] = 1 – S(t). In an optional embodiment, in step 601, a discrete estimate 11 CDFe(nΔt) of the cumulative distribution function CDF(t) is obtained by computing 1 – Se(nΔt), n 12 = 0, 1, 2… 13

[0072] In step 602, in one embodiment, an estimate of the probability of recombination 14 between time [nΔt] and [(n+1)Δt], n = 0, 1, 2… is obtained. The probability is given by the 15 probability mass function PMFe[(n+1)Δt], which is obtained by taking successive differences of 16 the estimate of the survival function Se(t). That is, the estimate PMFe[(n+1)Δt], n = 0, 1, 2… is 17 given by Se[nΔt] - Se[(n+1)Δt]. Alternatively, if in step 603, CDFe(nΔt) is calculated, then 18 PMFe[(n+1)Δt] is given by CDFe[(n+1)Δt] – CDFe[nΔt]. 19

[0073] In step 603, one or more summary statistics are computed. In one embodiment, an 20 estimate of the mean of τ denoted as E[τ] or μτ is calculated. In one embodiment, Se(t) is used 21 directly to calculate E[τ] performing the summation of Se(t) from n = 1 onwards. In another 22 embodiment PMFe[(n+1)Δt] is used.

[0074] In another embodiment, the variance of τ denoted as Var(τ) or alternatively στ 23 2 is 24 computed. 25

[0075] Other summary statistical computations can be performed including moment 26 generation, Laplace transform and characteristic function generation. Moments can also be 27 calculated. Other expectations can also be calculated using the generalized formulae such as, for 28 example E(1 / τ3) and E(1 / τ2). 29

[0076] In another embodiment, in step 604, one or more survival statistical computations 30 are applied. In one embodiment, the discrete time hazard probability λe[(n+1)Δt], which is the 31 probability of recombination for a minority carrier between times [nΔt] and [(n+1)Δt] given that CA 3085115 Date reçue / Received date 2026-01-08 14 the minority carrier has not recombined before time [nΔt] is calculated. Mathematically 1 this is 2 given by: λ􀭣[(n + 1)Δt] = PMF􀭣[(n + 1)Δt] S􀭣(nΔt) 3 4

[0077] Alternatively it can be calculated as: λ􀭣[(n + 1)Δt] = 1 − S􀭣[(n + 1)Δt] S􀭣(nΔt) 5 6

[0078] Quantiles of Se(nΔt) can be calculated as well. For example, the lowest decile of 7 Se(nΔt), that is, the time after which 90% of the minority carrier population at t = 0 have not 8 recombined can be calculated by determining when Se(nΔt) drops below 0.90. Similarly the 9 highest quartile of Se(nΔt), that is, the time after which 25% of the minority carrier population at t 10 = 0 have not recombined can be calculated by determining when Se(nΔt) drops below 0.25. 11

[0079] Another survival statistical computation which can be performed is calculating the 12 mean residual time E(τ – nΔt|τ ≥ nΔt). This gives the expected time until recombination for a 13 minority carrier, given that the minority carrier survived up to time nΔt. This can be calculated 14 using well known mathematical formulas and will not be discussed in detail within this 15 specification. 16

[0080] It may be necessary to compare minority carrier decay behavior for two or more 17 samples, or at two or more locations within the same sample, to determine if there is nonuniformity 18 between samples or whether there is spatial nonuniformity within the same sample. Then, known 19 mathematical techniques to compare survival behaviour for different populations of generated 20 minority carriers can be employed. This involves using a process similar to that outlined in FIG. 21 5A, except that step 503 is not performed. An embodiment is shown in FIG. 7. Steps 701 and 702 22 are identical to steps 501 and 502, except that step 502 is not optional. These two steps are 23 performed for every sample, or for every point or location within the same sample. These steps 24 are implemented using for example, data analysis subsystem 203 as previously detailed. 25

[0081] In step 704, the minority carrier population decay curves obtained in step 702 are 26 analyzed to perform comparisons between samples. In one embodiment, in step 704, methods of 27 semiparametric testing are used to detect spatial nonuniformities in the semiconductor sample or 28 differences between semiconductor samples. In one embodiment, as described in, for example, p. 29 251–266 of N. Balakrishnan, and C. R. Rao “Handbook of statistics: advances in survival analysis. 30 Vol. 23” Access Online via Elsevier, 2004. the Cox proportional hazard analysis model is used. CA 3085115 Date reçue / Received date 2026-01-08 15 This assumes that the discrete time hazard probabilities λe[(n+1)Δt] for 1 the samples are 2 proportional to each other. In a further embodiment, results can be tested for validity of the 3 proportional hazard assumption. Examples of tests for validity are described in D. Schoenfeld, 4 "Partial residuals for the proportional hazards regression model." Biometrika vol. 69 no .1 pp. 5 239-241 (1982); and T. M. Thernau et al “Modeling Survival Data: Extending the Cox Model” 6 New York: Springer-Verlag 2000. 7

[0082] In another embodiment, in step 704, various nonparametric comparison techniques 8 can be used to analyse the p(t) obtained in step 702. In one embodiment, the Mantel-Cox or 9 logrank test is used, as described in Section 7.3 and 7.7 of Klein et al “Survival Analysis: 10 Techniques for Censored and Truncated Data” Springer, 1997. In another embodiment, the 11 Gehan-Breslow test is used as described in the references E. A. Gehan, "A generalized Wilcoxon 12 test for comparing arbitrarily singly-censored samples." Biometrika vol 52, no. 1-2 pp. 203-223 13 (1965); and N. Breslow "A generalized Kruskal-Wallis test for comparing K samples subject to 14 unequal patterns of censorship." Biometrika vol. 57 no.3 pp. 579-594 (1970). In another 15 embodiment, the Tarone-Ware test is used as described in the reference R. E. Tarone et al "On 16 distribution-free tests for equality of survival distributions." Biometrika vol 64 no. 1 pp. 156-160 17 (1977). In yet another embodiment, the tests proposed in T. R. Fleming et al “Counting processes 18 and survival analysis” Wiley.com, 1991 are used. In another embodiment, one or more such 19 comparisons are performed, depending on, for example, whether the survival curves to be 20 compared cross with each other or the requirements of the analysis. In one embodiment, these 21 tests are performed by statistical analysis subsystem 204. In another embodiment, these tests are 22 performed by a combination of statistical analysis subsystem 204 and data analysis subsystem 203. 23

[0083] In yet another embodiment, in step 704, a combination of the previously described 24 Cox proportional hazards analysis approach and the nonparametric approaches described above 25 are used. Firstly, a visual check is performed to see if the discrete time hazard probabilities for the 26 samples cross. If not, then the validity of the assumption of proportional hazards is tested. If the 27 assumption of proportional hazards is valid, then the logrank test is used. If the discrete time 28 hazard probabilities cross, a different test is used, such as the test outlined in A. Renyi “On the 29 Theory of Order Statistics” Acta Mathematica Hungarica vol. 4 pp. 191–231, 1953. 30

[0084] In a further embodiment, in step 704, one or more combinations of analyses are 31 performed. For example, once the non-parametric tests have been performed and differences CA 3085115 Date reçue / Received date 2026-01-08 16 between the populations have been observed, then the summary statistics for each 1 sample or each 2 point can be calculated and compared. An example flowchart is shown in FIG. 8. Steps 801-803 3 are similar to steps 601–603 respectively, and performed for each sample or each point within a 4 sample using, for example, statistical analysis subsystem 204 as previously detailed. 5

[0085] The advantage of the new analysis approaches over the previous parametric 6 analysis approaches is that there are no assumptions of the form of the minority carrier population 7 decay curve p(t). This therefore overcomes the problems due to relying on the use of models with 8 unrealistic assumptions. By using minority carrier population decay curves p(t) or converting to a 9 normalized decay curve and applying the understanding that this can be converted to a discrete 10 time estimate of the CDF, methods of probabilistic analysis can be applied as described above 11 without having to perform fitting to models which are inherently unrealistic. 12

[0086] In an additional embodiment, one or more “windows” of interest are determined. 13 Each of these windows comprises a lower bound and an upper bound, and the decay curve between 14 these bounds is extracted. Then one or more statistical computations are performed using these 15 one or more windows. For example, in one embodiment the mean of the values within the window 16 given by E[τ|n1Δt ≤ τ ≤ n2Δt]; n1 = 0, 1, 2… is computed using known formulas. Similarly, other 17 computations such as calculation of variance, Laplace transform, characteristic function, moments 18 can also be performed. In another embodiment, the survival statistical computations and the 19 comparison of survival behavior techniques outlined above and in FIG. 7 are performed using 20 these one or more windows. 21

[0087] Various methods can be used to determine the window size. In one embodiment, 22 in order to analyse the decay of the minority carrier population within a localized region of interest 23 surrounding the point where minority carriers are generated by the incidence of light, a window 24 with lower bound t = 0 and upper bound t = twin is set. The upper bound can be set in a variety of 25 ways. 26

[0088] In one embodiment, twin is estimated by calculating the proportion of recombination 27 events taking place within the localized region of interest compared to the number of 28 recombination events taking place within the entire semiconductor sample, using one of the 29 previously derived models such as in equations (1) and (2). An example is presented in FIG. 9. 30 - Step 901: Determining the region of interest R CA 3085115 Date reçue / Received date 2026-01-08 17 - Step 902: Using the model, determining the partial time derivative of the 1 minority carrier concentration 􀮪 􀮪􀭲 2 [p(x, y, z, t)] - Step 903: Spatially integrating 􀮪 􀮪􀭲 3 [p(x, y, z, t)] within the region of interest R using, for example, a triple integral ∭ 􀮪 􀮪􀭲 [p(x, y, z, t)] 􀭖 4 - Step 904: Determining the proportion κ that the ∭ 􀮪 􀮪􀭲 [p(x, y, z, t)] 􀯋 5 comprises of the overall 􀭢 􀭢􀭲 6 [p(t)], that is κ = ∭ ∂ ∂t [p(x, y, z, t)] 􀭖 d dt [p(t)] 7 8 - Step 905: Determining a threshold proportion κT 9 - Step 906: Denoting the time when κ drops below κT as twin. 10

[0089] In another embodiment, twin is estimated by using one of the previously derived 11 models to estimate the proportion of minority carriers within the localized area as compared to the 12 entire semiconductor sample. An example is presented in FIG. 10: 13 - Step 1001: Determining the region of interest R 14 - Step 1002: Spatially integrating p(x,y,z,t) within region of interest R using the triple integral ∭ p(x, y, z, t) 􀭖 15 - Step 1003: Determining the proportion κ that the ∭ p(x, y, z, t) 􀯋 16 comprises of the overall 17 p(t), that is κ = ∭ p(x, y, z, t) 􀭖 p(t) 18 19 - Step 1004: Determining a threshold κT for the proportion 20 - Step 1005: Denoting the time when κ drops below κT as twin. 21

[0090] An example of the approach in FIG. 10 is provided in Chapter 7 of Ramesh 22 Rajaduray, “Investigation of Spatial Characterisation Techniques in Semiconductors,” Honours 23 Thesis 1998, University of Western Australia, for the model described in W. Van Roosbroeck, 24 "Injected Current Carrier Transport in a Semi‐Infinite Semiconductor and the Determination of 25 Lifetimes and Surface Recombination Velocities." Journal of Applied Physics 26.4 (1955): 380- 26 391 as explained earlier. CA 3085115 Date reçue / Received date 2026-01-08 18

[0091] In another embodiment, twin is determined using, for 1 example, numerical 2 simulations such as Monte Carlo simulations. 3

[0092] In another embodiment, twin is determined using, for example, historical results 4 from previous experiments or other types of characterization techniques. 5

[0093] In an embodiment, the setting of twin is performed using data analysis subsystem 6 203. In another embodiment, the setting of twin is performed using a combination of data analysis 7 subsystem 203 and statistical analysis subsystem 204. 8

[0094] In another embodiment, once twin is known, then referring to FIG. 3 the number of 9 measurements (M) needed to perform a valid analysis is determined. Referring to FIG. 3, for example if a minimum of Mmin samples are needed, then Δt (302) is set such that Δt ≤ 􀭲􀱭􀱟􀱤 􀭑􀱣􀱟􀱤 10 11

[0095] In a further embodiment, clustering is performed. For example, in the case where 12 tests are performed to spatially characterize a semiconductor sample, different data points are 13 grouped into spatial clusters based on different clustering metrics. In some embodiments, these 14 clustering metrics are based on similarity measures. The similarity measures are based on, for 15 example distance, connectivity and intensity. 16

[0096] In one embodiment, the clustering metric is the probability that two samples are 17 drawn from the same population, based on their survival curves. For example, referring to FIG. 18 4, if the probability that the survival curves belonging to points 401 and 402 are drawn from the 19 same population is above a threshold, then it is likely that points 401 and 402 have very similar 20 parameters, that is, there is no spatial variation between these points. Then 401 and 402 belong to 21 the same cluster. However if the probability that the survival curves belonging to points 401 and 22 403 are drawn from the same population is below a threshold, then it is likely that there is spatial 23 variation between points 401 and 403. Then points 401 and 403 do not belong in the same cluster. 24

[0097] Continuing the above example, assume that 402 and 403 also belong in the same 25 cluster. Then two clusters for the points A, B and C can be created: 26 - Cluster 1: (401, 402) 27 - Cluster 2: (402, 403) 28

[0098] This is an example of fuzzy clustering, whereby overlapping clusters are used, that 29 is, where a point belongs to a plurality of clusters. In the example above, point 402 belongs to 30 clusters 1 and 2. In some embodiments, hard clusters are used whereby clusters are non- CA 3085115 Date reçue / Received date 2026-01-08 19 overlapping, that is, where a point belongs to only one cluster. Then a given point 1 will be assigned 2 to the cluster which is the closest match. 3

[0099] In one embodiment, the clustering is performed using pairwise comparison, as 4 demonstrated above. In another embodiment, the clustering is performed on the basis of summary 5 statistics. In another embodiment, clusters are pre-defined using the results of other tests. 6

[00100] In a further embodiment, the clustering demonstrated above is extended to a 7 plurality of semiconductor samples. 8

[00101] Different examples of clustering techniques which may be used include, for 9 example, density-based clustering, centroid-based clustering, distribution-based clustering, 10 hierarchical-based clustering, partitioning-based clustering and grid-based clustering. 11

[00102] In a further embodiment, artificial intelligence (AI) or machine learning (ML) 12 techniques are used as part of the analyses to determine if there is nonuniformity between samples 13 or whether there is spatial nonuniformity within the same sample. 14

[00103] It is known that spatial non-uniformities and defects in semiconductor samples can 15 degrade the operability of devices and components fabricated using these semiconductor samples. 16 Examples of devices and components include transistors, integrated circuits (ICs) and infra-red 17 (IR) focal plane arrays (FPAs). 18

[00104] Defects can degrade the performance of devices and components fabricated using 19 these semiconductor samples. Defects can also lead to variation in performance across one or more 20 devices and components fabricated using the semiconductor sample. Spatial non-uniformities in a 21 semiconductor sample can lead to variation in performance across one or more devices and 22 components fabricated using the semiconductor sample. For example, non-uniformities in a 23 semiconductor sample used to fabricate an IR FPA, can lead to variation in performance across 24 the IR FPA. 25

[00105] Then, in a further embodiment, the results of the processes outlined above are used 26 to select semiconductor samples for use in fabrication of devices and components, by only 27 accepting those samples which do not have spatial non-uniformities and defects. In a further 28 embodiment all of these processes are combined into an integrated testing procedure for selecting 29 semiconductor samples from a plurality of samples. Two examples of integrated testing procedures 30 which use the results of the processes above for selecting semiconductor samples are presented 31 below: CA 3085115 Date reçue / Received date 2026-01-08 20 Example Integrated 1 Procedure 1 2

[00106] An example of an integrated testing procedure is demonstrated in FIG. 11. In step 3 1101, a grid of points such as grid 404 as shown in FIG. 4 is determined by data analysis subsystem 4 203, or statistical analysis subsystem 204, or both subsystems. The determination is based on, for 5 example, the size of the semiconductor sample, shape of the semiconductor sample and required 6 density of points on the semiconductor sample. 7

[00107] In step 1102, light is then shone at each of the points such as points 401, 402 and 8 403 in grid 404 using, for example, transient photoconductive decay measurement subsystem 201. 9 In step 1103, voltage decay curves such as voltage decay curve 300 of FIG. 3 are then obtained for 10 each point using, for example, transient photoconductive decay measurement subsystem 201. 11

[00108] Then in step 1104, the processes explained above and in FIGS. 5A and 6 are applied 12 for each of the obtained voltage decay curves from step 1103 using, for example, statistical analysis 13 subsystem 204 to obtain at least one of 14 - the one or more summary statistics, and 15 - the survival statistics. 16

[00109] In step 1105, in one embodiment, at least one of 17 - the one or more summary statistics, and 18 - the survival statistics 19 obtained in step 1104 are compared to one or more thresholds using, for example, statistical 20 analysis subsystem 204. If the summary statistics or the survival statistics fail to meet the one or 21 more thresholds, the semiconductor sample is rejected from use in fabrication in step 1114 by, for 22 example, statistical analysis subsystem 204. 23

[00110] In step 1106, if the summary statistics or the survival statistics for the grid of points 24 meet or exceed the one or more thresholds, further testing is performed using, for example, 25 statistical analysis subsystem 204 to determine the presence of non-uniformities within the sample. 26

[00111] In one embodiment, if after performing the steps of FIG. 7, similar results are 27 observed for all of the points within the grid of points 404 for sample 400, then there are no spatial 28 non-uniformities (step 1107) and the sample is accepted by, for example, statistical analysis 29 subsystem 204, for further use in device fabrication in step 1108. In another embodiment, if a 30 clustering operation is performed in step 1106 and it is shown that all of the points in the grid of CA 3085115 Date reçue / Received date 2026-01-08 21 points 404 belong to the same cluster; then it is likely that there are no spatial 1 non-uniformities 2 (step 1107) and the sample is accepted for further use in device fabrication in step 1108. 3

[00112] If the presence of non-uniformities is observed in step 1107, it may be possible to 4 modify the semiconductor sample so that the modified sample is free of non-uniformities and can 5 be selected for further use in device fabrication. Examples of modifications include, for example: 6 - removal of one or more portions of the semiconductor sample, and 7 - extra processing steps applied to one or more portions of the semiconductor sample 8

[00113] Then, in step 1109 the feasibility of modification of the sample is determined. In 9 some embodiments, step 1109 comprises performing a spatial mapping of the non-uniformities 10 using, for example, statistical analysis subsystem 204. Then the results of the spatial mapping are 11 used to decide whether it is feasible to modify the sample. 12

[00114] If it is feasible, the sample is modified in step 1110. In step 1111, the modified 13 sample is retested to determine if there are non-uniformities in the modified sample by repeating 14 step 1107 for the modified sample. If there are no non-uniformities the process moves to step 1108, 15 that is, the modified sample is accepted for further use in fabrication. If there are non-uniformities, 16 then in step 1114 the modified sample is rejected from use in the fabrication. 17 Example Integrated Procedure 2 18

[00115] An example flowchart for another integrated testing procedure is shown in FIGS. 19 12A and 12B. In step 1201 of FIG. 12A, for each semiconductor sample, a grid of points such as 20 grid 404 is determined, as explained previously for step 1101 of FIG. 11. In step 1202, light is 21 shone on each point within the grid of points. In step 1203, voltage decay curves such as voltage 22 decay curve 300 of FIG. 3 are then obtained for each point. 23

[00116] Then, in step 1204, the method to perform comparisons of survival behavior 24 outlined above and in FIG. 7 is carried out to determine if there are non-uniformities within the 25 sample or when compared to other samples. 26

[00117] If in step 1205 it is determined there are non-uniformities, in some embodiments, a 27 decision is made such that no further analysis or actions are carried out in step 1206 and the sample 28 is rejected from use in fabrication in step 1207. In other embodiments, in step 1206, a decision is 29 made to perform further analysis or actions are performed. In step 1208 spatial mapping of the 30 detected non-uniformities is performed. CA 3085115 Date reçue / Received date 2026-01-08 22

[00118] Then based on the spatial mapping in step 1208, further actions 1 are taken in step 2 1209. The further actions in 1209 comprise one or more of: 3 - deciding whether to modify the sample; and 4 - determining if there are defects, and quantifying these defects. 5

[00119] FIG. 12B demonstrates an illustrative embodiment of a process to carry out the 6 steps outlined in step 1209. In particular FIG. 12B demonstrates an embodiment to modify the 7 sample and to optionally decide whether to accept or reject the modified sample. Examples of 8 modifications have been described previously. In one embodiment, similar to as described before, 9 the results of the spatial mapping from step 1208 are used in step 12B-01 to decide whether it is 10 feasible to modify the sample. If it is deemed infeasible, then in step 12B-02 the sample is rejected. 11 If it is deemed feasible, in step 12B-03, the sample is modified. 12

[00120] In step 12B-04, the modified sample is retested by repeating step 1204. If the 13 modified sample is determined to be uniform in step 12B-05 and at least one of 14 - one or more computed summary statistics, and 15 - computed survival statistics 16 for all of the grid of points meet thresholds in step 12B-06, the sample is accepted in step 12B-09. 17 If the modified sample is determined to be non-uniform in step 12B-05, then it is rejected in step 18 12B-02. If the summary statistics or survival statistics for at least one of the grid of points does not 19 meet requirements in step 12B-06, then further testing is performed in step 12B-07 and a decision 20 is made in step 12B-08 as to whether the sample should be accepted. Based on the decision made 21 in step 12B-08, the sample is rejected in step 12B-02 or accepted in step 12B-09. 22

[00121] Returning to FIG. 12A, if there are no non-uniformities, in step 1210 further testing 23 is carried out using the method outlined in FIG. 8 and at least one of 24 - one or more computed summary statistics, and 25 - computed survival statistics 26 for one or more points within grid 404 are compared to one or more thresholds. If all of the one or 27 more summary statistics or the survival statistics meet or exceed the one or more thresholds, the 28 sample is accepted in step 1213 for further fabrication. 29

[00122] In a further embodiment, in step 1210, if at least one of the one or more summary 30 statistics or the survival statistics fall below the one or more thresholds, further testing is performed 31 in step 1211. In step 1212, further analysis is performed to decide whether to accept or reject the CA 3085115 Date reçue / Received date 2026-01-08 23 sample. If a decision is made to accept the sample, the process moves to step 1 1213, where the 2 sample is accepted for fabrication. If a decision is made to reject the sample, the process moves to 3 step 1207, where the sample is rejected from use in fabrication. 4

[00123] Variations to the above described embodiments are also possible. For example, in 5 further embodiments, once the presence of non-uniformities has been detected in step 1205, further 6 analysis is used to determine whether there are defects within the semiconductor sample before 7 rejecting the sample. If, as a result of the further analysis, it is observed that one or more of the 8 points have worse observed results than other points, then this is a potential indication of the 9 presence of defects at these points. In one embodiment, further testing is performed to determine 10 if there are defects. In one embodiment, the further testing comprises comparing at least one of 11 - one or more computed summary statistics, and 12 - computed survival statistics 13 obtained using the measured voltage decay curves corresponding to these points, to one or more 14 thresholds. If the summary statistics or the survival statistics fail to meet the one or more 15 thresholds, this indicates the presence of defects, and the sample is rejected from use in fabrication. 16

[00124] While two different integrated testing procedures have been described above, it 17 would be known to one of skill in the art that it is possible to combine steps from integrated 18 procedures 1 and 2 as described above. For example, after the sample is modified in step 1110 of 19 FIG. 11, the integrated testing procedure of FIG. 12 and 12B can be applied to the modified sample 20 to determine whether the modified sample is uniform and defect free before deciding whether to 21 accept or reject for further use in device fabrication. 22

[00125] The methods explained above are not just limited to the transient photoconductive 23 decay technique. The methods can be extended to other fields where a population is introduced 24 and outputs related to the decay curves of the introduced population are readily available for 25 measurement, so as to enable conversion into survival functions. 26

[00126] Although the algorithms described above including those with reference to the 27 foregoing flow charts have been described separately, it should be understood that any two or more 28 of the algorithms disclosed herein can be combined in any combination. Any of the methods, 29 algorithms, implementations, or procedures described herein can include machine-readable 30 instructions for execution by: (a) a processor, (b) a controller, and / or (c) any other suitable 31 processing device. Any algorithm, software, or method disclosed herein can be embodied in CA 3085115 Date reçue / Received date 2026-01-08 24 software stored on a non-transitory tangible medium such as, for example, a 1 flash memory, a CD2 ROM, a floppy disk, a hard drive, a digital versatile disk (DVD), or other memory devices, but 3 persons of ordinary skill in the art will readily appreciate that the entire algorithm and / or parts 4 thereof could alternatively be executed by a device other than a controller and / or embodied in 5 firmware or dedicated hardware in a well known manner (e.g., it may be implemented by an 6 application specific integrated circuit (ASIC), a programmable logic device (PLD), a field 7 programmable logic device (FPLD), discrete logic, etc.). Also, some or all of the machine8 readable instructions represented in any flowchart depicted herein can be implemented manually 9 as opposed to automatically by a controller, processor, or similar computing device or 10 machine. Further, although specific algorithms are described with reference to flowcharts depicted 11 herein, persons of ordinary skill in the art will readily appreciate that many other methods of 12 implementing the example machine readable instructions may alternatively be used. For example, 13 the order of execution of the blocks may be changed, and / or some of the blocks described may be 14 changed, eliminated, or combined. 15

[00127] It should be noted that the algorithms illustrated and discussed herein as having 16 various modules which perform particular functions and interact with one another. It should be 17 understood that these modules are merely segregated based on their function for the sake of 18 description and represent computer hardware and / or executable software code which is stored on 19 a computer-readable medium for execution on appropriate computing hardware. The various 20 functions of the different modules and units can be combined or segregated as hardware and / or 21 software stored on a non-transitory computer-readable medium as above as modules in any 22 manner, and can be used separately or in combination. 23

[00128] While particular implementations and applications of the present disclosure have 24 been illustrated and described, it is to be understood that the present disclosure is not limited to the 25 precise construction and compositions disclosed herein and that various modifications, changes, 26 and variations can be apparent from the foregoing descriptions without departing from the spirit 27 and scope of an invention as defined in the appended claims. CA 3085115 Date reçue / Received date 2026-01-08

Claims

1 CLAIMS 2 3 1. A system for characterizing a semiconductor sample comprising: 4 a measurement subsystem, a data analysis subsystem, and a statistical analysis subsystem 5 coupled to each other via an interconnection, wherein 6 the measurement subsystem excites the semiconductor sample at each point within a 7 grid of points, 8 the measurement subsystem measures a voltage decay curve corresponding to each 9 point within the grid of points based on one or more changes in conductivity, 10 the measurement subsystem transmits each measured voltage decay curve via the 11 interconnection to the data analysis subsystem, 12 the data analysis subsystem extracts a normalized decay curve corresponding to each 13 measured voltage decay curve, 14 the data analysis subsystem transmits the extracted normalized decay curve via the 15 interconnection to the statistical analysis subsystem; 16 the statistical analysis subsystem analyzes the transmitted normalized decay curve to 17 obtain at least one of: 18 a summary statistic, and 19 a survival statistic, and 20 the statistical analysis subsystem compares the at least one of the summary statistic 21 and the survival statistic to one or more thresholds, 22 based on the comparison, the statistical analysis subsystem either: 23 rejects the semiconductor sample, or 24 tests the semiconductor sample. 25 26 2. The system of claim 1, wherein the testing comprises determining presence of non27 uniformities within the sample. 28 29 3. The system of claim 1, wherein the measurement subsystem excites the semiconductor 30 sample at each point by shining light at each point. 31 32 4. The system of claim 2, further wherein when non-uniformities are determined to be present, 33 a spatial mapping of the non-uniformities is performed. CA 3085115 Date reçue / Received date 2024-06-28 1 2 5. The system of clam 4, wherein a result of the spatial mapping is used to determine a 3 feasibility of modification of the semiconductor sample. 4 5 6. The system of claim 5, wherein after a modification is performed, the semiconductor sample 6 is re-tested to determine presence of non-uniformities. 7 8 7. The system of claim 6, wherein the semiconductor sample is either accepted or rejected for 9 use in fabrication based on the re-testing. 10 11 8. A method for characterizing a semiconductor sample comprising: 12 exciting, by a measurement subsystem, the semiconductor sample at each point within a grid 13 of points; 14 measuring, by the measurement subsystem, a voltage decay curve corresponding to each 15 point within the grid of points based on one or more changes in conductivity; 16 extracting, by a data analysis subsystem, a normalized decay curve corresponding to each 17 measured voltage decay curve, 18 analyzing, by a statistical analysis subsystem, the normalized decay curve to obtain at least 19 one of: 20 a summary statistic, and 21 a survival statistic, and 22 comparing, by the statistical analysis subsystem, the at least one of the summary statistic and 23 the survival statistic to one or more thresholds, and 24 based on the comparing, either: 25 rejecting, by the statistical analysis subsystem, the semiconductor sample, or 26 testing, by the statistical analysis subsystem, the semiconductor sample. 27 28 9. The method of claim 8, wherein: 29 the testing comprises determining presence of non-uniformities within the sample, further 30 wherein: 31 when non-uniformities are determined to be present, performing a spatial mapping of 32 the non-uniformities, and 33 based on the spatial mapping, modifying the sample. CA 3085115 Date reçue / Received date 2024-06-28 1 2 10. The method of claim 9, wherein: 3 the testing comprises performing a clustering operation, further wherein 4 the clustering operation is one of: 5 a density-based clustering operation, 6 a hierarchical-based clustering, 7 a partitioning-based clustering, and 8 a grid-based clustering. 9 10 11. The method of claim 8, wherein: 11 the grid of points is determined based on at least one of: 12 size of the semiconductor sample, 13 shape of the semiconductor sample, and 14 a density of points on the semiconductor sample. 15 16 12. A method for characterizing a semiconductor sample comprising: 17 exciting a semiconductor sample at each point within a grid of points; 18 measuring a plurality of voltage decay curves, each of the plurality corresponding to each 19 point within the grid of points based on one or more changes in conductivity; 20 performing a first analyzing of the plurality of voltage decay curves using one or more 21 techniques to compare survival behaviour; 22 determining presence of non-uniformities within the semiconductor sample based on the first 23 analyzing; and 24 based on the determining, performing one of: 25 rejecting the semiconductor sample, 26 testing the semiconductor sample, and 27 at least one of further actions or a second analyzing. 28 29 13. The method of claim 12, wherein: 30 the testing comprises: 31 obtaining, for each point within the grid of points, at least one of: 32 a summary statistic, and 33 a survival statistic; and CA 3085115 Date reçue / Received date 2024-06-28 comparing the at least one of the summary statistic and the survival statistic 1 to one or 2 more thresholds; and 3 based on the comparing, either 4 accepting the semiconductor sample for fabrication, or 5 rejecting the semiconductor sample. 6 7 14. The method of claim 12, wherein: 8 the determining comprises detecting the presence of non-uniformities; and 9 the second analysis comprises a spatial mapping of the detected non-uniformities. 10 11 15. The method of claim 14, wherein: 12 the further actions comprising one or more of: 13 determining the presence of defects, and 14 determining whether to modify the semiconductor sample 15 are performed. 16 17 16. A system for characterizing a semiconductor sample comprising: 18 a measurement subsystem, a data analysis subsystem, and a statistical analysis subsystem 19 coupled to each other via an interconnection, wherein 20 the measurement subsystem excites the semiconductor sample at each point within a 21 grid of points, 22 the measurement subsystem measures a plurality of voltage decay curves, each of the 23 plurality corresponding to each point within the grid of points based on one or more changes 24 in conductivity, 25 the measurement subsystem transmits the plurality of voltage decay curves via the 26 interconnection to the data analysis subsystem, 27 the statistical analysis subsystem performs a first analysis of the transmitted plurality 28 of voltage decay curves using one or more techniques to compare survival behaviour, 29 the statistical analysis subsystem determines presence of non-uniformities within the 30 semiconductor sample based on the first analysis, and 31 based on the determining, the statistical analysis subsystem performs one of: 32 rejecting the semiconductor sample, 33 testing the semiconductor sample, and CA 3085115 Date reçue / Received date 2024-06-28 at least one of further actions or 1 a second analysis. 2 3 17. The system of claim 16, wherein 4 the testing comprises: 5 obtaining, for each point within the grid of points, at least one of: 6 a summary statistic, and 7 a survival statistic; and 8 comparing the at least one of the summary statistic and the survival statistic to one or 9 more thresholds; and 10 either 11 accepting the semiconductor sample for fabrication, or 12 rejecting the semiconductor sample 13 based on the comparing. 14 15 18. The system of claim 16, wherein: 16 the determining comprises detecting the presence of non-uniformities; and 17 the second analysis comprises a spatial mapping of the detected non-uniformities. 18 19 19. The system of claim 18, wherein: 20 the further actions comprising one or more of: 21 determining the presence of defects, and 22 determining whether to modify the semiconductor sample 23 are performed. 24 25 20. The system of claim 19, wherein: 26 the determining whether to modify the semiconductor sample comprises determining a 27 feasibility of modification based on the spatial mapping of the detected non-uniformities. CA 3085115 Date reçue / Received date 2024-06-28