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edfas.org 25 ELECTRONIC DEV ICE FA I LURE ANALYSIS | VOLUME 23 NO . 3 dividing the area under investigation. This leads to less precise localization of signals and lower emission image resolution. This lower image resolution is an additional factor that can limit the ease of interpretation of emission signals. Compared to time-integrated sensors, the time- resolved scheme offersmore options of signal observation due to the extra time dimension. Indeed, time-resolved emission (TRE) data can generate time waveforms (i.e., photon countinghistogram– 1Ddisplay) of the emissionat a single location, images like the time-integrated scheme (2D display) or movies (2D + time display) composed of slices of images generated by integrating photons over specific time intervals. The time-resolved method can operate in single-photon counting mode such that a triplet of coordinates ( x,y,t ) can be associated with each detectedphoton, where ( x,y ) are the spatial coordinates of the location where the photon has been detected and ( t ) is the time of detection with regards to a reference signal (e.g., the start of a test sequence). Taking this into consideration, a last mode of repre- sentation consists of displaying all the detected photons as a cloud of points in a 3D space. This mode may not be the most straightforward for interpretation but it has nonetheless been considered for some applications such as the localization of areas where emission is different from the rest of the circuit, [11] indicating a defect, or the identification of when and where two circuits can behave differently under a similar test sequences. [12] These results demonstrated that processing data directly in a 3D space can bring additional capabilities to TRE analysis. This also suggests that two closely related events can be differentiated with this approach, address- ing one of the pitfalls described above. In both studies, clustering of photons is a key concept. It designates a group of photons generated by the same group of tran- sistors (e.g., a logic gate). In dynamic photon emission, because most emission occurs during current spike in switching gates, clusters are identified by dense groups of photons in the ( x,y,t ) space. They are generated from randomemission and detection of photons (i.e., sampling in the sense of statistics and probability). Because this is a randomprocess, a statistical distribution can be associ- ated to each of these clusters with amatching probability density function. Furthermore, these functions can be interpolated to generate a higher-resolution image of the emission spots profile and address the image resolution pitfall. This article describes the development of such processes to generate higher-resolution images in time- resolved emission. Potential applications of this research include shorter scan duration and computation of images and identificationof emission spot locationbeyondoptical resolution limits. MACHINE LEARNING FOR THE ESTIMATION OF HIGHER-RESOLUTION EMISSION SPOT IN PHOTON EMISSION DISAMBIGUATION In this study, optical resolution refers to the physical limit to differentiate two close spots (i.e., Abbe resolution criterion), while image resolution refers to the spatial sampling frequency of the area under observation. In scanner-based detection schemes, this is defined as the step between each measurement. CLUSTERING AND INTERPOLATION PROCESS The process to generate higher resolution images of emission spots rely on two steps. First, identify the groups of photons emitted by the same portion of the circuits during a single change of biasing. These are named clus- ters. Second, for each cluster, compute some statistics to estimate a probability density function and generate a high-resolution image of this function. As mentioned in the introduction, photon emission is a randomprocess. For a single switching event, the prob- ability of emitting a photon is low, hence many rounds of repetition of the test sequence are required to generate and detect enough photons. Each execution of the test sequence is a random sampling process. When using a single-photon detection scheme, a triplet of coordinates ( x,y,t ) is associated to each detected photon. Assuming a long enough acquisitionduration, photons emittedduring the switching of transistors are more densely localized in the ( x,y,t ) space. On the other hand, photons resulting from dark counts, or noise, will be random and more sparsely placed (Fig. 1). Hence density, or the number of photons in a small volume unit, allows to make a distinc- tion between “signal” photons and “noise” photons. It is worth mentioning that this assumption is valid as long as the detector dark count rate is low enough. In case of very high dark count rate, photon density may not be a discriminative factor. In the field of machine learning, identification of clusters (i.e., clustering algorithms, part of unsupervised learning in machine learning) based on density criterionhas led to the development ofmany algo- rithms, [13] DBSCAN [14] being the first one reported. Studies have shown [11,12] that this algorithm can provide good results in photon emission. However, a single parameter (continued on page 28)