Linear Regression and Random Forests for Layer Identification in IC Layout Reverse-Engineering

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1 Linear Regression and Random Forests for Layer Identification in IC Layout Reverse-Engineering Anonymous Author(s) Affiliation Address Abstract Due to the tedious nature of the work, IC reverse-engineering is a process that is advantageous to automate. Linear prediction and random forests for layer identification are evaluated in this paper, and both approaches are shown to have good performance for this task, with random forests of relatively few (16) trees being able to achieve lower error rates (7-12%) than linear prediction (10-20%). 1 Introduction and motivation The reverse-engineering of integrated circuits is a process carried out widely by semiconductor manufacturers and researchers, who wish to analyse the layout of an IC and eventually derive the schematic of the circuit it implements. This process begins with depackaging the chip to expose the silicon die, which is then photographed under microscopy. While these steps are not trivial, they can be easily automated and represent a small fraction of the total effort spent in the process; the bulk of the work consists of tracing from the die images the regions which form components such as transistors, and their interconnects. This tracing is tedious work, and any methods which facilitate it are beneficial in increasing the efficiency of the process. 1.1 Basic structure of integrated circuits Integrated circuits are fabricated starting from a wafer of silicon, upon which various layers are deposited using a photolithographic process, to create the fundamental structures of electronic components such as transistors, resistors, and capacitors. The common types of layers are the bulk (substrate, i.e. the base silicon of the wafer), N-type and P-type diffusion (which occur together on one layer, the diffusion layer, and cannot overlap), polysilicon, and metal. For example, one type of transistor, an N-channel MOSFET, consists of two regions of N-diffusion on one layer forming the source and drain terminals, and another region of polysilicon located between these, forming the gate terminal. The diffusion layer is always the bottommost (excluding the bulk, which can be treated as a background for the purposes of this paper), followed by one or more layers of polysilicon, and finally one or more layers of metal. Layers are connected to each other by vertical structures called vias. This basic structure viewed from the top is illustrated in figure 1. Figure 1: Basic IC structure 1

2 The implication of this structure in reverse-engineering is that from an image of the die, it is possible to discern the various layers; while a newer chip may have over a dozen metal (topmost) layers, the very topmost metal layer will be immediately apparent since it is above all the others, and once it has been traced, either the image can be processed by subtracting the traced layer to rid it and make clear the layer below, or the die can be processed physically and chemically to remove the layer and re-imaged. By repeating these steps, the layout of all the layers (and the vias connecting them) can be determined, and this information used to derive the location of components (e.g. transistors) and their interconnections, which provides the information needed to recover the original design. 1.2 Approach and related work There appears to be little prior research in using machine learning approaches for IC reverseengineering, with the majority of work focusing on image processing techniques such as pattern recognition[1]. Degate[2] is a tool that works on this principle, and attempts to recognise common logic blocks by approximate matching against a libarary of known layout patterns. While pattern recognition is useful, the need to match features which are essentially a combination of all the layers limits its flexibility to only designs which exhibit this regularity. In contrast, a layer-by-layer approach as taken in this paper allows for full generality to any layout. Figure 2: Training image and label 1 Nintendo 3193A[3] In this paper, the focus is on identifying the first (metal) layer, which visually appears as the brightest and uppermost. Figures 2 and 3 show examples of the die images used, along with their labeling image that denotes the areas of metal; they are from the Visual6502 Project[4], which also hosts a large number of (unlabeled) die images for various ICs. For this paper, the Nintendo 3193A and RCA 1802E are the two ICs chosen for applying ML to recover the metal layer. As can be seen from these images, the appearance of the metal layer can vary considerably between images, likely necessitating re-training on each chip, but the advantage gained is from being able to use the results of training on a relatively small portion of the image to apply recognition to the rest of it and thus speed up the overall process. 2 Linear prediction 2.1 Overview Figure 3: Training image and label 2 RCA 1803E[5] The first method attempted is linear prediction. For each pixel in the source image (less a 4-pixel border), itself and the surrounding 80 pixels are used as the vector of input features, with the corresponding pixel in the labeling image (0 or 255) the expected output. Thus, each feature corresponds to a 9 9-pixel block centred at the pixel to be predicted. This size was chosen as a compromise to keep the computation reasonable (since the number of points is quadratic with respect to it) and 2

3 hopefully not lose too much accuracy; 9 pixels is slightly wider than the width of the thinnest metal traces in the images above. Two types of features were tried; one uses the 3 RGB (0-255) values of each pixel, while the second uses converted HSB colour space values, both resulting in 244 (243 prediction + 1 expected output) data points per pixel. This feature arrangement precludes the prediction of a 4-pixel border at the edge of the image without performing extra preprocessing, but it was decided to not implement this preprocessing for two reasons: the values of the pixels beyond the edge are not known and using approximations for them may reduce the accuracy of the prediction, and the whole-chip images this process is aimed at are sufficiently large (in the region of or larger) that a 4-pixel border is of little concern. The calculation of errors and other values below excludes this border. 2.2 Details Implementation of this method was done in C, and split into three programs for processing convenience. The first takes as input the training and labeling images, and outputs the n-by-244 matrix of training data. The second reads this matrix and uses the Intel MKL[6] to compute the least-squares regression estimate, while the third uses the output of the second and an input image to produce an output image with each pixel (less the border) corresponding to a linear combination of it and the 80 surrounding pixels, in accordance with the regression coefficients. Values below 0 or greater than 255 were clipped into this range. RGB and HSB colour space versions of the first and third program were written, and they were trained on the images of figures 2 and 3. The former image is , resulting in a matrix, while the latter is and results in a matrix. On an Intel Core i7 4GHz, computation of the regression coefficients required between 2-3 minutes of processor time, and prediction using the test images shown also took approximately the same amount of time. 470MB and 290MB respectively were consumed for the computation of these coefficients on figures 2 and 3. Figure 4: Test image and label A After training, prediction was done using both the training image and the test images shown in figures 4 and 5 (using the results of the training image from the same chip.) Using the accompanying labeling image for the test images, the error can also be calculated as the percentage of pixels that differ between the label and the prediction result; those pixels which are not 0 or 255 can be thresholded, and although it may seem reasonable to assume the 50% point (0-127 and ) is optimal, to provide evidence in support of that choice, a series of comparisons were made to determine the effects of the threshold on the overall error rate. Figure 5: Test image and label E 3

4 Results Figure 6: Linear prediction on figure 2 result and 50% threshold The result of training with RGB produces the image shown in figure 6. At a 50% threshold, most of the traces of the metal layer are reproduced adequately, but the error is still non-negligible, causing breaks in some of the traces (false negatives) and the creation of traces where there aren t any (false positives). Examples of this occur at the lower left and right, where slightly brighter green areas of P-diffusion have been identified as metal by the linear prediction. Figure 7: Linear prediction on figure 4 result and 50% threshold Figure 7 shows the output of training on RGB with figure 2 and testing with figure 4; it can be seen that while some regions such as the lower third appear to be predicted with good accuracy, in the upper two thirds of the image where there is more detail in the lower layers, it causes both false positives (metal layer detected where there isn t any) and negatives (no metal detected where there should be). Figure 8: Linear prediction on figure 2 result, HSB colour space Figure 9: Linear prediction on figure 4 result, HSB colour space The results of using HSB colour space in figures 8 and 9 appear worse than for RGB, with much larger areas of false positives. Although widely used in image processing tasks, HSB performs weaker than RGB in this application because the colours being discriminated seem to be more aligned with RGB polysilicon appears reddish, P-diffusion is green, while N-diffusion is bluishpurple, and the desired metal layer is also slightly greenish, explaining the tendency for the P- diffusion to be confused with the metal and causing the false positives. 4

5 Figure 10: Linear prediction on figure 3 result and 50% threshold Figure 11: Linear prediction on figure 5 result and 50% threshold Compared to the 3193A images above, the 1802E RGB test and train results in figures 10 and 11 show subjectively worse results, with many false positives arising from the brownish and bluish polysilicon layer. False negatives are also present, and from comparison with the original image, appear mainly at the edges where the metal is crossing over poly. One possible explanation of this is the wider traces in the image (8 pixels vs 6 for the 3193A) and its higher contrast and colour saturation. Although this gives the perception of a sharper image to the human vision, its containment of many dark edges disturbs linear prediction since pixels labeled as non-metal are also surrounded by these dark edge pixels. Figure 12: Linear prediction on figure 3 result, HSB colour space Figure 13: Linear prediction on figure 5 result, HSB colour space However, the results for 1802E HSB linear prediction show the opposite trend, with much of the brown polysilicon false positives having disappeared (note how the vertical false positive strip and square structures on the left half in figure 11 are not present in figure 13.) One reason for the HSB colour space giving better performance compared to RGB can be hypothesised to be related to the nature of the data; for the 3193A images, with their relatively low contrast, discrimination is based more heavily on the amount of green, whereas for the 1802E images the metal layer is nearly white and thus brightness becomes the main dimension of categorisation, matching well with the 3rd component of HSB. 5

6 Figure 14: Error vs prediction threshold The effect of the threshold on the error rate is shown in figure 14. At low thresholds, the number of false positives is high, while the opposite with false negatives occurs when the threshold is too high. Thus the optimal threshold can be expected to be between these two extremes and that corresponds with the shape of the error curves obtained in figure 13, but the optimal is not exactly in the middle of the range (50% or 128). Moreover, the threshold of minimum error is different for each specific image, with e.g. the 1802E HSB test image giving a minimum error at 86 while the 1802E HSB train image has its minimum error at a threshold of 140. With the exception of the 1802E HSB test image with its 2%, the difference between the minimum error and the error at a 50% threshold is below 1%, meaning that a fixed threshold of 50% is a reasonable compromise. Overall, the errors at 50% threshold range from 10-20%, meaning that while linear prediction certainly has its benefits in getting the majority of the layer pattern identified, the output still requires manual inspection and correction of the errors. 3 Random forests 3.1 Overview The second method under consideration in this paper is random forests. For this method, the same 9 9-pixel (243-dimension) feature set was used as with linear prediction, but due to the time needed to generate the forests, it was decided to only use RGB input data. At each node of the tree, n random dimensions of the 243 are chosen, and the best threshold among all of them, with the highest information gain, was used to decide the split. For prediction, the average across all the trees was taken as the output pixel value. 3.2 Details Two additional programs were written in C, one to generate a random forest and the other to predict. For generation, an in-place sort-based algorithm was used which does not require copying data at each split, in order to reduce memory usage and increase performance. Incremental updating approach when scanning through a dimension was adopted for information gain calculation, decreasing the computation required. Nevertheless, random forests proved to require much more time to generate than the linear prediction coefficients; all of the latter needed less than 5 minutes on an Intel Core i7 4GHz, while the same machine required nearly an hour to generate each of the forests with the parameters mentioned below. For the two sets of chip images used, 3193A and 1802E, forests were generated varying t, the number of trees, and n, the number of random dimensions considered at each split. (t, n) pairs were chosen to keep the overall workload relatively constant; they were (1, 243), (2, 120), (4, 60), (8, 30), and (16, 16). Nodes were leafed if they contained less than 256 points, or their depth reached

7 Results Figure 15: Error vs prediction threshold random forests The quantitative error rates for 16 trees and 16 random dimensions are shown in figure 15 (not shown due to brevity, but errors were higher with fewer trees and more dimensions). For random forests, the choice of threshold appears to have a greater effect, with lower thresholds preferred. The cause of this has not been entirely determined but it maybe an artifact of how random forests output is an average of individual trees, where the decision of any one tree should have a higher weight on the overall decision. These results show random forests able to achieve higher accuracy than linear prediction, and thus 2-fold cross validation was employed to further verify the accuracy of the model, by training using the test data and testing on the training data. The results of this are shown in figure 16. Figure 16: Error vs prediction threshold random forests cross validation Keeping in mind that the CV results are when the forests are generated from the test data and then tested on the training data, it appears that the errors are within the same range as before, although the minimum error thresholds have changed. The errors at 50% threshold for testing (1802train cv and 3193train cv, since they were trained with the test image) remain at 12% and 8% respectively, comparable to the 12% and 9% obtained in figure 15. From these results, it can be stated that this application of random forests generalises well to similar datasets. Figures 17 and 18 show examples of predictions made on figures 4 and 5 by training on figures 2 and 3 using 16 trees with 16 random dimensions at each split, and their decisions using thresholds of 112 and 16, respectively. These correspond to errors of 10% and 7%. In particular, it can be seen 7

8 that the false positives are much reduced compared to linear prediction, and most of the errors that are present are small discontinuities that could be easily removed using an inpainting algorithm.[7] 4 Conclusion Figure 17: Random forest result on figure 4, and threshold 112 Figure 18: Random forest result on figure 5, and threshold 16 Random forests provide superior accuracy to linear prediction for the identification of layers in IC reverse-engineering. Even with a fixed threshold of 50%, linear prediction achieves an 11-20% error rate, while random forests can achieve 9-12%. These error rates mean that the tedious task of manually tracing the layers can be reduced to only verification and small corrections of errors, and the nature of the errors with random forests also lends them to easy correction via inpainting. An interactive system can be envisioned for threshold finding, presenting the user with the decision made at a particular threshold, and allowing her to adjust it while comparing with the die image until the results are as desired. Further processing can also exploit the regular polygonal nature of the IC layout, using e.g. the adherence to a grid pattern to decide that metal is present in a grid pixel if a certain threshold of its pixels were decided by the random forest to be metal. In conclusion, the results achieved show a strong positive benefit to this application with random forests. References [1] G. Masalskis, R. Navickas; Reverse Engineering of CMOS Integrated Circuits. In Electronics and Electrical Engineering, 2008, vol.88 pp [2] M. Schobert; Reverse engineering integrated circuits with degate. [3] Visual6502 team; Nintendo 3193A A.html [4] Visual6502 team; Visual6502 site. [5] Visual6502 team; RCA die shots.html [6] Intel Corporation; Intel(R) Math Kernel Library. [7] A. Telea; An image inpainting technique based on the fast marching method. In Proceedings of Journal of Graphics Tools, 2004, vol.9 no.1 pp