The Current State of the Problem on the Placement of LSI Elements Boris Chernikov 1,2[0000-0002-6622-888X], Arina Mozhzhukhina 2,3[0000-0001-5480-3157] and Elena Chernikova1 1 Plekhanov Russian University of Economics, 36 Stremyanny lane, Moscow, 115998, Russia bor-cher@yandex.ru, lb20062006@yandex.ru 2 National Research University of Electronic Technology (MIET), ld. 1, Shokin Square, Zelenograd, 124498, Moscow, Russia 3 Scientific-Manufacturing Complex "Technological Centre", house 1, bld. 7, Shokin Square, Zelenograd, 124498, Moscow, Russia reania@rambler.ru Abstract. The article discusses one of the stages of creating a microcircuit - physical (topological) design. At this stage, two main operations are: placing cells on the field of the base matrix crystal and tracing these elements. To create a high-quality microcircuit, it is necessary to follow certain design rules and carefully check the criteria for optimal placement. The basic rule for microcir- cuits: minimum power consumption with high speed and small area. The article presents a brief analysis of some disadvantages of the main techniques for plac- ing elements on the field of the base matrix crystal. In addition, the main op- tions for calculating the lengths of connections between the elements are con- sidered, which also affects the accuracy of evaluating the parameters of the mi- crocircuit. At present, in Russia, attention is increasing to the modification and improvement of domestic computer-aided design systems. In this regard, the most promising direction for further research was selected, as well as the main goals and objectives were formulated. Keywords: physical design, topological design, placement, routing, CAD. 1 Introduction Microcircuit design is a complex and lengthy process. It includes a wide range of different tasks. The complexity and degree of integration of large integrated circuits (LSI) is growing every year. Specialized microcircuits for sensors of various purposes [1] and intelligent sensors are currently the most priority and difficult to develop. Such sensors are in demand in many industries, including medicine, safety (radiation sensors, rangefinders, portable weapons, explosives, sensors for autopilot, computer vision, video and image processing, video surveillance), various exploration (space exploration, exploration in crevices and depressions of the oceans), automotive (adap- tive braking, parking assistance, autopilot system) and many others [2]. Each stage of designing such microcircuits can be considered as an independent optimization prob- Proceedings of the 10th International Scientific and Practical Conference named after A. I. Kitov "Information Technologies and Mathematical Methods in Economics and Management (IT&MM-2020)", October 15-16, 2020, Moscow, Russia © 2021 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0). CEUR Workshop Proceedings (CEUR-WS.org) lem. To solve it, an extensive mathematical apparatus is required, including mathe- matical analysis, optimization methods, graph theory, and others. Thus, at present, one of the priority directions in the manufacture of domestic LSI is the improvement of computer-aided design (CAD) tools, including subsystems responsible for the most optimal placement and routing of elements on the substrate. It is necessary to automate the design process of microcircuits, because, due to the increase in the number of elements that make up modern microcircuits, their routing and placement even on powerful computers in automatic mode can take a significant amount of time. 2 Literature Review Basically, the analysis and work with the subject area was carried out on the basis of progress not only in the field of microelectronics and CAD, but also on the basis of the current development and widespread introduction of artificial intelligence (AI) and machine learning (ML) systems in various areas of modern science and life. The article by M. Makushin and A. Fomina "Artificial Intelligence and Profitabil- ity as Driving Factors of CAD Development" (DOI: 10.22184/1992- 4178.2019.185.4.90.100) [3], which examines the CAD market and substantiates the urgent need for modern and high-speed solutions, made it possible to establish itself in the chosen direction. In addition, the possibilities of using AI as such in CAD systems are discussed in the book Ibrahim (Abe) M. Elfadel, Duane S. Boning Xin Li "Machine Learning in VLSI Computer-Aided Design" (DOI: 10.1007 / 978-3-030- 04666-8) [4]. General algorithms for working with ML, AI and deep learning were mastered on such books as: Andrew W. Trask "grokking Deep Learning" (ISBN 978-5-4461- 1334-7) [5], Nikolenko S., Kadurin A., Arkhangelskaya E . "Deep Learning. Diving into the world of neural networks" (ISBN: 978-5-4461-1537-2 , 978-5-496-02536-2) [6], Deitel P., Deytel H." Python. Artificial Intelligence, Big Data and Cloud Compu- ting" (ISBN: 978-5-4461-1432-0) [7]. Research and analysis of the field of rein- forcement learning is currently underway: Sutton Richard S., Barto Andrew G. Rein- forcement Learning (ISBN: 978-5-97060-097-9) [8] and Lapan M. "Deep Reinforce- ment Learning. AlphaGo and Other Technologies" (ISBN: 978-5-4461-1079-7) [9], Sudkharsan Ravichandiran "Deep Reinforcement Learning in Python. OpenAI Gym and TensorFlow for the Pro" (ISBN: 978-5-4461-1251-7) [10]. Currently, many large firms are working on solutions in the field of CAD im- provement, in particular Google [11], Synopsys [12, 13], HPE [3], TSMC [3], Ca- dence [3] and others. 3 Materials and methods Over time, developers strive to make microcircuits more and more compact, but at the same time high-speed and low power consumption. This was mainly achieved by reducing the size of the transistor. In addition, the materials from which it was made, the geometry, and the technological process changed. Based on empirical observation of the development of microcircuits, Gordon Moore predicted that the number of transistors placed on an integrated circuit chip would double every 24 months. The main problems faced by the developers are the increase in power consumption and overheating of microcircuits due to current leakage through the dielectric layer. Since many solutions for improving transistors are currently in the development stage, many scientists believe that reaching the threshold of silicon technology is approaching [14, 15, 16]. Due to a decreasing the size of transistors and the distance between elements on microcircuits, the number of transistors on microcircuit increases, and therefore the number of elements that must be placed and connected during development (fig. 1). The graph shows that the number of transistors actually doubled approximately every 2 years. Fig. 1. Moore's Law transistor growth To create high-quality microcircuits, in particular, it is necessary to optimally place the elements on the substrate. The way in which the elements are placed and connect- ed can directly affect both the time and power characteristics, and the stability of the microcircuit. Despite many years of research in the field of creating and improving algorithms and placement technologies, the optimization problem is still relevant. Often, with a large number of elements, placement and tracing algorithms work for an unacceptably long time - from several hours to several days. Thus, for most formulations of the problem of placing and tracing elements, there are no sufficiently effective algorithms that can find the optimal solution in an acceptable time. That is because the majority of algorithms are modifications of the algorithm for full enumeration of placements. In this regard, it is important to develop algorithms that find solutions close to optimal in a limited time. The purpose of this article is to analyze the criteria for the optimal placement of el- ements and consider the main existing methods for placing elements in the process of developing microcircuits in the interests of the subsequent search for ways to opti- mize the placement of elements in designing microcircuits. 4 Materials and methods of creating LSI When creating a microcircuit, it goes through a number of stages. The main route for the design of microcircuits combines the following stages proposed by the Scientific- Manufacturing Complex "Technological Center" [17]: - system design - development of system specifications and requirements for LSI; - functional design - based on the behavioral model, an RTL description is created (register transfer level - register transfer level, in the development of integrated cir- cuits - a description of the operation of a synchronous digital circuit) of the designed microcircuit, as well as its modeling; - logical design - a structural description of the circuit is generated, consists of log- ical gates and their connections (list of connections), logical synthesis, functional- logical modeling (FLM) is carried out; - physical (topological) design - the placement of cells on the field of the basic ma- trix crystal (BMC) is carried out, the synthesis of the topology taking into account the circuits, the calculation of the circuit delays of the LSI topology, the stability of the LSI design is estimated under various external influences, the influence of the topolo- gy parameters on the correct functioning and stability is analyzed project; - production of LSI; - testing LSI in wafers and body composition; - LSI qualification tests - tests for reliability, radiation resistance, etc; - testing LSI as part of the customer's equipment. Thus, by the time the elements are placed and traced on the substrate, the require- ments for the microcircuit, the technology, the functional library of cells are already known, the list of connections has been created and the simulation has been carried out. 5 Materials and methods of palcement The smallest LSI in CAD “Kovcheg” is the 5503 family: 576 to 5478 gates and 28 - 64 pins [18]. The standard procedure for placing elements on the BMK: 1) arrangement of the periphery in accordance with the statement of work and / or the direction of information (current); 2) possible placement of some elements manually - triggers, memory elements, etc. Possible layout (color) of the arrangement of blocks and subcircuits (inside them, triggers, buffers, etc. can also be pre-assigned before the automatic mode); 3) the rest of the elements are placed automatically according to the algorithms of the selected CAD; 4) correcting the position of individual elements, if necessary; 5) trace the elements; 6) if the routing did not work out (the connections did not go through), then return to placement, making edits or scattering elements from scratch (paragraph 4) or 2)). 6 Materials and methods for optimal placement criteria Important indicators for the development of a high-quality microcircuit are power, frequency and area. This is reflected in the requirements for LSI: energy consump- tion, speed and dimensions. Thus, to create a microcircuit, it is necessary to minimize power consumption, increase performance and reduce size. This means that a high- quality microcircuit should be as small as possible in size, consume as little energy as possible, and work as quickly as possible. The minimum placement criterion currently used in CAD "Kovcheg" of the 5503 family is the total length of connections between elements. This is due to the fact that, mainly because of this characteristic, it is possible to increase performance, minimize area and reduce energy consumption. In this case, it is necessary to observe certain restrictions on minimizing the connections, since with a short length of connections, their density increases, which leads not only to difficulties for their implementation, but also to a possible increase in cross-talk between connections. In this regard, a criterion for the possibility of laying connections is usually introduced - congestion, or density. Algorithms that take this criterion into account try to distribute all the ele- ments evenly throughout the microcircuit. In addition, performance metrics such as latency and power consumption are eval- uated. All data streams are split into parts using triggers. Between two triggers, the signal must pass within a certain time - a period. However, the greater the distance between the elements, the longer the signal goes, that is, the capacity increases. This is the delay [19]. Thus, during placement, the algorithm must arrange the elements so that the signal has time to cover the distance between the triggers in the allotted time. In general, the signal switching should look like fig. 2, a. If the elements are far from each other or this connection unites many elements, then the capacity (respectively, and the signal switching time) will increase, the signal front on the diagram "falls" (fig. 2, b). Unlike the two previous criteria, the indicators for this case are difficult to assess using simple geometric calculations. Fig. 2. Change of signal switching time at small (a) and large (b) capacitance At the same time, despite the introduced optimality criteria, there is a dangerous ef- fect that is difficult to predict in advance. This is the possibility of forming a capacitor from adjacent connections, which leads to an increase in power consumption, time delays or even voltage fluctuations. It is possible to reveal this effect only after plac- ing and tracing the elements of the microcircuit. Since the main criterion for optimal placement is still the minimum length of the joints, it is necessary to consider the basic methods for calculating the distance between the elements, that is, to calculate the theoretical distance for placing the elements, as well as to determine the basic algorithms for minimizing the length of the joints. For the case of the criterion for minimizing the length of joints, the problem state- ment is as follows. Let the elements of the microcircuit be given to place e 1, e2, …, en …, eN. To de- termine the connections of elements, you can set, for example, an adjacency matrix, since in the general case, connected elements can be represented in the form of a graph. In addition, a plan is set on the microcircuit - a fixed set of positions in which the elements P1, P2, …, Pm, …, PM should be placed, and the sum of N elements in area cannot exceed the area of the microcircuit (1): (1) So there are M!/(M-N)! options for the placement of elements, when calculating which it is necessary to take into account rn,m- the distance between the centers of positions Pn and Pm of elements. After moving any element en to a new position P m, the change in the contribution of the distance between this and the elements connected to it in the total amount of distances is estimated (2): (2) To create a high-quality microcircuit, in particular to achieve high performance, it is necessary to find such an optimal arrangement, at which the minimum amount of distances will be ensured (3): (3) 7 Materials and methods for minimizing the length of joints When placing the elements in the BMC field, it is necessary to approximately cal- culate the distance between the elements, evaluating the length of the connection ob- tained with this formulation of the element, as well as its contribution to the total sum of the length of the microcircuit connections. The most effective and widely used method in practice is the semi-perimeter meth- od, bordering the connection of a rectangle. In practice, the method allows a fairly accurate estimate of the length of the connection between two or three elements, how- ever, if there are more elements, then the method gives an underestimate. In this case, there are several options for the bordering rectangle itself (fig. 3). In the figure, the element to be placed is highlighted in yellow with a dot, and the elements already placed are presented in the form of schematic cells of the BMC. Fig. 3. Options for the bordering rectangle: a) the bordering rectangle covers the contacts entirely; b) the centers of the elements are covered; c) the part of contacts that would be cap- tured when constructing the Steiner tree is covered; d) the bordering rectangle is drawn through the lower left corners of the elements The most commonly used methods are b) and c). Of these, method c) estimates the distance between the connected elements most accurately, and method b) is the easiest to implement. In CAD Kovcheg, for example, variant b) of the bordering rectangle is used [17]. The calculation of the lengths of joints by the semi-perimeter method is carried out as follows (fig. 4). Fig. 4. Simplified display of links when moving an element The calculation of the total contribution to the connections from the movement of the cell is carried out with the help of bordering rectangles for groups of elements. The diagram shows an example of calculation for several groups of interconnected elements and an external contact of the circuit - a peripheral cell (light green element 3). The field with cells for placing the main elements (1, 2, 4-8) is a schematic field of the BMC used for the production of LSI, where one cell contains four unconnected transistors, forming one conditional gate. In this case, the amount consists of several components, including distances between elements 2 and 3 (green bordering rectan- gle) and the distance between the five elements 4 - 8 (blue bordering rectangle). Fur- ther, the distances from the semi-perimeter rectangles (black lines) to the element being placed (purple rectangle) are added to the sum of these semi-perimeters. Thus, it can be concluded that the total length of the connections decreases or increases. 8 Materials and methods of placing elements Basically, the following methods are distinguished when placing elements. 1. The first method was the simulated annealing method. With regard to the place- ment problem, the initial placement of elements is taken, which, by means of permu- tations of elements, attempts are made to improve by accepting or rejecting transfor- mations in accordance with the optimization criteria. The permutation element is se- lected based on the selected probability distribution. Most often, for minimization, they are guided by the total approximate length of the connections from the bordering rectangle. The disadvantages of this method are the significance of the time spent on its operation, since the annealing method, which consists in enumerating all possible combinations, most often works until the sum becomes close to the specified one, since with a large number of elements it can minimize the sum to infinity even when using parallelism technologies. Accordingly, the judgment about the optimality of the resulting placement is subjective. However, in comparison with genetic algorithms, according to Ingberg, the method does not lose in most problems, and even wins in many problems. 2. Various genetic algorithms were applied in a similar manner. Most often they were used with parallelism, i.e. using the capabilities of the computer to perform sev- eral operations at the same time, since they were too slow. The advantage of genetic algorithms is that they are relatively resistant to hits in local optima. However, due to this, they find even an approximate global optimum much more slowly. In the 2000s, there is a surge of interest in this topic, attention is paid to improving the algorithm and techniques for its parallelization (for example, [20]). However, according to the authors themselves, the time of work is still very high. 3. Iterative or dichotomous approach - methods based on a gradual decrease in the dimension of the problem. At each iteration, the set of micro-circuit elements is split into several subsets, each of which is split again, and so on. Among the general draw- backs of algorithms of this type, they are distinguished by their relatively high com- plexity of constructing an optimal partitioning tree of a scheme (the problem of bal- anced partitioning of a graph is NP-complete, therefore, heuristic algorithms that are not guaranteed to be accurate or optimal are used to solve it) and a simplified estimate connections. In addition, the use of heuristic algorithms does not guarantee finding the correct solution and finding a solution in principle, even if it exists, which, togeth- er with the time spent on the operation of the algorithm with a large number of placed elements, makes it undesirable for use without modifications and improvements. 4. The so-called forceful or analytical methods. Their peculiarity lies in the fact that the placement problem is formulated as a mathematical problem or a problem in mechanics. In the first case, a mathematical programming problem with a quadratic cost function is presented. In the second, the laws of physics are applied. The more weight the connection has, the stronger the connected elements should attract and the closer they should be. In addition, additional forces are added to compensate for the attraction and prevent all elements from being grouped in the center of the microcir- cuit. The simplest case is when a force is introduced that is inversely proportional to the distance. Sometimes peripheral cells or input-output cells are used as such forces [21]. The disadvantages of the algorithms of this group are their complexity for im- plementation and slowness with a large number of elements and connections in the micro-circuit. Thus, since each approach has certain drawbacks, in particular, associated with the complexity of the microcircuit, the number of elements and imposed restrictions, it seems appropriate to use neural networks in the analysis of microcircuit designs to select the most suitable method for placement. Genetic algorithms are mainly used with parallelization, therefore, their use, which directly depends on the processor power, is not suitable for speeding up placement. Another option for solving this problem is the placement of elements based on an innovative method of reinforce- ment learning - a new section of AI, since this option can be much faster than stand- ard algorithms. 9 Results The proposed method should help to reduce the time of placement and routing of LSI elements at the stage of topological design. Reinforcement learning will allow, based on the use of an agent, to train a neural network to simulate the decisions of developers, both separately taken and several. In addition, the created neural network can be trained during operation, allowing you to adapt the placement for a particular developer. The main direction of further research will be related to the choice of technology, architecture, teaching methods and the choice of technology for imitation in the choice of a specialist. 10 Discussion At the present time in Russia there is a growing interest in specialized microcir- cuits [1, 22-25]. Due to the impossibility of using free foreign and domestic CAD systems due to the low level of security and the inexpediency of buying entire lines of expensive foreign CAD systems for one specific subsystem or function, as well as due to the lack of domestic topological design tools comparable in power, it is necessary not only to develop a reliable and a proven domestic CAD system, but also to ensure the availability of modern, high-speed tools in it in order to reduce the labor costs of domestic developers, increase the safety of LSI projects and reduce the time of the process of bringing microcircuits to the market. In order to achieve the set goals, it is necessary to solve the following tasks. 1. Analyze the existing techniques for tracing elements on a micro-circuit substrate in order to identify the most costly stages of techniques for improving them or creat- ing your own method. 2. To develop a methodology and algorithms for placing and tracing elements on a microcircuit substrate that implement it to reduce the resource intensity of the topo- logical design stage based on the identified bottlenecks in the stages of other methods using deep learning [26 – 28] or reinforcement learning [29 – 32]. 3. Substantiate and prove the advantage of the new method in comparison with the used ones. 11 Conclusions 1. The main disadvantages of the existing methods for placing microcircuit ele- ments are high time costs, especially when placing a large number of elements, as well as low flexibility in solving problems with varying degrees of complexity, which indicates the need to develop a new, more efficient solution. 2. Based on the analysis of the main approaches to solving the problem of placing microcircuit elements during design and due to the lack of worthy domestic analogues of such algorithms, as well as the high cost of foreign software, which does not al- ways fully correspond to the design routes of domestic LSIs, the need to create our own innovative methodology to solve the problem was identified. 3. The goals and objectives for the subsequent research aimed at improving the methods of placing and tracing elements on the microcircuit substrate and creating a new technique using AI - reinforcement learning - are formulated. References 1. Patrusheva T.N. Sensory. 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