SIMULATION OF THE SIZE EFFECT IN THE PROCESS OF FAILURES OF MICROELECTRONIC DEVICES ON THE BASIS OF THE APPROACH OF PERCOLATION CLUSTER FORMATION

Abstract

Introduction. A computer model was created and the failure process based on the percolation cluster approach was studied. The indicator dependences of the average time to failure, standard deviation and the asymmetry coefficient of time distributions to failures from the system size are established.
The component base of the modern microelectronic industry, the basis of which is the use of integrated circuits based on semiconductor crystals (chips), is rapidly improving and becoming more complex. The development of modern electronic devices is aimed at miniaturization and reduction of the linear dimensions of the element base of microelectronic components. During operation, there is a degradation of components and at some point in time it leads to device failure. Common causes of failures in the operation of microelectronic devices are the failure of elements in the electrical connection of conductors due to the formation of cracks or pores due to thermal migration, electromigration, thermal stress and other phenomena. Reducing the size of electronic components leads to an increase in current density through individual elements and intensification of the processes of degradation of electrical contact. At the same time, the requirements for the reliability of electronic devices are also growing. Given the concept of miniaturization of the element base of modern electronic devices, understanding the general behavior of the characteristics of the failure process of electronic systems while reducing their size is relevant and important from an applied point of view.
Purpose. The aim of the article is to develop a computer model and statistical study of the behavior of the main characteristics of the failure process depending on the size of the system.
To study the size effect, a series of computer experiments of the model system failure process was performed and a statistical analysis of time to failures distributions was performed to establish the characteristic dependences of the main characteristics of distributions for model systems of different sizes.
Results. The computer model is based on the analysis of the possibility of electric current passing through a two-dimensional system the size of N * N sites in the form of a square lattice. The main provisions of the model:
- Each site has 4 nearest neighbors.
- In the initial state, all sites of the system are filled with elements.
- Current can only flow if there are elements in two adjacent sites.
- At each iteration, remove the element from a randomly selected system site.
- The time to failure will be considered the ratio of the number of iterations to the total number of system sites, when the leading cluster between the left and right boundaries of the model system disappears.
Based on the described model, a series of computer experiments was performed and the results formed the distribution of time to failure for a model system of a certain size N * N sites.
The considered model is equivalent to the problem of percolation of sites. The formation of a percolation cluster of sites of deleted elements of the model system will correspond to the time to failure.
Conclusion. A two-dimensional computer model was created to simulate the process of failures in microelectronic systems. Based on the developed model, a series of computer experiments were performed to analyze the characteristics of the distributions of time to failure depending on the size of the model system.
The size effect of the failure process is obtained - the characteristics of time distributions to failures depend on the size of the system:
- As the system size decreases, the average time to device failure increases.
- The standard deviation of the time to failure distribution increases as the system size decreases.
- The time to failure distribution asymmetry coefficient (Skewness) increases with decreasing system size.
- The dependences of the average time to failure, standard deviation and the asymmetry coefficient of time distributions to failures from the system size are established.
- The Kurtosis of time to failure distribution decreases as the size of the system decreases.