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THE ROLE OF PROBABILITY THEORY IN THE MODELING OF SEMICONDUCTOR DEVICES
Ziyoitdinova M.
Andijon State University
Abstract
Today, the future of the voluntary field and the expected innovations in this field are predicted based on the foundations of probability theory and statistics. It is also widely used in the modeling of physical processes. Therefore, this paper provides information on the role of probability theory in the modeling of semiconductor devices.
Keywords: program, probability theory, statistics, modeling, semiconductor.
The study of semiconductor devices and solar cells was based on statistical and probability theory methods. A clear example of this is the fact that the results obtained in the PVLighthouse program are constantly different, proving that not only the laws of physics, but also the theory of probability was used in its construction [1]. For example, when the same virtual experiment is performed twice in a row on the same structure of a solar cell, there is a difference between the values obtained. In the first case, the photogeneration current was 77.21%, and in the second case - 76.87% [2]. In addition, elements of probability theory are widely used in other applications used in the modeling of semiconductor devices [3]. In addition to standard programs, programming languages are also used in modeling. Sometimes modeling using a programming language focuses only on the laws of physics and does not use probability theory or statistics. Therefore, there is a difference between the obtained values and the experimental results. That is, probability theory helps to bring the results closer to the experimental results [4]. The best and most convenient programming language for statistical analysis and modeling today is Python.
Programming Mathematical and Scientific Computations Python can be used in large projects. Because it has no limits, the chances are high. It is also the best among programming languages with its simplicity and versatility.
There are many models of the Python programming language designed to model solar elements. These are Solcore, pvlib, solpy, Pypvcell and others.
Solcore is a modular set of computing tools written in Python 3 for modeling and simulating photovoltaic solar cells. Calculations can be performed on ideal, thermodynamic constraints by adapting them to experimentally determined parameters such as volt-ampere characteristics and luminescence in the dark and radiation. Uniquely, it can model the optical and electrical properties of many solar cells, from quantum walls to multi-pass solar cells, using the laws of semiconductor
physics. Solcore cannot be added to the library normally. You must have Fortran installed on your computer before you can add it to your library. Because this module performs numerical calculations by calling the fortran compiler.
Pvlib python is a community-supported open source module that provides a set of features and classes to simulate the operation of photovoltaic power systems. Pvlib python aims to provide reference programs for solar-related models, including solar position, open sky radiation, radiation transposition, DC power, and DC-AC conversion algorithms. Pvlib python is an important component of an evolving ecosystem of open source vehicles for solar energy.
The Solpy module is a module designed to study and model the environmental effects of solar panels.
In addition, a new library called Perkier.Energy has been developed, which includes the characteristics and prices of solar panels produced so far. The main purpose of this is to estimate and statistically analyze the volume of use of solar panels and their growth. That is why this library is constantly updated.
Computer modeling is a combination of theory and practice. There are many modeling programs. These include Synopsys's Sentaurus TCAD (Technology Computing Aided Design) and Silvaco Atlas TCAD, which are widely used in modeling semiconductor devices [5]. In these modeling programs, TCL (Tool Command Language) is used to create the model. This requires programming skills from the user. The advantage of this software package is the ability to create models in 3D and 2D [6]. If we want to model a semiconductor device in 2D, we need to pay attention to the symmetry of the device. Suppose we want to create a model of a simple p-n transition solar cell. In order to do that, we need to have knowledge about the process of making the solar cell, its structure, and the physical processes that take place inside it. But the results obtained in these modeling programs are very close to the results obtained in the experiment. That is, the error rate is very low. Together with the staff of the Renewable
Energy Sources Scientific Laboratory, we experimentally measured the photoelectric parameters of the solar cell and created a model of this solar cell using the Sen-taurus TCAD [7]. The results obtained actually proved that the accuracy of the modeling program was high. In addition, scientists around the world also acknowledge that the results obtained at the Sentaurus TCAD are close to reality. We have currently modeled the designs of many solar cells using the Sentaurus TCAD. A clear example of this is the model of a solar cell embedded in a nanoparticle. There are also modeling programs designed for a specific purpose. For example, the
PVLighthouse online program is designed to model solar cells only. We use PVLighthouse's Wafer Ray Tracer module to determine the optical properties of textured and optically coated solar cells [8].
Even physics uses probability theory. For example, it is the probability that charged particles photogen-ically generated in different areas of the solar cell will accumulate at the contacts. In this case, the probability is a function of the location of the fields. Formula 1 gives the formula for the photogeneration current. In this formula, the current density can be found using the probability that charges in different fields will reach the contacts.
rW fWrr "I
JL = qj G(x)CP(x)dx = qJ |J a(Ä)H0 exp(-a(Ä)x)dA CP(x)dx
' 0 J 0
In short, probability theory and statistical methods must be used in the modeling of semiconductor devices, regardless of whether they are standard or programming languages. Because today statistics are widely used to predict the future in all areas.
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