Numerical simulation of solar cell based on graphene nanostrip using non-equilibrium Green's function (NEGF) method

Dissertation of Master of Electrical-Electronic Engineering

Abstract

In this thesis, for the first time, we have used graphene nano-ribbon as an active layer of a solar cell. To simulate this cell, the non-equilibrium Green's function method was used in the mode space, and the effect of electron-photon interactions was calculated by means of Born's self-consistent approximation. In order to increase the simulation speed, we used the potential profile obtained in the dark state for the simulations under irradiation, and thus we have avoided re-solving the Poisson equation in the form of a couple with the Schr?dinger equation. In addition, we have used the local (diagonal) approximation in the calculation of the self-energy caused by the electron-photon interaction.

Key words: solar cell, graphene nanoribbon, numerical simulation, non-equilibrium Green's function (NEGF) method.

Chapter 1- Introduction

1-1-Preface

Solar energy is the most unique source of renewable energy in the world and is the main source of all energy on earth. This energy can be directly and indirectly converted into other forms of energy[[i]].

Generally, the energy emitted from the sun is about 3.8e23 kilowatts per second. Having about 300 sunny days per year, Iran is one of the best countries in the world in the field of solar energy potential. Considering the geographical location of Iran and the dispersion of the country's villages, the use of solar energy is one of the most important factors that should be considered. The use of solar energy is one of the best ways of electricity supply and energy production compared to other models of energy transmission to villages and remote areas in the country in terms of cost, transportation, maintenance and similar factors[1]. According to international standards, if the average solar radiation energy per day is higher than 3.5 kilowatt hours per square meter, the use of solar energy models such as solar collectors or photovoltaic systems is very economical and cost-effective. is This is despite the fact that in many parts of Iran, the radiant energy of the sun is much higher than this international average, and in some places it has been measured even higher than 7 to 8 kilowatt hours per square meter, but on average, the radiant energy of the sun on the surface of Iran is about 4.5 kilowatt hours per square meter [1].

1-2-History of solar cells

Photovoltaics was first demonstrated experimentally in 1839 by Beckuehrle[1], a French physicist [[ii]]. After that, Charles Fritz [2] was able to make the first solid state solar cell in 1883. He coated the selenium semiconductor with a thin layer of gold to form a junction and was able to achieve an efficiency of 1%. In 1946, Russell Ohl[3] managed to build a modern junction solar cell.

However, the first practical solar cell[4] was built in 1954, at Bell Laboratory[5]. Chapin[6], Fuller[7] and Pearson[8] used a silicon p-n penetration junction[9] to make this cell and were able to achieve 6% efficiency[2]. After that, cells were made in which thin layers of silicon or other semiconductors were used instead of wafers. Currently, in addition to these two types of solar cells, there are many other types of cells, such as polymer cells, organic cells, pigment cells (sensitized with color [12]), multi-junctions and so on. is used.

In this chapter, the important types of solar cells, which are grouped into three generations, are briefly examined: the first generation (including silicon crystal cells [13]), the second generation (including various cells in which thin semiconductor layers are used) and the third generation (including cells whose design is such that they can achieve efficiency beyond the Shockley-Quiser limit) find).

1-3-Types of solar cells

1-3-1-The first generation of solar cells (silicon crystal cells)

In this category of solar cells, silicon wafers are used as active semiconductors. Silicon with an energy gap of ev1.12 is considered a very suitable material for absorbing the sun's spectrum. It is also the second most abundant element in nature. This means that obtaining raw silicon will not cost much and there is no worry about running out of its resources.

In order to achieve high conductivity, increase cell life and prevent loss of efficiency (due to recombination of carriers), silicon is used in single crystal and high quality. Sometimes multi-crystal silicon is used to reduce costs.

1-3-1-1-Semiconductor crystal growth process

The growth conditions of semiconductor crystals (crystals) used to make electronic components are much more precise and difficult than the conditions of other materials. In addition to the fact that semiconductors must be available in crystalline form, their purity must also be controlled within a very fine range. For example, the density of most impurities used in today's Si crystals is less than 1 part in ten billion. Such degrees of purity require great precision in the use and application of materials at each stage of the manufacturing process [[iii]].

Single-element semiconductors Si and Ge are obtained from the chemical decomposition of compounds such as GeO2, SiCl4 and SiHCl3. After separating and performing the initial stages of purification, a semiconductor material is melted and made into ingots [14]. Si or Ge obtained after an annealing step [15] is polycrystalline.

If the cooling process is not controlled, the crystal regions will have completely random directions. For crystal growth in only one direction, it is necessary to have a precise control at the boundary between the molten and solid material during cooling [3]. A common method for growing single crystals is the selective cooling of a molten material so that solidification is done in the direction of a specific crystal direction. For example, consider a container made of silica containing molten Ge; It can be taken out of the furnace in such a way that freezing starts from one end and gradually progresses to the other end. By placing a small crystal seed [16] at the starting point of freezing, the quality of crystal growth can be increased. If the cooling rate is carefully controlled and the solid-melt interface is moved slowly along the melt, the germanium atoms will form a diamond lattice along with the cooling of the crystal. The shape of the obtained crystal is determined by the melting vessel. Ge, GaAs and other semiconductor crystals are usually grown by this method, which is called the horizontal Bridgman [17] method. In another form of this method, a small area of ??a crystalline material is melted and then a molten area is moved to the other side so that a crystal is formed behind the molten area and during its movement [3].

One ??of the disadvantages of crystal growth in a molten container is that a molten material comes into contact with the walls of the container, and as a result, during freezing, tensions are created that take the crystal out of the state of a complete network structure. makes This is a serious problem, especially in the case of Si, which has a high melting point and tends to stick to the materials of the melting pot. An alternative method, which overcomes this problem, involves pulling the crystal from the melt as it grows. In this method, a crystal grain is placed inside a molten material and is slowly pulled up, allowing the crystal to grow on the grain. Usually, during growth, the Ylor is rotated slowly to moderate any temperature changes (which lead to impossible freezing) in addition to gently stirring the melt. This method, which is called the Chukralsky method, is widely used in the growth of Si, Ge and some compound semiconductors [3]. 1-3-1-2-crystalline silicon solar cells These cells can be divided into two categories depending on the crystal structure of silicon: single-crystal silicon solar cells and multi-crystalline silicon solar cells. In the second category, polycrystalline silicon is used as an active semiconductor.