An Introduction to the Physics and Electrochemistry of Semiconductors: Fundamentals and Applications

Preface

Life has made me realize that the best way to learn is to teach. During my 30 years of teaching at IIT Bombay as a professor in chemistry to MTech energy students, especially topics such as photovoltaic solar cells and photoelectrochemical (PEC) solar cells, I realized the necessity of writing a specific book so as to expose the students to the physics and electrochemistry of semiconductors, an understanding of which is needed to develop wet-type photovoltaic solar cells.

Physics and Electrochemistry of the Semiconductor and Its Application was written with a view to helping researchers and students understand the basics of physics in developing a PEC solar cell, including the electrochemistry of metals and semiconductors, a knowledge required for understanding the basic principles of a PEC cell. While dealing with PEC cells, it is also necessary to understand some specific electronic and electrochemical methods needed to interpret the equivalent circuits of a PEC cell. Finally, it is also necessary to study the various applications of PEC cells, in addition to generating electrical power from solar rays, such as carrying out certain one-step syntheses that conventionally may comprise more than a few steps. Application of photochromism is another area needing development, in which the least effort has been made by present-day researchers. Dye-sensitized solar cells are also becoming very popular. This science has developed many highly efficient solar cells, which are also discussed.

My effort has been to highlight some specific questions that are normally in the mind of the purchaser, such as the following.

What is the theme and scope of this book? This book was written with the intention of including only relevant topics in the fundamentals of the physics of semiconductors and of electrochemistry needed for understanding the intricacy of the subject of PEC solar cells. Readers interested in carrying out either teaching or research in the electrochemistry of semiconductors will find this book extremely handy.

What prompted the undertaking of writing this book? I had been teaching MTech students and MSc students of physics and chemistry at IIT Bombay, giving them the basic concepts of semiconductors, p:n junctions, PEC solar cells, electrochemistry of semiconductors, and photochromism. Students in this course were coming from various disciplines. It was very difficult to prescribe for them a suitable textbook, not because there are no books on these topics, but because they are either too exhaustive or very elementary. Students wanted something that dealt with the topics needed in their own specific fields. Faced with such a demand, I started writing this book, and students in my class found it very useful. I was enthused by this to further compile my lecture notes into book form.

What special features are covered? Students carrying out research or engaged in teaching PEC cells or knowledge of our sun, its energy, and its distribution to the earth will find essential topics such as the physics of semiconductors, the electrochemistry of semiconductors, p:n junctions, Schottky junctions, the concept of Fermi energy, and photochromism and its industrial applications. It is very difficult to get all this information into one book, but this book covers all these topics; hence this book could be considered many books in one. This book does not need a teacher to explain the subjects. Some examples are humorous in style, which helps the student relate to the topic. Students will like such examples because they will help them to remember the intricacy of the subject.

What new approaches are taken in this book? Most of the books dealing with these topics assume some minimum knowledge from students. Because I was teaching this subject to multidisciplinary students, I had to begin by assuming that students did not have a common knowledge base. This book does not need much by the way of basic concepts, because it starts almost from the beginning. I have noticed that students of my class like this approach.

This book is suitable as a textbook for students interested in learning these special topics at various levels, undergraduate or postgraduate, such as MTech, BTech, or MSc (chemistry and/or physics), and also for teachers from colleges, universities, and IITs. It will also be suitable for R&D industries dealing with electrochemistry, the physics of semiconductors, the electrochemistry of semiconductors/metals, photovoltaic solar cells, and photchromism and its applications.

Last, I would request readers to point out any misconceptions that either need more explanation or should have been corrected in some other suitable form or any mistakes which should be corrected in the next edition. This information will help me to improve the quality of the book in its second edition.

Maheshwar Sharon

Retd Prof IIT Bombay, India

[email protected]

[email protected]

July 2016

Chapter 1

Our Universe and the Sun

All forms of energy stored inside our planet or available throughout the earths atmosphere are a consequence of processes involved in forming the universe. The sun is the main source of energy for the earth; its energy sustains the evolution and growth of living beings. The ongoing survival of human beings on earth depends on the life of the sun. Therefore, before learning about methods for utilizing solar energy, it is appropriate to describe in brief how the universe, and consequently our solar system, was formed and the factors that control the release of solar energy. The processes by which this energy arrives at our planet also need to be understood.

1.1 Formation of the Universe

Many theories have been put forward to explain the formation of the universe [1]. However, none of these theories can be experimentally confirmed. One theory advocates that the universe was formed as it exists today. George Gamov, conversely, theorized the big bang, which proposes that the universe was originally concentrated into a very small volume and that its temperature was 10¹⁶ K. The radiation pressure in this volume increased so greatly that the universe exploded with a big bang. Masses started to move away from their point of reference. Finally, these masses took the shape of various planets, stars, and other bodies. The big bang is theorized to have occurred approximately 10¹⁰ years ago.

Many stars (on the order of 10¹¹) are believed to exist in our galaxy, the Milky Way, of which our sun is one. The name Milky Way is derived from the galaxy’s appearance as a dim, glowing band arching across the night sky in which the naked eye cannot distinguish individual stars. The term is a translation of the Latin via lactea. From Earth, the Milky Way appears as a band because its disk-shaped structure is viewed from within. The diameter of the Milky Way is approximated to be 10⁵ light-years. To appreciate the magnitude of the Milky Way’s diameter, it is worth mentioning that light takes 100,000 years to cross the galaxy from one end to the other. Within a radius of 2 × 10⁶ light-years from the Milky Way are approximately 15 galaxies, and the universe is approximated to contain 1 billion galaxies.

1.2 Formation of Stars

How can the big bang theory explain the formation of these stars? In the process of cosmic dust moving away from the nucleus of the big bang, a star (i.e., a sun) was formed by the mutual gravitational attraction of its constituents. The individual particles condensed from the cloud of cosmic dust and fell together to one central point. The particles’ kinetic energy increased as they moved toward the central point. Owing to this process, the size of the dust cloud started to decrease. The gravitational energy was converted into energy of motion, heating the interior of the star to a very high temperature (of the order of 2 × 10⁷ K). This high temperature initiated a thermonuclear reaction involving the burning of hydrogen. The fusion reaction of hydrogen thus became the source of the energy we experience as solar energy.

An explanation is needed as to why only stars accumulated hydrogen gas so that the fusion of hydrogen could release energy. According to the Vedas of Indian scripture, in the beginning of the formation of the universe were speed and sound, which collided to generate positive and negative charges. On collision of these charges, a great sound was made, which we know as the sound of om. This sound is like what we call the big bang, through which the universe was formed. It is also believed that the entire universe is moving toward one focal point. This means that when all materials meet at their destination point in space, there will be another big bang. Furthermore, according to the Vedas, there have been several collisions of the universe. This means that the universe has been formed several times and destroyed several times. Hindu philosophy also puts forth so-called satyug (when people believed in honesty), treta, dwyeta and kalyug. Kalyug will be an era when people will be very dishonest and the world will be destroyed, and when yug will start afresh. This comparison also suggests that there is great similarity between Western and Hindu philosophy.

1.2.1 Formation of Energy in the Sun

Now we shall discuss the formation and release of energy from the sun. The energy released within the core of the sun is a consequence of nuclear fusion. From the atomic weights of a proton and a neutron, it is possible to calculate theoretically the weight of any atom. For example, 1H² contains one proton and one neutron, so the weight of 1H² (Deuterium) should be the sum of the weight of one proton and one neutron, that is,

But the actual weight of 1H² is 2.01355 amu, which is lower than the added weight of one proton and one neutron by 0.0024 amu—this is known as excess mass. This weight (i.e., 0.0024 amu) is converted into energy (931 × 0.0024 = 2.23 MeV) to keep the proton and neutron together, which is known as the binding energy. The factor 931 is used to convert amu into MeV units. The binding energy per nucleon becomes 2.23/2 = 1.1172 MeV. In other words, this is the energy used up to keep hydrogen in its stable form. If this exercise is carried out with all elements of the periodic table and a graph is plotted between the binding energy per nucleon and the corresponding atomic number, one obtains a graph such as that shown in Figure 1.1.

Figure 1.1 Variation of binding energy per nucleon as a function of mass number.

The graph in Figure 1.1 suggests that 2He⁴ has the maximum weight difference among the lighter atoms. Likewise, Fe⁵⁶ has the maximum mass difference among the heavier atoms. This means that U²³⁸ is unstable in comparison to Fe⁵⁵ and that hydrogen is unstable in comparison to 2He⁴. When U²³⁸ is depleted to Fe⁵⁵, the difference in binding energy per nucleon of these materials is released as γ-rays along with a few nucleons. The process of such decomposition is known as a fission reaction. Likewise, four hydrogen atoms can be fused to get a helium atom, and the excess binding energy per nucleon is released in the form of γ-rays and a few other particulate radiations, such as β particles. This process is known as a fusion reaction. The fusion of hydrogen, which is the predominant reaction occurring in the sun, can take place by the following process:

(1.1)

(1.2)

or

(1.3)

or

(1.4)

where 1D² is known as a deuteron, an isotope of the hydrogen atom with two neutrons.

The net result is that four protons fuse to produce one 2He⁴ atom, and excess energy is released to form electromagnetic radiation, such as γ-rays. The excess energy released under this process can be calculated:

Thus the energy released in the hydrogen fusion reaction per four hydrogens is 25.7 MeV. A byproduct of the hydrogen fusion reaction is the formation of a helium atom. It is expected that hydrogen fusion reactions in the sun will occur for about 5 billion years. Once all of the hydrogen gas is converted into helium-4, fusion will stop, until the temperature rises to approximately 10⁸ K. At this temperature, helium-4 is converted into heavier elements, predominantly carbon-12 and oxygen-16, both of which are multiples of helium-4 in their proton and neutron compositions. The conversion of helium-4 into carbon-12 is therefore accomplished through the following two reactions:

(1.5)

(1.6)

It is interesting to realize that the temperature released in hydrogen fusion reactions to produce helium is much less than the temperature released in helium fusion to produce carbon, because the mass difference for the latter reaction is more than the mass difference for the hydrogen–helium process. As a result of this difference, the surface temperature of the sun rises during helium fusion. In addition, the wavelength of UV light produced by helium fusion is shorter than what has been observed with hydrogen fusion. Therefore global warming is the result of an increase in the sun’s temperature and not of industrialization, as some have advocated. Moreover, the depletion of the ozone layer is also a consequence of the shorter wavelengths of the UV light produced by helium fusion and is not due to factors that are being wrongly advocated.

1.2.2 Description of the Sun

The sun is a peculiar hydrodynamic object, with an equator rotating about its axis in 27 days, while the polar region rotates about this axis once every 31 days. Energy in the form of photons is generated in the interior of the sun, that is, near the core of the sun. About 1 × 10⁶ year is required for these photons to get transported from the core to the surface of the sun. This is because photons have to undergo a succession of radiative processes in which emission, absorption, and reradiation occur. The radiation that finally reaches the earth comes from a narrow, cooler surface region called the photosphere. This is a region of low-density (about 10–4 the density of air at sea level) ionized gases and is rather opaque to visible light. Outside the photosphere, almost three transparent regions are found. The first region (the reversing layer) is several hundred miles deep and contains much cooler gases. The next, thicker layer (the chromosphere) is about 6000 miles thick and has the same temperature as the photosphere. The last layer (the corona) is of low density and very high temperature (2 × 10⁶ K). These regions are shown in Figure 1.2. The sun is assumed to be a perfect radiator and emits at a temperature of about 6000 K. This radiation falls in the range of 300–2000 nm. The spectral distribution of energy emitted by the sun is of importance in the design and development of gadgets that run on solar energy.

Figure 1.2 A schematic of the various regions of the sun.

1.2.3 Transfer of Solar Rays through the Ozone Layer

Radiation emitted from the sun’s outer surface (i.e., its chromosphere) interacts with many types of particles before it reaches the earth. The first interaction takes place with ozone molecules some 10–20 miles above the earth’s surface. Ozone is a highly reactive molecule comprising three atoms of oxygen and is denoted by O3. It coexists in the upper atmosphere with two other forms of oxygen: molecular oxygen, O2 (which we breathe), and free elementary oxygen, O. The more energetic short-wavelength photons of solar radiation (having wavelength 0.32µ or less) are absorbed by O3 and O2 molecules, supplying the necessary energy to break the bonding forces and dissociate these molecules into O2 and O. The simpler forms of oxygen subsequently collide and react with other oxygen molecules to recombine to give O3 and O2. This type of reaction thus maintains the equilibrium concentration of ozone with O2 and O. This process, at the same time, helps to prevent short-wavelength radiation from reaching the earth’s atmosphere:

(1.7)

The ozone layer can be characterized as a steady state condition of dissociation and recombination. This is not to be confused with a state of perfect equilibrium, however. The ozone concentration in our atmosphere does vary with time and location. The passage of solar radiation through the ozone layer reduces the intensity of UV photons reaching the earth. This reduction in UV radiation minimizes its harmful effects, such as sunburn, skin cancer, and blindness. Some of the cosmic and X-ray radiation is also prevented from reaching the earth’s surface by the same absorption process. It is because of these factors that we are concerned with the destruction of the ozone layer. Helium fusion in the core of the sun produces radiation of higher energy than what is produced during hydrogen fusion. The higher energy of radiation is expected to disturb the ozone–oxygen equilibrium layer. As a result, the intensity of radiation arriving at earth will be of higher energy. This will cause an increase in temperature on the earth.

1.2.4 Transfer of Solar Layers through Other Layers

Solar photons, while penetrating into the earth’s atmosphere (i.e., into its stratosphere, which is 12–50 km from earth), interact with gas molecules. Photons undergo collision with gas molecules and are deflected, being scattered more or less uniformly in all directions. As a result, some photons are redirected away from earth into space. The scattering process affects photons of shorter (more energetic) wavelengths, including those at the blue end of the visible spectrum. That is why a clear sky appears blue. In addition, clouds, which cover almost 50 percent of earth’s surface, absorb or reflect approximately 80 percent of solar photons, especially those of longer infrared wavelengths.

In a tropical country like India, during summertime, hot winds blow dust from the surface of the earth into the atmosphere, where it exists as hanging dust particles. These dust particles reflect the sun’s radiation to the extent of the yellow region of the visible spectrum, making the sky appear yellowish in color during the summertime.

Thus the intensity of solar radiation that is finally received at the surface of the earth is much less than what is actually emitted by the sun.

1.2.5 Effect of Position of the Sun vis-à-vis the Earth

Another factor that reduces the intensity of the solar radiation reaching the surface of the earth is the angle and position at which the intensity of radiation is being measured. Light passing through the atmosphere in a direction perpendicular to the earths surface will encounter a minimum thickness on the way down and thus arrive at some maximum intensity. This is equivalent to the sun’s position at noon. As the angle of approach deviates from perpendicularity, the sunlight encounters more and more atmosphere, with a corresponding decrease in intensity. This is demonstrated by relatively weak sunlight intensity near sunrise and sunset.

1.2.6 Distribution of Solar Energy

Considering all these conditions, the solar intensity finally arriving at the earth’s surface can be evaluated; 1/(2000 × 10⁶) of total energy of the sun reaches earth (i.e., 1.7 × 10¹⁵ MW), of which 30 percent is reflected back into space, 47 percent is absorbed by the earth’s atmosphere, land, sea, and so on, and 23 percent is used up in processes such as evaporation and the rainfall cycle. Thus the actual energy reaching the surface of the earth is 7 × 10⁶ MW, of which only 0.004 percent is absorbed by earth’s plants and less than 0.5 percent is used for food production by photosynthesis processes.

The total distribution of solar energy that eventually reaches the earth has a spectrum as shown in Figure 1.3. The distribution of intensity for various wavelengths is found to be as follows: UV (200–400 nm) 8.7%, Visible (400–700 nm) 39.6% and near infrared (700–3500 nm) 51.7%.

Figure 1.3 A schematic spectrum of solar radiation reaching the surface of the earth approximate.

1.2.7 Solar Intensity Calculation

The atmosphere surrounding the earth is under dynamic conditions. Localized concentrations of different constituents of the earth’s atmosphere continuously shift and thus allow dissipation of continuously different amounts of the sun’s light to reach the surface of the earth at different times and locations. Predicting with precision the amount of sunlight that will occur at a specific location at a specific instant is impossible. Averages based on records of the past several years of weather behavior must therefore be employed to generate a rough estimate of the availability of solar radiation for any given region at any given time of the year.

However, superimposed on such unpredictability is a strong cyclic behavior caused by the motion of the earth, including the earth’s annual revolution around the sun, the earth’s daily rotation about its own axis, and the tilt of the earth’s axis with respect to the plane of the earth’s orbit. About 2 percent variation in solar intensity occurs because of the elliptical orbit of the earth, which is farthest from the sun in summer, that is, on June 21 (95.90 million miles), and closest in winter, that is, on December 21 (89.83 million miles). Earth’s equator is tilted 23.47° with respect to an imaginary but very precise plane in space. This plane is defined by earth’s orbit, and in turn, it defines the sun’s equator. As the earth circles the sun, a slight daily variation occurs in the angle between the earth–sun line (on the ecliptic) and the equatorial plane (of earth). This angle is called solar declination, δ, which varies continuously. The variation of δ causes the earth to present a slightly different face to the sun each day, and this motion is responsible for the seasonal changes in weather we all experience each year.

If one were to observe the motion of the sun from any fixed position on the earth’s surface for a sufficiently long period of time, the sun would be seen to exhibit regular patterns of daily movement across the sky. Of course, these patterns do vary gradually throughout the year. The position of the sun at any given instant can be defined fully using two angles that are measured from a fixed location (i.e., the point of our location on the surface of the earth). One of these angles is called the solar altitude, θ, and is measured vertically from the sun’s apparent position in the sky to the horizon directly below it (Figure 1.4). The horizontal angle described between this point on the horizon and the direction to true south is called the solar azimuth, θ. Solar altitude is the angle measured from the horizon vertically up to the sun; it is equal to O° when the sun is on the horizon and 90° when the sun is at its zenith (i.e., directly overhead). Solar azimuth (θ) is the angular distance of the sun from true north, measured clockwise around the horizon. It is equal to O° at the north point of the horizon, 90° at the east point, 180° at the south point, and 270° at the west point. The direction of true south should not be assumed as magnetic south, because this would be an error.