Semiconductor

Introduction

 Have you ever thought about how semiconductors make your life easier. Did you know that semiconductor effects exist in every step of daily life? There is no doubt that semiconductors are constantly changing the world. We are constantly using semiconductors every moment. The device you have right now is also made of semiconductors. We come across many devices made of these semiconductors such as mobile phones, telephones, TVs, laptops etc. The term semiconducting was first used by Alessandro Volta in 1782. According to many, the semiconductor was born around 1874 with the invention of the rectifier. Around 1946, the University of Pennsylvania developed a computer using a vacuum tube. Using vacuum tubes is huge and requires huge amounts of electricity. John Bardeen and Brattain invented the point-contact transistor at Bell Labs in America in 1947. After this, William Shockley invented the junction transistor in 1948, the transistor was introduced. Through which the calculator (computer) becomes smaller in size. In 1956, William Shockley, Bardeen and Brattain jointly won the Nobel Prize in Physics for their contributions to semiconductors and transistor research and development. The semiconductor industry continued to expand rapidly after the invention of the transistor. In 1957 it was already 100 Jack Kilby invented the bipolar IC, this invention was a breakthrough in the history of semiconductors. The semiconductor industry has reached another stage of world-shaking, it is widely used all over the world due to its small size and light weight. Semiconductor devices are the foundation of the electronics industry, which is the largest industry in the world, with global sales of over one trillion dollars since 1998. Figure shows the sales volume of the semiconductor device-based electronics industry in the past 20 years and projects sales to the year 2010. Also shown are the gross world product (GWP) and the sales volumes of the automobile, steel, and semiconductor industries.' Note that the electronics industry surpassed the automobile industry in 1998. If current trends continue, the sales volume of the electronics industry will reach three trillion dollars and will constitute about 10% of GWP by 2010. The semiconductor industry, a sub set of the electronics industry, will grow at an even higher rate to surpass the steel industry in the early twenty-first century and to constitute 25% of the electronics industry in 2010.

 

 

 Definition of Semiconductor? 

A semiconductor is a material which has an electrical conductivity value falling between that of a conductor, such as copper, and an insulator, such as glass. Its resistivity falls as its temperature rises; metals behave in the opposite way.

 

Semiconductor in Equilibrium

                                        • Energy bands

                                        • Intrinsic and Extrinsic Semiconductor

                                        • Fermi levels

                                        • Electron and Hole concentrations

                                        • Temperature Dependence of Carrier and Invariance of Fermi level

SEMICONDUCTOR MATERIALS

•Semiconductors are a group of materials having conductivities between those of metals and insulators. Two general classifications of semiconductors are the elemental semiconductor materials, found in group IV of the periodic table. and the compound semiconductor materials, most of which are formed from special combinations of group III and group V elements.

Table 1 shows a portion of the periodic table in which the more common semiconductors are found and Table 2 lists a few of the semiconductor materials.

Table 01. A portion of the periodic table 

Table 02. List of some semiconductor material 

i) Elemental semiconductors 

•  Silicon          Si
• Germanium   Gi 

ii) Compound Semiconductors 

• Aluminum phosphide         AIP
• Aluminum arsenide AIAS
• Gallium phosphide Gap
• Gallium arsenide GaAs
• Indium phosphide           InP

ALLOWED AND FORBIDDEN ENERGY BANDS

In the last chapter, we considered the one-electron, or hydrogen, atom. That analysis showed that the energy of the bound electron is quantized: Only discrete values of electron energy are allowed. The radial probability density for the electron was also determined. This function gives the probability of finding the electron at a particular distance from the nucleus and shows that the electron is not localized at a given radius. We can extrapolate these single-atom results to a crystal and qualitatively de- rive the concepts of allowed and forbidden energy bands. We will then apply quantum mechanics and Schrodinger's wave equation to the problem of an electron in a single crystal. We find that the electronic energy states occur in bands of allowed states that are separated by forbidden energy bands.

Formation of Energy Bands

Figure a. shows the radial probability density function for the lowest electron energy state of the single, noninteracting hydrogen atom, and Figure b shows the same probability curves for two atoms that are in close proximity to each other. The wave functions of the electrons of the two atoms overlap, which means that the two electrons will interact. This interaction or perturbation results in the discrete quantized energy level splitting into two discrete energy levels, schematically shown in Figure c. The splitting of the discrete state into two states is consistent with the Pauli exclusion principle.

A simple analogy of the splitting of energy levels by interacting particles is the following. Two identical race cars and drivers are far apart on a race track. There is no interaction between the cars, so they both must provide the same power to achieve a given speed. However, if one car pulls up close behind the other car, there is an interaction called draft. The second car will be pulled to an extent by the lead car. The lead car will therefore require more power to achieve the same speed since it is pulling the second car, and the second car will require less power since it is being

 (a) Probability density function of an isolated hydrogen atom. (b) Overlapping probability density functions of two adjacent hydrogen atoms. (c) The splitting of the n = 1 state.

Figure: The splitting of an energy state into a band of allowed energies.

pulled by the lead car. So there is a "splitting" of power (energy) of the two interacting race cars. (Keep in mind not to take analogies too literally.)

Now, if we somehow start with a regular periodic arrangement of hydrogen-type atoms that are initially very far apart, and begin pushing the atoms together, the initial quantized energy level will split into a band of discrete energy levels. This effect is shown schematically in Figure 3.2, where the parameter re-presents the equilibrium interatomic distance in the crystal. At the equilibrium interatomic distance, there is a band of allowed energies, but within the allowed band, the energies are at discrete levels. The Pauli exclusion principle states that the joining of atoms to form a system (crystal) does not alter the total number of quantum states regardless of size. However, since no two electrons can have the same quantum number, the discrete energy must split into a band of energies in order that each electron can occupy a distinct quantum state.

We have seen previously that, at any energy level, the number of allowed quantum states is relatively small. In order to accommodate all of the electrons in a crystal, we must have many energy levels within the allowed band. As an example, suppose that we have a system with 1019 one-electron atoms and also suppose that, at the equilibrium interatomic distance, the width of the allowed energy band is 1 eV. For simplicity, we assume that each electron in the system occupies a different energy level and, if the discrete energy states are equidistant, then the energy levels are separated by 10-19 eV. This energy difference is extremely small, so that for all practical purposes, we have a quasi-continuous energy distribution through the allowed energy band. The fact that 10-19 eV is a very small difference between two energy states can be seen from the following example.

Consider again a regular periodic arrangement of atoms, in which each atom now contains more than one electron. Suppose the atom in this imaginary crystal contains electrons up through the n = 3 energy level. If the atoms are initially very far apart, the electrons in adjacent atoms will not interact and will occupy the discrete energy levels. If these atoms are brought closer together, the outermost electrons in the n = 3 energy shell will begin to interact initially, so that this discrete energy level will split into a band of allowed energies. If the atoms continue to move closer together, the electrons in the n = 2 shell may begin to interact and will also split into a band of allowed energies. Finally, if the atoms become sufficiently close together, the innermost electrons in the n = 1 level may interact, so that this energy level may also split into a band of allowed energies. The splitting of these discrete energy levels is qualitatively shown in Figure If the equilibrium interatomic distance is Ro, then we have bands of allowed energies that the electrons may occupy separated by bands of forbidden energies. This energy-band splitting and the formation of allowed and forbidden bands is the energy-band theory of single-crystal materials.

The actual band splitting in a crystal is much more complicated than indicated in Figure 3schematic representation of an isolated silicon atom is shown in Figure 3.4a. Ten of the 14 silicon atom electrons occupy deep-lying energy levels close to the nucleus. The four remaining valence electrons are relatively weakly bound and are the electrons involved in chemical reactions. Figure 3.4b shows the band splitting of silicon. We need only consider the n = 3 level for the valence

electrons, since the first two energy shells are completely full and are tightly bound to the nucleus. The 3s state co responds to n = 3 and /= 0 and contains two quantum states per atom. This state will contain two electrons at T = 0 K. The 3p state corresponds to n = 3 and /= 1 and contains six quantum states per atom. This state will contain the remaining two electrons in the individual silicon atom.

As the interatomic distance decreases, the 3s and 3p states interact and overlap. At the equilibrium interatomic distance, the bands have again split, but now four quantum states per atom are in the lower band and four quantum states per atom are in the upper band. At absolute zero degrees, electrons are in the lowest energy state, so that all states in the lower band (the valence band) will be full and all states in the

 Allowed and Forbidden Energy Bands

upper band (the conduction band) will be empty. The bandgap energy E, between the top of the valence band and the bottom of the conduction band is the width of the forbidden energy band.

We have discussed qualitatively how and why bands of allowed and forbid- den energies are formed in a crystal. The formation of these energy bands is directly related to the electrical characteristics of the crystal, as we will see later in our discussion.