Physical Principles of Semiconductors

Degree in Sound and Image Engineering

Fundamentals of Physics in Engineering I

Unit 8.- PHYSICAL PRINCIPLES OF SEMICONDUCTORS

• Types of solids for Ge. There are two types of current carriers in a There are various types of bonds between atoms; semiconductor, electrons and holes, and the total current however, in order to systematize their study two main is the sum of the currents due to each type of carrier. types of bonds are considered: (a) ionic (formed between a metal and a non-metal) and (b) covalent (formed • Intrinsic and extrinsic semiconductors between non-metals). In practice, no substance forms In pure semiconductors (intrinsic) conduction takes place totally ionic or totally covalent bonds and these two due to the electrons that are present simply because the types are extreme cases. material is purely crystalline (for example, Ge or Si) and From the macroscopic point of view a solid is a rigid or not due to the presence of impurities. The only way in elastic substance, that is, a substance that has an elastic which conduction may take place is to provide the behaviour under the influence of either hydrostatic forces electrons with an energy equal to or greater than EG – or strain and tension. thus enabling them to jump to the conduction band. This may be done by light or thermal excitation. Considering their structure, solids may be divided into two types: amorphous and crystalline. Solids may also be When minuscule quantities, of the order of one part per classified based on the predominant type of bond million, of the right impurities (different atoms) are between the atoms or ions making up the crystals. In this added to a pure semiconductor, the latter may exhibit classification, five types may be considered: covalent, electrical conductivity over a greater range of ionic, those with hydrogen bonds, molecular and temperatures (extrinsic semiconductor). This is known as metallic. doping. Thus, the electrical properties of a semiconductor may change drastically when small

• Energy bands. Conductors, insulators and semi- concentrations of donor impurities (n-type conductors semiconductor) or acceptor impurities (p-type semiconductor) are added. The concept of energy band is very useful for understanding various properties of solids such as • Semiconductor equation and electrical neutrality electric conductivity. Semiconductor equation When atoms join together to form a solid, their external Let n and p are the concentrations of free electrons and energy levels overlap giving rise to bands. At absolute holes in a semiconductor, respectively. In an intrinsic zero, insulators and semi-conductors have a full valence semiconductor, and due to thermal excitation, an electron band separated by a prohibited band of energy from an moves out of the valence band and leaves behind a hole, empty conduction band. the number of free electrons is equal to the number of In conductors, the occupied energy bands - valence and holes conduction bands (allowed bands) - are separated by n = p = ni = pi prohibited bands that can not be occupied. where ni and pi are the intrinsic concentrations of Only partially filled bands can give rise to electric carriers. In general, for any semiconductor, the processes currents in a solid when an electric field is applied. In the of electron€-hole pair generation and recombination are theory of bands, the difference between conductors and continuous, and an equilibrium is reached at each insulators thus resides in whether or not there are any temperature in which the product np is constant. Thus partially occupied bands. 2 2 n ⋅ p = n = p = constant (for fixed T and EG ) Silicon and germanium have the same external structure i i as carbon; thus they would be expected to have an This equation, known as the semiconductor equation or energy band diagram similar to that of diamond. mass action law, is essential when studying semiconductors and semiconducting devices and is valid However, since the energy gap EG between the valence € and conduction bands is small, when the temperature is for both intrinsic and extrinsic semiconductors in thermal raised some electrons in the valence band may acquire equilibrium. When there is no equilibrium, that is, when sufficient energy to jump to the conduction band. This n and p are governed by external conditions, the above enables an electric current to be created when an electric equation is not valid. field is applied, as in the case of a conductor. Therefore, such substances are called semiconductors. The condition of electrical neutrality The distinction between an insulator and a If a semiconductor is doped, the mass action law is not semiconductor resides solely in the value of EG. At sufficient to determine the concentration of carriers. In ambient temperature, EG is 1.12 eV for Si and 0.72 eV addition, it is necessary to include an expression that

links concentration and density of donor or acceptor (a) Electric conduction due to charge transport impurities. This expression is given by the electrical caused by applying a uniform electric field. neutrality condition: (b) Electric conduction due to diffusion of charge caused by the existence of a carrier gradient. [positive charges] = [negative charges] (c) The Hall effect, whereby application of a If Na denotes the concentration of acceptor impurities magnetic field gives rise to an electric field (that and N that of donor impurities (number of atoms per is, a potential difference). d unit volume), the electrical neutrality condition is written Since there are two types of charge carriers in a as: semiconductor (electrons and holes), the expression for displacement (or drift) current has two terms, one for p + N = n + N d a electrons and one for holes:   which is easy to understand considering the following J = e(nµ + pµ )E points: (a) The semiconductor is electrically neutral if no n p and so the conductivity of semiconductors is given by: external field€ acts upon it. (b) When donor and acceptor impurities are added, additional electrons and holes are σ = e(nµn + pµ p) present. (c) All the donor and acceptor impurities are € ionized. • Semiconductor devices • Transport phenomena in semiconductors When a € type p semiconductor is joined to a type n Charge transport phenomena may occur in a semiconductor a junction diode (p-n junction) is formed semiconductor due to either application of electric fields which is the basis for manufacturing semiconductor or the existence of carrier concentration gradients, that is, devices such as diodes or transistors. These devices play when the concentration varies depending on the position a fundamental role in modern electronics. in the semiconductor material. A diode contains a p-n junction, whereas a bipolar There are numerous types of transport phenomena but junction transistor contains two p-n junctions that may be only the following will be considered p-n-p or n-p-n.