ApPENDIX A The Electron Volt Before we discuss the electron volt (e V) let us go over the following phe­ nomenon without the use of that unit. When a potential difference exists between two points, and a charged particle is in that field, a force is exerted on this particle by the electric field. An example of this is the beam of electrons in a TV picture tube. Each electron in this beam is accelerated by the force exerted on it by the electric field. As it is accelerated its kinetic energy is increased until it is maximum just prior to striking the screen at the front of the picture tube. When it strikes the front of the picture tube this energy must be conserved so the kinetic energy is converted into the form of electromagnetic energy or x rays. One problem is to find a description of the emitted x-ray photon. Let us assume that the accelerating voltage in the TV picture tube was 20 kV. Without the use of the electron volt as a unit the following units would be required in this calculation: 1. The charge on an electron (q) = 1.602 x 10- 19 coulomb. 2. Planck's constant (h) = 6.547 x 10-27 erg-second. 3. One angstrom (A) = 1 x 10- 10 meter (used to measure the wavelength of light). 4. The velocity of light (C) = 3 x 1010 cm/s. The force on an electron, due to the presence of an electric field, can be ex­ pressed as qE, where q is the charge on an electron and E is the potential differ­ ence, in volts, between the two points, divided by the distance between the two points, in meters. Therefore the units for E are volts/meter. The equation for that force including the units would be F = qE volts joule ) = coulombs x ( (A.1) meter but a volt = couomI b joule = coulombs x -~===--­ coulomb meter 302 The Electron Volt 303 F _ joule (but a joule = newton meter (NM)) (A.2) - meter newton meter (or newton which is a unit of force) = meter If an electron is accelerated across this field it will acquire an energy equal to the work done on it by the electric field, or the force x distance (work = F x s). Notice that when the answer to Eq. (A.2) is multiplied by the distance across the electric field in meters, the unit "meter" is canceled and the kinetic energy is in joules. Therefore, the distance across the electric field does not enter into the calculation of the kinetic energy of the electron due to its acceleration by the electric field. Only the potential difference or voltage across the field is needed for the calculation. Therefore, the energy given to the electron by the electric field would be q V, where q is the charge on the electron stated above and V is the potential difference or volts across the field. This gives the energy of the x ray in joules. However, x rays are usually described by the wavelength in angstroms. The energy of a photon of electromagnetic radiation is expressed as: Energy =hv (A.3) In this expression h is Planck's constant, given above, and v (nu) is the fre­ quency of the radiation, or in this case the x ray. Now we substitute the calculated energy and the value for h in Eq. (A.3) and solve for v. Since x rays are defined by their wavelength in angstroms, it is necessary to divide the velocity of light (C) by the frequency (v), found above, in order to determine the wavelength of the emitted x rays and then convert this wavelength to angstroms. It is evident that the description of the x ray emitted as a result of accelerated electrons would be quite complicated if basic units were used in the calculations. Now let us use the electron volt (eV) unit in describing the same action. The electron volt is defined as the energy given to an electron when accelerated by a potential difference of one volt. Therefore if the high voltage applied to a TV picture tube is 20 kV, then the energy of the electron when it collides with the front of the picture tube would be 20 ke V. Therefore the energy of the x ray emitted by the TV tube above would be 20 keV. Thus, the electron volt is a very convenient unit to use when discussing electrons and electric fields. The descriptions of x- and y-radiation are now given as energy in kilo­ electron-volts or mega-electron-volts as well as the wavelength in angstroms. The wavelength is often of interest to physicists, but for others a knowledge of the energy of radiation is of more interest than its wavelength. Although other charged particles can be accelerated by electric fields, the electron is the particle of interest for most electronics students. When a beam of electrons is accelerated by a high voltage the energy of the x ray is determined by the magnitude of the high voltage. ApPENDIXB Current in Semiconductors Electrical current in a solid conductor is considered to be a movement of electri­ cal charges in that solid. How could a particle such as an electron move through something that was solid? The Bohr model of an atom uses the concept that it is composed of a dense nucleus containing a number of protons that carry positive charges and neutrons that are uncharged. Strong nuclear forces bind these components in the nucleus. Located outside the nucleus, at different distances from it, are the same number of electrons carrying negative charges as there are protons in the nucleus. Coulombic forces between the opposite charges bind the electrons to the atom. The following analogy is sometimes used as a description of an atom. Attach a basketball to a rope a quarter mile long and swing it in circles around your head. Your head would represent the nucleus of the atom and the basketball would represent the innermost electrons outside the nucleus. Although the sizes of the objects and the distances involved may not be proportional, this analogy indicates that an atom is composed in the most part by open space and is not really solid. Therefore it would be easy for electrons to pass through the atoms without colliding with other electrons or the nucleus. In Chapter I, the diameter of a silicon atom was calculated to be approxi­ mately 3 x 10-8 cm. In the Chemistry and Physics Handbook the diameter of an electron is estimated to be in the order of 10-13 cm and the nucleus of an atom to be between 10-13 cm and 10-12 cm. These figures indicate that the nucleus of an atom and its electrons occupy a very small part of the total atomic space and that the nucleus must be very dense. Since there is a Coulombic force of attraction between an electron and the nucleus, another force would be required to move it farther from the nucleus. When a force on an object moves it through a distance, then work is done on the object. Work =F x s. Work done on an object increases its kinetic and/or poten­ tial energy. Therefore the electrons that are farthest from the nucleus have the most energy. The outermost electrons are said to be in the valence band. The word "valence" is derived from the Latin word "valere" which means "to be strong." When sufficient additional energy is given to enough of these valence electrons they can break loose from the atoms and become free electrons and thus 304 Current in Intrinsic Semiconductors 305 become available to move as electrical current. These electrons are then said to be in the conduction band of energies. Current in Intrinsic Semiconductors Intrinsic semiconductors, such as silicon and germanium, have very few free electrons at low temperatures. The application of heat is one method of giving additional energy to an atom. Part of this energy becomes vibrational energy of the atom as a whole and part is transferred to the electrons. As the temperature of the semiconductor rises many of the valence electrons become free, or move into the conduction band, and then are available to move as electrical current. Thus the silicon or germanium becomes a better conductor of electricity. When a va­ lence electron becomes free, it leaves behind a hole in the crystal lattice. This hole would have an attraction for an electron so it would act like a positive charge. Thus we say that electron-hole pairs are formed. This hole may be filled in one of two ways. A free electron may move into it. In this case the hole dis­ appears. This action is called recombination. This hole may also be filled by an­ other valence electron moving into it. In this case the hole would move to the location that the valence electron left when filling the original hole. This would constitute hole current which would be the movement of holes or positive charges. There are two general types of movement of the electrons and holes, diffusion and drifting. Diffusion can be described by the following analogy. Suppose that you have a rectangular tank that is filled with water and has a permeable mem­ brane separating it into two equal parts. On one side of this membrane pour a solution of salt water (sodium chloride) and on the other side pour a solution of potassium chloride. If you let the tank remain unmoved for a few hours and then test the liquid on both sides of the membrane you would find that each of the two solutions is distributed about equally throughout the tank on both sides of the membrane.