Resistivity and Doping
Embedded systems—or even modern electronics in general—couldn’t exist without semiconductor technology. In this new article series, George delves into the fundamentals of semiconductors. In Part 1, he examines the math, chemistry and materials science that are fundamental to semiconductors, with a look at the basic structures that make them work.
Without semiconductors, there would be no electronics as we know them today. With that in mind, I want to cover some basic concepts in semiconductors, starting with resistivity and doping. But first I want to take a few steps back into the history of semiconductors and talk about their early days. A great many scientists participated in the development of semiconductors. Thomas Johann Seebeck was the first to describe semiconductor behavior as early as 1841. And the lineup seems endless, including Michael Faraday, Alexandre Becquerel, Walter H. Schottky, William Shockley, Herbert Mataré and many others.
To compare different materials and their electrical properties, a material-specific resistance called “resistivity” has been introduced. It is designated by the symbol ρ (Greek letter Rho), expressed in Ohm-meters (Ω-m) and specified at 20°C (68°F) unless otherwise noted. All materials can be characterized by their electrical resistivity, among other properties. Resistivity, however, depends not only on the material being measured but also on its temperature and other factors.
Conductivity is sometimes used instead of resistivity. It is the inverse value of resistivity, that is 1/ρ. Materials can be divided into three major categories: conductors, semi-conductors and insulators. Figure 1 depicts resistivity ranges of the three groups.
What makes electrical current flow in a material? The two fundamental mechanisms are the movement of ionized atoms and the movement of electrons in the material. The former can be seen in electrolytes, whereas the latter is what is happening in conductors and semiconductors.
Electrons are fundamental building blocks of atoms, with their mass of 9.1×10-28 g. They carry negative charge q of 1.602×10-19 C (Coulombs). All conductors contain a quantity of free electrons. Due to thermal oscillations, the electrons move around in a chaotic way. Their collisions with atoms alter their trajectories and speed, but when there is no electric or magnetic field present, they travel in straight lines at constant speed.
The time between two collisions τ and the speed at which the electron travels ν determine the distance L the electron has traveled:
The overall motion of the electrons causes no electrical current to flow, because the sum of all the electron motions in many directions add up to zero. However, in the presence of an external power field, such as an electric field, electrons are accelerated in the direction of the field. The increase in their speed νd is quite small, corresponding to a fraction of a percent of the original speed ν. If the concentration of free electrons per cubic centimeter (cm3 = 0.061 cubic inches) is n, then n × νd electrons move through a conductor with 1 cm2 (0.15 in2) cross section exposed to a constant power field every second. With νa being the average electron velocity increase, there will flow electric current of density J:
Conductors have very low resistivity—less than about 5×10-3 Ω-m. They contain an abundance of free electrons between their atoms. If there is a potential difference—that is, a voltage across the conductor—the free electrons travel through the material from the negative to the positive terminal. In other words, they cause an electric current to flow. The amount of electrons capable of flowing through the conductor depends on the conductor’s resistivity, which is, to some degree, affected by temperature.
Insulators generally are made of non-metallic materials with very few free electrons in their atomic structure. Therefore, they have high resistivity—typically one million Ω-m and higher. Insulators’ resistivity is mostly independent of temperature, although some materials, such as plastics, may disintegrate and lose their isolating characteristics when exposed to a high temperature.
Early semiconductors were made of germanium (Ge) but the most commonly used materials nowadays are silicon (Si) and gallium arsenide (GaAs). In terms of their resistivity, semiconductors are generally poor conductors as well as poor isolators, located between the two as shown in Figure 1.
Pure semiconductor materials, such as silicon, suffer from shortages of free electrons, because their atoms, arranged in a “crystal lattice,” have their valence electrons (those in the outermost orbit) mutually interlocked. Consequently, not many free electrons are available to conduct current, and the resistivity values are quite high. A crystal of pure silica, which is a silicon dioxide we know as glass, for example, is a good isolator (Figure 1).
By adding or replacing certain donor or acceptor atoms into the lattice—that is, by adding a tiny amount of another element into the base of chemically pure germanium or silicon—more free electrons or holes are generated. This, in turn, can enhance the semiconductor’s conductivity. Addition of impurities on the order of approximately one atom per ten million of Si or Ge atoms is called “doping,” and the doped element becomes a semiconductor. It should be noted that semiconductor characteristics, namely their resistivity, are affected by temperature, humidity, electric and magnetic fields, light, radioactivity, pressure and other factors.
As previously mentioned, the most prevalent base material used today is silicon. The silicon atom has 14 electrons orbiting its nucleus, four of which—the valence electrons—are in its outermost orbit, as shown schematically in Figure 2. Each atom shares those valence electrons with neighboring atoms, thus bonding to form a very stable crystalline structure, also known as a crystal lattice (Figure 3).
By doping the silicon base with certain impurities, we create positive and negative poles, allowing an electric current to flow. Arsenic (As), antimony (Sb) or phosphorus (P) are typical impurities introduced to the crystalline structure and sharing their outer electrons with the adjoining atoms. They have five valence electrons in their outer orbits and are, therefore, referred to as “pentavalent impurities.” Because only four of the silicon orbital electrons bond, one electron becomes free and will be able to carry current when a voltage is applied.
Because the arsenic, antimony or phosphorus elements donate free electrons, they are referred to as “donors.” Antimony and phosphorus are the most frequently used donors. The excess free electrons carry negative charges, and therefore, a doped semiconductor is called “N-type.” The electrons are majority carriers and the resulting holes are minority carriers. As a stimulus—a voltage, for example—frees the electrons from the silicon atoms, they are quickly replaced by the free electrons obtainable from the donors. Nevertheless, it still leaves more negatively charged electrons. For that reason, the N-type semiconductor contains more electrons than holes.
In contrast, a trivalent impurity used for doping has only three valence electrons in the outer orbit. Such impurities would be aluminum (Al), boron (B) or indium (In). Doping with these creates a shortage of electrons, and this provides the semiconductor with a lot of positively charged carriers known as holes. While electrons from the adjacent atoms try to fill the holes, they leave other holes behind. The result is that, we might say, the holes move a positive charge through the crystalline structure.
And because of the resultant shortage of electrons, the doped crystal structure becomes a positive pole. The trivalent impurities are also called acceptors, since they accept free electrons in the semiconductor crystal. Boron is frequently used to create this “P-type” semiconductor (Figure 4). Here the positive holes are the majority carriers and the free electrons are minority carriers. In contrast to the N-type semiconductor, the acceptor density is greater than its donor density, and there are more holes than electrons in the P-type semiconductor.
Now, let us consider what happens when a P and an N semiconductor are joined together to form a P-N junction. Immediately, some free electrons from the N-atoms begin to migrate across the junction and combine with the holes in the P-atoms, producing negative ions. This leaves positive donor ions in the N-material, to which holes from the P-material tend to migrate (Figure 5). Consequently, a thin layer of the P-type material along the junction contains negatively charged acceptor ions, while a thin layer of the N-type material on the opposite side of the junction becomes positive.
This movement of electrons and holes across the junction is called “diffusion.” The process continues until equilibrium is reached. A potential barrier around the junction is created and the regions on either side of the junction are depleted of any free carriers. This area around the P-N Junction is referred to as the “depletion layer.” The potential barrier depends on the materials used and on temperature, and is about 0.35 V for germanium and 0.7 V for silicon junctions. We perceive it as the forward voltage drop in specifications.
If we apply a positive voltage to the P-side of the junction and negative voltage to the N-side of the junction—that is, we apply a forward voltage—extra energy will be provided for the free electrons and holes to overcome the potential barrier, and electric current will flow.
When we connect the junction in a reverse polarity—that is, a positive voltage is applied to the N-type material and a negative voltage is applied to the P-type material—two things happen. The positive voltage attracts electrons toward the positive electrode and away from the junction, while the holes in the P-type material are also attracted away from the junction and toward the negative electrode. As a result, the depletion layer increases in width due to the lack of electrons and holes. Its impedance increases, almost becoming an insulator. The high potential barrier is thus created, preventing current from flowing through the junction.
I think that’s enough about electrons and doping for now. Next month we’ll continue this series, first taking a closer look at diodes, then at other devices comprising more than two P-N junctions.
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PUBLISHED IN CIRCUIT CELLAR MAGAZINE• SEPTEMBER 2019 #350 – Get a PDF of the Issue