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The p-n Junction Diode

Contents

• Introduction
• Conduction in Solids
• Doped Semiconductors
• Current Flow in Semiconductors
• The P-N Junction
• Junction Diode Behaviour
• The Diode Equation
• Summary
• References

Introduction

The most basic property of a junction diode is that it conducts an electric current in one direction and blocks it in the other. This behaviour arises from the electrical characteristics of a junction, called a p-n junction. fabricated within a semiconductor crystal. The most commonly used semiconductor material is silicon. The junction diode is useful in a wide variety of applications including the rectification of ac signals (producing dc from ac), the detection of radio signals, the conversion of solar power to electricity, and in the generation and detection of light. It also finds use in a variety of electronic circuits as a switch, as a voltage reference or even as a tunable capacitor. The p-n junction is also the basic building block of a host of other electronic devices, of which the most well-known is the junction transistor. For this reason, a study of the properties and behaviour of the p-n junction is important.
In this chapter, the conduction of electricity in solids is reviewed first and the conduction properties of semiconductors are then explained. The construction of the p-n junction of an ideal diode is described and an explanation of the operation of the device is presented.

Conduction in solids

All matter consists of atoms. Each atom has electrons orbiting the nucleus. The nucleus contains the same amount of positive charge as the negative charge possessed by the orbiting electrons. The ability of any material to conduct electricity depends primarily on the behaviour of the electrons in the outer orbits. Therefore, it is necessary to review briefly some aspects of solid-state physics. This subject will be dealt with in more detail later in the course.

Conductors

In a metallic conductor such as copper, the atoms are arranged in a regular array called a crystal lattice. The electrons in the outer orbits of each metal atom are only loosely bound to the nucleus. These electrons are not closely associated with any particular atom and are free to move through the crystal lattice. Once an electron has left its orbit around a particular atom, that atom is left with an excess positive charge. The electron-deficient atom is called a positive ion. The electron that is now free to move is called a free electron. The free electrons in a conductor can be visualized as a cloud of electrons surrounding fixed positive ions as shown in Figure 1.
At normal temperatures, the ions possess energy and vibrate. Collisions between vibrating ions and free electrons cause the electrons to move in a random manner. Over a long period of time, the net motion of these free electrons is zero.
If an electric field is applied to the conductor, the free electrons will acquire additional energy and will tend to move in the direction dictated by the field. There will be a resulting net motion of free electrons. The net motion of charge carriers constitutes an electric current.

Insulators

In an insulator, nearly all electrons are very tightly bound to their respective atoms. There are practically no electrons that are able to move under the influence of an applied electric field. Therefore, an insulator cannot conduct any appreciable electric current under normal conditions.

Semiconductors

A semiconductor, such as silicon, has properties somewhere between those of a conductor and an insulator. The ability of a semiconductor to conduct electricity can be changed dramatically by adding small numbers of a different element to the semiconductor crystal. This process is called doping. Early experiments showed that an electric current through a semiconductor was carried by the flow of positive charges as well as negative charges (electrons).

Doped Semiconductors

A semiconductor crystal is called n-type if the addition of an impurity element results in a large number if free electrons (negative charge carriers) available for conduction. Each impurity atom is called a donor atom since it donates an electron. The electron is free to move and can contribute to an electric current. The positive ion left behind is fixed and cannot take part in conduction (see Figure 2).
A semiconductor crystal can be made p-type by doping it with a different element so that there are a large number of positive charge carriers available for conduction. The positive charge carriers actually correspond to vacancies or deficiencies of electrons in the bonds holding the atoms in the crystal lattice. The positive charges are called holes. These holes can move through the lattice as illustrated in one dimension in Figures 3(a) and 3(b). The dotted lines represent the crystal lattice.
Note that the movement of a hole is due to the movement of a bound electron from one bond to another. It is not due to the motion of freeelectrons.
In a p-type semiconductor, most of the mobile charge carriers are holes. A hole moving away from its host impurity atom is equivalent to the atom gaining or accepting an electron into its bonding structure. The host atom gains an excess negative charge and is then called anacceptor ion. This situation is illustrated in Figure 4.
Note again that the ions are locked in the crystal lattice and therefore reperesent fixed charges and cannot contribute to current. On the other hand, the holes are mobile charge carriers and can contribute to current flow.
Even in a highly doped p-type semiconductor there will always be some free electrons. This very small number of free electrons have been omitted in Figure 4 for clarity. Similarly, n-type semiconductors always contain some holes. The predominant mobile charge carriers are called majority carriers, whilst those in the minority are called minority carriers. For example, the majority carriers in n-type material are free electrons.
The terms majority carriers and minority carriers have meaning only if the type of semiconductor (n- or p-) is specified.
A pure or undoped semiconductor is said to be intrinsic. Such material has equal numbers of holes and free electrons. These carriers are produced as a result of thermal agitation of the atoms, even at room temperature. Some bound electrons can acquire sufficient energy to escape from their atoms, becoming free electrons and leaving holes behind., This process of producing hole-electron pairs is called thermal generation.
It is possible for a free electron and a hole to come near each other in the course of their random wandering through the crystal. The free electron can then occupy the vacant position represented by the hole. The hole and electron are said to recombine. There is then no mobile charge carrier at that point. The rate of recombination depends upon the number of carriers present.
Thermal generation and recombination occurs in both doped and undoped semiconductor material. When a semiconductor material is in thermal equilibrium, the rate of generation of hole-electron pairs equals the rate of recombination. The density or concentration of both holes and electrons then remains constant.

Current flow in Semiconductors

An electric current can flow through a semiconductor as a result of the movement of holes and/or free electrons. There are two important processes that account for current flow in semiconductors. These processes are called drift and diffusion.

Drift

Applying an electric field across a semiconductor will cause holes and free electrons to drift through the crystal in the directions shown in Figure 5.
The total current is equal to the sum of hole current (to the right) and electron current (tpo the left).

Diffusion

A drop of ink in a glass of water diffuses through the water until it is evenly distributed. The same process, called diffusion, occurs with semiconductors. For example, if some extra free electrons are introduced into a p-type semiconductor, the free electrons will redistribute themselves so that the concentration is more uniform. In the example shown in Figure 6, the free electrons will tend to move to the right. This net motion of charge carriers constitutes a diffusion current. (In Figure 6 the holes and acceptor ions are omitted for clarity.)
In this example, the free electrons move away from the region of highest concentration. The higher the localized concentration, the greater will be the rate at which electrons move away. The same process applies to holes in an n-type semiconductor.
Note that when a few minority carriers (such as the electrons in Figure 6) are diffusing through a sample, they will encounter a large number of majority carriers. Some recombination will occur. A number of both types of carrier will be lost.

The p-n Junction

Imagine that a p-type block of silicon can be placed in perfect contact with an n-type block. Free electrons from the n-type region will diffuse across the junction to the p-type side where they will recombine with some of the many holes in the p-type material. Similarly, holes will diffuse across the junction in the opposite direction and recombine, as shown in Figure 7.
The recombination of free electrons and holes in the vicinity of the junction leaves a narrow region on either side of the junction that contains no mobile charge. This narrow region which has been depleted of mibile charge is called the depletion layer. It extends into both the p-type and n-type regions as shown in Figure 8(a). Note that the diffusion of holes from the p-type side of the depletion layer leaves behind someuncovered fixed negative charges (the acceptor ions). Similarly, fixed positive charges (donor ions) are uncovered on the n-type side of the depletion layer. There is then a separation of charges: negative fixed charges on the p-type side of the depletion layer and positive fixed charges on the n-type side. This separation of charges causes an electric field to extend across the depletion layer. A potential difference must therefore exist across the depletion layer. The variation of potential with distance is shown in Figure 8(b).
The uncovered charges give rise to a built-in potential of $V\_i\_$ volts. For a typical silicon p-n junction,  to 0.7 volts. It varies with doping levels and temperature. The significance of this built-in potential is that it opposes the flow of holes and electrons across the junction. For this reason, the built-in potential is called a potential barrier or potential hill.
In practice, a p-n junction is formed within a single crystal rather than simply joining two pieces together. Electrical contacts on either side of the crystal enable connection to an external circuit. The resulting device is called a junction diode.

Junction Diode Behaviour

The most important property of a junction diode is its ability to pass an electric current in one direction only. If the diode is connected to a simple circuit consisting of a battery and a resistor, the battery can be connected in either of two ways as shown in Figures 9(a) and 9(b).
When the p-type region of the p-n junction is connected to the positive terminal of the battery, current will flow. The diode is said to be underforward bias. However, when the battery terminals are reversed, the p-n junction almost completely blocks the current flow. This is calledreverse bias. If the diode is not connected at all, it is said to be open-circuited and of course no current can flow through the diode.

Forward bias

The application of a forward bias voltage $V$ to a junction diode reduces the built-in potential from $V\_i\_$ to $V\_i\_\; -\; V$, as shown in Figure 10.
The reduction in the built-in potential is due to the applied voltage forcing more electrons into the n-type region and more holes into the p-type region, thus covering some of the fixed charges and narrowing the depletion layer. Since the total uncovered charge is reduced, the built-in potential must be lower. Remembering that the built-in potential opposes the flow of majority carriers across the junction, a reduction in that potential makes it easier for holes in the p-type region to cross the junction and for electrons in the n-type region to cross the junction in the opposite direction. As the forward bias voltage is increased, the current through the junction becomes greater. When the applied voltage $V$ approaches $V\_i\_$, the potential hill is almost removed. There is then little opposition to the flow of carriers across the junction and a large current can flow through the diode.
The variation of diode current with voltage under forward bias is shown in the first quadrant of a typical junction diode current-voltage characteristic shown in Figure 11.

Reverse Bias

The application of a reverse voltage $V\_R\_$ extracts holes from the p-type region and free electrons from the n-type region and so uncovers more bound charges near the junction, as shown in Figure 12. The depletion layer therefore widens and the height of the potential hill is increased to $(V\_i\_\; +\; V\_R\_\; )$ volts. Majority carriers are thereby firther inhibited from crossing the junction. As the reverse voltage is increased, the current is reduced to almost zero.
However, a very small reverse current does flow. This reverse saturation current depends only on the thermal generation of holes and electrons near the junction, not on the height of the potential barrier. In practice, this reverse saturation current is quite small but it increases with increasing temperature.

Junction Breakdown

The large increase in reverse current evident in Figure 11 is the result of junction breakdown. It occurs when the reverse voltage reaches a critical value.

The diode equation

A complete analysis of the abrupt p-n junction shows that that current $I$ varies exponentially with applied voltage $V$. The exact relationship between current and voltage is given by the diode equation
$I\; =\; I\_S\_\; (e^qV/kT^\; -\; 1\; )$ where $I\_S\_$ is the saturation current, $q$is the electronic charge, $k$ is Boltzmann's constant and $T$ is temperature (\(deK). The diode equation applies for both forward and reverse bias. At extremes of high forward bias and large reverse voltages the behaviour of practical devices deviate from the above diode law.
The diode equation is a very important description of diode behaviour and is the basis for the mathematical description of the behaviour of many other electronic devices which employ p-n junctions.
Exercise:
Derive an expression for the slope of the current-voltage characteristic of a forward-biased junction diode, and state how this slope can be related to the resistance of the diode.

Summary

1. Semiconductors contain two types of mobile charge carriers, holes and electrons. The holes are positively charged, the electrons negatively charged.
2. A semiconductor may be doped with donor impurities (n-type doping) so that it contains mobile charges which are primarily electrons.
3. A semiconductor may be doped with acceptor impurities (p-type doping) so that it contains mobile charges which are mainly holes.
4. There are two important mechanisms for current flow in a semiconductor:
5. • diffusion of carriers as a result of a concentration gradient; and
   • drift of carriers in an electric field.
6. At equilibrium, a built-in potential or potential barrier of $V\_i\_$ volts is developed across a p-n junction.
7. With the application of a forward bias voltage $V$, the built-in potential is reduced to $V\_i\_\; -\; V$, and current flows through the diode.
8. With the application of a reverse bias voltage $V\_R\_$, the height of the potential barrier is increased to $V\_i\_\; +\; V\_R\_$ and little current can flow.
9. The total diode current $I$ is related to the applied voltage $V$ by
10. $I\; =\; I\_S\_\; (\; e^\{\; q\; V\; /\; k\; T\; \}^\; -\; 1\; )$ where $I\_S\_$ is the reverse saturation current.