Digital Electronics.pdf

INTRODUCTION

Electronics is heavily relied on by most other areas of electrical engineering. While there is a

considerable body of theory in communications, controls, etc., these areas ultimately use

electronics to actually implement the functions.

Electronic circuits use electronic devices to perform functions on signals such as amplification,

filtering, rectifying, switching, etc.. Electronics has been a major topic of study in Electrical

Engineering for nearly a century. Early electronic circuits used devices such as spark gaps and

point-contact crystal diodes to perform signal processing. Later on, vacuum tubes were

invented which made electronic communications and control systems widely available. In the

late 1940’s, semiconductor devices such as diodes and transistors became available which

created an electronics revolution. With these changes in technology, the study of electronics did

not change significantly, only the devices changed. The circuits and the methods did not change

substantially.

The study of electronics can be roughly divided into two areas, devices and circuits. The study

of devices is concerned with physical processes such as electron flow while the study of circuits

emphasizes using the devices in applications and signal processing functions. The study of

electronic circuits is further subdivided into analog, or linear, and digital, or switching,

electronics. This course focuses on digital electronic circuits.

By far, the greatest use of digital electronic circuits occurs in digital computers. Logic circuits

are widely available from simple logic gates in small-scale integrated (SSI) circuits to very

complex digital functions in very large-scale integrated (VLSI) circuits. In almost all digital

circuits, transistors and diodes operate in two modes, on or off, carrying current or not carrying

current; in essence, a switch. We will look at how digital logic circuits operate and what the

terminal characteristics and manufacturer’s specifications mean. We will then look at how to go

beyond the logic circuits with interfaces both at the inputs and outputs.

We begin this course with a brief discussion of semiconductor materials and pn junctions. This

material is neither rigorously developed nor complete. A rigorous study of semiconductor

electronics is left for later. However, to effectively use semiconductor devices, it is necessary to

have a basic understanding of how they work.

Because electronic devices are non-linear, we will look at their terminal characteristics and

make circuit models of the devices that will allow us to use to linear circuit analysis techniques to

analyze the circuits. We will then look at application of semiconductor devices in switching

circuits including logic gates, interface circuits, and special applications. Many electronic systems

involve both analog and digital circuits and during this course, we will look at some of these

cases requiring a mixture of applications. The ultimate test of understanding the material of this

course will be found in the design exercises.

Introduction

Chapter 1

Semiconductors

THE ELECTRON IN ELECTRIC FIELDS

If we were to take two parallel plates and connect a voltage source across them as shown

in Figure 1, an electric field would be set up between the plates. Neglecting fringing

around the edges, the electric field would be uniform everywhere between the plates. The

electric field strength would be

E = /d

(1)

where V is the applied voltage and d is the distance between the plates. Thus, the electric

field strength E has the units volts per centimeter and is a vector quantity going from a

positive charge to a negative charge. Note: CGS units are normally used in

semiconductor physics - centimeters, grams, seconds.

Now if a tiny person, let's call her Millie Micron, was able to carry an electron into the

region between the plates and release it as shown in Figure 2, the electron would be

attracted to the positive plate and repelled by the negative plate. The force on the electron

would be

F x = -q E x

(2)

where q is the electronic charge. The negative sign occurs because the electron is

accelerated in the negative x direction, toward the positive plate. Of course, the electron

would obey Newton's laws and the acceleration, a x , would be a function of the mass of

the electron, m, and the force exerted by the electric field,

F x = -ma x

(3)

Semiconductors

Chapter 1

Figure 2. Millie releasing an electron

within the electric field

As the electron accelerates, it gains kinetic energy. Just as with objects with mass in a

gravitational field, the electron in an electric field has potential energy that can be

converted to kinetic energy. The total energy then is

W = U + 1/2mv 2

(4)

where U is the potential energy and v is the velocity. The energy associated with a single

electron is quite small compared to units we normally work with so we use the units

electron volts defined as moving one electron across a potential difference of one volt.

1 eV = 1.602 x 10 -19 joules (1 joule = 1 watt second)

The electronic charge is 1.602 x 10 -19 coulombs (ampere-seconds).

In our example, if the voltage source is 5 volts and Millie released the electron at the

negative plate, the electron would gain five electron volts of energy as it fell to the

positive plate. At that point it would have zero potential energy. Thus, at the point of

release, the electron had a potential energy of 5 eV. This 5 eV would be converted to

kinetic energy by the time it arrived at the positive plate.

To look at this another way, let's look at a plot of the electric potential within the field.

We will assume the positive plate is grounded and at zero potential. The negative plate is

at negative five volts with the potential changing linearly in between as shown in Figure

3. In this example, let's assume Millie is standing on the positive plate and throws the

electron toward the negative plate. If she throws it gently, it will start with only a small

kinetic energy which is soon converted to potential energy as the electron goes against the

electric field. When all the kinetic energy is converted to potential energy, the electron

has zero velocity. The electric field accelerates the electron back toward the positive

plate. The effect is that the electron falls back to Millie and she catches it. If she then

throws it again, but this time a little harder, it will go further, but will again fall back.

Say, this is a neat game isn't it?. This is similar to throwing a ball up a sloping roof and

Semiconductors

Chapter 1

catching it as it rolls back down. Just as with the roof, if Millie throws the electron hard

enough, it will overcome the potential hill and escape. In this case, we must envision the

negative plate as having lots of holes, like a wire screen, the electron can go through to

escape; for example. This potential barrier concept will be used when we look at p-n

junctions.

Figure 3. Illustration of the potential energy barrier.

ELECTRON EMISSION FROM THE METAL

Now, we can describe current flow between two metal plates. If a voltage is applied

across the two metal conductors with just vacuum in between the two conductors,

obviously no current flows between the two plates in the vacuum. There will be an

electric field (E = V s /x, where x is the distance between the two plates) dropped across

two conductors. Charge builds up on each surface of the metal conductors that are facing

each other. On one conductor, the cathode, electrons collect on the surface. On the other

conductor, the anode, electrons are repelled from the surface, leaving the fixed metal ions

at the surface. If a strong enough voltage (or a sufficiently high electric field) is applied,

the electrons have a total energy equal to the vacuum energy, E vac . The electrons at the

surface of one metal conductor will be ripped out of the conductor and then move to the

anode. And, current does flow across the vacuum!

This is called thermionic emission, a process by which tungsten filaments emit beams of

electrons in cathode ray tubes for television, oscilloscope screens, and other instruments.

The electric field required to rip the electrons out of the metal and into the vacuum is

equal to q

m , where

When additional energy is added to the system, for example by heating the metal, the

kinetic energy of the electrons in the metal is increased and the electric field required for

Semiconductors

m is the work function of the metal and q is the charge on an

electron. Different metals have different work functions. So, some metals work better

than others as “electron guns”.

Chapter 1

thermionic emission is decreased. Thus, there are some “electron guns” that are called

cold cathode emitters and others called hot filament emitters, denoting the temperature of

the metal from which the electrons are escaping. The tungsten filament in your television

is a hot filament emitter, running at over 2500K. Cold cathode emitters are used when a

high temperature filament is impractical in the system. The cold cathode emitters are

being researched for thin film displays and other applications where the system can not

handle a large thermal gradients.

CURRENT CONDUCTION IN METALS

Metal atoms have one or more very loosely bound valence electrons. These are the

electrons in the outer most orbital or electron shell, in an s or d orbital. At normal

temperatures, the valence electrons have enough thermal energy to be easily separated

from the metal atom and move randomly throughout the material. The metal atom, then,

becomes a positively charged ion. Figure 4 is a two-dimensional representation of the

situation where the electrons are free and the metal ions are immobile. The material still

has zero net charge as there are still as many electrons in the metal as there are positive

charges on the metal ions. In its random motion, an electron occasionally collides with a

metal ion, but with its thermal energy, it is not captured and rebounds at a random angle.

The motion of electrons in metal described here is similar to the motion of molecules in

gas. Thus, it is called the electron gas model.

metal ion

- free electron

If we were to average the motion or velocity of the electrons in the metal in Figure 4, we

would find zero net motion and zero average velocity. However, if we were to apply a

voltage between the ends of the metal conductor, a field would be set up between the ends

of the conductor and the electrons would be accelerated toward the positive end. Thus,

there is a drift of electrons in the conductor toward the positive end and a current results.

This current is called drift current. The average speed at which the electrons drift is

called the drift velocity, v d . It seems as though the electrons might continue to accelerate

in the field and reach very high velocities, but instead, the electrons soon collide with a

fixed ion and recoil in a random direction, to again be accelerated by the field. Therefore,

the electron's drift velocity reaches a maximum at some electric field and does not

increase any further with increasing electric field. This is called the saturation velocity.

The drift velocity under low field conditions, when the drift velocity is well below the

Semiconductors

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