It is highly probable that you will use a laptop computer when doing the exercises in this book. If so, you may be interested to know that the central processing unit of your computer resides in a thin sliver of silicon, about 1 square centimetre in area. This small chip contains over 100,000,000 Si MOSFETs, each about a thousand times smaller than the diameter of a human hair! The slender computer that you nonchalantly stuff into your backpack has more computing power than the vacuum-tube computers that occupied an entire room when I was a student over 40 years ago.

When you are reading this book, you may be distracted by an incoming call on your cell 'phone. That may get you wondering what's inside your sleek ‘mobile’. If you opened it up, and knew where to look, you'd find some GaAs HBTs. These transistors can operate at the high frequencies required for local-area-network telecommunications, and they can deliver the power necessary for the transmission of signals.

Of course, a cell 'phone nowadays is no longer just a replacement for those clunking, tethered, hand-sets of not so long ago: it is also a camera and a juke box. The immense storage requirements of these applications are met by Flash memory, comprising more millions of Si MOSFETs.

Understanding Modern Transistors and Diodes is a textbook on semiconductor devices with three objectives: (i) to provide a rigorous, yet readable, account of the theoretical basis of the subject of semiconductor devices; (ii) to apply this theory to contemporary transistors and diodes so that their design and operation can be thoroughly understood; (iii) to leave readers with a sense of confidence that they are well equipped to appreciate the workings of tomorrow's devices, and to participate in their development.

There are many books on semiconductor devices, often with similar objectives, and it is reasonable to ask: why write another one? The answer is two-fold: firstly, after teaching and researching in the area for 40 years, I have a strong personal viewpoint on how the subject can best be presented to students; secondly, we are at a particularly interesting point in the development of the subject – we are at the micro/nano boundary for high-performance transistors, and we are on the threshold of seeing optoelectronic diodes make a contribution to our planet's sustainability.

These circumstances are new, and are quite different from those of 20 years ago when I was last moved to write a book on semiconductor devices. At that time the major development was the incorporation of thousands of transistors into monolithic integrated circuits.

Thermal equilibrium in a semiconductor refers to the state when the temperature is uniform and has been steady for a long time, and when there are no sources of energy other than heat, e.g., no applied electric field nor optical irradiation. Obviously, semiconductor devices will not be in thermal equilibrium when they are in operation. However, it turns out that parts of a device often remain in a state very close to thermal equilibrium and, furthermore, knowledge of the carrier concentrations in thermal equilibrium is often a good starting point for understanding how a device works.

In this chapter, we briefly discuss the collision processes that tend to randomize the momenta of excited electrons and holes, then we introduce the thermal-equilibrium distribution function, develop some useful expressions for the carrier concentrations in equilibrium, and finish by considering the mean thermal velocity associated with an equilibrium distribution of electrons. The last property is a further step towards developing an understanding of current in diodes and transistors.

Collisions

In the previous chapter, we showed how the processes of recombination and generation alter the carrier concentrations in the conduction and valence bands. Under thermal-equilibrium conditions, the thermally activated band-to-band and chemical generation processes are operative, along with one or all of the following recombination mechanisms: radiative, RG centre, Auger.

This chapter deals with temporal and spatial fluctuations in electronic devices, with strong emphasis on MOSFETs. The spontaneous fluctuations over time of the current and voltage inside a device, which are basically related to the discrete nature of electric charge, are called electrical noise. Noise imposes minimum values for the input signals of amplifiers and other analog circuits.

Time-independent variations between identically designed devices in an integrated circuit due to the spatial fluctuations in the technological parameters and geometries are called mismatch. Since digital and analog integrated circuits often rely on the matched behavior between identically designed devices, mismatch affects the performance of most integrated circuits.

Mismatch (spatial fluctuation) and noise (temporal fluctuation) are accuracy-limiting factors, both depending on the fabrication process, device dimensions, temperature, and bias. The shrinkage of the MOSFET dimensions and the reduction in the supply voltage of advanced technologies have made the consideration of matching and noise even more important for analog design. Consequently, we have included a detailed presentation of mismatch and noise so that they can be considered in the subsequent study of the basic circuits and building blocks. This chapter begins with a short summary of the various sources of noise. The general model for drain-current fluctuations in MOSFETs is then introduced, and the fundamental thermal- and flicker-noise models are developed. Small-dimension and high-frequency effects on thermal noise are considered. Design-oriented models for thermal and flicker noise are then presented.

The current mirror is one of the most useful building blocks for analog integrated circuits. It is largely employed as a biasing element and as a load device for amplifier stages. It can also find other uses such as arrays of current sources in D/A converters and current amplifiers in current-mode filters. Basically, a current mirror is a circuit that copies a current flowing through one active device (input) to another active device (output) of a circuit, keeping the output current independent of loading. Current mirrors, from their simplest version to more elaborate circuits, together with analysis of their characteristics, are the subject of this chapter.

A simple MOS current mirror

The ideal current mirror

The simplest configuration of the ideal current mirror is shown in Figure 5.1. Ideally, the current gain AI is independent of the input frequency, and the output current is independent of the output voltage; in other words, the output impedance is infinite. Additionally, the input impedance is zero, i.e., the voltage drop across the input device is zero for any input current. The ideal current mirror is equivalent to a two-port current-controlled current source having a common terminal that connects the input and output ports.

In the section that follows, we will present a first-order analysis of the current mirror implemented with a pair of MOS transistors.

The light-emitting diode (LED) is a pn-junction diode in which radiative recombination is encouraged to occur under forward-bias operating conditions. Thus, there is conversion of electrical energy to optical energy. In essence, the LED is the complement of the solar cell. In the example shown in Fig. 8.1, the internally generated photons escape through the top surface, which cannot, therefore, be covered entirely by the top metallic contact.

In the first part of this chapter, we develop an understanding of the LED by considering a number of efficiencies that relate to the various stages of the conversion of electrical energy to optical energy:

• voltage efficiency. This relates the applied voltage to the bandgap of the semiconductor. The latter would be chosen to obtain the desired colour of emitted light;

• current efficiency. This relates the current due to recombination in the desired part of the device to the current due to recombination elsewhere. Consideration of this efficiency leads to the heterostructural design that is a feature of modern, high-brightness LEDs;

• radiative efficiency. This relates to the relative amounts of radiative recombination and unwanted, non-radiative radiation. It leads to material selection (direct bandgap), and specifications on doping and purity;

• extraction efficiency. This relates to getting the photons out of the semiconductor in which they are generated. Consideration of this efficiency largely determines the substrate, contacts, and, in some cases, the shape of the device.

• […]

Analog integrated circuits in bipolar technology, beginning with operational amplifiers and advancing to data conversion and communication circuits, were developed in the 1960s and matured during the 1970s. During this period, the metal–oxide–semiconductor (MOS) technology evolved for digital circuits because of its better efficiency in terms of silicon-area use and power consumption compared with bipolar digital technologies. To reduce the system cost and power consumption, chips including digital and analog circuits appeared in MOS technology in the late 1970s. The first analog circuits in MOS technology were for audio-frequency applications. With the scaling of the MOS technology, driven by the need for large-scale integration levels, enhanced performance and reduced cost, even radio-frequency (RF) applications in MOS technology have become possible. Compared with digital design, analog design requires much more careful device modeling, and for this reason analog designers were at the origin of many MOS modeling enhancements.

The strong similarities between the basic operating principles of many bipolar and MOS analog building blocks and circuits have led some textbook authors to combine their presentation. On the other hand, there are profound differences between bipolar and MOS circuits in terms of the electrical performance and design approaches, and for this reason other texts focus only on MOS analog circuits. In this textbook we take this area of specialization a step further, focusing on analog MOS circuits at transistor level, using an accurate but simple MOS transistor model for design in order to reduce the distance between hand design and simulation results.

The first commercial bipolar junction transistors (BJTs) were made from germanium. Because of the low bandgap of this material (0.67 eV), the intrinsic carrier concentration is high. As ni increases exponentially with temperature (see (4.19)), these Ge BJTs were unstable, unless operating in a temperature-regulated circuit. Silicon, with its larger bandgap, proved to be a better proposition, and the first Si BJTs appeared in the early 1950s. These transistors ushered in the era of solid-state electronics. They were not challenged until MOSFETs started to appear in the 1960s, and to provide a superior transistor for circuits in which a high input impedance was important. With the advent of CMOS in 1963, the age of large-scale integration began, and the MOSFET became the more ubiquitous transistor. However, as we show elsewhere in this book, the bipolar transistor has inherent advantages in high-frequency performance, due to its superior transconductance, and in high-power applications, due to its favourable geometry. BJTs are also more robust than MOSFETs, which is why many readers will have become familiar with them during their electronics laboratory classes.

Perhaps the biggest event in BJT development in the last 20 years has been the advent of heterojunction bipolar transistors (HBTs). In the single heterojunction version of these transistors, dissimilar semiconducting materials are used for the emitter and the base, whereas the base and collector are made from the same semiconductor.

The principal application of switching theory is in the design of digital circuits. The design of such circuits is commonly referred to as logical (or logic) design. Most digital systems are constructed from electronic switching circuits. In this chapter, we describe some components that are typical of the basic building blocks used in constructing digital systems. Switching algebra will be used to describe the logical behavior of networks composed of these building blocks as well as to manipulate and simplify switching expressions, thereby reducing the number of components used in the design. We shall be concerned with the logic functions that a circuit performs rather than with its electronic structure or behavior. Special attention will be given to the design of high-speed binary adders. These examples will introduce us to some practical aspects of logic design in which the speed of operation and area limitations require ingenuity in arriving at a proper compromise.

Design with basic logic gates

Although modern digital systems are composed of a large number of components, they usually employ only a small number of different kinds of elementary circuits, called gates, whose task is to perform logic operations on input signals. In Section 3.2, we showed that in order to implement any switching function, it is necessary to have a set of two-valued switching devices capable of implementing a functionally complete set of operations. The objective of this section is to present some commonly used devices of this type.