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Chapter 3: the MOS Transistor (Pdf) chapter3.fm Page 43 Monday, September 6, 1999 1:50 PM CHAPTER 3 THE DEVICES Qualitative understanding of MOS devices n Simple component models for manual analysis n Detailed component models for SPICE n Impact of process variations 3.1 Introduction 3.3.3 Dynamic Behavior 3.2 The Diode 3.3.4 The Actual MOS Transistor—Some Secondary Effects 3.2.1 A First Glance at the Diode — The 3.3.5 SPICE Models for the MOS Transistor Depletion Region 3.2.2 Static Behavior 3.4 A Word on Process Variations 3.2.3 Dynamic, or Transient, Behavior 3.5 Perspective: Technology Scaling 3.2.4 The Actual Diode—Secondary Effects 3.2.5 The SPICE Diode Model 3.3 The MOS(FET) Transistor 3.3.1 A First Glance at the Device 3.3.2 The MOS Transistor under Static Conditions 43 chapter3.fm Page 44 Monday, September 6, 1999 1:50 PM 44 THE DEVICES Chapter 3 3.1Introduction It is a well-known premise in engineering that the conception of a complex construction without a prior understanding of the underlying building blocks is a sure road to failure. This surely holds for digital circuit design as well. The basic building blocks in today’s digital circuits are the silicon semiconductor devices, more specifically the MOS transis- tors and to a lesser degree the parasitic diodes, and the interconnect wires. The role of the semiconductor devices has been appreciated for a long time in the world of digital inte- grated circuits. On the other hand, interconnect wires have only recently started to play a dominant role as a result of the advanced scaling of the semiconductor technology. Giving the reader the necessary knowledge and understanding of these components is the prime motivation for the next two chapters. It is not our intention to present an in- depth treatment of the physics of semiconductor devices and interconnect wires. We refer the reader to the many excellent textbooks on semiconductor devices for that purpose, some of which are referenced in the To Probe Further section at the end of the chapters. The goal is rather to describe the functional operation of the devices, to highlight the prop- erties and parameters that are particularly important in the design of digital gates, and to introduce notational conventions. Another important function of this chapter is the introduction of models. Taking all the physical aspects of each component into account when designing complex digital cir- cuits leads to an unnecessary complexity that quickly becomes intractable. Such an approach is similar to considering the molecular structure of concrete when constructing a bridge. To deal with this issue, an abstraction of the component behavior called a model is typically employed. A range of models can be conceived for each component presenting a trade-off between accuracy and complexity. A simple first-order model is useful for man- ual analysis. It has limited accuracy but helps us to understand the operation of the circuit and its dominant parameters. When more accurate results are needed, complex, second- or higher-order models are employed in conjunction with computer-aided simulation. In this chapter, we present both first-order models for manual analysis as well as higher-order models for simulation for each component of interest. Designers tend to take the component parameters offered in the models for granted. They should be aware, however, that these are only nominal values, and that the actual parameter values vary with operating temperature, over manufacturing runs, or even over a single wafer. To highlight this issue, a short discussion on process variations and their impact is included in the chapter. 3.2The Diode Although diodes rarely occur directly in the schematic diagrams of present-day digital gates, they are still omnipresent. Each MOS transistor implicitly contains a number of reverse-biased diodes that directly influence the behavior of the device. Especially, the voltage-dependent capacitances contributed by these parasitic elements play an important role in the switching behavior of the MOS digital gate. Diodes are also used to protect the input devices of an IC against static charges. Therefore, a brief review of the basic proper- ties and device equations of the diode is appropriate. Rather than being comprehensive, chapter3.fm Page 45 Monday, September 6, 1999 1:50 PM Section 3.2 The Diode 45 we choose to focus on those aspects that prove to be influential in the design of digital MOS circuits, this is the operation in reverse-biased mode.1 3.2.1 A First Glance at the Diode — The Depletion Region The pn-junction diode is the simplest of the semiconductor devices. Figure 3.1a shows a cross-section of a typical pn-junction. It consists of two homogeneous regions of p- and n- type material, separated by a region of transition from one type of doping to another, which is assumed thin. Such a device is called a step or abrupt junction. The p-type mate- rial is doped with acceptor impurities (such as boron), which results in the presence of holes as the dominant or majority carriers. Similarly, the doping of silicon with donor impurities (such as phosphorus or arsenic) creates an n-type material, where electrons are the majority carriers. Aluminum contacts provide access to the p- and n-terminals of the device. The circuit symbol of the diode, as used in schematic diagrams, is introduced in Figure 3.1c. To understand the behavior of the pn-junction diode, we often resort to a one-dimen- sional simplification of the device (Figure 3.1b). Bringing the p- and n-type materials together causes a large concentration gradient at the boundary. The electron concentration changes from a high value in the n-type material to a very small value in the p-type material. The reverse is true for the hole concentration. This gradient causes electrons to B Al A SiO2 p n (a) Cross-section of pn-junction in an IC process A Al A p n B B Figure 3.1 Abrupt pn-junction diode (b) One-dimensional and its schematic symbol. (c) Diode symbol representation 1 We refer the interested reader to the web-site of the textbook for a comprehensive description of the diode operation. chapter3.fm Page 46 Monday, September 6, 1999 1:50 PM 46 THE DEVICES Chapter 3 diffuse from n to p and holes to diffuse from p to n. When the holes leave the p-type mate- rial, they leave behind immobile acceptor ions, which are negatively charged. Conse- quently, the p-type material is negatively charged in the vicinity of the pn-boundary. Similarly, a positive charge builds up on the n-side of the boundary as the diffusing elec- trons leave behind the positively charged donor ions. The region at the junction, where the majority carriers have been removed, leaving the fixed acceptor and donor ions, is called the depletion or space-charge region. The charges create an electric field across the boundary, directed from the n to the p-region. This field counteracts the diffusion of holes and electrons, as it causes electrons to drift from p to n and holes to drift from n to p. Under equilibrium, the depletion charge sets up an electric field such that the drift currents are equal and opposite to the diffusion currents, resulting in a zero net flow. The above analysis is summarized in Figure 3.2 that plots the current directions, the charge density, the electrical field, and the electrostatic field of the abrupt pn-junction under zero-bias conditions. In the device shown, the p material is more heavily doped than Hole diffusion Electron diffusion (a) Current flow p n Hole drift Electron drift r Charge density + x (b) Charge density Distance - Electrical E field x (c) Electric field Potential V x (d) Electrostatic potential -W1 W2 f0 Figure 3.2 The abrupt pn-junction under equilibrium bias. chapter3.fm Page 47 Monday, September 6, 1999 1:50 PM Section 3.2 The Diode 47 the n, or NA > ND, with NA and ND the acceptor and donor concentrations, respectively. Hence, the charge concentration in the depletion region is higher on the p-side of the junc- tion. Figure 3.2 also shows that under zero bias, there exists a voltage f0 across the junc- tion, called the built-in potential. This potential has the value N N f = f ln -------------A D- (3.1) 0 T 2 ni where fT is the thermal voltage kT f =------= 26mVat300K (3.2) T q The quantity ni is the intrinsic carrier concentration in a pure sample of the semiconductor and equals approximately 1.5 ´ 1010 cm-3 at 300 K for silicon. Example 3.1 Built-in Voltage of pn-junction 15 3 16 3 An abrupt junction has doping densities of NA = 10 atoms/cm , and ND = 10 atoms/cm . Calculate the built-in potential at 300 K. From Eq. (3.1), 1015 ´ 1016 f =26 ln-------------------------- mV= 638mV 0 2.25´ 1020 3.2.2 Static Behavior The Ideal Diode Equation Assume now that a forward voltage VD is applied to the junction or, in other words, that the potential of the p-region is raised with respect to the n-zone. The applied potential low- ers the potential barrier. Consequently, the flow of mobile carriers across the junction increases as the diffusion current dominates the drift component. These carriers traverse Minority carrier concentration n n n o o o i i i g g g e e e r r r Excess carriers - - n p n o i o o t p t n0 t e l t t c p c a e a t t D n n o o c c l Excess carriers l a a t t e e np0 M M –W –W1 0 W2 n-region x p p-region Wn Figure 3.3 Minority carrier concentrations in the neutral region near an abrupt pn-junction under forward-bias conditions.
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