CHARACTERISTICS

A p-n junction can be viewed as isolated p-type and n-type materials brought into intimate contact (Fig. 1.2). Being abundant in n-type material, electrons diffuse to the p-type material. The same process happens for holes from the p-type material. This flow of charges sets up an electric field that starts to hinder further diffusion until an equilibrium is struck. The energy-band diagram under equilibrium is shown in Fig. 1.2(b). (Notice that when NA * Np, where Ј, crosses Ep does not coincide with the metallurgical junction.) Since the overall charge has to be conserved, it follows that for an abrupt (step) junction,

as shown in Fig. 1.2(c). An important parameter is the built-in potential y/bi. According to Fig. 1.2(b), it is the sum of y/Bn and y/Bp, given by

 2 In./

 Vbi = y’Bn+y’Bp = q

(1.2)

which is the total band bending at equilibrium by definition.

Under bias, the following can be obtained using the Poisson equation with appropriate boundary conditions,

(1.3)

 (1.4)

 m

Equation (1.5) can be interpreted as the area under the field-distance curve in Fig. 1.2(d). The partition of band bending and depletion width between the n — and /7-regions can be related by

(1.6)

It can further be shown that

(1.7)

In practical devices, one side usually has a doping concentration much higher than the other, and the junction can be treated as a one-sided junction. The depletion width and potential variation in the heavily doped side can then be neglected.

Figure 1.3, which shows the energy-band diagram and the carrier concentrations under bias, is used to derive the 1-V characteristics. The forward current of a p-n junction under bias is determined by diffusion of injected minority carriers. The carrier concentration at the edge of the depletion region is given by

(1.8)

Combining the continuity equation with the current equation, assuming steady state, zero generation rate and zero drift current, one gets

(1.9)

where x = 0 now corresponds to the edge of the depletion region. (Notice the x-coordinate in Fig. 1.3(c).) Solving these differential equations gives the minority-carrier profiles

 (a)

 -i — qVf

 FIGURE 1.3 Energy-band diagram showing a p-n junction (a) under forward bias (positive voltage applied to p-type material and (b) under reverse bias, (c) Minority-carrier concentration profiles under forward and reverse bias.

 (b)

 (c)

FIGURE 1.4

/-^characteristics of a p-n junction in (a) linear current scale and (b) logarithmic current scale.

 qIf kT,
 exp
 n„ (*) = » p po po
 6XP|f nJ

 (1.10)

 exp
 xL pj
 qh kT
 exp
 (1.11)

 qnwd
 qVj akT,
 -1
 exp
 2t
 D n no n po +—
 qh kT, kT,
 F’*
 J = q
 exp
 D » P W
 D
 — 1
 exp
 qn,
 L Nn ■ p D
 (1.12) At each side of the junction the diffusion current is a function of distance. It maximizes at x = 0 where Eq. (1.12) is obtained. Since the current has to be continuous, the diffusion current is supplemented by the majority-carrier drift current. This equation is also valid for reverse bias when Vjis negative. In cases where the thickness of the p-type or n-type material is less than the diffusion length Lp or L„, the latter parameter should be replaced by the corresponding thickness in Eq. (1.12) and thereby increasing the current. The I-Vcharacteristics described by Eq. (1.12) is shown in Fig. 1.4. In both the linear current scale and the logarithmic current scale, additional features at high forward bias and reversed bias are to be noticed. In the forward direction, currents rises exponentially with Vj until the slope becomes more gradual. This can be due to high-level injection of carriers such that the applied voltage is no longer totally developed across the depletion region. Series resistance, Rs, can also cause the same effect. At high reverse bias, breakdown can occur due to impact ionization (see Appendix B3) or Zener tunneling. These mechanisms can be separated by temperature dependence. At higher temperature, the ionization rate decreases and the breakdown voltage due to avalanche multiplication increases. The opposite dependence holds for Zener breakdown. Normally avalanche multiplication occurs first, with breakdown voltage shown in Fig. B3.3. An additional current component besides Eq. (1.12) is due to recombination/generation through mid-gap states within the depletion region (see Appendix B2). This mechanism gives rise to a current described by
 The two diffusion currents give a total of

 (1.13)

If the term qntWJ2T is comparable to or larger than the pre-exponential factor in Eq. (1.12), the current for small Vf as well as the reverse current will be increased.

A common use of the p-n junction requires it to switch between the on-state and the off-state. Because of minority-carrier storage under forward bias, the immediate response to reverse bias is shown in Fig. 1.5, with Ir =

7

 (1.14)

t.«r In 1 +

 erf

t, r exp (rttJ r)

 (1.15)

= 1 + 0.1 —

This reverse recovery limits a p-n junction to about 1 GHz operation. In order to increase the frequency response, the carrier lifetime r can be intentionally shortened by introducing impurities for recombination. The penalty for this is an increased leakage current. An alternative approach is to use a step-recovery diode (Section 1.5.2).

The equivalent circuit for a p-n junction is shown in Fig. 1.6. Since capacitance is defined by dQldV, the depletion-layer capacitance Cj is associated with the depletion-layer charge, while the diffusion capacitance CD is related to injected carriers. The CD is significant only under forward bias conditions and is proportional to the forward current, given by

 ,(! Ur

q I ■/ Vf

 (1.16)

— (Lv + L n ) exp ‘

2kT F no n P°

The Cd is determined by the depletion width and for a one-sided step junction,

qeN

(1.17)

where N is from the lightly doped side. A measurement of 1/C2 vs. Vn as shown in Fig. 1.7, can extrapolate j/bj and its slope can determine the doping

FIGURE 1.5

Transient current characteristics of a p-n junction when switched from forward to reverse direction. td and tir are called delay time and transition time, respectively.

concentration (or area). This technique can be extended to obtain nonuniform doping profile,

 (1.18)

dcj-

dV qe N (x)

APPLICATIONS

1. Because it is the most common rectifier, a p-n junction has many circuit applications. See Appendix Cl-Applications of Rectifiers.

2. Many devices are special forms of p-n junction. Examples are LED, laser, solar cell, and photodiode. A p-n junction also serves as a building block for many other devices such as the bipolar transistor, MOSFET, junction FET, etc.

3. Due to the non-linear, exponential nature of the current, the p-n junction can be used as a varistor.

4. The variable depletion capacitance at reverse bias can be utilized as a varactor.

5. A p-n junction is a very common protection device for electro-static discharge (ESD). It discharges a voltage surge when it exceeds a certain value comparable to the built-in potential.

6. A p-n junction is a robust device and is a good choice for a diode required in power electronics.

7.

 Rs

The p-n junction can be used to isolate devices or regions of semiconductors. An example can be found in the tub isolation for CMOS circuits.

 FIGURE 1.6 FIGURE 1.7 Equivalent circuit of a p-n junction. A is the A plot of capacitance (I/C2) under reverse bias area of the diode. yields y’i/ and doping concentration (or area).

8. The well-behaved forward characteristics of a p-n diode enable it to be used as a temperature sensor. In operation, a constant current is applied and the voltage is monitored. This forward voltage drop is a fairly linear function of temperature. GaAs diodes can be good sensors in a wide temperature range from a few degree K to « 400 K, and Si diode from « 20 K.

STRUCTURE

The early version of the structure was made by pressing a metal wire onto the surface of a semiconductor. A junction was then formed by passing a pulse of current through the wire and semiconductor. It is believed that doping is diffused from the metal wire as shown in Fig. 1.1(a). Such a structure is referred to as the point contact and the metal wire as a cat’s whisker. (A point contact has the characteristics of either a p-n junction or a Schottky barrier, depending on the forming process. See Section 3.2.) Another old process is the alloy method in which a metal containing the appropriate impurity is placed onto the semiconductor surface. Heating above the eutectic temperature would form an alloy with a thin heavily doped region at the interface. This technique, along with

T

(b)

FIGURE 1.1

The cross-section structure of a p-n junction as in (a) point contact and (b) planar technology.

 FIGURE 1.2 Formation of p-n junction by bringing (a) isolated materials into (b) intimate contact. The potential variation is a result of (c) charge distribution, or (d) field distribution in the depletion layer.

the point contact, is no longer used. A planar structure is shown in Fig. 1.1 (b). The surface doping is usually introduced by ion implantation. Diffusion at high temperature can also be used, and the impurity source can be in a carrying gas or deposited material. A less common technique is to incorporate doping during epitaxial growth. The area of the diode is usually defined by an opening in an insulator layer.

JUNCTION DIODE

The p-n junction diode is among the oldest semiconductor devices. It was mainly used as mixers in the 1940s during World War II. The theory for the p-n diode was developed later by Shockley in 1949,1 and it was instrumental in the invention of the bipolar junction transistor. The theory was subsequently refined by Sah et al.2 and Moll.3 More recent review articles on the device can be found in Refs. 4-7. The p-n junction has been the most common rectifier used in the electronics industry. It also serves as a very important fundamental building block for many other devices.

COMPLETE GUIDE TO SEMICONDUCTOR DEVICES

Kwok K. Ng

It is difficult to have a clear quantitative definition of semiconductor. Based on conductivity, materials can be classified into three groups: (1) metal (conductor), (2) semiconductor, and (3) insulator (non-conductor). A general guideline indicating their ranges of conductivity is shown in Fig. 1.1. Note that one important feature of a semiconductor is that it can be doped with impurities to different concentration levels, so every semiconductor material can cover a range of conductivity. The total range of conductivity for semiconductors is from 10~8 S/cm to 103 S/cm (resistivity from 10-3 fl-cm to 108 fl-cm).

The conductivity of materials is ultimately related to the energy-band structure as shown in Fig. 1.2. For an insulator, the energy gap Eg is large. Consequently, the valence band is completely filled with electrons, and the conduction band is completely empty. Since current is a movement of electrons, and electrons need available states to move to, current cannot be generated from a completely filled band and a completely empty band. A semiconductor has a smaller Eg. Even when the Fermi level is within the energy gap, thermal energy excites electrons into the conduction band, and some empty states are left behind in the valence band. These partially filled bands make electron movement possible. In a metal, the energy gap is even smaller, and the Fermi level resides within either the conduction band or the valence band. Another possibility for a metal is that the Ј(/ is above the Ec so that the two bands overlap, and there is no energy gap. In such a system, the Fermi level can be in any position. Since for the semiconductor, the Fermi-Dirac statistics are necessary to determine the electron populations, temperature is also a crucial factor. At a temperature of absolute-zero, all semiconductors would become insulators. For practical consideration, at room temperature, semiconductors have energy gaps ranging from k 0.1 eV to « 4 eV.

 1 | I | 1 -| 1 | 1 GLASS 1 | i • | i | i • | i | GERMANIUM (Ge) 1 ‘ r ‘ SILVER NICKEL OXIDE (PURE) SILICON (Si) COPPER DIAMOND (PURE) GALLIUM ARSENIDE (GaAs) ALUMINUM SULFUR • GALLIUM PHOSPHIDE (GaP) PLATINUM • FUSED QUARTZ 1 i L ! 1 » J-. 1 . 1 . CADMIUM SULFIDE (CdS) U 1 ! „1 I I 1 BISMUTH • 1 !.. 1… ! ,
 RESISTIVITY p(Q-cm) ] 01 ® 1016 1014 1012 1010 10* 106 104 102 1 IO’2 lor* KT6 IO"8

 l

 10"’

 1(T

 10-"

 Iff

 r2

 1

 CONDUCTIVITY CT (S/cm)

 METAL-

 INSULATOR—

—-I*———- SEMICONDUCTOR—

FIGURE 1.1

A semiconductor is distinguished from the insulator and the metal by the range of resistivity (or conductivity) it spans. Note that, unlike the metal and insulator, each semiconductor can be doped to vary its resistivity (After Ref. 1)

For a historic perspective, some common electronic devices with the years they were developed are shown in Fig. 1.3. The earliest device, not necessarily made of semiconductor material, is probably the resistor, implied by Ohm’s law back in 1826. Vacuum tubes started around 1904, and were the major electronic components in the early radio era through World War II. The real birth of the semiconductor industry was in 1947 with the invention of the bipolar transistor. Ever since, new semiconductor devices have been invented at quite a steady pace, although some are more commercially significant than others. Figure 1.3 shows only the more common kinds. There are some devices whose development is too gradual to assign a milestone. An example is the solar cell. Starting from the mid-1970s, with the advent of MBE and MOCVD technologies, there are numerous heterojunction devices that are also omitted because it is too early for them to have an impact commercially.

Currently, there are more than 100 semiconductor devices. To include such a large collection, the hierarchy of semiconductor devices used in this guide needs to be clarified. This also explains why certain devices are put in separate chapters. Figure 1.4 shows that, for example, the LED, laser, solar cell, and tunnel diode are all variations of a p-n junction. But since each of these is made for a special purpose, their designs consider different device physics, and their structures are very different. A person who wants information about a solar cell, which receives light and converts it into electrical power, does not have to understand how a p-n
junction emits light in an LED. It is for these reasons that a total of 67 major devices are identified and put into individual chapters. For the next level of variation, the deviations are relatively minor and additional materials needed to describe them do not require separate chapters. These devices are attached to some of the major devices as “related devices.” The total number of devices falling into this category is found to be 114. This, of course, will change with time and rearrangement might be necessary for future editions. It is intentional that this guide includes older devices that have become obsolete. Old information is important to avoid duplication of effort, and is often the ground for new concepts.

The word complete in the book title refers to the inclusion of all devices, to the best of the author’s knowledge. It does not mean complete in covering details on every device. References are always given if the readers are interested in more in-depth studies. As a guide, this book presents only the key background, principles, and applications.

To help gain a better perspective on this large variety of devices, chapters are ordered according to their functions or structures, with group names assigned to describe them. This also provides a means for comparison among devices in the same group. These groups are:

1. Diodes: I-rectifiers

2. Diodes: II-negative resistance

3. Resistive devices

4. Capacitive devices

5. Two-terminal switches

6. Transistors: I-field-effect

7. Transistors: II-potential-effect

8. Transistors: III-hot-electron

9. Nonvolatile memories

10. Thyristors

11. Light sources

12. Photodetectors

13. Bistable optical devices

14. Other photonic devices

15. Sensors

While most of these group names are self-explanatory, a few need clarification. The name diode comes from vacuum tubes, and refers to a 2-element diode tube. Other vacuum tubes are the triode tube, tetrode tube, and pentode tube, with the number of active elements being 3, 4, and 5, respectively (see Appendix Al). Since in the diode tube, the cathode emits only one kind of carriers-electrons-the diode tube has asymmetric /-F behavior and is a rectifier. Although semiconductor diodes inherited the name, some of them actually do not have

 (a)

 (b)

 (c)

 (d)

 FIGURE 1.2 Energy-band diagrams showing that (a) in an insulator, the bands are completely filled or completely empty, (b) in a semiconductor, both bands are partially filled, and in a metal, (c) the Fermi level resides within one of the bands, or (d) Ey is above Ec so that there is no energy gap. In (d), the Ep can be in any position.

rectifying characteristics. Examples are the tunnel diode and the Gunn diode. A more proper definition for a diode now is simply a two-terminal device having nonlinear DC characteristics.2 Rectifiers are therefore only a subgroup of diodes. Another subgroup of diodes that are distinctively different from rectifiers are those having negative differential resistance. Within this group of negative-resistance devices, there are two types: one that has a negative dl/dV region, and the transit-time devices where the negative resistance is due to the small-signal current and voltage that are out of phase.

A switch, in semiconductor terms, is a device that has two states-a low-impedance state (on) and a high-impedance state (off). Switching between these two states can be controlled by voltage, current, temperature, or by a third terminal. A transistor, for example, is considered a three-terminal switch in digital circuits. Thyristors are also a special case of switch. They are included in a separate group from switches because they usually contain p-n-p-n layers, have more than two terminals, and are used mainly as power devices.

Unlike diode, transistor (transfer-resistor) was a new name coined at the beginning of the semiconductor era for the bipolar transistor, instead of keeping the old equivalent of triode. In the classification of devices, this book does not follow the common approach in literature to divide devices into bipolar and unipolar types. For transistors, the bipolar transistor has been used as a representative of the first type, and MOSFET and JFET of the second type. The reason behind that classification is for a bipolar transistor, the base current is due to one type of carrier while the emitter-collector current is of the opposite type; thus, both types of carriers are involved. For a MOSFET, the gate current is negligible, and the carriers in the channel are the only kind responsible for the current flow. The author, however, feels that the classification based on this

(1826) RESISTOR

VACUUM TUBES (1904)

(1938) SCHOTTKY BARRIER

 (1949) p-n JUNCTION (1951) LED (1956) SCR (1958) TUNNEL DIODE (1962) LASER (1963) GUNN DIODE (1965) IMPATT DIODE (1970) CCD

BIPOLAR TRANSISTOR (1947) JFET (1952)

MOSFET (I960)—

MESFET (1966) FAMOS (1967)

 MODFET (1980)

FIGURE 1.3

Some major milestones of the electronics industry.

(1974) RESONANT-TUNNELING DIODE

 67 MAJOR DEVICES
 FIELD-EFFECT TRANSISTOR
 SOLAR TUNNEL DIODE
 MOSFET MESFET MODFET
 p-n JUNCTION

 p-n

 »110 RELATED DEVICES

 ZENER DIODE

 VARACTOR

 TFT DMOS

FIGURE 1.4

Hierarchy of semiconductor devices. Major devices are included in individual chapters, and their variations are included as “related devices.”

bipolar-unipolar terminology is not clear, or maybe even incorrect. For example, in a bipolar transistor, the base current is a sort of leakage current. It is only a by-product of a base potential needed to modulate the emitter-collector current. If this base current is somehow made zero, the bipolar transistor would still work, and work even better. In fact, the main purpose of a heterojunction bipolar transistor is to suppress this base current, without affecting the main current. Next, let us consider an enhancement JFET. To turn the transistor on, the p-n junction gate is forward biased. This injects minority carriers into the channel. The JFET is therefore as “bipolar” as the bipolar transistor. This argument can also be extended to diodes. A p-n junction has been referred to as a bipolar device while a Schottky barrier as a unipolar device. For practical p-n junctions, they are usually one-sided in that one side is much more heavily doped than the other. A typical Si p-n junction has doping levels of 1020 cm-3 and 1016 cm-3, and the ratio of the two types of current is « 10“4. For a practical Schottky-barrier diode, even though the current is dominated by majority carriers, the minority-carrier current is not zero. It is a factor of « 10-4— 10~6 (injection efficiency) smaller. As seen from these diodes, the transition from a bipolar device to a unipolar device is not clear.

In this book, transistors are divided into three groups, following the notation used in Ref. 3. These are (1) field-effect transistor (FET), (2) potential-effect transistor (PET), and (3) hot-electron transistor (HET). The field effect is defined, originally by Shockley when the first field-effect transistor (JFET) was envisaged, as “modulation of a conducting channel by electric fields.”4 An FET differs from a PET in that its channel is coupled capacitively by transverse electric fields while in a PET, the channel’s potential is accessed by a direct contact. This distinction is illustrated in Fig. 1.5. The capacitive coupling in an FET is via an insulator or a space-charge layer. A hot-electron transistor is a special case of PET, whose emitter-base junction is a heterostructure such that the emitted carriers in the base have high potential or kinetic energy (Fig. 1.5(e)). Since a hot carrier has high velocity, HETs are expected to have higher intrinsic speed, higher current, and higher transconductance. One also notes that the energy-band diagrams of the FET and the PET (excluding HETs) are similar. This is because the way the channel is influenced, either capacitively for FET or directly for PET, is not indicated in these diagrams. One observation on FETs is that almost all have channel conduction by the drift process, and have a well-defined threshold voltage.

To achieve the goal of including this large variety of devices as a guide, a special format is created. First, each chapter is dedicated to one device only. The chapters are written to be independent, and readers can go directly to the intended

* FET and PET are defined in Ref. 3 differently by the editor (S. Sze) and by one of the contributors (S. Luryi). Sze’s definition (pp. 3 and 6 in Ref. 3), adopted in this book, is based on the physical structure, while Luryi’s definition (p, 400 in Ref. 3) is based on the current-control mechanism. In the latter definition, the same device can switch from an FET to a PET, depending on the bias regime.

CONTROL (GATE) CONTROL (BASE)

 PONT ACT CAPACITOR / CONTACT CONTACT CONTACT I CHANNEL | | CHANNEL
 (a) (b)
 У _____________ v ____________ / N____________ c. ) CHANNEL bV CHANNEL EV CHANNEL——— Er (<0 (d) (e) FIGURE 1.5 Schematic structures of (a) FET and (b) PET. Energy-band diagrams of n-channel (c) FET, (d) PET, and (e) НЕТ. Note that (c) and (d) are similar. НЕТ is a special case of PET.

device to get an overview quickly by reading only a few pages. Second, each chapter consists of four main sections:

1. History

2. Structure

3. Characteristics

4. Applications

With these, the essential information about each device is given: When was it invented and by whom? (History) How is it made? (Structure) How does it work? (Characteristics) What is it for? (Applications) For more than half of the chapters, there is another section-5. Related Devices, to cover slightly different structures. This is necessary to account for all devices to meet the goal of completeness and yet not have more than the existing 67 chapters. This book is intended to be an engineering approach to understand semiconductor devices, giving a pragmatic overview. Because of its complete coverage, readers can also pick up the subtle differences that sometimes exist between devices. With this rigid format, the listing of sections.1-4 are omitted from the Contents to avoid repetition in every chapter, with the exception of Chapter 1 as an example. In effect, only the device names are listed in the Contents.

The appendixes are extensive compared to those in other semiconductor — device books. Appendix A includes some non-semiconductor devices that one might encounter in this broad field. Appendix B covers the device physics and phenomena that are common to some devices, to avoid repetition. This appendix also makes up the lost opportunity in this book format to go over some

 FIGURE 1.6 Energy-band diagrams showing the basic device building blocks, or interfaces. Inserts indicate that ohmic contact, planar-doped barrier, and quantum well are special cases of Schottky barrier, doping interface, and heterojunction, respectively.

fundamental device physics. Appendix C covers the general applications of various device groups, again to avoid repetition in some chapters. Appendixes D and E are the more typical kind of semiconductor data and background information, but attempts have been made to collect as much information needed for a stand-alone handbook.

In the course of writing this book, several thoughts arose that are worth mentioning. Semiconductor devices can be viewed as consisting of device building blocks. In spite of the large number of devices, there are only a few building blocks, which are interfaces of two materials or doping types. These fundamental interfaces are all included in the energy-band diagram of the book cover, repeated here in Fig. 1.6. They are, from left to right, a metal- semiconductor interface, doping interface, heterojunction, semiconductor — insulator interface, and an insulator-metal interface. The metal-semiconductor interface, known as the Schottky barrier, also includes the ohmic contact which is inevitable in every semiconductor device. The doping interface also includes the planar-doped barrier. The heterojunction is also the basis for quantum-well devices. A bipolar transistor, for example, is built of two p-n junctions. A

TABLE 1.1

Curreut-conduction mechanisms of semiconductor devices.

 Mechanisms Examples Drift Resistor, most FETs Diffusion p-n junction, bipolar transistor Thermionic emission Schottky barrier, PDB diode Tunneling Tunnel diode, ohmic contact Recombination LED, diode Generation Solar cell, photodetectors Avalanche IMPATT diode, Zener diode

MOSFET has two p-n junctions, one semiconductor-insulator interface, and one insulator-metal interface.

Since the compositions vary among different semiconductor devices, their current-conduction mechanisms also vary accordingly. All the current-conduction mechanisms are summarized in Table 1.1 for an overview. These currents are due to drift, diffusion, thermionic emission, tunneling, recombination, generation, and avalanche.

Finally, we discuss what is meant by the recent, commonly used term high-speed device. Is it a device that has intrinsically fast response, or is it one that enables a high-speed circuit? This is important to clarify since different criterion calls for a different device design. Table 1.2 summarizes the different parameters that are used to indicate the first-order estimate of the device speed, with a different amount of parasitics and loading taken into consideration. The fundamental parameter is the transit time, the time it takes for the carriers to travel between the source-drain or emitter-collector. Direct measurement of this parameter is extremely difficult. The next level is parameters deduced from two-port, small-signal S-parameter microwave measurement.5 This is done with a single device, and thus not as a circuit. It is the highest frequency that can be

TABLE 1.2

Parameters pertaining to the speed of a transistor. Using an FET as an example, CG, Cjp, Cout, Cru„, and Cloall are the capacitances of the intrinsic gate, input parasitics, output, runner, and load, respectively.

 Parameters Considerations Speed figure-of-merit of FET Transit time Intrinsic, no capacitance sJCG S-para. meas. (fT) No output capacitance, no runner gJ(CG+Clp) (/max) Optimized load, no runner Ring oscillator Fan-out = 1, short runner SmKCG+Cip+Coul) Real circuit Multiple fan-outs, long runner, load capacitance ^OT/(CG+C//)+Cou/+CrM„+C/oorf)

measured on the device, but certain parasitics are ignored. The cutoff frequency, for example, is a current-gain measurement. The output is shorted so that the output capacitance is not included. fmax includes the output capacitance but the load is matched to optimize the power transfer. The simplest circuit measurement is a ring oscillator. It is usually designed with a minimum fan-out of one, and minimum interconnect distance. A real circuit has much larger load capacitance as well as larger interconnect capacitance. From this viewpoint, if the circuit speed is to be optimized, the current drive or transconductance of a transistor is more important than the intrinsic response. It is possible to predict the ultimate circuit speed based on the transit time, microwave measurements, or ring-oscillator speed, but care has to be taken to account for realistic parasitics. For PETs, the parasitic resistance is also critical since the input current is much higher than that in FETs.