Neamen D. Microelectronics: Circuit Analysis and Design

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188 Part 1 Semiconductor Devices and Basic Applications

0.8 = 2.5



1 −

2.5



which yields

= 1.086 V

Then

= 1 − V

= 1 −1.086 =−0.086 V

and

= V

− V

=−0.086 − (−5.8) = 5.71 V

Again, we see that

= 5.71 V > V

− V

= 2.5 −1.086 = 1.41 V

which veriﬁes that the transistor is biased in the saturation region, as assumed.

Comment: In the same way as bipolar or MOS transistors, junction ﬁeld-effect tran-

sistors can be biased using constant-current sources.

EXERCISE PROBLEM

Ex 3.21: For the p-channel transistor in the circuit in Figure 3.64, the parameters

are:

DSS

= 6mA

= 4V

, and

λ = 0

. Calculate the quiescent values of

, and

. Is the transistor biased in the saturation or nonsaturation region?

(Ans.

= 1.81 V

= 1.81 mA

= 2.47 V

, saturation region)

DESIGN EXAMPLE 3.22

Objective: Design a circuit with an enhancement-mode MESFET.

Consider the circuit shown in Figure 3.65(a). The transistor parameters are:

= 0.24 V

= 1.1mA/V

, and

λ = 0

. Let

+ R

= 50 k

. Design the cir-

cuit such that

= 0.50 V

and

= 2.5V

Solution: From Equation (3.38(a)) the drain current is

= K

− V

)

= (1.1)(0.5 −0.24)

= 74.4 μA

From Figure 3.65(b), the voltage at the drain is

= V

− I

= 4 −(0.0744)(6.7) = 3.5V

Therefore, the voltage at the source is

= V

− V

= 3.5 −2.5 = 1V

The source resistance is then

0.0744

= 13.4k

The voltage at the gate is

= V

+ V

= 0.5 +1 = 1.5V

= 0.4 kΩ

= 1 kΩ

–5 V

Figure 3.64 Circuit for

Exercise Ex 3.21

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Chapter 3 The Field-Effect Transistor 189

Since the gate current is zero, the gate voltage is also given by a voltage divider equa-

tion, as follows:



+ R



)

1.5 =





(4)

which yields

= 18.75 k

and

= 31.25 k

Again, we see that

= 2.5V> V

− V

= 0.5 −0.24 = 0.26 V

which conﬁrms that the transistor is biased in the saturation region, as initially

assumed.

Comment: The dc analysis and design of an enhancement-mode MESFET circuit is

similar to that of MOSFET circuits, except that the gate-to-source voltage of the

MESFET must be held to no more than a few tenths of a volt.

= 6.7 kΩ

= 4 V

74.4 mA

+4 V

= 6.7 kΩ

= V

– V

= 1 V

= V

+ V

= 1.5 V

= 4 – (0.0744)(6.7)

= 3.5 V

= 2.5 V

= 0.5 V

–

(a) (b)

= 13.4 kΩ

0.0744

Figure 3.65 (a) An n-channel enhancement-mode MESFET circuit and (b) the n-channel

MESFET circuit for Example 3.22

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= 1.2 kΩ

= –20 V

Figure 3.66 Circuit for

Exercise Ex3.22

190 Part 1 Semiconductor Devices and Basic Applications

EXERCISE PROBLEM

Ex 3.22: Consider the circuit shown in Figure 3.66 with transistor parameters

DSS

= 8mA

= 4V

, and

λ = 0

. Design the circuit such that

= 100 k

= 5mA

, and

SDQ

= 12 V

. (Ans.

= 0.4k

= 387 k

135 k

)

Test Your Understanding

TYU 3.17 The n-channel enhancement-mode MESFET in the circuit shown in

Figure 3.67 has parameters

= 50 μ

A/V

and

= 0.15 V

. Find the value

so that

= 5 μA

. What are the values of

and

(Ans.

= 0.516 V

= 0.466 V

= 4.45 V

)

= 10 kΩ

–

= 100 kΩ

= 5 V

Figure 3.67 Circuit for

Exercise TYU 3.17

= 2.5 V

Figure 3.68 Circuit for

Exercise TYU 3.18

TYU 3.18

For the inverter circuit shown in Figure 3.68, the n-channel enhancement-

mode MESFET parameters are

= 100

μA/V

and

= 0.2

V. Determine

the value of

required to produce

= 0.10 V

when

= 0.7V

. (Ans.

= 267 k

)

3.7 DESIGN APPLICATION: DIODE THERMOMETER

WITH AN MOS TRANSISTOR

Objective: • Incorporate an MOS transistor in a design application

that enhances the simple diode thermometer design discussed in

Chapter 1.

Speciﬁcations: The electronic thermometer is to operate over a temperature range

of 0 to 100 °F.

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Chapter 3 The Field-Effect Transistor 191

Design Approach: The output diode voltage developed in the diode thermometer

in Figure 1.47 is to be applied between the gate–source terminals of an NMOS

transistor to enhance the voltage over the temperature range. The NMOS transistor is

to be held at a constant temperature.

Choices: Assume an n-channel, depletion-mode MOSFET is available with the

parameters



= 80

μA/V

W/L = 10

, and

=−1V

Solution: From the design in Chapter 1, the diode voltage is given by

= 1.12 −0.522



300



where T is in kelvins.

Consider the circuit shown in Figure 3.69. We assume that the diode is in a

variable temperature environment while the rest of the circuit is held at room

temperature.

From the circuit, we see that

= V

, where

is the diode voltage and not

the drain voltage. We want the MOSFET biased in the saturation region, so

= K

(

− V

)



(

− V

)

We ﬁnd the output voltage as

= 15 − I

= 15 −



· R

(

− V

)

The diode current and output voltage can be written as

0.080

(

)

= 0.4(V

+1)

(mA)

and

= 15 −[0.4(V

+1)

](10) = 15 −4(V

+1)

(V)

From Chapter 1, we have the following:

We ﬁnd the circuit response as:

T (°F) I

(mA) V

(V)

0 1.124 3.764

40 1.072 4.278

80 1.021 4.791

100 0.9973 5.027

T (°F) V

(V)

0 0.6760

40 0.6372

80 0.5976

100 0.5790

= V

= 10 kΩ

= +15 V

–

Figure 3.69 Design

application circuit to measure

output voltage of diode

versus temperature

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192 Part 1 Semiconductor Devices and Basic Applications

Comment: Figure 3.70(a) shows the diode voltage versus temperature and

Figure 3.70(b) now shows the output voltage versus temperature from the MOSFET

circuit. We can see that the transistor circuit provides a voltage gain. This voltage

gain is the desired characteristic of the transistor circuit.

Discussion: We can see from the equations that the diode current and output voltage

are not linear functions of the diode voltage. This effect implies that the transistor

output voltage is also not a linear function of temperature. We will see a better circuit

design using operational ampliﬁers in Chapter 9.

We can note from the results that

= V

> V

(sat)

in all cases, so the tran-

sistor is biased in the saturation region as desired.

3.8 SUMMARY

• In this chapter, we have considered the physical structure and dc electrical charac-

teristics of the MOSFET.

• The current in the MOSFET is controlled by the gate voltage. In the nonsatura-

tion bias region of operation, the drain current is also a function of drain voltage,

whereas in the saturation bias region of operation the drain current is essentially

independent of the drain voltage. The drain current is directly proportional to the

width-to-length ratio of the transistor, so this parameter becomes the primary de-

sign variable in MOSFET circuit design.

• The dc analysis and design techniques of MOSFET circuits were emphasized in

this chapter. The use of MOSFETs in place of resistors was investigated. This

leads to the design of all-MOSFET circuits.

• Basic applications of the MOSFET include switching currents and voltages, per-

forming digital logic functions, and amplifying time-varying signals. The am-

plifying characteristics will be considered in the next chapter and the digital ap-

plications will be considered in Chapter 16.

• MOSFET circuits that provide constant-current biasing to other MOSFET cir-

cuits were analyzed and designed. This current biasing technique is used in inte-

grated circuits.

02040

Temperature (°F)

(a)

60 80 100

0.5790

0.6760

(V)

02040

Temperature (°F)

(b)

60 80 100

3.5

4.0

4.5

5.0

5.5

Figure 3.70 (a) Diode voltage versus temperature and (b) circuit output voltage versus

temperature

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Chapter 3 The Field-Effect Transistor 193

• The dc analysis and design of multistage MOSFET circuits were considered.

• The physical structure and dc electrical characteristics of JFET and MESFET

devices as well as the analysis and design of JFET and MESFET circuits were

considered.

• As an application, a MOSFET transistor was incorporated in a circuit design that

enhances the simple diode electronic thermometer discussed in Chapter 1.

CHECKPOINT

After studying this chapter, the reader should have the ability to:

✓ Understand and describe the structure and general operation of n-channel and

p-channel enhancement-mode and depletion-mode MOSFETs.

✓ Apply the ideal current–voltage relations in the dc analysis and design of vari-

ous MOSFET circuits using any of the four basic MOSFETs.

✓ Understand how MOSFETs can be used in place of resistor load devices to cre-

ate all-MOSFET circuits.

✓ Qualitatively understand how MOSFETs can be used to switch currents and

voltages, to perform digital logic functions, and to amplify time-varying signals.

✓ Understand the basic operation of a MOSFET constant-current circuit.

✓ Understand the dc analysis and design of a multistage MOSFET circuit.

✓ Understand the general operation and characteristics of junction FETs.

REVIEW QUESTIONS

1. Describe the basic structure and operation of a MOSFET. Deﬁne enhancement

mode and depletion mode.

2. Sketch the general current-voltage characteristics for both enhancement-mode

and depletion-mode MOSFETs. Deﬁne the saturation and nonsaturation bias

regions.

3. Describe what is meant by threshold voltage, width-to-length ratio, and drain-to-

source saturation voltage.

4. Describe the channel length modulation effect and deﬁne the parameter

Describe the body effect and deﬁne the parameter

5. Describe a simple common-source MOSFET circuit with an n-channel

enhancement-mode device and discuss the relation between the drain-to-source

voltage and gate-to-source voltage.

6. How do you prove that a MOSFET is biased in the saturation region?

7. In the dc analysis of some MOSFET circuits, quadratic equations in gate-to-

source voltage are developed. How do you determine which of the two possible

solutions is the correct one?

8. How can the Q-point be stabilized against variations in transistor parameters?

9. Describe the current–voltage relation of an n-channel enhancement-mode

MOSFET with the gate connected to the drain.

10. Describe the current–voltage relation of an n-channel depletion-mode MOSFET

with the gate connected to the source.

11. Describe a MOSFET NOR logic circuit.

12. Describe how a MOSFET can be used to amplify a time-varying voltage.

13. Describe the basic operation of a junction FET.

14. What is the difference between a MESFET and a pn junction FET?

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194 Part 1 Semiconductor Devices and Basic Applications

PROBLEMS

[Note: In all problems, assume the transistor parameter

λ = 0

, unless otherwise

stated.]

Section 3.1 MOS Field-Effect Transistor

3.1 (a) Calculate the drain current in an NMOS transistor with parameters

= 0.4



= 120 μ

A/V

W = 10 μ

L = 0.8 μ

m, and with ap-

plied voltages of

= 0.1

V and (i)

= 0

, (ii)

= 1

(iii)

= 2

V, and (iv)

= 3

V. (b) Repeat part (a) for

= 4

3.2 The current in an NMOS transistor is 0.5 mA when

− V

= 0.6

V and

1.0 mA when

− V

= 1.0

V. The device is operating in the nonsatura-

tion region. Determine

and

3.3 The transistor characteristics

versus

for an NMOS device are shown

in Figure P3.3. (a) Is this an enhancement-mode or depletion-mode device?

(b) Determine the values for

and

. (c) Determine

(sat) for

= 3.5

V and

= 4.5

0.2

0.4

0.6

0.8

123456

(V)

(mA)

= 5 V

= 4 V

= 3 V

= 2 V

Figure P3.3

3.4 For an n-channel depletion-mode MOSFET, the parameters are

−2.5

V and

= 1.1

mA/V

. (a) Determine I

for

= 0

; and: (i)

0.5 V, (ii)

= 2.5

V, and (iii)

= 5

V. (b) Repeat part (a) for

= 2

3.5 The threshold voltage of each transistor in Figure P3.5 is

= 0.4

V. De-

termine the region of operation of the transistor in each circuit.

–

2.2 V

–

2.2 V

–

1 V

–

1 V

–

3 V

–

1 V

–

0.6 V

(b) (c)(a)

Figure P3.5

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Chapter 3 The Field-Effect Transistor 195

3.6 The threshold voltage of each transistor in Figure P3.6 is

=−0.4

Determine the region of operation of the transistor in each circuit.

–

2.2 V

–

2.2 V

–

1 V

–

2 V

–

1 V

–

2 V

(b) (c)(a)

Figure P3.6

3.7 Consider an n-channel depletion-mode MOSFET with parameters

=−1.2

V and



= 120 μ

A/V

. The drain current is

= 0.5

mA at

= 0

and

= 2

V. Determine the

W/L

ratio.

3.8 Determine the value of the process conduction parameter



for an NMOS

transistor with

= 600

/V–s and for an oxide thickness t

(a) 500 Å, (b) 250 Å, (c)100 Å, (d) 50 Å, and (e) 25 Å.

3.9 An n-channel enhancement-mode MOSFET has parameters

= 0.4

W = 20 μ

L = 0.8 μ

= 200

Å, and

= 650

/V–s. (a) Calcu-

late the conduction parameter

(b) Determine the drain current when

= V

= 2

V. (c) With

= 2

V, what value of

puts the device

at the edge of saturation?

3.10 An NMOS device has parameters

= 0.8

L = 0.8 μ

m, and



= 120 μ

A/V

. When the transistor is biased in the saturation region with

= 1.4

V, the drain current is

= 0.6

mA. (a) What is the channel

width

? (b) Determine the drain current when

= 0.4

V. (c) What

value of

puts the device at the edge of saturation?

3.11 A particular NMOS device has parameters

= 0.6

L = 0.8 μ

= 200

Å, and

= 600

/V–s. A drain current of

= 1.2

mA is re-

quired when the device is biased in the saturation region at

= 3

V. De-

termine the required channel width of the device.

3.12 MOS transistors with very short channels do not exhibit the square law volt-

age relation in saturation. The drain current is instead given by

= WC

− V

sat

where

sat

is a saturation velocity. Assuming

sat

= 2 ×10

cm/s and using

the parameters in Problem 3.11, determine the current.

3.13 For a p-channel enhancement-mode MOSFET,



= 50 μ

A/V

. The device

has drain currents of

= 0.225

mA at

= V

= 2

V and

= 0.65

mA at

= V

= 3

V. Determine the

W/L

ratio and the

value of

3.14 For a p-channel enhancement-mode MOSFET, the parameters are

2 mA/V

and

=−0.5

V. The gate is at ground potential, and the source

and substrate terminals are at

V. Determine

when the drain terminal

voltage is: (a)

= 0

V, (b)

= 2

V, (c)

= 4

V, and (d)

= 5

3.15 The transistor characteristics

versus

for a PMOS device are shown in

Figure P3.15. (a) Is this an enhancement-mode or depletion-mode device?

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196 Part 1 Semiconductor Devices and Basic Applications

(b) Determine the values for

and

. (c) Determine

(sat) for

= 3.5

V and

= 4.5

123456

(V)

(mA)

= 5 V

= 4 V

= 3 V

= 2 V

Figure P3.15

3.16 A p-channel depletion-mode MOSFET has parameters

=+2



= 40 μ

A/V

, and

W/L = 6

. Determine

(sat) for: (a)

=−1

(b)

= 0

, and (c)

=+1

V. If the transistor is biased in the saturation

region, calculate the drain current for each value of

3.17 Calculate the drain current in a PMOS transistor with parameters

=−0.5



= 50 μ

A/V

W = 12 μ

L = 0.8 μ

m, and with ap-

plied voltages of

= 2

V and (a)

= 0.2

V, (b)

= 0.8

(c)

= 1.2

V, (d)

= 2.2

V, and (e)

= 3.2

3.18 Determine the value of the process conduction parameter



for a

PMOS transistor with

= 250

/V–s and for an oxide thickness

(a) 500 Å, (b) 250 Å, (c) 100 Å, (d) 50 Å, and (e) 25 Å.

3.19 Enhancement-mode NMOS and PMOS devices both have parameters

L = 4 μ

m and

= 500

. For the NMOS transistor,

=+0.6V

= 675

/V–s, and the channel width is

; for the PMOS transistor,

=−0.6

= 375

/V–s, and the channel width is

. Design

the widths of the two transistors such that they are electrically equivalent

and the drain current in the PMOS transistor is

= 0.8

mA when it is

biased in the saturation region at

= 5

V. What are the values of

, and

3.20 For an NMOS enhancement-mode transistor, the parameters are:

1.2V, K

= 0.20

mA/V

, and

λ = 0.01 V

−1

. Calculate the output resis-

tance

for

= 2.0V

and for

= 4.0V

. What is the value of

3.21 The parameters of an n-channel enhancement-mode MOSFET are

= 0.5



= 120 μ

A/V

, and

W/L = 4

. What is the maximum value

and the minimum value of

such that for

= 2

≥ 200



3.22 An enhancement-mode NMOS transistor has parameters

TNO

= 0.8V

γ = 0.8V

1/2

, and

= 0.35 V

. At what value of

will the threshold

voltage change by 2V due to the body effect?

3.23 An NMOS transistor has parameters

= 0.75 V



= 80

μA/V

W/L = 15

= 0.37 V

, and

γ = 0.6V

1/2

. (a) The transistor is biased at

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Chapter 3 The Field-Effect Transistor 197

= 2.5V

= 3V

, and

= 3V

. Determine the drain current

(b) Repeat part (a) for

= 0.25 V

3.24 (a) A silicon dioxide gate insulator of an MOS transistor has a thickness of

= 120

Å. (i) Calculate the ideal oxide breakdown voltage. (ii) If a safety

factor of three is required, determine the maximum safe gate voltage that

may be applied. (b) Repeat part (a) for an oxide thickness of

= 200

Å.

3.25 In a power MOS transistor, the maximum applied gate voltage is 24 V. If a

safety factor of three is speciﬁed, determine the minimum thickness neces-

sary for the silicon dioxide gate insulator.

Section 3.2 Transistor dc Analysis

3.26 In the circuit in Figure P3.26, the transistor parameters are

= 0.8V

and

= 0.5

mA/V

. Calculate

, and

3.27 The transistor in the circuit in Figure P3.27 has parameters

= 0.8V

and

= 0.25

mA/V

. Sketch the load line and plot the Q-point for

(a)

= 4

= 1k

and (b)

= 5V

= 3k

. What is the

operating bias region for each condition?

Figure P3.29

+3 V

–3 V

0.5 kΩ

5 kΩ

= 8 kΩ

= 22 kΩ

Figure P3.30

D3.28 The transistor in Figure P3.28 has parameters

= 0.4



= 120

A/V

, and

W/L = 80

. Design the circuit such that

= 0.8

mA and

= 200



3.29 The transistor in the circuit in Figure P3.29 has parameters

=−0.8V

and

= 0.20

mA/V

. Sketch the load line and plot the Q-point for

(a)

= 3.5V

= 1.2k

and (b)

= 5V

= 4k

. What is

the operating bias region for each condition?

3.30 Consider the circuit in Figure P3.30. The transistor parameters are

=−0.8

V and

= 0.5

mA/V

. Determine

, and

3.31 For the circuit in Figure P3.31, the transistor parameters are

=−0.8V

and

= 200

μA/V

. Determine

and

D3.32 Design a MOSFET circuit in the conﬁguration shown in Figure P3.26. The

transistor parameters are

= 0.4

V and



= 120 μ

A/V

, and

λ = 0

The circuit parameters are

= 3.3

V and

= 5



. Design the circuit

so that

DSQ

∼

1.6

V and the voltage across

is approximately 0.8 V. Set

= 0.8

V. The current through the bias resistors is to be approximately

5 percent of the drain current.

= 10 V

= 4 kΩ

= 2 kΩ

= 32 kΩ

= 18 kΩ

Figure P3.26

Figure P3.27

= 1.8 V

0.5 kΩ

Figure P3.28

+5 V

–5 V

= 5 kΩ

= 0.4 mA

= 50 kΩ

Figure P3.31

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