360

:..:

CHAPTER 4

M O S F I E L D - E F F E C T T R A N S I S T O R S (MOSFETs)

PROBLEMS

what value of % will the drain end of the MOSFET channel just reach pinch off, and what is the corresponding drain current?

P R O B L E M S SECTION 4 . 1 : DEVICE STRUCTURE AND PHYSICAL OPERATION

in the following cases:

4.1 MOS technology is used to fabricate a capacitor, utiliz­ ing the gate metallization and the substrate as the capacitor electrodes. Find the area required per 1-pF capacitance for oxide thickness ranging from 5 nm to 40 nm. For a square plate capacitor of 10 pF, what maximum dimensions are needed? 4 . 2 A particular MOSFET using the same gate structure and channel length as the transistor whose i -v characteristics are shown in Fig. 4.4 has a channel width that is 10 times greater. How should the vertical axis be relabelled to repre­ sent this change? Find the new constant of proportionality relating i and (v V,)v . What is the range of drain-tosource resistance, r , corresponding to an overdrive voltage (v - V ) ranging from 0.5 V to 2 V? D

D

cs

DS

% = 5 V and % = 1 V %s = 2 V a n d t / = 1 . 2 V v = 5 V and v = 0.2 V % = % = 5V

DS

M

GS

t

4 . 3 With the knowledge that n — 0.4/i„, what must be the relative width of n-channel and p-channel devices if they are to have equal drain currents when operated in the saturation mode with overdrive voltages of the same magnitude?

DS

S

DS

SECTION 4.2: CURRENT-VOLTAGE CHARACTERISTICS

GS

4 . 8 Consider an NMOS transistor that is identical to, except for having half the width of, the transistor whose i - v charac­ teristics are shown in Fig. 4.11(b). How should the vertical axis be relabeled so that the characteristics correspond to the nar­ rower device? If the narrower device is operated in saturation with an overdrive voltage of 1.5 V, what value of i results? D

DS

D

4 . 9 Explain why the graphs in Fig. 4.11 (b) do not change as V, is changed. Can you devise a more general (i.e., V independent) representation of the characteristics presented in Fig. 4.12? t

p

4.4 An n-channel device has k'„ = 50 / l A / V , V, = 0.8 V, and W/L = 20. The device is to operate as a switch for small v , utilizing a control voltage v in the range 0 V to 5 V. Find the switch closure resistance, r , and closure voltage, V , obtained when % = 5 V and i = 1 mA. Recalling that \i — 0.4ti„, what must W/L be for a p-channel device that provides the same performance as the n-channel device in this application?

4 . 1 0 For the transistor whose i -v characteristics are depicted in Fig. 4.12, sketch i versus the overdrive voltage v = GS ~ V, f ° DS - ov- What is the advantage of this graph over that in Fig. 4.12? Sketch, on the same diagram, the graph for a device that is identical except for having half the width. D

D

r V

GS

DS

DS

D

v

(a) the device width is halved? (b) the device length is halved? (c) both the width and length are halved?

D 4 . 2 2 For a particular n-channel MOS technology, in which the minimum channel length is 1 /an, the associated value of X is 0.02 V . If a particular device for which L is 3 /an operates at % = 1 V with a drain current of 80 fiA, what does the drain current become if v is raised to 5 V? What percentage change does this represent? What can be done to reduce the percentage by a factor of 2? - 1

DS

4 . 2 3 An NMOS transistor is fabricated in a 0.8-/an process having k' = 130 u A / V and V = 20 V//an of channel length. If L = 1.6 / a n and W = 16 /an, find V and A. Find the value of I that results when the device is operated with an overdrive voltage of 0.5 V and V = 2 V. Also, find the value of r at this operating point. If V is increased by 1 V, what is the corresponding change in 7 ? 2

A

A

4 . 1 8 When the drain and gate of a MOSFET are connected together, a two-terminal device known as a "diode-connected transistor" results. Figure P4.18 shows such devices obtained from MOS transistors of both polarities. Show that

ov

•• = * - f ( * - M )

v

D

DS

0

D

2

(b) the incremental resistance r for a device biased to operate at v = \V \ + V is given by t

DS

4 . 2 4 Complete the missing entries in the following table, which describes characteristics of suitably biased NMOS transistors:

(a) the i-v relationship is given by

2

MOS

ov

4 . 1 1 An NMOS transistor having V = 1 V is operated in the triode region with v small. With V = 1.5 V, it is found to have a resistance r of 1 kQ. What value of V is required to obtain r = 200 SI? Find the corresponding resistance values obtained with a device having twice the value of W. . t

DS

MV)

as

DS

0.01

50 5

/ (mA) D

GS

T (kß)

200 0.1 100

30

B

DS

1000

4 . 1 2 A particular enhancement MOSFET for which V, = 1 V and k' (W/L) = 0.1 mA/V is to be operated in the satura­ tion region. If i is to be 0.2 mA, find the required -v and the minimum required v . Repeat for i = 0.8 mA.

4 . 2 5 An NMOS transistor with X = 0.01 V~ is operating at a dc current I = 1 mA. If the channel length is doubled, find the new values of X, V , I , and r for each of the following two cases:

4 . 1 3 A particular n-channel enhancement MOSFET is mea­ sured to have a drain current of 4 mA at V = V = 5 V and of 1 mA at V = V = 3 V. What are the values of k' (W/L) and V, for this device?

(a) V and V are fixed. (b) I and V are fixed.

2

D

n

4.5 An n-channel MOS device in a technology for which oxide thickness is 20 nm, minimum gate length is 1 /an, k' = 100 /lA/V , and V, = 0.8 V operates in the triode region, with small v and with the gate-source voltage in the range 0 V to +5 V. What device width is needed to ensure that the minimum available resistance is 1 kQ?

A

n

GS

2

DS

4 . 1 7 An NMOS transistor, fabricated with W= 100 / a n and L = 5 / a n in a technology for which k' = 50 aA/V" and V, = 1 V, is to be operated at very low values of v as a linear resis­ tor. For v varying from 1.1 V to 11 V, what range of resistor values can be obtained? What is the available range if n

V

100 /LA is found to have an output resistance of 0.5 MO., about \ of that needed. What dimensional change can be made to solve the problem? What is the new device length? The new device width? The new W/L ratio? What is V for the standard device in this IC? The new device?

GS

S

DS

DS

GS

(a) (b) (c) (d)

4 . 1 6 For an NMOS transistor, for which V, = 0.8 V, operat­ ing with v in the range of 1.5 V to 4 V, what is the largest value of v for which the channel remains continuous?

361

D

A

as

DS

D

a

D

2

n

DS

4.6 Consider a CMOS process for which L 15 nm, u„ = 550 cm /V- s, and V, = 0.7 V.

= 0.8 am, t =

min

ox

2

GS

GS

DS

DS

D 4 . 1 4 For a particular IC-fabrication process, the transconductance parameter k' = 50 yiA/V , and V, = 1 V. In an application in which v = v = V i, =-5 V, a drain current of 0.8 mA is required of a device of minimum length of 2 am. What value of channel width must the design use? 2

ox

n

ov

GS

DSmin

D

ov

GS

DS

GS

DS

supp

4 . 1 5 An NMOS transistor, operating in the linear-resistance region with v = 0.1 V, is found to conduct 60 a A for v = 2 V and 160 a A for v = 4 V. What is the apparent value of threshold voltage V,? If k' = 50 a A / V , what is the device W/L ratio? What current would you expect to flow with v = 3 V and v = 0.15 V? If the device is operated at v = 3 V, at DS

GS

GS

2

ox

2

GS

DS

GS

4 . 2 6 An enhancement PMOS transistor has k' (W/L) = 80 / i A / V , V, = - 1 . 5 V, and X = - 0 . 0 2 V . The gate is con­ nected to ground and the source to +5 V. Find the drain current for v = +4 V, +1.5 V, 0 V, and - 5 V. p

IGURE P 4 . 1 8

2

4 . 1 9 For a particular M O S F E T operating in the satura­ tion region at a constant v , i is found to be 2 mA for v = 4 V and 2.2 mA for v = 8 V. What values of r , V , and X correspond? GS

D

DS

DS

0

A

- 1

D

4 . 2 7 Ap-channel transistor for which |V \ = 1 V and |V | = 50 V operates in saturation with \ v \ = 3 V, \ v \= 4 V, and i = 3 mA. Find corresponding signed values for v , v , v , v , V„ V , X, and k' (W/L). t

GS

D

4 . 2 ® A particular MOSFET has V = 50 V. For operation at 0.1 mA and 1 mA, what are the expected output resistances? In each case, for a change in v of 1 V, what percentage change in drain current would you expect? A

DS

n

4.7 Consider an n-channel MOSFET with t = 20 nm, u„ = 650 cm /V- s, V, = 0.8 V, and W/L = 10. Find the drain current

DS

DS

(b)

(a)

n

n

(a) Find C and k' . (b) For an NMOS transistor with W/L = 16 um/0.8 am, calcu­ late the values of V , V , and V needed to operate the transistor in the saturation region with a dc current 7 = 100 uA. (c) For the device in (b), find the value of V and V required to cause the device to operate as a 1000-fl resistor for very small v .

GS

D

D 4 . 2 1 In a particular IC design in which the standard channel length is 2 /an, an NMOS device with W/L of 5 operating at

A

DS

GS

SD

A

SG

DS

p

4 . 2 8 In a technology for which the gate-oxide thickness is 20 nm, find the value of for which j = 0.5 V . If the dopmg level is maintained but the gate oxide thickness is increased to 100 nm, what does y become? If y is to be kept constant at 0.5 V , to what value must the doping level be changed? 1/2

3 6 2

..

'

CHAPTER 4

M O S FIELD-EFFECT TRANSISTORS (MOSFETs)

+ 10 V

4 . 2 9 In a particular application, an n-channel MOSFET operates with V in the range 0 V to 4 V. If V, is nominally 1.0 V, find the range of V, that results if y = 0.5 V and 2 = 0.6 V. If the gate oxide thickness is increased by a factor of 4, what does the threshold voltage become? SB

PROBLEMS

+ 1V

Q4.35 Consider the circuit of Fig. E4.12. Let Q and Q have V, = 0.6 V,p C = 200 pATV' , L i = L = 0.8 um, Wi = 8 pm, andA = 0.

+1V

X

t

0

I / 2

n

f

Q.2, and Q-i to obtain the voltage and current values indicated.

(a) Find the value of R required to establish a current of 0.2 m A i n Q . (b) Find W and a new value for R so that Q operates in the saturation region with a current of 0.5 mA and a drain voltage of IV.

+5 V

X

4 . 3 0 A p-channel transistor operates in saturation with its source voltage 3 V lower than its substrate. For j = 0.5 V , 2