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11.42 An n-channel MOSFET has the following parameters:





r , 400 A Vfb = -0.5 V Ж = 10 /im

= 5 x 10 cm-

II, =450cm-/V-s

Plot /T7) versus Vqs over the range 0 5 In < 1 mA when the transistor is biased the saturation region for the following values of sourcc-to-body voltage: V; = 0,1, and 4 V.

Consider a p-channel MOSFET with

600 A and .4/ = 5x Ю^Ч-т-

Determine the body-to-source voUage, Vbs. such that the shift in threshold voltage, A Vr, from the i 0 curve is A Vy- = -1.5 V.


An NMOS device has the following parameters: n+ poly gate, t = 400 A, N, = 10* cm~\ and Q 5 x 10 cm~- {a) Determine Vj- [b] Is it possible to apply a Vsii voltage such that Vj = 0? If so, what is the value of Vsb

Investigate the threshold voltage shift due to substrate bias. The threshold shift is given by Equation (11.72). Plot Д V; versus Vsb over the range 0 < Vsb 5 5 Vfor several values of and rx. Determine the conditions for which AV-j is limited to aj maximum value of 0,7 V over the range of Vsb

Section 11.4 Frequency Limitations




Consider an ideal n-channel MOSFET with a width-to-length ratio oi (W/L) 10, an electron mobility of - 400 cm-/V-s, an oxide thickness of fx = 475 A, and a threshold voltage of Vj = H-0.65 V. [a) Determine the maximum value of source resistance so that the saturation transconductance g, , is reduced by no more than 20 percent from its ideal value when Vcs = 5 V. (h) Using the value of calculated in part (a), how much is g j reduced from its ideal value when Vqs = 3 V?

An n-channel MOSFET has the following parameters:

fi, = 400 cmVV-s L = 2 iim Vr +0.75 V

500 A

W = 20 i.im

Assume the transistor is biased in the saturation region at Vs = 4 V. (a) Calculate the ideal cutoff frequency, (b) Assume that the gate oxide overlaps both the source and drain contacts by 0.75 дт. If a load resistance of Rt = 10 is connected to the output, calculate the cutoff frequency.

Repeat Problem 11.47 for the case when the electrons are traveling at a saturation velocity of = 4 x 10 cm/s.

Summary and Review

*11.49 Design an ideal silicon n-channel MOSFET with a polysilicon gate to have a threshold voltage of Vr = 0.65 V, Assume an oxide thickness of f, - 300 A, a channel length of L = 1.25 pm, and a nominal value of <2= x lO cm~-. It is desired to have a drain current of In = 50 д Aat Vqs = 2.5 V and Vps = 0.1 V. Determine the substrate doping concentration, channel width, and type of gate required.

Reading List 521

*11.50 Design an idea! silicon n-channel depiction mode MOSFET with a polysilicon gate to have a threshold voltage of W = -0.65 V. Assume an oxide thickness of tx = 300 A, a channel length of L = 1.25 дт, and a nominal value of Q,. = 1.5 x 10 cm h is desired to have a drain current of /о (sat) = 50 дА at Vs = 0. Determine the type of gate, substrate doping concentration, and channel width required.

* 11.51 Consider the CMOS inverter circuit shown in Figure 11.60a, Ideal n- and p-channel

devices are to be designed with channel lengths of L =2.5 д mand oxide thicknesses of t, = 450A. Assume the inversion channel mobilities anc one-half the bulk values. The threshold voltages of the n- and p-channel transistors are to be -1-0.5 V and -0.5 V, respectively. The drain current is to be ? - 0.256 mA when the input voltage to the inverter is 1.5 V and 3.5 V with V/? = 5 V, The gate material is to be the same in each device. Determine the type of gate, substrate doping concentrations, and channel widths.

*11.52 A complementary pair of ideal n-channel and p-channel MOSFETs are to be

designed lo produce the same /-V characteristics when they are equivalently biased. The devices are to have the same oxide thickness of 250 A and the same channel length of L = 2 дт. Assume the SiO: layer is ideal. The n-channel device is to have a channel width of W = 20 дт. Assume constant inversion layer mobilities of д„ = 600 cm-/V-s and jip = 220 cm*/V-s, {a) Determine p-type and n-type substrate doping concentrations, (h) What are the threshold voltages? (c) What is the width of the p-channel device?


1. Dimitrijev, S. Understanding Semiconduaor Devices. New York: Oxford University Press, 2000.

2. Kano, K. Semiconductor Devices. Upper Saddle River, NJ: Prentice Hall, 1998.

3. Muller, R. S., and T, 1. Kamins. Device Electronics for Integrated Circuits, 2nd ed. New York: Wiley, 1986.

4. Ng, K. K. Complete Guide to Semiconductor Devices. New York: McGraw-Hill, 1995.

5. Nicollian, E. H., and J. R. Brews, MOS Physics and Technology, New York: Wiley, 1982,

6. Ong, D. G. Modern MOS Technology: Processes, Devices, and Design. New York: McGraw-Hill, 1984.

7. Pierret. R. F. Semiconductor Device Fundamentals. Reading, MA: Addison-Wesley, 1996-

8. Roulston, D. J. An Introduction to the Physics a/Semiconductor Devices. New York: Oxford University Press, 1999.

9. Schroder, D. K. Advanced MOS Devices. Modular Series on Solid State Devices, Reading, MA: Addison-Wesley, 1987.

10. Shur, M. Introduction to Electronic Devices. New York: John Wiley & Sons, Inc., 1996.

* 11. S hur, M. Physics of Semiconductor Devices. En g 1 с wood С li ff s, N J: Prentice H al1, 1990.

12. Singh, J. Semiconductor Devices: An Introduction. New York: McGraw-Hill, 1994.

13. Singh, J. Semiconductor Devices: Basic Principles, New York: Wiley, 2001.

14. Streetman, B. G., and S. Banerjee. Solid State Electronic Devices. 5th ed. Upper Saddle River, NJ: Prentice Hall, 2000.

CHAPTERll Fundamentalsofthe Metal-Oxide-Semicond uctor Field - Effect Transistor

15, Sze, S. M. High-Speed Semiconductor Devices. New York: Wiley, 1990.

16. Sze, S. M, Physics of Semiconductor Devices. 2nd ed. New York: Wiley, 1981.

*17. Taur, Y., and T. H. Ning. Fundamentals of Modem VLSI Devices. New York:

Cambridge University Press, 1998. j

*18. Tsividis, Y Operation and Modeling of the MOS Transistor 2nd ed. Burr Ridge, IL.: McGraw-Hill, 1999.

19. Werner, W. M. The Work Function Difference of the MOS System with Aluminum Field Plates and Polycrystalline Silicon Field Plates. Solid State Electronics 17 (1974), pp.769-75.

20. Yamaguchi, Т., S. Morimoto, G. H. Kawamoto, and J. C. DeLacy. Process and Device Performance of 1 дт-Channel n-Well CMOS Technology.* IEEE Transactions on Electron Devices ED-31 (February 1984), pp. 205-14.

21. Yang, E. S. Microelectronic Devices. New York: McGraw-Hill, 1988.

Mo Permeability of free space (H/crn)

V Frequency (Hz)

p Resistivity (Q-cra), volume charge density (C/cm-*)

a Conductivity cm )

Да Photoconductivity (Q~ cm~ )

a, Intri nsicconductivity(~cm~)

cr, ap Conductivity of n-type and p-type semiconductor (Q cm~)

r Lifetime (s)

T , Tp Electron and hole lifetime (s)

TfiO tfA) Excess minority earner electron and hole lifetime (s)

To Lifetime in space charge region (s)

Ф Potential (volt)

ф{0 Time-dependent wave function

Аф Schottky barrier lowering potential (volt)

фвп Schottky barrier height (volt)

Фво Ideal Schottky barrier height (volt)

Ф/г^у Ф/р Potential difference (magnitude) between Ef and Ef

in n-type and p-type semiconductor (volt)

Ф/-!, Фгр Potential difference (with sign) between £/r, and Ejr

in n-type and p-type semiconductor (volt)

Фт Metal work function (volt)

0 Modified metal work function (volt)

фтх Metal-semicond uctor work function difference (volt)

< , фр Potential difference (magnitude) between E and Ej.

in n-type and between E. and £f in p-type semiconductor (volt)

фх Semiconductor work function (volt), surface potential (volt)

X Electron affinity (volt)

x Modified electron affinity (volt)

Ф (x) Time-independent wave function

0) Radian frequency (s ~)

Г Reflection coefficient

E Electric field (V/cm)

Eh Hall electric field (V/cm)

Ecrit Critical electric field at breakdown (V/cm)

B() Angular wave function

Ф Photon flux (cm s~)

Ф(ф) Angular wave function

Ф(л,г) Total wave function

А Р Р £ IN D I X

Selected List of Symbols

his list does not include some symbols that are defined and used specifically in only one section. Some symbols have more than one meaning; however, the context in which the symbol is used should make the meaning unambiguous. The usual unit associated with each symbol is given.

Unit cell dimension (A), potential well width, acceleration.

gradient of impurity concentration, channel thickness of a

one-sided JFET (cm)

Bohr radius (A)


Speed of light (cm/s)

Distance (cm)

Electronic charge (magnitude) (C), Napierian base

Frequency (Hz)

Ferini-Dirac probability funcrion

Cutoff frequency (Hz)

Generation rate (cm- s)

Generation rate of excess carriers (cm~ s~)


Density of states funcrion (cm~ eV~)

gc. gv

Density of states function in the conducrion band and

valence band (cm~- eV)

Channel conductance (S), small-signal diffusion

conductance (S)

Transconductance (A/V)

gn gp

Generation rate for electrons and holes (cm~- s~)

Plancks constant (J-s), induced space charge width in a

JFET (cm)

Modified Plancks constant ihjln)

hf Small-signal common emitter current gain

j Imaginary constant, л/-T

к Boltzmanns constant (J/K), wavenumber (cm~)

k Conduction parameter (A/V)

m Mass (kg)

Rest mass of the electron (kg)

m* Effective mass (kg)

m*, m* Effective mass of an electron and hole (kg)

л Integer

nj,m,s Quantum numbers

, p Electron and hole concentration (cm~)

n Index of refraction

n[ p Constants related to the trap energy (cm )

nq, Pco Thermal-equilibrium minority carrier electron

concentration in the base and minority carrier hole concentration in the emitter and collector (cm~)

rid Density of electrons in the donor energy level (cm *)

rii Intrinsic concentration of electrons (cm-)

no, /?o Thermal-equ i 11 brium conce n trari on of el ectron s

and holes (cm *)

Pn Minority carrier eleclron and minority carrier hole

concentration (cm~)

fpi) pno Thermal-equilibrium minority carrier electron and

minority carrier hole concentration (cm)

rig Density of a two-dimensional electron gas (cm~)

p Momentum

Pa Density of holes in the acceptor energy level (cm~-)

pi Intrinsic hole concentration (= п^){ст~)

q Charge (C)

г^О.ф Spherical coordinates

rj, rjj Small-signal diffusion resistance (Q)

rds Small-signal drain-to-source resistance (П)

s Surface recombination velocity (cm/s)

t Time (s)

td Delay time (s)

Гох Gate oxide thickness (cm or A)

ts Storage time (s)

u{x) Periodic wave function

V Velocity (cm/s)

Vd Carrier drift velocity (cm/s)

ds. vat Carrier saturation drift velocity (cm/s)

x,y\z Cartesian coordinates

x Mole fracrion in compound semiconductors

xb,xe,xc Neutral base, emitter, and collector region widths (cm)

Xd Induced space charge width (cm)

XdT Maximum space charge width (cm)

jc; Xp Depletion width from the metallurgical junction into n-type

and p-type semiconductor regions (cm)

A Area (cm)

Л* Effecrive Richardson constant (A/K/cm)

В Magnetic flux density (Wb/m)

B, E,C Base, emitter, and collector

В VcBO Breakdown voltage of collector-base junction with emitter

open (volt)

В Vceo Breakdown voltage of collector-emitter

with base open (volt)

С Capacitance (F)

С Capacitance per unit area (F/cm)

Cd, Cj Diffusion capacitance (F)

CfB Flat-band capacitance (F)

Cgs. Cd Cds Gate-source, gate-drain, and drain-source capacitance (F)

Cj Junction capacitance per unit area (F/cm)

Cm Miller capacitance (F)

C , Cp Constants related to capture rate of electrons and holes

Cyjt Gate oxide capacitance per unit area (F/cm)

C Reverse-biased B-Cjuncrioncapaci tance (F)

D, S,G Drain, source, and gate of an FET

Ambipolar diffusion coefficient (cm?/s)

Db, De, Dc Base, emitter, and collector minority carrier diffusion

coefficients (cm/s)

Dit Density of interface states (#/eV-cm-)

D , Dp Minority carrier electron and minority carrier hole

diffusion coefficient (cm/s)

E Energy (joule or eV)

Ea Acceptor energy level (eV)

Ec, £u Energy at the bottom edge of the conduction band and top

edge of the valence band (eV)

AEc, Difference in conduction band energies and valence band

energies at a heterojuncrion (eV)

Ed Donor energy level (eV)

Ef Fermi energy (eV)

Efi Intrinsic Fermi energy (eV)

Efri, Efp Quasi-Fermi energy levels for electrons and holes (eV)

E Bandgap energy (eV)

AEg Bandgap narrowing factor (eV), difference in bandgap

energies at a heterojunction (eV)

£f Trap energy level (eV)

F Force (Л^)

F, Electron and hole particle flux (cm~ )

Fi/2(r]) Fermi-Dirac integral function

G Generation rate of electron-hole pairs (cm~ s~ )

Gl Excess carrier generation rate (cm- sM

Gfio, Gpo Thermal equilibrium generarion rate for electrons and

holes (cm - s )

Goi Conductance (S)

/ Current (A)

Anode current (A)

Ib, h:y Base, emitter, and collector current (A)

Icbo Reverse-bias collector-base junction current with

emitter open (A)

IcEO Reverse-bias collector-emitter current with base open (A)

If) Diode current (A), drain current (A)

/£,(sat) Saturation drain current (A)

Il Photocurrent (A)

I PI Pinchoff current (A)

Is Ideal reverse-bias saturation current (A)

Isc Short-circuit current (A)

Photon intensity (energy/cm/s)

J Electric current density (A/cm)

/gen Generation current density (A/cm)

Д Photocurrent density (A/cm)

y , Jp Electron and hole electric current density (A/cm)

J~, J+ Electron and hole particle current density (cm~ s~ )

Jrec Recombination current density (A/cm)

JfQ Zero-bias recombination current density (A/cm)

Jn Reverse-bias current density (A/cm)

Js Ideal reverse-bias saturation current density (A/cm)

JT Ideal reverse saturation current density in a

Schottky diode (A/cm)

L Length (cm), inductance (H), channel length (cm)

AL Channel length modulation factor (cm)

Lb, Lt, Lc Minority carrier diffusion length in the base, emitter,

and collector (cm)

L i) Debye length (cm)

L , Lp Minority carrier electron and hole diffusion length (cm)

M, Mn Multiplication constant

N Number density (cm~)

Na Density of acceptor impurity atoms (cm~)

Nb, Ne, Nc Base, emitter, and collector doping concentrarions (cm~-)

Nc, Ni) Effective density of states funcrion in the conduction band

and valence band (cm~)

Nd Density of donor impurity atoms (cm -)

Nij Interface state density (cm -)

Nt Trap density (cm~)

P Power (watt)

P(r) Probability density function

Q Charge (C)

Q Charge per unit area (C/cm)

Qв Gate controlled bulk charge (C)

Q Inversion channel charge density per unit area (C/cwr)

Qig Signal charge density per unit area (C/crr?)

Qj(max) Maximum space charge density per unit area (C/cm)

Qs Equivalent trapped oxide charge per unit area (C/cm)

R Reflecrion coefficient, recombination rate (cm s ),

resistance (Q)

R(r) Radial wave function

Rc Specific contact resistance (Q-cm)

Ren, Rep Capture rate for electrons and holes (cm~ s~)

Rem Rep Emissiou rate for electrons and holes (cm * s~)

Rfj, Rp Recombination rate for electrons and holes (cm~ s~)

RnO- RpO Thermal equilibrium recombinarion rate of electrons

and holes (cm~ s~)

T Temperature (K), kinetic energy (J or eV),

transmission coefficient

V Potential (volt), potenrial energy (J or eV)

Va Applied forward-bias voltage (volt)

Va Early voltage (volt), anode voltage (volt)

Vbi Built-in potenrial barrier (volt)

Vb Breakdown voltage (volt)

Vbd Breakdown voltage at the drain (volt)


APPENDIXA Selected List of Symbols

Vbe, Vcb. Усе

Vds Ус5 VD.v(sat)


Vsb V,

on, op

8пр, 8pn

Д/11 Ц-р

Base-emitter, collector-base, and collector-emitter voltage (volt)

Drain-source and gate-source voltage (volt)

Drain-source saturation voltage (volt)

Flat-band voltage (volt)

Gate voltage (volt)

Hall voltage (volt)

Open-circuit voltage (volt)

Potential difference across an oxide (volt)

Pinchoff voltage (volt)

Punch-through voltage (volt)

Applied reverse-bias voltage (volt)

Source-body voltage (volt)

Thermal voltage {kTje)

Threshold voltage (volt)

Threshold voltage shift (volt)

Total space charge width (cm), channel width (cm)

Metallurgical base width (cm)


Photon absorption coefficient (cm~), ac common base current gain

Electron and hole ionization rates (cm) dc common base current gain Base transport factor Common-emitter current gain Emitter injection efficiency factor Recombination factor

Excess electron and hole concentration (cm *)

Excess minority carrier electron and excess minority carrier hole concentration (cm~)

Permitfivity (F/cm)

Permitfivity of free space (F/cm)

Permitrivi ty of an oxide (F/cra)

Relative permittivity or dielectric constant

Permittivity of a semiconductor (F/cm-)

Wavelength (cm or m)

Permeability (H/cm)

Ambipolar mobility (cmVV-s)

Electron and hole mobility (cm/V-s)

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