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Новосибирский государственный технический университет

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Книги2 / 1988 Kit Man Cham, Soo-Young Oh, John L. Moll, Keunmyung Lee, Paul Vande Voorde, Daeje Chin (auth.) Computer-Aided Design and VLSI Device Development 1988

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362	Table of Symbols
Cp	peripheral capacitance coefficient
Cp	coefficient of auger recombination
Cp	peak concentration
CT	total impurity concentration
Cv	normalized vacancy density
ct	electrically active impurity concentration
C·	equilibrium oxidant concentration in the oxide
c	speed of light in vacuum
D	diffusivity
Dc	counter-doping dose
Deff	effective diffusion coefficient
D j+	diffusivity due to positive vacancies
Di	diffusivity due to negative vacancies
Dr	diffusivity due to doubly negative vacancies
Df	diffusivity due to neutral vacancies
dk	mask thickness at kth segment
Dn	n- pocket dose
DN	diffusivity under non-oxidizing condition
D<lK	diffusivity due to oxidizing ambient
E	electric field strength
Ee	electron energy of conduction band edge
Efp	quasi-Fermi level for holes
Ej	electron energy at the intrinsic Fermi level
Em	maximum electric field
En	electric field normal to current flow
Ep	electric field parallel to current flow
ESAT	critical field for velocity saturation
E ~	activation energy of oxide viscosity
F, fF, pF	Farad unit, lE-lS F, lE-l2F
F,F1, F 2, F 3	oxidants fluxes

Table of Symbols

363

	empirical parameter in mobility model
	channel conductance
	transconductance
	oxide growth rate in the z-direction
h	transport coefficient
I	current
I (x,y)	Implant profile
IDD	maximum available current from power supply
IDs	drain to source current
IDSAT	drain to source current at saturation
IH	latchup holding current
h	transistor subthreshold leakage current
Imax	maximum concentration
IPT	punchthrough current
ISUB	substrate current
IT	latchup triggering current
ITH	transistor threshold current
	impurity flux
	electron current density
	hole current density
	coefficient of current density
K	scaling factor
k	Boltzmann constant
k	surface reaction coefficient
L	inductance
L	channel length
L	decay length in thin oxide regime
LD	length of uniform drain region
Leff	effective channel length

364	Table of Symbols
	minimum channel length
	polysilicon gate length
	length of uniform source region
	diffusion length of vacancies
	effective length of potential barrier
m	segregation coefficient
N	NA-ND
N	number of nodes
N+	doping concentration in n+ polysilicon
NA	acceptor concentration
N;"	ionized acceptor concentration
NB	substrate doping
Nc	correction concentration for oxidation
ND	donorconcenuation
Nt,	ionized donor concentration
N;	inuinsic carrier density
N;	dopant concentration, inert ambient
Nix	concentration in x-direction, inert ambient
Niy	concentration in y-direction, inert ambient
No	coefficient of band gap narrowing
No	dopant concentration, oxidizing ambient
Nox	concentration in x-direction, oxidizing ambient
Nqy	concentration in y-direction, oxidizing ambient
Np,N;	implantation dose
Ns	subsuate surface impurity concentration
Nw	N-well doping concentration
	surface electron concentration
n	unit vector normal to the surface

nelectron density intrinsic carrier density

n;,e	effective intrinsic carrier density
run	nanometer unit (lE-9 m)

Table of Symbols

365

p	Gaussian probability distribution
p	pressure
p	hole density
Q	minority carrier concentration in GEMINI
QB	integrated carrier in GEMINI punchthrough simulation
QL	integrated carrier in GEMINI channel-length simulation
QNA	channel implant dose
QND	depletion implant dose
Qn	electron density per unit area in the channel
Qss	interface fixed charge density
Qw	integrated carrier in GEMINI channel-width simulation

qelectron charge

resistance recombination

drain series resistance N° pocket peak depth

range of Gaussian implant distribution source series resistance

subthreshold slope

empirical parameter in mobility model poly gate side-wall spacer thickness

T	absolute temperature
Tax;	oxide thickness
t	time

U	active impurity concentration
U(n,p)	electron and hole recombination rate

366

V·

V+

VBS

VDD

VDS

VDSAT

Vjb

VGS

Vin

Vout

VPT

VSB

VSS

VTO

VT(LOW)

VT(HI)

VTLC

VTN

VTP

oxide growth velocity negative vacancies doubly negative vacancies positive vacancies substrate bias voltage

substrate to source bias voltage empirical parameter in mobility model drain bias voltage

circuit bias voltage

drain to source bias voltage saturation drain voltage flat-band voltage

gate bias voltage

gate to source bias voltage

itb device parameter in sensitivity matrix nominal value of V;

inverter input voltage inverter output voltage punchthrough voltage barrier potential source bias voltage saturation velocity

source bias with respect to the substrate circuit ground voltage

transistor threshold voltage

threshold voltage at zero substrate bias low drain bias threshold voltage

high drain bias threshold voltage long channel threshold voltage n-channel threshold voltage p-channel threshold voltage

transistor channel width drawn channel width

Table of Symbols

Table of Symbols		367
Weff	effective channel width
x	x-coordinate
X	process feature
X	average value of process feature
Xd	depletion depth
Xi	initial oxide thickness
Xj	diffusion junction depth
X 0	oxide thickness
1'j	counter-doping junction depth
y	y-coordinate
Zc	characteristic impedance
Z •	effective width of potential barrier
t:.L	channel length variation
Mp	standard deviation in y-direction
6.W	channel width loss per side
n	material boundaries
e	vector stream function
V	gradient operator
Q	empirical parameter in mobility model
o¢n	increment of electron quasi-Fermi potential
o<fJp	increment of hole quasi-Fermi potential

edielectric constant JJ. mobility

JJ.oxide viscosity

J.I.i	ith moment of an implant distribution
J.'n	electron mobility
JJ.o	zero-field mobility
I1p	hole mobility
<fJ	electric potential

368

()

1-D

2-D

Table of Symbols

hole quasi-Fermi potential electron quasi-Fermi potential internal potential

difference between intrinsic and hole Fermi level oxide density

resistivity standard deviation

standard deviation of Gaussian implant distribution electron life time

hole life time

z-component of stream function one-dimensional two-dimensional

Subject Index

Avalanche breakdown, 171,212,295	grid,92-93
	input file, 98
BIRD,14	input format, 97-100
Bird's beak, 235, 259	input structure, 88-89
Body effect, 188-190	mobility model, 93-97
Boron encroachment	numerical technique, 92
LOCOS, 252, 258	output, 101
modified LOCOS, 259-261	CMOS, 271-273
SWAMI, 265-267	cross-section, 25
Boundary-value method, 61	n-well, 235, 277
Breakdown, source-drain, 171, 212,	p-well, 246, 248
295	submicron, 271-273
Buried channel, 328	trench isolated, 233
	Capacitance
CAD, 8	depletion layer, 170
CADDET	gate oxide, 170
basic equation, 90-92	Channel implant
device simulations, 97-101,	deep, 187
211-230,315-333	depletion, 328-333
flow chart, 92-94	n-channel, 186-188

370

shallow, 187

Channel length, effective, 183, 317 Channel profile

n-channel, 179, 182 p-channel, 279, 290

Channel width drawn, 252

effective, 167, 183,252,257 extraction of effective, 255-257 loss, 255-257, 268

Channeling, 279 Characteristic impedance, 133 Counter-doping, 144, 277-280

dose, 144,278 energy, 144 junction, 279-280

Critical electric field, 212 Current continuity equation stream function form, 91 time dependent form, 103

Current transport equation, 104

Degradation

hot electron, 212-213, 295 linear transconductance, 217

saturation transconductance, 217 Depletion layer capacitance, 170 Depletion mode MOSFET, 326-333 Device optimization, 174

Device simulation, history, 13-14 DIBL (see Drain-induced barrier lowering)

Diffusion

across interfaces, 38-39

Subject Index

concentration enhanced, 163 continuity equation, 35 field-driven, 35-36 gradient-driven, 35

high concentration, 36-38, 51-53, 163

low concentration, 37, 48-49 moving boundary, 49-51 oxygen enhanced, 38,157-162 vacancy assisted, 36-37

Diffusivity arsenic, 37 boron,37,157 effective, 59 intrinsic,36-37

phosphorus, 37-38 Direct matrix solution, 106

Double diffused drain, 213, 295 Drain electric field, 221-229 Drain-induced barrier lowering,

197-207, 280-289 Duality, 135

Einstein's relation, 90 Electric field

channel, 212

critical, velocity saturation, 212 drain,212,221-229

maximum, drain, 212, 225-226 normal,94

parallel, 94 Electromigration, 4

FCAP2,13O

Subject Index

371

FCAP3,136 FIELDAID, 14

Factorial experiments, 144 Fermi-Dirac integral, 75 Fermi-Dirac statistics, 90 Finite-difference method, 79 Flat-band voltage, 326 Fringing component, 338

GEMINI

basic equation, 75-77

device simulations, 177, 181-184 capability, 72-73

channel length simulation, 80-83 channel width simulation, 83-85 five-point finite-difference approximation, 79

grid,77

input file, 80-86 numerical technique, 79

punchthrough current calculation, 76-77

SWAMI simulations, 265-268 trench simulations, 238-245

Gate oxide capacitance, 180

effect on subthreshold slope,

284-285

Gaussian implant profile, 27 Glass-transition temperature, 59 Graphical post-processing, 16 Green's function, 14-15,61 Gummel's iteration, 92,105 Gummel-Scharfetter formula, 105

Hot electron degradation, 174,212, 295

ICCG, 105, 130 Impact ionization, 212

Implantation energy, 324 Impurity profile

n - pocket, 303 n-channel, 45,179,182 p-channel, 158,279,290 sourcejdrain,45,68,179 SWAMI,266

trench structure, 239 Inductance, 133

Interconnect capacitance, 335-345, 348-355

Interconnect resistance, 346-347 Interface damage, 212

Inverter circuit, 181, 320 Ion implantation

boron, 153-154

distribution moments, 29-30 gaussian profile, 27

Pearson IV profile, 30,153-154 projected range, 29

standard deviation, 29 Isolation, 251-269

Jacobian matrix, 106

LDD (see lightly-doped drain) LOCOS, 252-258

modified,259-261 Latchup, 233-234

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