introduction to silvaco athena tool and basic concepts in process

EEE 533 Semiconductor Device and Process Simulation

Introduction to Silvaco ATHENA Tool and

Basic Concepts in Process Modeling

Part - 2

Instructor: Dragica Vasileska

Department of Electrical Engineering

Arizona State University


3. Description of the diffusion process

� The diffusion process is a main step in the fabrication of integrated circuits.

� Some characteristic features of the diffusion process are listed below:

� temperature: 900 °C to 1300 °C

� type of diffusion: selective and non-selective

� amount of diffused impurities:determined via solid-solubility limits

Solid-solubility of impurity elements in silicon


� The process of diffusion is described via the two Fick’s laws:

( )

iiti

citiiitiii

Gt

C

CCZCD

=⋅∇+∂

∂

−µ−∇−=

J

EJ

Ji � flux of diffusing species

Cti � total concentration

Cci � concentration of electrically inactive impurities

Zi � charge state of the i-th particle

Di � diffusion coefficient

µi � mobilityE � electric field

Gi � net generation term which equals zero for impurity

diffusion


� The electric field term that appears in the expression describing first Fick law should, in principle, be calculated by solving Poisson’s equation, of the form:

where the net concentration of ionized impurities is:

� For simplicity, the potential, and therefore, the electric field are calculated using charge-neutrality, which gives:

( )AD NNnpe

−+−ε

−=ψ∇2

( )∑ −−=i

citii CCZC

=ψ −

iT

n

CV

2sinh 1


� The magnitude of the diffusion coefficient depends upon the concentration of defects in the crystal

� There are four different types of defects that can be observed in a crystal:

� point defects

� line defects

� area defects

� volume defects

Silicon atoms

Impurity on substitutional siteVacancy

Silicon interstitial

Impurity on interstitial site

Frenkeldefect

Point defects description


� The position of the interstitial voids in a zincblende lattice is schematically illustrated in the figure below:


� Listed below are the characteristic features of vacancies:

� Vacancy is a missing atom in the crystalline lattice

� The energy of formation of a vacancy equals 2.3 eV (to break four bonds), and the energy of migration is 0.18 eV

� Since divacancy requires breaking of six covalent bonds, the energy of formation of divacancy is only slightly higher, and is, therefore, commonly encountered

� The # of vacancies per unit volume is given by:

� Since the presence of a vacancy results in four unsatisfied bonds, vacancies are of an acceptor-type with energy levels:

(EV + 0.71 eV) for V-

(vacancy)

(EV + 1.0 eV) for V= (divacancy)

−=

Tk

ENn

B

ss exp

N � total # of atoms in a crystal(5×1022 cm-3)

Es � energy of formation

ns � density of vacancies


� The characteristic features of interstitials are listed below:

� Interstitial is a Si atom located on one of many interstitial sites

� The energy of formation of an interstitial equals 1.1 eV

� The # of interstitials is calculated in the same manner as the # of vacancies

� Interstitials have four valence electrons that can be donated to the conduction band, and are of a donor-type, with energy level

(EC - 0.91 eV) for V+

� Some characteristic properties of Frenkel pairs:

� The energy of formation of a Frenkel pair is comparable to the energy of formation of an interstitial

� The # of Frenkel pairs is calculated from:

−=

Tk

ENn

B

ff

2exp Ef � energy of formation

of a Frenkel defect


� The diffusion process in a semiconductor occurs via vacancies and interstitials, which is schematically shown in the figures below:

� The magnitude of the diffusion coefficient is of the following form for the two dopant concentration limiting cases:

(a) low concentration:

(b) high concentration:

−=

Tk

EDD

B

aexp0 Ea � activation energy

+=−

++==−−

+

+

+=

⋅+⋅+⋅+=

ii

ii

ii

i

iiii

Dn

pD

n

nD

n

nD

VDVDVDDD

20

0

Vacancydiffusion

Interstitialdiffusion


� For doping concentrations close to the solid-solubility limit, the impurities start to cluster and stop diffusing:

� The relationship between the total Ct and the electrically inactive concentration Cc due to clustering effect, is found by solving the following equation:

� The clustering effect is important when the doping concentra-tion is on the order of 3×1020 cm-3 for arsenic.

( ) cm

ctc CkdCCkcm

t

C⋅−−⋅⋅=

∂

∂

Cluster size

Clustering rate Declustering rate


� Under the assumption of zero electric field and constant diffusion coefficient, one needs to solve the following differential equation using, for example, Laplace transform:

� Depending upon the type of boundary conditions, two possible solutions exist:

� diffusion from an infinite source� diffusion from a finite source

Diffusion from an infinite source

� The initial and boundary conditions for this case are:

� This leads to the following form of the solution:

2

212

x

CD

t

CCD

t

C D

∂

∂=

∂

∂→∇=

∂

∂

0)0,0()0,0( ==>=≥= txCandCtxC s

,2

),(

=

Dt

xerfcCtxC s Dt � characteristic length


Diffusion from a finite source

� Using a predeposition process, a certain ammount of impurity atoms is added in a very narrow region near the surface. Then the sample is heated and diffusion process takes place.

� The initial and boundary conditions for this case are:

� This leads to the following form of the solution:

.),(000,0

constdxtxCQandx

C

tx

=∫==∂

∂ ∞

≥=

−

π=

Dt

x

Dt

QtxC

4exp),(

2

C/Cs

x

Dt

Infinitesource

C/Cs

x

DtFinite

source


� Junction depth determination

During the diffusion of, for example, acceptor-type impurities, the net acceptor concentration equals to:

The junction depth is, then, given by the following expressions:

(a) Infinite source:

(b) Finite source:

DAnetA NtxNtxN −= ),(),(

),( txN

x

⋅= −

0

12N

NerfcDtx D

j

π=

DtN

QDtx

Dj ln2

.constND =

),( txN A

p-type n-type

jx


� Lateral diffusion

The previously described model accurately describes the diffusion process, except near the edges of the mask windows, where impurities also diffuse laterally.

� The ratio of the lateral to vertical penetration is about 75% for concentration independent diffusivities and about 65% to 70% for concentration dependent diffusivities.

� Since electric field intensities are higher for cylindrical and spherical junction regions, avalanche breakdown voltages will be substantially lower when compared to the plane junction case.

2D - diffusion profileshowing the lateral diffusion


� Impurity redistribution during subsequent oxidation

Dopant impurities near the silicon surface are redistributed during the subsequent thermal oxidation process. The redistribution process depends upon several factors listed below:

� The magnitude of the segrega-tion coefficient:

� The magnitude of the impurity diffusivity in the oxide

� The consumption of the underlying Si layer

2SiOin

Si in

C

Ck =


� Diffusion constant determination

Decribed below are two methods for the experimental deter-mination of the diffusion constant:

(A) pn-junction method

The requirement here is to make one or more diffusions into semicon-ductors with known background concentration and opposite impurity type. After determining the junction depth, one gets:

(B) Boltzmann-Matano method

This method is used when the depth-dependence of the doping profile is obtained, for example, via SIMS technique. Then, for initially undoped substrates, one has:

( )( ) ( )[ ]

−

≈⇒

=

=

2112

22

21

202

101

ln4

1

2

2

jBjB

jj

jB

jB

xNxN

xx

tD

DtxerfcNN

DtxerfcNN

∫−==

1

102

1 N

NN xdNdN

dx

tD

The diffusion constant is determinedfrom the knowledge of the slope at arbitrary depth and the total # of dif-fused impurities.


� Most important statements for ATHENA diffusion simulation

DIFFUSE statement

� This statement initiates a time temperature step for oxidation, silicidation and diffusion of impurities

� Important parameters that can be specified here are:

� Surface impurity concentration via: C.ARSENIC, C.BORON, C.ANTIMONY, etc.

� CONTINUE � continuation of the diffusion process

� DRYO2, WETO2, NITROGEN, AMMONIA, ARGON� gas present in the furnace (one type is specified)

� F.02, F.H2, F.H20, F.N2 and F.HCL � flow-rates

� HCL.PC � percentage of HCL in the oxidant stream

� PRESSURE � partial pressure of active species

� TEMPERATURE � furnace temperature

� T.FINAL, T.RATE � final T and ramp-rate

� TIME � amount of time spent in the furnace


METHOD statement

� This statement is used to set flags for selecting various mathematical algorithms used in the simulation and to select the desired diffusion model complexity


� VACANCIES, INTERSTIT, ARSENIC, .., OXIDANT, VELOCITY, TRAPS, PSI, etc. � parameters used tospecify a single impurity, trap or a potential

� FERMI � the defects are assumed to be a function of the Fermi level only

TWO.DIM � full time-dependent transient simula-tion has to be performed

STEADY � defects are in steady-stateFILL.CPL � full coupling between defects and dopants is included

� CLUSTER.DAM � Stanford cluster model enabled

� HIGH.CONC � doping concentration dependent point defect recombination model terms enabled


4. Description of the oxidation process

� The oxidation process involves thermal growth of SiO2 or deposition of silicon nitride

� The deposited SiO2 layer can be used for the following purpose:

� diffusion mask for selective dopant diffusion� pn-junction protection from atmospheric influence� dielectric layer in MOS-transistors (gate oxide)� isolation between transistors fabricated on the same

chip (field oxide)

� Some figures of merit for the oxidation process:

� oxidation temperature: 900 °C to 1200 °C

� typical gas flow rate: 1 cm/sec

� depending upon the ambient, one can have:

(a) Dry oxidation process: Si + O2 � SiO2

(b) Wet oxidation process: Si + 2H20 � SiO2 + 2H2


� During the oxidation process, the underlying Si material is consumed:

Si thickness = 0.44 × (oxide thickness)

� the basic structural unit of thermally grown SiO2 is shown in the figure below:

(a) Basic structural unit of SiO2

(b) Quartz crystal lattice(c) Amorphous structure


� The kinetics of thermal oxidation is described via the Deal-Grove model that is given below:

F1 = h(C*-C0) - flux of oxidant from the bulk of the gasto the gas-oxide interface

C* = oxidant concentration in the bulkC0 = oxidant concentration at gas/oxide interfaceh = gas-phase mass transfer ratio

F2 = D(C0-Cs)/Xox - flux across the oxide

Cs = oxidant concentration at the SC/oxide interfaceD = diffusion coefficient

F3 = ksCs - oxide/SC oxidation reaction

ks = chemical surface-reaction coefficient

F1 = F2 = F3 = N1dXox/dt

N1 = # of oxidant molecules incorporated into unit volume 0 Xox x

C(x)

C0

Cs

F1

F2 F3

silicon


� The analytic solution of the kinetic equations gives:

where:

(a) short-time limit behavior:

- the linear rate constant B/A varies as exp(-Ea/kBT) with activation energy Ea of about 2 eV

- B/A has orientation dependence

(b) long-time limit behavior:

- The activation energy for the parabolic rate constantequals to: Ea(dry)=1.24 eV and Ea(wet)=0.71 eV

- does not exhibit orientation dependence

−+

+= 1

4)0(21

2)(

2

2

A

Bt

A

XAtX ox

ox

1

*2,

112

N

DCB

hkDA

s

=

+=

( ) )(/)( τ+≈ tABtXox

BttXox ≈)(


� For thin oxides, the differential equation that describes the oxide growth is modified to:

� In the SSUPREM4 implementation of the oxidation process, one can distinguish between:

� analytical oxidation models� numerical oxidation models

(A) Analytical oxidation models

The initial silicon surface must be planar. Also:

B/A = L0LpLHClLbaf L0 = intrinsic linear oxidation rate

Lp = pressure dependent coefficient

LHCl = chlorine dependent coefficient

Lbaf = doping-dependent coefficient

B = P0PpPHCl same meaning as above

−

−=+

+=

L

ox

B

Ethth

ox

ox

Th

X

Tk

ThThRR

XA

B

dt

dXexpexp ,

20


(B) Numerical oxidation models

� Three numerical models have also been implemented in SSUPREM4:

VERTICAL, COMPRESS and VISCOUS

� In all three models, the oxidation equations are solved to obtain the growth rate at each point of the Si/SiO2 inter-face

� COMPRESS and VISCOUS solve:

µ∇2V = ∇P, where: ∇P = hydrodynamic pressuregradient

V = velocity

µ = E/(2+2ν) = viscosity

� The VISCOUS model is more advanced than COMPRESS, since it incorporates strain into the problem.


� Most important statements for oxidation simulation

OXIDE statement

� All parameters related to the description of the oxidation process are specified here

� Important parameters include:

� DRY02, WET02 � type of oxidation process for which specific coefficients apply

� LIN.L.0, LIN.L.E, LIN.H.0, LIN.H.E, L.BREAK �

specification of linear-rate coefficient B/A� PAR.L.0, PAR.L.E, PAR.H.0, PAR.H.E, P.BREAK

� parabolic rate coefficient B specification

METHOD statement

� ERFC, ERF1, ERF2, ERFG � “Bird’s beak” spec.

� VERTICAL � vertical oxide growth

� COMPRESS � compressible liquid model

� VISCOUS � incompressible liquid model


� Charged states at the interface and in the oxide

� The electronic properties of the oxide and the oxide/SC interface have profound effect on the properties of the devices

� There are a number of allowed states within the forbidden gap, called Shockley or Tamm states:

� Fast surface states:

- density: 1011 to 1012 cm-2

- time constant: 1 µsec

- responsible for generation-recombination effects at the surface

- increased leakage current when junction penetrates the surface

- Shorter minority carrier lifetimes

- early fall-off in transistor gain

� Slow states:

- behave as traps and are essentially ionized silicon- time constant on the order of seconds and months- do not influence electrical properties, but affect threshold voltage

� Oxygen-ion vacancies and alkali ions


Location of the oxide charges

• The charges that exist in a realistic MOS structure can be

classified into four different categories:

(1) Mobile ionic charges

(2) Oxide-trapped charges

(3) Fixed oxide charges

(4) Interface-trap charges

+ ++aN +

K

+-

+-

+-

+-

+-

+-

+ + + +


• Mobile oxide charges: Due to ionic impurities such as Na,

K, etc.

• Oxide-trapped charge: May be positive or negative and is

due to holes or electrons trapped in the bulk of the oxide.

• Fixed oxide charges: Due to structural defects (ionized

silicon) in the oxide layer.

• Interface-trapped charges: Positive or negative charges due

to:

structural, oxidation induced defects

metal impurities

other defects due to bond-breaking processes

Unlike other oxide charges, interface-trapped charge is in

electrical communication with the underlying silicon and

can be charged and discharged.


• The expression for the voltage drop across the oxide layer

Vox in the presence of a non-zero charge distribution ρ(x) is

found from the solution of the 1D Poisson equation, using

the boundary conditions: ϕox(0)=0 and ϕox(dox)=Vox .

• The final result of this calculation is given below:

• Special cases:

� uniform charge distribution: γ=1/2

� Charges at the SC/oxide interface: γ=1

� Charges at the metal/oxide interface: γ=0

∫ρ

∫ ρ

=γγ−=ox

ox

d

ox

d

ox

oxox

oxoxoxoxox

dxx

dxxx

dC

QdFdV

0

0

)(

)(1

,)(


• The threshold voltage shift due to workfunction difference

and charges in the oxide is given by:

• Important note: All the charges (mobile ion charges, fixed

oxide charges, oxide trapped charges) except the interface-

trap charges lead to rigid shift of the CV curve.

FBMSox

oxGGG V

qC

QVVV =Φ+γ−=−=∆

1'

Voltage applied to realMOS capacitor with

oxide charges

Voltage applied to idealMOS capacitor

Oxide charges Work functiondifference

Flat-bandvoltage


• More information on interface-trapped charges:

Most of the interface-trapped charges can be neutralized

by low-temperature hydrogen annealing.

The interface trap density is given by:

Interface trap charges can be:

- acceptor-like (above the intrinsic level)

- donor-like (below the intrinsic level)

=

eVcmdE

dQ

qD it

it 2

charges of #1 <111>

<100>

0 Eg

itD


FSE

CE

VE

iE

Use simplified model that all of the states below the Fermilevel are full and all of the states above the Fermi level are empty.

The excess negative charges

lead to positive shift.

FSE

CE

VE

iE

The excess positive charges

lead to negative shift.

Depletion: Accumulation:


Modification of the HF-CV curve due to interface-trapped charges.

HFC

oxC

GV

totC

Interface-traps close to valence band.

Interface-traps close to mid-gap.

Interface-traps close to conduction band.

oxC

accCdeplCinvC itC

Contribution from the charging and

discharging of the interface traps.

Gate


� Modeling of charge states

� The density of trapped carriers on the discrete set of defects/trap centers is given by:

where:

ββββ

ββββ

αααα

αααα

=β

β

=α

α

+++

+=

+++

+=

∑=∑=

npnp

nptdt

npnp

pntat

m

tt

k

tt

KKGG

GKNp

KKGG

GKNn

ppnn

,

,11

−−γσ=

−σ

γ=

σ=σ=

Tk

EEnVG

Tk

EEnVG

nVKpVK

B

tiinnn

B

tiippp

nnnppp

exp ;exp1

;

αααα: # of acceptor traps; ββββ: # of donor traps

Et : energy level of the trapγ :γ :γ :γ : degeneracy factorVn, Vp : thermal velocitiesσσσσn, σσσσp : capture cross-sections


� The introduction of traps into the model gives rise to

(a) Additional charge term in the Poisson equation:

(b) Modification of the SRH recombination term

where:

� The ATLAS implementation is via the TRAP statement:

DONOR, ACCEPTOR � trap type

E.LEVEL � trap energy level

DENSITY � density Nt of traps

DEGEN.FACTOR � γSIGN, SIGP � capture cross-sections for electrons and holes

TAUN, TAUP � electron and hole lifetimes (alternative)

( )ttt npq −=ρ

−−+τ+

−

γ+τ

−=

βαβα

βα

βα

Tk

EEnn

Tk

EEnp

npnR

B

tiip

B

tiin

i

,,

,

2

,

expexp1

( ) ( ) 11 ;

−− σ=τσ=τ tppptnnn NVNV


5. Description of the etching process

� Within the SSUPREM4 software, there is a very rudimentary model for the etching process, which considers etching as a purely geometrical problem

� Etch steps are simulated using the ETCH statement in which the material to be etched and the geometrical shape of the etch region are specified:

� polygonal region� region to the left or right of a line segment� region between top boundary and a line obtained by

translating top boundary down in the y-direction (DRYand THICKNESS parameters)

� All regions of a particular material type (ALL parameter)

� All materials in the defined region will be etched

� Specifying the material to be etched limits the etching pro-cess to the pre-selected material type


ETCH statement

This statement allows simulation of the etching process. SSUPREM4 only purely geometrical etch model, and ELITEincludes physical etch model.


� SILICON, OXIDE, POLYSILICON, GAAS, PHOTORESIST, INP, … , � material to be etched

� ALL � all of the specified material is removed

� DRY � resulting surface replicates the exposed surface

� LEFT, RIGHT, ABOVE, BELOW � quick means of etching in a trapezoidal region (P1.X, P1.Y, P2.X, P2.Y)

� START, CONTINUE, DONE � arbitrary complex region to be etched

� THICKNESS � thickness to be etched


6. Description of the deposition process

� Deposition process is described via a simple algorithm that describes conformal deposition

� Parameters that are specified within the DEPOSIT state-ment include:

MATERIAL � specify material to be deposited

NAME.RESIST � type of photoresist to be deposited

THICKNESS � specifies the deposited thickness, in micrometers

DIVISIONS � number of vertical grid spacings in deposited layer

CONC � concentration of impurity (type must be specified also)

MIN.SPACE � minimum spacing between points on the surface

DY � nominal spacing in the layer

YDY � depth at which nominal spacing is applied relative to the surface

MIN.DY � minimum spacing allowed between grid-lines(default value is 10 angstroms)


7. Description of the epitaxy process

� This process simulates epitaxial deposition of silicon. It is limited to silicon on silicon applications and should not be used when other materials are present

� Parameters that are specified within the EPITAXY state-ment include:

ARSENIC, BORON, PHOSPH � specify material to be deposited

CONC � concentration of impurityDIVISIONS � number of vertical grid spacings in deposited layerDY � nominal spacing in the layerYDY � depth at which nominal spacing is applied relative to the

surfaceMIN.DY � minimum spacing allowed between grid-lines

(default value is 10 angstroms)PRESS � defines the pressure of epitaxial deposition processT.FINAL � final temperature for ramped epitaxial stepsTEMP � defines the temperature of the epitaxial depositionTIME, THICKNESS, RATE � parameters of epitaxial process

introduction to silvaco athena tool and basic concepts in process

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