Transcript Device Simulation

School of Microelectronic Engineering
UniMAP – PSDC INSEP Training Program 2007
• 2D cross-section of wafer
– X-coordinate: parallel to the wafer surface
– Y-coordinate: depth into the wafer
• Grid structure:
– The continous physical process are modeled
numerically by using finite difference (for
diffusion) and finite element (for oxide flow)
solution techniques.
– Each region is divided into a mesh of nonoverlapping triangular elements
– Solution values are calculated at the mesh nodes
(at the corners of the triangular elements), value
between the nodes are interpolated
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• MEDICI solves Poisson’s equation & the current
continuity of electrons and holes in two
dimensions
• These equations can be extended to include the
heat equation and the energy balance equations
• The following modes of analysis can be
considered: DC simulation, AC simulation &
transient simulation
• A wide range of mobility &
recombination/generation models available
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• Advanced Application Modules are available
– Lattice temperature AAM – solves the heat equation
– Optical device AAM – enhanced radiation effects, ray
tracing
– Heterojunction device AAM – conduction across a
material boundary with discontinuous energy
– Programmable device AAM – allows a charge
boundary condition on a floating electrode
– Circuit analysis AAM – allows devices to be treated as
circuit elements in a SPICE type circuit
– Anisotropic device AAM – allows anisotropic material
parameters useful in the treatment of SiC type
applications
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DEVICE STRUCTURE
GENERATING DEVICE STRUCTURE IN
MEDICI/DAVINCI
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DEVICE STRUCTURE DEFINITION
SEQUENCE OF STATEMENTS:
 MESH statement
 X.MESH statements
 Y.MESH statements
 Z.MESH statements (Davinci only)
 ELIMINATE statements (optional)
 TSUPREM4 statements (optional)
 REGION statements
 ELECTRODE statements
PROFILE statements
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UniMAP – PSDC INSEP Training Program 2007
STRUCTURE INFORMATION
MESH
Initiates a mesh and must appear first when
defining a structure. Can be used to import an
existing mesh and invoke the Automatic
Conforming Boundary (ABC) mesher
X.MESH
Y.MESH
ELIMINATE
Used to specify exact locations of mesh lines.
X.MESH & Y.MESH produce a rectangular grid
which can be reduced in density by using
ELIMINATE to remove excess nodes away from
area of interest
TSUPREM4
Used to transfer surface features and doping
profiles from TSUPREM4 onto existing MEDICI
mesh
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STRUCTURE INFORMATION
REGION
Used to define regional properties
where no material data already exists
ELECTRODE
Adds location of electrodes to structure
RENAME
Rename electrodes or regions
PROFILE
Allows addition of doping information
either by creating simple profiles or
inputting from a process simulator
REGRID
Allows regridding of mesh based on
some internal quantities
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DEVICE STRUCTURE: MESH
• The MESH statement initiates the mesh generation or
reads a previously generated mesh
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DEVICE STRUCTURE: MESH
[extracted from user guide]
MESH
Initial Mesh Generation
{ ( [ { RECTANGULAR | CYLINDRI } ] [DIAG.FLI])
Mesh File Input
| (IN.FILE=<c> [QT.FILES=<c>] [PROFILE]
[ { ASCII.IN | (TSUPREM4 [ ELECT.BOT [Y.TOLER=<n>] [POLY.ELE]
[X.MIN=<n>] [X.MAX=<n>] [Y.MIN=<n>] [Y.MAX=<n> [FLIP.Y] [SCALE.Y=<n>]
)
| (TIF [ELECT.BOT [Y.TOLER=<n>] [POLY.ELE] ] )
}
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DEVICE STRUCTURE: MESH
PARAMETER
RECTANGU
CYLINDRI
DIAG.FLI
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TYPE
logical
DEFINITION
DEFAULT
Specifies that the simulation mesh
uses rectangular coordinates
True
logical
Specifies that the simulation mesh
uses cylindrical coordinates. If this
parameter is specified, the
horizontal axis represents the radial
direction and the vertical axis
represents the z-direction
False
logical
Specifies that the direction of
diagonals is changed about the
horizontal center of the grid. If this
parameter is false, all diagonals are
in the same direction
False
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DEVICE STRUCTURE: X.MESH
• The X.MESH specifies the placement of nodes in the x direction
• Description:
If an initial mesh is being generated, X.MESH and Y.MESH
statements should immediately follow the MESH statement
X.MESH
{LOCATION=<n> | ({ WIDTH=<n> | X.MAX=<n> }
[X.MIN=<n>] )}
[ {NODE=<n> | N.SPACES=<n>} ]
[SPACING=<n> | H2=<n>} ] [H3=<n>] [RATIO=<n>]
[MIN.SPAC=<n>]
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[ SUMMARY ]
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DEVICE STRUCTURE: Y.MESH
The following Y.MESH statement specifies
the placement of nodes in the y direction
Y.MESH
{LOCATION=<n> | ({DEPTH=<n> | Y.MAX=<n>} [Y.MIN=<n>] ) }
[ {NODE=<n> | N.SPACES=<n>} ]
[ {SPACING=<n> | [MIN.SPAC=<n>]
[SUMMARY]
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DEVICE STRUCTURE: REGION
The region statement defines the location of
materials in a rectangular mesh
REGION
NAME=<c>
Semiconductor Materials
{ ( { SILICON | GAAS | POLYSILI | GERMANIU | SIC | SEMICOND |
SIGE | ALGAAS | A-SILICO | DIAMOND | HGCDTE | INAS | INGAAS |
INP | S.OXIDE | ZNSE | ZNTE | ALINAS | GAASP | INGAP | INASP }
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DEVICE STRUCTURE: REGION
Semiconductor material Parameters
[X.MOLE=<n>] [X.END=<n> | X.SLOPE=<n>} {X.LINEAR |
Y.LINEAR} ]
)
Insulator Materials
| OXIDE | NITRIDE | SAPPHIRE | OXYNITRI | HFO2 |
INSULATO
}
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DEVICE STRUCTURE: REGION
Location{ ( [ {X.MIN=<n> | IX.MIN=<n>} ] [ {X.MAX=<n>
| IX.MAX=<n>} ] [ {Y.MIN=<n> | IY.MIN=<n>}
[{Y.MAX=<n> | IY.MAX=<n> }] [ { (ROTATE
R.INNER=<n> R.OUTER=<n> X.CENTER=<n>
Y.CENTER=<n>)
|POLYGON X.POLY=<a> Y.POLY=<a>) } ] ) | (X=<n>
Y=<n>)
|CONVERT
}
[VOID]
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DEVICE STRUCTURE: ELECTRODE
The ELECTRODE statement specifies the placement of
electrodes in a device structure
ELECTRODE
NAME=<c> [VOID]
{ ( [ {TOP | BOTTOM | LEFT | RIGHT | INTERFAC | PERIMETE} ] [ {
X.MIN=<n>} ] [X.MAX=<n> | IX.MAX=<n>} ] [ { Y.MIN=<n> | IY.MIN=<n>}] [
{Y.MAX=<n> | IY.MAX=<n>} ] [ { ( ROTATE X.CENTER=<n> Y.CENTER=<n>
R.INNER=<n> R.OUTER=<n>) | (POLYGON X.POLY=<a> Y.POLY=<a>) } ] )
| [X=<n> Y=<n>]
| [REGION=<c>] }
[MAJORITY]
Lattice Temperature AAM Parameters
[THERMAL]
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DEVICE STRUCTURE: PROFILE
PROFILE
[REGION=<c>]
[X.MIN=<n>] [ {WIDTH=<n> | X.MAX=<n>} ]
[Y.MIN=<n>] [ {DEPTH=<n> | Y.MAX=<n>} ]
Output Doping File
[OUT.FILE=<c>]
The PROFILE
statement defines
profiles for
impurities and other
quantities to be
used in the device
structure
Uniform Profiles
{ (UNIFORM {N-TYPE | P-TYPE | IMPURITY=<c> | OTHER=<c>}
N.PEAK=<n>)
Analytic Profiles
| ( {N-TYPE | P-TYPE IMPURITY=<c> | OTHER=<c>} {N.PEAK=<n> |
DOSE=<n>} { (Y.CHAR=<n> [Y.ERFC] ) | Y.JUNCTI=<n>} {X.CHAR=<n> |
XY.RATIO=<n>} [X.ERFC]
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$ Structure Generation of 1D SiGe Bipolar
Mesh
X.mesh width=0.5 spaces=1
EXAMPLE: CREATING
1D SiGe HBT
Y.mesh width=0.1 H2=0.005 Ratio=1.2
Y.mesh width=0.1 H2=0.005
Y.mesh width=0.6 H2=0.005 H2=0.050
Region silicon
Region SiGe Y.min=0.100 y.max=0.125 x.mole=0 x.end=0.2 Y.linear
Region SiGe Y.min=0.125 y.max=0.200 x.mole=0.2
Region SiGe Y.min=0.200 y.max=0.230 x.mole=0.2 x.end=0.0
Electr Name=Emitter Top
Electr Name=base Y.min=0.125 Y.max=0.125 Majority
Electr Name=collector bottom
Profile N-type N.peak=2e16 Uniform
Profile N-type N.peak=5e19 Y.min=0.80 y.char=0.125
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EXAMPLE:
RESULTS
Basic SiGe Mesh
Corresponding doping profile
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DEVICE STRUCTURE
IMPORTING DEVICE STRUCTURE
FROM MEDICI/TSUPREM4
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MESH STATEMENTS
• IN.FILE – name of input file which contains structure.
• Tsuprem4 – logical parameter signaling that IN.FILE was created
by TSUPREM4
• TIF – logical parameter signaling that IN.FILE is in universal (TIF)
format
• ELECT.BOT – logical flag signaling that the structure bottom
(substrate) electrode is supposed to be appended to the structure
• POLY.ELEC – logical parameter signaling that all polysilicon
regions in the imported structure are to be converted to electrode
NOTE: Once Poly Region is converted to Electrode, its doping
information is lost and intrinsic work function of 4.6eV is assign to it
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EXAMPLE:
IMPORTING STRUCTURE FILE
• From TSUPREM4
MESH
RENAME
RENAME
SAVE
in.file=s4filename tsuprem4 elec.bot poly.elec
y.max=3
electr oldname=1 newname=source
electr oldname=2 newname=drain
mesh out.file=mdfile
• From previous MEDICI execution
MESH
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in.file=mdfile
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MESH ADJUSTMENT
• Default structure depth in TSUPREM4 is 200m. Use
Y.MAX or alternatively TRUNCATE the device within
TSUPREM4 first
• X.SPLIT, WIDTH and N.SPACES allow the structure to
be expanded at point x.split by an amount width and
subdivided into n.spaces. A typical use of this would be
to model various channel lengths without repeating the
process simulation
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MESH ADJUSTMENT
• REGRID statement
• Regrid doping log ratio=2 in.file=test.dop
smooth=1
Which test for the log of the doping being greater than
2 between mesh points. It uses a doping file stored
from the original PROFILE statement so that
information on doping is not lost through successive
refinements. A number of different techniques from
smooth=-1 to 2 can be selected (-1 is usually the best)
• Regrid potential ratio=1.1
• Regrid min.carr ratio=2 log smooth=-1
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REGRID
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MESH ISSUES
• Increasing mesh density results in increasing
accuracy of potential and carrier concentrations
• Care must be taken in aligning the mesh to the
current flow
• High density mesh needs computing space and
time
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CHOICE OF MODELS :
RECOMBINATION & GENERATION
MODEL
SRH
CONSRH
AUGER
R.TUNNEL
IMPACT.I
II.TEMP
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DESCRIPTION
Shockley – Read – Hall recombination
SRH + concentration dependent lifetime
Note: lattice temp dependence can also be modeled by specifying
non-zero values of EXN.TAU and EXP.TAU on the MATERIAL
statement (Lattice temp AAM only)
Auger recombination
SRH including tunneling in presence of strong electric fields
Classic Chynoweth expression
Invokes a temperature based version of the impact ionization
model for use with the energy balance model
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CHOICE OF MODELS : MOBILITY
MODEL
LOW
FIELD
TRANSVERS
E FIELD
PARALLEL
FIELD
COMMENTS
CCSMOB
Carrier-carrier scattering
CONMOB
Concentration dependence from
tables 300K
ANALYTIC
Analytic alternative to CONMOB
with temp. dependence
PHUMOB
Carrier-carrier scattering,
different donor and acceptor
scattering, screening, useful for
bipolars
LSMMOB
Treats surface scattering and
bulk effects
GMCMOB
Modified LSMMOB to include
impurity scattering
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CHOICE OF MODELS : MOBILITY
MODEL
LOW
FIELD
SRFMOB
SRFMOB2
TRANSVE
RSE FIELD
PARALLEL
FIELD
COMMENTS
Basic and enhanced model for
surface scattering. Requires vertical
grid spacing > inversion layer
UNIMOB
Needs rectangular grid in inversion
layer – models surface scattering
PRPMOB
General model for degradation of
mobility with transverse electric field
– applies all over –not just at surface
TFLDMOB
Univ. Texas mobility model
FLDMOB
Carrier heating and velocity
saturation effects
HPMOB
Accounts for both parallel and
perpendicular field dependence
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CHOICE OF MODELS :
ENERGY GAP & CARRIER DENSITY
MODEL0
DESCRIPTION
FERMIDIR
Fermi Dirac statistics instead of Boltzman.
Recommended to be used in conjunction with:
INCOMPLE
Incomplete ionization of impurities
BGN
Bandgap narrowing modelling – especially important
for bipolars
QM.PHILI
Accounts for quantum mechanical effects in MOSFET
inversion layers using Van Dort’s bandgap widening
model. Implemented as a shift in the energy gap just
as in BGN modeling
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CHOICE OF MODELS : ENERGY BALANCE
MODEL
DESCRIPTION
ET.MODEL
Uses the energy transport model where the spatial
derivative of the mobility is included in the diffusion
term of the current equation
COMP.ET
Invokes an energy balance eq. suitable for compound
material such as GaAs
TMPMOB
A carrier temperature based mobility – alternative to
FLDMOB
EF.TMP
Solves effective electric fields exactly in Si instead of
approx for use in TMPMOB
TMPTAUW
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Invokes an electron temperature model for the electron
energy relaxation
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CHOICE OF MODELS : ENERGY BALANCE
MODEL
DESCRIPTION
II.TEMP
Uses the energy transport model where the spatial
derivative of the mobility is included in the diffusion
term of the current equation
EFI.TMP
Invokes an energy balance eq. suitable for compound
material such as GaAs
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MODEL DECISION: MOS
• Use mobility model specifically calibrated on MOSFETS
as surface scattering effects are a dominant feature such
as CONMOB LSMMOB FLDMOB
• For <0.2m technologies, one of the newer models i.e
UNIMOB, GMCMOM or TFLDMOB should be
considered i.e TFLDMOB (for NMOS)
• When modeling breakdown CONSRH, IMPACT.I are
important
• AUGER and BGN which has a small effect on the
source/drain resistance can be included but both of
these will not significantly impact the results
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MODEL DECISION: BIPOLAR
• Carrier-carrier scattering is a more important mechanism for bipolars
and PHUMOB would be a good choice. Bandgap narrowing and the
recombination mechanisms are also important so a full set would be:
CONMOB PHUMOB AUGER CONSRH BGN IMPACT.I
• Change the lifetimes and bandgap coefficients on the material
statement:
material silicon
v0bgn=n0.bgn=con.bgn=taun=taup=
• For a general device, then an all purpose choice would be:
CONMOB FLDMOB PRPMOB CONSRH AUGER BGN IMPACT
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SOLUTION TECHNIQUE
STATEMENTS
STATEMENTS
SYMBOLIC
METHOD
LOG
SOLVE
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DESCRIPTION
Selects with equations to solve as well as the method
of the solution either coupled (Newton) or de-coupled
(Gummel)
Control the iteration process – number of iterations use
of numerical damping, selection of linear solver
To open the file which will contain terminal values
calculated during the solution process
Starts the solution process either DC, AC or transient
UniMAP – PSDC INSEP Training Program 2007
SOLUTION TECHNIQUE: SYMBOLIC
• Solve only Poisson’s equation
symbolic carr=0
• Solve Poisson’s equation and electron-current
continuity equation using Gummel’s method
symbolic carr=1 electron gummel
• Solve Poisson’s equation and electron-current
continuity equation using coupled method
symbolic carr=1 electron newton
• Solve Poisson’s equation and both hole and
electron Drift-Diffusion (DD) equations
symbolic carr=2 newton
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SOLUTION TECHNIQUE: METHOD & LOG
• Method – contains more than fifty parameters,
only a few are normally used
• Itlimit, which controls the number of iterations
which are tried before the bias is cut back by the
program
method itlimit=100
• Log
log outfile=drain.ivl (filename)
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SOLUTION TECHNIQUE: SOLVE
• There are two fundamental rules when using the solve
statement:
– At the beginning of the simulation, all electrode potentials are set to
0V
– Terminal values stay unchanged until they are addressed by the
next solve statement. In other words, terminal values are not
implicity reset to their initial values in subsequent solve statements
• When the program solves for a new bias condition, it must
rely on an initial guess. There are three types (initial,
previous, project) which are automatically selected by the
program
• Rules for succesful solution strategy:
– Specify all models (with the possible exception of impact.i before
the first solve statement
– Build-up solution gradually
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SOLUTION TECHNIQUE: SOLVE
• DC ANALYSIS
• Apply 1V gate electrode
solve v(gate)=1
• Ramp voltage of gate electrode at 1V interval for 5 times
solve elec=gate vstep=1 nstep=5
• Ramp current of base while applying 5V at collector
solve elec=base istep=1e-6 nstep=10
v(collector)=5
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SOLUTION TECHNIQUE: SOLVE
• TRANSIENT ANALYSIS
solve v(base)=1 tstep=1e-13 tstop=1e9
• To define a pulse we need two solve statements:
Solve v(base)=1 tstep=1e-13 tstop=1e-9
Solve v(base)=0 tstep=1e-13 tstop=5e-9
V
tstop
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tstop
t
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SOLUTION TECHNIQUE:
CONVERGENCE ISSUE
• The primary causes of non-convergence are:
– Poor initial guess – bias step too large (for some structures even
0.1V can be too large)
– Lack of necessary physical models
– Poor simulation grid
– Depletion layer touching the electrode
Iter
V-error
px.tol
itlimit
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#of iterations
V-error
1
3.4567e+4
2
2.7543e+02
3
1.6734e+00
4
1.0000e+00
5
1.0000e+00
…
1.0000e+00
20 1.0000e+00
UniMAP – PSDC INSEP Training Program 2007