christoph zechner, alexander tsibizov, nik zographos · mla model in sentaurus process atemox...
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© Synopsys 2013 1
Christoph Zechner, Alexander Tsibizov, Nik Zographos
© Synopsys 2013 2
Atemox Overview
“Advanced Technology MOdelling for eXtra-functionality devices“
Partners:
Fraunhofer IIS-B, STM, Synopsys, Excico, IBS, Probion, Semilab
LAAS CNRS (Toulouse), ETH (Zurich), UNEW (Newcastle), CNR-IMM (Catania)
Duration: July 2010 – November 2013 Website: http://www.atemox.eu
© Synopsys 2013 3
Workshop Overview
Models in Sentaurus Process:
• Melt laser annealing
• Electrostatic gate-substrate interaction and quantum-mechanical corrections
to the charge carrier density: Impact on dopant pile-up at gate oxide
interfaces
• Dopant redistribution during solid phase epitaxial regrowth
• Plasma ion implantation
© Synopsys 2013 4
MLA model in Sentaurus Process ATEMOX Workshop at EMRS-2013
Alexander Tsibizov
30 May 2013
© Synopsys 2013 5
Target Applications for Melting Laser
Anneal (MLA)
• Pulsed excimer laser annealing enables the activation of
dopants implanted into silicon with a high electrically
active fraction and well-defined junction depth.
• Using an excimer laser with a wavelength of 308 nm, a
pulse duration of ~160 ns, and a high energy density of
up to 8 J/cm2, the melting temperature is reached at the
surface within few 10s ns. After the end of the laser
pulse, the temperature decreases rapidly by heat
conduction so that only a surface-near layer is affected.
• This process is ideal for back-side processing without
affecting already existing structures on the front-side of a
thinned structure as in power IGBT or Back Side
Imagers (BSI).
© Synopsys 2013 6
Laser Pulse Characteristics [1]
Figure 2.3: Laser pulse shape as a function of the
time for the EXCICO LTA15 laser (wave length l =
308 nm, pulse duration 180 ns).
um
© Synopsys 2013 7
Melting Depth [1]
Figure 2.6.: Melt depth as a function of laser
energy densities (2.0, 2.6, 3.0, and 3.6 J/cm2).
Simulation estimates are shown as solid line
while rectangles indicate SIMS measurements.
Figure 2.7.: Time evolution of the melt depth during
the melting laser processes for 2.6 (dot), 3.0 (dash)
and 3.6 (solid) J/cm2 laser fluences. From [1].
© Synopsys 2013 8
Literature on MLA
1. Giuseppe Fisicaro “Micro-structural modifications of semiconductor systems under irradiation:
experiment, modeling and simulation analysis”, Ph.D. Thesis - University of Catania a.a.
2008/2011
2. M. Hackenberg et al., “Modeling Boron Profiles After Pulsed Excimer Laser Annealing”,
International Conference on Ion Implantation Technology 2012
3. Antonino La Magna et al., “A phase-field approach to the simulation of the excimer laser annealing
process in Si”, J. Appl. Phys., Vol. 95, No. 9 (2004), pp. 4806-4814
4. A. Karma and W.-J. Rappel, ” Quantitative phase-field modeling of dendritic growth in two and
three dimensions”, Phys.Rev. E, Vol. 57, No. 4 (1998), pp. 4323-4349.
5. A. Mittiga, L. Fornarini, and R. Carluccio, “Numerical modeling of laser induced phase transitions
in silicon,” Applied Surface Science, vol. 154–155, pp. 112–117, February 2000.
6. E. Yamasue et al., “Thermal conductivities of silicon and germanium in solid and liquid states
measured by non-stationary hot wire method with silica coated probe”, Journal of Crystal Growth
234 (2002), pp. 121–131.
7. J.P. Garandet, ”New Determinations of Diffusion Coefficients for Various Dopants in Liquid
Silicon“, International Journal of Thermophysics, Vol. 28, No. 4, (2007), p. 1285.
8. K. Huet et al., "Experimental and Theoretical analysis of Dopant Activation in Thin Double
Implanted Silicon by pulsed Excimer Laser Thermal Annealing”, 17th IEEE International
Conference on Advanced Thermal Processing of Semiconductors – RTP 2009.
9. S. De Unamuno and E. Fogarassy, "Thermal description of the melting of c- and a-Si under pulsed
excimer laser", Applied Surface Science, Vol. 36, (1989), pp. 1 - 11.
© Synopsys 2013 9
MLA Model in Sentaurus Process
Yong-Seog Oh, Alexander Tsibizov
© Synopsys 2013 10
MLA Model in Sentaurus Process
• The phase field variable (φ) is introduced to describe whether the
material is liquid (φ=0) or solid (φ=1). The solution name of the phase is HeatPhase. Phase Field Model (PFM), where phase
equation is fully coupled with Heat equation, has been implemented
based on [Karma and Rappel, PRE 1998]:
Here s(T, φ) is the seed function to start melting.
See H-2013.03 S-Process User Guide for details
© Synopsys 2013 11
Heat Generation via Laser Pulse
Absorption
The heat generation rate is calculated by:
,
where I, α, and d represent the intensity, absorptivity, and depth,
respectively. Time-dependent laser pulse intensity can be set via table:
pdbSet Heat Intensity.Model Table
pdbSet Heat Intensity.Table {
Time1 Intensity1
Time2 Intensity2
… …
}
© Synopsys 2013 12
Dopant Diffusion and Segregation at
Solid/Liquid Interface
• 100 % dopant activation is assumed in liquid and recrystallized
silicon. All point defects and clusters are dissolved in liquid phase.
• Dopant diffusion equation is coupled with Heat and HeatPhase
equations:
© Synopsys 2013 13
MLA Model Calibration
© Synopsys 2013 14
MLA Model Calibration
• Calibration was performed in the frame of ATEMOX EU research
project to experimental results of Excico’s UV 308 nm laser with
pulse duration 150-200 ns. Laser irradiating area was ~ 1 cm^2 (full
chip) per short. Please note, that the technical characteristics of
the laser anneal equipment used in the calibration experiments
may differ from the contemporary ones, please refer to Excico
(www.excico.com) for details. Flat silicon wafers with native oxide
only were used, therefore 1D simulation was possible in these
cases.
• 1D calibration projects for B and P are available for internal usage
• Calibration consisted of two stages:
– Calibration of melting dynamics was done to tune melting depth and
melting duration
– Calibration of dopant diffusion in liquid phase and its segregation at
solid/liquid interface
© Synopsys 2013 15
Melting Dynamics Calibration
• Cp, kappa, rho, L, Tm, vint(T-Tm) in liquid and solid silicon are chosen according to
the best known literature data for bulk silicon
• The value of the light absorptivity in silicon for 308 nm laser is set:
pdbSet Si Absorptivity 1.46e6
Absorptivity 1.46e6 cm^-1 corresponds to the liquid silicon and is close to the value for crystalline silicon at room
temperature [S. De Unamuno and E. Fogarassy 1989]. It becomes larger for large temperatures, but since the used
value is already large enough, its further increase does not influence much the melting dynamics, thus the above
constant value is recommended for the simulations. In principle any temperature and phase dependent expression can
be used for Absorptivity, it will became time dependent with the following flag:
pdbSet Heat UpdateHeatRate 1 ;#default 0
• The temperature-dependent reflectivity (R) of solid and liquid silicon surface
substantially influences the absorbed laser energy. The laser energy absorbed in the
silicon is then scaled by factor (1-R):
pdbSet Heat Intensity.Table.Factor "\[expr $fluence*(1-( $SurfPhase * (0.55 + 4e-
5*$SurfTempK) + (1-$SurfPhase)*0.785 )) \]“
Reflectivity is the parameter recommended for tuning, because typically its exact value
and temperature dependence are not measured for 308 nm and may vary a lot
depending on the surface quality
• Melting depth extracted from SIMS is the first value to calibrate. Second check can
be done on the melting duration (if such measurements are available).
© Synopsys 2013 16
Dopant Diffusion Calibration 1
• Phosphorus and Boron were calibrated (mainly against available SIMS)
• Initial data for dopant diffusion in liquid silicon and equilibrium solid/liquid
partition coefficients in silicon were taken from J.P. Garandet,”New
Determinations of Diffusion Coefficients for Various Dopants in Liquid
Silicon“, International Journal of Thermophysics, Vol. 28, No. 4, (2007), p.
1285.
• Equilibrium partition coefficient k, is determined by Eseg and was set to 0.8
for B and 0.368087=0.332*2.55/2.3 for P, according to [Garandet 2007]
• Diffusion in the interface layer was set small in order to reproduce B pile-up
visible in SIMS and avoid deep at the solid side of the interface:
pdbSetDouble Si Boron Dils.0 1e-9 ;# default for B 1e-6
• Heat Max.Liquid.Phase 0.4 was set for default, because it allows to
create the increase of dopant concentration towards solid/liquid interface,
when segregation at the solid/liquid interface is required. The value 0.4 is
close, but always smaller than the phase value corresponding to the
maximum Ceq.
© Synopsys 2013 17
Dopant Diffusion Calibration 2
• Dopant diffusivity in the liquid silicon Dliquid.0 and
Melting.Intf.Seg.E were tuned to reproduce SIMS
• Temperature dependences of diffusion parameters were not set
because there are no data available. Also in many cases
temperature of liquid silicon is close to Tm=1687 K, especially at
solid/liquid interface. But sometimes it is much larger than Tm, for
example it reaches 2125 K at the surface for 6.1 J/cm^2 pulse).
• Multiple-pulse experiments proved that thermodiffusion is
unimportant for B [Hackenberg et al. IIT2012]. Therefore it was set
to zero for all dopants:
pdbSetDouble Si Boron Heat.Transfer 0.0 ;#default
• Many calibrated parameters are already set as defaults in S-Process
© Synopsys 2013 18
Calibrated Boron Parameters
Parameter values which are different from S-Process defaults are
marked in red:
pdbSetDouble Si Boron Dliquid.0 2.6e-4 ;#default 2.4e-4
pdbSetDouble Si Boron Dils.0 1e-9 ;#default 1e-6
pdbSetDouble Si Boron Melting.Seg.E 0.033
pdbSetDouble Si Boron Melting.Intf.Seg.E -0.15
pdbSetDouble Si Boron Heat.Transfer 0.0
– Calibrated Boron parameters are close to the parameters obtained in
[Hackenberg et al., IIT2012]
© Synopsys 2013 19
Calibrated Phosphorus Parameters
Parameter values which are different from S-Process defaults are
marked in red:
pdbSetDouble Si Phosphorus Dliquid.0 3.0e-4 ;#default 1e-3
pdbSetDouble Si Phosphorus Dils.0 1e-9 ;#default 1e-4
pdbSetDouble Si Phosphorus Melting.Seg.E 0.145 ;#default 0
pdbSetDouble Si Phosphorus Melting.Intf.Seg.E -0.11
;#default -0.2
pdbSetDouble Si Phosphorus Heat.Transfer 0.0
© Synopsys 2013 20
SIMS Have Error for Fast Varying Profiles From [Hackenberg et al., IIT2012]: convolution of the
simulated results is necessary for direct comparison with SIMS
© Synopsys 2013 21
Calibrated Boron SIMS 1
© Synopsys 2013 22
Calibrated Boron SIMS 2
© Synopsys 2013 23
Calibrated Boron SIMS 3
© Synopsys 2013 24
Calibrated SIMS: P 200 keV
from [Huet RTP2009] (log scale)
© Synopsys 2013 25
Calibrated SIMS: P 200 keV
from [Huet RTP2009] (linear scale)
© Synopsys 2013 26
Calibrated SIMS: P 600 keV
from [Huet RTP2009]
As-implanted SIMS
was used for initial
distribution of P in
simulation.
Two different laser
energies close to
the specified 6.4
J/cm^2 were used
in the simulation to
check the
sensitivity.
)
© Synopsys 2013 27
General MLA Settings
• Switches the MLA model on:
pdbSet Heat Use.Melting.Laser 1
• Insure convergence:
math fullNewton
pdbSet Math NegErrCntrl 1
• Speed-up simulation:
pdbSet Si Interstitial ClusterModel None
pdbSetBoolean Defect ForcedTurnOff 1
© Synopsys 2013 28
Important Notes 1
• Many calibrated parameters are already set to S-Process defaults
• Correction for melting velocity Vint(T):
pdbSet Si FV.Melting.Velocity.0 3.27e4 ;#default 3.62e4
pdbSet Si FV.Amorphous.Melting.Velocity.0 5.45e4 ;#default 6.03e4
This correction does not change the simulated results much for typical cases, but it
corresponds to the maximum crystalline/liquid silicon interface velocity 15 m/s and 25 m/s
reported in [A. Mittiga et al., Applied Surface Science, Vol. 154-155, (2000), pp. 112-117].
• Thermal conductivity of liquid silicon in pdb is defined according to [Yamasue2002].
For S-Process MLA model, which does not take the density change during the phase
transition explicitly it should be corrected for the density change by factor 2.33/2.57.
This correction has very small influence on the simulation results.
pdbSet Si Liquid.ThermalConductivity {(0.502 +
2.93e-4*(Temperature-[pdbGet Silicon Melting.Point]))}
© Synopsys 2013 29
Important Notes 2
• Setting which prevents unphysical increase of the temperature
above Tm near the silicon surface at the end of the recrystallization:
pdbSet Heat SeedOnPhase 0.002 ;#default 1.0
SeedOnPhase might be increased in case of bad convergence at the end
of recrystallization
© Synopsys 2013 30
Meshing
• Default value (1e-7 cm) of Heat.Phase.Width is typically good for
simulation of melting depths ~ 100 nm. For the larger melting depths, e.g. 1
um, value 2e-7 cm can reduce the simulation time and still maintaining
reasonable accuracy.
• Mesh spacing (MSp) must be smaller than Heat.Phase.Width (HPW) to
obtain proper convergence.
• Larger MSp results in faster simulation and smaller noise. Larger values of
HPW can speedup convergence even for the fixed MSp. Simulated dopant
distribution depend on both MSp and HPW.
• For equidistant 1D mesh the simulation results are almost the same for MSp
< HPW. For inhomogeneous 1D mesh the simulated melting front speed
changes when the solid/liquid interface reaches the region of the mesh
inhomogeneity, unless the maximum MSp is smaller than HPW/8. meshes
finer than HPW/8 may result in large CPU time. This basically means, that
refinement boxes are allowed only if the background mesh is finer than
HPW/8. Hence equidistant meshes should be used in the melting region
when possible, see also limitations on the next slide.
© Synopsys 2013 31
Inaccuracy of Heat Generation for large
Absorptivity
• Numerical error appears in the expression for heat generation, if MSp is not much smaller than
1/Absorptivity:
• The total integrated dose of HeatRate is a good indicator for
the presence of such error. It can be checked in the output file:
Dose in: Silicon_1 Oxide_1 Total Silicon Oxide Phosphorus 9.8530e+13 9.9982e+02 9.8530e+13 Int 6.9511e-28 1.7375e-33 2.0000e+05 Vac 3.0085e-17 7.5198e-23 2.0000e+05 HeatRate 1.0004e+14 9.9982e+06 1.0004e+14 HeatPhase 4.0000e-02 9.9982e-08 2.0400e+00 P3 4.0000e+05 9.9982e-01 6.0000e+05
• For 0.5 nm mesh and alpha=1.46e6 cm^-1 the HeatRate dose is equal 1.0004e14. Analytical
total integrated HeatRate dose is equal to 1.0e14. The difference more than 1e-3 may cause
pronounced increase of the melting depth. Two solutions are possible:
– Finer mesh at the outer silicon interface. It may be limited by the increase of CPU time related to the mesh
inhomogeneity constrain, described on the previous slide.
– Laser fluence can be (manually in rel. H-2013.03) multiplied by factor 1e14/TotalHeatRateDose.
© Synopsys 2013 32
Time Step Control
• For precise simulation of the MLA profiles smaller time steps are required,
but reduction of the time steps leads to larger CPU-time. Reasonable
balance can be achieved with the following settings:
for better resolution outside melting, which is especially important at the
beginning of the laser pulse:
pdbSet Heat MaxTimeStep 1.0e-9
Error control for HeatPhase, T and dopants provides automatic time step control during melting, it helps to avoid further reduction of “Heat MaxTimeStep”
without loosing the quality of the results. One may try further reduction of Transient.Rel.Error for HeatPhase, Temperature and dopants when the
sow-like noise appear in the simulated dopant profiles. The following settings are
not defaults, but they are recommended for MLA simulation:
pdbSetDouble Si Temperature Abs.Error 1e-8
pdbSetDouble Si Temperature Rel.Error 1e-6
pdbSetDouble Si Temperature Transient.Rel.Error 3.0e-6
pdbSetDouble Si Boron Abs.Error 1e-3
pdbSetDouble Si Boron Rel.Error 1e-8
pdbSetDouble Si Boron Transient.Rel.Error 1e-5
© Synopsys 2013 33
Current Limitations of MLA Model
• Current implementation of Heat generation term works only in 1D
and 2D. Only a simple model of light propagation and absorption is
available in Sentaurus Process.
• Current MLA code does not take into account the fact that molten
Silicon in practically all cases solidifies as crystalline (single or poly:
depending on the substrate), regardless of whether it was
amorphous or solid before melting. In the current implementation
thermodynamic properties of amorphous silicon region do not turn
into the ones of the crystalline silicon upon solidification. This may
lead to inaccuracies of MLA simulation results in the presence of
amorphous regions (not occurring in this example).
• Only simple diffusion equations for dopants are coupled to heat
equation. For the rest (e.g. complex clusters, etc.) only constant
temperature is supported. This impedes simulation and calibration of
dopants activation and defects anneal in solid phase during MLA.
© Synopsys 2013 34
2D IGBT+MLA Simulation Deck
Application Note
Alexander Tsibizov, Jiyong Lim, Arsen Terterian,
Tommaso Cilento, Chan-Su Yun
© Synopsys 2013 35
Introductory Remarks on IGBT+MLA
• SWB project (application note will be available for
download shortly) for simulating 600V and 1200V IGBT
with backside field-stop and collector activation by MLA
• The simulations were performed with rel. H-2013.03
• The 2D process simulation represents a realistic trench-
gate IGBT flow
• 2D device simulation together with plotting/extraction of
IcVg, IcVc, BV, resistive/inductive switching, and short
circuit ruggedness are included
Example is available for downloading at SolvNet since June 15th 2013,
please check Examples Index at
https://solvnet.synopsys.com/retrieve/026036.html
© Synopsys 2013 36
Simulation Deck - Process
600V
1200V
w/wo field stop implant
2D front side 1D back side
1D profiles
into 2D and
meshing
© Synopsys 2013 37
Simulation Deck - Device
AF: current scaling factor
ThermalR: thermal resistance @ contacts
Tamb: ambient temperature
Vc: Collector voltage for IcVg
DC
S
witchin
g
Short
Circuit
© Synopsys 2013 38
Device Structure and Doping – 600V IGBT
MLA (λ=308 nm, Elas=6.1 J/cm2, FWHM=155 ns,
melting depth ~ 1.1 um
BF2 5e13/80keV
P 1e13/600keV
P 7.5e12/300keV
1D cut
G
E
C
65
um
P 1.5e14
© Synopsys 2013 39
DC Device Characteristics – 600V IGBT
Red: T=398K
Blue: T=300K
© Synopsys 2013 40
Resistive Switching Characteristics
600V IGBT
Process Conditions Switching Parameters
Wafer Thick Drift Conc. Body Dose Tem (K) td_on(ns) tr(ns) Eon(uJ) td_off(ns) tf(ns) Eoff(uJ)
65um 1.50E+14 5.45E+12 300 24.31 28.82 72.07 169.48 170.48 181.33
398 21.01 35.45 85.44 174.30 211.02 230.00
120um 5.00E+13 5.00E+13 300 20.66 49.75 57.89 187.00 391.60 237.01
398 9.28 86.33 86.06 195.31 380.11 250.13
T=300K T=300K
© Synopsys 2013 41
Short Circuit Ruggedness (B Mode) - 1 600V IGBT
t1 t2 t3
© Synopsys 2013 42
Short Circuit Ruggedness (B Mode) - 2 600V vs. 1200V IGBT
Short circuit failure times
600V rated IGBT (wafer thickness 65um): 4.7us
1200V rated IGBT (wafer thickness 120um): 7 us
© Synopsys 2013 43
Poisson Equation Boundary Conditions
and Quantum Correction to Carrier
Concentration in Process Simulation
Alexander Tsibizov, Synopsys
30 May 2013
© Synopsys 2013 44
Importance of Correct Potential (and
Boundary Conditions for It)
• In some cases (e.g. under the gate of CMOS transistor)
BC can
– significantly change electrostatic potential and Fermi level
position
– create strong electric field.
Dopant drift pile up or depletion towards surface
Diffusion, activation (clustering), dose loss
• Since dopant and point defects diffusion, activation (clustering) and
segregation depend on electric field and Fermi level position, the
simulated dopant distribution (and hence transistor characteristics)
depend on the boundary conditions of Poisson equation.
© Synopsys 2013 45
Previous TCAD Process Simulation
• The importance and influence of the surface potential
(electric field) for doping redistribution in semiconductors
is understood [Dev PRB2003, Gorai JAP2012], but the
following two effects were never taken into account in
TCAD process simulation:
– Electrostatic interaction between the gate and the substrate of a
submicron CMOS transistor
– Reduction of carrier (electrons and holes) concentration at
semiconductor/dielectric interface due to quantum confinement
© Synopsys 2013 46
BC: Problem Description
• Current practice:
– Poisson equation for Potential is solved only in Silicon and
PolySilicon with the HomNeumann boundary conditions, i.e. the
normal to interface component of electric field is zero (ZEF BC)
at the Silicon (and PolySilicon) boundary.
– This approximation is correct for the free (or covered with Oxide)
flat surface of Silicon since it results in zero electric field outside
of the simulated region.
• The correct boundary conditions at materials interfaces for
Poisson equations must preserve the continuity of electrostatic
potential, tangential component of electric field and normal
component of electric displacement. See the band structure of a
nMOS transistor on the next slide for the illustration
© Synopsys 2013 47
Band Diagram of Poly/Ox/Si System
Figure has been copied
from the online dissertation
of Predrag Habas “Analysis
of Physical Effects in
Small Silicon MOS
Devices” (1997).
http://www.iue.tuwien.ac.at/
phd/habas/node13.html
Note, that for the process
simulation electrical
equilibrium is assumed: i.e.
the Fermi level is constant
in the whole simulated
system, hence UGB=0 V.
Also φi=0
n=ni(T)*exp[qφ/(kBT)]
© Synopsys 2013 48
Two Types of New Boundary Conditions
for Potential
1. “Continuous” boundary conditions, Suitable for most of interfaces,
like dielectric/semiconductor and dielectric/dielectric:
pdbSetBoolean Oxide_Silicon Potential Continuous 1
2. “Metal-like” Dirichlet boundary condition, which provide fixed
potential at “metal” interfaces:
pdbSetBoolean Oxide_TiNitride Potential Fixed_Oxide 1
pdbSetString Oxide_TiNitride Potential Equation_Oxide
”(Potential_Oxide - 0.4)”
© Synopsys 2013 49
Potentials at Metal Interfaces
• In S-Process zero electrostatic potential corresponds to the Fermi
energy at the intrinsic level of silicon Ei(T).
• At the Metal interface Potential should be equal to
MeWorkFunction(T) - Ei(T). The exact temperature dependencies of
MeWorkFunction(T) and Ei(T) are not known. For the test, constant
differences +0.4 V and -0.4 V for nMOS and pMOS were used, since
these values are typical for the gate metal in current CMOS
technology at T=300 K.
© Synopsys 2013 50
Initialization of Potential Equations in
Dielectrics
In dielectric materials zero charge is assumed. Only their permittivities are taken
into account. In rel. H-2013.03 and earlier the Potential equations in dielectrics are not defined, so Laplace’s equation PotentialEquation (the name is
arbitrary) must be defined in them. Then initialization is performed, for example
in Oxide:
pdbSetString Oxide Potential InitProc PotentialInitProc
pdbSetString Oxide Potential InitSolve PotentialInitProc
pdbSetString Oxide Potential EquationProc PotentialEquation
pdbSetString Oxide Potential EquationInitProc PotentialEquationInit
pdbSetDouble Oxide Potential Permittivity 3.9
pdbSetDouble Oxide Potential DampValue 0.025
pdbSetBoolean Oxide_Silicon Potential Continuous 1
etc.
Complete example is available from Alexander Tsibizov.
© Synopsys 2013 51
Quantum Corrections for Process
Simulation: Introduction
• The importance of the quantum effects in deep-
submicron CMOS device simulation is well recognized in
device TCAD simulations and multiple methods for their
simulation were established [Schenk ESSDRC2001].
• We have introduced effect of carrier concentration
reduction at silicon/dielectric interfaces due to quantum-
mechanical repulsion into a continuum process
simulation using the modified local-density
approximation (MLDA)[Paasch PSS(b)1982,83; Penzin TED2011]
– This changes the carrier distributions in a nanometre thin layer in
semiconductors close to their interfaces with dielectrics, therefore
it modifies electrostatic potential and hence dopant distribution.
© Synopsys 2013 52
MLDA QC (1)
• Detailed derivation of MLDA is given in the literature [Paasch
PSS(b)1982,83; Penzin TED2011]. For a multi-valley semiconductor
with nV, valleys at the conduction band edge, without mechanical
stress, based on formula (22a) from [Paasch PSS(b)1983] for
electron concentration in the case of Boltzmann statistics :
𝑛 𝒓 = 𝑛0 𝒓 1 −1
𝑛𝑉 𝑒
− 𝑥3/𝐿𝐶𝑖
2𝑛𝑉
𝑖=1
= 𝑛0 𝒓 1 − 𝑄𝐶 𝑥3, 𝑇 , 𝐿𝑐𝑖 =
ℏ2𝑤33𝑖
2𝑘𝐵𝑇
x3 is the distance to the interface, wi33 is the effective mass in i-valley in the
direction normal to the interface
• For silicon with interface normal to (100):
At T=1300 K: Ltc=1.34 nm and Ll
c=0.59 nm
• Similar expression can be obtained for holes
𝑛 𝒓 = 𝑛0 𝒓 ∙ 1 −1
6 2𝑒− 𝑥3/𝐿𝐶
𝑙 2
+ 4𝑒− 𝑥3/𝐿𝐶𝑡
2
© Synopsys 2013 53
MLDA QC (2) Plots of (1-QC) for electrons (green), holes (red) and a Simplified QC
function 𝑆𝑄𝐶 = 𝐸𝑥𝑝 −𝑥3 1𝑛𝑚 (blue) for two T=1300K and T=1000K.
SQC has been used in process simulation of CMOS as QC for both
electrons and holes instead of original ones to achieve good convergence
0 1. 10 9 2. 10 9 3. 10 9 4. 10 9 5. 10 9
0.0
0.2
0.4
0.6
0.8
1.0
distance to interface x3 , m
1Q
C
T 1300 K
0 1. 10 9 2. 10 9 3. 10 9 4. 10 9 5. 10 9
0.0
0.2
0.4
0.6
0.8
1.0
distance to interface x3 , m
1Q
C
T 1000 K
© Synopsys 2013 54
Effect of QC in 1d Simulation Semi-infinite Si structure in contact with Gas homogeneously doped by
phosphorus annealed for 1e-10s, 1s and 1000s at 1050C. No
doseloss, ZEF BC for Poisson equation.
Initial Conc. P = 1e20 cm^-3
QC’s impact is stronger for large doping concentration!
Initial Conc. P = 1e18 cm^-3
© Synopsys 2013 55
“Realistic” 2D Test NMOS Simulation
• A generic 65nm-like CMOS process:
• 1.4 nm SiO2 gate dielectric
• Initially undoped Polysilicon (doping via SD/Ext/Halo implants), or metal-first
technology with metal EFMe-EiSi=0.4eV
• RTA 1050 C 1s for SD anneal
© Synopsys 2013 56
Simulated NMOS Vt roll-off
Metal gate (EFMe-EiSi=0.4eV) Polysilicon gate
, um , um
, V
, V
QC mostly reduce doping in
Poly near Poly/Ox interface
New BC increase B pile-up;
QC reduces screening in Si
© Synopsys 2013 57
Section of 2D NMOS in the middle of 1um-long gate, after RTA 1s 1050C
Poly Silicon Oxide Silicon
QC causes Poly depletion near Si/Ox interface. New BC cause B pile-up in the
channel.
© Synopsys 2013 58
2D Potential Distribution in NMOS with
Metal-first-like (0.4 V) Gate, Lg=120nm After RTA (1s at 1050 C), T=1050 C
© Synopsys 2013 59
2D Doping Distribution in NMOS with
Metal-first-like (0.4 V) Gate, Lg=120nm After RTA (1s at 1050 C), T=1050 C
© Synopsys 2013 60
Future Work
• Detailed investigation of the new BC and QC influence
on the simulation results. First maybe also in the frame
of ATEMOX:
– Injection and recombination of point defects at interfaces
– OED
– Dose loss for dopants
• Achieve good convergence for standard MLDA QC.
Currently it is done via Simplified QC. With standard
MLDA QC convergence is much worse (investigation is
necessary). With Simplified QC simulation time is almost
the same as without any QC.
Internal Confidential
© Synopsys 2013 61
Conclusions
• “Correct” boundary conditions for Poisson equation must be applied
for CMOS simulations. They are available in S-Process via
ALAGATOR scripts and can be used for regular simulations. The
simulation time and convergence do not become worse.
• For typical CMOS structures noticeable (but moderate in most of the
cases) difference in the simulation results in comparison to the old
settings, is demonstrated. The larger VT changes occur for heavily
doped Poly gates and Metal-first technology, very small ones for
Metal-last (undoped Poly). The VT differences increase for smaller
gate lengths: e.g. in the test metal-first-like NMOS simulation
dVt(Lg=40nm)=27 mV, dVt(Lg=1.0um)=8 mV.
• Further improvements are necessary in S-Process for correct
simulation of structures with interface charges
© Synopsys 2013 62
References
• Dev PRB2003: Kapil Dev, M. Y. L. Jung, R. Gunawan, R. D. Braatz, and E. G.
Seebauer*, “Mechanism for coupling between properties of interfaces and bulk
semiconductors”, PHYSICAL REVIEW B, Vol. 68, p.195311 (2003)
• Gorai JAP2012: Prashun Gorai, Yevgeniy V. Kondratenko, and Edmund G. Seebauer,
“Mechanism and kinetics of near-surface dopant pile-up during post-implant
annealing”, JOURNAL OF APPLIED PHYSICS, Vol. 111, p. 094510 (2012).
• Schenk ESSDRC2001: Schenk A., “Physical Modeling of Deep-Submicron Devices”,
Proceeding of the 31st European Solid-State Device Research Conference, 11-13
September 2001, pp. 9-16.
• Paasch PSS(b)1982: Paasch G. and Übensee H., “A Modified Local Density
Approximation Electron Density in Inversion Layers”, phys. stat. sol. (b), Vol. 118, pp.
165-178, (1982)
• Paasch PSS(b)1983: Paasch G. and Übensee H., “Carrier Density near the
Semiconductor-Insulator Interface. Local Density Approximation for Non-Isotropic
Effective Mass”, phys. stat. sol. (b), Vol. 118, pp. 255-266 (1983)
• Penzin TED2011: Oleg Penzin, Gernot Paasch, Frederik O. Heinz, and Lee Smith,
“Extended Quantum Correction Model Applied to Six-Band k·p Valence Bands Near
Silicon/Oxide Interfaces”, IEEE TRANSACTIONS ON ELECTRON DEVICES, Vol. 58,
No. 6, JUNE 2011, pp. 1614-1619.
© Synopsys 2013 63
Dopant Redistribution during SPER
Christoph Zechner, Nikolas Zographos, Synopsys
May 30, 2013
© Synopsys 2013 64
Doping Redistribution During SPER
SPER: Solid Phase Epitaxial Regrowth (of amorphized regions)
• Phenomena observed:
– Snow plow effect: Some dopants are pushed towards the surface (In, F).
– Significant diffusion in amorphous silicon (B)
– Transient enhanced diffusion.
– Immobile clusters in amorphous Si.
– Formation of thread dislocations (stress memorization … not a topic in ATEMOX)
• History in S-Process Continuum:
– First robust implementation: F-2011.09
– First parameters in AdvancedCalibration: G-2012.06
– Calibration update: H-2013.03
© Synopsys 2013 65
Snow-Plow Effect
R. Duffy et al., 2004
© Synopsys 2013 66
Snow-Plow Effect: Model
• Phase Field:
– SPERPhase = 1: Crystalline
– SPERPhase = 0: Amorphous
• After implant:
– Initialization of SPERPhase is based on field Damage
• During SPER:
– Partial differential equation gives time evolution of SPERPhase.
– Gradient of the phase field acts as a driving force on dopants
– Typically from crystalline towards amorphous region.
• Model Usage in Sentaurus Process:
AdvancedCalibration 2013.03
AdvancedSPERModel
© Synopsys 2013 67
Snow Plow Effect: SIMS vs. TCAD
a/c interface
after implant
During SPER, indium is pushed towards the surface.
SIMS: R. Duffy et al., J. Vac. Sci. Technol. B 22(3), 2004
Simulation: AdvancedCalibration 2013.03 with AdvancedSPERModel
© Synopsys 2013 68
Implementation (1/2)
fproc AdvancedSPERModel { } {
# Phase-Field Model for SPER
pdbSet Diffuse SPER 1
pdbSet Diffuse SPER.Model PhaseField
# Recrystallization velocity from G.L. Olsen, MSR 3 (1988)
pdbSet Si SPER PhaseTransWidth 0.003
pdbSet Si SPER Lambda.Fac 1.61
pdbSet Si SPER Relax.Rate {[Arr 3.08e8 2.68]/[pdbGet Si SPER PhaseTransWidth]/ \
[pdbGet Si SPER PhaseTransWidth]}
pdbSet Si SPER R.Fac.Aniso { 100 20.0 110 10.0 111 1.0 }
pdbSet Si SPER E.Aniso { 100 0.0 110 0.0 111 0.0 }
pdbSet Si SPER R.Fac "(0.8+0.2*3.e18/(3.e18+Fluorine))"
© Synopsys 2013 69
Implementation (2/2)
pdbSet Si B SPER.Energy 0.0
pdbSet Si B DAmor {[Arr 1.0 2.68]}
pdbSet Si As SPER.Energy 4.0
pdbSet Si As DAmor {[Arr 0.4 2.68]}
pdbSet Si P SPER.Energy 1.5
pdbSet Si P DAmor {[Arr 0.4 2.68]}
pdbSet Si In SPER.Energy 1.5
pdbSet Si In DAmor {[Arr 1.0 2.57]}
pdbSet Si C SPER.Energy 0.12
pdbSet Si C DAmor {[Arr 40 2.60]}
pdbSet Si F SPER.Energy 0.35
pdbSet Si F DAmor {[Arr 12 2.58]}
pdbSet Si Ge SPER.Energy 0.018
pdbSet Si Ge DAmor {[Arr 5.0 2.60]}
} ; # end of AdvancedSPERModel
© Synopsys 2013 70
2D Test Case: 45nm nMOS
Process flow:
• B well and channel implant
• Well anneal
• Gate formation
• As LDD + In pocket implant
• RTA
• Spacer deposition
• As + P source/drain implant
• RTA
• Contact formation
Final doping concentration
© Synopsys 2013 71
2D Test Case: 45nm nMOS
Process flow:
• B well and channel implant
• Well anneal
• Gate formation
• As LDD + In pocket implant
• RTA
• Spacer deposition
• As + P source/drain implant
• RTA
• Contact formation
Final doping concentration
© Synopsys 2013 72
SPERPhase: Initialization
After implant:
Damage
Start of Anneal:
SPER
Phase
© Synopsys 2013 73
SPERPhase: Time Evolution
Start of Anneal
Ramp up completed 739 °C
Ramp up to 703 °C
(150K/s)
© Synopsys 2013 74
SPERPhase: Time Evolution
Start of Anneal
Ramp up completed 739 °C
Ramp up to 703 °C
(150K/s)
© Synopsys 2013 75
Indium during first RTA
Start of Anneal
Ramp up completed 739 °C
Ramp up to 703 °C
(150K/s)
© Synopsys 2013 76
1D Profiles during first RTA
© Synopsys 2013 77
SPER: Anisotropy
Compared to 100 direction (all SIMS data) SPER is 2 times slower in 110 direction,
and 20 times slower in 111 direction.
pdbSet Si SPER R.Fac.Aniso { 100 20.0 110 10.0 111 1.0 }
Does this lead to 2 times (20 times) more dopant redistribution ?
100 direction:
SPER is fast
110 direction:
SPER is slow
a-Si
c-Si
Orientation dependend SPER for amorphized pocket.
Time evolution of crystallinity field.
0 sec 15 sec 30 sec
c-Si
a-Si
© Synopsys 2013 78
Anisotropy in our Test Example
Three cases compared:
• Simulation without SPER model
• SPER model
• SPER model, isotropic SPER velocity
R.Fac.Aniso { 100 20.0 110 20.0 111 20.0 }
VT difference is mainly due to:
• Lateral snow-plow effect for As in
LDD region.
Note:
• Sensitivity depends on process details.
• More lateral snow-plow effect after
deep pre-amorphization.
© Synopsys 2013 79
A Closer Look on Anisotropy (1/3)
111 direction: Slow growth. It takes time to create a seed for the next layer.
100, 111 direction: Formation of nanofacets and nanoridges with 111 surfaces.
Figures from: K. L. Saenger et al.,
J. Appl. Phys. 101, 024908 (2007)
© Synopsys 2013 80
A Closer Look on Anisotropy (2/3)
Figures from: K. L. Saenger et al.,
J. Appl. Phys. 101, 104908 (2007)
Nanofacet / nanoridge model shows
qualitative agreement with TEM.
Continuum SPER model Nanofacet/nanoridge model
Snow plow
effect is
different in
this region.
© Synopsys 2013 81
Anisotropy: LKMC Capabilities
LKMC in Sentaurus Process [I. Martin-Bragado and V. Moroz, APL 95, 123123 (2009)]
• Strain is generated by volume expansion during amorphization.
• Shear strain reduces recrystallization velocity.
111
100
Atomistic SPER Strain field Saenger model vs LKMC
LKMC LKMC
© Synopsys 2013 82
SPER: Other topics
• Dependence of SPER velocity on impurities and Fermi Level.
– In reality: This is quite complex
– Doping speeds up SPER
– Some impurities (F) slow down SPER
– Strain influence
– Very simple velocity correction factor in AdvancedSPERModel
• Clustering inside amorphous silicon
• SPER “activation level”
© Synopsys 2013 83
SPER: Diffusion in a-Si
B SIMS before and after RTA. B was co-implanted with Ge (30keV) and F.
The depth of amorphized layer was 50nm.
Picture is from: [N.E.B. Cowern et al., APL 86, 101905 (2005)].
Boron diffusion in a-Si
B clusters in a-Si
© Synopsys 2013 84
SPER: Diffusion in a-Si
Green: AdvancedSPERModel default: Constant diffusivity in a-Si
Red: term BoronDAmorFactor defined.
equation = "6e40 * (Boron + ni) / (1e20+Boron)^3"
Tail region: diffusivity
proportional to B
(“Fermi-Level
dependent diffusivity”)
Diffusivity reduced in region with very high B
Idea: immobile.clusters
© Synopsys 2013 85
SPER Recommendations
The SPER model often improves the process simulation accuracy. It is turned on by:
AdvancedCalibration 2013.03
AdvancedSPERModel
Mesh spacing should be fine (< 3nm with current model parameters).
Possibly, isotropic SPER velocity gives better results for snow plow effect.
Continuum: pages 101 – 103
KMC, LKMC: pages 162 – 164, 175, 181 Continuum: pages 216 – 220
KMC, LKMC: chapter 5
© Synopsys 2013 86
Plasma Implant
Christoph Zechner, Synopsys
May 30, 2013
© Synopsys 2013 87
Plasma Implant
• Sentaurus MC with keyword plasma:
– Conformal doping:
– Ions enter device at all surfaces.
– Direction is perpendicular to surface
– Dose per surface area is constant.
– Ions have energy distribution.
• Atemox:
– More realistic energy distribution.
– BF, BF3 allowed as pre-defined species
© Synopsys 2013 88
Plasma Implant: Calibration
pdbSetSwitch MCImplant PlasmaEnergyDistributionModel Burenkov
pdbSet Si B surv.rat [expr 10.0/(@Energy@+0.25)] ;# calibration
pdbSet Si F surv.rat [expr 20.0/(@Energy@+0.25)] ;# calibration
implant plasma.source = { BF2=0.5 Boron=0.1 BF=0.4 } dose=2e14
energy=@Energy@ sentaurus.mc tilt.stdev = 1
SIMS: Burenkov
et al., IIT 2012
© Synopsys 2013 89
PlasmaEnergyDistributionModel
© Synopsys 2013 90
Beyond Conformal Doping
• Dose per surface area is not constant (e.g. smaller in deep, narrow
trenches).
• No easy solution.
– Investigations for example by IMM Catania (Antonino La Magna), but it is not
clear, if and what can be transferred to S-Process.
© Synopsys 2013 91
Thank You
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