Monolithic sensor simulations mtg, 26/1/2021 - Recombination, generation and mobilities in Silvaco - CERN Indico
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Monolithic sensor simulations mtg, 26/1/2021
Recombination, generation and mobilities in Silvaco
M. Bomben – LPNHE & Univ. de Paris, Paris
M. Bomben - 26/1/2021 1
Outline • Introduction • Recombination & generation models • Mobility models • Conclusions M. Bomben - 26/1/2021 2
Introduction • The Silvaco tool to model devices’ physics is called ATLAS • ATLAS works for both 2D and 3D structures • ATLAS manual is ~ 1800 pages long • It contains several models for many of the physics processes involved in device simulations • In the following examples for recombination & generation and mobility M. Bomben - 26/1/2021 3
RECOMBINATION & GENERATION M. Bomben - 26/1/2021 4
Recombination & Generation (R&G): intro
• Silvaco ATLAS considers six main categories for R&G processes:
Ø phonon transitions
Ø photon transitions
Ø Auger transitions
Ø surface recombination
Ø impact ionization
Ø Tunnelling
• In the following I will present some models for the underlined
categories
M. Bomben - 26/1/2021 5R&G: SRH • Default model is SRH with a single level wrt to the intrinsic Fermi level M. Bomben - 26/1/2021 6
R&G: CONSRH • Modification of SRH to take into account impurity concentration dependence for the recombination lifetimes: • Several other conc. dep. SRH models are available M. Bomben - 26/1/2021 7
R&G: generation vs recombination lifetime
• For TAUN0=TAUP0 the generation
lifetime* is equal to the recombination
lifetime
* calculated from:
τG
τR
M. Bomben - 26/1/2021 8Digression: bandgap energy
• In both Silvaco and Synopsys the bandgap energy dependence with
temperature is modelled in the following way
• What is different between the two
tools is the default value of Eg(300K):
– Eg(300K) = 1.08 eV in Silvaco Atlas
– Eg(0K) = 1.1696 eV in Synopsys Sentaurus (ó Eg(300K)~1.12 eV)
M. Bomben - Band gap energy modelisation in Silvaco TCAD Atlas Device simulator - 31st RD50 WS, CERN
M. Bomben - 26/1/2021 9Leakage current vs Temperature
χ2 / ndf 1.52 / 6
I vs 1/T
I [A/cm]
Prob 0.9581
1.0/Tref 0.003411 ± 0
10−13
I evaluated at Vdepl + 50 V
n 1.919 ± 0.3528
Ea 1.134 ± 0.01666
Iref 1.654e−13 ± 1.16e−16
(Vdepl does not depend from T)
10−14
n free to float Ea ~ 1.13 eV χ2 / ndf 1.573 / 7
n~2
I [A/cm]
Prob 0.9797
1.0/Tref 0.003411 ± 0
10−13 n 2 ± 0
1/T [K-1] Ea 1.13 ± 0.0003565
Iref 1.654e−13 ± 9.064e−17
M. Bomben - Band
gap energy
modelisation in
Silvaco TCAD Atlas 10−14
Device simulator - n fixed to 2
31st RD50 WS,
CERN
1/T [K-1]
M. Bomben - 26/1/2021 10Ea vs Eg(300K)
Ea [eV]
1.17
1.165 TCAD Simulation
1.16 Linear fit
1.155
1.15
1.145
SILVACO TCAD
M. Bomben - Band 1.14 Empirical rule:
gap energy
modelisation in
1.135
Ea = Eg(300)+0.05 eV
Silvaco TCAD Atlas 1.13
Device simulator -
31st RD50 WS,
1.08 1.085 1.09 1.095 1.1 1.105 1.11 1.115 Sil 1.12
CERN Eg (300) [eV]
M. Bomben - 26/1/2021 11Leakage current rescaling
(Reverse current @ -20 C scaled to 20 C)/I(20 C)
Ratio of Reverse currents scaled to 20 C
Iscaled/I(293.15 K)
1.02 1.02
Iscaled/I(293.15 K)
Slope consistent with 0
1 1.015 Intercept consistent with 1 TCAD Simulation
0.98
Linear fit
1.01
0.96
0.94
±2% 1.005
0.92 1
0.9 0.995
0.88
0.99
250 255 260 265 270 275 280 285 290
−500 −400 −300 −200 −100 0 T [K]
Vbias [V]
M. Bomben - Band gap energy
1% the accuracy on average of the rescaling
modelisation in Silvaco TCAD Atlas Device
simulator - 31st RD50 WS, CERN
M. Bomben - 26/1/2021 12R&G: C-interpreter for SRH
• A C-function can be supplied to program your own SRH tunnelling model
• Calculate
recombination rate per
node using observables
values
• Return recombination
rate and its derivative
M. Bomben - 26/1/2021 13R&G: coupled defects
Coupled Defect Level
Recombination Model
This model is a modification of the SRH
model to the situation where there is
charge transfer between two defect
levels. This can lead to large excess
currents in devices.
M. Bomben - 26/1/2021 14Digression: traps • Of course one way to alter R&G is by adding traps M. Bomben - 26/1/2021 15
R&G: trap assisted tunnelling • In a strong electric field, electrons can tunnel through the bandgap via trap states: trap assisted tunnelling (TAT) • Example for irradiated detectors: M. Bomben - 26/1/2021 16
R&G: TAT & Hamburg Penta Trap Model
• Possibility to turn on tunnelling
for each trap separately TAT for all
TAT for Ip
No TAT
https://arxiv.org/pdf/1904.10234.pdf
M. Bomben - 26/1/2021 17R&G: C-interpreter for TAT • A C-function can be supplied to program your own trap-assisted tunnelling model • There are two types of this: F.TATRECOMB & F.TATTRAPRECOMB 1. F.TATRECOMB: provides the composition information, temperature, carrier densities, and electric field at a node as input, and expects a recombination rate as a return parameter, as well as the derivatives of the recombination rate with respect to carrier densities, temperature, and electric field. This will apply to the SRH model if enabled, as well as any TRAPS present. M. Bomben - 26/1/2021 18
R&G: C-interpreter for TAT • A C-function can be supplied to program your own trap-assisted tunnelling model • There are two types of this: F.TATRECOMB & F.TATTRAPRECOMB 2. F.TATTRAPRECOMB: specific to TRAPS, and only applies to TRAPS. This function is like the F.TATRECOMB function, but additionally supplies the trap density, trap specific electron, and hole recombination lifetimes. If has the same return variables as the F.TATRECOMB function. M. Bomben - 26/1/2021 19
R&G: C-interpreter for TAT
• Calculate
recombination rate per
node using observables
values
• Return recombination
rate and its derivative
M. Bomben - 26/1/2021 20R&G: Surface Recombination
Independent from bulk recombination
definition
M. Bomben - 26/1/2021 21MOBILITY MODELS M. Bomben - 26/1/2021 22
Mobilities • In Silvaco ATLAS mobility models are divided in four categories: 1. Low field behaviour 2. High field behaviour 3. Bulk semiconductor regions 4. Inversion layers • In the following some examples for the underlined cases will be given M. Bomben - 26/1/2021 23
In Atlas, the choice of mobility model is specified on the MODELS statement. Th
Low field behaviour – default model
MOBILITY
specifiedMUPon a separate500MOBILITY
2
associated with mobility models are statem
cm /(V· s)
MOBILITY TMUN 1.5
more mobility models should always MOBILITY
be specified TMUP
explicitly.1.5The default is to
low-field mobilities within eachConcentration-Dependent
region of a Low-Field device. This default model is in
Mobility Tables
doping concentration, carrier densities and electric field. It does account for latt
Temp. dep.: power law Atlas provides empirical data for the doping dependent low-field mobilities of electrons and
due to temperature according to: MODELSConc. dep.: lookup table for T = 300 K
holes in silicon at T =300K only. This data is used if the CONMOB parameter is specified in the
L
statement. The data that is used is shown in Table 3-37.
Table 3-37 Mobility of Electrons and Holes in Silicon at T=300K
T L – TMUN Concentration (cm-3 ) Mobility (cm2 /V s)
----------
n0 = MUN 300 Electrons Holes
1.0 1014 1350.0 495.0
2.0 1014 1345.0 495.0
T L – TMUP 4.0 1014 1335.0 495.0
----------
p0 = MUP 300
6.0 1014 1320.0 495.0
8.0 1014 1310.0 495.0
1.0 1015 1300.0 491.1
Low field
where T ismob.
the lattice temperature. The low-field mobility
(it continues parameters:
for higher conc.) MUN, MU
TMUP can be specified in the MOBILITY statement with the 167 defaults as shown in MT
Atlas User’s
Tested at 0 V (to be in low field regime) and several temperatures
Table 3-36 User-Specifiable Parameters for the Constant Low-Field Mobili
Values from manual are confirmed:
• MUN, MUP = 1350, 500 cm^2/VsParameter
Statement Default
• TMUN, TMUP = 1.5
M. BombenMOBILITY
- 26/1/2021 MUN 1000 24reduction of the effective mobility since the magnitude of the drift velocity is the product of
High field behaviour – default model
the mobility and the electric field component in the direction of the current flow. The
following Caughey and Thomas Expression [48] is used to implement a field-dependent
mobility. This provides a smooth transition between low-field and high field behavior where:
1
1
------------------
BETAN Caughey and Thomas,
n E = n0 ----------------------------------------------------
n0 E
BETAN
-
“Carrier Mobilities in Silicon 3-323
Empirically
1 + ------------------
VSATN Related to Doping and Field.” Proc. IEEE
55, (1967): 2192-2193.
1
------------------
1 BETAP
p E = p0 ----------------------------------------------------- 3-324
BETAP
p0 E
1 + ------------------
VSATP
Tested
Here, Eatis0thefluence parallel and electric 300 field K and n0 and p0 are the low-field electron and hole
Values from
mobilities manualThe
respectively. arelow-field confirmed: mobilities are either Surprising that
set explicitly beta’s
in the are different
MOBILITY
statement or calculated by one of the low-field mobility models. The BETAN and BETAP
µn0, µn0are=user-definable
• parameters 1350, 500incm^2/Vs the MOBILITY statement But this
(seewas
Tablethe
3-70finding of the model’s authors
for their defaults).
VSATN,
• The VSATP
saturation velocities = 1.02e7 are calculated cm/s by default from the temperature-dependent see next slide models
BETAN = 2
• [281]:
BETAP= =------------------------------------------------------------------------------------------------
• VSATN 1 ALPHAN.FLD -
TL
M. Bomben - 26/1/2021
1 + THETAN.FLD exp --------------------------------- 25Extra
Caughey and Thomas,
“Carrier Mobilities in Silicon
Empirically Related to
Doping and Field.” Proc.
IEEE 55, (1967): 2192-2193.
M. Bomben - 26/1/2021 26Mobilities: ATLAS experiment, C-interpreter
• Extensive comparison of mobility
models and comparison of some
to Lorentz Angle data from ATLAS
• The model used in ATLAS https://cds.cern.ch/record/2629889
experiment is the Canali model
(IEEE Transactions on Electron
Devices 22 (1975) 1045)
• Using C-interpreter it was
possible to implement the
mobility used in ATLAS
experiment into Silvaco TCAD
M. Bomben - 26/1/2021 27Mobilities: C-interpreter
Temperature, dopant conc., electric field, saturation
velocities and low field mobilities are provided
M. Bomben - 26/1/2021 28Mobilities: C-interpreter
Mobility and the derivative of mobility with
respect to electric field is returned
M. Bomben - 26/1/2021 29Mobility and its impact
IBL (planar n-in-n), Phi = 6.4e14 (using Chiochia model)
6
×10
-
Carrier velocity minimum [cm/s]
TCAD - e
(ATHENA is the ATLAS experiment
12 TCAD - h
+
- software framework)
As expected carriers are slower
ATHENA - e
ATHENA - h
+ for smaller mobility
10
8
6
e- velocity
4
2
0
100 200 300 400 500 600 700 800 900 1000
Vbias [V] Bulk depth [µm]
M. Bomben - 26/1/2021 30Mobility: changes in electric field
1.25
ATHENA/TCAD E Field
200 V
1.1 1.2
ATHENA/TCAD E Field
400 V
1.15 500 V
600 V
1.08 400 V 1.1 800 V
1000 V
500 V 1.05
1.06 600 V 1
1.04 800 V 0.95
1000 V 0.9
0.85
1.02
0.8 Same including 200 V
1 0.75
20 40 60 80 100 120 140 160 180
Bulk Depth [µ m]
0.98
0.96 Less than 10% change for
0.94 ATHENA/TCAD E Field bias of 400 V and more
(ATHENA is the ATLAS experiment
0.92
software framework)
0.9
20 40 60 80 100 120 140 160 180
Bulk Depth [µ m]
M. Bomben - 26/1/2021 31CONCLUSIONS M. Bomben - 26/1/2021 32
Conclusions • In Silvaco tool for device simulations ATLAS recombination and mobility can be modelled with great flexibility • Many models exist, several per process (phonon, photon; low & high field) • The possibility to use the C-interpreter makes easy to extend simulator capabilities • As usual, testing modifications in the simplest possible situation is the best way to proceed M. Bomben - 26/1/2021 33
Backup M. Bomben - 26/1/2021 34
IBL (planar n-in-n), Phi = 6.4e14 (using Chiochia model) M. Bomben - 26/1/2021 35
Vdepl ~ 250 V
Electron velocity
along the bulk
M. Bomben - 26/1/2021 36Vdepl ~ 250 V
Hole velocity
along the bulk
M. Bomben - 26/1/2021 37You can also read
