Advances in Ion Implantation Modeling for Doping of Semiconductors
Outline
• Basic Concepts • Predictive Modelling of Implantation • Low Energy Model • Morphology of Implant Distribution • Conclusions
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Some Interesting Dates in History of Ion Implantation Modeling
1958
Bredov et al., Sov. Phys. Tech. Phys., 3, 228(1958) - the first BCA simulation of “ion implantation” of 4 keV K+ ions in Ge.
1959
Gibson et al., Phys. Rev., 120, 1229 (1960), J. Appl. Phys., 30, 1322 (1959) - the MD method first used in radiation defects studies.
1962
Robinson and Oen, Appl. Phys. Lett., 2, 30 (1963), Phys. Rev., 132, 2385 (1963) prediction of channeling, later, in 1963, experimentally confirmed by John A. Davies
1974
Robinson and Torrens, Phys. Rev., B9, 5008 (1974) - first major description of the BCA program MARLOWE
1991
Klein, Park and Tasch, IEEE Trans. Electron Devices, 39, 1614 (1992) the UT-MARLOWE projects starts with a goal for predictive ion implantation simulation.
1996
Cai et al., Morris et al., Phys. Rev., B54, 17147 (1996), IEDM Technical Digest, (1996) new treatment of inelastic energy losses, essentially separating the velocity dependence of the local and the non-local electronic stopping thus, giving high predictive quality of ion implantation simulations.
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Ion Channeling
"This remarkable effect had actually been 'discovered' in computer 'experiments' at ORNL," said Datz. Because of concern about neutron-induced radiation damage in nuclear reactors, in 1962 Mark Robinson and Dean Oen, two researchers in ORNL's Solid State Division (SSD), attempted to model the effects of an energetic copper projectile ion on a copper crystal lattice. "They wanted to know how far a copper ion goes before it stops," Datz said. "They let their Monte Carlo computer program run for a long time, but they sometimes couldn't find where the particle went. They changed the code and their simulation showed that the copper atom often came out the other side of the lattice." Their 1963 modeling led to their prediction that ions can travel through a crystal in the space, or channel, between rows of atoms and planes in the lattice—hence the term, ion channeling. ... http://www.ornl.gov/ORNLReview/v34_2_01/fermi.htm
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Ion Implantation: 1970 sample, 120 keV P into Si, 7o to direction
• G. Dearnaley et al., 1970, “Atomic collision phenomena in solids”, eds. D. Palmer, M. Thompson and P. Townsend
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Ion Implantation: 1975 sample, 100 keV B into SiO2
• R. Schimko et al. 1975, Phys. Stat. Sol. (a), vol 28
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Ion Implantation: 1987 sample, 50 keV P into (100) Si
• H. Kang et al., 1987, “Journal of Applied Physics”, p.2733, vol 62
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Classification of Simulation Models
Molecular Dynamics
Binary Collision Approximation
Classical MD: many, more recent studies by T.Diaz de la Rubia et al. on defects in silicon
BC(Binary Collision) programs: the location of target atoms are determined by welldefined crystal structure. Stochastic methods play only an auxiliary role, supplying, for example, initial ion positions and directions, thermal vibrations, chemical disorder, etc. Typical programs are: MARLOWE, UT-MARLOWE, CRYSTAL in Silvaco’s process simulator, etc.
Recoil approximation MD: many, for example the REED program by Beardmore & Jensen for ion implantation, Hobler & Betz’s, etc.
Advances in Ion Implantation Modeling for Doping of Semiconductors
MC(Monte-Carlo) codes: stochastic methods are used to locate the target atoms or to determine the impact parameters, flight distances, scattering angles, etc. The best known code is the TRIM(SRIM).
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Different Orientation of Silicon Crystal Structure
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Time Scale
10-15 s Balistic processes: > 10 .. 100 eV Binary Collisions creation of atomic displacements
10-11
s
Binary Collision (BC) simulations
Athermal, Rapid thermal processes: < 1 .. 10 eV collective interactions rapid local melting/quenching, creation of disordered regions and amorphization
Classical Molecular Dynamics (MD) simulations
Thermally activated processes: > 1s
strong dependence temperature recrystallization, decrease and rearrangement of damage, point defect migration
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Kinetic Monte-Carlo (KMC) simulations
Hierarchy of Ion Implantation/Radiation Damage Models
transfer of physical parameters
Quantum mechanics (ab-initio) CPU intensive, small systems most exact, static calculations
Classical molecular dynamics (MD) low-energy impacts, limits at amorphyzation and defect evolution for times > 1ns.
can validate/calibrate higher level methods
damage at the cooling-down stage of cascade evolution
Binary collision approximation (BCA)
leading atomistic approach, better coupling to MD ion range profiles, successful and experiment will improve modeling of damage. for ballistic processes
Kinetic Monte Carlo (KMC) thermally activated processes, strong dependence on temperature
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self-annealing, point defect migration, clustering of defects
Basic Concepts of Ion Implantation (II)
ion
lattice e-
ee-
For predictive modeling of II we need to have physically realistic treatment of:
• Nuclear stopping & interatomic potentials • local & non-local electronic stopping • damage buildup & amorphization
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nuclear collisions
Scattering Dynamic in a Collision Event
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Nuclear & Electronic Stopping of Boron in Amorphous Silicon
Nuclear
10
120
Electronic
9
Nuclear, eV/A
7
80
B
6
C
5
60
4 40
3 2
A
1
20
vB
0 1
10
100
1000
Boron energy, keV
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10000
0 100000
Electronic, eV/A
100
8
Electronic Energy Loss – Part 1
• Firsov’s semi-classical model (local) The transfer of energy, DE, from the ion to the atom is due to passage of electrons. This results in a change of momentum of the ion, which arises from the retarding force acting on the ion. When the ion moves away, the electrons return. However, there is no back transfer of momentum because electrons fall into higher energy levels.
• Lindhard & Scharff electronic stopping (non-local) Electrons, impinging on the ion, transfer net energy which is proportional to their drift velocity relative to the ion.
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Electronic Energy Loss - Part 2
• Local, impact parameter dependent • Non-local • Velocity dependence • Energy loss due to inelastic collisions and energy loss due to electronic stopping are two distinct mechanisms, each of which, has its own velocity dependence
• Z1 dependence • Recent modifications of Brandt-Kitagawa’s model to work for semiconductors introduce only one fitting parameter, rs, the radius of the average volume occupied by each valence electron. This parameter can be adjusted to account for the oscillations in the Z1 dependence of the electronic stopping cross section
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Z1 Oscillations of Electronic Stopping
P
Al
Stereographic and schematic views of the channel in silicon.
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The Z1-depence of the electronic stopping cross-section (v = 1.5 x 108cm s-1) for the direction in crystalline silicon. Experimental points are from Eisen (1968).
Z1 Oscillations of Electronic Stopping - Example
Al
P
Random and channeled atom depth distributions for Al and P implanted into crystalline Si at 200 keV and 3 X 1013 cm-2.
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Velocity Dependence Separation of Local & Non-Local e-stopping in Silvaco’s BCA Implant program
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80 keV Boron –> c-Si, Native Oxide
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15 keV Boron –> c-Si, Native Oxide
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Low-Energy Model (see the “round-robin” comparisons)
MD codes
pure BC approximation simultaneous collisions
UT-MARLOWE 4.1
nobody is using BC in its original approximation
approximation
time integration of local electronic stopping
soft collisions: 3-body collisions
Advances in Ion Implantation Modeling for Doping of Semiconductors
CRYSTAL (ATHENA)
approximation
approximation
approximation
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Nature of the Physical Problem
Beam of accelerated ions entering the SiC
Ions slowed down and scattered due to nuclear collision and electronic interaction
Implanted ion profile calculation
Advances in Ion Implantation Modeling for Doping of Semiconductors
Fast recoil atoms induce collision cascades
Defects generation (vacancies & intersticials)
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Crystal amorphisation
Damage Accumulation Model
As implantation proceeds, deposited energy increases, and crystalline structure gradually and dynamically turns into amorphous. This is modeled through the Amorphization Probability function
E c is the critical energy density which represents the deposition energy per unit volume needed to amorphize the structure
⎛ -ΔE(r) ⎞ ⎟ f (r ) = 1 - exp⎜⎜ ⎝ Ec ⎠
⎛ ⎡ E0 (T - T∞ )⎤ ⎞ ⎜ ( ) = Ec t ⎜1 exp ⎢ ⎥ ⎟⎟ ⎣ 2kTT∞ ⎦ ⎠ ⎝
F L Vook, Radiation Damage and Defects in Semiconductors, J. E. Whitehouse Ed., IoP, London, pp.60-71, 1973 W. P Maszara and G. A. Rozgonyi, J. Appl. Phys. 60, 2310 (1986)
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-2
Low Energy Corrections to Silvaco’s Ion Implantation Program
Low Energy Model: (corrections to BCA)
Effect on stopping: T1
Reduces energy loss of channeled ions
Simultaneous and nearlyP simultaneous collisions T2 T2
P
Soft collisions and 3-body collisions
Time-integration of local electronic stopping
Reduces nuclear energy loss
R2
e- T2 v
P
S
Advances in Ion Implantation Modeling for Doping of Semiconductors
T1
R1
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Reduces local electronic energy loss for head-on collisions, i.e. off channeling conditions
Statistical Sampling
w =1 1/2 1/4
Al+
1/8
x
Al+ concentration
Even t T1 Even t T2
x
d0
d1
d2
R2 replica d3 s
SiC
1/16
x x x x
x
x x
x
d4 threshold states(depth)
Depth Advances in Ion Implantation Modeling for Doping of Semiconductors
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With the rare event trajectory splitting technique, the speed-up is due to changes in the statistical behavior such that rare vents are provoked to occur more often. The rare event algorithm achieves this by identifying subspaces from which it is more likely to observe given collision event, and then making replicas of the cascade sequences that reach these subspaces. The figure illustrates the trajectory splitting and restart of events(replicas) as a new threshold is reached. When applying splitting to collision cascades the two main parameters needed to be determined are: i) when to split and ii) how many sub-trajectories to create when splitting. There are different criteria which can be used to obtain the threshold states when splitting need to occur. Our algorithm uses the integrated dose as a criterion when to split, i.e. to determine the splitting depths. Dose integration is carried out along the radius vectors of ions’ co-ordinates, thus, roughly taking into consideration the threedimensionality of the ion distribution.
SIMS vs Implant Modeling (after Michael Duane)
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Low Energy Model: 1 keV As into (100) Si, tilt=0o, rotation=0o, dose=1012 ions/cm2
UT-MARLOWE LE
1.E+19
UT-MARLOWE BCA Molecular Dynamics ATHENA (Silvaco)
Concentration, cm-3
1.E+18
1.E+17
pure BCA
1.E+16
1.E+15 0
0.002
0.004
0.006
Depth, um
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0.008
0.01
Low Energy Model: 0.5 keV B into (100) Si, tilt=0o, rotation=0o, dose=1012 ions/cm2
1.E+19
SIMS REED ATHENA (Silvaco)
Concentration
1.E+18
UT-MARLOWE 4.1
1.E+17
1.E+16
1.E+15
1.E+14 0
0.01
0.02 Depth, um
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0.03
0.04
Low Energy Model: 2 keV As into (100) Si, tilt=0o, rotation=0o, dose=1012 ions/cm2
SIMS
1.E+19
REED ATHENA (Silvaco) UT-MARLOWE 4.1
Concentration
1.E+18
1.E+17
1.E+16
1.E+15
1.E+14 0
0.005
0.01
0.015
Depth, um
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0.02
0.025
Low Energy Model: 2 keV As into (100) Si, tilt=7o, rotation=45o, dose=1012 ions/cm2
1.E+19
SIMS REED ATHENA (Silvaco)
Concentration
1.E+18
UT-MARLOWE 4.1
1.E+17
1.E+16
1.E+15
1.E+14 0
0.005
0.01
0.015
Depth, um
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0.02
0.025
Low Energy Model: 2 keV B into (100) Si, tilt=0o, rotation=0o, dose=1012 ions/cm2
1.E+18
SIMS REED ATHENA (Silvaco)
Concentration
1.E+17
UT-MARLOWE 4.1
1.E+16
1.E+15
1.E+14
1.E+13 0
0.02
0.04
0.06
Depth, um
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0.08
0.1
Low Energy Model: 2 keV B into (100) Si, tilt=7o, rotation=45o, dose=1012 ions/cm2
1.E+18
SIMS REED ATHENA (Silvaco)
Concentration
1.E+17
UT-MARLOWE 4.1
1.E+16
1.E+15
1.E+14
1.E+13 0
0.02
0.04
0.06
Depth, um
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0.08
0.1
The Low Energy Limit of The BC Approximation
limit?
G. Hobler, G. Betz (Inst. f. Allg. Physik, TU Wien) www.fke.tuwien.ac.at/hobler/jb00/md00.htm
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2D Low Energy Boron Distributions – Comparisons Between Silvaco’s BCA and MD Simulations
G. Hobler, G. Betz (Inst. f. Allg. Physik, TU Wien) www.fke.tuwien.ac.at/hobler/jb00/md00.htm
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2D Low Energy Arsenic Distributions - MD and Silvaco’s BCA, MD Simulations - Beard more, et. al.
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Channeling Components of 3D Ion Implantation
• The Final Ion Distribution is a Linear Combination of all of them • Projection in the XZ Plane
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Channeling Components of 3D Ion Implantation
• The Final Ion Distribution is a Linear Combination of all of them • Projection in the XY Plane
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2D Ion Distribution Generated as a Linear Combination of Moments Extracted From the Separate Distributions
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Contribution of Different Channels to Total Ion Distribution – 500ev B into Silicon
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Doping Challenges for SiC Technology
• Ion implantation is the only practical selective-area doping method because of extremely low impurity diffusivities in SiC • Due to directional complexity of 4H-SiC, 6H-SiC it is difficult ad-hoc to minimize or accurately predict channeling effects • SiC wafers miscut and optimizing initial implant conditions and avoiding the long tails in the implanted profiles • Formation of deep box-like dopant profiles using multiple implant steps with different energies and doses • I. Chakarov and M. Temkin, “Modeling of Ion Implantation in SiC Crystals,” IBMM-2004, to be published in Nuclear Instruments Methods
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Effects of Crystallographic Orientation
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Al in 4H-SiC: Athena vs. Experiments
• Experimental (SIMS) and calculated (BCA simulation) profiles of 60 keV Al implantation into 4HSiC at different doses(shown next to the profiles) for a) on-axis direction, b) direction tilted 17° of the normal in the (1-100) plane, i.e. channel [11-23], and c) a “random” direction - 9° tilt in the (1-100) plane. Experimental data are taken from J. Wong-Leung, M. S. Janson, and B. G. Svensson, Journal of Applied Physics 93, 8914 (2003).
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Multiple Al Implantation into 6H-SiC
• Box profile obtained by multiple Al implantation into 6H-SiC at energies 180, 100 and 50 keV and doses , and cm-2 respectively. The accumulated dose is cm-2. Experimental profile is taken from T. Kimoto, A. Itoh, H. Matsunami, T. Nakata, and M. Watanabe, Journal of Electronic Materials 25, 879 (1996).
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Al in 6H-SiC: Athena vs. Experiments
• Aluminum implants in 6H-SiC at 30, 90, 195, 500 and 1000 keV with doses of 3x1013, 7.9x1013, 3.8x1014, 3x1013 and 3x1013 ions cm-2 respectively. SIMS data is taken from S. Ahmed, C. J. Barbero, T. W. Sigmon, and J. W. Erickson, Journal of Applied Physics 77, 6194 (1995).
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A Typical 4H-SiC MESFET Obtained by Multiple Al Implants
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Conclusions
• With appropriate corrections, the applicability of BCA for predictive Ion Implantation can be extended down to100-200 eV • The low energy model and advanced electronic energy loss significantly increase the predictive capabilities and the quality of BC models for their use in research and technology • Using an appropriate electronic stopping model for SiC, one can obtain highly predictive simulation results of ion implantation within the Binary Collision approximation formalism. Accounting for the anisotropy of the electronic density distribution in the 4H-SiC and 6H-SiC lattices is critical for the simulation of predictive implant distributions not only along open channel directions, but at “random” one as well
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