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Advances in Ion Implantation Modeling for Doping of Semiconductors

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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Advances in Ion Implantation Modeling for Doping of Semiconductors

Some Interesting Dates in History of Ion Implantation Modeling

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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.

Advances in Ion Implantation Modeling for Doping of Semiconductors

Ion Channeling

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"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

Advances in Ion Implantation Modeling for Doping of Semiconductors

Ion Implantation: 1970 sample, 120 keV P into Si, 7o to <111> direction

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• G. Dearnaley et al., 1970, “Atomic

collision phenomena in solids”,

• eds. D. Palmer, M. Thompson

and P. Townsend

Advances in Ion Implantation Modeling for Doping of Semiconductors

Ion Implantation: 1975 sample, 100 keV B into SiO2

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• R. Schimko et al. 1975, Phys. Stat. Sol. (a), vol

28

Advances in Ion Implantation Modeling for Doping of Semiconductors

Ion Implantation: 1987 sample, 50 keV P into (100) Si

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• H. Kang et al., 1987,

“Journal of Applied Physics”, p.2733, vol 62

Advances in Ion Implantation Modeling for Doping of Semiconductors

Classification of Simulation Models

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Molecular Dynamics

Classical MD: many, more recent studies by T.Diaz de la Rubia et al.

• n defects in silicon

Recoil approximation MD: many, for example the REED program by Beardmore & Jensen for ion implantation, Hobler & Betz’s, etc.

Binary Collision Approximation

BC(Binary Collision) programs: the location

• f target atoms are determined by well-

defined 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. MC(Monte-Carlo) codes: stochastic methods are used to locate the target atoms

• r to determine the impact parameters, flight

distances, scattering angles, etc. The best known code is the TRIM(SRIM).

Advances in Ion Implantation Modeling for Doping of Semiconductors

Different Orientation of Silicon Crystal Structure

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Advances in Ion Implantation Modeling for Doping of Semiconductors

Time Scale

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Athermal, Rapid thermal processes: < 1 .. 10 eV

collective interactions rapid local melting/quenching, creation of disordered regions and amorphization

10-15 s Balistic processes: > 10 .. 100 eV

Binary Collisions creation of atomic displacements

10-11 s > 1s Thermally activated processes:

strong dependence temperature recrystallization, decrease and rearrangement of damage, point defect migration

Binary Collision (BC) simulations Classical Molecular Dynamics (MD) simulations Kinetic Monte-Carlo (KMC) simulations

Advances in Ion Implantation Modeling for Doping of Semiconductors

Hierarchy of Ion Implantation/Radiation Damage Models

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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.

Binary collision approximation (BCA)

leading atomistic approach, better coupling to MD and experiment will improve modeling of damage.

can validate/calibrate higher level methods damage at the cooling-down stage of cascade evolution ion range profiles, successful for ballistic processes Kinetic Monte Carlo (KMC)

thermally activated processes, strong dependence on temperature

self-annealing, point defect migration, clustering of defects transfer of physical parameters

Advances in Ion Implantation Modeling for Doping of Semiconductors

Basic Concepts of Ion Implantation (II)

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ion lattice nuclear collisions e- e- e-

• Nuclear stopping & interatomic potentials
• local & non-local electronic stopping
• damage buildup & amorphization

For predictive modeling of II we need to have physically realistic treatment of:

Advances in Ion Implantation Modeling for Doping of Semiconductors

Scattering Dynamic in a Collision Event

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Advances in Ion Implantation Modeling for Doping of Semiconductors

Nuclear & Electronic Stopping of Boron in Amorphous Silicon

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1 2 3 4 5 6 7 8 9 10 1 10 100 1000 10000 100000 Boron energy, keV Nuclear, eV/A 20 40 60 80 100 120 Electronic, eV/A Nuclear Electronic

vB

A B C

Advances in Ion Implantation Modeling for Doping of Semiconductors

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

• n 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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Advances in Ion Implantation Modeling for Doping of Semiconductors

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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Advances in Ion Implantation Modeling for Doping of Semiconductors

Z1 Oscillations of Electronic Stopping

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Stereographic and schematic views of the <110> channel in silicon. The Z1-depence of the electronic stopping cross- section (v = 1.5 x 108cm s-1) for the <110> direction in crystalline silicon. Experimental points are from Eisen (1968).

Al P

Advances in Ion Implantation Modeling for Doping of Semiconductors

Z1 Oscillations of Electronic Stopping - Example

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P Al

Random and <110> channeled atom depth distributions for Al and P implanted into crystalline Si at 200 keV and 3 X 1013 cm-2.

Advances in Ion Implantation Modeling for Doping of Semiconductors

Velocity Dependence Separation of Local & Non- Local e-stopping in Silvaco’s BCA Implant program

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Advances in Ion Implantation Modeling for Doping of Semiconductors

80 keV Boron –> c-Si, Native Oxide

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Advances in Ion Implantation Modeling for Doping of Semiconductors

15 keV Boron –> c-Si, Native Oxide

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Advances in Ion Implantation Modeling for Doping of Semiconductors

Low-Energy Model (see the “round-robin” comparisons)

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MD codes UT-MARLOWE 4.1 CRYSTAL (ATHENA) pure BC approximation simultaneous collisions time integration

• f local electronic

stopping soft collisions: 3-body collisions nobody is using BC in its original approximation approximation approximation approximation approximation

Advances in Ion Implantation Modeling for Doping of Semiconductors

Nature of the Physical Problem

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Beam of accelerated ions entering the SiC Ions slowed down and scattered due to nuclear collision and electronic interaction Fast recoil atoms induce collision cascades Defects generation (vacancies & intersticials) Crystal amorphisation Implanted ion profile calculation

Advances in Ion Implantation Modeling for Doping of Semiconductors

Damage Accumulation Model

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As implantation proceeds, deposited energy increases, and crystalline structure gradually and dynamically turns into amorphous. This is modeled through the Amorphization Probability function Ec is the critical energy density which represents the deposition energy per unit volume needed to amorphize the structure

( ) ( )

• =

c

E r E r f exp 1

( ) ( )

2

2 exp 1

• =

kTT T T E t E

c

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)

Advances in Ion Implantation Modeling for Doping of Semiconductors

Low Energy Corrections to Silvaco’s Ion Implantation Program

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Low Energy Model: (corrections to BCA)

Simultaneous and nearly simultaneous collisions

P T1 T2

Soft collisions and 3-body collisions

P T2 T1 R2 R1

Time-integration of local electronic stopping

P T2

v e- S

Effect on stopping:

Reduces energy loss of channeled ions Reduces nuclear energy loss Reduces local electronic energy loss for head-on collisions, i.e. off channeling conditions

Advances in Ion Implantation Modeling for Doping of Semiconductors

Statistical Sampling

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w = 1 1/2 1/4 1/8 1/16

Al+

SiC

x x x x x x x x x x Depth Al+ concentration

d0 d1 d2 d3 d4 threshold states(depth) Even t T1 Even t T2 R2 replica s

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

• bserve 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 three- dimensionality of the ion distribution.

Advances in Ion Implantation Modeling for Doping of Semiconductors

SIMS vs Implant Modeling (after Michael Duane)

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Advances in Ion Implantation Modeling for Doping of Semiconductors

Low Energy Model: 1 keV As into (100) Si, tilt=0o, rotation=0o, dose=1012 ions/cm2

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1.E+15 1.E+16 1.E+17 1.E+18 1.E+19 0.002 0.004 0.006 0.008 0.01

Depth, um Concentration, cm-3

UT-MARLOWE LE UT-MARLOWE BCA Molecular Dynamics ATHENA (Silvaco)

pure BCA

Advances in Ion Implantation Modeling for Doping of Semiconductors

Low Energy Model: 0.5 keV B into (100) Si, tilt=0o, rotation=0o, dose=1012 ions/cm2

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1.E+14 1.E+15 1.E+16 1.E+17 1.E+18 1.E+19 0.01 0.02 0.03 0.04 Depth, um Concentration SIMS REED ATHENA (Silvaco) UT-MARLOWE 4.1

Advances in Ion Implantation Modeling for Doping of Semiconductors

Low Energy Model: 2 keV As into (100) Si, tilt=0o, rotation=0o, dose=1012 ions/cm2

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1.E+14 1.E+15 1.E+16 1.E+17 1.E+18 1.E+19 0.005 0.01 0.015 0.02 0.025 Depth, um Concentration SIMS REED ATHENA (Silvaco) UT-MARLOWE 4.1

Advances in Ion Implantation Modeling for Doping of Semiconductors

Low Energy Model: 2 keV As into (100) Si, tilt=7o, rotation=45o, dose=1012 ions/cm2

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1.E+14 1.E+15 1.E+16 1.E+17 1.E+18 1.E+19 0.005 0.01 0.015 0.02 0.025 Depth, um Concentration SIMS REED ATHENA (Silvaco) UT-MARLOWE 4.1

Advances in Ion Implantation Modeling for Doping of Semiconductors

Low Energy Model: 2 keV B into (100) Si, tilt=0o, rotation=0o, dose=1012 ions/cm2

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1.E+13 1.E+14 1.E+15 1.E+16 1.E+17 1.E+18 0.02 0.04 0.06 0.08 0.1 Depth, um Concentration SIMS REED ATHENA (Silvaco) UT-MARLOWE 4.1

Advances in Ion Implantation Modeling for Doping of Semiconductors

Low Energy Model: 2 keV B into (100) Si, tilt=7o, rotation=45o, dose=1012 ions/cm2

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1.E+13 1.E+14 1.E+15 1.E+16 1.E+17 1.E+18 0.02 0.04 0.06 0.08 0.1 Depth, um Concentration SIMS REED ATHENA (Silvaco) UT-MARLOWE 4.1

Advances in Ion Implantation Modeling for Doping of Semiconductors

The Low Energy Limit of The BC Approximation

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• G. Hobler, G. Betz (Inst. f. Allg. Physik, TU Wien)

www.fke.tuwien.ac.at/hobler/jb00/md00.htm limit?

Advances in Ion Implantation Modeling for Doping of Semiconductors

2D Low Energy Boron Distributions - Comparisons Between Silvaco’s BCA and MD Simulations

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• G. Hobler, G. Betz (Inst. f. Allg. Physik, TU Wien)

www.fke.tuwien.ac.at/hobler/jb00/md00.htm

Advances in Ion Implantation Modeling for Doping of Semiconductors

2D Low Energy Arsenic Distributions - MD and Silvaco’s BCA, MD Simulations - Beard more, et. al.

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Advances in Ion Implantation Modeling for Doping of Semiconductors

Channeling Components of 3D Ion Implantation

The Final Ion Distribution is

a Linear Combination

• f all of them

Projection in the XZ Plane

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Advances in Ion Implantation Modeling for Doping of Semiconductors

Channeling Components of 3D Ion Implantation

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The Final Ion Distribution is a Linear Combination of all of them Projection in the XY Plane

Advances in Ion Implantation Modeling for Doping of Semiconductors

2D Ion Distribution Generated as a Linear Combination

• f Moments Extracted From the Separate Distributions
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<110> <011> <001>

Advances in Ion Implantation Modeling for Doping of Semiconductors

Contribution of Different Channels to Total Ion Distribution – 500ev B into Silicon

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<001> “random” <125> <011>

Advances in Ion Implantation Modeling for Doping of Semiconductors

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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Advances in Ion Implantation Modeling for Doping of Semiconductors

Effects of Crystallographic Orientation

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Advances in Ion Implantation Modeling for Doping of Semiconductors

Al in 4H-SiC: ATHENA vs. Experiments

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Experimental (SIMS) and calculated (BCA simulation) profiles of 60 keV Al implantation into 4H-SiC at different doses(shown next to the profiles) for a) on-axis direction, b) direction tilted 17°

• f 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).

Advances in Ion Implantation Modeling for Doping of Semiconductors

Multiple Al Implantation into 6H-SiC

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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).

Advances in Ion Implantation Modeling for Doping of Semiconductors

Al in 6H-SiC: ATHENA vs. Experiments

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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).

Advances in Ion Implantation Modeling for Doping of Semiconductors

A Typical 4H-SiC MESFET Obtained by Multiple Al Implants

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Advances in Ion Implantation Modeling for Doping of Semiconductors

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

• btain 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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