Advances in Ion Implantation Modeling for Doping of Semiconductors - PowerPoint PPT Presentation

Advances in Ion Implantation Modeling for Doping of Semiconductors

Outline � � Basic Concepts � � Predictive Modelling of Implantation � � Low Energy Model � � Morphology of Implant Distribution � � Conclusions - 2 - Advances in Ion Implantation Modeling for Doping of Semiconductors

Some Interesting Dates in History of Ion Implantation Modeling Bredov et al ., Sov. Phys. Tech. Phys. , 3 , 228(1958) - the first BCA simulation of “ion 1958 implantation” of 4 keV K + ions in Ge. Gibson et al. , Phys. Rev. , 120 , 1229 (1960), J. Appl. Phys. , 30 , 1322 (1959) - the MD 1959 method first used in radiation defects studies. Robinson and Oen , Appl. Phys. Lett. , 2 , 30 (1963), Phys. Rev. , 132 , 2385 (1963) - 1962 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. Cai et al. , Morris et al. , Phys. Rev. , B54 , 17147 (1996), IEDM Technical Digest , (1996) - 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. - 3 - Advances in Ion Implantation Modeling for Doping of Semiconductors

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 - 4 - Advances in Ion Implantation Modeling for Doping of Semiconductors

Ion Implantation: 1970 sample, 120 keV P into Si, 7o to <111> direction G. Dearnaley et al., 1970, “Atomic collision phenomena in solids”, eds. D. Palmer, M. Thompson and P. Townsend - 5 - Advances in Ion Implantation Modeling for Doping of Semiconductors

Ion Implantation: 1975 sample, 100 keV B into SiO2 R. Schimko et al. 1975, Phys. Stat. Sol. (a), vol 28 - 6 - Advances in Ion Implantation Modeling for Doping of Semiconductors

Ion Implantation: 1987 sample, 50 keV P into (100) Si H. Kang et al., 1987, “Journal of Applied Physics”, p.2733, vol 62 - 7 - Advances in Ion Implantation Modeling for Doping of Semiconductors

Classification of Simulation Models Molecular Dynamics Binary Collision Approximation Classical MD: many, more BC(Binary Collision) programs: the location recent of target atoms are determined by well- studies by T.Diaz de la Rubia et defined crystal structure. Stochastic methods al. play only an auxiliary role, supplying, for on defects in silicon example, initial ion positions and directions, thermal vibrations, chemical disorder, etc. Recoil approximation MD: Typical programs are: many, MARLOWE, UT-MARLOWE, CRYSTAL in for example the REED program Silvaco’s process simulator, etc. by MC(Monte-Carlo) codes: stochastic Beardmore & Jensen for ion methods are used to locate the target atoms implantation, Hobler & Betz’s , or to determine the impact parameters, flight etc. distances, scattering angles, etc. The best known code is the TRIM(SRIM). - 8 - Advances in Ion Implantation Modeling for Doping of Semiconductors

Different Orientation of Silicon Crystal Structure - 9 - Advances in Ion Implantation Modeling for Doping of Semiconductors

Time Scale 10 -15 s Balistic processes: > 10 .. 100 eV Binary Collision (BC) simulations Binary Collisions creation of atomic displacements Athermal, Rapid thermal processes: < 1 .. 10 eV 10 -11 s collective interactions Classical Molecular Dynamics rapid local melting/quenching, creation of disordered regions (MD) simulations and amorphization Thermally activated processes : > 1s strong dependence temperature Kinetic Monte-Carlo recrystallization, decrease (KMC) simulations and rearrangement of damage, point defect migration - 10 - Advances in Ion Implantation Modeling for Doping of Semiconductors

Hierarchy of Ion Implantation/Radiation Damage Models Quantum mechanics ( ab-initio ) can validate/calibrate higher CPU intensive, small systems transfer of physical parameters level methods most exact, static calculations Classical molecular dynamics (MD) damage at the cooling-down low-energy impacts, limits at amorphyzation stage of cascade evolution and defect evolution for times > 1ns. Binary collision approximation (BCA) ion range profiles, successful leading atomistic approach, better coupling to MD for ballistic processes and experiment will improve modeling of damage. Kinetic Monte Carlo (KMC) self-annealing, point defect thermally activated processes, strong migration, clustering of defects dependence on temperature - 11 - Advances in Ion Implantation Modeling for Doping of Semiconductors

Basic Concepts of Ion Implantation (II) ion lattice e - e - e - For predictive modeling of II we need nuclear collisions to have physically realistic treatment of: • � Nuclear stopping & interatomic potentials • � local & non-local electronic stopping • � damage buildup & amorphization - 12 - Advances in Ion Implantation Modeling for Doping of Semiconductors

Scattering Dynamic in a Collision Event - 13 - Advances in Ion Implantation Modeling for Doping of Semiconductors

Nuclear & Electronic Stopping of Boron in Amorphous Silicon Nuclear 10 120 Electronic 9 100 8 B 7 80 Electronic, eV/A Nuclear, eV/A C 6 5 60 4 40 3 A 2 v B 20 1 0 0 1 10 100 1000 10000 100000 Boron energy, keV - 14 - 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 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. - 15 - 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 - 16 - Advances in Ion Implantation Modeling for Doping of Semiconductors

Z 1 Oscillations of Electronic Stopping P Al The Z1-depence of the electronic stopping cross- Stereographic and schematic views of the section ( v = 1.5 x 10 8 cm s -1 ) <110> channel in silicon. for the <110> direction in crystalline silicon. Experimental points are from Eisen (1968). - 17 - Advances in Ion Implantation Modeling for Doping of Semiconductors

Z1 Oscillations of Electronic Stopping - Example Al P Random and <110> channeled atom depth distributions for Al and P implanted into crystalline Si at 200 keV and 3 X 10 13 cm -2 . - 18 - Advances in Ion Implantation Modeling for Doping of Semiconductors

Velocity Dependence Separation of Local & Non- Local e-stopping in Silvaco’s BCA Implant program - 19 - Advances in Ion Implantation Modeling for Doping of Semiconductors

80 keV Boron –> c-Si, Native Oxide - 20 - Advances in Ion Implantation Modeling for Doping of Semiconductors

15 keV Boron –> c-Si, Native Oxide - 21 - Advances in Ion Implantation Modeling for Doping of Semiconductors

Low-Energy Model (see the “round-robin” comparisons) MD codes UT-MARLOWE 4.1 CRYSTAL (ATHENA) pure BC nobody is using BC in its original approximation approximation simultaneous collisions approximation approximation time integration of local electronic approximation stopping soft collisions: approximation 3-body collisions - 22 - Advances in Ion Implantation Modeling for Doping of Semiconductors