Prediction of the morphology of the asimplanted damage in Si
Matthias Posselt
Motivation
The asimplanted defect structure in Si is still not fully understood. However, its precise knowledge is decisive for the understanding of many effects occuring during ion implantation and at postimplantation annealing. For example, the defect accumulation during ion bombardment causes enhanced dechanneling of the subsequently implanted ions. This leads to the alteration of the shape of the depth profiles of the implanted particles with increasing ion dose. Other important processes are the rearrangement and the reduction of defects during annealing. They are strongly dependent on the type and the amount of defects which exist immediately after implantation. The stateoftheart theoretical description of the effects mentioned has to use phenomenological models as "substitute" for the lacking information about the asimplanted defect structure.Method
A novel combination of timeordered computer simulations based on the binary collision approximation (BCA) with classical molecular dynamics (MD) calculations is used in order to predict the type and the amount of defects created by ion implants which are typical of Si technology. The BCA simulations are applied to ballistic processes with characteristic energies above about 100 eV. The athermal, rapid thermal and thermally activated processes with characteristic energies below some 10 eV are treated by MD calculations. They yield the asimplanted defect structure formed several 10 ps after the ion impact. The combined simulation method becomes practicable since MD simulations need to be performed only in representative regions which are small compared to the entire volume of a collision cascade and since cascade statistics based on BCA simulations can be employed.Results
timeordered BCA simulations
The connection of BCA and MD simulations requires the description of ballistic processes in dependence on time. Since this is not accomplished in conventional BCA codes, the new timeordered BCA program CrystalTCAS had to be developed. It allows the timeordered simulation of the collision cascades of incident ions. The cascade is followed until the energy of the moving recoils becomes less than 100 eV. The time and the position of the creation of empty lattice sites, the time and the position of the generation of hit target atomsas well as their momentum, and the position and momentum of moving recoils at the time when their energy falls below 100 eV are stored. These data are used as inputs for subsequent MD calculations.MD calculations
The athermal and rapid thermal processes as well as the first stage of the thermally activated processes initiated by the collision cascade of a single ion in a registration cell are treated by MD calculations. The simulation starts at the time of ion impact. Depending on the position of the cell, empty lattice sites, hit target atoms and moving recoils are "inserted" after some 10...100fs. Some outermost atomic layers of the cell are coupled to a heat bath the temperatures of which is equal to R.T. (300 K).515 ps after ion impact the athermal and rapid thermal processes are finished . The metastable defect structure found after 18 ps is considered to be the asimplanted damage. Its further change due to thermally activated processes at R.T. is in the order of a few per cent. An example for an asimplanted defect structure formed in a registration cell is illustrated in the following picture.
The analysis of the results of MD calculations showed that the amount of nuclear energy deposition by a single ion in a registration cell determines (nearly) completely the asimplanted damage created by this ion in the cell. That means an important simplification of the combined simulation method since MD simulations need to be performed only in one cell, for different values of nuclear energy deposition by a single ion into this cell.
The consideration of about 40 different cases of nuclear energy depositions into a registration cell (8000 atoms, see above) led to the following representation for the total number of disordered atoms versus the nuclear energy deposition:
As shown above, one method to analyze the asimplanted defect structure is the identification of disordered atoms. The second method applied is the WignerSeitzcellVoronoypolyhedron analysis which allows the identification of vacancies (V) and intersitials (I).It is illustrated in the following picture:
The average number of disordered atoms per V and per I is about 10. 
Cascade statistics
In order to use the results of MD calculations for the determination of thetype and the amount of defects formed on average per incident ion, cascade statistics has to be considered. The large amount of data generated by the timeordered BCA simulations is analyzed with respect to the different values of nuclear energy deposition into a cell i (at given depth, see figure above) by the collision cascades of single ions. The number of events per incident ion g_{i}(E)dE, at which the nuclear energy deposition is between E and E+dE is determined. The normalization of g_{i}(E) with respect to the total number of deposition events N_{i} in cell i per incident ion leads to the probability q_{i}(E)dE for a given nuclear energy deposition at a certain event.The average number of the different defect species produced per incident ion in cell i can be calculated using
 the results of MD calculations: h_{i}^{D}  the number of defects (V,I, isolated I, disordered atoms in complex defects...) created in cell i if the nuclear energy deposition is E (cf. figures above)
 the results of cascade statistics: g_{i}(E)dE  the average number of events in cell i, at which the nuclear energy deposition is between E and E+dE (calculated from q(E), cf. figures above)
15 keV B^{+} 7^{0} tilt, 0^{0} rotation 
30 keV P^{+} 7^{0} tilt, 0^{0} rotation 
15 keV As^{+} 6^{0} tilt, 0^{0} rotation 

nuclear energy deposition (eV) 
3690  9650  7840 
atomic displacements  107  290  237 
disordered atoms (total) 
464  1067  911 
disordered atoms in complex defects 
36  220  303 
disordered atoms in amorphous pockets 
10  111  199 
V or I (total)  46  106  91 
isolated I  16  36  30 
It is clear that the ratio of the total number of atomic displacements and the total nuclear energy deposition per incident ion is about the same in the three examples due to the validity of the (modified) KinchinPease relation. But also the ratio of the total number of disordered atoms and the nuclear energy deposition as well as the ratio of the total number of V and I and nuclear energy deposition are nearly equal. That means that some quantities characterizing the asimplanted damage structure are almost completely determined by the nuclear energy deposition per ion. However, this does not hold for all characteristics of the damage morphology:The ratio of the number of disordered atoms in complex defects and the nuclear energy deposition is very different in the three cases due to the difference in the probability function q(E). The difference still increases if the ratio between the number of disordered atoms in amorphous pockets and the nuclear energy deposition is considered. In the case of 15 keV B^{+} implantation most of the complex defects are diV and diI, i.e. clusters with up to 20 disordered atoms containing exactly two V or two I. On the other hand, most of the complex defects formed by 15 keV As^{+} implants are amorphous pockets.
The predictions on the asimplanted damage morphology have been used to give a microscopic interpretation of the phenomenological model which is employed to describe the defect accumulation during ion bombardment in atomistic computer simulations of ion implantation.
Collaboration
ISE Integrated Systems Engineering AG Zürich,Institute of Integrated Systems, Federal Institute of Technology, Zürich,