Prediction of the morphology of the as-implanted damage in Si

Matthias Posselt

Motivation

The as-implanted 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 post-implantation 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 state-of-the-art theoretical description of the effects mentioned has to use phenomenological models as "substitute" for the lacking information about the as-implanted defect structure.

Method

A novel combination of time-ordered 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 as-implanted 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

time-ordered 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 time-ordered BCA program Crystal-TCAS had to be developed. It allows the time-ordered 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.

In order to predict the average as-implanted damage formed per incident ion statistically reliably, a sufficiently high number of ion impacts has to be considered. The incident points are randomly distributed within the irradiated area which is chosen large enough so that in the middle stripe (cf. figure below) all physical quantities related to ion irradiation depend only on the depth coordinate. In this stripe cubic registration cells are defined in which the relevant data on the state of collision cascades obtained after the termination of time-ordered BCA simulations of single ion impacts are recorded. In a perfect crystal such a cell contains 8000 atoms.

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).

5-15 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 as-implanted 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 as-implanted defect structure formed in a registration cell is illustrated in the following picture.

The black line shows the trajectory of the ion through the cell. Only target atoms are depicted the potential energy of which is at least 0.2 eV above the ground state value. They are calleddisordered atoms. Atoms with such a high potential energy are not observed in the perfect crystal. The potential energy of the (disordered) atoms is shown by the different colors. The dark blue and the red atoms have an excess potential energy of 0.2 eV and 0.35 eV, respectively. The great cluster containing 145 atoms is an amorphous pocket. Small clusters with less than 10 atoms are formed by disordered atoms around isolated vacancies (V) and interstitials (I).

If one magnifies the region around the lower left cluster (in the figure above) consisting of 5 disordered atoms, one obtains the following representation for a single V. The red atoms are the disordered atoms shown in the picture above, the green atoms are the other lattice atoms in that region.

If one magnifies the region around the cluster in the middle containing 8 disordered atoms (in the figure above), one observes this representation for the stretched <110> dumbell I which is the stable interstitial configuration in Stillinger-Weber Si. (The Stillinger-Weber potential was used in the MD calculations.)

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 as-implanted 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 as-implanted defect structure is the identification of disordered atoms. The second method applied is the Wigner-Seitz-cell-Voronoy-polyhedron analysis which allows the identification of vacancies (V) and intersitials (I).It is illustrated in the following picture:

identification of disordered atoms

Note: This procedure of defect identification cannot explicitely determine V- and I-like defects.

identification of V and I

Note: The Wigner-Seitz-cell-Voronoy-polyhedron analysis cannot distinguish between isolated V and I, and V and I in complex defects.

The average number of disordered atoms per V and per I is about 10.

A third method of defect analysis was applied: The disordered atoms were subjected to a cluster analysis which was performed in connection with the Wigner-Seitz-cell-Voronoy-polyhedron analysis. As the cut-off distance of the cluster analysis the cut-off radius of the Stillinger-Weber potential was employed. Different defect types can be identified: isolated V and I, di-V and di-I, ..., and more complex defects:

Note that the more complex defects are formed above a certain threshold for the nuclear energy deposition into the cell.
The dotted lines show analytical approximations for the dependence of the number of defect species on the nuclear energy deposition into the cell.

The scattering of the data in the figures is due to fluctuations of the individual properties of the collision cascades of different ions.

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 time-ordered 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.

It is found that q_i(E) is nearly independent of the depth of the cell i, i.e. q_i(E) ~= q(E). This allows a great simplification in the calculation of g_i(E):g_i(E) ~= N_i q(E) where N_i can be easily obtained from the depth profile of the nuclear energy deposition per incident ion.
The dotted lines show the analytical fit for q(E).

The probability q(E) is an important characteristic of each ion species at given implantation conditions: Since heavy ions like As⁺ form much denser cascades than light ions like B⁺ a high nuclear energy deposition by a certain As⁺ ion in a given cell is much more probable than by a certain B⁺ ion. This difference is the cause for the fact that for each ion species a characteristic damage morphology is obtained as discussed below.

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)

Depth dependence of the average number of different defect species produced per incident ion (and per Å). The depth profile of the average number of atomic displacements per incident ion as well as the depth dependence of the deposition probability of a B⁺ ion are shown for comparison.

Total number of different defect species produced on average per incident ion for three examples. The total number of displacements and the total nuclear energy deposition per ion impact are also given:

	15 keV B⁺ 7⁰ tilt, 0⁰ rotation	30 keV P⁺ 7⁰ tilt, 0⁰ rotation	15 keV As⁺ 6⁰ tilt, 0⁰ 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) Kinchin-Pease 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 as-implanted 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 di-V and di-I, 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 as-implanted 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,