Dynamic Simulation of Ultra-Shallow Implantation Profiles in Single-Crystalline Silicon
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In the present work the BC code Crystal-TRIM is applied to 15 keV BF+ and As+ implantations into (100) Si at different doses, and for channeling and "random" directions of ion incidence. The following phenomenological model for the damage buildup is considered: (i) accumulation of local amorphous regions and (ii) formation of extended amorphous zones if the density of local amorphous regions or their sizes exceed a critical value. The validity of this model is discussed by comparison of range and damage profiles calculated by Crystal-TRIM with recently published experimental data. MODEL The general formalism and the basic physical inputs of the BC code Crystal-TRIM were explained in previous work [7,8,10]. In the following the model used to treat damage accumulation is elucidated in detail. In the case of atomic ions of initial energy Eo the implantation dose Do is simulated by N pseudoprojectiles, each of which contributes with a dose increment dD = Do/N. Molecular ions consisting of M atoms, e.g. BF+ with M = 3, are assumed to dissociate upon entry into the target. Their implantation is simulated by N sequences of implantations of M atomic pseudoprojectiles. Each pseudoprojectile corresponds to a dose increase Do/(N M) where Do is the implantation dose of the molecular ions. The initial energy of a certain atomic pseudoprojectile j is given by (mrj/ YiMj mi)Eo. E, denotes the implantation energy of the molecular ions. Ballistic processes in collision cascades initiated by the incident energetic particles produce a large number of displaced atoms. The energy transferred from a pseudoprojectile to a primary-knock-on 227 Mat. Res. Soc. Symp. Proc. Vol. 389 ©1995 Materials Research Society
atom (PKA) is further transferred to secondary recoils. The motion of the recoiled target atoms in subcascades is not simulated. Their contribution to nuclear and electronic energy deposition is estimated by a formula derived by Robinson [13]. It is assumed that the energy is deposited at the position where the PKA is generated. This approximation is justified if the extension of the recoil cascade is small compared to the ion range. It has the advantage that a lot of computing time can be saved.
For atomic ions the probability dpd that in a certain depth interval (x, x + Ax) of the target a pseudoprojectile displaces a target atom from its site is given by N-(dD) (I -- Pd)
dpd =
Nd is the number of atomic displacements that would be created in the depth interval (x, x + Ax) if the pseudoprojectile were implanted into a virgin crystal. The value of Nd is determined by the nuclear energy deposition in the given depth interval via the modified Kinchin-Pease formula [ 14]. For silicon a displacement energy of 15 eV is used. P.denotes the atomic density of the target. The
factor (1 - Pd) accounts for the reduction of the number of atoms which can be displaced from their sites. Integration of (1) yields the probability for atomic displacements in the depth interval (x, x + Ax) at a dose DI < Do Pd
exp(- l
1
-
n Ax
(2)
D')
I
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