2.2.4 Multilayered Structures



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2.2.4 Multilayered Structures

 

Ion implantation is frequently performed through masking layers consisting of oxide (), nitride () or photo resist. Thin dielectric layers (screening oxide) are used to avoid contamination of the substrate or for scattering of the implanted ions to reduce the channeling effect.

The basic assumptions of analytical approaches based on moments of a distribution function restrain their applicability to half spaces. Extentions to multilayered structures mostly give acceptable results but suffer from lacking underlying physics.

Each layer usually has a different stopping power for the ions and, therefore, the covering layer has a strong influence on the velocity distribution of the ions at the interface to the underneath layer. An approach to model the velocity (energy) distribution analytically has been proposed by Pantic [Pan89]. As mentioned before, the Monte Carlo and the Boltzmann Transport method are applicable to arbitrary target structures.

For simplicity we first assume a two-layer target (see Figure 2.2-2) composed of a mask (layer 1) and a substrate (layer 2). Analytical models presume that a profile in pure mask material and in pure substrate material is known. Dependent on the thickness of the mask and the properties of mask and substrate material, the profiles and are stretched, shifted and scaled to get the profile in the compound target.

 

A first analytical model for the calculation of the profile in multilayered structures has been published by Ishiwara et al. [Ish75]. Several modifications and improvements have been proposed later on, e.g. by Ryssel [Rys83a], [Rys87], [Wie89]. Comparisons of analytical models with Monte Carlo results are collected in [Rys87] and [Hob87b].

We use the numerical range scaling (NRS) method proposed by Ryssel [Rys83a]. The profile in a two-layer structure is given by (2.2-27). The scaling factor has to be chosen to satisfy the dose matching condition and consequently the normalization condition (2.2-28).

 

 

In theories describing the stopping of particles in matter, it is generally assumed that the range is inversely proportional to the material density. Therefore, the shift is calculated from (2.2-29). This model is sufficiently correct for very thin masking layers as well as thick masking layers. The condition of dose conservation is fulfilled inherently.

 

For some applications, however, the predicted profiles do not agree sufficiently well with measurements. Therefore, an approved numerical range scaling model has been developed [Wie89]. This model uses a modified standard deviation (2.2-30) for the substrate layer for the calculation of .

 

The generalization of the numerical range scaling to a target with layers is evident. Within layer (), where denotes the position of interface between layer and layer (see Figure 2.3-5), the distribution is given by (2.2-31) with the distribution function for infinitely thick material . For the first layer the shift vanishes and the profile has not to be scaled (2.2-32).

 

 

Then, the shift in layer is calculated from (2.2-33) using the thickness of layer and the projected ranges and .

 

The normalization condition yields the relation for the scaling factor (2.2-35).

 

 

From detailed discussions of multilayer models, e.g. in [Rys87], [Hob88a], it seems obvious that only Ryssels numerical range scaling model is capable of describing profiles in multilayer targets with larger differences in stopping power to a reasonable degree of accuracy.

 

In Figure 2.2-3, you find a comparison between a Monte Carlo simulation and an analytical description using the numerical range scaling algorithm for a boron implantation with and a dose of into amorphous silicon covered by nitride. The result of the NRS algorithm shows reasonable agreement with the Monte Carlo simulations.

For most common combinations in silicon technology, e.g. , and on silicon, and some semiconductor technologies the profiles obtained by the numerical range scaling model fit best with Monte Carlo results. However, it leads to totally incorrect profiles if the coating layer consists of atoms much heavier or much lighter than the target atoms, e.g. tungsten on top of silicon [Hob88a].



next up previous contents
Next: 2.3 Two-Dimensional Profiles Up: 2.2 One-Dimensional Distribution Functions Previous: 2.2.3 Getting the Range



Martin Stiftinger
Wed Oct 19 13:03:34 MET 1994