Date of Award

Spring 2012

Degree Type


Degree Name

Doctor of Philosophy (PhD)


Electrical and Computer Engineering


Yaser M. Haddara


Andrew P. Knights




We propose a physically based model that describes the density and size of voids in silicon introduced via high dose helium ion implantation and subsequent annealing. The model takes into account interactions between vacancies, interstitials, small vacancy clusters, and voids. Void evolution in silicon occurs mainly by a migration and coalescence process. Various factors such as implantation energy and dose, anneal temperature, atmospheric pressure, and impurity level in silicon can influence the migration and coalescence mechanism and thus play a role in the void evolution process. Values for model parameters are consistent with known values for point defect parameters and assumed diffusion limited reaction rates. A single “fitting parameter” represents the rate of bubble migration and coalescence and is therefore related to surface diffusion of adatoms. Results obtained from simulations based upon the model were compared to our experimental results and to previously reported experimental results obtained over a wide range of conditions.

Our own experiments involved the implantation of silicon samples and samples with a thin Si1-xGex (x = 0.05, 0.09) epilayer on silicon with 30 keV, 5×1016 cm-2 helium. Anneals were done in the range 960-1110°C for 15-30 minutes in nitrogen and dry oxygen. Void size distributions were measured from transmission electron microscopy images. Average void diameter and void density values and void size distribution did not show any significant differences between the samples annealed in nitrogen and dry oxygen. However, the presence of Si1-xGex epilayer on silicon resulted in increased average void diameter and reduced average void density when compared with Si samples as well as more selective void size distribution.

Data from the literature included experiments with helium ion implantation energies in the range 30 - 300 keV, doses of 1×1016 - 1×1017 cm-2, subsequent annealing temperatures in the range 700 - 1200°C, and annealing duration in the range 15 minutes - 2 hours. Excellent agreement is found between the simulated results and those from reported experiments. The extracted migration and coalescence rate parameter shows an activation energy consistent with surface diffusivity of silicon. It shows a linear dependence on helium dose, and increases with decreased implantation energy, decreased ambient pressure, decreased substrate impurities, increased temperature ramp rate, or increased Ge fraction in cavity layer, all consistent with the proposed physical mechanism. Our mathematical model specifically ignores the long time saturation in void size, although we propose a simple explanation consistent with the physical picture. Similarly, we give physical reasons for a threshold implant dose resulting in the formation of small vacancy clusters during implant. But in modeling void growth we simply show that when such clusters exist voids will evolve according to our model.

In our experiments, the presence of a Si0.95Ge0.05 epilayer on silicon resulted in retarded B diffusion when compared with Si samples. This phenomenon is correlated to the role of the Si0.95Ge0.05 epilayer on silicon in the void evolution mechanism and both are attributed to Ge interdiffusing from the epilayer into the Si bulk. The B diffusion data also allows us to predict conditions for the SiGe epilayer to modify the injection of interstitials from surface during dry oxidizing anneal.

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