Measuring Point Defects

The study of point defects in silicon has been plagued by our inability to measure defect concentrations directly. In metals, vacancy formation energies are relatively low, thermal concentrations are high, and diffusion mechanisms were rapidly established through experiments that directly linked diffusivities to vacancies detected by direct means, e.g. positron annihilation spectroscopy (PAS). In silicon, however, the high formation energies of point defects mean that concentrations of both vacancies and interstitials are extremely low. Typical thermal concentrations of point defects are in the 1010 cm"3 range, far below the detection limit of direct measurement schemes involving positrons or other vacancy-sensitive techniques. As a result, debates over the relative importance of interstitial- and vacancy-assisted diffusion continue to this day. The degree of uncertainty is startling, given the importance of the problem. Silicon has grown to be one of the largest single industries, and it depends very heavily on precise control of diffusion profiles. The 'Roadmap' for the IC industry shows crucial unsolved issues regarding our ability to produce well-controlled diffusion profiles at 30 nm length scales. The practical problem relates immediately to point defects: when dopant impurities are implanted, the resulting implant damage leads to supersaturation of point defects. Because dopant diffusion is mediated by point defects, annealing out the damage results in transient enhanced diffusion (TED): the dopants diffuse rapidly until the excess point defects have annealed out.

A wide range of techniques has been applied to the indirect measurement of point defects in silicon. Metal impurity diffusion studies have been extremely important in the history of the field, as metal diffusion couples very strongly to the point defects. However, the interpretation of these results depends very heavily on the model used to interpret the measured profiles. Consequently, it was possible to have almost symmetric models built on assumptions about either vacancy or interstitial concentration profiles.

A major breakthrough in the determination of point defect profiles in silicon came with the use of TEM to identify the sign of point defect fluxes. In early definitive experiments, it was shown by Hu that stacking faults that were known to be interstitial from diffraction contrast (g.b) analysis would grow when the neighbouring surface was oxidized. Once it had been conclusively demonstrated that oxidation led to the growth of stacking faults, it was indisputable that oxidation led to an interstitial supersaturation (or vacancy undersaturation). Given this simple fact, it could then be stated with confidence that those impurities which displayed oxidation-enhanced diffusion (OED) were interstitial-assisted diffusers. By extension, it has since been possible to quantify the vacancy- and interstitial-assisted components of the diffusion of many of the important impurities in silicon (in particular in the work by Gossmann et al.).

Methods
There is a long history of the measurement of extended defect dimensions in order to gain insight into the point defects responsible for their growth or dissolution (a
summary of the classic experiments can be found in Hull and Bacon). In metals, measurements of void growth have been the key to understanding damage processes. In
silicon, low equilibrium concentrations of both interstitials and vacancies make comparable measurements far more challenging. However, we have been able to exploit two key features of the silicon system to make comparable measurements. The first is that silicon interstitial clusters, rather than only forming two-dimensional dislocation loops, also form pseudo-one-dimensional rod-like defects, known as (311} defects from the habit plane of the rod. The second is that certain metal impurities in silicon, in particular Au, have a strong tendency to diffuse to vacancy clusters, giving us a 'labelling' technique for quantification of vacancy clusters

[311] defects arise naturally from dopant implantation, and we have been able to correlate the evaporation of [311] defects with the occurrence of TED. During the initial stages of annealing, interstitials rapidly cluster to form [311] defects, the rapid clustering being a consequence of the high formation energy of the point defect. Subsequently, the defects either evaporate, or undergo unfaulting to form true dislocations. Measurement of these [311] defects in TEM allows us to obtain a very sensitive measurement of interstitial defects that they emit during annealing, even at quite low concentrations. The sensitivity arises from the one-dimensional nature of the rod-like defect. The typical defect shown consists of a 3 X 50 nm platelet: given an accurate width measurement, it is relatively simple in TEM to determine the length of a given defect to within a few nm. At 3 nm width, this corresponds to determining the interstitial content of the defect to within =30 interstitials. At this level of accuracy, it is possible to carry out precise measurements of the interstitial supersaturation (or, equivalently, the expected diffusion enhancement) even at the low equilibrium defect levels typical for Si.

Eaglesham,(2000)Quantitative TEM of point defects in Si,www.oxfordjournals.org

Eaglesham D J. et al (1998) Depth profiling of vacancy clusters in Mev-implanted Si using AU labeling. Appl. Phys. Lett. 73

Hull D and Bacon D J (1997) Introduction to Dislocations. (Pergamon Press, London).

Bracht H, (1995) Properties of intrinsic point defects in silicon determined by zinc diffusion experiments under non equilibrium conditions; Phys Rev. B 52