Determination of breakdown rates and defect densities in SiO 2

Abstract

Breakdowns in SiO 2 have been classified as defect related, due to wear-out and intrinsic. However, techniques to ascertain defect densities and breakdown rates at defects have not been available, nor has the distinction between wear-out and defect- related or intrinsic breakdowns been clearly demonstrated. A particular problem has been the inability to distinguish defect types, i.e. defects having different breakdown rates. Another source of confusion has been the tacit assumption that breakdown field histograms obtained from ramp breakdown tests are independent of the ramp rate, which cannot be valid for finite breakdown rates. We obtained relationships specifying the statistics of breakdown, including the effect of defects. These actually derive from results describing a Markov death process and depend on the time integrals of breakdown rates in defect-free regions and at defects and on parameters describing the defect distributions. For Poisson distributions of the defect, these parameters are the mean number of defects per device for each defect type. Any breakdown test is described by the same relations since the nature of the test enters only through the time integral of the breakdown rates. If a wear-out mechanism is operative, then the breakdown rates will depend on the time explicitly, i.e. not only via the time dependences of the applied field and temperature. procedures for obtaining defect densities and breakdown rates follow from the derived dependence on these quantities of the expectation value of the fraction of devices broken down. Ramp tests at various ramp rates are advantageous for this purpose. The field dependence of the breakdown rates can be extracted directly from the experimental data and no a priori form for this dependence need be assumed. Experimental results obtained from multiple ramp breakdown tests will be presented. The field dependence of the breakdown rates is found to vary significantly from a simple exponential dependence. Following Klein, the effect of fluctuations on the breakdown rates will be considered qualitatively to rationalize their observed field dependence. No explicit time dependence of the breakdown rates is indicated over the range of field covered by the data, implying the absence of wear-out.