Error analysis of the residence time of bistable Poisson states obtained by periodic measurements

We performed error analysis on the periodic measurement schemes to obtain the residence time of bistable Poisson states. Experimental data were obtained by periodical level-sensitive samplings of oxygen-induced states on Si(111)-7 X 7 that stochastically switches between two metastable states. Simulated data sequences were created by the Monte Carlo numerical method. The residence times were extracted from the experimental and simulation data sequences by averaging and exponential-fitting methods. The averaging method yields the residence time via the summation of the detected temporal width of each state weighed by the normalized frequency of the state and the exponential fitting via fitting a single exponential function to the frequency histogram of the data. It is found that the averaging method produces consistently more accurate results with no arbitrariness, when compared to the exponential fitting method. For further understanding, data modeling using the first-order approximation was performed; the enhanced accuracy in the averaging method is due to the mutual cancellation of errors associated with detection of zero-width states and long-tail states. We investigated a multi-interval detection scheme as well. Similar analysis shows that the dual-interval scheme produces larger error compared to the single interval one, and has narrower optimum region. (C) 2010 American Institute of Physics. [doi:10.1063/1.3429946]