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A discharge probability model is proposed to analyze the stochastic distribution of the discharge delay time. The distribution is described as a hybrid function between the exponential and Gaussian distributions and their characteristic properties, such as the emission time constant of an exoelectron and the average and standard deviations of the formative delay time. The calculated results of the probability of a successful discharge show a good agreement with the experimental results measured in plasma display panels. The analytical protocol allows the discharge delay time to be accurately separated into the statistical and formative delay times. A thermal excitation and emission model is devised to analyze the effective number and the activation energy of electron emission sources (EESs) in a MgO layer using the emission time constant of an exoelectron. The effective number of the EES, i.e., 3.79 × 105 per cell, decreases after a long time interval because of the thermal excitation; thus, the emission time constant increases significantly. The effective number of the EES after 1000 h of sustain discharge decreases to 2.07 × 104 per cell, which is 0.055 times that before the sustain discharge. This degradation is explained by 2.6-4.3 times of increase in the density of electron traps due to the ion sputtering of noble gases against the MgO surface. The emission time constant is found to decrease to 0.45 times when the wall voltage near the MgO surface is increased by 11 V, which demonstrates that the exoelectron emission can be controlled by the electric field.