Analysis of the Correlation Between the Programmed Threshold-Voltage Distribution Spread of nand Flash Memory Devices and Floating-Gate Impurity Concentration

The effect of the activated floating-gate (FG) impurity concentration on the programmed threshold-voltage ( V_t) distribution was newly investigated and analyzed. The lower FG impurity concentration leads to a wider threshold-voltage distribution, which is explained by the time-dependent tunnel-oxide electric-field enhancement effect induced by the reduction of the depletion region in the FG as the programming time is lengthened. Initially, the FG is deeply depleted at the interface of the tunnel oxide. However, as the programming time is prolonged, electrons by Fowler-Nordheim (FN) tunneling in the FG generate electron-hole pairs, and generated holes are gathered at the interface of the tunnel oxide, which reduces the depletion region, and enhance the oxide electric filed. The enhancement effect of the electric field for the tunnel oxide is coupled to the FN tunneling statistics and enlarges the distribution of the programmed Vt. This effect is more clearly observed at the lower FG impurity concentration, which gives the limitation of the minimum impurity concentration in FG. Monte Carlo simulations considering both the tunnel-oxide electric-field enhancement effect and FN tunneling statistics were carried out and showed good agreement with the experiments.