Analytical Markov Model to Calculate TDDB at Any Voltage and Temperature Stress Condition
Andrea Vici, R. Degraeve, J. Franco, B. Kaczer, Philippe Roussel, Ingrid De Wolf
Abstract
We propose an analytical approach for calculating the time-to-breakdown of metal-oxide-semiconductor (MOS) systems under different stress conditions. Our method relies solely on fresh <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${I}_{\text {g}} {V}_{\text {g}}$ </tex-math></inline-formula> measurements, making it easy to implement. Building on the percolation model and incorporating experimental trends from the literature, we accurately determine the voltage, gate oxide thickness, and temperature dependencies of time-to-breakdown. These calculated values are compared to experimental data under various operating conditions, allowing for a comprehensive assessment. Consequently, we introduce a time-to-breakdown map in the {Temperature-Voltage} space for immediate identification of the maximum stress condition for any target lifetime.