Resistance and Threshold Switching Voltage Drift Behavior in Phase-Change Memory and Their Temperature Dependence at Microsecond Time Scales Studied Using a Micro-Thermal Stage

Abstract

We study the drift behavior of RESET resistance <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$R_{\rm RESET}$</tex> </formula> and threshold switching voltage <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$V_{\rm th}$</tex></formula> in phase-change memory (PCM) and their temperature dependence. To extend the temperature-dependent measurement to microsecond time scales, we integrate an innovative micro-thermal stage (MTS) on the PCM cell. The MTS changes the temperature of the programmed region of the PCM cell within a few microseconds by placing the Pt heater in close proximity of the programmed region. First, we experimentally verify the existing phenomenological <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$R_{\rm RESET}$</tex></formula> and <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$V_{\rm th}$</tex></formula> drift model for constant annealing temperature at various temperatures between 25 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$^{\circ}\hbox{C}$</tex></formula> and 185 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$^{ \circ}\hbox{C}$</tex></formula> down to 100 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\mu\hbox{s}$</tex></formula> and show that the measured temperature dependence of the drift coefficient agrees well with what is expected from the existing drift models. Based on the existing drift model for a constant annealing temperature, we derive the analytical expression for the <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$R_{\rm RESET}$</tex></formula> drift for time-varying annealing temperature and experimentally verify the analytical expression. The derived analytical expression is important to understand the impact of thermal disturbance on PCM reliability such as variations in <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$R_{\rm RESET}$</tex></formula> and <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$V_{\rm th}$</tex></formula> .