Transconductance Distribution in Program/Erase Cycling of NAND Flash Memory Devices: a Statistical Investigation

Abstract

A new method for characterizing the evolution of oxide charge (Q <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</sub> ) generation during program/erase (P/E) cycles is developed. The concentration of Q <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</sub> can be separated from the floating gate charge (QFG) by statistically analyzing the distribution of transconductance reduction (ΔGm,max) after P/E cycles. The effect of the number and position of discrete Q <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</sub> on the distribution of ΔGm,max is studied. The cycling dependence of the Q <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</sub> generation is given by a fractional equation that includes a power of the number of P/E cycles in the denominator. For fewer than 30k cycles, the equation can be simplified as a power-law equation in the number of cycles with a power factor of 0.58. For more than 30k cycles, the Q <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</sub> generation gradually goes to a plateau value Q <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> = 1.5 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">20</sup> cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> . It is indicated that the Q <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</sub> generation is limited by the concentration of inherent weak bonding points inside SiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> or the Si/SiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> interface. The temperature dependence of the Q <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</sub> generation is also provided. The activation energy (EA) of the Q <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</sub> generation is approximately 0.1 eV, which is compatible with the E <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A</sub> value of electron traps creation in SiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> .