Investigation of Inhibited String Characteristics According to Dimple Structures in 3D NAND Flash Memory

In this letter, we investigated the boosted channel potential (V<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$_{\mathbf {\textit {ch}}}$ </tex-math></inline-formula>) in inhibited strings with dimple (concave and convex) structures and analyzed the program (PGM) disturbance caused by <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$V_{\mathbf {{ch}}}$ </tex-math></inline-formula>. In concave structures, the electric field (e-field) concentrated in the spacer (SP) region, resulting in a decrease in V<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$_{\mathbf {\textit {ch}}}$ </tex-math></inline-formula> as the degree of concavity increases. In convex structures, the e-field concentrates in the center of the word line (WL) region, boosting <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$V_{\mathbf {{ch}}}$ </tex-math></inline-formula> as the degree of convexity increases. This occurs due to the dispersion or concentration of the PGM voltage applied to the WL. High V<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$_{\mathbf {\textit {ch}}}$ </tex-math></inline-formula> in the selected WL increases the potential difference (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Delta $ </tex-math></inline-formula>V<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$_{\mathbf {\textit {ch}}}$ </tex-math></inline-formula>) between adjacent WLs. Due to structural characteristics, the lateral e-field (E<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$_{\mathbf {m}}$ </tex-math></inline-formula>) is largest in concave structures, whereas the vertical e-field (E<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$_{\mathbf {\textit {ox}}}$ </tex-math></inline-formula>) dominates in convex structures. Consequently, PGM disturb characteristics caused by hot carrier injection (HCI) are significantly degraded in convex structures.