# SiGe-Surrounded Bitline Structure for Enhancing 3D NAND Flash Erase Speed
## 2 SiGe-Surrounded BL PAD Structure and Erase Speed Enhancement
Figure 4 confirms that the SiGe-surrounded device sustains higher GIDL current than the Si-only case, with SiGe\({}_{0.5}\) achieving 2775% higher GIDL current than SiGe\({}_{0}\) at 0.1 ms.  
Figure 4: (**a**) The average channel potential; (**b**) GIDL current over time for various Ge composition ratios. Figure 5: Simulation result with various tSiGe at VERS = 14 V: (**a**) The average channel potential; (**b**) GIDL current over time. Figure 3: Band diagram of Si (SiGe\({}_{0}\)) and SiGe\({}_{0.5}\) immediately after the ramp-up phase at V\({}_{\text{ERS}}\) = 14 V.  
Figure 5 illustrates how t\({}_{\text{SGe}}\) affects the average channel potential at a fixed Ge ratio of 0.5. When calculating capacitance for a parallel-plate capacitor, the capacitance is inversely proportional to its dielectric thickness. For a cylindrical capacitor, the capacitance is inversely proportional to the natural logarithm of the ratio of its outer radius and inner radius. If we define this value as the effective thickness of a cylindrical capacitor, the effective thickness increases superlinearly with the layer thickness. This means the capacitance of a cylindrical capacitor decreases more rapidly as thickness increases, compared to the parallel-plate structure. Therefore, the voltage-division rule causes the voltage across the SiGe layer in the cylindrical structure to increase superlinearly with the layer thickness. Consequently, the electric field in the SiGe layer increases as the thickness increases, causing higher BTBT rate and accelerating the rise of the average channel potential. However, beyond a t\({}_{\text{SiGe}}\) of 16 nm, the BL PAD area reduction causes a steep rise in its series resistance. Although the BTBT-active region grows, the high resistance of cylindrical BL PAD region hinders the potential increase and hole generation, so the erase operation time increases significantly and limits its use in actual devices. Figure 6 shows a detailed comparison of the erase threshold voltage shift (\(\Delta\)V\({}_{\text{th}}\)) as a function of Ge composition ratio for different t\({}_{\text{SiGe}}\) values under (a) a 0.5 ms and (b) a 1 ms erase execution time. When the erase execution time is shorter, the Ge composition ratio has larger impact on the threshold voltage shift. This indicates that increasing Ge composition ratio is essential for reducing the erase execution time. Additionally, for a Ge composition ratio exceeding 0.3, a thinner t\({}_{\text{SiGe}}\) layer results in the highest \(\Delta\)V\({}_{\text{th}}\). This is due to the increased series resistance caused by the thicker undoped SiGe layer itself, inducing 0.2-0.3 V of voltage drop in the SiGe region and reducing the maximum voltage reaching the channel. The reduced voltage eventually limits the saturating channel potential level. However, since a higher erase voltage at the BL can easily offset this voltage drop effect, we can fully obtain the erase speed improvement benefit resulting from the increased SiGe thickness. We confirmed that applying a SiGe layer does not degrade the read performance. As shown in Figure 7, increasing the Ge ratio reduces the read on-current because the electron and hole mobility of SiGe drop by up to 80% and 25%, respectively. In Figure 7, the read on-current gradually decreases as the t\({}_{\text{SiGe}}\) increases, reflecting both the material's lower mobility and the increased series resistance of a thicker layer. However, on-current decrease relative to the mobility degradation is small because the SiGe layer occupies only  
Figure 6: Simulation results with various t\({}_{\text{SiGe}}\) at V\({}_{\text{ERS}}\) = 14 V: (**a**) Erase execution time of 0.5 ms; (**b**) 1 ms over SiGe\({}_{\text{X}}\). a small fraction of the total area, limiting its impact on overall current. Since the maximum on-current reduction remains within 4%, the erase process can still be accelerated by up to 861% with only a minimal effect on read performance.