## 3 Results  
The fundamental operation of the device is analyzed through transfer curves and output curves. In Figure 2a,b, the threshold voltage (Vth) is calculated from the transfer curves and the corresponding transconductance (g\({}_{\text{m}}\)) with V\({}_{\text{ds}}\) of 0.1 V applied [32,33]. The Vth in the ERS state was about 0.03 V, while in the PGM state, it was about 1.8 V. The subthreshold swing (SS) was calculated as 113 mV/decade for the ERS state and 110 mV/decade for the PGM state. The device incorporates a composite dielectric layer (HfO\({}_{2}\)/SiO\({}_{2}\)) and a mesh-type floating gate structure, which result in a measured SS higher than the theoretical limit of 60 mV/decade due to factors such as interface traps and electric field non-uniformity. This increase in SS is interpreted as being caused by structural characteristics of the flash memory device and defects introduced during the fabrication process. Figure 2c shows the output curve for the ERS state, revealing a cut-off region at V\({}_{\text{gs}}\) of 0 V and a saturation region between 1 and 5 V. Figure 2d illustrates the output curve for the PGM state, showing cut-off regions at V\({}_{\text{gs}}\) = 0 V and V\({}_{\text{gs}}\) = 1 V, with saturation confirmed from 2 to 5 V. The gate leakage current ranged from 10\({}^{-13}\) A/\(\upmu\)m to 10\({}^{-11}\) A/\(\upmu\)m for both the ERS state and the PGM state, demonstrating excellent insulation properties and suppression of leakage current, as shown in Figure 2e,f. To verify the stable operation of the Mesh-FGT under appropriate voltage conditions, the channel mobility and Fowler-Nordheim (F-N) tunneling characteristics were evaluated. First, based on the transfer curve shown in Figure 2a, the channel mobility of the Mesh-FGT was calculated. Since the device operates in the linear region at V\({}_{\text{ds}}\) = 0.1 V, the channel mobility satisfies the following Equation (1):  
\[\mu=\frac{1}{C_{ox}}\cdot\frac{L}{W}\cdot\frac{1}{V_{ds}}\cdot\left(\frac{dI_{ ds}}{dV_{gs}}\right) \tag{1}\]  
\(\mu\): channel mobility [units: m\({}^{2}\)/V\(\cdot\)s or cm\({}^{2}\)/V\(\cdot\)s];  
\(C_{ox}\): oxide capacitance per unit area [units: F/m\({}^{2}\)];  
\(L\): channel length [units: m];  
\(W\): channel width [units: m];  
\(V_{ds}\): drain voltage [units: V];  
\(\frac{dI_{ds}}{dV_{gs}}\): slope of I\({}_{\text{ds}}\)-V\({}_{\text{gs}}\) curve [units: S = A/V]. Here, \(L\) is 3 \(\upmu\)m (3 \(\times\) 10\({}^{-6}\) m), and \(W\) is 50 \(\upmu\)m (50 \(\times\) 10\({}^{-6}\) m). The value of \(\frac{dI_{ds}}{dV_{gs}}\) corresponds to the peak point of the mutual conductance (\(g_{m}\)), which is calculated as 9.8236 \(\times\) 10\({}^{-7}\) S/\(\upmu\)m \(\times\) 50 \(\upmu\)m = 4.9118 \(\times\) 10\({}^{-5}\) S. To determine the oxide capacitance (\(C_{ox}\)), which is a variable in the channel mobility equation, Figure 3a,b were utilized. Figure 3a shows the stack structure used to extract \(C_{ox}\), which shares the same configuration and conditions as the fabricated Mesh-FGT device. Based on this structure, the capacitance-voltage curve was measured using an Agilent 4284A LCR Meter (Keysight Technologies, Santa Rosa, CA, USA), as shown in Figure 3b, and \(C_{ox}\) was calculated to be 1.508 \(\times\) 10\({}^{-10}\) F. Given that the electrode area is 200 \(\upmu\)m \(\times\) 200 \(\upmu\)m, the areal capacitance \(C_{ox}\) is 3.77 \(\times\) 10\({}^{-3}\) F/m\({}^{2}\). Consequently, the channel mobility (\(\mu\)) is calculated to be 0.007817 m\({}^{2}\)/V\(\cdot\)s, which corresponds to 78.17 cm\({}^{2}\)/V\(\cdot\)s. This value is within the typical range reported for similar devices, suggesting that the Mesh-FGT operates with stable electrical performance. Figure 3c-e illustrate the Fowler-Nordheim (F-N) tunneling characteristics of the Mesh-FGT and provide insight into the operating voltages for the program (PGM) and  
Figure 3: Measurement results for evaluating oxide capacitance (\(C_{ox}\)) and Fowler-Nordheim (F–N) tunneling characteristics.