# Design and Analysis of Heavily Doped n+
## 3 Investigation Results and Discussion
It can be seen that there is a significant variation in threshold voltage with a change in oxide thickness. Changing the oxide thickness also changes the thickness of the cavity region. The effect of variation in oxide thickness is considered for dielectric materials in air, silicon nitride, and silicon dioxide. From Equations (6) and (7) mentioned earlier, a change in oxide thickness is observed concerning the threshold voltage. Figure 5: (**a**) Drain current versus gate voltage with different dielectric constants (L\({}_{\rm cavity}\) = 3 nm); (**b**) Drain current versus gate voltage with different dielectric constants (L\({}_{\rm cavity}\) = 5 nm); (**c**) Drain current versus gate voltage with different dielectric constants (L\({}_{\rm cavity}\) = 7 nm). Therefore:  
\[V_{th}\propto\ \frac{1}{t_{oxide}} \tag{8}\]  
and  
\[V_{th}=\frac{E_{g}}{2Q}+\frac{\frac{\varepsilon_{Si}}{\varepsilon_{ox}}t_{ox}}{t_{ si}+\frac{\varepsilon_{Si}}{\varepsilon_{ox}}2t_{ox}}\Delta\Phi_{2}+\frac{t_{si}+ \frac{\varepsilon_{Si}}{\varepsilon_{ox}}t_{ox}}{t_{si}+\frac{\varepsilon_{Si}} {\varepsilon_{ox}}2t_{ox}}\Delta\Phi_{1} \tag{1}\]0  
Equation (8) shows that the thickness of the cavity region (t\({}_{\rm cavity}\)) is inversely proportional to the threshold voltage. Therefore, decreases in oxide thickness (\(t_{oxide}\)) will increase the threshold voltage. Figure 6a-c shows the variation in the drain current relative to gate voltage with different oxide material regions (air, silicon nitride, silicon dioxide, etc.) present in the cavity region. The observation indicates that when the gate oxide thickness increases, the threshold voltage decreases in proportion. Additionally, the device is highly sensitive to changes in the thickness of the oxide or the height of the cavity region for different dielectric constants. This shows that the suitability of the proposed device for the detection of variation in biomolecules is mainly due to the variation of the dielectric constant in the cavity region. Figure 7a,b shows the variation in the threshold voltage when different charge particles are introduced in the cavity region. It can be seen that the concentration of charged particles in the cavity region varies with the threshold voltage, and the changes also occur in OFF-state current. Hence, it can be used in detecting the variation in charged particles (both positive and negative). The changes in the number of particles in the cavity region at a certain level show (from \(5\times 10^{19}\) to \(10^{18}\)) a sharp effect in OFF-state leakage as well as in subthreshold slope. These changes can be measured in terms of electrical parameters like OFF-state current and threshold voltage. Hence, the device is capable of detecting biomolecules with different dielectric constants and different charge concentrations. \[V_{th}=\frac{E_{g}}{2Q}+\frac{\frac{\varepsilon_{Si}}{\varepsilon_{ox}}t_{ox}}{t_{ si}+\frac{\varepsilon_{Si}}{\varepsilon_{ox}}2t_{ox}}\Delta\Phi_{2}+\frac{t_{si}+ \frac{\varepsilon_{Si}}{\varepsilon_{ox}}t_{ox}}{t_{si}+\frac{\varepsilon_{Si}} {\varepsilon_{ox}}2t_{ox}}\Delta\Phi_{1} \tag{1}\]1 Drain current versus gate voltage curve, with (**a**) air (K = 1) as the dielectric material; (**b**) silicon nitride (K = 7.5) as the dielectric material; (**c**) silicon dioxide (K = 3.9) as the dielectric material.