# Investigation of High-Sensitivity pH Sensor Based on Au-Gated AlGaN/GaN Heterostructure
## 3 Results and Discussion  
### Transfer Characteristics and Potential Sensitivity  
Figure 5a-d shows the transfer (I\({}_{\text{DS}}\)-V\({}_{\text{Ref}}\)) and transconductance (G\({}_{\text{m}}\)-V\({}_{\text{Ref}}\)) characteristics versus the reference-source voltage of the Au-gated AlGaN/GaN heterostructure-based pH sensor in three pH standard buffered solutions at the different drain-source voltages (V\({}_{\text{DS}}\)) of 0.1 V, 0.5 V, 1.0 V, and 2.0 V, respectively. The gate width (W) and length (L) of the sensor were 160 \(\upmu\)m and 40 \(\upmu\)m, respectively. The reference-source voltage (V\({}_{\text{Ref}}\)) was swept from \(-\)4.5 V to 0.5 V. A refined parallel shift was observed in the I\({}_{\text{DS}}\)-V\({}_{\text{Ref}}\), when the pH value changed from 4.0 to 9.18, indicating the corresponding potential change at the gate surface. The experimental results reveal that the drain-source current (I\({}_{\text{DS}}\)) decreased with the increase in the pH. Figure 4: EDS of the Au-gated sensing membrane. Figure 3: SEM images of the device: (**a**) top view of the sensing area; (**b**) zoom-in view of the Au-gated sensing membrane. The transconductance (G\({}_{\rm m}\)) is defined as the change of the drain-source current (\(\Delta\)I\({}_{\rm DS}\)) against the change of the reference-source voltage (\(\Delta\)V\({}_{\rm Ref}\)), which can be expressed as:  
\[G_{m}=\frac{\Delta I_{DS}}{\Delta V_{Ref}}=\frac{W}{L}\mu_{n}C_{i}V_{DS} \tag{1}\]  
where W and L are the width and length of the sensing membrane, \(\mu_{\rm n}\) is the electron mobility of the 2 DEG, C\({}_{\rm i}\) is the capacitance per unit area between the quasi-reference electrode and the 2 DEG channel, and V\({}_{\rm DS}\) is the drain-source voltage. At pH = 6.86, the maximum transconductance (G\({}_{\rm m,\ max}\)) of the sensor at V\({}_{\rm DS}\) = 0.1 V, 0.5 V, 1.0 V, and 2.0 V was 0.25 mS, 1.23 mS, 2.45 mS, and 4.44 mS, respectively. The V\({}_{\rm Ref}\) of the G\({}_{\rm m,\ max}\) at V\({}_{\rm DS}\) = 0.1 V, 0.5 V, 1.0 V, 2.0 V was \(-\)2.60 V, \(-\)2.29 V, \(-\)1.93 V, and \(-\)1.09 V, respectively. The V\({}_{\rm Ref}\) corresponds to the G\({}_{\rm m,\ max}\) shift positively with the increasing V\({}_{\rm DS}\). The threshold voltage (V\({}_{\rm th}\)) is defined as the V\({}_{\rm Ref}\) at which a conductive channel forms between the source and drain, initiating current flow within the sensor. The role of V\({}_{\rm th}\) in the sensor is critical as it is influenced by the surface potential, which in turn is affected by the pH value. Therefore, by observing changes in V\({}_{\rm th}\), the sensor can accurately detect and measure pH value fluctuations. At V\({}_{\rm DS}\) = 2.0 V, the V\({}_{\rm th}\) of the sensor at pH = 4.0, 6.86, and 9.18 is \(-\)3.42 V, \(-\)3.21 V, and \(-\)3.12 V, respectively. The V\({}_{\rm th}\) shifts positively with the increasing pH value, indicating that the sensor is sensitive to the different pH values. It demonstrates that the pH change of the electrolyte solution modulates the surface potential, leading to a change in the 2 DEG density of the sensor. It needs less voltage to deplete the 2 DEG, causing a positive shift of the V\({}_{\rm th}\). Figure 5: Transfer characteristics of the Au-gated pH sensor in the three pH standard buffered solutions at different drain-source voltages: (**a**) V\({}_{\rm DS}\) = 0.1 V, (**b**) V\({}_{\rm DS}\) = 0.5 V, (**c**) V\({}_{\rm DS}\) = 1.0 V, (**d**) V\({}_{\rm DS}\) = 2.0 V.  
The sensor's potential sensitivity (S\({}_{\text{V}}\)) is defined as the surface potential change (\(\Delta\varphi\)) with the pH value change (\(\Delta\)pH):  
\[S_{V}=\frac{\Delta\varphi}{\Delta pH}=\frac{\Delta V_{Ref}}{\Delta pH} \tag{2}\]  
Figure 6 shows the relationship of the reference-source voltage versus the pH value (V\({}_{\text{Ref}}\)-pH). The potential sensitivity (S\({}_{\text{V}}\)) was obtained from the slope of the V\({}_{\text{Ref}}\)-pH plot.