## 3 Experiment and Discussion
### Results and Discussion
#### 3.2.4 The Relationship between Current Variation and Voltage Bias  
Adjusting the voltage bias conditions \(V_{0}\), \(\Delta I\) will generate a series of complex changes (Figure 11a). As mentioned above, there exists a critical voltage \(V_{\rm c}=1.94\) V.  
When \(V_{0}\) is set between 1.8 V and 3.5 V, the OBIRCH technique dominates, and \(\Delta I\) is negative. According to Equation (16), the contribution of OBIRCH, \(-\frac{V_{0}}{R^{2}}\Delta R\), is proportional to \(V_{0}\) and inversely proportional to \(R^{2}\). Next, the resistance \(R\) decreases as the bias voltage \(V_{0}\) increases (Figure 4b). Besides, \(\Delta V_{\rm S}\) is invariable because the Seebeck voltage is only related to the temperature gradient \(\
abla T\) according to Equation (14). \(\Delta R/R\) is also a constant because of the following formula:  
Figure 11: Curve of the current variation and the bias voltage: (**a**) \(\Delta I\sim V_{0}\); (**b**) \(RAI\sim V_{0}\).  
Figure 10: Curve of the current variation and the irradiation time at different bias voltages \(V_{0}\). The laser beam starts to irradiate at \(t=10\) s with no scanning velocity. The laser power is set at 40 mW: (**a**) Point A (abnormal spot); (**b**) Point B (normal spot).  
\[\frac{\Delta R}{R}=\frac{\int\rho_{0}\alpha_{\text{TCR}}\frac{\Delta T}{A}\text{d}I} {\int\rho_{0}\frac{\text{d}I}{A}}=\alpha_{\text{TCR}}\overline{\Delta T} \tag{24}\]  
where \(\overline{\Delta T}\) is the average value of the temperature variation. Equation (13) is used in this formula. Therefore, the absolute value of \(\Delta I\)'s slope gradually increases as the \(V_{0}\) increases. In order to find the values of \(\Delta V_{\text{S}}\) and \(\Delta R/R\), Equation (16) is modified to:  
\[R\Delta I\approx\Delta V_{\text{S}}-\frac{\Delta R}{R}V_{0} \tag{25}\]  
The relationship between \(R\Delta I\) and \(V_{0}\) is shown in Figure 11b. After linear fitting, the values of \(\Delta V_{\text{S}}\) and \(\Delta R/R\) are calculated and listed in Table 4. These two values at Point A are much larger than those at Point B, showing that the thermal property at the abnormal spot is more sensitive than that at the normal spot. Besides, the critical voltage \(V_{\text{c}}\) can be calculated through Equation (17) using the data in Table 4, which is respectively 2.09 V at Point A and 1.75 V at Point B. These two values are close to the measured values \(V_{\text{c}}=1.94\) V.  
When \(V_{0}\) is set between 0 V and 1.8 V, the SEI technique dominates, and \(\Delta I\) is positive. Near 0 V (no bias applied), the resistance is so large that the value of \(\Delta I\) tends to be zero. As the voltage increases, the resistance reduces, causing an increasing \(\Delta I\). In this period, OBIRCH's contribution is still small. At about 1.5 V (Figure 11a), \(\Delta I\) is most affected by the SEI. After that, \(\Delta I\) starts to fall.  
In general, although the comprehensive model has many shortcomings, such as the inability to describe the temperature variation in the z direction, the inability to describe the temperature field evolution with different structures of the IC, the infinite increase of the temperature when the scanning velocity is zero, etc., it fits well with the experimental results. An in-depth study on the optimization of the comprehensive model is under way.