The LPV varies with the position of laser irradiation point linearly as shown in Fig. 3(a). The sensitivity is calculated to be 59mV/mm. The linearity of LPV is 0.9924 as shown in Fig. 3(b) and Table 1. As shown in Fig. 4, when the laser irradiates at the midpoint O between the two electrodes, that is D1D2 = 0, the LPV value is close to zero. Because the diffusion distances of the carriers are equal. However, when the laser irradiation position is close to an electrode, that is D1D2 > 0, a potential difference is generated which can be measured with a voltmeter. When the laser irradiates at different positions between the two electrodes, the change trend of LPV is the same, but the LPV value is different. LPV shows a gradual upward trend and eventually reaches saturation. The LPV response time and LPV value are affected by the distance from the laser irradiation point to the electrode. The phenomenon can be explained by the diffusion motion of the carriers. When the laser irradiates on the surface of the TiSiO2Si sample, the equilibrium state of the Schottky barrier is broken, resulting in the local generation of photogenerated carriers at the laser irradiation point of the Si substrate. The photogenerated electronhole pairs are then separated by the builtin electric field. The photogenerated electrons diffuse along the interface, forming a certain concentration gradient in the lateral direction. Once the carrier concentration at any two points on the same side is different, LPV can be detected by a voltmeter [9]. Since the photo induced electron concentration is highest at the point of laser irradiation, then it diffuses to the two electrode points in the silicon wafer. The electrons are immediately diffused to the electrode close to the laser irradiation point. However, the number of electrons that diffuse to the other electrode away from laser irradiation point is small, and can be neglected due to the long diffusion distance. Therefore, LPV has an extrem ely fast response time and a large LPV value when the laser irradiates on electrode. Conversely, when the laser irradiation point is close to point O, it takes a period of time for the electrons to diffuse to the electrode close to the laser irradiation point, and the LPV value of the laser irradiation spot at point O is smaller than the LPV value of the laser irradiation spot at point A as shown in Fig. 4. Because the diffusion distances of electrons from the laser irradiation point to the two electrodes are probably equal when the laser irradiation point is close to the point O. At the same time, the difference of electron concentration is relatively small and thus the LPV value is small. It is also worth mentioning that it takes a period of time for electrons to diffuse to the electrode, even if the time is short, and the carrier lifetime affects the electron concentration. Hence, the rise time and the LPV value vary with the laser irradiation point. In other words, the rise time of LPV depends on the distance from the laser irradiation point to the electrode. The response time of LPV is shorter when the laser irradiation point is close to the electrode. And larger LPV values can be obtained with increasing D1D2. When the energy of the irradiated laser beam is greater than the band gap
of silicon, the upward bending of the energy band of the interfacial space charge region is shown in Fig. 5, ψm and ψc is the work function of Ti film and Si substrate, respectively. The photogenerated electronhole pairs are excited. The electrons of the semiconductor are transported through the SiO2 to the Ti film by the tunneling effect. For the ntype silicon substrate, electrons are the majority carriers, and the electron concentration at the laser irradiation point is high. The diffusion of electrons can be described by the following diffusion equation [26]:
$${D_m}\frac{{{d^2}N(x)}}{{d{r^2}}}=\frac{{N(x)}}{{{\tau _m}}}$$
1
Where Dm is the diffusion constant of electrons in the metal, r is the coordinates of the laser irradiation point, and \({\tau _m}\) is the lifetime of the electrons.
Therefore, the photogenerated electronhole pair concentration in the structure can be calculated as [26]:
$$N(x)={N_0}\exp (  \frac{{r  x}}{{{\lambda _m}}})$$
2
Where x is the coordinate variable, N0 is the concentration of the electron at the laser irradiation point, and \({\lambda _m}\) is the diffusion length of the electron.
The number of carriers is collected by the two ohmic contacts depend on their distances to the illuminated point. A lateral electric field can be formed in this way and LPE is generated, as shown in formula (3) [26].
\(LP{V_{\text{m}}}={K_m}N(0)[\exp (  \frac{{\frac{L}{2}  x}}{{{\lambda _m}}})  \exp (  \frac{{\frac{L}{2}+x}}{{{\lambda _m}}})]=\frac{{2{K_m}N(0)}}{{{\lambda _m}}}\exp (  \frac{{\frac{L}{2}}}{{{\lambda _m}}})x\)
Where Km=1/(4πe) [(ħ2/2m)]3/2EF1/2 is a proportionality coefficient of metal side related to electron charge(e), mass(m) and Fermi level in equilibrium state (EF), x is the laser irradiation position. When x satisfies x << λ m, LPE can be idealized to change with x linearly.
We propose to introduce a differential equation for the potential distribution u (x, t).
$$B\frac{{du(x,t)}}{{dt}}  D\frac{{{d^2}u(x,t)}}{{d{x^2}}}+Eu(x,t)=F(x,t)$$
4
Where B corresponds to R, C of Eq. (5), D and E describe the carrier diffusion along the device and F corresponds to the electronhole separation function.
$$R\frac{{du({x_0},t)}}{{dt}}+\frac{1}{C}u({x_{0,}}t)=F({x_0},t)$$
5
Where the time dependent solution of Eq (4) at a fixed x0, corresponds to the RC circuit.
Table 1
The fitting results data of LPV
Item

result

Equation

y = a + b*x

Plot

B

Weight

No Weighting

Intercept

2.20337 ± 0.60983

Slope

96.13623 ± 1.83871

Residual Sum of Squares

179.62563

Pearson's r

0.99618

RSquare (COD)

0.99238

Adj. RSquare

0.99201

The semiconductor interface accumulates a large number of electrons, which can act as a charging capacitor C. And the capacitor and the semiconductor resistor R form an RC series circuit as shown in Fig. 6(a). Saturated lateral photovoltage (SPV) is regarded as the voltage source U0. Since a large number of carriers are concentrated on the laser irradiation point at the moment when the laser irradiates on the substrate, and it can be regarded as the input U0 according to RC circuits. Then start charging to saturation, which is similar with the charging process of RC circuits as shown in Fig. 6(b). The experimental results are shown in Fig. 7(a), and the black lines (red, blue, and green lines) represent the transient LPVs when the laser irradiates at points A (B, C, O), respectively. The results show that the fastest response time is about 1.6s, and the maximum LPV value of 47 mV can be obtained when the laser irradiates at point A. Conversely, the LPV value is zero when the laser irradiates at the point O. In summary, the results show that the LPV is larger and has a shorter response time when the laser irradiation spot is close to the electrode. We find that the transient LPV curve is similar to the RC circuits rise curve. RC circuits are introduced to simulate the dynamic process. The calculated results are in good agreement with the experimental results, as shown in Fig. 7(b). The TiSiO2Si structure resistor was measured to be 20 kΩ. And the capacitor simulation parameters are 26uF, 60uF, and 100uF, which corresponding to the laser irradiation points A, B, and C, respectively.
We measured the visible and nearinfrared absorption spectrum of the TiSiO2Si as shown in Fig. 8. It can be seen that the cutoff wavelength occurs approximately at 320 nm to 1100 nm corresponding to the band gap of silicon. The sample has a good absorption value in the infrared region. The structure presented a relatively high absorption rate in the region from 620 nm to 1020 nm. When the laser irradiates on the Ti film, most of the laser is absorbed by Si substrate, because the Ti film and SiO2 layer are thin, the laser can pass Ti film and SiO2 directly. Laser can be selectively absorbed by any material. Generally speaking, the molecular energy of the substance in the ground state is the lowest and the most stable. When a material is irradiated by a laser with sufficient energy greater than or equal to a certain energy, the material can absorb the laser of the corresponding wavelength, so that the energy level of the material molecules reaches an excited state. As shown in Fig. 8, the most suitable absorption wavelength of the TiSiO2Si structure is 710 nm, The band gap of Si was calculated to be 1.72ev by absorption spectroscopy. However, it is well known that the band gap of Si is 1.12ev. The reason for this error is obviously due to the selective absorption of the laser by the Ti film and the oxide layer (SiO2). Therefore, when the TiSiO2Si structure is irradiated with visible laser, the valence band electrons are more easily transitioned to the conduction band.