Transient lateral photovoltaic effect observed in Ti–SiO2–Si structure

The transient response of the lateral photovoltaic effect (LPE) was observed when Ti–SiO2–Si structure was irradiated by a 650 nm laser which is attributed to the remarkable absorptivity. LPE is linearly dependent on the laser irradiation position. The LPE has high sensitivity of 68.4 mV/mm and linearity of 0.9853, respectively. This paper focuses on the transient response process of LPE at different laser irradiation positions. The mechanism of the response time of the MOS structure is caused by the diffusion of electrons to the positive and negative electrodes. We experimentally verified this mechanism by laser irradiation on different positions. The principle of transient LPE is revealed by carrier diffusion and recombination theory. LPE has faster response time and larger amplitude when the laser irradiation points are close to electrodes. A resistor–capacitor (RC) circuit model combines with LPE which is established to simulate and analyze the transient process. The research provides a new direction for LPE-based sensors with regard to the amplitude and response time which change with laser irradiation position in Ti–SiO2–Si structure for researchers to develop position-sensitive sensors.

The dynamic process cannot be ignored when LPE is observed on silicon-based devices. So far, transient LPE has been studied for many years [18][19][20][21][22][23][24], such as irradiating the sample with a UV pulsed laser or with a CO 2 laser, respectively. In this work, the transient LPE was investigated in the Ti-SiO 2 -Si structure under 650 nm laser irradiation. We mainly studied the transient response process of LPE at different laser irradiation positions. The principle of transient LPE is revealed by carrier diffusion and recombination theory. The rising edge of transient LPE is similar to that of the charging RC circuits. The space charge region of the MOS structure collects electrons and thus can be regarded as a charging capacitor [25,26]. Therefore, the MOS structure can be considered as RC circuits under laser irradiation. An RC circuit model combines LPE to analyze transient response. This research provides a new direction for LPEbased sensors with regard to the response time and amplitude which change with laser irradiation position.

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of 15 × 15 mm. The RCA cleaning method was used to clean Si substrates [27]. The first step in the RCA clean (called SC-1, where SC stands for standard clean) which the Si substrates were immersed in the de-ionized (DI) H 2 O:NH 4 OH:H 2 O 2 (5:1:1) at 80 ℃ for 10 min to remove organic, contaminants and particles. Followed step (called SC-2) which metallic contaminants were removed using DI H 2 O:HCL:H 2 O 2 (6:1:1) at 80 °C for 10 min. And SC-1 and SC-2 would be used repeatedly. The last step which thin oxide layer and the ionic contaminants dissolved in the oxide were removed by DI H 2 O:HF (50:1) at 70 °C for 5 min. The Si wafers then were rinsed under DI water for 30 min and subsequently blow dry using N 2 gas at 100 °C for 2 h. Then they were placed in incubator at 27 °C for 90 days [4,14,[28][29][30]. The Si wafers were taken out of the incubator, subsequently Si wafers were cleaned by SC-1 and SC-2 in cooperation. Finally, the Si wafers were cleaned and dried. The n-type single crystal Si (1 1 1) is used the substrate which covered 1.2 nm native SiO 2 layer, 6.1 nm Ti thin films were prepared by DC magnetron sputtering to form a stable Ti-SiO 2 -Si structure [4,14]. The schematic diagram of LPV measurement is shown in Fig. 1. Points A and A' are indium electrodes which are made by pressing method. The electrodes are about 1 mm in diameter and show no measurable rectification behavior. As shown in Fig. 2, there are seven spots uniformly distributed along the x direction on the Ti film irradiated by the laser. Here, D 1 is the distance from the laser irradiation point to electrode A, and D 2 is the distance from the laser irradiation point to electrode A′. In addition, D 1 + D 2 = 1.7 mm. In this experiment, we used the manual probe (ST-103A) to measure the transverse I-V characteristic curve of the Ti-SiO 2 -Si structure. As shown in Fig. 3, where the inset is a schematic diagram of the measured I-V characteristic curve. The voltage was swept from -2.5 V to + 2.5 V. The transverse I-V curve shows that the indium electrode forms ohmic contact with Ti layer. The diameter of the laser spot is 60 μm. During the measurement of transient LPE, the laser power was set to 2 mW. First, the laser was blocked by the photoelectric shutter. After 30 ms, the laser irradiated point A on the titanium film when the shutter was opened. The laser was blocked again by the shutter after 150 ms. A digital multimeter (HAMEG HMC8012) was used to continuously record the transient response of LPE at point A under laser irradiation. The rest of the records for the other three points (including B, C, and O) operate in the same way.

Results and discussion
The results of theoretical calculations performed in Ref. [31] demonstrate that metals with high work functions and resistivities should enhance the LPE in MOS structures. The Ti (6.1 nm)-SiO 2 (1.2 nm)-Si structure is chosen for the experiment with reference to the LPE sensitivity of some other structures as shown in Table 1. The LPV linearly varies with the position of laser irradiation point as shown in Fig. 4.  The LPV curve shows good linearity between two electrode point areas, but show a nonlinear relationship outside the electrodes. The sensitivity is measured to be 68.4 mV/mm. The linearity of LPV is 0.9853 as shown in Table 2. When the laser irradiates at the midpoint O between the two electrodes, that is, |D 1 -D 2 |= 0, the LPV value is close to zero.
Because the diffusion distances of the electron are equal theoretically. While the laser irradiation position is close to an electrode, that is, |D 1 -D 2 |> 0, a potential difference is generated which can be measured with a voltmeter. As shown in Fig. 5, when the laser irradiates at different positions between the two electrodes, the change trend of transient process is similar, but the LPV value is different. The transient LPV shows a gradual upward trend and eventually reaches saturation. The response time and LPV value are affected by the distance from the laser irradiation points to the electrodes. The phenomenon can be explained by the carrier motion theory. When the laser irradiates on the surface of the Ti-SiO 2 -Si sample, resulting in the local generation of photogenerated carriers at the laser irradiation point of the Si substrate, the equilibrium state of the Schottky barrier is broken. The photogenerated electron-hole   pairs are then separated by the built-in electric field. The photogenerated electrons diffuse along the metal layer, forming a certain concentration gradient in the lateral direction. Once the carrier concentration at any two positions is different, LPV can be detected by a voltmeter [10]. The schematic diagram of the band structure of Ti-SiO 2 -Si is shown in Fig. 6, the upward bending of the energy band of the interfacial space charge region, ψ m and ψ c are the work function of Ti film and Si substrate, respectively. When the energy of the irradiated laser is greater than the band gap of silicon, the photogenerated electron-hole pairs are excited with laser irradiation. The electrons of the semiconductor are transported through the SiO 2 to the Ti film by the tunneling effect. For the n-type silicon substrate, electrons are the majority carriers, and the electron concentration at the laser irradiation region is higher than nonillumination. The diffusion of electrons can be described by the following diffusion equation [37]: where D m is the diffusion coefficient of electrons in the metal, and m is the lifetime of diffusion electrons in the metal.
Therefore, the density of electrons in the metal at position r can be calculated as [37]: where x is the coordinate of the laser spot position, N (0) is the transition electrons from semiconductor to metal at light position, and λ m is the diffusion length of the electron in the metal.
The number of carriers collected by the two ohmic contacts depends 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 [37]: where K m = 1/(4πe) [(ħ 2 /2 m)] 3/2 E F −1/2 is a proportionality coefficient of metal side related to electron charge(e), mass(m) and Fermi level in equilibrium state (E F ), L is the distance between two electrode. When x satisfies |x|< < λ m , LPE can be idealized to change with x linearly.
Sensitivity is defined as the first derivative of LPV with laser irradiation position, Linearity w is defined as: where σ is standard deviation. The coefficient w gives a good indication of Ti-SiO 2 -Si structure linearity of perfect linearity when w is ± 1. In our experiment, the linearity w is 0.9853 which is measured in Ti-SiO 2 -Si structure.
We propose to introduce a differential equation for the potential distribution u (x, t). where the time dependent solution of Eq. (6) at a fixed x 0 , corresponding to the RC circuits.
The semiconductor space charge region accumulates a large number of electrons, which can act as a charging capacitor C. The capacitor C and the Ti-SiO 2 -Si structure resistance R form an RC series circuit as shown in Fig. 7(a). The electrons diffuse laterally under non-uniform illumination and are subsequently collected by the electrodes. The LPV can be regarded as the output U C . Saturated lateral photovoltage (SPV) is regarded as the voltage source U 0 according to RC circuits. The process of LPV rising gradually from zero to saturation is similar to the charging process of RC circuits as shown in Fig. 7(b). The transient experimental results at different laser irradiation points are shown in Fig. 8(a), and the black (red, blue, and green) curves 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 1.6 ms, 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 amplitude is larger and has a shorter response time when the laser irradiation spot is close to the electrode. This experimental phenomenon can be explained by the carrier recombination theory. J. Henry and J. Livingstone proposed the main mechanism for determining the sensitivity of LPE which is the resistance of the lateral path length that photogenerated carriers must travel to recombine with the bunched carriers in the low conductivity medium [3,38]. As shown in Fig. 9, when the laser irradiates on the surface of the Ti-SiO 2 -Si sample, the photogenerated electron-hole pairs are then separated by the built-in electric field. The electrons then enter the metal layer and diffuse to electrodes. Subsequently, the electrons re-inject into the semiconductor layer and recombine with holes. LPV = K c (L 1 -L 2 ), K c is a parameter, which can be understood as the length of the path traveled by carrier recombination. Therefore, the LPV is larger when the laser irradiation spot is close to the electrodes. The transient response time of LPE is the electron-hole pairs from generation to recombination to reach a dynamic equilibrium state. The LPE response time varies with the laser irradiation position. Because the relative electron concentration of the re-injected semiconductor layer is high when the laser irradiation point is close to the electrodes. However, the path length of the carriers seeking recombination which is constant relatively. The velocity of the carriers seeking recombination which is proportional to the carrier concentration. Therefore, the transient LPE has shorter response time when the laser irradiation point is close to the electrodes. We find that the rising edge of transient LPV is similar to that of the charging RC circuits. Therefore, the RC circuits are introduced to simulate the dynamic process. The calculated results are in good agreement with the experimental results, as shown in Fig. 8 (b).
According to the first-order circuit equation: where U C is the output and U 0 is the voltage source when the RC circuits is charging, respectively. R, C are the resistor and capacitance, respectively. The time constant (τ = RC) is an important characteristic that reflects the transient characteristics, which is jointly determined by the circuit structure, capacitance C and resistor R. The time constant is a physical quantity that measures the speed of the transition process of the circuit, and the time required for the circuit to change from a transient state to a steady state. Here, 3τ represents the response time of the LPE. Theoretically, since the voltage of the transient process in the circuit changes exponentially, it takes an infinite amount of time for the circuit to reach a steady state. However, it is generally believed that the circuit will be in a stable state after the transient process of the circuit ends after 3τ ~ 5τ time. If t = 3τ, U C (3τ) = U 0 (1-e −3 ) ≈ 95% U 0 . Basically, it can be viewed as a state of charge to full. The resistor value of the sample was measured to be 2 × 10 3 Ω. As can be seen from the black curve in Fig. 8(a), it takes 1.6 ms for the LPV amplitude to gradually rise from zero to a steady state when the laser irradiates at point A. Therefore, we set the simulating parameter 1.6 ms = 3RC A . The capacitance parameter of the RC circuits (i.e. C A ) is calculated as 0.26 μF to simulate the transient process of the LPE corresponding to the point A irradiated by the laser. And the transient response time are 3.2 ms and 5.6 ms when laser irradiate on point B and C, respectively. According to the same method, the simulating capacitance is calculated as C B = 0.52 μF and C C = 0.93 μF corresponding to the laser irradiation points at B and C, respectively. We measured the absorption rate of the Ti-SiO 2 -Si structure using a spectrophotometer (UV-2600) as shown in Fig. 10. The laser with wavelength of 650 nm is chosen for the experiment which is easily absorbed by the Ti-SiO 2 -Si structure. Since absorption rate is directly related to the number of electron-hole pairs generated and thus affects the LPE sensitivity. The Ti-SiO 2 -Si structure presented a relatively high absorption rate in the region from 630 to 1020 nm. The relative absorption rate β is defined as: where W a is the absorption rate of Ti-SiO 2 -Si corresponding to wavelength 320 nm-1100 nm. W m is the largest absorption rate among the W a .
When the laser irradiates on the Ti film, most of the energy is absorbed by Si substrate. Because the thicknesses of Ti film and SiO 2 layer are 6.1 nm and 1.2 nm, respectively, the laser can pass them 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. When the Ti-SiO 2 -Si structure is irradiated with visible laser to nearinfrared region, the valence band electrons are more easily transitioned to the conduction band. Therefore, the laser with wavelength of 650 nm is chosen for our experiment.

Conclusions
In this paper, we observe the dynamic process of the LPE from generation to stabilization under 650 nm laser irradiation. Since the Ti-SiO 2 -Si structure has a high absorption rate for 650 nm laser due to the selective absorption by Ti film. The sensitivity of LPV is measured to be 68.4 mV/mm. The linearity is 0.9853. This paper focuses on the transient response process of LPE at different laser irradiation positions. The amplitude of LPV increase and response time decrease when the laser irradiation point is close to the electrodes. The mechanism of the transient LPE which is caused by the diffusion of electrons to the positive and negative electrodes. We experimentally verified this mechanism by laser irradiating on different irradiation points. The principle of LPE is revealed by carrier diffusion and recombination theory. And an RC circuit model combines LPE is established to simulate and analyze transient response. The trapped carriers in the space charge region can be regarded as a capacitor according to the RC circuit characteristics. Si substrate and oxide layer (SiO 2 ) are regarded as a resistor according to RC circuits characteristics. We set simulating capacitance as 0.26 μF, 0.52 μF and 0.93 μF when laser irradiated on A, B and C, respectively. The simulating results are in good agreement with the experimental results. The results providing a new direction for LPE-based sensors with regard to the amplitude and response time which change with laser irradiation position.