## Abstract

The linear output of lateral photovoltage (LPV) with light position is the main feature of conventional lateral photovoltaic effect (LPE), which can be used to detect small displacement. In this study, we report a novel oscillating LPE in a surface-patterned metal-semiconductor structure, which can be well manipulated by the metal thickness and the comb properties. Compared with the conventional linear LPE, this oscillating LPE not only contributes a considerable higher sensitivity of LPV along the lateral direction, but also shows a distinguishable response to the vertical direction, indicating a new way of detecting two-dimensional displacement with much higher precision.

©2010 Optical Society of America

## 1. Introduction

Since the lateral photovoltaic effect (LPE) was first discovered by Wallmark in floating Ge p-n junctions in 1957 [1], it was boosted very quickly in many different systems [2–12], such as Ti/Si amorphous superlattices, modulation-doped AlGaAs/GaAs heterostructures, hydrogenated amorphous silicon Schottky Barrier structures, perovskite materials, metal-oxide-semiconductor structures, and metal-semiconductor (MS) structures. Due to the output of lateral photovoltage (LPV) changing with light position linearly, the LPE can be used to detect small displacement as position-sensitive detectors (PSDs) [13,14]. The present sensitivities of LPV in above structures are mainly in the range of 1-100 mV/mm, and the minimum displacement that can be detected by LPV is only about several tens of μm. In addition, almost all the previous LPE works were focus on their linear characteristic, and works concerning non-linear LPE were rarely reported; the most convincing work should be the work done by B. F. Levine et al. [15], where they have developed a high resolution photovoltaic position sensing with Ti/Si superlattices. In that work, by making a narrow scratch on the surface of the structure, they realized an extremely high LPV sensitivity of 1.5 mV/μm. But due to the small gap width, the effective detecting region in their structure is only several μms, although the LPV sensitivity is enormous. So based on this idea, we propose a new type oscillating LPE in a surface-patterned MS structure, in which the LPV oscillations can be well manipulated by the metal thickness and the patterned-comb properties. Thus, as long as the oscillating period is small enough, the LPV sensitivity can be greatly enhanced. This means a detection of a nano-scaled displacement will be possible. Besides, this oscillating LPV shows not only a high LPV sensitivity with a large effective detecting region in lateral direction but also exhibits a distinguishable response to vertical position, providing a method of detecting two-dimensional displacement with much higher sensitivity and precision.

## 2. Oscillating LPE in surface-patterned MS structures

The general understanding of LPE mechanism in MS structure can be interpreted as follow [12]. When the light nonuniformly illuminates on the surface of MS structure, the electron-hole pairs are generated inside the semiconductor at light position. Soon the excited electrons will be swept into metal film due to the non-equilibrium state with holes remain in the semiconductor. The excess electrons in metal will thus generate a gradient along the metal film between illumination zones and nonillumination zones, which results in electrons diffusing lateral away from the light spot. If the lateral distance of the light spot from each electrode is different, then the density of electrons at the two contacts is different, generating the LPV.

Based on the above LPV mechanism in conventional MS structure, we propose the following improved MS structure, as shown in Fig. 1(a)
, which concludes a thin metal-layer-1 (M1) and a thick metal-layer-2 (M2). We can see from Fig. 1(b) that M2 is a patterned metal layer formed by two interdigitated-combs, where one comb-patterned layer (the blue one, called as M2_{A}) is connected with contact A and another comb-patterned layer (the red one, called as M2_{B}) is connected with contact B. (Actually, the structure in Ref. 15 can be regarded as a particular case of our proposed structure with only one-comb-period). Thus, quite similarly to the situation in conventional MS structure as discussed above, when the light illuminates on this structure, the excited electrons will transit from semiconductor to M1 and then diffuse along the M1 away from the light position as shown in Fig. 2(a)
. According to Ref. 12, the density of diffusion electrons in M1 at position *r* can be presented as

*x*, and ${\lambda}_{1}$ is the electron diffusion length in M1. Please note, to simplify the problem, here we only consider the lateral (

*x*) direction, and the light position in vertical (

*y*) direction is supposed to be zero. From Ref. 12, the electron diffusion length is proportional to the metal thickness, which can be written as ${\lambda}_{1}=\alpha {d}_{1}$, where ${d}_{1}$ is the thickness of M1 and

*α*is a proportional coefficient. Thus electrons in this thin M1 layer will have a very small diffusion length as shown in Fig. 3(b) .

Therefore, the diffusion electrons in M1 are confined in a very small area and can hardly defuse to a long distance. As a result, the electrons will transit from M1 to M2 as shown in Fig. 2(a), and then continue diffusing along patterned M2 toward the two contacts as shown in Fig. 2(b), where the electrons in M2_{A} at position ${r}_{A}$ will diffuse towards contact A, and those in M2_{B} at position ${r}_{B}$ will diffuse towards contact B. Here ${r}_{A}\in [ND,ND+a]$ and ${r}_{B}\in [(N+\frac{1}{2})D,(N+\frac{1}{2})D+a]$, where $N=\cdot \cdot \cdot -2,-1,0,1,2\cdot \cdot \cdot $ is the integer, and *D* and *a* is the comb period and the comb width respectively as shown in Fig. 1(b). So the total electron densities at contacts A and B after diffusion can be calculated as

*β*is a proportional coefficient. According to Ref. 12, the LPV is proportional to the difference of electron density between two contacts, thus the LPV in this improved MS structure can be obtained as

*K*is the proportional coefficient. Figure 4(a)-(c) show the LPVs response to light position in the improved MS structure with different M1 thickness. It is obvious that an oscillating characteristic can be achieved when the thickness of M1 is small, and vanishes gradually when the thickness of M1 becomes large. This is because, for a large M1 thickness, the electrons in M1 are easy to diffuse along the film, resulting in small gradient of electron density in M1 as shown in Fig. 3(a). Thus the difference of total density of diffusion electrons between M2

_{A}and M2

_{B}that transited from M1 is negligibly small, which leads to the small LPV. Figure 4(d)-(f) show the LPVs response to light position in the improved MS structure with different M2 thickness. It is interesting that the oscillating LPE will become more obvious when the thickness of M2 is increased. This is because, for a small M2 thickness, the electrons in M2 can hardly diffuse along the film and arrive to the contacts unless the light spot is near the contacts (see Fig. 4(f)).

To better understand this oscillating LPE, we also investigate the LPV response to light position with different comb period and comb width. We can see from Fig. 5(a)-(c) that the oscillating period is equal to the comb period, indicating the LPV oscillation in such an improved MS structure can be manipulated by changing the comb period. Besides, as shown in Fig. 5(a), this LPV shows a perfect linear characteristic response to light position within half of oscillating period when the comb period is small. But the linearity will turn bad when the comb period becomes large as shown in Fig. 5(b) and (c). We can also see from Fig. 5(d)-(f) that, when the comb width is increased, the oscillating amplitude will be decreased but the linearity will become better. In addition, the oscillating peak will become more flat as the comb width is increased. Therefore, from the above discussion, a small comb period with an appropriate comb width is crucial for obtaining a perfect oscillating LPV.

The above discussion of oscillating LPV response to light position (as shown in Fig. 4 and Fig. 5) are all investigated in *x* direction with $y=0$. In fact, the *y* position can greatly influence the above oscillating amplitude. We have calculated

*x*with $y\ne 0$. Different with ${V}_{A}(0)={V}_{B}(0)$ in the situation of $y=0$, ${V}_{A}(y)$ will be different with ${V}_{B}(y)$ in the condition of $y\ne 0$ according to Eqs. (5)-(6), where a larger $\left|y\right|$ results in a larger difference. Thus if we define a difference coefficient as $\eta \equiv \frac{{V}_{A}(y)}{{V}_{B}(y)}$, then the position of

*y*can be obtained aswhere ${\kappa}_{y}=\frac{2}{{\lambda}_{2}}$ is the sensitivity (response to

*y*), and here we suppose $y<<{\lambda}_{2}$. Clearly, we can see from Fig. 6(b) that

*η*presents a linear characteristic response to

*y*. Thus, by measuring

*η*, the position of

*y*can be detected. Please note, it is the voltage rate of

*η*(not the voltage itself) that shows the linear response to laser position, which is different from the conventional linear voltage response in position. It is easy to understand from above discussion that the oscillating LPV also shows almost a linear characteristic with the light position

*x*within the range of half oscillating period ($\Delta =D/2$) when

*D*is small as shown in Fig. 5(a). Thus, by counting the observable number of half-period, the position of

*x*can be obtained aswhere ${\kappa}_{x}$ is the sensitivity (response to

*x*), ${N}_{hp}$ represents the observable number of half-period as light moves, and ${V}_{o}$ and

*V*are the LPVs with light position of ${x}_{0}$ and

*x*, respectively. Ideally, the sensitivity (within a half-period) of oscillating LPV in improved MS structure can be obtained asHere ${\kappa}_{x}\text{'}$ is the sensitivity of conventional linear LPV in MS structure, where $L={L}_{A}-{L}_{B}$ is the contacts’ distance. Therefore, compared with the traditional one-dimensional position detection based on linear LPE [12], a two-dimensional position detection concerning displacement of

*x*(according to Eq. (8)) and

*y*(according to Eq. (7)) becomes feasible, as shown in Fig. 6. We stress that, as long as $\Delta <<L$, the LPV sensitivity response to

*x*will be greatly enhanced (according to Eq. (9)), indicating that a much more precision can be obtained. For example, if $\Delta =1\text{\mu m}$, then the LPV sensitivity can be enhanced by 10

^{3}times, compared with conventional LPV sensitivity of 1-10 mV/mm. Therefore, this oscillating LPV has a great potential to be applied in the future nano-scaled displacement detection.

## 3. Conclusions

To summarize, we have reported an oscillating LPE in an interdigitated-comb-patterned MS structure. The LPV oscillations can be well manipulated by the metal thickness and the comb properties. Compared with the conventional linear LPE, this new type oscillating LPE not only contributes a considerable higher sensitivity of LPV along the lateral direction, but also shows a distinguishable response to the vertical direction, providing a method of detecting two-dimensional displacement with much higher sensitivity and precision.

## Acknowledgments

We acknowledge the financial support of National Natural Science Foundation of China (NNSFC) (grant numbers 60776035 and 10974135).

## References and links

**1. **J. T. Wallmark, “A new semiconductor photocell using lateral photoeffect,” Proc. IRE **45**, 474–483 (1957).

**2. **R. H. Willens, “Photoelectronic and electronic properties of Ti/Si amorphous superlattices,” Appl. Phys. Lett. **49**(11), 663–665 (1986). [CrossRef]

**3. **B. F. Levine, R. H. Willens, C. G. Bethea, and D. Brasen, “Lateral photoeffect in thin amorphous superlattice films of Si and Ti grown on a Si substrate,” Appl. Phys. Lett. **49**(22), 1537–1539 (1986). [CrossRef]

**4. **B. F. Levine, R. H. Willens, C. G. Bethea, and D. Brasen, “Wavelength dependence of the lateral photovoltage in amorphous superlattice films of Si and Ti,” Appl. Phys. Lett. **49**(23), 1608–1610 (1986). [CrossRef]

**5. **N. Tabatabaie, M. H. Meynadier, R. E. Nahory, J. P. Harbison, and L. T. Florez, “Large lateral photovoltaic effect in modulation-doped AlGaAs/GaAs heterostructures,” Appl. Phys. Lett. **55**(8), 792–794 (1989). [CrossRef]

**6. **J. Henry and J. Livingstone, “A comparative study of position-sensitive detectors based on Schottky barrier crystalline and amorphous silicon structures,” J. Mater. Sci. Mater. Electron. **12**(7), 387–393 (2001). [CrossRef]

**7. **J. Henry and J. Livingstone, “Optimizing the response of Schottky barrier position sensitive detectors,” J. Phys. D Appl. Phys. **37**(22), 3180–3184 (2004). [CrossRef]

**8. **K.-J. Jin, K. Zhao, H.-B. Lu, L. Liao, and G.-Z. Yang, “Dember effect induced photovoltage in perovskite p-n heterojunctions,” Appl. Phys. Lett. **91**(8), 081906 (2007). [CrossRef]

**9. **H. Wang, S. Q. Xiao, C. Q. Yu, Y. X. Xia, Q. Y. Jin, and Z. H. Wang, “Correlation of magnetoresistance and lateral photovoltage in Co3Mn2O/SiO2/Si metal–oxide–semiconductor structure,” N. J. Phys. **10**(9), 093006 (2008). [CrossRef]

**10. **C. Q. Yu, H. Wang, and Y. X. Xia, “Giant lateral photovoltaic effect observed in TiO_{2} dusted metal-semiconductor structure of Ti/TiO_{2}/Si,” Appl. Phys. Lett. **95**(14), 141112 (2009). [CrossRef]

**11. **C. Q. Yu, H. Wang, and Y. X. Xia, “Enhanced lateral photovoltaic effect in an improved oxide-metal-semiconductor structure of TiO2/Ti/Si,” Appl. Phys. Lett. **95**(26), 263506 (2009). [CrossRef]

**12. **C. Q. Yu, H. Wang, S. Q. Xiao, and Y. X. Xia, “Direct observation of lateral photovoltaic effect in nano-metal-films,” Opt. Express **17**(24), 21712–21722 (2009). [CrossRef] [PubMed]

**13. **S. Q. Xiao, H. Wang, C. Q. Yu, Y. X. Xia, J. J. Lu, Q. Y. Jin, and Z. H. Wang, “A novel position-sensitive detector based on metal–oxide–semiconductor structures of Co–SiO2–Si,” N. J. Phys. **10**(3), 033018 (2008). [CrossRef]

**14. **J. Henry and J. Livingstone, “Thin-Film Amorphous Silicon Position-Sensitive Detectors,” Adv. Mater. **13**(12-13), 1022–1026 (2001). [CrossRef]

**15. **R. H. Willens, B. F. Levine, C. G. Bethea, and D. Brasen, “High resolution photovoltaic position sensing with Ti/Si superlattices,” Appl. Phys. Lett. **49**(24), 1647–1648 (1986). [CrossRef]