## Abstract

Lateral photovoltaic effect (LPE) observed on the metal films is unusual because it violates a principle that the LPEs are always observed on the surface of a semiconductor. Compared with early studies, we have realized an obvious metal film LPE in a metal-semiconductor (MS) structure. By further arguing with experimental results, this work also intensively elucidates many features of LPE which the early models never touched upon. All the data and analyses in this study indicate that metal side LPE in MS structure has some natural superiorities to the semiconductor side LPE and may open many exciting opportunities for realizing multifunctional devices.

©2009 Optical Society of America

## 1. Introduction

The lateral photovoltaic effect (LPE) is an attributive character of some semiconductor structures and can be always observed on semiconductor surface. Due to its output of lateral photovoltage (LPV) changing with light spot position linearly, this effect can be used in position-sensitive detectors (PSDs) which can detect very small displacement. In general, LPE is mechanically deduced from the lateral diffused flow and recombination of the photogenerated electron-hole pairs (EHPs) away from the point of incident radiation. Since the LPE effect was first discovered by Schottky and later expanded upon by Wallmark in floating Ge p-n junctions in 1957 [1], it was boosted very quickly in many different semiconductor systems, such as Ti/Si amorphous superlattices [2–5], modulation-doped AlGaAs/GaAs heterostructures [6], hydrogenated amorphous silicon Schottky Barrier structures [7], and perovskite materials [8]. Recent research shows that the LPE can also be observed in some metal-semiconductor (MS) structures [9–12]. This is interesting because MS structure has been treated as solar cell for many decades [13–18]. The MS structure serving as LPE device is pretty new. The present understanding of operation mechanism of LPE in MS structure is similar to that of a MS solar cell, which utilizes the transverse photovoltaic effect (TPE) due to the Schottky barrier formed (SB) at the interface between the metal film and semiconductor.

When light uniformly illuminates a MS (say n-type semiconductor) junction, electron–hole pairs are generated inside the semiconductor within the minority-carrier diffusion length of the depletion region. The minority holes in the depletion region are swept into the metallic film by the Schottky field with electrons remaining in the n-region. This leads to the development of a transverse photovoltage, as is observed in a MS or MOS solar cell. If now the light impinges at one point on the surface, the presence of the excess remaining electrons and injected holes will give rise to a non-equilibrium distribution because of all the other points on the film surface without any illumination, generating a gradient between the illuminated and the non-illuminated zones. So the excess majority carriers in the metallic layer and the Si layer move laterally away from the illuminated spot. If the lateral distance of the laser spot from each electrode is different, then the quantity of the collected carriers at the two contacts is different. A lateral field is therefore set up, as well as the LPV. Ideally, there should be a linear relationship between the LPV output and the position of the light spot.

We must stress here, though LPEs in MS structures are obvious, the LPEs are mostly observed in semiconductor side. The observed metal side LPEs in early studies were always negligibly small due to the shorting effect. In fact, metal side LPE is very sensitive to the metal film thickness. In particular, when the metal film thickness is reduced to nano-scale, the metal film LPE can become very obvious. This has been confirmed by our recent preliminary studies in similar structures of Co/SiO_{2}/Si, Co/Mn/Co/c-Si and Co_{3}Mn_{2}O/Si [19–22]. However, few people could be aware of this in their early studies and understood that this phenomenon widely exists in a variety of MS structures. In fact, the importance of metal film LPE is not only the obvious LPE. It may open opportunities for multifunctional PSD devices if the metal’s properties can be added in the metal film LPEs. This means the LPE can potentially coexist with other metal physical properties, such as thermal conductivity or even superconductivity. For example, we have realized a coexistence of LPE and magnetoresistance in our recent works [20,22]. Therefore, this characteristic allows the LPE to develop to its full potential in more applications, such as biomedical applications, robotics, astronautics, process control and position information systems, possibly even in magnetic storage.

In this context, a variety of metals have been used in the MS structures in order to manifest this phenomenon is prevalent among the most of metals. Interestingly enough, each metal and semiconductor we used in our experiments is hardly to produce any LPE, but their combination can create an obvious one. This is because the electrons excited by light in the semiconductor can be easily introduced to the metal film in this kind of structure, resulting in an effective separation from holes. This will reduce the possibility of recombination. In the meanwhile, the electrons can diffuse much longer distance in the metal film than it does in the semiconductor. These two factors are great important for an obvious LPE. Based on these ideas, we put forward a new model which contains more parameters affecting the LPE. Although early models based on SB still remain challenging in qualitatively describing the LPE in some conventional semiconductor structures, it is incapable to quantitatively explain the MS LPE, especially in explanation of thickness effect of metal side LPE.

## 2. Experimental results

The metal films with a variety of thicknesses are all grown on n-type Si(111) (20 mm × 5 mm rectangles) by dc sputtering at room temperature. The thickness of the substrates is around 0.3 mm and the resistivity of the substrates is in the range of 50-80□Ωcm at room temperature. In this paper, to concentrate our discussion on MS LPE, we only choose three kinds of metal of Ti, Co, Cu as control samples at a typical metal thickness of 6.2 nm because, at this thickness, Ti/Si structure has the strongest LPE. All the samples were scanned spatially with an He-Ne laser (3mW and 632 nm) focused on a roughly 50 μm diameter spot at the surface and without any spurious illumination (e.g. background light) reaching the samples, and all the contacts (less than 1mm in diameter) to the films were formed by alloying indium and showed no measurable rectifying behavior (very perfect ohmic contact).

The typical transverse Schottky barrier (SB) I-V characteristics of Ti(Co, Cu)/Si metal-semiconductor structures were measured with a pulse-modulated current source. As shown in Fig. 1 , all the results exhibit good nonlinearity and rectifying current-voltage behavior, demonstrating that the Ti(Co, Cu)/Si structures in this study can fully develop a Schottky barrier, which is main feature of the ordinary metal-semiconductor junctions.

Figure 2 shows our experimentally observed LPEs in three different MS structure of Ti/Si, Co/Si and Cu/Si. We can obviously see that the sensitivities of the metal side (40.0 mV/mm for Ti/Si, 31.2 mV/mm for Co/Si, and 6.5 mV/mm for Cu/Si) are higher than those of the semiconductor side (27.2 mV/mm for Ti/Si, 21.8 mV/mm for Co/Si, and 5.1 mV/mm for Cu/Si). These results demonstrate the metal side LPEs are quite obvious, and have better sensitivities than that of semiconductor side. In previous studies, the semiconductor side LPEs are prevalent and dominant. This is because the metal side LPE is very sensitive to metal film thickness. If the thickness is outside an appropriate range, the metal side LPE can hardly be observed. Also, we can find that the nonlinearities of the metal side (nonlinearity: 4.8% for Ti/Si, 3.9% for Co/Si, and 3.4% for Cu/Si) are also better than those of the semiconductor side (nonlinearity: 8.3% for Ti/Si, 6.2% for Co/Si, and 5.8% for Cu/Si). As we know, in judging whether a PSD works well, the two main criteria are the linearity and sensitivity. Therefore, these results indicate the metal side LPEs are competent in novel PSDs devices.

## 3. Band Model of LPE

By far, the well accepted models on LPE are so called Dember Effect [23] and PN junction mechanism [24]. Though these models can explain some simple LPE phenomena, they are incapable of explaining our experimental results in many aspects. To fully understand this metal side LPE, we therefore establish a new model based on the energy band in the MS structure. With this model, we cannot only quantitatively explain why metal side LPE can be better than semiconductor side LPE, but also give some crucial factors which determine the metal side LPE.

Generally, when a metal film is attached to the semiconductor, a schottky potential will exist in the MS structure in order to correlate two Fermi levels which we define as ${E}_{F0}$. However, when a laser is nonuniformly incident onto the structure, as shown in Fig. 3
, the equilibrium state is broken and the electrons in the valence band at light position (position 1 in Fig. 3) will be exited to the conduction band, the number of which we defined as $n(0)$. Soon these electrons will transit to the metal film (position 1’) where the electrons can easily transmit, the number of which we defined as $N(0)$. A short time after that, these $N(0)$ electrons in the metal film will spread toward two sides (position 2’ and 3′) according to the diffusion equation ${D}_{m}\frac{{d}^{2}N(r)}{d{r}^{2}}=\frac{N(r)}{{\tau}_{m}}$. Thus the distribution of the number of electrons in the metal film can be calculated as$N(r)=N(0)\mathrm{exp}(-\frac{r}{{\lambda}_{m}})$, in which *r* is the distance from light spot position and ${\lambda}_{m}$ is the electron diffusion length in the metal film. To finish a circulation, these light-induced electrons in the metal will transit back to the semiconductor at non-illumination position (position 2 and 3), the number of which we define as $n(r)$, and then go back to their starting position (position 1). If a light keeps illuminating, the circulation will continue and a stable photovoltage distribution can thus be formed in the metal film. Please note the reason why we don’t discuss the holes motion here is that the diffusion length of the holes in the semiconductor side is negligibly small, and meaningless in the metal side.

Using the diffusion length equation in bulk semiconductor, the electron diffusion length in the metal film can be similarly written as

Here ${D}_{m}=\frac{{k}_{B}T}{{N}_{m}{q}^{2}{\rho}_{m}}$ (according to the Einstein relation) is the diffusion constant in the metal, in which ${\rho}_{m}$ is the resistivity and ${N}_{m}=\frac{8\pi}{3}{(\frac{2m{E}_{F0}}{{\hslash}^{2}})}^{\frac{3}{2}}$ is the density of electrons in the metal film at equilibrium state. ${\tau}_{m}$ here is the life time of non-equilibrium electrons in the metal film. Interestingly, as a crucial attribute, the metal film state ${\lambda}_{m}$ has never been discussed in any previous works. This is because we used to treat the ${\lambda}_{m}$ in thin film state as that in bulk state. In fact, ${\lambda}_{m}$ is of significance only in case of thin film state and meaningless in bulk state. In the bulk state, the ${\lambda}_{m}$ is always infinite, which results in an equipotential surface, no potential difference can be observed. But in the thin film state, the situation is quite different, the metal surface is not again equipotential due to the limited diffusion length ${\lambda}_{m}$. This will result in a potential gradient on the surface. Obviously, this is the root of the LPE phenomenon in the metal side. The metal side LPE has a great bearing on ${\lambda}_{m}$, and ${\lambda}_{m}$ depends on thickness of metal film. This means metal film thickness directly determine the metal side LPE in a given MS structure. Fortunately, the ${\lambda}_{m}$ at different metal thickness can be easily obtained by experimental method (it will be discussed later).

Figure 4 is the schematic energy band profile in MS structure illuminated by a light. We can clearly see that the Fermi levels at four typical positions (position 1, 1’, 2, 2’) are different due to the light illumination, in which the electrons will move towards the lower Fermi levels. Thus the metal side LPV can be obtained by calculating the difference of Fermi level between position 2’ (A) and 3′ (B) in Fig. 3.

Here${K}_{m}=\frac{1}{4\pi q}{E}_{F0}^{-\frac{1}{2}}{(\frac{{\hslash}^{2}}{2m})}^{\frac{3}{2}}$, $L=\frac{\left|AB\right|}{2}$ is the half distance between A and B, and x is the light position, as shown in Fig. 3.

When the light spot moves outside the region between contact A and B (for example $x>L$), the LPV will decreases exponentially with *x* and can be written as$LP{V}_{m}={K}_{m}N(0)\mathrm{exp}(-\frac{x-L}{{\lambda}_{m}})$. By measuring the relationship between LPV and *x* from experimental curves shown in Fig. 2(a), the electron diffusion length ${\lambda}_{m}$ (which is the exponential coefficient) can be obtained. Actually, this provides a method to detect electron diffusion length in the metal film. Obviously, in the experiments as shown in Fig. 2(a), we easily obtain that ${\lambda}_{m}$ = 2.8 mm for Ti/Si, ${\lambda}_{m}$ = 3.1 mm for Co/Si and ${\lambda}_{m}$ = 3.4 mm for Cu/Si. Please note, ${\lambda}_{m}$ will increase rapidly with the increase of the metal thickness, which results in shorting effect in the metal. This is why the LPE appears obvious in the metal film only at the thickness around several nanometers.

When the light spot moves back and forth inside the region between contacts A and B ($-L<x<L$), the LPV is$LP{V}_{m}={K}_{m}N(0)[\mathrm{exp}(-\frac{L-x}{{\lambda}_{m}})-\mathrm{exp}(-\frac{L+x}{{\lambda}_{m}})]$. If light spot position satisfy $\left|x\right|<<{\lambda}_{m}$(In fact, this condition can be easily met. For example, in our experiment,$\left|x\right|\le L=1.6mm<{\lambda}_{m}$, as shown in Fig. 2(a)), the $LP{V}_{m}$ can be idealized as

Similarly, the lateral photovoltage in the semiconductor side can be also obtained by calculating the difference of Fermi level between position 2 and 3 in Fig. 3.

Here${K}_{s}=\frac{{k}_{B}T}{{n}_{0}}$, in which ${\lambda}_{s}$ is the electron diffusion length in the semiconductor and ${n}_{0}$ is the number of electrons in the conduction band due to temperature fluctuation. Similarly, we can also get ${\lambda}_{s}$(Ti/Si) = 1.9 mm, ${\lambda}_{s}$(Co/Si) = 2.3 mm and ${\lambda}_{s}$(Cu/Si) = 2.5 mm from Fig. 2(b).

## 4. Superiority of nonlinearity of metal side over semiconductor side

Nonlinearity of metal side LPE strongly depends on the distance of two contacts. It deteriorates in condition of $L>{\lambda}_{m}$, as shown in Fig. 5(a)
. This is because, in this case, precondition $\left|x\right|<<{\lambda}_{m}$ of Eq. (3) is no longer satisfied for the whole region between A and B, then the lateral photovoltage is no longer linear with the light spot position. The perfect linearity can only be achieved in the case of short contacts’ distance. Ignoring error of measurement, the nonlinearity mainly originates from inherent nonlinear result caused by the long contacts’ distance. For a fixed *L*, the nonlinearity ${\delta}_{m}$ is also fixed and can be obtained by simply comparing the LPV with the idealized LPV, as shown in Fig. 5(b).

Similarly, the nonlinearity of LPE in the semiconductor side can be written as

For a fixed *L*, a crucial factor that influences the nonlinearity is *λ* which depends greatly on the material properties. According to Eq. (5) and Eq. (6), a long diffusion length will lead to a high linearity. We have known, in some cases, the electron in metal side possesses a longer *λ* than that in the semiconductor side. This is why the linearity of LPE in the metal side is better than that in the semiconductor side, as shown in Fig. 2. However, we do not expect an infinite diffusion length in the metal because of the above-mentioned shorting effect. Therefore, a proper diffusion length determined by the film thickness is important for metal side LPE. To substitute ${\lambda}_{m}$(Ti/Si) = 2.8 mm, ${\lambda}_{m}$(Co/Si) = 3.1 mm, ${\lambda}_{m}$(Cu/Si) = 3.4 mm and *L* = 1.6 mm into Eq. (5), we can easily get that δ_{m}(Ti/Si) = 4.1%, δ_{m}(Co/Si) = 3.4%, and δ_{m}(Cu/Si) = 2.9%. Also, if we substitute ${\lambda}_{s}$(Ti/Si) = 1.9 mm, ${\lambda}_{s}$(Co/Si) = 2.3 mm, ${\lambda}_{s}$(Cu/Si) = 2.9 mm and *L* = 1.6 mm into Eq. (6), we can easily get that δ_{s}(Ti/Si) = 8.9%, δ_{s}(Co/Si) = 6.1%, and δ_{s}(Cu/Si) = 5.2%. Comparing these calculated results with experimental results shown in Fig. 2, we can find that they are well consistent with each other.

## 5. Optimum contacts’ distance of metal side LPE

Equation (5) clears up a long standing issue about the relationship between linearity and contacts’ distance. Obviously, the linearity deteriorates when two contacts’ distance 2L is increased to some extent, which is consistent with the experimental results shown in Fig. 5(c). In this case, ie L becomes long enough, the nonlinearity less than a given δ_{0} can only be kept in a relatively small central area. We define the length of this area with a nonlinearity less than δ_{0} as R(L) (acceptable region), as shown in Fig. 5(b). To evaluate the linearity in whole region of 2L (R(L) is always less than 2L), we define a linear rate$\eta =\frac{R(L)}{2L}$.We can clearly see from Fig. 5(d) that the linear rate will become worse when the contacts’ distance is increased (here we suppose the acceptable nonlinearity δ_{0} is 5%). Therefore we can define an optimum contacts’ distance 2L_{opt} as the longest distance of two contacts within which the linear rate keeps $\eta =1$. This means the optimum distance of two contacts is the biggest linear region within which the nonlinearity is less than δ_{0}. We can easily find from Fig. 5(d) that the optimum distance of two contacts in our experiment is 3.2 mm. Also, we can obtain the theoretical result of optimum distance of two contacts by deducing the equation of$2{L}_{opt}=R({L}_{opt})$. This equation can be established by simply replacing δ with δ_{0} in Eq. (5). Thus the L_{opt} can be written as

Clearly, the optimum distance of two contacts in metal side LPE is determined by the electron diffusion length in the film and the acceptable nonlinearity.

## 6. Superiority of sensitivity of metal side over semiconductor side

From Eq. (3) and Eq. (4), the sensitivity in the metal side and semiconductor side can be respectively written as

We can clearly see from Eq. (8) and Eq. (9) that a small L leads to a high sensitivity. To validate this mechanism, we compare the theoretical result according to Eq. (8) with our experimental result, as shown in Fig. 5(c), and find they are totally consistent with each other.

In order to make a comparison of sensitivity between metal side and semiconductor side, we compared Eq. (8) with Eq. (9) and obtain

Here$C=\frac{{n}_{0}{\lambda}_{s}}{4\pi q{k}_{B}}{E}_{{F}_{0}}^{-\frac{1}{2}}{(\frac{{\hslash}^{2}}{2m})}^{\frac{3}{2}}$. Obviously, the ratio of sensitivities in two sides depends on several physical parameters. For a given MS structure, this ratio mainly depends on the ${\lambda}_{m}$ and T. That is to say the metal film thickness is crucial factor in determining the magnitude of metal side LPE because ${\lambda}_{m}$ depends on film thickness. So it is very likely that the metal side LPE to surpass the semiconductor side LPE if we choose a suitable metal and control the film thickness within a proper range. This again supports our foregoing analysis. Interestingly, the temperature influences the LPE and reveals metal side LPE could behave more effectively than semiconductor side LPE in low temperature.

## 7. Crucial metal factors to the metal side LPE

In fact, the metal side sensitivity has a bearing on the properties of metal we used. Substituting Eq. (1) into Eq. (8), the sensitivity of metal side LPE can be written as

According to Eq. (11), we can clearly see that the resistivity and the Fermi level are the two crucial factors to the metal side LPE. The metal with higher resistivity and higher Fermi level can produce a higher sensitivity. Obviously, for the control metals of Ti, Co and Cu, Ti/Si presents the highest sensitivity while Cu/Si presents the lowest sensitivity. This is because Ti has the highest resistivity while Cu has the lowest resistivity as presented in Fig. 1. This result is totally consistent with the experimental result shown in Fig. 2(a). Interestingly, our result that higher resistivity metal film can obtain larger LPV is quite similar to the reported result that substrate with higher resistivity can obtain larger LPV [25].

## 8. Thickness effect on metal side LPE

To further investigate the thickness effect of metal film on LPV in MS structure, we also measured the LPVs with different Ti thickness in Ti/Si structures, as shown in Fig. 6(a) . We can clearly see that the position sensitivity of LPV in Ti/Si structure will decrease when the thickness of Ti is away from the optimum value of 6.2 nm. The thickness effect can be explained by the above diffusion model. We have clearly presented the relationship between resistivity and electron diffusion length in Eq. (1). Therefore, as shown in Fig. 6(b), if the metal film is very thick, then the electrons can easily diffuse from the light spot position toward two contacts because of the small resistivity, thus the density of electrons at two contacts are both high, resulting in a small difference of metallic potential between them, ie a small LPV. Similarly, if the metal film is very thin, the electrons can hardly diffuse because of the large resistivity, thus the density of electrons at two contacts are both low, also resulting a small difference of metallic potential between them, ie a small LPV. Therefore, in order to obtain a large difference of metallic potential between two contacts which is necessary for a large LPV in metal side, an appropriate metal thickness is crucial.

Based on the foregoing analyses, a quantitative explanation of the thickness effect can be easily given. Suppose the electrons diffusion length is proportional to the metal film thickness: then it can be written as ${\lambda}_{m}=\alpha ({d}_{m}-{d}_{0})$, where *α* is a proportional coefficient and ${d}_{0}$ is the threshold thickness. Thus from Eq. (8), the position sensitivity of metal side LPV can be written as

This result is well consistent with the experimental result, as shown in Fig. 6(a).

## 9. Conclusions

To summarize, an obvious LPE with both large sensitivity and good linearity in nano-scaled metal films of MS structure is interpreted mechanically and proved experimentally. Compared with previous LPE mechanism, this work has cleared up many features of metal side LPE and manifested some natural superiorities of metal side LPE over that of semiconductor side. We believe this work will trigger a wide interest in the study of metal-side LPE because the LPE merging with the metal’s properties can potentially add new functionalities to the conventional LPE.

## Acknowledgments

We acknowledge the financial support of National Nature Science Foundation (grant numbers 60776035 and 60378028) and support of National Minister of Education Program for Changjiang Scholars and Innovative Research Team in University (PCSIRT).

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