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Multifunctional high-performance position sensitive detector based on a Sb2Se3-nanorod/CdS core-shell heterojunction

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Abstract

Sb2Se3 exhibits fascinating optical and electrical properties owing to its unique one-dimensional crystal structure. In this study, a Sb2Se3-nanorod/CdS core-shell heterostructure was successfully constructed, and the lateral photovoltaic effect (LPE), as well as the lateral photocurrent and photoresistance effects, were first studied. The measurements indicate that this heterojunction exhibits excellent lateral photoelectric performance in a broad range of 405-1064 nm with the best position sensitivities (PSs) of 525.9 mV/mm, 79.1 µA/mm, and 25.6 kΩ/mm for the lateral photovoltage, photocurrent, and photoresistance, respectively, while the nonlinearity is maintained below 7%, demonstrating its great potential in a novel high-performance multifunctional position sensitive detector (PSD). Moreover, this PSD could work well at different frequencies with good stability and repeatability, and the rise and fall times were deduced to be 48 and 180 µs, respectively. Besides, large linear working distances are achieved in this heterojunction PSD, and the PS can still reach 75.5 mV/mm even at an ultra-large working distance of 9 mm. These outstanding performances can be attributed to the high-quality Sb2Se3 nanorod arrays and the fast charge-carrier separation and transport properties of this core-shell heterojunction. This study provides important ideas for developing high-performance, broadband, large working distances, and ultrafast multifunctional PSDs based on the new core-shell heterostructure.

© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

1. Introduction

A position-sensitive detector (PSD), which is a vital non-contact sensor, is based on the lateral photovoltaic effect (LPE), which was first discovered by Schottky in 1930 and then promoted by Wallmark and other researchers [1,2]. As the lateral photovoltage (LPV) generated in the LPE varies linearly with the laser position with a high resolution of position determination and excellent sensitivity of light sensing, PSD has been demonstrated to have great potential applications in motion tracking, precision machining, vibration monitoring, angle determination, and laser radar tracking [3]. Therefore, they have attracted increasing attention and have been extensively investigated. Various material configurations and strategies have been proposed and exploited for broadband high-performance PSDs [48]. However, from previous results, most PSDs are designed based on traditional semiconductors, and the position sensitivities are still very low. In particular, with the increasing demand for low power consumption, weak signal detection, and long working distances, the poor sensitivity of these PSDs has become a bottleneck for practical applications. Therefore, novel materials or structures and effective working mechanisms are urgently required.

Recently, Sb2Se3 has been considered an ideal semiconductor owing to its suitable bandgap (1.1-1.3 eV), high absorption coefficient (>105 cm-1), low toxicity, and earth abundance [9]. In addition, owing to the special one-dimensional ribbon-like crystal structure, the theoretical and experimental results have demonstrated that carrier transport is more favorable in the [001] direction, resulting in a longer diffusion length than those in other directions [10]. Therefore, the [001]-oriented Sb2Se3 structures are expected to achieve tempting photoresponse performance, which has been verified by a record high power conversion efficiency of 9.2% in a [001]-oriented Sb2Se3 nanorod array solar cell with a typical Sb2Se3/CdS structure [11]. Notably, the working principle of the solar cell is extremely beneficial to that of the PSD, as the efficient longitudinal separation and transport of the photogenerated carriers is the fundamental prerequisite of the LPE. Therefore, the Sb2Se3 nanorod structure should exhibit a large LPE response and show great potential in high-performance self-powered PSD. However, LPE has not been studied in this structure, and the related working mechanisms and modulation methods are still unknown. In addition, previous PSDs were primarily based on the LPV response, which may limit their application in various fields. Therefore, to promote the advantages of LPE and expand its operating range, it is imperative to develop multifunctional PSD with different detection capabilities. However, based on the working principle of the LPE, a lateral photocurrent (LPC) can also be induced between the two electrodes and exhibits a linear dependence on the laser position; therefore, that it is feasible to achieve an LPC-based PSD simultaneously [12]. In addition, the transverse diffused carriers in the LPE can be utilized to effectively tune the transport of intrinsic carriers in the conductive layer; thus, the lateral photoresistance (LPR), as well as the LPR-based PSD, is promising to be generated [13].

In this study, a Sb2Se3-nanorod/CdS core-shell heterojunction was developed as an LPV, LPC, and LPR-based multifunctional PSD. It is observed that this PSD shows excellent LPE performance in a broadband response range from visible to infrared, with PSs reaching 525.9 mV/mm, 79.1 µA/mm, and 25.6 KΩ/mm, and nonlinearities of no more than 6%, 4%, and 7% for LPV, LPC, and LPR, respectively. Moreover, the LPE response exhibits great stability and repeatability under the illumination of a pulsed laser with different frequencies, and the rise and fall times were deduced to be 48 and 180 µs, respectively. In addition, the working distance is also well evaluated in this heterojunction PSD, and a substantial PS of 75.5 mV/mm, along with excellent linearity, can still be obtained even at an ultra-large working distance of 9 mm. These outstanding performances can be attributed to the high-quality Sb2Se3 nanorod arrays and the fast charge-carrier separation and transport properties of this core-shell heterojunction.

2. Experimental methods

2.1. Sb2Se3-nanorod/CdS core-shell heterojunction preparation

The preparation process of the Sb2Se3-nanorod/CdS core-shell heterojunction is illustrated in Fig. 1. A 3.2 mm-thick commercially purchased soda-lime glass (SLG) (with ∼72% SiO2, ∼15% Na2O, and ∼9% CaO), which was cleaned with a soap solution and deionized water was used as the substrate. Similar to acetone, methanol, and other organic solutions, the soap solution can be used to clean oil and other pollutants at a relatively low cost. First, a Mo thin film was deposited on the SLG substrate by magnetron sputtering, and a selenization treatment was carried out at 620°C for 20 min. The Sb2Se3 nanorod arrays were then grown on Mo film by a close spaced sublimation (CSS) system with a thickness of approximately 1000 nm. Subsequently, a 60 nm-thick CdS layer, which is a typical n-type functional material in solar cell structures owing to its suitable bandgap and easy preparation method, was grown by chemical bath deposition at a bath temperature of 70 °C without annealing. As the Sb2Se3-nanorods were a vertically split structure, the CdS layer was not only present on top side but also penetrated into the space and conformally coated the sidewalls of the nanorods, forming a Sb2Se3-nanorod/CdS core-shell heterojunction [11]. Subsequently, the zinc oxide and indium tin oxide (ITO) layers were sputtered on the surface. Experimental details of the preparation process can be found in Refs. 11. Finally, two Ag point electrodes (diameter of ∼0.5 mm) were evaporated on the ITO layer by a thermal evaporation technique with distances of 0.5, 1.6, 3, 5, 7, and 9 mm, controlled by a steel shadow mask, and the conducting wires were connected on them by using silver paste.

 figure: Fig. 1.

Fig. 1. Preparation process illustration of the Sb2Se3-nanorod/CdS core-shell heterojunction

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2.2. Electrical and LPE response measurements

The current-voltage (I-V) curves were characterized using a Keithley SourceMeter(2400). The laser position-dependent LPV, LPC, and LPR curves were measured using home-built equipment including a Keithley SourceMeter (2400), three-dimensional linear electric motorized stage, and continuous-wave (CW) laser with wavelengths of 405, 532, 671, 808, and 1064 nm. Time-dependent LPV (LPV-t) curves were determined using a digital oscilloscope (Agilent DSO X 4022A) under illumination by a pulsed laser of different frequencies. All the measurements were performed at room temperature in the air.

3. Results and discussion

Figure 2(a) shows a schematic diagram of the longitudinal electrical measurement of the Sb2Se3-nanorod/CdS core-shell heterojunction under illumination by a nonpoint laser with a diameter of ∼1.0 mm. The distinct rectification feature observed in the dark indicates that a good p-n junction was produced in this heterojunction, as shown in Fig. 2(b). In addition, there is a substantial photoresponse under illumination by a 671 nm laser, and the photocurrent increases with the laser power. As this is a solar cell structure, an open-circuit voltage between the top and bottom sides of the heterojunction is induced under illumination. This voltage, which represents the current down peak position, is dependent on the power density owing to the equilibrium processes of the photogenerated electron-hole pairs. Figure 2(c) shows the transverse I-V result between the two top electrodes. The normal linear behavior confirms the Ohmic relationship between the top electrodes and the ITO layer, and the resistance value of the ITO layer was determined to be ∼23 kΩ, nearly independent of the bias voltage. A typical LPV curve for the heterojunction is shown in Fig. 2(d). The valley position of the LPV corresponds to one electrode, and the peak position corresponds to the other electrode. When the laser sweeps across the two top electrodes from left to right, the LPV changes linearly with the laser position (x) (referring to the distance from the center of the two electrodes), which can be explained from the diffusion theory of the separated carriers with equation expressed as follows [5,6]:

$${\rm{LPV}}(x )= \kappa {N_{\rm{\lambda }}}\left[ {\exp \left( { - \frac{{|{x - L} |}}{{{l_0}}}} \right) - \exp \left( { - \frac{{|{x + L} |}}{{{l_0}}}} \right)} \right]$$
where κ, L, Nλ, and l0 represent the constant coefficient, half-distance of the two electrodes, number of separated electrons, and electron diffusion length, respectively. When the laser moved outside the region of the electrodes, the LPV turned in the reverse direction. For a PSD, the effective working region is from one electrode to another. Based on Eq. (1), the LPV curve can be well fitted (solid red line in Fig. 2(d)), which confirms the validity of the theoretical diffusion model of the LPE. In particular, when l0 is significantly larger than L, Eq. (1) can be simplified as [5,6]:
$${\rm{LPV}}(x )= \frac{{2\kappa {N_{\rm{\lambda }}}}}{{{l_0}}}\exp \left( { - \frac{L}{{{l_0}}}} \right)x{\rm{\;\;}}({ - L \le x \le L} )$$

 figure: Fig. 2.

Fig. 2. Schematic diagram of the I-V measurement in the Sb2Se3-nanorod/CdS core-shell heterojunction. (b) Longitudinal I-V curves under illumination of different powers. (c) The transverse I-V curve and the extracted R results. (d) A typical LPV curve as a function of the laser position at a 0.7 mW laser power.

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The LPV is linearly proportional to the laser position, demonstrating the great potential application of this heterojunction in PSD.

The measurement diagram of the LPV in the Sb2Se3-nanorod/CdS core-shell heterojunction is presented in Fig. 3(a). When the laser is vertically irradiated on the surface of the ITO, the absorption in the photoactive layer of the Sb2Se3 nanorods could generate electron-hole pairs. Subsequently, these carriers are separated by the built-in interface field with holes sweeping into the Mo layer and electrons driving into the ITO layer. Under the force of the concentration gradient, the electrons accumulated around the illumination position diffused to the non-illuminated area and were collected by the two Ag electrodes. Generally, the number of electrons collected by the two electrodes differs because of their different distances from the illumination position. Therefore, when measured with a voltmeter between the two top electrodes, an LPV can be obtained. Figure 3(b) shows the laser position-dependent LPV curves under the illumination of a 671 nm laser with different powers ranging from 0.005 to 15 mW. The LPV response improved substantially with laser power. To evaluate the performance of the PSD well, a key parameter is the position sensitivity (PS), which reflects the slope factor of the LPV curve. The PS under each laser power was deduced by linear fitting, as shown in Fig. 3(c). The PS increased rapidly from 31.4 mV/mm to 489.5 mV/mm when the laser power changed from 0.005 to 1 mW and then slowly increased to a near-saturated value of approximately 525.9 mV/mm. This is because, in a low laser power regime, more electron-hole pairs can be generated at a larger laser power, and these carriers can be easily separated by the built-in field. Therefore, Nλ increases significantly, resulting in a significant improvement of the PS [8]. However, as the laser power increases to a high-power regime, although there are a large number of photogenerated carriers, these carriers cannot be effectively separated by the built-in field owing to the increased recombination rate [14]. Some separated carriers can also be easily annihilated during transverse diffusion. Therefore, the total number of separated electrons does not always increase but tends to saturate. However, the LPV response does not remain constant in the saturated power regime but may fluctuate slightly owing to laser instability, temperature rise of the device under long-time large-power illumination, and other factors, such as the decrease at 15 mW, as shown in Fig. 3(b). In addition, nonlinearity, which represents the deviation of the experimental results from the ideal linear curve, is another key figure of merit of a PSD and can be deduced by calculating the sum of their mean square deviations, with the equation as follows [15]:

$${\rm{Nonlinearity\;}}({\rm{\%}} )= \frac{{2 \times \sqrt {\left[ {\mathop \sum \nolimits_{i = 1}^n {{({{\rm{LP}}{{\rm{V}}_i} - {\rm{LPV}}_i^l} )}^2}} \right]/n} }}{{2L}} \times 100{\rm{\%}}$$
where n is the number of measured points and LPVi and LPVil represent the measured and linearly fitted LPV values by Eq. (2) at point i, respectively. Based on Eq. (3), the nonlinearities were calculated and summarized in the inset of Fig. 3(c). The nonlinearity of the LPV curve remains below 6% over the entire laser power range, which is far less than the requirement of a maximum nonlinearity of 15% for a qualified device [15]. This demonstrates the high measurement accuracy of this Sb2Se3-nanorod/CdS core-shell heterojunction PSD in determining the position signal.

 figure: Fig. 3.

Fig. 3. (a) LPV measurement diagram of the Sb2Se3-nanorod/CdS core-shell heterojunction. (b) Laser position-dependent LPV curves under illumination of a 671 nm laser at different laser powers. (c) Extracted PSs and nonlinearities (inset) as a function of the laser power. (d) Laser position-dependent LPV curves under illumination of different lasers at 0.7 mW. (e) Extracted PSs as a function of the laser wavelength. (f) The extracted PSs as a function of laser power for different lasers.

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To evaluate the response range, the laser-position-dependent LPV curves were also measured under several lasers ranging from visible to infrared, including 405, 532, 671, 808, and 1064 nm, with the typical results of a 0.7 mW power illumination plotted in Fig. 3(d). Good linear behavior can be observed in all the LPV curves, and the LPE response is strongly dependent on the laser wavelength, which can be directly observed from the extracted PS results, as shown in Fig. 3(e). The PS increases from 340.5 mV/mm to a maximum of 469.3 mV/mm with the laser wavelength increasing from 405 to 671 nm and then begins to decay gradually to a minimum of 147.7 mV/mm when the laser wavelength reaches 1064 nm, which may result from the laser wavelength-dependent external quantum efficiency of this heterojunction [11]. In addition, the LPV curves of all these lasers were measured under illumination with different laser powers, with the extracted PSs shown in Fig. 3(f). Similar to the 671 nm laser, the PS of each laser increased gradually to saturate with an increase in the laser power, and the wavelength dependency of the PS remained within the entire laser power range. It is worth noting that not only is the best PS of 525.9 mV/mm at 671 nm much larger than that in the other structure systems [48], but also the relatively lower saturated PS of 436.8 mV/mm at 1064 nm is comparable to the best results reported so far [1620], as shown in Table 1, indicating the great potential of this heterojunction in high-performance broadband PSD, especially in the infrared range.

Tables Icon

Table 1. Performance comparisons of PSDs with different structures

Considering the lateral diffusion of separated carriers, an LPC can also be induced between the two electrodes. When the voltmeter in the LPV equipment is replaced with an ammeter, an LPC can be obtained, as shown in Fig. 4(a). The laser position-dependent LPC curves measured under illumination by a 671 nm laser at different laser powers are shown in Fig. 4(b). The LPC response increased gradually with laser power and showed a good linear relationship with the laser position. To evaluate the sensitivity of this heterojunction as an LPC-based PSD, PSs were extracted from the LPC curves and are summarized in Fig. 4(c). Similar to the LPV response, here the PS also improves quickly from 2.6 to 42.9 µA/mm with the laser power increasing from 0.005 to 1 mW, and then increases slowly to a maximum of 79.1 µA/mm when the laser reaches 15 mW. In addition, the nonlinearity of the LPC curve at each power was calculated, as shown in the inset of Fig. 3(c). The nonlinearity was less than 4% over the entire measurement range, indicating the exceptional LPC response of this heterojunction. Moreover, the LPC responses to different laser wavelengths were determined, with the LPC curves under illumination of 405, 532, 671, 808, and 1064 nm lasers at 0.7 mW, as shown in Fig. 4(d). A good linear relationship between the LPC and laser position was maintained within the illumination wavelength range, and the LPC response was also strongly dependent on the laser wavelength. The extracted PS increases gradually from 19.3 to 39.6 µA/mm with the laser wavelength increasing from 405 to 671 nm and then starts to decrease and reduces to 35.4 and 7.4 µA/mm at 808 and 1064 nm, respectively, which shows the same regularity as the LPV, as given in Fig. 4(d). In addition, the LPC responses to different laser powers were well studied under the illumination of these lasers, with the laser-power-dependent PSs illustrated in Fig. 4(f). When the laser power is increased from 0.005 mW to 15 mW, the PS shows a similar increasing tendency for different lasers and maintains the same wavelength dependency, which can also be attributed to the wavelength-dependent external quantum efficiency.

 figure: Fig. 4.

Fig. 4. (a) LPC measurement diagram of the Sb2Se3-nanorod/CdS core-shell heterojunction. (b) Laser position-dependent LPC curves under illumination of a 671 nm laser at different laser powers. (c) Extracted PSs and nonlinearities (inset) as a function of the laser power. (d) Laser position-dependent LPC curves under illumination of different lasers at 0.7 mW. (e) Extracted PSs as a function of the laser wavelength. (f) The extracted PSs as a function of laser power for different lasers.

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Because of the difference in the carrier concentration gradient between the illuminated and non-illuminated regions, the LPV and LPC can be obtained, and the resistance of the device is regularly adjusted by their scattering to the drift intrinsic carriers in the ITO layer. Therefore, LPR is expected to be induced when an external bias is added to the two electrodes and measured with a two-wire method, with the schematic diagram of the LPR measurement, as shown in Fig. 5(a). Under an applied bias voltage, the current flows directionally between the two electrodes, and the movement of the drift electrons on both sides of the laser position is enhanced and weakened owing to the reverse and same directions as the transverse diffusion carriers, respectively. When the laser moves from one side to the other, the enhanced and weakened regions change accordingly, and the LPR response is also dependent on the laser position. Figure 5(b) shows the laser position-dependent LPR curves under illumination by a 671 nm laser at different laser powers and a 0.5 V bias voltage. The LPR curves exhibit very good linearities over the entire laser power range with a maximum nonlinearity of no more than 7%, as shown in the inset of Fig. 5(c). Moreover, the LPR response increases gradually with the laser power owing to the enhanced scattering effect under the condition of a larger number of diffused electrons, demonstrating the great potential of this heterojunction in LPR-based PSD. However, the entire LPR curve moves downward with an increase in the laser power, which may be attributed to the contribution of photogenerated electrons to the conductivity of the ITO layer [21]. The PS extracted as a function of laser power is summarized in Fig. 5(c). The PS increases almost linearly from 2.1 kΩ/mm to a maximum of 25.6 kΩ/mm as the laser power changes from 0.005 to 1 mW but starts to decrease slightly as the laser power increases again, which is more or less different from the LPV and LPC results. This can be mainly attributed to two reasons: one is the gradually decreased conductivity of the ITO layer induced by the photo-generated electrons so that the scattering effect induced by the diffusion electrons is correspondingly weakened [13,22]; the other is the complex drift and scattering mechanism around the electrodes, especially at a larger power, giving rise to bad linear behavior of the LPR curve, which can be indirectly reflected from the non-linearity results.

 figure: Fig. 5.

Fig. 5. (a) LPR measurement diagram of the Sb2Se3-nanorod/CdS core-shell heterojunction. (b) Laser position-dependent LPR curves under illumination of a 671 nm laser at different laser powers. (c) Extracted PSs and nonlinearities (inset) as a function of the laser power. (d) Laser position-dependent LPR curves under illumination of different lasers at 0.7 mW. (e) Extracted PSs as a function of the laser wavelength. (f) The extracted PSs as a function of laser power for different lasers.

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The LPR curves were also measured under the illumination of different lasers at 0.7 mW and 0.5 V bias voltage to detect the LPR responses to different laser wavelengths, and the results are shown in Fig. 5(d). The LPR curve exhibits good linearity over the measurement range of the laser wavelength, confirming the broadband response range of this multifunctional PSD. In addition, the LPR response shows the same wavelength dependence as that of the LPV and LPC, and the extracted PSs as a function of the laser wavelength are shown in Fig. 5(e). To better understand the wavelength effect, the LPR curves were also measured under illumination with different laser powers, and the laser-power-dependent PSs of different wavelengths are summarized in Fig. 5(f). For both 532 and 808 nm, the PS quickly reaches a maximum and then decreases slightly when the laser power is increased from 0.005 to 15 mW, which is similar to that at 671 nm. However, under the illumination of the 405 and 1064 nm lasers, the PS increases quickly and tends to a constant value, and nearly no decline processes of the PS can be observed at higher laser powers, which may result from the lower number of separated electrons owing to their lower external quantum efficiencies [11]. Besides, the LPR response is also related to the bias voltage. When under illumination of a constant power, the LPR response could improve with decreasing the bias voltage, and get reduced with an increase of the bias voltage, the phenomenon of which is similar to the result of changing the laser power under a constant bias voltage [22].

To better understand the LPC and LPR responses in the Sb2Se3-nanorod/CdS core-shell heterojunction, the band structure diagram and corresponding physical model were analyzed, as shown in Fig. 6. Under the illumination of a suitable laser, electron-hole pairs in the Sb2Se3 layer would be excited and separated into the ITO and Mo layers because of the built-in field, as shown in Fig. 6(a). The separated electrons gathering at the illumination position of the ITO layer could diffuse toward the non-illuminated regions, and the electron number density distribution equation Nλ(x) at a one-dimensional x0 position can be expressed as follows [21]:

$${N_\lambda }(x )= \left\{ {\begin{array}{{c}} {{N_\lambda }(0 ){\rm{exp}}\left( { - \frac{{{\rm{x - }}{{\rm{x}}_0}}}{{{l_0}}}} \right)({x < {x_0} \le L} )}\\ {{N_\lambda }(0 ){\rm{exp}}\left( { - \frac{{{x_0}{\rm{ - x}}}}{{{l_0}}}} \right)({ - L \le {x_0} < x} )} \end{array}} \right.$$
where -L and L represent the left and right positions, respectively, and Nλ(0) is the electron number density at the laser position. The electron numbers collected by the two electrodes are dependent on their distance from the laser position. Therefore, when a voltmeter is connected between the two electrodes (Fig. 6(b)), an LPV can be induced because of the different numbers of collected electrons, as described in Eq. (1).

 figure: Fig. 6.

Fig. 6. (a) Band alignment diagram of the Sb2Se3-nanorod/CdS core-shell heterojunction. The working principle diagrams of the (b) LPV, (c) LPC, and (d) LPR measurements.

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In addition, diffusion currents can also form during the lateral diffusion of the electrons, which can be expressed as $- \frac{{d({{N_\lambda }(x )} )e}}{{dx}}$, and $\frac{{d({{N_\lambda }(x )} )e}}{{dx}}$ (where e represents the electron quantity) in the left and right electrodes of the laser position, respectively. Based on Eq. (4), the LPC between the two electrodes is deduced and written as follows [12]:

$${\rm{LPC}}\left( x \right) = \frac{{{N_\lambda }\left( 0 \right)e}}{{{l_0}}}\left[ {\exp \left( { - \frac{{\left| {L - x} \right|}}{{{l_0}}}} \right) - \exp \left( { - \frac{{\left| {L + x} \right|}}{{{l_0}}}} \right)} \right]\,\left( { - L \le x \le L} \right)$$

Therefore, when an ammeter is added to the two electrodes, an LPC is generated, as shown in Fig. 6(c). Similar to Eq. (1), Eq. (5) can also be simplified under the premise of ${l_0} \gg L$ as follows [12]:

$$LPC(x )= \frac{{2{N_\lambda }(0 )x}}{{{l_0}^2}}\exp \left( { - \frac{L}{{{l_0}}}} \right)x\;\;({ - L \le x \le L} )$$

A linear relationship can also be observed between the LPC and laser position x, confirming its potential in developing an LPC-based PSD.

For both LPV and LPC measurements, there was no external bias. In contrast, when a bias voltage is applied to the two electrodes, an additional drift current is produced, as shown in Fig. 6(d). Notably, in the left region of the illumination position, the diffusion electrons move in the same direction as the drift electrons, and the scattering effect is weakened, resulting in a decrease in layer resistance. However, in the right region of the illumination position, the diffusion electrons move in the opposite direction to the drift electrons, and the scattering effect is enhanced, increasing the layer resistance. Assuming that the density of drift electrons is N0, and the transient carrier density is determined by both the diffusion and drift carriers, the effective electron number densities can be simply expressed as N(x)=N0 + Nλ(x) and N(x)=N0-Nλ(x) for the left and right regions, respectively. Therefore, the resistivity (ρ(x)) can be written as [13,21,22]:

$$\rho (x )= \left\{ {\begin{array}{{c}} {\frac{1}{{\left( {{N_0} + {N_\lambda }(0 )exp\left( { - \frac{{x - {x_0}}}{{{l_0}}}} \right)} \right)e{\mu_e}}}(x < {x_0} \le L)}\\ {\frac{1}{{\left( {{N_0} + {N_\lambda }(0 )exp\left( { - \frac{{{x_0} - x}}{{{l_0}}}} \right)} \right)e{\mu_e}}}( - L \le {x_0} < x)} \end{array}} \right.$$
where ${\mu _e}$ is electron mobility. Based on the relation of $R(x )= \mathop \smallint \nolimits_{ - L}^L \rho ({{x_0}} ){\rm{d}}{x_0}/S$ (where S is the cross-sectional area coefficient), the LPR is derived as [21,22]:
$${\rm{LPR}}(x )\approx \left( {{\rm{D}} + \frac{{2{N_\lambda }(0 )}}{{{N_0}^2e{\mu_e}{l_0}}}\exp \left( {\frac{{ - L}}{{{l_0}}}} \right)x} \right)/{\rm{S}}$$
where D=$\frac{{2L}}{{{N_0}e{\mu _e}}} - \frac{{{l_0}}}{{{N_0}e{\mu _e}}}\ln \left( {1 - \frac{{N_\lambda^2(0 )}}{{N_0^2}}} \right)$. Similar to the LPV and LPC, the LPR can theoretically be linearly proportional to the laser position.

For the laser power and wavelength-dependent LPE response, it can be observed that the number of separated electrons is strongly dependent on both the laser power (P) and laser wavelength ($\lambda $) with the relation of ${N_\lambda }(0 )\approx \frac{{\eta P}}{{\hbar c}}\lambda $, where $\eta $ represents an external quantum efficiency coefficient, ${\hbar}$ represents the Planck constant, and c represents the velocity of light in a vacuum. In the low-power regime, the $\eta $ is thought to be constant, so that ${N_\lambda }(0 )$ increases nearly linearly with the laser power, resulting in a rapid improvement of the LPE response. However, the $\eta $ decays quickly in the large power regime owing to the increased recombination probability. Therefore, the ${N_\lambda }(0 )$ tends to remain constant. In addition, the $\eta $ is also dependent on the illumination wavelength [11]. When $\lambda $ changes from 405 to 671 nm, $\eta $ increases gradually, and then the Nλ (0) and LPE response, is enhanced accordingly. However, the $\eta $ starts to decrease as the $\lambda $ increases again, which could result in a reduction in Nλ(0) and the LPE response.

The response time, another important parameter of the PSD, was then evaluated in the Sb2Se3-nanorod/CdS core-shell heterojunction. Figure 7(a) shows the time-dependent LPV (LPV-t) curves under the illumination of a mechanical chopper modulated 671 nm continuous-wave laser at 5 mW with frequencies ranging from 10 to 400 Hz. From the previous results [17], it was suggested that the response time was not dependent on the laser position. The balanced LPV value at the laser on or off stage keeps nearly constant over the entire frequency range (Fig. 7(b)), indicating the good stability and excellent capability of this heterojunction PSD in detecting fast optical signals. Typical LPV-t curves at 10 and 400 Hz were amplified to obtain the response time, as shown in Fig. 7(c) and 7(d). The rise times are extracted to be 2.2 and 0.048 ms by evaluating the time interval of the LPV increasing from 10% to 90% of the maximum value, while the decay times are deduced to be 2.6 and 0.18 ms by determining the time interval decreasing from 90% to 10% of the maximum value. The response time decreases quickly with increasing frequency, as shown in Fig. 7(e), which can be attributed to the shorter optical switching time and high time resolution of the oscilloscope at a higher frequency. However, when the laser frequency increased again, the LPV amplitude started to decrease, indicating that the LPE response did not follow the optical signal well. Therefore, the best response time of this PSD should be about 0.048/0.18 ms at 400 Hz.

 figure: Fig. 7.

Fig. 7. (a) LPV-t curves of the Sb2Se3-nanorod/CdS core-shell heterojunction PSD at different frequencies. (b) Extracted maximum LPV and minimum LPV results as a function of the frequency. Typical magnified LPV-t curves at (c) 10 and (d) 400 Hz for determining the response times. (e) The corresponding frequency-dependent rise and fall times.

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Furthermore, a large PSD working distance is essential for practical applications. Then, the LPV response was studied under different contact distances of 0.5, 1.6, 3, 5, 7, and 9 mm, with the typical results under the illumination of a 671 nm laser at 0.7 mW, as shown in Fig. 8(a). It is observed that the linearity of the LPV curve is excellent when the contact distance is less than 3 mm and then worsens with an increase in the distance. There are two possible reasons for this phenomenon: one is the smaller electron diffusion length (l0). It has been demonstrated that the excellent linear relation in Eq. (2) can only be obtained on the premise of l0 >> L[4]. With an increase of the electrode distance, the L approaches or even exceeds the l0. At this moment, the separated holes have a large possibility of returning to recombine with the electrons, and can not be able to diffuse an enough distance to be collected by the two electrodes when illuminated in the central region. Therefore, the LPV is no longer linearly dependent on the laser position again. The other is the uneven surface of the heterojunction induced by the nanorod array structure. However, the nonlinearity is still less than 15% under the largest contact distance of 9 mm, which is much larger than the best working distance in most other systems reported presently [2326], indicating the large linear working range of this heterojunction. In addition, the LPV curves for different contact distances were measured under illumination with different laser powers, and the PS results are summarized in Fig. 8(b). The PS of each contact distance exhibited a similar increasing tendency with the laser power. However, there was a larger improvement in PS at a shorter contact distance. To clearly show the relationship between the PS and the contact distance, the saturated PS of each contact distance was extracted and plotted in Fig. 8(c). The PS decays exponentially from 525.9 mV/mm to 75.5 mV/mm as the contact distance increases from 0.5 to 9 mm, which is in accordance with Eq. (2) (LPV is exponentially proportional to L). It is worth noting that the minimum PS of 75.5 mV/mm at an ultra-large contact distance of 9 mm is much larger than that of most other heterostructures with very small contact distances [57,18,27,28], as shown in Table 1, indicating the potential of this heterojunction in large-area PSD. Finally, the response times of different contact distances were also characterized, with the LPV-t results at 10 Hz, as shown in Fig. 8(d). The LPE responses of different contact distances can all follow the pulse signals at low frequencies with the same LPV amplitudes as the corresponding results in Fig. 7(a). However, upon gradually increasing the frequency, the LPV amplitude starts to decrease for larger contact distances, indicating that the contact distance has an important effect on the working frequency range. Figure 8(e) shows the contact-distance-dependent response times. It is observed that the rise time increases from 0.048 ms to 0.56 ms, and the fall time rises from 0.18 ms to 1.1 ms with the contact distance increasing from 0.5 mm to 9 mm, which may result from the longer transverse diffusion time at a larger contact distance [17]. In addition, similar to the LPV, the LPC and LPR can work well at a very large contact distance of 9 mm with acceptable nonlinearities (<15%), as shown in Fig. 9.

 figure: Fig. 8.

Fig. 8. (a) Laser position-dependent LPV curves of different contact distances under illumination of a 671 nm laser at 0.7 mW. (b) The extracted PSs as a function of the laser power for different contact distances. (c) The best PSs as a function of the contact distance. (d) The LPV-t curves of different contact distances at 10 Hz. (e) The extracted rise and fall times as a function of the contact distance.

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 figure: Fig. 9.

Fig. 9. Laser position-dependent (a) LPC and (b) LPR curves of a 9 mm contact distance under illumination of a 671 nm laser at different laser powers.

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4. Conclusions

In conclusion, we studied the LPV, LPC, and LPR responses in a Sb2Se3-nanorod/CdS core-shell heterojunction and successfully developed it as a multifunctional PSD. It is observed that this PSD shows a broadband response range from visible to infrared and exhibits excellent LPE performances with PSs reaching 525.9 mV/mm, 79.1 µA/mm, and 25.6 KΩ/mm, and nonlinearities of 6, 4, and 7%, respectively. In addition, the response time and working distance were studied in this heterojunction PSD. An ultrafast optical response speed is obtained, with the rise and fall times of 48 and 180 µs, respectively, and a near-centimeter-level ultra-large working distance is achieved simultaneously. This work reveals the great application prospects of Sb2Se3-nanorod/CdS core-shell heterojunctions in high-performance, broadband, large working distances, and ultrafast LPE-based PSDs and also provides insight into other heterostructures in developing multifunctional PSDs.

Funding

National Natural Science Foundation of China (62175058, U20A20166, 11704094); Nature Science Foundation of Hebei Province (A2022201014, F2019201289); Science and Technology Plan Project of Hebei Province (216Z1703G); Education Commission of Hebei Province (ZD2019037).

Disclosures

The authors declare no conflicts of interest.

Data availability

The data underlying the results presented in this paper are not publicly available presently but may be obtained from the authors upon reasonable request.

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Data availability

The data underlying the results presented in this paper are not publicly available presently but may be obtained from the authors upon reasonable request.

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Figures (9)

Fig. 1.
Fig. 1. Preparation process illustration of the Sb2Se3-nanorod/CdS core-shell heterojunction
Fig. 2.
Fig. 2. Schematic diagram of the I-V measurement in the Sb2Se3-nanorod/CdS core-shell heterojunction. (b) Longitudinal I-V curves under illumination of different powers. (c) The transverse I-V curve and the extracted R results. (d) A typical LPV curve as a function of the laser position at a 0.7 mW laser power.
Fig. 3.
Fig. 3. (a) LPV measurement diagram of the Sb2Se3-nanorod/CdS core-shell heterojunction. (b) Laser position-dependent LPV curves under illumination of a 671 nm laser at different laser powers. (c) Extracted PSs and nonlinearities (inset) as a function of the laser power. (d) Laser position-dependent LPV curves under illumination of different lasers at 0.7 mW. (e) Extracted PSs as a function of the laser wavelength. (f) The extracted PSs as a function of laser power for different lasers.
Fig. 4.
Fig. 4. (a) LPC measurement diagram of the Sb2Se3-nanorod/CdS core-shell heterojunction. (b) Laser position-dependent LPC curves under illumination of a 671 nm laser at different laser powers. (c) Extracted PSs and nonlinearities (inset) as a function of the laser power. (d) Laser position-dependent LPC curves under illumination of different lasers at 0.7 mW. (e) Extracted PSs as a function of the laser wavelength. (f) The extracted PSs as a function of laser power for different lasers.
Fig. 5.
Fig. 5. (a) LPR measurement diagram of the Sb2Se3-nanorod/CdS core-shell heterojunction. (b) Laser position-dependent LPR curves under illumination of a 671 nm laser at different laser powers. (c) Extracted PSs and nonlinearities (inset) as a function of the laser power. (d) Laser position-dependent LPR curves under illumination of different lasers at 0.7 mW. (e) Extracted PSs as a function of the laser wavelength. (f) The extracted PSs as a function of laser power for different lasers.
Fig. 6.
Fig. 6. (a) Band alignment diagram of the Sb2Se3-nanorod/CdS core-shell heterojunction. The working principle diagrams of the (b) LPV, (c) LPC, and (d) LPR measurements.
Fig. 7.
Fig. 7. (a) LPV-t curves of the Sb2Se3-nanorod/CdS core-shell heterojunction PSD at different frequencies. (b) Extracted maximum LPV and minimum LPV results as a function of the frequency. Typical magnified LPV-t curves at (c) 10 and (d) 400 Hz for determining the response times. (e) The corresponding frequency-dependent rise and fall times.
Fig. 8.
Fig. 8. (a) Laser position-dependent LPV curves of different contact distances under illumination of a 671 nm laser at 0.7 mW. (b) The extracted PSs as a function of the laser power for different contact distances. (c) The best PSs as a function of the contact distance. (d) The LPV-t curves of different contact distances at 10 Hz. (e) The extracted rise and fall times as a function of the contact distance.
Fig. 9.
Fig. 9. Laser position-dependent (a) LPC and (b) LPR curves of a 9 mm contact distance under illumination of a 671 nm laser at different laser powers.

Tables (1)

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Table 1. Performance comparisons of PSDs with different structures

Equations (8)

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L P V ( x ) = κ N λ [ exp ( | x L | l 0 ) exp ( | x + L | l 0 ) ]
L P V ( x ) = 2 κ N λ l 0 exp ( L l 0 ) x ( L x L )
N o n l i n e a r i t y ( % ) = 2 × [ i = 1 n ( L P V i L P V i l ) 2 ] / n 2 L × 100 %
N λ ( x ) = { N λ ( 0 ) e x p ( x x 0 l 0 ) ( x < x 0 L ) N λ ( 0 ) e x p ( x 0 x l 0 ) ( L x 0 < x )
L P C ( x ) = N λ ( 0 ) e l 0 [ exp ( | L x | l 0 ) exp ( | L + x | l 0 ) ] ( L x L )
L P C ( x ) = 2 N λ ( 0 ) x l 0 2 exp ( L l 0 ) x ( L x L )
ρ ( x ) = { 1 ( N 0 + N λ ( 0 ) e x p ( x x 0 l 0 ) ) e μ e ( x < x 0 L ) 1 ( N 0 + N λ ( 0 ) e x p ( x 0 x l 0 ) ) e μ e ( L x 0 < x )
L P R ( x ) ( D + 2 N λ ( 0 ) N 0 2 e μ e l 0 exp ( L l 0 ) x ) / S
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