Short-wave infrared position-sensitive detector enabled by lateral diffusion of thermalized carriers in lead salts

The measurement of displacements,¹ angles,² frequencies,^3,4 and size and shapes^5,6 is important in modern metrology with broad applications including motion tracking,^7,8 pilotless aircraft,⁹ precision machining, and laser radars.^10–12 The position-sensitive detector (PSD) with a noncontact optical model is a central route to realize these measurements.^13–17 So far, the PSD designs are based on the lateral photovoltaic (LPV) effect^18–20 or segmented sensors.^21,22 The former utilizes the heterojunctions with built-in field to separate the optically excited electron–hole pairs. The carrier diffusion results in a space-dependent distribution of electrical signals. The lateral photovoltaic effect PSD gives the position information independent of laser beam shape, size, and intensity profile, and features better position resolution in the range of a few nm/ $Hz$ compared with segmented sensors.²³ However, the heterojunctions required in the LPV effect show slow response speed²⁴ due to its multi-physics process, complicated architectures, and narrow response waveband limited by the bandgap. The segmented PSD typically has four quadrants each of which is separated by a gap. The four-quadrant PSD is dominating the commercial market due to its fast response and large operation bandwidth. However, the gap in four-quadrant PSD^21,22 leads to very nonlinear intensity profile and, thus, the strong nonlinear position response if the laser spot is not fully centered.

In the optoelectronic conversion process, there are a type of carriers with energy higher than the band edge.²⁵ There are the so-called hot carriers, which are formed due to strong carrier–carriers scattering immediately after optical absorption. These carriers can have a temperature of several thousand kelvins^26,27 and carrier diffusion coefficient of a few thousand cm²/s.²⁸ The temperature gradient drives the diffusion of hot carriers toward the surroundings. This behavior inspires us that the PSD is possibly realized in the thermalized carriers-dominated photothermoelectric effect (PTE). Specifically, this kind of PSD should show a high-speed response due to high kinetic energy of thermalized carriers, broad response waveband through thermal effect, and simple device architecture. However, the hot carriers always decay within one hundred nanometers,^29,30 which restrict its position response range. Recently, the lead salts (such as PbS and PbSe), as a type of thermoelectric materials, have exhibited intriguing properties in PTE conversion. The single-crystalline thin film of these materials possesses distance transport of hot carriers as long as 558 nm and slow decay dynamics (nanoseconds scale) of thermalized carriers.^31,32 This raises the interesting questions of how long the photo-excited thermalized carriers could transport in lead salts thin film and whether they can be applied to PSD if they are long enough.

Herein, we report a short-wave infrared (SWIR), an essential optical communication waveband and atmosphere window, PSD based on the hot-carrier PTE effect in a single-crystalline thin film of lead salts. In combination with numerical simulation of two-temperature model (electron and lattice), the microscopy photovoltage measurements provide insight into the underlying physics of spatial-sensitive temperature distribution induced by focused laser excitation. The position-sensitive electrical signals are achieved in PbS micro-ribbon with two-pair electrodes through the hot-carrier Seebeck effect.³³ Thanks to the long transport length of photo-excited thermalized carriers, the ultrafast and broadband position sensing are, thus, realized in our PSD.

First, we apply the microscopy photovoltage setup [Fig. 1(a) and supplementary material Notes 2] to investigate the diffusion length of laser-excited carriers in lead salts. To fabricate lead salt devices, the PbSe and PbS single-crystalline thin films were grown on the SrTiO₃ substrate via chemical vapor deposition.³² The crystal quality of PbSe and PbS thin films with highly oriented (h00) planes is confirmed by x-ray diffraction (XRD) (Fig. S1). The two-terminal PbSe micro-ribbon devices with 5 nm Cr/150 nm Au electrodes are fabricated via lithography technology. Additional details on device fabrication and characterization can be found in Methods. The device used in our experiments [depicted in Fig. 1(b) and characterized in Fig. S2] has a channel length of 500 μm, a width of 80 μm, and a thickness of 594 nm.

The current–voltage (I–V) curves of PbSe and PbS micro-ribbon device exhibit excellent linearity across a wide voltage range (−3 to 3 V) as depicted in Fig. S3, indicating that the Au electrode is in good Ohmic contact with the device. The resistance value of the transport channel is ∼5 and 28.8 kΩ for PbSe and PbS, respectively. In addition, the microscopy photovoltage setup enables precise definition of position-dependent photovoltage (PV) by simultaneously identifying the reflectance and PV distribution. The incident 808 nm laser with internally modulated frequency is focused onto the PbSe micro-ribbon device, which is mounted onto a piezostage capable of moving the device with a 1 μm step. The PV signals are collected via a lock-in amplifier. The laser spot radius is about 4 μm (Fig. S4), significantly smaller than the channel size of the device. The results were obtained at a laser fluence of 16.7 mJ/mm² at room temperature. All the experiments were performed at zero voltage bias except specifically noted.

To gain insight into the PV generation principle, we analyze the position dependence of local response PV. As shown in Fig. 1(c), the PV signals cover almost the entire PbSe channel and is nearly centrosymmetric with respect to the channel center. The location of the electrodes (black dashed line) and the PbSe channel (green dashed line) are labeled through the reflectance image [Fig. 1(b)], and their interfaces can be inferred from the reflectance derivative. The open-circuit voltage (V_oc) vs position (x) is captured along the channel, indicated by the red line in Fig. 1(c). In Fig. 1(d), the V_oc is positive in the left side (x < 0) of the channel, and it rises rapidly with increasing x, reaching a maximum value of 0.56 mV. The peak of the V_oc appears at 35–50 μm away from the left electrode edge. The PV then decays exponentially and turns negative as laser moves toward the right side (x > 0) of the device, with a profile that is almost centro-symmetrical with positive V_oc [V_oc(x) ≈ −V_oc(−x)]. Finally, V_oc returns to 0 as the laser moves to another Au electrode. Moreover, to eliminate the impact of interface potential between the lead salt and the electrode, we performed PV mapping on non-local structure of another PbS device [Figs. 1(e) and 1(f)]. Consistent with the variation in V_oc-x observed in the local structure, |V_oc| exhibits an exponential increase near the probe position [Fig. 1(g)]. Additionally, the lateral transport of photogenerated carriers exhibits similar characteristics to those of local PV generation, and its V_oc demonstrates great symmetry.

Now we focus on the mechanism of the optoelectronic conversion process to interpret the V_oc characteristic in the lead salts device. The photoconductive and bolometric effect can be excluded first, as they necessitate an external bias. Assuming that the photovoltaic effect produces the V_oc, the photoexcited minority carriers are separated by the build-in field within the junction area (i.e., Schottky junction), leading to an anticipated location of the V_oc peaks at the electrode–PbSe interface. Regrettably, the fitting curve [black line in Fig. 1(d)] based on this hypothesis deviates significantly from the experimental data obtained. Consequently, we believe that the PTE effect, triggered by the localized light-induced temperature gradient,³⁴ is responsible for the V_oc observed instead. The giant PTE effect holds the potential to enhance the LPV effect. While minority carrier or temperature gradient-driven intrinsic carrier diffusion may be attributed in generating V_oc, their contribution is relatively minor due to the limited diffusion length of minority carriers and the slower response exhibited by intrinsic carriers driven by temperature gradients (to be discussed in more detail later).

In addition, the V_oc-x curve should satisfy the exponential decay as $V o c=P ( e − x λ + e − ( D − x ) λ)$⁠, where P is the power of laser beam irradiation on the device, λ is the length of non-equilibrium carrier diffusion, and D is the distance traveled along the channel. Both transverse and lateral devices are fitted, depicted by the red curves in Figs. 1(d) and 1(g), respectively. A transverse diffusion length as long as 47.8 μm is observed in the former case, equivalent to that of the implanted ion p-type PbSe single crystal (∼51.4 μm).³⁵ Moreover, the lateral diffusion exhibits a comparable scale of 11.8 μm, demonstrating close resemblance to the transverse device.

To understand the giant PTE effect and long carrier diffusion length in PbSe micro-ribbon, we perform the power density dependence of V_oc and temperature difference (ΔT) between two electrodes. The laser is focused on one point of the PbSe channel. The light-induced ΔT is deduced from a pair of T-type thermocouples. The detailed measurements of V_oc and ΔT are depicted in Fig. S5. The V_oc and ΔT are linearly dependently on 800 nm laser power. The ΔT increases from 0.6 to 1.1 K as the laser power density rises from 475.7 to 527.5 W/cm² [Fig. 2(a)]. The Seebeck coefficient S is 94 μV/K calculated through V_oc/ΔT, which is comparable with pervious reported PbSe nanowires.³⁶ In addition, considering the fast carrier–carrier interactions (femtoseconds scale) and carrier–phonon interactions (picosecond scale) after optical excitation, the carriers and phonons undergo thermalization, reaching a quasi-equilibrium state with temperatures surpassing that of the surroundings. As a result, a substantial internal temperature gradient arises, which effectively drives the diffusion of carriers toward the electrodes. Study of ultrafast carrier dynamics in PbSe reveals a slow cooling of thermalized carriers, leading a giant PV signal in leads salts PTE detector.³¹ To further elucidate the underlying factors contributing to the significant PV response, we apply the simulations to retrieve the system's temperature based on the two-temperature model (see the supplementary material). The increase in system temperature of quasi-stable state reaches more than 1.0 K [upper panel of Fig. 2(b)] considering the carriers–phonon coupling. The simulated temperatures (green dashed line) in Fig. 2(a) fits the experimental results well thanks to the electron–phonon coupling. However, without the electron–phonon coupling, the ΔT [down panel of Fig. 2(b)] produced only by phonon thermalization deviates severely from the experimental value by nearly an order of magnitude [black dashed line in Fig. 2(a)]. Therefore, the thermoelectric voltage is dominated by light-induced carriers thermalization rather than phonon thermalization.

Long-distance propagation of photo-excited carriers over long distances enables the design of SWIR PSDs. Our device is designed as a symmetrical T-shaped structure [Fig. 3(a)]. The photovoltage, detected by both sides of the remote probe [V₁ and V₂, Fig. 3(b)], can be regarded as a non-local voltage signal resulting primarily from the diffusion of thermalized carriers. The non-local voltage is determined by the temperature gradient (T_h → T_c) created by the thermalized carriers when the laser beam, with a wavelength of 808 nm, is focused on different lateral positions. We take measurement of the non-local response in each of the four points at specific distances from the probe, as shown in Fig. 3(b). Figure 3(c) shows a gradual decrease in the V_oc as the laser moves away from the electrode. However, the photoresponse cycles remain remarkably stable at all four locations. The photoresponse near the probe can reach up to 7 mV, while still maintaining a value of 0.4 mV at the far end.

Subsequently, the photoresponse at various wavelengths near position 2 is studied. The device exhibited the excellent responses at wavelengths ranging from 0.8 to 2.3 μm [Fig. 3(g)]. This spectral response range is much wider than that of current infrared positioners [PDP90A(Thorlabs), PDQ30C(Thorlabs), and C30845EH(Excelitas)] in the industry. Then, we analyzed the time response and find that the rise and fall times are ∼970 and ∼590 ns [Fig. 3(h)], respectively, where the rising and falling parts of the curves are defined as 10 and 90% of the stable values. Our results (Table I) indicated that this time response is superior to that of most of PSDs, including G/Ge (2.6 μs),³⁷ V-MoS₂/Si (6.9 μs),³⁸ and Ag₂Se/p-Si (3 μs).³⁹ In Fig. 3(d), the position of the target can be given by a pair of voltages (V₁, V₂) as depicted schematically. These voltages are obtained from intersection of two sets of temperature (voltage) contours. This approach differs from the conventional lateral photovoltaic effect based on p-n junction, in which photo-excited electrons and holes are separated by the built-in field before diffusing toward the low-density region. In our design, the high kinetic energy of the hot carriers is capitalized and rapid position response and broad spectra response are promised through the hot carrier Seebeck effect.

Now we perform the position-sensitive detection in a PbS device. In this PSD, the positioning range is 40 × 90 μm². A x–y coordinate with a polarization angle θ is plotted to help us to elucidate the question. The measured region is labeled by the red dashed square. The voltage distribution in x–y plane is shown in Fig. 3(e). The voltage distribution is observed to be uniform across the entire scanning region (18 × 37 μm²) as expected. To gain insight into this behavior, we extracted the voltages–distance relation at angles of 15°, 30°, 45°, 60°, and 75° as shown in Fig. 3(f). The voltages are independent of the angle θ while exponentially decays with distances, indicating the isotropic transport of thermalized carriers due to the identical crystal orientation and high crystal quality of the PbS thin film. This property is essential in enabling us to accurately determine the position.

To evaluate the position sensitivity of our PbS PSD, we performed linear fitting on the extraction line in Fig. 3(f). It is shown that the position sensitivity is 275.8 mV/mm, which was relatively high value compared to other position-sensitive sensors (refer to Table I). The positioning resolution is 45.8 nm/ $Hz$ according the ratio of noise at 1 Hz to position sensitivity (Fig. S6). The nonlinearity represents degree of linearity between the theoretical position (⁠ $x i A$⁠) and the actual measured position (⁠ $x i$⁠) of a conventional linear position sensor, which can be expressed by $∑ i = 1 N ( x i − x i A ) 2 ] / N L×100%$⁠, where L is the operating distance between two electrodes, which is chosen as the carrier diffusion length of lead salts thin film. N is the number of measuring points. We calculate that the nonlinearity of our devices is 13.42%, which is in line with the industry standard of 15%.¹³ 

Accurate trajectory tracking is of great significance in optical sensing applications. In this regard, we showcase an application of our device in the field of microscopic motion tracking [Fig. 4(a)]. As shown in Fig. 4(b), the device is plated with two electrodes on each end of a square PbS single crystal. The target is a moving infrared laser beam with a wavelength of 808 nm. The lens focuses the laser onto the upper electrode region, allowing the computer to simultaneously capture the V_oc of the paired electrodes located on either side of the PbS. The photovoltages of the left (V₁, red) and right (V₂, blue) are simultaneously recorded with focused laser scanning across the white dashed square region. Figure 4(c) displays the results obtained from scanning the entire area using a 1.97 mW laser, which was conducted as the initial step of our test. We then set a database according to Fig. 4(c) (and Fig. S7), which contains a series of normalized (V₁, V₂) with corresponding coordinate (x, y). As the target moves through space, a laser mounted on its surface scans the area enclosed by the white dashed square. This process generates a series of (V₁, V₂), which are recorded over time and presented in Fig. 4(d). By utilizing mapping relationships, the computer is capable of automatically converting the (V₁, V₂) into corresponding coordinate positions. This enables the accurate capture of the circular motion trajectory, as depicted in Fig. 4(e), which represents the real motion of the object. Correspondingly, the velocity [Fig. 4(f)] can be derived from Fig. 4(e). The uniform motion at y > 20 μm is well recorded, exemplifying the high spatial resolution. Therefore, we believe that the PbS PSD possesses the capability to track fast near-IR target trajectories.

In summary, we propose a SWIR PSD based on photo-excited thermalized carriers diffusion effect in the lead salts single crystalline thin film. By combining the numerical simulation of electron–phonon coupling, we found a long thermalized carriers diffusion length (47.8 μm) in a lead salts single crystal, which inspires us a unique design of PSD by collecting focused laser position-dependent diffusion carriers in the PbS thin film. By comparing with conventional PSD, the thermalized carriers-assisted PSD enables a broad spectral response, fast response speed, high position sensitivity, and simpler architecture. Furthermore, the microscopic motion tracking technology is developed based our thermalized carriers-assisted PSD, indicating the great potential of our PSD in areas, such as nano-robots, micro-localization, and laser collimation.