Abstract
Dynamic control of nonlinear signals is critical for a wide variety of optoelectronic applications, such as signal processing for optical computing. However, controlling nonlinear optical signals with large modulation strengths and nearperfect contrast remains a challenging problem due to intrinsic secondorder nonlinear coefficients via bulk or surface contributions. Here, via electrical control, we turn on and tune secondorder nonlinear coefficients in semiconducting CdS nanobelts from zero to up to 151 pm V^{−1}, a value higher than other intrinsic nonlinear coefficients in CdS. We also observe ultrahigh ON/OFF ratio of >10^{4} and modulation strengths ~200% V^{−1} of the nonlinear signal. The unusual nonlinear behavior, including superquadratic voltage and power dependence, is ascribed to the highfield domain, which can be further controlled by nearinfrared optical excitation and electrical gating. The ability to electrically control nonlinear optical signals in nanostructures can enable optoelectronic devices such as optical transistors and modulators for onchip integrated photonics.
Introduction
Interest in electrically controlled optical functionalities have been motivated by applications in linear and nonlinear optical systems^{1,2,3}, and for fundamental understanding of the electronic and structural symmetry and lightmatter interaction in materials^{4}. Two most commonly studied phenomena for controlling optical signals via applied electric fields are: electrooptical effect^{3} and electric fieldinduced secondharmonic generation (EFISH)^{5,6,7}. EFISH was first observed in a bulk calcite crystal in 1962^{6}, in which a strong electric field (F_{l}) was applied to break structural inversion symmetry and induce effective secondorder nonlinear coefficients \(\chi _{\rm ijk}^{\left( 2 \right)}\left( {2\omega ;\omega ,\omega ,0} \right)\) by interacting with thirdorder nonlinear coefficients \(\chi _{\rm ijkl}^{\left( 3 \right)}\left( {2\omega ;\omega ,\omega ,0} \right)\). The effective secondorder tensor can be written as, \(\chi _{\rm ijk}^{\left( 2 \right)}\left( {2\omega ;\omega ,\omega ,0} \right) = \chi _{\rm ijk}^{\left( 2 \right)}\left( {2\omega ;\omega ,\omega } \right) + \chi _{\rm ijkl}^{\left( 3 \right)}\left( {2\omega ;\omega ,\omega ,0} \right)F_{\rm l},\) where \(\chi _{\rm ijk}^{\left( 2 \right)}(2\omega ;\omega ,\omega )\) are the intrinsic secondorder nonlinear coefficients and correspond to a conventional secondharmonic generation (SHG) process, while \(\chi _{\rm ijkl}^{(3)}(2\omega ;\omega ,\omega ,0)F_{\rm l}\) represents the d.c. fieldinduced secondorder nonlinear coefficient. The symbol 0 in \(\chi _{\rm ijk}^{\left( 2 \right)}\left( {2\omega ;\omega ,\omega ,0} \right)\) and \(\chi _{\rm ijkl}^{(3)}(2\omega ;\omega ,\omega ,0)\) denotes the d.c. field (\(\omega = 0\)). EFISH has been utilized in a variety of systems to enhance and modulate SHG signals, such as in silicon/electrolyte^{7} and metal–semiconductor^{8} interfaces, metaloxidesemiconductors^{9}, polymerfilled plasmonic nanoslits^{10}, and metamaterials^{11}. For most reports, the initial SHG signal at zero applied voltage was not zero and only intrinsic nonzero secondorder nonlinear coefficients were typically modified via the electric field. Typically EFISH is a weak effect due to the small thirdorder nonlinear coefficients, and consequently the fieldinduced secondorder nonlinear coefficients are small (<10 pm V^{−1})^{6}, and optical modulation is weak (<10% V^{−1}) with a small tuning range due to the presence of large intrinsic secondorder nonlinear coefficients (~10 pm V^{−1})^{10,11}. Even if a strong electric field is applied to an insulating bulk material or an interface such as semiconductor/electrolyte, it is challenging to switch bulk secondorder nonlinear coefficients from zero to verylarge values (e.g., >100 pm V^{−1}), let alone in semiconductors, which typically have a large density of free carriers. It would be desirable if new nonlinear coefficients could be obtained in semiconductors with perfect contrast and strong modulation strengths, via controlling the unique electric field profile, to enable their use for practical applications and integration with other onchip electronic/photonic devices.
In this paper, we report extremely large tunability of an intrinsically zero secondorder nonlinear coefficient (\(\chi _{\rm xxx}^{(2)}\), or d_{11}) in individual semiconducting CdS nanobelts to a value as high as 151 pm V^{−1} (approximately twotimes larger than other intrinsic tensor elements of CdS) by applying a symmetrybreaking electric field. The fieldinduced secondorder nonlinear coefficients, in contrast to intrinsically nonzero coefficients, are intrinsically zero and are produced by applying an external field, which breaks certain relevant mirror symmetries along the field direction. The voltagedependence of the SHG signal corresponding to d_{11} (d_{11}SHG) exhibits veryhigh modulation strengths of ~200% V^{−1}, and, importantly, with an error functionlike shape (rapid rise followed by saturation), which is different from the linear or quadratic response typically observed in EFISH^{6,7,10,11} and important for device applications, such as nonlinear optical transistors. These unusual properties are attributed to the formation of a highfield domain in the material, which initiates at the electrical contacts and the domain wall moves with the applied field leading to veryhigh optical nonlinearities to turn on tensor elements that are otherwise zero. The highfield domain can be manipulated by infrared (IR) excitation and gate voltage, which further allows for SHG signal modulation in addition to applied electric fields.
Results
Observation of d_{11}SHG with applied voltage
To study dynamically controlled SHG, we fabricated twoterminal devices on a singleCdS nanobelt with a d.c. electric field applied along the CdS aaxis (defined as xaxis in Fig. 1a), with optical excitation via the fundamental wave (FW) polarized along the CdS xaxis, with crystallographic axes confirmed via SHG polarimetry (Supplementary Fig. 1) (see section Methods)^{12}. The dimensions (L × W × H) of the sample in Fig. 1a are 8.2 × 2.43 × 0.45 μm^{3}. Asymmetric contacts (Ti/Au for Ohmic and Au/Al for Schottky) were fabricated in order to apply strong electric field to the sample via the Schottky field (see section Methods) at one junction. A femtosecond pulsed Ti:sapphire laser, tuned from 680 to 1080 nm with ~140 fs pulse width and 80 MHz repetition rate was focused to a spot size of ~3 μm to perform the SHG measurements. Wurtzite CdS has mirror symmetry along its aaxis with a uniform distribution of its electron wave function without a net nonlinear dipole moment (Fig. 1b), hence corresponding secondorder nonlinear coefficients, e.g., d_{11} and d_{13}, are zero and produce no SHG signal (Fig. 1c). However, at V_{DS} = 60 V bias applied between the source (S) and drain (D) electrodes (Fig. 1c, inset), a verystrong d_{11}SHG signal that corresponds to d_{11} appears near the Selectrode (discussed later) at a FW wavelength of 1018 nm. The external normalized conversion efficiency of d_{11}SHG signal (\(\eta _{2\omega } = P_{2\omega }/P_\omega ^2\) = 4.4 × 10^{−9} W^{−1}) is 3.76 times stronger than d_{33}SHG at zero bias, an intrinsic and largest secondorder nonlinear coefficient of CdS (Fig. 1c). The strong d_{11}SHG signal at 60 V bias indicates that the d.c. field breaks mirror symmetry along the xaxis by distorting the electron distribution (Fig. 1b) and induces a net nonlinear dipole moment. By noting d_{33} = 78 pm V^{−1}^{13}, the fieldinduced secondorder nonlinear coefficient, d_{11} = 1.94 × d_{33} = 151 pm V^{−1} at V_{DS} = 60 V (measured at a fundamental wavelength of 1018 nm), is significantly larger than any other intrinsic secondorder nonlinear coefficients of CdS and also other commonly used nonlinear crystals (e.g., LiNbO_{3} with 27.2 pm V^{−1}). The SHG signal ON/OFF ratio is estimated to be >10^{4}, with the ON state corresponding to the saturation SHG (SHG_{max}) (~57 V in Fig. 1c) and the OFF state being the SHG intensity (SHG_{min}) at ~22 V, where SHG starts to appear and can be reliably recorded above the noise floor (see Supplementary Note 6 for more details). SHG signal contrast, defined as (SHG_{max}−SHG_{min})/(SHG_{max}+SHG_{min}) is ~1 due to the large ON/OFF ratio.
Voltagedependence and wavelengthdependence of d_{11}SHG
In order to study the dynamic properties of d_{11}SHG, we measured the d_{11}SHG signal with respect to applied voltage at different fundamental wavelengths (1018, 1028, and 1043 nm) (Fig. 2a) and simultaneously measured current–voltage (I–V) behavior (Fig. 2b) of the device. Voltagedependence of d_{11}SHG signals exhibits qualitatively similar trends at the three excitation wavelengths: it is always below the noise level at low voltage (V_{DS} < V_{t} ~ 20 V, where V_{t} is the threshold voltage), then increases dramatically when V_{t} < V_{DS} < V_{s} (where V_{s} ~ 40 V is the saturation SHG voltage) and eventually saturates at V_{DS} > V_{s} (Fig. 2a). d_{11}SHG excited by 1018 nm laser shows a higher V_{s} and saturation SHG (I_{2ω,s}) signal compared to 1043 nm and is expected since the thirdorder nonlinear coefficient (\(\chi _{\rm xxxx}^{(3)}\)) is larger near the band edge of CdS (at half the wavelength of FW, 1018 nm). Interestingly, the I–V curve exhibits qualitatively similar behavior as the d_{11}SHG signal, with the current increasing and then saturating with the applied voltage (Fig. 2b). The slope of the I–V curve increases when V_{DS} < V_{t}, decreases (V_{t} < V_{DS} < V_{c}) and eventually becomes zero (V_{DS} > V_{c}, where V_{c} ~35 V is the saturation current–voltage) (Fig. 2b). Similar I–V characteristics are also observed at 1043 nm, but with a smaller saturation current–voltage (V_{c}) and saturation current (J_{s}). Although, higher saturation SHG (I_{2ω,s}) and higher saturation current (J_{s}) are observed at 1018 nm compared to 1043 nm (Fig. 2a, b), the electric field is the dominant cause rather than the current to induce SHG. This is because no SHG is observed (Fig. 2a) while the current increases with voltage (VDS < V_{t}) (Fig. 2b), and the SHG signal increased monotonically (Fig. 2a) while the current remained unchanged between V_{c} < V_{DS} < V_{s} (Fig. 2b). Moreover, the corresponding current density (~10^{3} A cm^{−2}) observed in our case is several orders of magnitude lower in comparison to other reports where current density > 10^{6} A cm^{−2} was observed to modify SHG signals^{14,15}. Therefore, the saturation of SHG signals at V_{DS} > V_{s} indicates that a constant electric field is built in the optical excitation region (Fig. 2a).
Highfield domain model for d_{11}SHG
This I–V behavior can be understood to originate from the Schottky junction (Fig. 2b and Supplementary Fig. 2), since one contact is near Ohmic (i.e., Schottky with very small builtin potential), while the other is Schottky. While a typical Schottky barrier can enable observable SHG^{9}, it is unlikely to induce verylarge signals and also saturation of SHG, because the internal electric field changes with applied voltage. However, in semiconductors, one can achieve domains with constant and strong electric fields, called the highfield domain^{16,17}. For example, in materials such as GaAs, the highfield domains can be formed with the electrons scattered into different conduction band valley states accompanied by a decrease in electron mobility with an increase in electric field^{16}. In other semiconductors, such as CdS, another proposed mechanism for the highfield domain is due to carrier quenching^{17,18,19,20,21}. At high electric fields, trapped holes can be ionized, which can then recombine with electrons in the conduction band, thereby decreasing the overall freecarrier density. This process, described as field quenching^{18}, can create distinct high and low electric field domains. While the highfield domain has been studied in bulk CdS (thickness > 100 μm) requiring veryhigh applied voltage (~kV)^{20,21}, it still remains unclear if the highfield domain can be achieved in nanostructures (~100 nm thickness), and thus its dynamics (e.g., initiation and propagation) and unique attributes, such as their control by external stimuli remain unknown. Additionally, the nonlinear optical properties of highfield domains remain unknown along with their interactions with excitons that can influence bulk nonlinear optical processes.
The stationary highfield domain observed in bulk CdS in earlier studies produces a strong and constant electric field, which spatially expands with increasing voltage^{17,19,20}. Once the highfield domain is initiated, the current also starts to saturate^{17,19} due to carrier depletion. Due to the similar features (i.e., constant field and current), our observations (SHG and I–V) are likely related to a stationary highfield domain formation in the CdS nanobelt. In order to validate this hypothesis, we studied the underlying mechanism of the highfield domain in our system and present a model based on fieldinduced ionization of deeplevel acceptor traps in a Schottky barrier (i.e., Schottky highfield domain model, Supplementary Note 3). In CdS, the majority of defects are stoichiometric defects, which are formed during synthesis^{22} and consist of sulfur (V_{S}) and cadmium (V_{Cd}) vacancies and interstitials (Cd_{1} and S_{1})^{23,24,25,26,27,28}. CdS is intrinsically ntype due to the presence of V_{S} as donor traps (ionized donor density: N_{D})^{23,24}. V_{Cd} in CdS have also been studied^{27} and demonstrated to function as acceptor traps^{28}, which are initially neutral and become ionized or negatively charged after accepting an electron^{29}. An increase in the reverse bias voltage can expand the Schottky barrier along the device and increase the internal electric field. As the internal field approaches a critical value (F_{c}) at V_{c}, the strong electric field can excite electrons from the valence to the acceptor states in the forbidden bandgap region^{25,26,27}, which then become ionized and negatively charged (ionized acceptor density: N_{A})^{29}. We refer to this process as fieldinduced ionization, which reduces the net space charge density (ρ) in the Schottky region from ρ = qN_{D} (below the critical field) to ρ = q(N_{D}−N_{A}) at F_{c} (Supplementary Fig. 3). If N_{D} = N_{A}, the net space charge is zero (ρ = 0) and the internal field remains constant at F_{c} (\(\mathrm{d}F/\mathrm{d}x \propto \rho = 0\)) (Fig. 2d and Supplementary Fig. 3). The region that develops a constant field is the socalled highfield domain^{17,19}, followed by a domain boundary and a lowerfield region (Fig. 2d). The domain boundary region has a similar field profile as a Schottky barrier, which is formed at V_{DS} = V_{c}, and then moves away from the metal–semiconductor interface if V_{DS} > V_{c}. Further increase of voltage only expands the spatial length of the highfield domain by ionizing more traps in the new region.
Based on the Schottky highfield domain model, we can quantitatively understand the experimental results by calculating the SHG field (Supplementary Note 4)^{13},
where I_{ ω } is the FW intensity, \(x_{\rm c} = \left( {V  V_{\rm c}} \right)/F_{\rm c}\) represents the length of highfield domain, L is the total sample length between the two contacts, f (x, x_{c}) is the spatial profile of the internal field (Supplementary Equation 10 in Supplementary Note 3) and g(x, x_{0}, w) stands for the Gaussian beam profile of FW, centered at x_{0} with a width, w (Supplementary Equation 11 in Supplementary Note 4). \(G\left( {x_{\rm c},x_0,w} \right) = {\int}_0^L {f\left( {x,x_{\rm c}} \right)} g\left( {x,x_0,w} \right){\rm d}x\) is the overlap between the Gaussian beam and the region with the spatial field profile given by the function f(x, x_{c}). Therefore, the SHG signal is \(I_{2\omega } = E_{2\omega }^2 = \left( {\chi _{\rm xxxx}^{(3)}F_{\rm c}I_\omega G} \right)^2\) and exhibits an error functionlike behavior (Supplementary Equations 12 and 19 in Supplementary Note 4), which matches the experimentally measured voltagedependence of d_{11}SHG (Fig. 2a, the red curve fitted to equation 1). Once the highfield domain completely overlaps with the excitation region (x_{c} > x_{0}), A is constant and the average field equals F_{c}, upon which the SHG signal saturates (Fig. 2a). Therefore, the saturation SHG voltage (V_{s} at x_{c} > x_{0} > 0) is distinct from the saturation current–voltage (V_{c}), describing when the highfield domain is initiated (at x_{c} = 0) with V_{s} = V_{c} + F_{c}x_{0}.
Position dependence of d_{11}SHG
In order to further validate the Schottky highfield domain model, we fixed the applied voltage at V_{DS} = 30 V in our experiment and measured the d_{11}SHG signal over the entire length of the device (Fig. 3a, inset) by scanning the FW laser. We observe that the d_{11}SHG signal first increases when the laser spot gradually moves onto the CdS region from the metal, and then decays suddenly as the laser is moved away from the metal–CdS interface (Selectrode), where the Schottky barrier is initially formed, as predicted by the Schottky highfield domain model (Eq. 1). To understand the spatial dependence of the highfield domain, we measured SHG at different excitation positions (X_{1}–X_{5}) on the device with the same FW intensity (Fig. 3b). It can be seen that the voltagecontrolled d_{11}SHG exhibits qualitatively similar behavior at different positions (X_{1}–X_{5}), but greatly differs in threshold (V_{t}) and saturation voltage (V_{s}) values. For example, at X_{1} (close to the Selectrode at x = 0) where the highfield domain is initiated, the SHG signal saturates at V_{s} = 38 V, while at position X_{2} and X_{3}, V_{s} = 45 and 60 V, respectively, indicating the highfield domain expands from position X_{1} to position X_{3}, and eventually to position X_{4} and X_{5} with a continued increase of applied voltage. This is consistent with our model, thus demonstrating that the highfield domain due to fieldinduced ionization enables the swtiching of otherwise zero secondorder nonlinear coefficients and contributes to the unique SHG behavior. The slight differences in the saturation SHG at some positions is likely due to inhomogeneity in the CdS nanobelt (Fig. 3b). Sample inhomogeneities may affect the highfield domain in internal field strength, and hence related output SHG intensity, but will not impact the origin of modulation and mechanism of SHG. These inhomogeneities can be minimized with higherquality sample growth techniques.
Fundamental wave power dependence of d_{11}SHG
While the highfield domain is demonstrated to induce verystrong SHG signals, the ability to further control the highfield domain can broaden its applications for onchip photonic devices. The SHG signals, intrinsically linked to highfield domains can be manipulated by changing the occupation of the trap states, which can be either activated via nearIR excitation or gate voltage. To study the influence of nearIR excitation on highfield domains, we measured the excitation intensity dependence of d_{11}SHG by tuning the FW at 1018 nm near the Delectrode, under reverse bias, i.e., V_{DS} < 0, (Fig. 4a, inset). The normalized SHG conversion efficiency (\(\eta _{2\omega } = P_{2\omega }/P_\omega ^2\)) plotted against applied voltage shows that higher nearIR excitation intensity (or FW) leads to a higher saturation intensity of SHG signals and also saturation voltage (V_{s}) (Fig. 4a). This process is distinct from the conventional SHG process, where the normalized conversion efficiency (η_{2ω}) is independent of the excitation intensity^{30}. Moreover, higher nearIR intensity also induces higher saturation currents (J_{s}) and saturation current–voltage (V_{c}) (Fig. 4b). We can understand this observation by noting that in CdS there are many available midgap donor and acceptor traps^{27}. Upon IR excitation, the electrons can be excited from the valence band into midgap states (which usually decreases the current)^{25}, or from midgap states into the conduction band (which increases electron density in the conduction band and the overall current)^{27}. Typically, IR quenching would dominate, although because of the presence of the highfield domain, most of the lowlevel acceptor traps are already filled, allowing for more electrons to be excited from trap states (unionized donor and ionized acceptor) into the conduction band, and thereby increase the current (Fig. 4b, Supplementary Fig. 4b and Supplementary Note 5). Since IR excitation increases N_{D} and decreases N_{A} (thus, N_{D} > N_{A}), a higher electric field is required to induce additional N_{A} (i.e., ionize more acceptor traps) to maintain the condition (N_{D} = N_{A}) for space charge neutrality (Supplementary Equation 9 in Supplementary Note 3), therefore reestablishing a new highfield domain with a higher critical field that produces stronger SHG (Fig. 4c). Based on this explanation, a shorter excitation wavelength (e.g., 1018 nm) can excite electrons from deeperlevel ionized acceptor traps than 1043 nm, thus inducing higher saturation voltage (V_{s}), current (J_{s}), and field (F_{c}), which are consistent with our observations (Fig. 2a, b).
The influence of nearIR excitation on SHG signal intensity can also be observed at the highfield domain boundary (Fig. 4a). At V_{DS} = −30 V, the SHG signal does not saturate yet and the nearIR excitation region is partially or completely overlapping with the highfield domain boundary (Fig. 4a). If the nearIR laser intensity is increased, the SHG signal (η_{2ω}) decreases (e.g., at −30 V, Fig. 4d) showing the opposite trend that was observed earlier inside the highfield domain where the SHG signal increases (e.g., V_{DS} = −70 V, Fig. 4c). In addition, the higher nearIR intensity results in a larger saturation voltage (V_{s} in Fig. 4a) at the same nearIR excitation region, which implies that high nearIR intensity causes a reduction in the spatial length of the highfield domain at a fixed voltage, V (x_{c} = (V−V_{c})/F_{c} = X _{0} + (V−V_{s})/F_{c}, Fig. 4a) leading to a poor overlap between the highfield region and the laser spot (centered at x _{0}), generating weaker SHG (Fig. 4d) signals. This is in agreement with our earlier observation that the highfield domain length is proportional to applied voltage (Fig. 3b). These observations demonstrate that the highfield domain can also be controlled via nearIR excitation, which can be useful for their optical manipulation.
Gate voltagedependence of d_{11}SHG
The dynamic control over the SHG signal can be further demonstrated with the application of a gate voltage, which can change the occupation density (N_{D}) of ionized donor traps and consequently change the condition for initializing the highfield domain (N_{D} = N_{A}). We observed that when a negative (positive) gate was applied, the current (J_{DS}) decreased (increased), whereas SHG within the highfield domain (at V_{DS} = 80 V, Supplementary Fig. 5b) showed the opposite response and increased (decreased) (Fig. 4e). Upon application of a positive gate voltage (e.g., V_{G} = 20 V), a large number of electrons are injected from the contact, which can increase the current (red curve, Fig. 4e). Ionized donor traps can be filled and neutralized more easily by accepting electrons, which decreases N_{D}. Therefore, fewer acceptor traps need to be ionized (lower N_{A}) to satisfy N_{D} = N_{A}, which require lower applied electric fields and hence induce weaker SHG signals (black curve, Fig. 4e). Alternatively, the application of a negative gate voltage (e.g., V_{G} = −20 V) can remove electrons from the traps, causing a decrease in the current (red curve, Fig. 4e) and increase in N_{D} by ionizing neutral donor traps. Therefore, in order to achieve the highfield domain, more deeplevel acceptor traps need to be ionized by a higher electric field to increase N_{A}, which thus generates a stronger SHG signal in comparison with no gate voltage (V_{G} = 0 V). This behavior is in contrast to previously reported gatecontrolled SHG owing to gatetuned charged excitons^{31} or gateinduced accumulation of carriers^{32}, and demonstrates a completely different mechanism through gate voltageengineered density of ionized donor traps to control the electric field strength and profile inside the material to generate verystrongly modulated SHG signals that may find applications in highcontrast optical modulator and transistor devices.
Discussion
We observed d_{11}SHG with an applied voltage with important attributes, such as superquadratic voltage and power dependence of the nonlinear signal and saturation, and demonstrated the underlying mechanism (i.e., highfield domain) through a range of control measurements. The secondorder nonlinear coefficient, d_{11}, is intrinsically zero due to the mirror symmetry and can be tuned up to 151 pm V^{−1}. This value was obtained by comparing d_{11}SHG with d_{33}SHG signals, which are produced from the same sample and with the same experimental conditions (except fundamental wave polarization). In CdS, d_{33} = 78 pm V^{−1} is the largest intrinsic secondorder nonlinear coefficient^{13} and cannot be tuned when the electric field is applied along the xaxis. Analogous to a conventional electrical transistor, the signal ON/OFF ratio of our SHG device is estimated to be >10^{4}. The modulation strength or subthreshold slope is around 200% V^{−1}, which is obtained near the threshold voltage (see Supplementary Note 6 and Supplementary Fig. 6). Please note that the saturation and threshold voltages depend on pump conditions, such as fundamental wavelength, spatial location, and power. The response time of the device (see Supplementary Note 7) was estimated to be <1 μs from the density of acceptors (N_{A}), the thermal velocity of the electrons, and the fieldenhanced crosssection for capturing electrons^{27}. However, the response time can become much faster due to strong applied fields that modify the carrier trapping/detrapping rates. The response time could also be improved via improved device geometries, such as smaller crosssection and smaller interaction region with the fundamental beam, and also by operating the device close to the threshold region. At high current densities, the sample heating may also influence SHG signals; however, in comparison to the strong fieldinduced SHG signals, heating does not have a significant impact on d_{11}SHG signals in our case (see Supplementary Note 8).
In conclusion, by applying an external voltage, which breaks certain mirror symmetries, we are able to turn on and modulate the secondorder nonlinear coefficient (d_{11}), which is otherwise zero in CdS nanobelts. The fieldinduced d_{11}SHG signal rapidly increases with the applied voltage and eventually saturates, exhibiting a large ON/OFF ratio of ~10^{4} and a steep subthreshold slope of ~200% V^{−1} and is much larger than previously reported values^{10,11}. This unusual SHG behavior is attributed to the highfield domain generated in the CdS nanobelts, which is initiated at the Schottky contact region owing to the fieldinduced ionization of acceptor traps and can also be controlled by nearIR excitation and source–drain and gate voltage. Further improvement in device properties may be obtained by engineering defects in these materials and one can also envision utilizing highfield domains to induce large optical nonlinearities in materialslike GaAs for similar functionalities. Our study demonstrates a new way to dynamically control nonlinear optical signals in nanoscale materials with ultrahigh signal contrast and signal saturation, which can enable the development of nonlinear optical transistors and modulators for onchip photonic devices with highperformance metrics and smallform factors, which can be further enhanced by integrating with nanoscale optical cavities^{28}.
Methods
CdS nanobelt growth and device fabrication
Aucatalyzed singlecrystalline CdS nanowires and nanobelts were grown on quartz substrates at 850 °C in a quartz tube with vapor phase transport of CdS powder by argon (99.999% purity, 100 SCCM) and then drytransferred onto a silicon substrate with a 300 nm SiO_{2} thermally grown oxide layer. The devices were fabricated by electron beam lithography (Elionix) followed by electron beam evaporation (Kurt Leskter PVD 75) of metal. In order to fabricate Schottky diode devices, lithography and metal deposition were performed for each metal contact in separate steps, with either (200/100/200) Ti/Au/Al or (200/100) Au/Al. No current leakage was observed in the device via the SiO_{2} layer (source–drain or gate) and also no measurable SHG was observed without the presence of a CdS nanobelt. If the laser was moved away from CdS device, no optical SHG signals were observed. Furthermore, SHG polarimetry data (Supplementary Note 1) matches with crystalline CdS showing that the measured signals were recorded from the CdS.
Optical and electrical measurement
The CdS nanobelt devices were mounted in a continuous flow optical microscopy cryostat (ST500, Janis research) with electrical feedthroughs connected to an electrical measurement system, for roomtemperature and lowtemperature measurements. The voltage bias was sourced (0–200 V) and the output current signal was converted to an amplified voltage signal by a current preamplifier (DL instruments model 1211) and recorded continuously (~10 data points per second) by PCI card (National Instrument, NI PCI6281). A femtosecond pulsed Ti: sapphire laser (Chameleon), tuned from 680 to 1080 nm with ~140 fs pulse width and 80 MHz repetition rate, was used to perform SHG measurements. The laser polarization was controlled by a halfwave plate (HWP) and then focused (spot size ~3 μm) onto individual nanobelts by a homebuilt microscope equipped with a ×60, 0.7 NA objective (Nikon). The backscattered SHG signals were imaged by a cooled chargecoupled device (CCD) and detected by a spectrometer (Acton) with a 300 groove mm^{−1} 500 nm blaze grating with a CCD detector (Princeton instruments) with a spectral resolution of 0.1 nm.
Data availability
The data that support the findings of this study are available from the authors upon reasonable request.
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Acknowledgements
This work was supported by the US Army Research Office (grant numbers W911NF1110024 and W911NF12R001203) and NSFMRSEC (LRSM) seed grant under award number DMR1120901. Nanofabrication and electron microscopy characterization was carried out at the Singh Center for Nanotechnology at the University of Pennsylvania.
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M.L.R. and R.A. conceived the concept and designed the devices and experiments. M.L.R. was responsible for the growth of CdS nanobelts and measurement of SHG signals and developed the highfield domain model. J.B. fabricated and tested CdS devices and performed control measurement. W. L. helped measure SHG from CdS. G.L. performed fitting on experimental results using the highfield domain model. M.L.R., J.B., and R.A. analyzed the results and wrote the manuscript.
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Ren, ML., Berger, J.S., Liu, W. et al. Strong modulation of secondharmonic generation with very large contrast in semiconducting CdS via highfield domain. Nat Commun 9, 186 (2018). https://doi.org/10.1038/s41467017025483
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DOI: https://doi.org/10.1038/s41467017025483
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