Terahertz Strong-Field Physics in Light-Emitting Diodes for Terahertz Detection and Imaging

Intense terahertz (THz) electromagnetic fields have been utilized to reveal a variety of extremely nonlinear optical effects in many materials through nonperturbative driving of elementary and collective excitations. However, such nonlinear photoresponses have not yet been discovered in light-emitting diodes (LEDs), letting alone employing them as fast, cost effective,compact, and room-temperature-operating THz detectors and cameras. Here we report ubiquitously available LEDs exhibited gigantic and fast photovoltaic signals with excellent signal-to-noise ratios when being illuminated by THz field strengths>50 kV/cm. We also successfully demonstrated THz-LED detectors and camera prototypes. These unorthodox THz detectors exhibited high responsivities (>1 kV/W) with response time shorter than those of pyroelectric detectors by four orders of magnitude. The detection mechanism was attributed to THz-field-induced nonlinear impact ionization and Schottky contact. These findings not only help deepen our understanding of strong THz field-matter interactions but also greatly contribute to the applications of strong-field THz diagnosis.


I. INTRODUCTION
THz field strength and polarization dependence. To understand the origin of the photovoltaic effect in the LEDs, we examined the THz pump fluence and polarization dependence of the response of the blue LED. In the pump-fluence-dependent experiments, we used six different peak fields: 81. 4,119,155,190,223, and 241 kV/cm (see Fig. 2a, the mentioned THz field strength value was the maximum peak electric field over the whole temporal duration. The details of the field strength calculation can be found in Supplementary Note 4). Observed time-dependent photoresponse curves are summarized in Fig. 2b. From this figure, we can see that all these signals are negative, i.e., the THz-pulse-induced current flew in the reverse direction, from the n-side to the p-side of the device. When the THz electric field was 81.4 kV/cm, the peak-to-peak photoresponse signal was ~41 mV, while it increased to ~600 mV when the THz field strength was increased to 241 kV/cm. Figure 2c plots the photovoltaic signals of the LED when it was illuminated by THz radiation with three different pulse energies: 80.0, 52.8, and 24.7 μJ. The response curves exhibit a two-fold symmetric period of 180°, which is similar to the previous work on the nonlinear photoresponse of type-II Weyl semimetals [24], manifesting an anisotropic photoresponse related to crystallographic symmetry. We interpret this polarization-dependent photoresponse as a result of different threshold energy due to the orientation-dependent electron effective mass of GaN (see Methods). Figure 2d shows two photoresponse curves as a function of THz pump fluence for specific THz polarizations (marked (1) and (2) in Fig. 2c).
For pump fluences lower than 1.2 μJ/mm 2 , the response tendency exhibited a quasi-quadratic behavior, while it increased linearly when the fluence was larger than 1.2 μJ/mm 2 . As an example, a response signal of a blue LED is illustrated in Fig. 2e. The response time of the detected photovoltaic signal was four orders of magnitude shorter than that of a commercial pyroelectric detector (SDX-1152, Gentec, sensor diameter = 8.0 mm, see Fig. 2e). Furthermore, the responsivity of these LEDs was as high as ~10 times that of the pyroelectric detector without an amplifier, reaching 750 V/W. Corresponding ultrafast photovoltaic signals monitored by the oscilloscope (load=50 Ω). The maximum photovoltaic signal is ~600 mV. c, Anisotropic photovoltaic signals obtained under different THz energies of 80.0, 52.8, 24.7 μJ, respectively. The photovoltaic response has strong correlation to the crystal symmetry. However, it has no strong correlation to the THz energy. Two specific THz polarization dependent responses labeled as Perpendicular (1) and Parallel (2) in c are systematically measured by illuminating various THz pump fluences, as exhibited in d. When the THz pump fluence is <1.2 μJ/mm 2 , both polarization dependent photovoltaic signals obey quasi-quadratic relationship with respect to the THz pump fluence, while a linear behavior is predominant for the higher fluence region. e, Photoresponse comparison between the blue LED and the commercial pyroelectric detector (SDX-1152, Gentec). The photoresponse signal and response time from the LED is 11 times larger and 4 orders of magnitudes faster than those obtained in the pyroelectric detector, respectively.
THz field induced impact ionization. When a strong THz field interacts with a semiconductor, various nonperturbative nonlinear optical phenomena can occur, including high-harmonic and sideband generation [25], the dynamic Franz-Keldysh effect [26,27], Zener tunneling [28], metallization [29], and impact ionization [6,30]. Carrier generation can result in unconventional ways through some of these processes, even though the THz photon energies used are much smaller than the bandgap. For example, Zener tunneling-induced photocarrier generation has been demonstrated, although the density achieved remained relatively low [28]; metallization can also instantaneously produce carriers but requires much higher (>100 MV/cm) field strengths. Hence, in order to explain our observed huge photovoltaic signals in the LEDs, we propose impact ionization to be the dominant mechanism. We developed a theoretical model based on this mechanism, which reproduced all salient features of our experimental results, as detailed below.
Let us first focus on the GaN-based blue LED depicted in Fig. 3a. The device structure included a sapphire substrate, a buffer layer, an n-type layer, activation layers, an electronblocking layer, a p-type layer, and two electrodes. When the THz electric field direction is perpendicular to the stacking direction (the z-axis) and parallel to the x-y plane, the strength and shape of the incident THz pulse is modified through interaction with free carriers, which we take into account by scaling it down in amplitude within the multiple quantum wells (MQWs) [21]. Namely, we introduced a scaling factor of = 1.5 for the THz field strength.
This value was obtained as the best value that fits the experimental results based on our theoretical model. It also reflected the overall screening effect of the THz temporal waveform by the induced carriers. Strictly speaking, the induced carriers should have influence on the a trailing part of THz waveform, but such an averaged treatment in an overall statistical way also worked fine. From now on, the THz field strengths discussed are scaled down by this factor inside the LED.
In an impact ionization process [31], an electron in the conduction band (e11) is subject to an external THz electric field, gains kinetic energy, and then transfers its energy to another electron in the valence band, leading to the creation of an electron-hole pair (e21 + h21) in addition to the initial electron which has now a reduced kinetic energy (e12). To satisfy energy and momentum conservation, the threshold energy Eth can be written as [28] (1) where me (= 0.22m0) [32] and mhh (= 0.85m0) [33] are the electron and hole effective masses, respectively, m0 is the electron mass in vacuum, and Eg is the material bandgap (2.8 eV for In0.12Ga0.88N). From equation (1), we can estimate Eth to be 3.37 eV for an electron impact ionization process to occur. That is, electrons have to be accelerated to acquire 3.37 eV in order to induce impact ionization. Since a single electron-initiated impact ionization event doubles the number of electrons and creates one hole, the electron and hole densities after the system experiences impact ionization processes by times can be estimated to be N = and , respectively, where is the initial electron density. Apparently, N is a function of peak THz electric field ε, hence N(ε) is implemented hereafter to represent the total carrier density at certain peak field ε. We neglect hole-impact processes because their large effective mass would increase the Eth to 5.02 eV, which is harder to reach.
To numerically analyze our observations, we used an equation of motion based on the Drude model:

dk t k t q t dt
Here, q is the electron charge, is the reduced Planck constant, ε(t) and k(t) are the THz transient electric field and the wavenumber of electron, respectively. In this equation, we added a characteristic collision time , which prevents the accelerated electrons from transferring their energy to other electrons. The term proportional to represents the effect of phonon scattering. We set = 1 ps to reproduce our results. This value is larger than the can increase to a picosecond scale due to a high population density [35] or another effect like phonon bottleneck [36]. Thus, at this noise level, the minimum field strength we can detect was ~50 kV/cm (free-space field strength). When the THz field strength is enhanced to ∼160 kV/cm, the number of impact ionization events is calculated to be 9 times, under the assumption that the wavenumber is immediately reset to zero once the average wavenumber of all electrons reaches to = ±5.3 ´ 10 9 m −1 . For the given , , and , the obtained theoretical curve is represented as the black solid dot line in Fig. 3b.
Where denotes the short-circuit photocurrent density under illumination while is the dark current, q is the elementary charge, kBT is the thermal energy at the temperature T of the LED, and is the ideality factor. If is proportional to THz fluence , which is a common situation in solar cells, we should get a logarithmic relation with respect to the THz fluence.
However, a linear relation severely violates the above assumption, so that in turn we can deduce an exponential relation, (see Methods), which not only leads to a linear relation between the photovoltaic signal and THz fluence but also implies a highly nonlinear and exponentially increasing impact ionization process.
Furthermore, considering the relation of (see Methods), we can finally correlate the macroscopic photovoltaic signal and microscopic carrier density through the ratio Here, an ideality factor of 13 fits data well, implying an effective temperature of 3900 K during the whole process. Eventually, the growth of the number of impacting events due to the variation of the THz field strength from ∼30 kV/cm to 160 kV/cm can be evaluated from the experimental results to be ∼10 (red solid circles in Fig. 3b). Accordingly, we can also estimate the impact ionization rate to be ~ 1.25 ´ 10 12 s −1 within the ∼8 ps THz pulse duration. We summarize all experimental data fit by the theoretical prediction in Fig. 3b, where theoretical and experimental results agree very well. This model further tells us that this linear trend will photocarriers, such that the saturation voltage will reach more than 3 V based on the built-in potential inside the blue LED. In short, we fortunately observed such gigantic photovoltaic signals in blue LEDs that stimulated much interest in investigating the impact ionization process. Although this process is common in some typical devices like photomultiplier, the large and effective photocarrier multiplication is often obscured by other effects, such as phonon absorption [38], valley scattering [39], and exciton dissociations [40]. Huge photovoltaic signals observed here show that the carrier multiplication process induced by intense THz pulses is efficient and not obscured by other effects. We believe studying this field-induced high efficiency of photocarrier multiplication is a very important driving force for future material theory physics and device optimization in the THz frequency range.

III. THZ PHOTOVOLTAIC RESPONSE IN DIFFERENT COLOR LEDS
We next studied four other LEDs with different colors (green, white, yellow, and red, see  The most striking aspect is that the sign of the THz-photoresponse of all these LEDs is opposite to that of conventional photovoltaic signals in solar cell devices (see Fig. 2b). To explain this, we propose a Schottky contact based mechanism, as shown in Fig. 4e. Under a simple approximation, there will be a single abrupt junction between n + like metal and p-type semiconductor (Schottky contact), which leads to the generation of an electric field with According to the proposed model in Fig. 4e, it is possible to observe a positive photovoltaic signal from LEDs if their structures did not contain Schottky junctions. We observed such a phenomenon from LEDs produced by the same company with 850 nm and 940 nm emission wavelengths. As shown in Supplementary Figure 8, appreciable positive photovoltaic signals were observed in the 850 nm LED, which can also be well understood by the proposed model.
In this case, there is no Schottky junction replacing with the ohmic contact. We also observed a saturation behavior in the 940 nm LED, which has a lower saturation voltage than the 850 nm LED as expected because the saturation value is determined by the built-in potential which is proportional to the bandgap. LEDs (see Supplementary Figure 8).
THz-LED camera prototypes. Since LEDs can be used for THz detection, one can straightforwardly think about fabricating a THz-LED camera. As illustrated in Fig. 5d, we demonstrated a prototype scanning THz-LED camera. We use a blue LED, and mounted it onto an automatically controlled three-dimensional translation stage with 25 μm spatial resolution.
We used this prototype to scan the LED at the focal plane, obtaining the profile of a THz beam, as shown in Fig. 5a. The obtained circular beam profile has a diameter of ~2 mm (FWHM), which agrees well with that imaged by the commercial camera (Spiricon-Ⅳ, Ophire) (see Fig.   5b). LED displays and various large screen devices are widely available at low costs, indicating the feasibility of a large-area, high-resolution THz-LED real-time camera. Furthermore, we extended the THz-LED camera to a one-dimensional 1×6 array, and its prototype is given in Fig. 5e. With this LED array, we achieved a real-time THz camera, and the recorded THz beam profile is depicted in Fig. 5c. In this first-generation device, due to the large size of the market available LEDs, we could not directly image a focused THz beam. However, we could measure the THz beam profile in a non-focal plane, which in turn proves the high responsivity of the THz-LED detectors. With these results, we believe that LED-based THz detectors and cameras may have some valuable applications in strong-field THz science and technology.

IV. DISCUSSION
final carrier concentration generated during the THz field induced impact ionization. Only 'Multiplication factor' can be calculated out shown in Fig. 3b.
In terms of other factors which may affect the applicability of our model, we need to conduct more discussions. The assumptions of this model base on a uniform system which does not include information about defects and other channels, such as an impact ionization event occurring between a free carrier and a confined carrier within an impurity state, an impurity band or confined quantum-well state. For defects, we actually measured three regular and symmetric anisotropic two-fold photoresponse curves and plotted them in Fig. 2c. However, the defects can prevent carriers from attaining high multiplication [45] and render the photoresponse irregular while the anisotropic photoresponse of blue LEDs is relatively regular.
Therefore, we can conclude that the defects affect little and attest to the applicability of the model in this sense.
With regard to the second factor, we pick up the confined quantum-well state as an example, the impact ionization between the free carriers and confined carriers will result in the spacecharge neutrality no longer being maintained [46]. This will alter the electric field profile within the device and subsequently the device performance. However, the measured Voltampere characteristics before and after the illumination of THz pulses exhibit no hysteresis phenomenon (see Supplementary Figure 4), implying the confined quantum-well state affect little on this model as well. This is a reasonable result because the activation layer (MQWs part) is much thinner than other layers. The confined states are very few such that the second effect plays a small role in the total carrier multiplication process.
After the carrier multiplication process, combining the previous theory with the large negative photovoltaic signal we have observed, we can infer the carrier transport process in the blue LED and green LEDs. Because the strong-field THz pulse excited carriers at 15 ps, it was quite short compared with the carrier lifetime of a few nanoseconds. The carrier multiplication can be regarded as an instantaneous process. In the blue and green LEDs, since there is no positive signal at the tail of the photovoltaic signal, it can be deduced that most of the carriers inside the device were mostly generated in the p-type region. Due to the presence of the surface electric field (Fig. 4e), the generated electrons drifted outwards. The holes diffused into the bulk. Electrons accumulated near the surface of positive electrode side, while holes accumulated in the middle of the p-type region. Subsequently, the accumulated electrons and holes formed an electric field opposite to the surface electric field direction. These fields partially canceled out the original surface electric field. In the external circuit, the electrons on the surface reduced the potential at the positive electrode, forming a large negative signal. The internal carrier recombination process gradually reduced the surface potential, and finally decayed to zero while all excess carriers recombined.
Moreover, the relaxation time t is in fact an energy dependent parameter which decreases mostly with more energetic electrons produced when applying higher electric field strengths.
Thus, this value 1 ps for t is an average number owning statistic meaning that does not reflect the real distribution of scattering process. In the future, full quantum mechanical theoretical investigation is expected to be employed to capture more information with which advanced THz detectors will be designed and manufactured.

D. The empirical exponential law
In the condition of single photon absorption, namely, the common case in typical photodetectors, there is a known relation between the short circuit current and generated carrier density N, . Furthermore, the generated carrier density is proportional to the pump fluence as well, that is . According to the above relation, we can obtain the relation leading to the relation , which is exactly the case in solar cell [37].
However, it should be emphasized that the experimentally obtained photovoltaic signals profoundly violated the logarithmic relation between the and . This behavior indicates the photoresponse in LEDs to strong-field THz pulses does not belong to the case of single photon absorption. When inspecting the equation (3), the relation and , the most possible and obvious relation which can be broken down is . The underlying impact ionization obeys exactly an exponentially increasing law. The other two relations still make sense because they are universal rules regarding the external circuits and the definition of current density rather than the mechanism in materials.
Accordingly, we have to modify the relation based on the results in Fig. 2d. We