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The new optical gating technique uses a femtosecond optical laser pulses for the photoconductive detection of short pulses of terahertz (THz) radiation. This technique reproduces the shape of the THz pulse and after pulse plasmonic response of the two-dimensional electron gas in a short channel high electron mobility transistor (HEMT). The results are in excellent agreement with the electro-optic effect measurements and with the simulation results obtained in the frame of a two-dimensional hydrodynamic model. The femtosecond optical laser pulse time is delayed with respect to the THz pulse and generates a large concentration of the electron-hole pairs in the AlGaAs/InGaAs HEMT. This drastically increases the channel conductivity on the femtosecond scale and effectively shorts the device quenching the transistor response. The achieved time resolution is better than 250 femtoseconds and could be improved using shorter femtosecond laser pulses. The spatial resolution of this technique is on the order of tens of nanometers or even smaller. It could be applied for studying the electron transport in a variety of electronic devices ranging from silicon MOSFETs to heterostructure bipolar transistors.
© 2016 Optical Society of America
1. Introduction
The emergence of high resolution video stimulated interest in future wireless communications operating at frequencies of 300 GHz and above [1–4], which, in turn, stimulated research on new terahertz detectors and sources [5–8], including plasmonic devices [8–21] operating in both collision dominated [7,8] and resonant quasi ballistic regimes [9]. Theoretical predictions [13–17] and experimental results [18–21] show that these plasmonic devices could operate at terahertz frequencies making them ideal for applications as THz modulators, detectors, and, potentially, sources [13,18–21] for many applications [20], including THz wireless communications.
In this paper, we report on the new optical gating technique that was used for the photoconductive detection of short pulses of terahertz radiation with the resolution up to 250 femtoseconds and could also trace after the THz pulse response of the two dimensional electron gas. The proposed photoconductive High Electron Mobility Transistor (HEMT) technique could be considered as an extension and modification of the photoconductive detection technique used in the THz Time Domain Spectroscopy (TDS) systems [22–25]. The latter technique detects THz electric field superimposing it on the femtosecond laser pulse. Changing the time delay between the start of the THz pulse and the femtosecond pulse allows reproducing the temporal profile of the THz pulse electric field. In contrast to a photoconductive antenna (typically fabricated on highly defective low temperature grown (LT) GaAs), we use a deep submicron InGaAs High Electron Mobility Transistor (HEMT) as a THz detector. The lifetime of the electron-hole pairs generated by a femtosecond optical laser pulse in the LT GaAs is on the order of 100 fs due to nonradiative recombination in this highly defective material. The lifetime of the electron-hole pairs generated by a femtosecond optical laser pulse in the HEMT channel is on the order of 100 ps and might be even longer. In the photoconductive HEMT technique, a femtosecond pulse abruptly increases the electron-hole concentration shorting the channel for the time period of a much longer lifetime (on the order of 100 ps or even longer).
Ideally the HEMT channel impedance ZHEMT is much larger than the input resistance of the measurement circuit when not illuminated and much smaller than the input resistance of the measurement circuit after the device is illuminated during the electron-hole lifetime (see Fig. 1). In this case, the input to the transmission line peaks during the transient caused by the optical pulse and the registered pulse amplitude is proportional to the value of the THz pulse induced drain-to-source voltage at the femtosecond laser pulse time. The shape of the response pulse is determined by the transmission line and the scope, but the amplitude of the registered pulse is proportional to the THz voltage (and, hence, to the THz field) at the moment of the optical pulse application. Therefore, the plot of the registered pulse amplitude as a function of the delay time between the start of the THz pulse and the optical pulse application reproduces the THz response waveform with the time resolution determined by the duration of the femtosecond laser pulse, which could be as short as 5 fs [22].
Fig. 1 Equivalent circuit of the photoconductive HEMT detector channel before (a) and after (b) laser pulse application. State (b) persists during the electron-hole recombination time (~100 ps or higher in an InGaAs HEMT.)
A schematic drawing in Fig. 2 compares the two techniques. The response is recorded at the moment of time when the femtosecond laser pulse is applied because at that moment, the drain-to-source voltage switches from dropping across the device channel to being applied to input of the transmission line. There are several important advantages of this photoconductive HEMT technique compared to the conventional electro-optic sampling and/or sampling using a photoconductive antenna [22–25].
Fig. 2 Qualitative comparison of the conventional photoconductive antenna technique and photoconductive HEMT technique. Left panel: scale, electron-hole concentration in the semiconductor region, conductance waveform in semiconductor region, and the measured pulse waveform for the he conventional photoconductive technique. Right panel: same plots for the photoconductive HEMT technique.
First, the drain to source voltage induced by the THz pulse persists longer than the THz pulse duration lasting while the electron density oscillations decay. In contrast to the electro-optic detection, the response could be measured even after the end of the THz pulse recording the oscillations or transients of the electron density in the device channel caused by the THz pulse. The time scale of such transients is on the order of the RHEMTCHEMT constant (where RHEMT is the channel resistance and CHEMT is the effective gate-to-channel capacitance) or on the order of the momentum relaxation time depending on the value of ωpτm, where ωp is the plasma frequency and τm is the momentum relaxation time and on the viscosity of the electronic fluid in the device channel [17,26]. Hence, the photoconductive HEMT technique could find applications for the time resolved measurements of ultra-short electric field pulses at femtosecond scale. The ultimate limit of the time resolution of this new technique is on the order of the femtosecond laser pulse duration that could be as short as 5 fs [27].
Second, the spatial resolution of this new technique is at least as good or better than the device feature size (on the order of tens of nanometers or even smaller compared to hundreds of microns for the conventional electro-optic technique [23]) making it ideal for two‐dimensional and three-dimensional imaging of THz beams.
Third, the measured response is electronic compared to the rotation of the polarization plane for the conventional electro-optic technique.
Finally, this new technique is not limited to HEMTs and could be applied for studying the electron transport in a variety of other devices, such as Heterostructure Bipolar Transistors that detect the THz radiation [28].
2. Theory
We simulated the response to a THz pulse using both a complete numerical hydrodynamic model accounting for the viscosity of the electronic fluid in the HEMT channel and solving the two-dimensional Poisson equation and the simplified version of the hydrodynamic model that substitutes the solution of the Poisson equation by using the Unified Charge Control Model (UCCM) [29]. Our hydrodynamic model [17] includes the effects of viscosity, temperature and pressure gradients, with the last one shown to be a dominant factor in the sub-threshold regime. The UCCM model [29] relies on the gradual channel approximation and uses the interpolation equation for the electron density in the device channel, ns:
Here q is the electronic charge, Cch is the effective gate-to-channel capacitance per unit area, η is the subthreshold current ideality factor, is the thermal voltage, kB is the Boltzmann constant, T is temperature, VGS is the gate-to-source voltage, VT is the threshold voltage and U is the voltage difference between the source and a point in the channel.We assumed that the impinging THz pulse induces the THz voltage between the source and the gate. In fact, the THz voltage could be also induced between the gate and the drain. If the device is symmetrical the drain-to-source voltage) could be only related to the direction of the electric field of the pulse. Under experimental conditions, one of the induced THz voltages (typically the gate-to-source voltage due to the typical circuit configuration) is dominant, and such a model is used in our simulations. A more detailed discussion of the relevant boundary conditions could be found in references [29,30].
Figure 3 shows the computed responses as a function of the THz pulse amplitude using both the full hydrodynamic and hydrodynamic-UCCM models. As seen, the agreement between the models is excellent. The reason for small difference at large values of the THz voltage is caused by neglecting the parasitic resistances and fringing effects in the UCCM version used in this calculation.
Fig. 3 (a) Simulation results using the full hydrodynamic simulation (solid line) and the simplified version using UCCM (dashed line). The inset shows the device geometry The HEMT parameters are drain-to source distance 1,100 nm, gate length 130 nm, barrier thickness 22 nm, dielectric permittivity of the barrier layer ε = 13.9. VGS – VT = 0.172 V, threshold voltage VT = −0.172 V, mobility μ = 3,500 cm2/Vs. (b) The waveform of the THz pulse used in the calculation (dotted like) and the shape of the output signal (solid line)
The response in proportional to the induced THz voltage, UTHz. The physics behind this dependence is very simple. The gate-to-channel current is equal to CghdUTHz/dt, where Cgh is the effective gate-to-channel capacitance, which is independent of UTHz, except near the threshold. (As can be seen from Eq. (1), the effective gate-to-channel capacitance per unit area sharply decreases near the threshold and/or for relatively large signals exceeding the thermal voltage [29]).
This linear dependence is in contrast to the response to a continuous wave THz signal, which is proportional to the squared THz voltage (with the THz voltage being proportional to the THz electric field) for low intensity excitation and to the THz voltage for high intensity excitation [31,32].
3. Experimental results and comparison with electro optical measurements
For experimental study of the HEMT response to the THz pulse, we used the femtosecond Tsunami/Legend laser system with the wavelength of 800 nm, pulse energy ~0.6 mJ, pulse duration of 120 fs and repetition rate of 1 kHz. A nonlinear ZnTe crystal exposed to the femtosecond laser pulses generated terahertz pulses focused on the active element of the device by a gold off-axis parabolic mirror. The amplitude of the THz electric field in the focal plane of the mirror (at the device) was 500-1000 V/cm (measured by the electro-optic sampling technique [22–25]), and the duration of the generated THz pulse was 1-2 ps. Figure 4 shows the schematics of the experimental setup.
Fig. 4 Schematics of the experimental setup. Optical pulses: 800 nm, 100 fs duration at 1 kHz, 0.6 mJ pulse energy. The inset shows the delayed optical pulse.
To scan the device response with a sub picosecond resolution in the photoconductive regime of the HEMT operation, a small fraction of the optical power (with the pulse energy of 0.15 to 5 micro Joule) was focused on the device channel with the controlled time delay with respect to the start of the THz pulse. This optical power was high enough to generate a large number of the electron hole pairs to drastically increase the conductivity on the femtosecond scale effectively shorting the source and drain as schematically shown in Fig. 1. This effect quenched the response and therefore allowed us to reproduce the waveform of the THz pulse by changing the time delay between the THz pulse and the quenching optical pulse.
The measurements were done at room temperature and at zero gate bias. The source was grounded and the drain connected to a transmission line (see Fig. 1). Figure 5 shows the measured and simulated current-voltage characteristics.
Fig. 5 Measured (solid lines) and simulated (dashed line) current-voltage characteristics of the device under test. The simulations at zero gate bias (used in the THz measurements) were done using the analytical model described in [29]. The parameters used in the simulation are the same as used in the hydrodynamic model (see Fig. 3).
Figure 6 shows the HEMT photovoltaic response to a single THz pulse. The obtained pulse duration of approximately 80 to 100 ps was limited by the bandwidth of RF HEMT package and acquisition electronics. Its shape is typical for the transmission line response to a short input pulse.
Fig. 6 HEMT photovoltaic response to a single THz pulse. The pulse width of 50 ps (FWHM) is limited by the bandwidth of detector RF package and acquisition electronics.
Figure 7 shows the response amplitude dependence on the time delay between the THz and femtosecond optical pulse. At each delay time, the waveform of the measured pulse is the same as shown in Fig. 5 but the amplitude is changing.
Fig. 7 Dependence of the photovoltaic response amplitude in case of optical gating as a function of optical pulse delay in respect to the THz pulse. The two insets show the output pulse shapes with the varying amplitude for two different time delays.
There are three delay time regions in Fig. 7. The first region corresponds to the negative delay times when the femtosecond laser pulse precedes the THz pulse. In this region, the response amplitude is zero confirming that the electron-hole plasma is shorting the device as shown in Fig. 1(b) during the time scale smaller than the electron-hole lifetime.
The second (and the most important and interesting) region corresponds to the small delay times that are of the order of the time duration of the THz pulse, τTHz, and the electron oscillation decay, τtr. These times (τTHz and τtr) are much smaller than the characteristic time of the transmission line and acquisition electronics, τtrl. The sharp peak in this region can be explained as follows. The femtosecond laser pulse generates the electron-hole plasma abruptly changing the voltage drop across the device and, therefore, producing the electric field transient of the duration determined by the electron-hole plasma generation time (on the order of 100 fs). When the THz pulse and the femtosecond optical pulse coincide, these two fields add up. Therefore, the resulting response, S, is given by
Here Uopt is the effective gate-to-source voltage induced by the optical pulse. The second term in the right-hand side of Eq. (2) is due to the system nonlinearity. There are three mechanisms contributing to such non-linearity: (1) the nonlinear dependence of the two dimensional electron concentration on the gate-to-channel voltage (see Eq. (1), especially significant near the threshold, and (2) strong transport nonlinearities induced by this electron-hole pair generation process (3) nonlinearity of the electron transport in the channel. At high optical voltages, the dominant term determining the THz response iswhere I is the intensity of the optical pulse. This means that the detector sensitivity could be dramatically enhanced by using strong optical pulses.Figure 8 shows the measured dependence of the peak response when the THz pulse and the optical pulse overlap. As seen, the measured dependence is in good agreement with the square root dependence predicted by Eq. (3).
Fig. 8 Central peak amplitude as a function of optical pulse intensity, points – measured, line – square root dependence predicted by Eq. (3).
The third delay time region in Fig. 7 corresponds to large positive delays that are longer than the time duration of the THz pulse and the electron oscillation decay time (τTHz and τtr). This region is determined by the characteristic time of the transmission line and acquisition electronics, τtrl, and, as expected, the amplitude dependence on the delay time saturates at approximately 80 ps, in good agreement with duration of the measured output pulse. Figure 9 presents the comparison of the results obtained using the photoconductive HEMT technique with the results obtained using the standard electro-optic detection technique using a ZnTe crystal and by the hydrodynamic simulation.
Fig. 9 Comparison of the photoconductive HEMT response (dashed line) with electro-optic effect measurements of the THz pulse (dotted line) and hydrodynamic simulations (solid line) using the electro-optic waveform as an input pulse. The gate voltage Vg = 0; the threshold voltage VT = −0.75 V. T = 300 K.
We took the THz waveform determined by the electro-optic technique as an input THz voltage waveform for the hydrodynamic simulations. This model predicted the ultra-fast transistor plasmonic response in full agreement with our measurement results. The simulated response is in good agreement with the experimental data. This agreement confirms the applicability of this new photoconductive HEMT technique for monitoring the waveforms of short THz pulses.
Figure 10 compares the Fourier spectra of the time-domain response on THz pulse, measured by the standard electro-optic technique using ZnTe nonlinear crystal (top curve)) and calculated from the photoconductive HEMT response shown on Fig. 9. This figure demonstrates more clearly the differences between the electro-optic technique and the photoconductive HEMT technique, which might be related to the accuracy of the electro-optic technique.
Fig. 10 (a) Fourier spectra of the THz pulse electro-optic measurements (dotted line in Fig. 9) and (b) photoconductive FET response (dashed line in Fig. 9).
The photoconductive HFET spectrum demonstrates narrower bandwidth compared to the ZnTe electro-optic measurement. However, the signal to noise ratio stays acceptable up to 2 – 2.5 THz. (The highest frequency of THz radiation detected by this device exposed to the CW gas terahertz laser was 4.25 THz.) The difference in the spectra might be attributed to inaccuracy of the electro-optic technique for reproducing small THz signals.
4. Conclusions
We presented the new photoconductive HEMT technique for the measurements of ultrafast transients with a subpicosecond resolution. The measured data are in good agreement with a well-established electro-optic technique and with the simulations in the frame of the hydrodynamic model and show that a plasmonic HEMT responds at subpicosecond time scale. This new technique has several advantages compared to the conventional electro-optic technique. It allows measuring the device response after the end of the THz pulse recording the oscillations or transients of the electron density in the device. The spatial resolution of this new technique is on the order of tens of nanometers or even smaller compared to hundreds of microns for the conventional electro-optic technique. The measured response is electronic compared to the rotation of the polarization plane for the conventional electro-optic technique. This new technique could also be applied for studying the electron transport in a variety of other devices, such as Heterostructure Bipolar Transistors.
Acknowledgments
The work at RPI was supported in part by the U.S. Army Research Laboratory through the Collaborative Research Alliance (CRA) for Multi-Scale Modeling of Electronic Materials (MSME).
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