We present the use of a “double optical pump” technique in terahertz time-domain emission spectroscopy as an alternative method to investigate the lifetime of photo-excited carriers in semiconductors. Compared to the commonly employed optical pump-probe transient photo-reflectance, this non-contact and room temperature characterization technique allows relative ease in achieving optical alignment. The technique was implemented to evaluate the carrier lifetime in low temperature-grown gallium arsenide (LT-GaAs). The carrier lifetime values deduced from “double optical pump” THz emission decay curves show good agreement with data obtained from standard transient photo-reflectance measurements on the same LT-GaAs samples grown at 250 °C and 310 °C.
© 2016 Optical Society of America
Several experimental techniques have been used to measure photo-excited carrier lifetimes and to study the carrier dynamics in semiconductors [1–15]. The most commonly implemented scheme is the optical pump-probe technique, which utilizes ultrafast laser pulses for transient photo-reflectance measurements [11–18]. In this technique, a femtosecond pump pulse is used to generate carriers in a semiconductor surface and the refractive index is effectively modified by mechanisms such as band filling, band gap renormalization, trap filling, and free-carrier absorption . The modulation of the refractive index is optically probed as transient reflectance signals and the carrier lifetime values are estimated from exponential fits to the photo-reflectance decay [10,12,15–18]. The time-decay profile may be used to study trapping and recombination in deep levels, surface recombination, and even diffusion [13–15]. Considering that pump and probe wavelengths can influence experimental results  and that there are several mechanisms like band gap renormalization which can contribute to the reflectance signal , ambiguities in the carrier lifetime evaluation may arise.
Carrier lifetime evaluation by optical pump and THz probe technique [4–7] offers less ambiguities. In this method, carrier mobility and lifetime are conveniently obtained from transient photoconductivity decay curves. An optical pump beam is used for photoexcitation of the semiconductor sample and for generation of THz pulses in a THz transmitter. The transient photoconductivity is measured by utilizing the THz pulsed signals to probe the charge carrier dynamics in the semiconductor. The technique is effective because photoexcitation of the semiconductor sample modifies the probe THz pulses by THz absorption. Since THz absorption is proportional to the change in conductivity, it provides information on carrier density and mobility. However, in order to generate enough optical carriers in the semiconductor, the optical pump source for the setup has to be a powerful femtosecond laser, such as the one with a regenerative amplifier.
In some works, THz emission has been directly investigated to obtain information on the carrier dynamics in the semiconductor surfaces they are radiated from [3,9]. The coherent generation and detection of THz radiation reveals the carrier dynamics in a sub-picosecond time-domain and examining the waveforms allows the study of ultrafast phenomena in condensed matter . Nĕmec et al. implemented time-domain terahertz emission spectroscopy (THz-TDES) and demonstrated a method of extracting carrier lifetime directly from the THz waveforms emitted by electrically biased samples . Shi et al. carried out femtosecond pump-generation measurements with THz detection by electro-optic sampling and studied ultrafast carrier dynamics by analyzing waveforms of the radiated THz pulse from unbiased samples at a series of pump-generation delay times .
Illuminating a semiconductor surface with femtosecond laser pulses generates THz radiation due to change in current and/or change in polarization in the sample. The static built-in field in a semiconductor surface provides a natural bias field for the induced photocurrent to produce the radiation . Upon ultrafast optical excitation of a semiconductor with built-in electric field or depletion region on its surface, electron-hole pairs are created and the carriers are accelerated in opposite directions under the surface depletion field, forming a surge current in the direction normal to the surface [20,21]. The fast time-varying surge current, J(t), which is basically proportional to the photo-excited carrier density and carrier acceleration, radiates electromagnetic waves with THz bandwidth. In the far field approximation, the amplitude, ETHz(t), of the pulsed THz radiation due to this surface depletion field mechanism is proportional to the time derivative of the surge current, as expressed in Eq. (1) .
Moreover, the polarity of the pulsed THz radiation is determined by the polarity, n or p, of the built-in electric field [20,21]. Thus, the THz emission exhibits the motion and time evolution of the free carrier population in the semiconductor. By analyzing the THz emission of the semiconductor surface, it is possible to elucidate significant information such as transient carrier mobility, the doping type, impurity concentration, and crystal symmetry . Furthermore, it is also possible to monitor the modulation of the THz peak emission as a function of time by implementing an appropriate ultrafast optical pump and probe THz generation technique. Such a technique has been used in some previous works [19,22–24], wherein two optical pulses were focused on an externally biased semiconductor device to study the THz generation following ultrafast screening of the applied bias field. One pulse was utilized for optically screening the applied bias field with free carriers while the other optical pulse was used for THz radiation. In this work, we apply a similar technique to a conventional THz-TDES setup in order to generate THz emission for the convenient measurement of carrier lifetime in bare and unbiased semiconductor samples.
We propose “double optical pump” terahertz time-domain emission spectroscopy (THz-TDES) as an alternative method to evaluate the lifetime of photo-excited carriers in unbiased semiconductors at room temperature. The advantage of this proposed technique over the commonly implemented optical pump-probe transient photo-reflectance technique and the optical pump-THz probe technique, which requires a separate THz emitter, is the relative ease in the optical alignment. Unlike previous optical pump-probe THz generation experiments, this proposed technique does not involve the application of external electrical bias to the semiconductor samples, thereby allowing less complications in the setup and in the carrier transport dynamics.
The key feature of THz-TDES is the coherent generation and detection of pulsed THz radiation by using an ultrafast femtosecond laser, which allows for sensitive measurements providing direct information on both amplitude and phase of the THz electric field . In a THz-TDES setup, an optical pulse from an ultrafast laser source is used to generate THz radiation from an emitter under study, such as a semiconductor. The detector, which can be a photoconductive antenna (PCA) or an electro-optic crystal, is gated by a time-delayed optical pulse coming from the same excitation laser source. Through this optical pump-probe configuration, the temporal profile of the pulsed THz electric field radiated from the emitter is measured in femtosecond time resolution using an optical delay line provided by a motorized stage.
In a “double optical pump” THz-TDES (or DOP THz-TDES) scheme, a carrier-injection pump pulse and a THz-signal-generation pump pulse from the same femtosecond laser source are used to probe the decay characteristics of the THz generation in a semiconductor surface emitter. Photo-excited carriers are generated on the sample by the carrier-injection pump pulse and the THz emission by the signal-generation pump pulse is observed. In this setup, the intrinsic surface electric field of the semiconductor is screened by the optical carriers and the THz emission amplitude is expected to change with the time delay between the two pump pulses due to carrier population decay. We demonstrate the application of this modified THz-TDES technique for measurements of carrier lifetime in low temperature-grown gallium arsenide (LT-GaAs) samples grown by molecular beam epitaxy (MBE).
LT-GaAs is chosen as a test sample as it is currently the active semiconductor substrate material of choice for the fabrication of PCA THz emitter and detector devices, which are common key components in many THz time-domain spectroscopy systems [1,25]. Although it has been extensively studied in the past years [1,5–18], considerable research interest still persists in this semiconductor material. LT-GaAs, which is typically grown well below the usual ~550 °C–580 °C temperatures for producing high quality GaAs, has an ideal combination of excellent optoelectronic properties such as relatively high carrier mobility, high dark resistivity, and short carrier lifetimes [15,16]. The short carrier lifetime of this semiconductor material is attributed to the high concentrations of carrier traps in the form of point defects and As precipitates, which are consequences of the nonstoichiometric MBE growth of GaAs at low substrate temperatures [14,15,17]. It is important to study the structural and optoelectronic properties and, in particular, the carrier lifetime of LT-GaAs to optimize this material for device applications.
The LT-GaAs samples which were investigated in this work were grown at substrate temperatures of 180 °C, 250 °C, and 310 °C using a Riber 32P MBE system. Each LT-GaAs layer was deposited on 600-µm thick semi-insulating (100) GaAs substrate with 0.3-µm undoped GaAs buffer layer. The LT-GaAs layers which were grown at 180 °C and 250 °C were both 1.7-µm thick with 0.02-µm n-GaAs cap and annealed in situ at 600 °C for 10 minutes. The LT-GaAs layer which was grown at 310 °C was 1-µm thick with 0.02-µm n-GaAs cap and annealed in situ at 600 °C for 5 minutes. The doping concentration of the n-GaAs cap layers were all ~1 x 1018 cm−3.
Figure 1 shows the schematic of the “double optical pump” THz-TDES setup that was used to study the LT-GaAs samples. The laser source is a mode-locked Ti:sapphire femtosecond laser emitting ~100 fs pulses with 800-nm central wavelength at 82 MHz repetition rate. The output of the laser is separated into two, the pump beam and the probe beam, with a variable optical delay between them. A 10-mW probe beam is split off the main output beam of the laser by a polarizing beam splitter and is focused by an objective lens onto the 3-µm gap of a LT-GaAs-based PCA detector. The pump beam, on the other hand, is further divided into two: a 60-mW pump beam for carrier injection and a 40-mW signal-generation pump beam chopped at 2 kHz for lock-in detection of the THz emission from the sample.
After achieving temporal separation using an appropriate time-delay, the two pump beams are brought together and are spatially overlapped cross-polarized on the sample surface using suitable optics. The cross polarization of the optical pump beams is implemented to avoid complicating the experiment due to interference effects. The beam spots are focused into a diameter of less than 1 mm and are incident onto the same spot on the sample at ~45° to the surface normal. The generated THz radiation is then collimated and focused by a pair of parabolic mirrors onto the PCA detector, which is mounted on the flat side of a silicon hyper-hemispherical lens. A direct current (dc) proportional to the transient electric field of the THz signal is induced in the detector. This dc THz signal is fed to a lock-in amplifier operated in “current mode” and data processing system. The reference signal for the lock-in detection is provided for by the chopping frequency of the signal-generation beam. Thus, only the THz pulse generated by the signal-generation pump is detected, while the carrier-injection pump merely excites the carriers.
Using this “double optical pump” THz-TDES scheme, experiments were carried out at room temperature and in reflection geometry to measure the decay characteristics of the THz emission from LT-GaAs samples grown by MBE on semi-insulating GaAs substrates.
For carrier lifetime measurements, the time-domain profile of the THz radiation emitted by the semiconductor sample was, at first, generated by varying the time delay between the pump and probe pulses while keeping the optical path lengths of the two pump pulses the same. Then, the probe pulse optical delay was fixed at the main peak of the THz waveform, as illustrated on the upper right side of Fig. 1 and as indicated by arrows in Fig. 2. The modulation of the THz peak signal was subsequently observed by scanning the relative time-delay between the carrier-injection and the signal-generation pump pulses. For each of the LT-GaAs samples, the carrier lifetimes were then deduced from exponential fits applied to the THz emission decay curves.
To verify the carrier lifetimes of the samples, transient photo-reflectance measurements were carried out at room temperature using a conventional reflection-type optical pump-probe system. Optical pulses of 30-fs duration were provided by a mode-locked Ti:sapphire laser system operating at a repetition rate of 80 MHz and tuned to a central wavelength of λ = 835 nm. The output laser beam was divided by a beam-splitter into a 3-mW probe beam and a 100-mW pump beam. After a suitable delay of the pump pulse, the pump and probe pulses were cross-polarized and spatially overlapped on the sample by a focusing lens. With this configuration, the change in the photo-reflectance as a function of the delay between the pump and the probe was measured. The delay was scanned over 10 ps and averaged for 1,000 scans by using an oscillating retroreflector with a 10 Hz scan frequency. The measured signal, ΔR/R, is proportional to the change in refractive index, which is a function of both carrier density and probe wavelength. Hence, the carrier lifetimes can then be estimated from the photo-reflectance decay curves.
4. Results and discussion
The THz waveforms of the LT-GaAs samples are shown in Fig. 2. The waveforms provide information on the THz emission efficiency of the samples relative to each other and their respective polarities. The THz emission efficiency is observed to decrease with decreasing growth temperature. This is expected since lower growth temperatures are associated with higher defect densities in the LT-GaAs material [14–17]. The defects, which are basically carrier traps, are detrimental to the THz emission since they can effectively suppress the efficient motion of the carriers by quick capture, which also limits the lifetime to ultrashort time scales. Moreover, the samples grown at 310 °C and 250 °C exhibited n-type GaAs THz emission while the sample grown at 180 °C manifested a p-type GaAs THz emission despite having an n-GaAs cap layer, which was meant to reinforce the built-in electric field on its surface. The peculiar polarity reversal is also observed in Fig. 3, where the transient photo-reflectance curve of the same sample grown at 180 °C registered as a series of negative transients, unlike the other two samples grown at 310 °C and 250 °C. Polarity reversal and negative transients have been reported previously in GaAs and in LT-GaAs grown at 150 °C and 200 °C [2,14,15]. This may be due to the more pronounced nonstoichiometric quality of the LT-GaAs especially when grown at temperatures below 190 °C. At such low growth temperatures, the strain likely produces grain boundaries, dislocations, and poly-crystallinity .
The arrows in Fig. 2 indicate the THz peak positions at which the probe delay was fixed for “double optical pump” THz-TDES of the LT-GaAs samples. Since the principle of utilizing the DOP THz-TDES technique is to monitor the change of the THz peak emission upon optical carrier injection as a function of the relative time delay between two optical pump pulses, it is important to optimize the alignment and properly identify the main peak of the THz emission. For semiconductors like GaAs, which radiate THz waves by surge current mechanism due to surface field depletion, the polarity of the waveform is opposite between that of the n-type and p-type material , as can be observed also in Fig. 2.
Figure 4 shows the normalized THz emission by “double optical pump” THz-TDES for the LT-GaAs sample grown by MBE at 310 °C. Upon optical carrier injection, a fast reduction of the THz emission signal at around −1 ps time-delay is initially observed. The THz signal rapidly decreased by 10% to 90% within 0.9 ps. After the significant reduction, the THz signal recovers exponentially, which corresponds to carrier population decay process. By applying a double exponential fitting to the curve, we obtain decay time constants of 1.32 ps and 5.72 ps for the LT-GaAs sample.
A fit equation with three or more exponential terms was initially considered to determine the time constants associated with the decay curves. However, the multiple exponential fits did not properly converge due to over-parametrization.
In this work, the equation of the exponential fit applied to each of the DOP THz-TDES and transient photo-reflectance decay curves is according to Eq. (2), where y0 and x0 are the offsets of the y and x values of the decay curve while the absolute values of A1 and A2 are the amplitudes of the exponential terms having τ1 and τ2 decay time constants, respectively.
With regards to the decay curve observed in the THz emission by DOP THz-TDES, for every time delay represented by x, the corresponding THz emission level is represented by y while the parameters A1 and A2 basically correspond to the estimated carrier populations which decayed within τ1_DOP and τ2_DOP time constants or lifetimes.
Based on the exponential fitting applied to the decay curve of the “double optical pump” THz emission of the LT-GaAs sample grown at 310 °C, 38% of the decay occurred within τ1_DOP = 1.32 ps while the rest of the decay process occurred with a lifetime of τ2_DOP = 5.72 ps. The transient photo-reflectance of the same sample, which is also shown in Fig. 4, exhibited something similar. The normalized ΔR/R plot for the sample, which has already been presented in Fig. 3, is inverted in Fig. 4 and plotted as -ΔR/R for better visual comparison with the THz emission by DOP THz-TDES. The decay constants deduced by double exponential fitting applied to the photo-reflectance curve are 1.25 ps and 4.64 ps. Only a minor portion of the decay (~24%) is associated with the faster time constant, τ1_ ΔR/R = 1.25 ps, and most of the decay process occurred at the slower time constant, τ2_ ΔR/R = 4.64 ps. In this case, the fast decay of the carriers in the LT-GaAs may be attributed to trapping and recombination at deep levels since other processes occur at a much slower time scale . The sharp narrow peak prior to the onset of the decay curve in the ΔR/R plot of the LT-GaAs sample grown at 310 °C may be due to some nonlinear effects outside the time scale of the carrier decay process.
In terms of the decay profiles and corresponding time constants with curve fitting, the results of the DOP THz-TDES so far show good agreement with the results of the transient photo-reflectance measurements. This good agreement between the two different techniques is similarly observed for the LT-GaAs sample grown by MBE at 250 °C. Figure 5 shows a comparison of the normalized THz emission and the normalized -ΔR/R plot of the sample. For this sample, the initial reduction of the THz signal by 10% to 90% occurs within a time scale of ~0.8 ps, which very closely resembles its counterpart steep slope in the transient photo-reflectance profile of the sample for the same relative time delay regime. The THz signal also recovers rapidly, implying fast carrier trapping with a sub-picosecond component, τ1_DOP = 0.71 ps, accounting for 37% of the process and the rest is described by a relatively slower time constant, τ2_DOP = 6.25 ps. A sub-picosecond carrier lifetime is also revealed by the transient photo-reflectance of the same sample. About 30% of the decay is defined by τ1_ ΔR/R = 0.64 ps but a dominant part of the process has a lifetime of τ2_ ΔR/R = 3.38 ps. A summary of the results for decay constants by curve fitting and standard errors is presented in Table 1.
The results for the LT-GaAs sample grown at 180 °C are ambiguous. As already pointed out, the THz waveform and the transient photo-reflectance of the sample exhibited a polarity contrary to its intended design. In Fig. 6, the ΔR/R plot of the sample shows a slow decay process. The carrier lifetime based on the fitting to the transient photo-reflectance curve is 7.21 ps, which is contrary to the expectation of ultrashort carrier lifetime for a sample grown below 200 °C. Based on the THz emission and on the carrier lifetimes of the samples grown at 250 °C and 310 °C, a more ultrafast carrier lifetime is expected for this LT-GaAs which was grown at 180 °C. The results of the exponential fitting applied to the sample’s THz emission by DOP is consistent with the observed weak THz emission efficiency in Fig. 2 and with the expectation of short carrier lifetime. A sub-picosecond time constant, τ1_DOP = 0.68 ps, governs the THz signal recovery process by 30% and the slower component is 1.65 ps. These results and observations suggest that the DOP THz-TDES may be a more reliable method for the evaluation of short carrier lifetimes in LT-GaAs grown below 200 °C.
For samples such as LT-GaAs grown at 180 °C with a main peak on the negative side of the THz waveform, the THz emission by DOP is expected to manifest the THz signal recovery process as an overshoot with respect to the onset because the baseline is already at the lowest point.
As can be deduced from quality of the plots and the standard errors of the decay constants by fitting particularly for the LT-GaAs sample grown at 180 °C, the measurement of the ultrashort carrier lifetime in a sample which likely has a high concentration of defects is challenging. Specifically, carrier lifetime evaluation by DOP THz-TDES relies on THz emission but samples with short carrier lifetime tend to exhibit weak THz emission efficiency, which sometimes makes the proper identification of major signal peaks versus minor peaks and/or dips difficult.
It is also worth noting that carrier lifetime evaluation based on THz emission can also be significantly influenced by pump intensities. In Fig. 7, the pump power dependence of the carrier lifetime is shown. With the LT-GaAs grown at 310 °C as the sample, the signal-generation pump of the DOP THz-TDES setup was varied from 20 mW, 40 mW, and 60 mW. The corresponding carrier lifetimes of the DOP THz emission increased with increased pump power. Moreover, persistent tails which are asymptotic to the level of the baseline are observed in the decay curves. A probable explanation for this observation, which was also noted in other carrier dynamics studies [8, 11, 14–16], is that the possible saturation of the defects by high carrier densities and the subsequent recombination of trapped carriers can manifest in the decay profile of the signal under study .
In order to optimize the “double optical pump” technique applied in THz-TDES for carrier lifetime evaluation, the limitations presented in the previous paragraph are acknowledged so that improvements to the measurements and appropriate considerations in the analysis of results can be implemented. Despite the identified limitations, the technique can still be exploited for the carrier lifetime evaluation of semiconductors. Please note that the time resolution of this technique is limited by the width of the optical pulses, which is ~100 fs, but not by the pulse width of THz radiation emitted by the sample surface.
In this work, we have evaluated the carrier lifetime in LT-GaAs samples by “double optical pump” terahertz time-domain emission spectroscopy and transient photo-reflectance measurements. For LT-GaAs grown at 250 °C and 310 °C, good agreement is found between the results of the two techniques. Based on the results, “double optical pump” THz-TDES, which is also a non-contact and room-temperature technique, presents itself as a convenient alternative to the more standard transient photo-reflectance technique. Carrier lifetime evaluation using THz emission by “double optical pump” THz-TDES allows relative ease in optical alignment and is particularly useful for research groups with existing THz time-domain spectroscopy setups. This approach may also be employed to measure the carrier lifetimes in other semiconductor surface emitters, such as InAs.
UP System Enhanced Creative Work and Research Grant (ECWRG-2014-10).
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