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Abstract
We investigate strain effects on the ultrafast carrier dynamics and transport of gallium arsenide films on silicon (GaAs/Si) and magnesium oxide (GaAs/MgO) substrates using temperature-dependent photoluminescence (PL) and terahertz time-domain spectroscopy (THz-TDS) from 11 K - 300 K. The PL shows that GaAs/Si and GaAs/MgO samples are under tensile and compressive strain at low temperature, respectively. The temperature-dependent THz emission from GaAs/Si does not show significant differences with the emission from bulk GaAs, while the THz emission from GaAs/MgO shows an order-of-magnitude decrease at low temperature. The THz emission from the samples exhibits an interplay between strain-induced effective mass changes and temperature-dependent electric field effects.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Strain engineering is an effective way to modify semiconductor device characteristics. Strain has been utilized to enhance channel currents in silicon germanium p-type metal-oxide-semiconductor field-effect-transistors (SiGe p-MOSFETs) [1], to lower threshold currents in III-V semiconductor-based lasers [2], and to increase electron mobilities in gallium arsenide (GaAs) core/shell nanowires [3]. The impact of strain on the performance of semiconductor structures originates from its effects on semiconductor properties like carrier effective mass [4], phonon scattering rates [5], and band degeneracy [6]. Strain-induced effects on crystals can also vary depending on the type and magnitude of the applied strain. Thus, strain analysis entails a wide variety of research on semiconductors.
Two common ways to induce strain on semiconductor thin films are (1) lattice-mismatched epitaxial growth and (2) external application through the diamond anvil cell (DAC) method [7]. Lattice-mismatched epitaxial growth consists of growing a semiconductor thin film on a substrate with a different lattice constant, resulting in heterostructures like p-doped indium arsenide on gallium antimonide (p-InAs/GaSb) [8] and gallium arsenide on silicon (GaAs/Si) [9]. The type of strain applied to the film depends on how the lattice constant of the film compares with its substrate. On the other hand, the DAC method is applied using mechanical devices on the semiconductor and is able to apply much larger strain magnitudes compared to lattice-mismatched growth. While both methods are widely used in strain-related research, they have their own disadvantages. Lattice-mismatched epitaxial growth is subject to strain relaxation effects which create crystal defects like threading dislocations or cracks [8]. The effects of strain on a lattice-mismatched heterostructure cannot be isolated in strain-related studies because crystal defects also affect carrier dynamics and transport properties like phonon scattering rates [10]. The DAC method, on the other hand, is only able to induce compressive strain on the semiconductor material. One way to induce both compressive and tensile strain while avoiding defect generation through strain relaxation is by using the epitaxial lift-off (ELO) method [11,12].
The ELO method enables the separation of an epitaxially grown thin film from its original host substrate. New thin films can then be regrown on the original substrate with no degradation in film quality [13], thereby allowing multiple thin films to be grown using only a single substrate. The ELO method is thus a cost-effective solution to expensive substrate prices that drive up semiconductor manufacturing costs [14]. ELO is also an effective way of introducing strain to semiconductor materials. Thin films can be bonded to new substrates with different thermal expansion coefficients. Thermally-induced biaxial strain can be induced on the bonded thin film by cooling the film-substrate system down to cryogenic temperatures [6]. The strain on the film can either be compressive or tensile depending on how the thermal expansion coefficient of the film compares with its new substrate. The efficacy of ELO in enabling strain-related studies on GaAs thin films [6], GaAs quantum wells [15], and InAs quantum dots [16] has already been demonstrated using optical characterization such as photoluminescence (PL) and reflectance spectroscopy.
In this work, we look at strain-induced effects on the ultrafast carrier dynamics and transport of GaAs/Si and GaAs on magnesium oxide (GaAs/MgO) via ELO using terahertz time-domain spectroscopy (THz-TDS). The THz-TDS technique is a useful tool for probing carrier dynamics because the THz emission from bare semiconductors depends on the acceleration of photo-generated charge carriers. Additionally, the carrier acceleration depends on semiconductor properties such as electric field strength, momentum relaxation time, and effective mass [17]. THz-TDS measurements can provide information on strain-related effects on these semiconductor properties. Since the strain is introduced to the bonded films through thermal mismatch, temperature-dependent PL and THz-TDS are utilized to confirm the presence of biaxial strain and to investigate strain effects on the carrier dynamics, respectively.
2. Methodology
The GaAs film was grown on a 3$^{\prime\prime}$ diameter 600 $\mu$m thickness (100)-oriented semi-insulating GaAs substrate using a Riber 32P Molecular Beam Epitaxy (MBE) system. From bottom to top, the thin film design schematic consisted of a 0.5 $\mu$m GaAs buffer, a 0.1 $\mu$m aluminum arsenide (AlAs) layer, and a 1 $\mu$m GaAs thin film. The temperature was maintained at 620°C for the entire growth duration. The growth rate used for the GaAs and AlAs layers was 1 $\mu$m/hr and 0.2 $\mu$m/hr, respectively. Three 5 mm x 5 mm samples were cut from the source 3$^{\prime\prime}$ wafer. One sample was kept as-grown, while the other two were subjected to an epitaxial lift-off (ELO) process. The surfaces of the two ELO samples were first covered with Apiezon$^{\textrm {TM}}$ wax. The wax provided mechanical support for the films upon lift-off and bonding [15]. Afterwards, the samples were then immersed in a 1:10 $48\%\; \textrm {HF:H}_2 \textrm {O}$ solution. The solution selectively etched the AlAs layer, thereby releasing the top 1 $\mu$m GaAs thin film from its host substrate [12]. The released thin films were then transferred onto Si and MgO substrates via a Van der Waals (VdW) bonding mechanism [11]. Both substrates have a thickness of 500 $\mu$m. Finally, the bonded samples were immersed in pure trichloroethylene (TCE) to remove the Apiezon$^{\textrm {TM}}$ wax on the sample surfaces. Temperature-dependent PL spectroscopy was performed to quantify the strain on the thin films at temperatures between 11 K $-$ 300 K. The samples were loaded in a closed-cycle helium (He) cryostat. A 515 nm LuxX diode laser with 30 mW average laser excitation power was used as the excitation source. The laser was made incident on the samples and the PL signal was collected using a SPEX 500M spectrometer coupled with a GaAs photomultiplier tube (PMT) detector.
Lastly, standard THz-TDS set up in reflection geometry was implemented to measure the THz emission from the samples at temperatures between 11 K $-$ 300 K. The samples were placed inside a closed-cycle He cryostat. A mode-locked 800 nm Ti:sapphire femtosecond laser with 80 MHz repetition rate and 100 fs pulse durations was used as an excitation source. The laser beam was split using a 50:50 beam splitter into pump and probe arms. The pump arm was incident on the samples at a 45° angle to photoexcite electron-hole pairs in the samples. Off-axis paraboloid mirrors were used to collect and direct the THz emission from the samples to a commercial photoconductive antenna (PCA) detector. Meanwhile, the probe arm was used to optically gate the PCA detector.
3. Results and discussion
Figure 1(a) shows the 300 K PL spectra for the films. All three samples show a peak at 1.42 eV, which corresponds to the band gap of bulk GaAs at 300 K. Figure 1(b) shows the 11 K PL spectra for the films. The peak corresponding to the band gap of bulk GaAs at 11 K is at 1.513 eV. The increase in the PL peak energy relative to that at 300 K is due to crystal lattice dilation and electron-lattice interaction as the temperature is lowered [18]. In comparison with bulk GaAs, the peak corresponding to the band gap of the GaAs/MgO sample is blueshifted by 3.1 meV to 1.516 eV. The GaAs/Si sample shows a main peak "GaAs/Si 1" and a shoulder peak "GaAs/Si 2" at 11 K with energies of 1.504 eV and 1.510 eV, representing peak shifts of 8.7 meV and 3 meV, respectively. Lastly, the 11 K spectra exhibit low energy peaks labeled "C" at 1.492 eV, 1.485 eV, and 1.497 eV for bulk GaAs, GaAs/Si, and GaAs/MgO, respectively. These three low energy peaks are from carbon acceptors, which originate from the solid arsenic source and elevated substrate temperatures used during MBE growth [19]. The carbon acceptor peaks shift in the same direction as the GaAs band gap peaks.
Fig. 1. PL spectra of the samples at (a) 300 K and (b) at 11 K. Low temperature spectral peak positions correspond to the type and magnitude of the thermally-induced strain on each film.
The type of strain on the samples can be verified via the direction of the PL peak shift relative to bulk GaAs. Luminescence peak redshifts and blueshifts represent tensile and compressive strain induced on the GaAs film, respectively. The PL peaks of the bonded films exhibit shifts due to the thermal expansion coefficient mismatch between GaAs and its substrate. As the bonded films are cooled, either the substrate or thin film will contract faster, resulting in either a tensile or compressive strain on the thin film. The thermal expansion coefficient of MgO ($8\ \times \ 10^{-6}$ K$^{-1}$) is larger than GaAs ($5.8\ \times \ 10^{-6}$ K$^{-1}$) [16]. The GaAs/MgO sample, which exhibits blueshifted PL peaks, is compressive strained at low temperatures [15]. Conversely, the thermal expansion coefficient of GaAs is larger than Si ($3\ \times \ 10^{-6}$ K$^{-1}$) [16]. The GaAs/Si sample, which exhibits redshifted PL peaks, is tensile strained at low temperatures.
In addition to the redshifted peak "GaAs/Si 1", the tensile strained GaAs/Si sample shows an additional shoulder peak at 1.510 eV labeled as "GaAs/Si 2". The appearance of the shoulder peak is due to strain-induced valence band splitting. The two peaks represent electronic transitions between the GaAs conduction band and the heavy hole (HH) or light hole (LH) band, respectively [15]. The valence band splitting energy, as calculated from the difference between the two peaks, is 6 meV. On the other hand, the compressive strained GaAs/MgO film does not show valence band splitting. The splitting could be negligible in this case, hence why no such features are seen. Omambac et al. [16] used the valence band splitting observed in PL to quantify the strain in InAs quantum dots. However, since the GaAs/MgO sample does not show this splitting, the GaAs peak shift will be the only basis for strain calculation. The induced biaxial stress $X$ (in kbar) and strain $\epsilon$ on the GaAs film can be calculated using the equations [16,20]:
Table 1. Summary of the strain and stress induced on each sample at 11 K.
Based on the calculations, the strain magnitude of the GaAs/Si sample is almost three times larger than the GaAs/MgO sample. Moreover, the samples are not strained at 300 K because there are no peak shifts observed [15]. The lack of strain at 300 K confirms that the ELO process cannot directly apply strain on the GaAs films. The strain originates from thermal expansion coefficient mismatch between the film and substrate.
Figure 2 shows the temperature-dependence of the PL peaks for each thin film sample: The temperature-dependence of semiconductor band gaps can be analyzed using the empirical Varshni model [18]:
where $E_g (0)$ is the semiconductor band gap at absolute zero while the constants $\alpha$ and $\beta$ are fitting parameters. Table 2 summarizes the results of Varshni fitting for the three samples:Fig. 2. Temperature-dependent band gap of the samples. The peaks corresponding to each thin film are fitted using a standard Varshni model [18].
Table 2. Summary of the Varshni fitting parameters for each sample.
For the bulk GaAs sample, the obtained fitting parameters are comparable to the literature values for GaAs, which are $E_g (0)=1.519$ eV [22], $\alpha =4.60\times 10^{-4}$ eV/K [23], and $\beta =204$ K [22,23]. The high-energy PL peaks follow the Varshni model in the range 11 K $-$ 300 K, indicating that these peaks represent direct band-to-band transitions. On the other hand, the lower-energy peaks can be verified to originate from defects because they do not change with temperature, thereby not following the Varshni model. Moreover, these peaks disappear above 77 K, which further indicates that these are defect-related transitions because of thermalization at 77 K [24].
Figure 3 shows the 300 K and 11 K TDS waveform and the corresponding frequency spectra of the samples, respectively. The TDS waveforms show a main pulse followed by relatively smaller oscillatory features, which are due to multiple reflections between the film’s surface and the substrate’s back side [25]. The frequency spectra are obtained by taking the Fourier transform of each TDS waveform signal. All samples have a comparable frequency bandwidth of 1.0 THz and maximum THz powers of magnitude 1E-10, suggesting that the ELO process did not affect the GaAs film quality in a way that may affect the 300 K THz emission. Moreover, the 300 K data also suggests that the propagation of light inside the 1 $\mu$m GaAs crystal (which has a penetration depth of 1 $\mu$m at 800 nm wavelength [25]), the subsequent interaction of this light with the different substrates (GaAs, Si, MgO), and the propagation through them does not affect the THz emission. Notably, the 11 K TDS waveforms in Fig. 3(c) exhibit the same pulse polarity compared to 300 K TDS waveforms. The lack of polarity reversal at low temperatures indicates that the dominant ultrafast carrier transport mechanism in all samples is carrier drift [26]. Figure 3(c) and 3d show that the THz emission intensity from the GaAs/Si sample is comparable to bulk GaAs at low temperature but the GaAs/MgO sample shows a significant decrease in emission intensity. Additionally, Figs. 3(b) and 3d show that the bandwidths for all the samples did not change upon cooling.
Fig. 3. TDS waveforms and the corresponding frequency spectra of the samples at 300 K (a, b) and 11 K (c, d). The TDS waveform signal levels are normalized with respect to the spectra of the bulk GaAs sample for each temperature. The frequency spectra are obtained by taking the Fourier transform of the TDS waveform signals.
Figure 4 shows the temperature-dependence of the THz integrated intensity for each sample. In general, the THz integrated intensities from all samples decrease upon cooling. Kinks in the temperature-dependent emissions may be explained by possible defects at the GaAs-substrate interface (either Si or MgO) resulting from the elastic deformation of atoms with an imperfect VdW bond. THz spectroscopy is sensitive enough to detect defects even in high-quality GaAs crystals [27]. Moreover, the temperature dependence of the THz emission of GaAs/Si is similar to bulk GaAs in intensity. On the other hand, the THz intensity from GaAs/MgO sample is one order-of-magnitude weaker at low temperature compared to the two other samples upon cooling. To explain the temperature-dependence of the THz emission from the samples, we discuss THz emission through carrier drift. Bare semiconductor surfaces generate THz radiation through photocurrent surges upon illumination with femtosecond laser pulses [28,29]. The radiated THz electric field in the far-field approximation is:
The photocurrent $J$ relates THz emission to ultrafast carrier transport in semiconductors. In a carrier drift transport mechanism, the photocurrent is expressed in terms of the fundamental charge $q$, density of free carriers $n_f$, and free carrier velocity $v$ of the semiconductor material using the equation [17]: The time derivative of the free carrier velocity can be written using the Drude-Lorentz model: where $\tau _s$ is the momentum relaxation time, $E$ is the semiconductor electric field, and $m^*$ is the effective mass. We consider only the transport of electrons and ignore holes since electrons contribute more to carrier drift owing to their lower effective mass and higher mobilities [28]. We then attribute the behavior of the temperature-dependence of the THz emission from the samples to strain and temperature effects on the variables in the Drude-Lorentz model.Fig. 4. Temperature-dependent integrated THz emission intensity of the samples. The THz emission intensities are plotted in logarithmic scale to show the order-of-magnitude difference between emissions of each sample at low temperatures.
Firstly, the momentum relaxation time is related to the carrier scattering in the semiconductor. When electrons scatter in crystals, their velocity changes in the process [30]. The electron velocity distribution during transport can be qualitatively assessed by using the frequency spectra of the THz emission [31]. Electrons that obtain higher velocities exhibit shorter carrier lifetimes, leading to higher frequency THz emission and enhanced frequency bandwidth. Conversely, electrons with lower velocities exhibit longer carrier lifetimes, leading to lower frequency THz emission and a reduced frequency bandwidth [32]. Figures 3(b) and 3d show that the bandwidth of the samples did not change with temperature, suggesting that neither strain nor temperature significantly affect the electron velocity distribution and the momentum relaxation time of the samples. Hence, we ignore the possible contribution of the momentum relaxation time due to strain and temperature effects.
Secondly, for bulk GaAs, the surface electric field originates from band bending owing to Fermi level pinning of bulk crystal electronic states with surface states [30]. For GaAs/Si and GaAs/MgO, the semiconductor electric field has contributions from both the surface and film-substrate interface. The interface electric field originates from band bending at the film-substrate interface [33]. Strain does not change the semiconductor electric field of [001] zinc-blende GaAs thin films like our samples [34–36]. Strain effects on the semiconductor electric field can thus be ignored. However, temperature effects on the semiconductor electric field cannot be ignored since band bending generally increases with temperature [37]. Thus, both the surface electric field [38] and the interface electric field [37] are directly proportional to the sample temperature.
Lastly, temperature and strain affect the effective mass of the electrons. Generally, the bulk GaAs electron effective mass increases upon cooling [39]. Under strain, the conduction band of GaAs undergoes warping, changing its parabolicity [4]. As a result, the electron effective mass of GaAs will change when it is strained. The electron effective mass increases under compressive strain. Conversely, the electron effective mass decreases under tensile strain. Strain effects are relative to temperature effects on the bulk GaAs effective mass upon cooling to low temperatures. The interaction of strain effects on the electron effective mass with the temperature effects on the semiconductor electric field could explain the temperature-dependent THz emission from the samples. The surface electric fields of all the samples will decrease upon cooling. In addition, the effect of temperature on the interface electric field would further decrease the semiconductor electric fields of GaAs/Si and GaAs/MgO compared to bulk GaAs. For the GaAs/Si sample, the tensile strain decreases the electron effective mass relative to bulk GaAs at low temperature. The relatively smaller effective mass should increase the carrier acceleration in GaAs/Si according to Eq. (6), leading to THz emission enhancement. However, the predicted enhancement is compensated by the decrease in the semiconductor electric field and the THz emission from GaAs/Si sample would not increase. For the GaAs/MgO sample, compressive strain increases the electron effective mass relative to bulk GaAs at low temperatures. Increased effective masses and reduced electric fields both decrease the carrier acceleration according to Eq. (6), leading to THz emission reduction. As a result, the THz emission from GaAs/MgO decreases more significantly as compared to GaAs/Si and bulk GaAs.
4. Conclusion
In summary, we have investigated the effects of thermally-induced biaxial strain on the carrier dynamics and transport of GaAs thin films bonded on Si and MgO substrates via the ELO method. Strain is applied to GaAs by exploiting the thermal expansion coefficient mismatch between GaAs and its host substrate (Si or MgO) through cooling of the bonded films. The PL at 11 K showed that the maximum tensile stress (strain) on the GaAs/Si sample was 1.87 kbar $(1.50\times 10^{-3})$ while the maximum compressive stress (strain) on the GaAs/MgO sample was 0.67 kbar $(0.53\times 10^{-3})$. The THz-TDS measurements show that the temperature-dependent THz emission of the GaAs/Si sample was similar to bulk GaAs for 11 K $-$ 300 K. The THz emission from the GaAs/Si sample was attributed to an interplay between strain-induced effective mass decrease and the temperature-induced electric field decrease that compensate each other in terms of their effects on the carrier acceleration and THz emission. The GaAs/MgO sample showed weaker THz emission compared to the other two samples at low temperatures. The THz emission from the GaAs/MgO sample is attributed to a strain-induced effective mass increase and temperature-induced electric field decrease, effects that both decrease the carrier acceleration and THz emission instead of compensating each other. The results of this study showed that ELO is a viable method for studying strain-induced optical characteristics of GaAs on different substrates.
Funding
University of the Philippines - Office of the Vice President for Academic Affairs (UP-OVPAA) (Grant Number: UP-OVPAA-BPhD-2012-03); Philippine-California Advanced Research Institutes (CHED-PCARI) (Grant Number: IIID-2015-013); Commission on Higher Education (CHED) (Grant Number: LAKAS 2021-010).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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