Physica E 9 (2001) 76–83
www.elsevier.nl/locate/physe
Few-cycle THZ spectroscopy of semiconductor quantum structures K. Unterrainera; ∗ , R. Kerstinga , R. Bratschitscha , T. Mullera , G. Strassera , J.N. Heymanb a Institute
for Solid State Electronics, Technical University Vienna, Floraagasse 7, A-1040 Vienna, Austria b Macalester College, Department of Physics & Astronomy, St. Paul, MN55105, USA
Abstract Optically excited plasma oscillations in n-doped GaAs epilayers emit intense THz pulses. From THz emission experiments in doped superlattices the miniband properties can be revealed. Using a THz-pump and THz-probe technique we observe the response of the intersubband polarization in semiconductor quantum structures. THz cross-correlation measurements of modulation doped semiconductor quantum structures allow to determine the absorption, the dispersion, and the dephasing times of the quantized electrons. ? 2001 Elsevier Science B.V. All rights reserved. Keywords: THz plasmon; Superlattices; Semiconductor quantum well; Intersubband transition; Time-resolved spectroscopy
1. Introduction Following recent advances in femtosecond laser technology, several groups showed that ultrafast photoexcitation of semiconductors and semiconductor heterostructures can be used to generate electromagnetic radiation at THz frequencies. Most of these works were performed using photoconductive antennas or transmission lines [1,2]. THz generation from semiconductor surfaces or by optical recti cation was introduced by Zhang [3,4]. Roskos et al. achieved for the rst time THz emission from coherently oscillating electrons in a double-well potential [5]. Charge oscillations due to light and heavy hole excitons in a quantum well [6] and THz emission ∗
Corresponding author. Tel.: +43-15880136231; fax: +43-15880136299. E-mail address:
[email protected] (K. Unterrainer).
from Bloch oscillations [7] were of similar concept. However, in heterostructures the THz emission frequency and magnitude are restricted. On one hand, the intersubband spacing or the miniband width of the Bloch superlattice gives the emission frequency. On the other hand, the dipole moment of the transitions is limited due to the spatial con nement of the heterostructures. An alternative concept is coherent plasma oscillations of charge carriers. Here, the charge carriers are bound by their coulomb potential and the plasma frequency depends on the carrier density. Since an oscillating current density leads to the emission of electromagnetic waves, plasma oscillations should emit submillimeter wave radiation. THz emission from coherent two-dimensional (2D) plasmons has been observed in time-resolved experiments in the accumulation layer of a GaAs heterostructure [8]. We have shown that THz pulses are emitted from coherent three-dimensional (3D)
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plasmon oscillations in n-doped GaAs epilayers [9]. We have investigated both, the excitation and the damping process of the plasmons in time-resolved measurements of the emitted few cycle THz radiation. In all experiments we observe temporally and spatially coherent THz radiation with intensities of up to 100 nW [10]. In addition, we investigate the THz emission from optically excited, doped superlattices. There are apparent reasons to use these few-cycle THz pulses to excite and probe carriers in quantum wells. The THz photon energies are comparable to the subband spacings, carrier kinetic energies, and phonon energies in the solid. In addition, THz radiation does not generate minority carriers, and the experiments directly probe-free carriers rather than excitons. THz radiation from free-electron lasers has been used to study intersubband population relaxation in semiconductors [11,12]. We have used few-cycle THz pulses to study intersubband transitions in quantum structures. Unlike Fourier Transform spectroscopy, our ultrafast technique can be combined with pulsed excitation to perform time-resolved spectroscopy on picosecond time scales. Additionally, the cross-correlation technique allows simultaneous measurement of both absorption and dispersion. 2. Experiment All experiments presented here are performed using a mode-locked Ti : Sapphire laser emitting 100 fs pulses at 800 nm (1.55 eV) with a pulse energy of 13 nJ. The pulses are transmitted through a Michelson interferometer and focused onto the emitter sample to spot sizes between 100 and 500 m. In re ection geometry, the generated THz emission is collected by o -axis parabolic mirrors and focused onto a 4.2 K bolometer. The experimental setup is purged with nitrogen to prevent absorption by atmospheric humidity. The signal is detected using standard lock-in techniques at a modulation frequency of about 400 Hz. Time resolution is achieved in our experiment by focusing two delayed laser pulses on the sample. In this correlation technique the time-integrated THz-signal emitted from the sample is detected with the bolometer as a function of the delay time between the two exciting pulses.
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For the measurement of the THz absorption of semiconductor quantum structures the THz pulses are transmitted through the sample which is mounted in a cryo ow cryostat. Applying a fast Fourier transform to the autocorrelation signal measured at the detector yields the intensity of the transmitted radiation as a function of frequency. In our cross-correlation measurements the sample is placed in one arm of an asymmetric THz interferometer. The Ti-Sapphire laser pulses are used to generate sample and analysis THz beams. The sample beam passes through the sample, and is superimposed with the analysis beam at a germanium beamsplitter. The detector measures the intensity i.e. the product of the two THz elds as a function of the delay between them. Cross-correlation measurements are analogous to dispersive Fourier transform spectroscopy, and both the absorption and dispersion of the sample can be extracted from cross-correlation measurements of the sample and of a reference. The cross-correlation signal is the convolution of the electric eld of the sample-arm pulse with the analysis-arm pulse. Z ∞ ES (t)EA (t + t0 ) dt; (1) X (t0 ) = −∞
where ES (t) and EA (t) describe the electric eld at the detector from the sample-arm and analysis-arm pulses, and t0 is the delay between the pulses. The measurements yield the transmission amplitude of the electric eld T (!), where ES (!) = T (!)E0 (!), and E0 (!) is the frequency spectrum of the beam passing through a suitable reference sample. The transmission is the ratio of the cross-correlation spectrum and a spectrum of the reference sample Z ∞ Z ∞ i!t0 X (t0 )e dt0 X (t0 )ei!t0 dt0 : (2) T (!) = −∞
−∞
T (!) is complex and is related to the absorption coef cient (!) and index of refraction n(!) of the sample [13]. T (!) = e(− =2+in!=c)z :
(3)
3. THz emission from n-doped GaAs epilayers For the plasmon emission experiments, n-doped GaAs epilayers were used. The doping concentration
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Fig. 1. THz autocorrelation signal from three GaAs samples with di erent doping concentration.
were 1:9 × 1015 , 1:7 × 1016 , and 1:1 × 1017 cm−3 , respectively. The thickness of the epilayers was a few m. The plasma oscillation of the extrinsic electrons is caused by the ultrafast dynamics of the surface eld which follows the femtosecond laser excitation. The extrinsic electrons are con ned between the undoped substrate of the structures and the surface depletion region. When photocarriers are excited by the femtosecond laser pulse in the surface eld region they rst perform an ultrafast ballistic motion and later a drift motion, both screening the surface eld. Additionally, the di erence of the di usion currents of photogenerated electrons and holes builds up a Dember eld [10]. Recent studies have shown that these impulsive eld changes can start coherent phonon oscillations with frequencies at several THz [14]. In our structures the cold electrons of the epitaxial layer respond to the single-sided eld change which initiates their plasma oscillation. Time-resolved THz emission data from these samples are shown in Fig. 1. Multiple oscillations are clearly visible form the THz auto correlation signal at higher doping concentrations. The oscillation period depends on the doping concentration and is well explained by thepplasma frequency !p of the extrinsic carriers !p = ne2 =0 m∗ , where n is the doping con-
Fig. 2. Frequency spectra of the few-cycle THz pulses obtained from the Fourier transformation of the autocorrelation data.
centration. The emission intensity reaches a maximum for a doping concentration of about 1 × 1016 cm−3 . Below that value the intensity decreases because the plasma oscillations are strongly damped; above that value the intensity decreases because the depletion width becomes smaller. Fig. 2 shows the Fourier transformation spectra of the auto correlation data. For all doping concentrations distinctive amplitude spectra are observed. From the observation that the frequencies do not depend on the density of photo excited carries we deduce that the emission results exclusively from the coherent plasma excitation of the extrinsic electrons in the n-doped GaAs layer [10]. 4. THz emission from n-doped superlattices In contrast to the electrons in bulk material, the electrons in a superlattice reside inside a miniband. Depending on the miniband width (which can be designed by the well and barrier widths) the miniband can be lled with electrons to a certain level by doping the superlattice. In our experiments we use four di erent superlattices, 70 (50, 40, 40) periods of 50 A (20, 25, 25) barriers, (75, 100, 200) wells and 20 A with a width of the rst electron miniband of 55
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Fig. 3. Right: The THz autocorrelation function for the three di erent superlattices recorded at T = 4:6 K. Left: miniband structure of the three di erent superlattices.
meV (26, 10, 2). The superlattices are all n-doped with n = 1 × 1017 cm−3 . This carrier concentration results in a lling percentage of the rst electron miniband of 19% (39, 86, 100) (Fig. 3). When a femtosecond laser pulse excites the sample, electron hole pairs are optically generated that screen the surface depletion eld. Due to the transient electric eld change the electrons inside the miniband begin to oscillate and emit THz radiation. The sample is mounted in re ection geometry in a He continuous
ow cryostat to allow for low-temperature measurements. Fig. 3 shows the THz autocorrelation function for the three di erent superlattices recorded at T = 4:6 K. While the autocorrelation signal for the superlattice with the full electron miniband (200=25) shows no oscillation the electrons in the 100=25 superlattice (86% miniband lling) begin to oscillate but this oscillation is strongly damped. For the 50=20 superlattice with a miniband lling of 19%, several oscillations can be seen. The frequency of the oscillations in the 50=20 superlattice is dependent on the optically generated carrier density (nopt = 1 × 1016 –1 × 1018 cm−3 ). However, this dependence cannot be explained by a simple plasma frequency formula where the bulk ef-
fective mass of the electron is replaced by the e ective mass of the electron inside the miniband. These oscillations are as prominent at room temperature as at T = 4:6 K. Near-infrared degenerate pump–probe re ectivity measurements also con rm the existence and the characteristic features of these plasma oscillations. In agreement with the THz emission experiments, these pump–probe experiments show that a nearly full or a full miniband prevents these oscillations. In contrast to the THz emission experiments mentioned above, electrons that are optically generated by a femtosecond laser pulse can also perform plasma oscillations in a previously empty miniband. For this purpose we used the 200=25 superlattice which has a full rst electron miniband but an empty second one. If the wavelength of the exciting laser pulses is tuned above the second miniband a strongly damped oscillation of the injected electrons appears [15]. Thermal saturation of a superlattice can be established if the thermal energy kB T becomes larger than the miniband width [16]. In this case the miniband becomes uniformly occupied although not full and the conductivity (mobility) decreases drastically. This decrease in mobility should also be seen in the THz oscil-
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Fig. 4. THz emission from two superlattices with di erent miniband widths at room temperature. Left: the miniband width is smaller than kB T . Right: the miniband width is smaller than kB T – the miniband is thermally populated and transport is saturated.
lations. Two superlattices with a miniband width of 55.4 and 26.2 meV were grown and the THz autocorrelation functions were recorded for both samples at T = 4:6 and 300 K. At low temperature both samples show distinct oscillations because in both cases the thermal energy kB T is much smaller than the miniband width. At room temperature (Fig. 4) the superlattice with the wide miniband ( = 55:4 meV) still shows the oscillations because kB T = 26 meV is smaller than the miniband width but the oscillations in the superlattice with the narrow miniband are strongly damped because kB T is as large as the miniband width . 5. THz time-domain spectroscopy of quantum structures We investigated two quantum-well structures with intersubband transitions in the range of 1–3 THz. A parabolic well and multiple wide-quantum well were grown by MBE on semi-insulating GaAs substrate. The multiple wide-quantum well consists of 10 peri GaAs ods of symmetrically modulation-doped 510 A Al0:3 Ga0:7 As bu ers. The wells separated by 1600 A sample has an aluminum Schottky gate on the surface and AuGe alloyed ohmic contacts to the quantum wells. The wells can be depleted of carriers by applying a negative gate voltage to the Schottky gate, and the zero-bias carrier density in each well was measured to be ns = 2:8 × 1010 cm−2 by capacitance–voltage techniques. THz pulses are coupled into the cleaved
edge of the quantum well sample with electric eld parallel to the growth direction to excite the intersubband transition. The parabolic quantum well consists of a single period of a modulation-doped parabolically graded AlGaAs=GaAs structure. According to Kohn’s theorem the electrons in parabolically con ned potentials will interact with lightponly at the bare harmonic oscillator frequency !0 = 8=L2 m∗ ( is the depth of the parabolic potential, L the width, and m∗ the effective mass) independent of the carrier concentration in the well [17]. The parabolic well was designed to wide and to have a resonance frequency be 2000 A !0 of about 1.8 THz [18]. The structure was modulation doped to give an electron concentration in the well of about 3 × 1011 cm−2 . A metal grating (8 m wide Au stripes, separated by 8 m spacers) was deposited on the surface of the structure to allow normal incidence coupling to the intersubband transition. Autocorrelation spectra: Autocorrelation spectra well by modulating were measured for the 510 A the carrier density between full and depleted, and detecting the change in signal with a lock-in ampli er. The intersubband absorption is clearly visible as oscillations in the modulated signal, which are due to coherent charge oscillations in the quantum well following THz excitation. Modulated autocorrelation spectra were recorded at T = 5 and 40 K (Fig. 5). At higher temperature a second absorption line appears which is due to transitions from the n = 2 to the n = 3 subbands. The n = 2 subband is already thermally populated at 40 K. Our measurements show that THz
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Fig. 5. Change in the autocorrelation spectrum obtained by modulating carrier density between full and depleted recorded at T = 5 and at 40 K. Inset: modulated time-domain signal.
time-domain spectroscopy can reliably measure linear spectra in quantum-well systems. The intersubband absorption line shapes and resonance frequencies measured by conventional FTIR and autocorrelation agree. The absorption line strength measured by autocorrelation is approximately 4 times stronger than that measured by FTIR. We believe that this improvement arises from the e ect that no more than 50% of the incoherent, unpolarized beam in the FTIR couples to the intersubband transition, while the coherent THz pulses are 100% polarized. Cross-correlation spectra: We recorded the QW with the cross-correlation signal of the 510 A gate bias modulated between 0 and −10 V (Fig. 6). The modulated signal can be interpreted as the convolution of electric eld emitted by the quantum well electrons versus time with the analysis pulse. The signal from the carriers rises during the rst 2 ps in response to the THz eld. The carriers continue to radiate after the driving THz pulse is over, and the signal is damped out by the free induction decay. In Fig. 7 we display the absorption coecient and index of refraction calculated from the time domain data [13]. We took the reference signal to be the signal measured with the quantum well depleted. The sample signal is obtained while modulating the carrier density.
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Fig. 6. Measured cross-correlation signal obtained by modulating quantum well sample, and recordthe charge density in the 510 A ing the change in signal with a lock-in ampli er. The THz pulse excites electrons into a coherent superposition of the n = 1 and 2 subband states. The resulting oscillating polarization radiates, producing the oscillations visible in the signal. The upper trace shows the signal recorded with no sample.
Fig. 7. Change in the absorption coecient and index of refraction in the quantum well sample due to the quantum well electrons. Solid points are calculated from the time-domain data.
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Fig. 8. Left: cross-correlation signal for the parabolic quantum well. Right: temperature dependence of the cross-correlation signal of the parabolic quantum well.
In addition, we show the recorded cross correlation data for the parabolic well. Fig. 8 shows the time-resolved THz pulse after passing through the sample. At short times (t ¡ 1:5 ps), the signal shows mainly the exciting THz pulse which has a center frequency of 1.5 THz. At longer time delays (t ¿ 1:5 ps) the dielectric response of the electrons in the parabolic well becomes visible. The harmonic oscillator frequency of this well is calculated to be at 1.8 THz which corresponds very well with the observed oscillation period. The temperature dependence shows a strong increase of the damping above 40 K (Fig. 8). The same temperature dependence is found for the intersubband relaxation in THz electroluminescence measurements [19]. 6. Conclusion Few-cycle THz radiation is emitted from coherent 3-D plasmons in n-doped epitaxial GaAs layers. The generation mechanism is ultrafast screening of the surface eld by optically generated carriers. The same THz generation mechanism is used to investigate unbiased, doped superlattices. THz emission due to superlattice plasmon oscillation is found in large miniband superlattices. Strong lling of the superlattice or thermal saturation prevents THz emission. We
have performed time-domain measurements of intersubband charge oscillations in quantum well systems. Our all-THz measurements quantitatively determine both the absorption and dispersion in the samples. Our results can be understood in terms of single oscillator models of the intersubband transitions, and determine the resonance frequencies, oscillator strengths and dephasing rates of quantized transitions in semiconductor nanostructures. Acknowledgements The authors acknowledge support by the Austrian Science Foundation (Start Y47) and the EU-TMR “INTERACT” and J.N.H. acknowledges the support of an award from Research Corporation.
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