Observation of anomalous linear photogalvanic effect and its dependence on wavelength in undoped InGaAs/AlGaAs multiple quantum well
© Zhu et al.; licensee Springer. 2014
Received: 7 July 2014
Accepted: 9 September 2014
Published: 14 September 2014
We observed an anomalous linear photogalvanic effect (ALPGE) in undoped InGaAs/AlGaAs multiple quantum well and studied its wavelength dependence in details. This effect is believed to originate from the optical momentum alignment effect and the inhomogeneity of light intensity. We find that the spot location with the maximum ALPGE current is wavelength independent. And the normalized ALPGE current decreasing at smaller wavelengths is attributed to the sharp decrease of the momentum and energy relaxation time. The electrical measurement of the spectra dependence of ALPGE is highly sensitive proving to be an effective method for detecting the momentum anisotropy of photoinduced carriers and band coupling.
where j0 is the amplitude of current, so it can be named as ALPGE current. Peng et al.  only revealed excitation by single wavelength, and there was not a regular transition corresponding to interband transition. While in this letter, we report the observation of ALPGE and its spectra dependence in an undoped (001)-oriented InGaAs/AlGaAs multiple quantum well (MQW) with C2v symmetry, which is a good supplement to the in-depth investigation of the spectra dependence of momentum anisotropy of the photoinduced carriers in semiconductors.
The sample studied here is an undoped In 0.15Ga0.85As/Al 0.3Ga0.7As quantum wells (QWs) grown by molecular beam epitaxy. A 200-nm buffer layer is initially deposited on (001) SI-GaAs substrate, followed by ten periods of 100-Å In 0.15Ga0.85As/100-Å Al 0.3Ga0.7As QWs. Then, a 500-Å Al 0.3Ga0.7As layer and 100-Å GaAs cap layer are deposited. The sample is cleaved into a narrow strip along the GaAs direction with a width of 4 mm and a length of 12 mm, respectively. The geometry has been shown in the inset of Figure 2a, where two ohmic electrodes with a distance of 3 mm were made along y direction by indium deposition and annealed at about 420°C in nitrogen atmosphere.
The experimental setup and method are described as follows: A 140-fs, 80-MHz Ti sapphire oscillator with a peak power of the optical pulses of 300 KW serves as the radiation source. As the full width at half maximum (FWHM) of the laser pulse is about 7 nm, the step-length of the spectral scanning should not be too small. In this experiment, the excitation wavelength is tuned from 865 to 1,000 nm with a step-length of 5 nm, which covers both 1hh-1e (the first valence subband of heavy hole to the first conduction) transition and 1lh-1e (the first valence subband of light hole to the first conduction) transition . The incident light goes through a polarizer and a photoelastic modulator (PEM), of which the peak retardation is set to be λ/4, to yield a modulated linearly polarized light with a fixed modulating frequency at 100 KHz. The angle between the polarization direction of the incident light and the optical fast axis of the PEM is set to be 45°. The Gaussian profile light beam irradiates vertically on the sample with a diameter of about 2 mm at the perpendicular bisector of the two circle electrodes (see the inset of Figure 2a). After the amplification by a preamplifier, the ALPGE current is collected by a lock-in amplifier through the two circle electrodes. At each light spot, one could get a spectrum dependence of ALPGE current. With the movement of the light spot along the perpendicular bisector of the two circle electrodes, one could get a two-dimentional graph of ALPGE currents as functions of wavelength and light spot, as shown in Figure 2b. As a comparison, the common photocurrent (I PC ) is also measured with reference frequency of 220 Hz provided by an optical chopper. The polarization independent light modulated by the optical chopper will induce photoinduced carriers on the plane of the QWs. When the electric field (100 V/cm in this letter) applies on the two circle electrodes, I PC will be generated, which is collected by the lock-in amplifier, so one can see that I PC is proportional to the density of the photoinduced carriers. All the experiments are carried out at room temperature.
Different from the ordinary LPGE due to asymmetry scattering on phonons, static defects, or other carriers in noncentrosymmetric media, the ALPGE is supposed to due to the optical momentum alignment effect [1, 7]. This ALPGE is similar to the so-called surface photogalvanic effect in [10–12] and the edge photogalvanic effect in , where the electrical detection of optical momentum alignment is carried out in metals as well as semiconductors. However, optical momentum alignment alone is not enough to induce a net electric current due to the symmetrical distribution of carriers with momenta k and −k in optical excitation. It has been believed that the diffuse scattering of the surface or the edge breaks the symmetrical distribution of carriers with opposite k. While in the MQW studied here, the optical absorption corresponds to the inner wells and the size of the sample is much larger than the diameter of the laser beam and can be considered edgeless, thus the surface as well as the edge photogalvanic effect can be neglected in our experiment. It is believed that in our experiments the inhomogeneity of light intensity plays the same role with the surface or the edge for generating a net electric current.
where τ∗ is the effective relaxation time, α is the optical absorption coefficient, ω is the photon frequency, υ is the velocity of carriers, k ex is the magnitude of the wave vector at the exciting point, and g(θ,θ0) is the momentum anisotropy factor. The g(θ,θ0) factor describes the probability of an excited carrier’s momentum being along the θ direction given the light polarization plane along the θ0 direction. According to the optical momentum alignment effect theory , g(θ,θ0) can be expressed as for 1hh-1e transition and as for 1lh-1e transition, where f0 is the symmetric part of the the momentum anisotropy factor (see Figure 1a,b). As a result, an anisotropy electric current will be induced around the light spot, which will further generate an observed ALPGE current.
Results and discussion
for 1lh-1e transition.
As shown in Figure 2b, the extreme positions are all focused on the location of x=±0.87 mm, which indicates that the extreme position of ALPGE current is wavelength independent. When the wavelength is tuned from 895 to 980 nm, the changes of the size of the light spot can be neglected. In fact, the vary of wavelength only changes the density of photoinduced electrons which can be written as and the effective relaxation time τ∗. Therefore, according to Equations (5) and (6), the vary of wavelength only affects the amplitude of the ALPGE current but does not change the extreme position.
The contribution to τ∗ contains three parts: the momentum relaxation time τ p , the energy relaxation time τ ε which describes the inelastic processes due to the scattering of longitudinal optical phonon, and the carrier lifetime τ0 which describes the carrier recombination, i.e., . Given the average mobility of the photoinduced electrons to be 8,000 c m2/(V·s) and the effective mass of electrons to be 0.06 m0 (where m0 is the mass of electron in a vacuum), the momentum relaxation time τ p is estimated to be 0.27 ps, which would be smaller at higher excited states. Since τ0∼1ns, τ ε ∼0.15−7ps, one can see that τ∗ is mainly determined by the momentum relaxation time τ p and the energy relaxation time τ ε . The decrease of the normalized I ALPGE can be attributed to the faster momentum and energy relaxation at smaller excitation wavelengths. We have also testified that the ALPGE current still exist in undoped GaAs/AlGaAs QWs; however, we observed no obvious ALPGE current in undoped bulk GaAs. What is more, the ALPGE current in this strained InGaAs/AlGaAs QWs is much stronger than that in undoped GaAs/AlGaAs QWs. Thus, we believe that the ALPGE is a common phenomenon in low-dimensional semiconductors, and the ALPGE is probably stronger in strained semiconductors.
The spectra dependence of ALPGE at normal incidence in undoped InGaAs/AlGaAs multiple quantum well has been studied. This effect is believed to originate from the optical momentum alignment effect and requires an inhomogeneous light illumination. We found that the spot location with the maximum ALPGE current is wavelength independent. We do not observe obvious opposite in the sign for 1hh-1e and 1lh-1e transitions, which is probably due to the fact that the detected current is mainly derived from 1hh-1e transition. And the normalized ALPGE current decreases at smaller wavelengths, which can be attributed to the sharp decrease of the momentum and energy relaxation time. This high sensitivity of electrical measurements proves to be an effective method for detecting the momentum anisotropy of photoinduced carriers and band coupling.
The work was supported by the 973 Program (2012CB921304, 2013CB632805, and 2012CB619306) and the National Natural Science Foundation of China (61474114 and 60990313).
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