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A GaAs/GaAlAs-based asymmetric microcavity structure was studied by various optical characterization techniques. The angle-dependent reflectance (R) spectra showed that the cavity mode (CM) superimposed on quantum well excitonic transitions. The resonance enhancement effect between the excitonic transitions and the CM in the weak-coupling regime was explored using the angle-dependent differential surface photovoltage spectroscopy (DSPS) and photoluminescence (PL), and temperature-dependent PL. In this work, we have also implemented a new modulation technique, namely, the angle modulation reflectance (AMR) to decouple the CM from the overlapped excitonic transitions. The AMR technique has been demonstrated to be an efficient method for the study of weak coupling effect in the microcavity structure.
©2005 Optical Society of America
1. Introduction
In recent years microcavity structures have attracted considerable interest because of both their basic and applied properties. Microcavity structure, which consists of quantum wells surrounded by distributed Bragg reflectors (DBRs), plays an important role in many light emitting devices such as various vertical-cavity surface emitting lasers (VCSELs) [1–3], Fabry-Perot modulators [4], microcavity light-emitting diodes (MCLEDs) [5–6] and resonant cavity light-emitting diodes (RCLEDs) [7]. A DBR mirror is a periodical structure made up of two semiconductor or dielectric materials with different refractive indices. The thickness of each layer is chosen so that the light reflected by all the interfaces interferes within a spectral range further referred to as the stop-band. It can be used to improve the brightness, modulation speed and external quantum efficiency of optoelectronic devices. It is also the key structure of a future generation of optoelectronic devices such as polariton lasers [8]. A microcavity structure consists of two DBR mirrors and a cavity. The cavity photons are confined between two mirrors, and interact with the excitonic transitions of a semiconductor quantum well. The one-dimensional confinement of the optical wave in the microcavity is similar to the confinement of excitonic states in a quantum well structure and results in a so-called cavity mode (CM). The interaction between CM and quantum well excitonic transitions can be divided into a strong- and a weak-coupling regime. For strong coupling, the energies of exciton and CM show a Rabi splitting. For weak coupling, the spontaneous emission can be modified by tuning the CM in and out of resonance with the excitonic transitions. The asymmetric microcavity structure consists of a bottom DBR but no top DBR mirror and a cavity between the air and semiconductor mirror. When the cavity is tuned to resonate with the excitonic transitions, the spontaneous emission [9–12] and absorption [13–14] in the microcavity are enhanced. In order to improve the devices performance and develop the new optoelectronic devices, it is necessary to develop new and simple methods to obtain further insight into the coupling effect between the excitonic transitions and the CM.
In this study, due to the absence of top DBR mirror the GaAs/GaAlAs asymmetric microcavity structure operates in the weak-coupling regime and no Rabi splitting is observed. The angle-dependent R spectra are used to inspect the reflectivity at different angle of incidence. It is found that both the fundamental conduction to heavy- and light- hole excitonic transitions of quantum well superimposing on the CM plus a rich interference pattern related to the mirror stacks. In order to distinguish the CM from the mixing reflectance (R) spectra, the angle modulation reflectance (AMR) technique is developed. It is performed as a function of angle of incidence by using the similar experimental setup to that of R measurement and implementing the angle modulation with a microstep stepping motor. Because the photon energy of CM is dependent on the angle of incidence while that of the excitonic states are not, only the feature related to the angle-dependent CM is detected by the AMR spectra and those of excitonic transitions are inhibited. By using the AMR technique the CM can be resolved unambiguously. We have also performed the angle-dependent differential surface photovoltage spectroscopy (DSPS) and photoluminescence (PL) measurements for cross check and comparison purposes as well as studying the resonance enhancement effect between the excitonic transitions and the CM in the weak-coupling regime. The DSPS has been demonstrated to be a good nondestructive characterization tool for VCSEL structures [15]. The angle-dependent PL spectra were detected at different angle of incidence with respect to the axis perpendicular to the device surface within a small solid angle. The temperature-dependent PL has also been performed in the temperature range between 15 K and 300 K. The amplitudes of the related features reveal the coupling effect between the CM and excitonic transitions.
2. Experimental details
The sample used in this study was grown by metalorganic chemical vapor deposition on an n+ -GaAs (001) substrate. The high reflectivity DBR was built by 30 pairs of Ga0.08Al0.92As/Ga0.88Al0.12As layers. Five undoped 60 Å GaAs wells and 70 Å Ga0.82Al0.18As barriers served as the active region and were sandwiched by Ga0.7Al0.3As/Ga1-xAlxAs (x=0.3 to 0.6) spacer layers to form a single wavelength cavity. The 613 Å Ga0.02Al0.98As layers are placed above and below the spacer layers for selective lateral oxidation to provide optical and electrical confinement.
For R measurement a 150 W tungsten-halogen lamp filtered by a model 270 McPherson 0.35 m monochromator was used as the light source. The monochromatic light used as probe light was modulated at 200 Hz by a mechanical chopper. It was then directed onto the sample at different angles of incidence controlled by a rotary mechanical stage. The reflected light was detected by a Si photodetector and the signal was recorded from an NF model 5610B lock-in amplifier.
The AMR measurement system utilizes similar experimental setup to the R measurement. The modulation mechanism is implemented by mounting the sample on the spool of the micro-step stepping motor controlled by a computer to perform the small angle periodic vibration at 25 Hz. A five phase step motor and a micro-step controller are used to perform high precision control of small angle vibration at ~3.6×10-3 degree. The small vibration of the reflected light spot on the detector due to the vibrating reflected angle may result in some spurious signals due to the position sensitivity of the Si detector. The effect can be eliminated by fixing the reflected light spot position on the detector by using a focusing lens to collect and focus the reflected light. A reference signal coming from the controller was fed into the lock-in amplifier to record the reflected light signal.
In DSPS, the derivative-like surface photovoltage is measured between the sample and a reference grid electrode in a capacitive manner as a function of the photon energy of the probe beam with a wavelength-modulation technique. The light from a 150 W tungsten-halogen lamp was filtered by a 0.25 m monochromator equipped with wavelength-modulation equipments and focused onto the surface of the sample. In this study the wavelength of the probe light is modulated by a vibrating entrance slit operated by a power amplifier, employing a 2 in. loudspeaker as transducer. A beam splitter was placed in the path of the incident light. The intensity of this radiation was monitored by a power meter and was kept constant by a stepping motor connected to a variable neutral density filter, which was also placed in the path of the incident beam. The incident light intensity was maintained at a constant level of 10-4 W/cm2. The illumination intensity and the amplitude of wavelength modulation were experimentally selected at levels not affecting the measured spectra; typically Δλ/λ was on the order of 10-3. Since our measurements were performed over a rather narrow photon energy range, constant intensity is essentially equal to constant photon flux.
The PL measurements were excited by a 6328 Å He-Ne laser with a power density of about 10 mW/cm2 and performed with the same equipments as R measurement. An RMC model 22 close-cycle cryogenic refrigerator equipped with a digital thermometer controller was used for low-temperature measurements. The measurements were made in the temperature range of 15 K<T<300 K with a temperature stability of 0.5 K or better.
3. Results and discussion
The R and AMR spectra at the angle of incidence ranging from 10° to 60° are shown in Fig. 1 by black solid lines. Each R spectrum can be separated into three regions: in the low and high energy regions, the interference features are observed. A high reflectivity stop band including the cavity dip and excitonic kinks is found in the middle region located around 1.45 to 1.55 eV. In the following, we will focus our discussion on the middle region. In the AMR spectra, we only showed the middle region to illustrate the CM feature (the excitonic feature is not present here) at different incident angles. At low angles of incidence, the cavity dip and the excitonic transition features superimposed with each other. For example, a wide dip with a small kink on its high-energy lobe is observed in the R spectrum at angle of 10°. When the incident angles are larger than 40°, the cavity dip has shifted away from the spectral region of the excitonic transitions. Two distinct shallow kink structures, labeled as E11H and E11L, are identified as the transitions coming from the ground state in the conduction band to the ground states in the heavy-hole (11H) and light-hole (11L) valence bands, respectively.
Fig. 1. The R and AMR (solid lines) spectra at the angle of incidence ranging from 10° to 60°. The middle region of the spectrum at 10° is enlarged for easy viewing of the features in the neighborhood of the small kink. The open circles are the least-squares fits to the first derivative Lorentzian line shape of the AMR spectra..
In order to identify these two transitions, one dimension Schrödinger equation has been solved, using the value of the conduction band offset Qc=0.65 and taking the quantum well width to be 60 Å and an Al composition of 0.178. The calculated values of 11H and 11L transitions are 1.462 and 1.479 eV, respectively. These values match quite well with the energies of the kink structures. As the angle of incidence is increased from 10° to 40°, the CM shifts to higher energies and crosses the 11L and 11H transitions sequentially. From the results of R spectra, we find that the excitonic states of the quantum well structure are angle independent while the CM shifts to higher energy with the increasing angle of incidence. In order to separate the effect of the CM from the mixing R spectra, the AMR was employed to identify the CM at different incident angles. For the AMR spectrum, due to the periodical modulation of the incident angle, the angle dependent CM dip is revealed in a derivative like feature while the angle independent excitonic transition features were excluded. Thus only a simple feature was found in the middle region of each AMR spectrum. The photon energy of CM has been determined by the least-squares fits to the first derivative Lorentzian line shape (FDLL) and illustrated by open circles. The AMR spectra also show the smooth shift, as guided by a solid line with an arrow at the end, with increasing angle of incidence.
Fig. 2. The DSPS (black solid lines) and the least-squares fits to the first derivative Lorentzian line shape (red open circles) at the angle of incidence ranging from 10° to 60°.
Fig. 3. The black solid lines show the PL spectra at the angle of incidence in the range between 10° and 60°. The open circles are the least-squares fits to Gaussian profiles.
In order to investigate the excitonic transitions clearly, the DSPS measurements have been performed in the photon energy range between 1.44 and 1.52 eV. The solid lines in Fig. 2 are the DSPS spectra at the angle ranging from 10° to 60°. Two clear features with different amplitudes are observed at the fixed energies, labeled as E11H and E11L. The amplitude of the first feature shows an increase at the small angles and then decreases quite rapidly. For the second feature a similar behavior is also observed except that it approaches the maximum value at a larger angle. Because the photon energy of CM located in the same photon energy region corresponding to the excitonic transitions at angles ranging from 10° to 40°, no obvious CM feature could be identified. At large incident angles, such as 50° and 60°, a clear feature, guided by a solid line with an arrow at the end, appeared at the higher energy end with respect to the features of excitonic transitions. In order to extract the transition energies and amplitudes of the excitonic features, least-squares fits to the FDLL have been done and shown by the open circles. Within experimental errors, the transition energies at 1.464 and 1.479 eV are assigned as 11H and 11L, respectively, and they remain unchanged while the angle of incidence is changed. The amplitudes of 11H and 11L features changed with increasing angle. These results are summarized in Figs. 4(a), 4(b), and 4(c) and will be discussed later.
Figure 3 depicts the PL spectra resulting from the excitonic recombinations and the cavity resonance at the angle of incidence in the range between 10° and 60° by solid lines. For better comparison, the spectra are displaced vertically and multiplied by different factors to normalize their amplitude. At angles ranging from 10° to 20°, only one luminescent feature is observed with the same peak energy. This feature is due to the 11H spontaneous emission coming from the direct recombination between the ground state electrons and holes in the conduction and heavy-hole valence bands, respectively. At the angle of 30°, the PL spectrum is broadened by another luminescent feature located at higher energy side. As the angle is gradually increased to 40°, due to the increased amplitude of the second feature the PL spectrum is continuously extended on the higher energy side and shown as a small terrace. This second feature remained at the fixed photon energy (11L) but its amplitude is enhanced by the cavity mode. For the angles larger than 50°, a PL feature possessing the energy matches with the cavity mode continuously moving to the higher energy side. As the cavity mode shifts toward high energy and moves away from 11L feature, the right side of the terrace gradually decays into a small slope as the result of the diminish of cavity mode enhance effect. The open circles show the least-squares fits to Gaussian profiles to extract the transition energies and amplitudes of the excitonic features and CM. The fitted amplitudes of 11H and 11L are shown by diamond symbols in Figs. 4(b) and 4(c).
Fig. 4. (a) The square and diamond symbols show the energies of 11H and 11L, respectively. The triangle symbols are the CM energies; (b) the square and diamond symbols show the 11H transition amplitude fitted from DSPS and PL spectra, respectively; (c) the square and diamond symbols show the 11L transition amplitude fitted from DSPS and PL spectra, respectively.
Figure 4 summarizes the results of the AMR, DSPS and PL spectra. The square and diamond symbols presented in Fig. 4(a), respectively, show the angle dependence of 11H and 11L excitonic transition energies determined from FDLL fits to the DSPS spectra. It is found that within experimental errors, E11H and E11L remain fairly constant with respect to the angle of incidence. The triangle symbols are the CM energies (ECM) determined from FDLL fits to the AMR spectra shown in Fig. 1. This curve shows the angular dependence of λ CM , where λ CM = 1240/ECM, which can be fitted with
In Eq. (1), m is an interger, λ CM(0°) is the wavelength at normal incidence, d is the effective thickness, and n is the effective refraction index for the cavity. The effective cavity length and effective refraction index are deduced to be 2424±50 Å and 3.514±0.002, respectively. The value of the determined effective cavity length is in reasonable agreement with the intended number. By comparing the angle dependence of 11H, 11L, and ECM, it has been found that the resonant crossing of ECM with E11H occurs at 15° and ECM resonates with E11L at 35°. The fitted amplitudes of 11H and 11L are shown by square and diamond symbols for DSPS and PL spectra, respectively, in Figs. 4(b) and 4(c). As indicated by the two vertical lines with arrow at the end, it is noted that maximum amplitudes occur at the energy where the cavity mode matches the quantum well excitonic transitions.
Fig. 5. The PL (solid lines) spectra at different temperature and at the angle of incidence of 60°. The open circles are the least-squares fits to the first derivative Lorentzian line shape.
Figure 5 shows the PL spectra measured at the temperature ranging from 15 K to 300 K and the angle of incidence is fixed at 60°. The open circles are least-squares fits to the Gaussian line shape. At 300 K, the PL spectrum can be well fitted by three PL structures located at 1.464, 1.479, and 1.506 eV, respectively, and labeled as E11H, E11L, and ECM. When the temperature decreases, E11H and E11L move to higher energy in a parallel attitude. This is due to the increasing of energy gap in well material. The ECM also shifts to higher energy due to the decreasing of effective cavity length as a result of thermal expansion and temperature-dependent refraction index [16]. It is found that the peak positions of excitonic features shift faster than that of the cavity mode, as guided by the solid lines. The photon energy of cavity mode matches the excitonic energy of 11L and 11H at about 220 K and 160K, respectively. As the temperature decreases below 160 K, only one PL peak is observed since no luminescent process can occurs at the photon energy lower than the lowest excitonic transition energy, the cavity mode enhancement effect is diminished.
4. Conclusions
In conclusion, the angle dependent R, AMR, DSPS, and PL measurements have been performed in this study to investigate a GaAs/GaAlAs asymmetric microcavity structure. When the CM crosses the 11L and 11H transitions no Rabi splitting is observed. This shows that the resonance effect between the excitonic transitions and the CM is in a weak-coupling regime. The newly implemented AMR technique is able to resolve the photon energy of CM unambiguously from that of the overlapped quantum well excitonic transitions. The coupling strength reflects on the amplitude of the DSPS and PL spectra, which will be enhanced when the CM matches up with the excitonic transitions. The temperature dependent PL has indicated that the cavity mode enhancement effect is diminished as the energy of CM is lower than the excitonic transition energy. These results give us useful information to check that growth has met the specifications. The experimental techniques of angle dependent R, DSPS, PL as well as the new AMR technique have been demonstrated to be effective optical diagnostic methods for studying the asymmetric microcavity structure.
Acknowledgments
The author would like to acknowledge the support of the National Science Council of the Republic of China under Project No. NSC 93-2112-M-018-006.
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