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Optical properties of a lattice matched GaAs/In0.5(AlxGa1-x)0.5P/GaAs heterostructure cavity have been characterized using piezoreflectance (PzR) measurements in the temperature range between 20 and 300 K. The measurements were carried out in the energy range of 1.3-6 eV. The PzR spectra of In0.5(AlxGa1-x)0.5P at 20 and 300K clearly show a lot of interband transition features present at energies above the band edge. There is also a feature of interference-fringes oscillations observed in each PzR spectrum below band gap E0 of In0.5(AlxGa1-x)0.5P. The oscillation period in between the PzR interference fringes can be utilized to determine the index of refraction (n) for the In0.5(AlxGa1-x)0.5P at different temperatures. The Al composition x of In0.5(AlxGa1-x)0.5P can be estimated from the evaluation value of E0 by PzR. The obtained Al composition of x=0.691 is in good agreements with the original design for growing the quaternary compound. Electronic band structure of In0.5(Al0.7Ga0.3)0.5P is determined by the interband transitions from PzR. The temperature variations of the transition energies and index of refraction n for the In0.5(AlxGa1-x)0.5P are analyzed discussed. The PzR is proven to be very sensitive in determining the optical parameters in III-V GaAs/InAlGaP/GaAs Fabry-Perot system.
©2007 Optical Society of America
1. Introduction
Quaternary alloy compounds of In0.5(AlxGa1-x)0.5P with lattice matched to GaAs are very attractive because of their various applications to visible laser diodes (LDs) [1, 2], light-emitting diodes (LEDs) [3], and high-electron mobility transistors (HEMTs) [4]. The In0.5(AlxGa1-x)0.5P/GaAs alloy lasers had been proven to possess high efficiency emitting in red to green portion. The InAlGaP LEDs also showed much better performance than the other devices made by GaAsP:N in the yellow and orange range [3]. Beyond the superior characteristic in the luminescence devices, the In0.5(AlxGa1-x)0.5P with x~ 0.2-0.7 was also utilized in a GaAs/In0.5(AlxGa1-x)0.5P/GaAs [or a GaAs/In0.5(AlxGa1-x)0.5P/InGaAs] system to be a high-gap material for achieving camel-gate high-electron mobility transistors (CAM-HEMTs) [4]. Such a CAM-HEMT demonstrates a lot of benefits of large gate voltage swing, high gate-source breakdown voltage, and improvements in the high-temperature threshold characteristics in III-V microwave devices [4]. A lattice-matched structure by GaAs/In0.5(AlxGa1-x)0.5P/GaAs is not only a good resonant cavity for a laser-diode device but also a fundamental unit for a microwave device with superior performance. The present work concentrates on studying the optical property of a GaAs/In0.5(AlxGa1-x)0.5P/GaAs heterostructure by using piezoreflectacne (PzR) measurement in the temperature range of 20-300 K. Modulation spectroscopic techniques such as thermoreflectance (TR) [5], photoreflectance (PR) [6], and piezoreflectance (PzR) [7] had proven to be very powerful for studying semiconductors and device structures. The derivative-like nature of modulation spectra suppresses uninteresting background effects and emphasizes the structures localized in the energy region near direct-interband transitions of semiconductors. In this study, a lattice-matched GaAs/In0.5(AlxGa1-x)0.5P/GaAs heterostructure has been characterized by PzR in a wide energy range from 1.3 to 6 eV. A lot of interband transition features and an interference-fringe oscillation are simultaneously detected in the PzR spectra of 20 and 300 K. The Al composition x of In0.5(AlxGa1-x)0.5P is determined to be x=0.691 from the evaluation value of E0. Electronic band structure of the InAlGaP is determined by the interband transitions of In0.5(AlxGa1-x)0.5P from PzR. The refraction index (n) for the In0.5(Al0.7Ga0.3)0.5P below the band edge is also evaluated by the oscillation period of the PzR interference fringes. Temperature dependences of refractive index n and band gap E0 for the In0.5(Al0.7Ga0.3)0.5P are evaluated. The GaAs/In0.5(AlxGa1-x)0.5P/GaAs system is shown to be lattice matched in whole the temperature range from 20 to 300 K.
2. Experiment
The GaAs/In0.5(AlxGa1-x)0.5P/GaAs heterostructure system was grown on a semi-insulating (001) GaAs substrate by low-pressure metallorganic chemical vapor deposition (LP-MOCVD). The heterostructure consists of a 300-nm undoped GaAs buffer grown on semi-insulating GaAs substrate (see Fig. 1), and then an 1500-nm thick In0.5(AlxGa1-x)0.5P layer with nominal Al composition of x~0.7 is epitaxial on the buffer layer, and finally the InAlGaP layer is capped with a 75-nm n+-GaAs layer to form a GaAs/InAlGaP/GaAs cavity system. The growth pressures of all of the layers were 100 Torr. The growth temperatures for InAlGaP and GaAs were 700 and 650 °C, respectively. Trimethylindium (TMI), trimethylgallium (TMG), trimethylaluminum (TMA), arsine (AsH3), and phosphine (PH3) were used as the In, Ga, Al, As, and P sources. Silane (SiH4) was adopted as the n-type source. X-ray diffraction measurements confirmed the zinc-blend phase of the InAlGaP layer with the lattice constant in consistent with GaAs.
Fig. 1. The representative scheme of the lattice-matched heterostructure system of GaAs/In0.5(AlxGa1-x)0.5P/GaAs. The lights’ resonant effect inside the cavity is shown.
The PzR measurements were achieved by gluing the thin GaAs/In0.5(AlxGa1-x)0.5P/GaAs specimen on a 0.15 cm thick lead-zirconate-titanate (PZT) piezoelectric transducer driven by a 200 Vrms sinusoidal wave at 200 Hz. The alternating expansion and contraction of the transducer subjects the sample to an alternating strain with a typical rms Al/l value of ~10-5. The measurements were done in a wide energy range of 1.25 to 6 eV. For low-energy measurement (E < 2.7eV), an 150 W tungsten-halogen lamp filtered by a PTI 0.2 m monochromator provided the monochromatic light. The reflected light from the sample was detected by an EG&G type HUV-2000B silicon photodiode. For higher-energy experiment (E ≥ 2eV), an 150 W xenon-arc lamp acted as the light source, and a Hamamatsu H3177-51 photomultiplier tube module employed as the photodetector. The ac and dc signals were recorded via an EG&G model 7265 dual phase lock-in amplifier. The PzR measurements were done in the temperature range between 20 and 300 K with a temperature stability of 0.5 K or better. A RMC model 22 closed-cycle cryogenic refrigerator equipped with a model 4075 digital thermometer controller was utilized to facilitate the temperature dependent measurements.
3. Results and discussion
Figure 2 shows the experimental PzR spectra of the heterostructure system of GaAs/In0.5(AlxGa1-x)0.5P/GaAs sample at 20 and 300 K. The dashed lines are the experimental data and solid curves are least-square fits to a Lorentzian line-shape function appropriate for the interband transitions expressed as [7, 8]:
where i represents the respective transition features in the PzR spectrum, Aex i and ϕ ex i are the amplitude and phase of the lineshape , and Eex i and Γex i are the energy and broadening parameter of the interband transitions. As shown in Fig. 2, a lot of critical-point transitions as well as a obvious feature of oscillation fringes are simultaneously detected in the PzR spectra of GaAs/In0.5(AlxGa1-x)0.5P/GaAs at 20 and 300 K. The feature of oscillation fringes is arisen from the resonant interference by multiple reflections in between the Fabry-Perot cavity of the GaAs/In0.5(AlxGa1-x)0.5P/GaAs (see Fig. 1). The critical-point transition features in Fig. 2 demonstrate an energy redshift behavior with increasing the temperatures from 20 to 300 K. The energy difference of the spectral period in between the oscillation fringes also shows somewhat shrinkage with respect to the increase of temperatures. The experimental data of PzR spectra shown in Fig. 2 can be fitted to Eq. (1), which yields transition energies are indicated with arrows. The obtained values of transition energies of the GaAs/In0.5(AlxGa1-x)0.5P/GaAs at 20 and 300 K are listed in Table 1 together with the values for a quaternary In0.34Al0.66As0.85Sb0.15 compound [9] are included for comparison. The value of E0 for the In0.5(AlxGa1-x)0.5P is determined to be 2.328 eV at 300 K. The value of E0 can be utilized to evaluate the aluminum composition x in the In0.5(AlxGa1-x)0.5P compound by using an empirical expression of E0(x)=1.89+0.51∙x+0.18∙x2 eV [2]. The Al composition of the quaternary compound is estimated to be x≈0.691. The Al composition is in good agreements with the nominal stoichiometry of x=0.7 for growing the quaternary compound. Also shown in Table 1, the energy difference of the band-edge transitions Eind g and E0+∆0 for a quaternary In0.34Al0.66As0.85Sb0.15 at 20 and 300 K is about 67±5 meV, the value is in good agreements with the difference of E0 for InP in a lattice-matched In0.34Al0.66As0.85Sb0.15/InP system [9]. This result implies that both In0.34Al0.66As0.85Sb0.15 and InP should possess the similar thermal expansion coefficient, which renders the III-V system being lattice matched in whole the temperature range from 20 to 300 K. Also observing in the transition energies of the GaAs/In0.5(AlxGa1-x)0.5P/GaAs system in Table 1, the energy difference of E0, E0+∆0, and E1 for the In0.5(Al0.7Ga0.3)0.5P at 20 and 300 K is about 100±6 meV, which agrees well with the energy deviation of E0 and E1 by temperature for the GaAs. This result verifies that both In0.5(Al0.7Ga0.3)0.5P and GaAs in the GaAs/In0.5(Al0.7Ga0.3)0.5P/GaAs system should also possess the similar thermal expansion coefficient. The system is lattice matched in whole the temperature range from 20 to 300 K. The mean thermal expansion coefficient α of a material with diamond or zinc-blend structure in temperature interval ∆T is expressed as [10]:
Table 1. Energies of critical-point transitions of a GaAs/In0.5(Al0.7Ga0.3)0.5P/GaAs system obtained by PzR measurements. The values for a quaternary compound system of In0.34Al0.66As0.85Sb0.15 epitaxy on InP are also included for comparison [9].
where ∆a is the change of lattice constant in ∆T. The thermal expansion coefficient of GaAs is about 6.01×10-6/°C [11]. The lattice constant for GaAs is a = 5.65 Å at 300 K. Initially, the as-grown thickness of the InAlGaP layer is 1500 nm at 300 K. It is inferred that if the temperature down to 20 K, the layer thickness of the In0.5(Al0.7Ga0.3)0.5P is shrinkage to about 1497.5 nm by the reduction of lattice constant from Eq. (2).
Temperature dependent PzR spectra of the GaAs/In0.5(Al0.7Ga0.3)0.5P/GaAs system below the band edge are displayed in Fig. 3. The solid lines are experimental data and hollow-circle lines are least-square fits to Eq. (1), which yield transition energies are indicated by arrows. The transition features of E0 and E0+∆0 for In0.5(Al0.7Ga0.3)0.5P demonstrate an energy red-shift character with respect to the increase of temperatures from 20 to 300 K. The temperature variations of transition energies of E0 and E0+∆0 for In0.5(Al0.7Ga0.3)0.5P in the temperature range of 20-300 K are shown in Fig. 4. The energy reduction of E0 and E0+∆0 with increasing temperatures is due to the thermal dilation of bond length in the In0.5(Al0.7Ga0.3)0.5P. The temperature dependence of transition energies of E0 and E0+∆0 for InAlGaP can be analyzed by a Varshni semiempirical relationship [12]:
where Ei(0) is the excitonic transition energy at absolute zero; α and β are constants. The constant α is related to the electron-phonon interaction and β is closely related to the Debye temperature [12]. The fits yield fitting parameters are E(0)=2.426±0.002 eV, α=0.63±0.05 meV/K, and β=260±50 K for E0, and E(0)=2.529±0.002 eV, α=0.65±0.05 meV/K, and β=260±50 K for E0±∆0, respectively. The values of α and β for the InAlGaP are in accordance with those obtained for GaAs by optical absorption [13]. This result also verifies that the GaAs/In0.5(Al0.7Ga0.3)0.5P/GaAs system is lattice matched in whole the temperature range from 20 to 300 K.
Also seeing in Fig. 3, with the energies lower than E0, an interference-fringes oscillation below the band edge of In0.5(Al0.7Ga0.3)0.5P are clearly observed in each PzR spectrum at different temperatures. The oscillation fringe is arisen from the interference effect in between the Fabry-Perot cavity of the GaAs/In0.5(Al0.7Ga0.3)0.5P/GaAs system below E0 of the InAlGaP. The oscillation period of the PzR fringes in Fig. 3 (i.e. h∆v) shows the gradually-enlarged energy separation with respect to the decrease of temperatures from 300 down to 20 K. The oscillation period of the interference fringes by PzR can be utilized to determine the below-band-edge refractive index n for the InAlGaP. The oscillation period in between the reflectivity peaks of a reflectance spectrum in the layers is expressed as [14]:
where n is the index of refraction below the band edge, and d is the layer thickness. If the probing light is nearly normal incidence to the sample in PzR, the value is of cos ϕ ≈1 taking in Eq. (4). The layer thickness d of In0.5(Al0.7Ga0.3)0.5P at various temperatures can be evaluated from Eq. (2) by taking into account the thermal expansion coefficient the same as GaAs. By using Eq. (4), the below-band-edge refractive index n of In0.5(Al0.7Ga0.3)0.5P from 20 to 300 K can be calculated and depicted in Fig. 5. When the temperature is raised, the index of refraction n for In0.5(Al0.7Ga0.3)0.5P is increased due to the shrinkage of energy gap as shown in Fig. 4. Temperature dependences of the refractive index of In0.5(Al0.7Ga0.3)0.5P shown in Fig. 5 can be analyzed by an expression of n(T) = n(0)+a1 *T+a2 *T2. The fitting result yields a solid line depicted in Fig. 5. The obtained fitting parameters are n(0)=3.038, a1=3×10-4 (K-1), and a2=3.2×10-8 (K-2) for the In0.5(Al0.7Ga0.3)0.5P. The fitting result shows approximately a linear temperature dependence of the below-band-edge refractive index n(T) for the quaternary In0.5(Al0.7Ga0.3)0.5P.
Fig. 5. Temperature dependence of the below-band-edge refractive index n for the In0.5(Al0.7Ga0.3)0.5P.
4. Conclusions
The GaAs/In0.5(AlxGa1-x)0.5P/GaAs heterostructure system has been characterized using PzR measurement in the temperature range between 20 and 300 K. The electronic band structure for the III-V quaternary system is determined. The Al composition of the In0.5(AlxGa1-x)0.5P is determined to be x=0.691 from the evaluation value of E0. Temperature dependence of transition energies of E0 and E0+∆0 for the In0.5(Al0.7Ga0.3)0.5P is obtained. The GaAs/In0.5(AlxGa1-x)0.5P/GaAs system is confirmed to be lattice matched in whole the temperature range from 20 to 300 K. The below-band-edge refractive index for the In0.5(Al0.7Ga0.3)0.5P is evaluated by the oscillation fringes of the PzR spectrum. The temperature variation of the below-band-edge refractive index for the In0.5(Al0.7Ga0.3)0.5P is determined to be n(T)= 3.038+3×10-4 ∙T+3.2×10-8T2. The PzR technique is proven to be very effective in the determination of critical-point transitions and refraction index for the III-V GaAs/In0.5(AlxGa1-x)0.5P/GaAs cavity system.
Acknowledgments
The authors would like to acknowledge the financial support from the National Science Council of Taiwan under the grant No. NSC 95-2221-E-259-031-MY3.
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