APPLIED PHYSICS LETTERS
VOLUME 76, NUMBER 8
21 FEBRUARY 2000
Refractive indices and absorption coefficients of Mgx Zn1À x O alloys C. W. Teng and J. F. Mutha) Department of Electrical and Computer Engineering, North Carolina State University, Raleigh, North Carolina 27695-7911
¨. O ¨ zgu¨r, M. J. Bergmann, and H. O. Everitt U Department of Physics and Department of Computer and Electrical Engineering, Duke University, Durham, North Carolina 27708
A. K. Sharma, C. Jin, and J. Narayan Department of Materials Science and Engineering, North Carolina State University, Raleigh, North Carolina 27695-7916
共Received 24 November 1999; accepted for publication 21 December 1999兲 Indices of refraction for Mgx Zn1⫺x O epitaxial films grown by pulsed-laser deposition on sapphire substrates with x up to 0.36 were determined in the range of wavelength 457–968 nm by analysis of optical transmission spectra and prism-coupled waveguide measurements. The dispersion follows the first-order Sellmeier dispersion equation. Absorption coefficients, exciton energy gaps, and binding energies of Mgx Zn1⫺x O alloys were determined by transmission spectroscopy. The excitonic absorption features were clearly visible at room temperature despite alloy broadening. These results provide important information for the design and modeling of ZnO/MgZnO heterostructure optoelectronic devices. © 2000 American Institute of Physics. 关S0003-6951共00兲01408-X兴
In the past several years, a great deal of research efforts on wide band gap semiconductors have resulted in the commercialization of group III-nitride based blue lasers, light emitting diodes, and ultraviolet photodetectors for use in display, optical data storage, and solar-blind detection applications.1 As an alternative to the GaN material system, ZnO and its alloys are of substantial interest. The exciton binding energy of ZnO is ⬃60 meV and results in extremely efficient emission with room temperature optically pumped lasing reported in thin films and microcrystallites.2–4 Alloying ZnO films with MgO facilitates band gap engineering for heterostructure device design.5 We have recently synthesized Mgx Zn1⫺x O films on sapphire by pulsed-laser deposition 共PLD兲. Intense ultraviolet band edge photoluminescence and excitonic absorption structures were observed at room temperature in films up to 36 at. % Mg incorporation.6 A superlattice structure made of ZnO and Mg0.2Zn0.8O was recently demonstrated by Ohtomo et al., suggesting the feasibility of ZnO based quantum structures.7 In order to accurately model and design MgZnO/ZnO heterostructure optoelectronic devices, a precise knowledge of the fundamental optical properties for ZnO and its alloys is important. Optical constants for single crystal ZnO have been previously reported.8–10 However, there are currently no reports on refractive indices of Mgx Zn1⫺x O alloys. The high exciton binding energies of these alloys are especially interesting. In typical semiconductor alloys, alloy broadening obscures the excitonic absorption features at room temperature. For example, while the exciton is clearly visible in GaN at room temperature, alloy broadening and internal electric fields disassociate the exciton in AlGaN alloy films of coma兲
Author to whom correspondence should be addressed; electronic mail: [email protected]
parable thickness.11 In this letter, the refractive indices obtained by prism-coupled waveguide measurements, absorption coefficients, exciton binding energies, and broadening parameters of Mgx Zn1⫺x O alloys obtained from optical transmission measurements are reported. Two series of Mgx Zn1⫺x O films grown on doublepolished 共0001兲 sapphire substrates by pulsed-laser deposition were examined. Details of the growth procedure were described in Ref. 6. Three samples (x⫽0.00, 0.24, and 0.36兲 with thickness ranging from 0.7 to 1 m were used in prism coupling measurements in order to support at least two waveguide modes. The other set of samples (x⫽0.00, 0.18, 0.27, and 0.36兲 less than 0.5 m thick were used for optical transmission measurements in order to observe excitonic absorption features. All films are highly crystalline as determined by x-ray diffraction 共XRD兲 and Rutherford backscattering 共RBS兲 ion channeling spectra. No second phase inclusions in these films were observed by transmission electron microscopy 共TEM兲 and the corresponding selected area diffraction patterns. The molar concentration of Mg was determined by RBS as well as photoluminescence spectra. A prism-coupling technique was used to measure the refractive indices of Mgx Zn1⫺x O films. A rutile TiO2 prism was used to couple light into the air/MgZnO/sapphire waveguide. In this geometry waveguide coupling only occurs at discrete mode angles when the photon tunnels through the air gap with the proper propagation constant to travel in the waveguide. Measurement of two or more mode angles permits one to obtain both the index of refraction and the film thickness to high accuracy.12 In birefringent materials such as MgZnO, the ordinary and extraordinary indices are obtained by performing the experiment for transverse electric and transverse magnetic polarization, respectively. The experiment setup used here has been used for Alx Ga1⫺x N thin
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Teng et al.
Appl. Phys. Lett., Vol. 76, No. 8, 21 February 2000
FIG. 2. The absorption coefficients for Mgx Zn1⫺x O alloys at room temperature 共solid lines兲 clearly show excitonic resonance despite alloy broadening. The fits using excitonic theory of absorption are plotted as dotted lines. The absorption spectrum for ZnO with the A and B excitons individually resolved at room temperature is shown in the inset for comparison.
FIG. 1. The ordinary and extraordinary refractive indices of Mgx Zn1⫺x O films (x⫽0, 0.24, and 0.36兲. The solid curves are least-square fit to the first-order Sellmeier dispersion relationships.
films.13 In this study, six laser wavelengths, 457.9, 488, 514.5, 632.8, 676.2, and 968.3 nm were used. Very little scattering was observed, indicating that the film morphology and crystallinity were good. The measured ordinary (n o ) and extraordinary (n e ) refractive indices of Mgx Zn1⫺x O films for x⫽0.00, 0.24, and 0.36 as functions of wavelength are plotted in Fig. 1. The index of refraction of cubic MgO crystal measured by Stephens and Malitson14 was also plotted in Fig. 1 for reference. The data at each Mg concentration were fitted by leastsquare method to the first-order Sellmeier dispersion relationship n 共 兲 2 ⫽1⫹
A 0 2 2 ⫺ 20
where A o and 0 are fitting parameters.15 The fitted values are listed in Table I. The refractive index of a thin film below the band gap can also be determined by analyzing the interference fringes of optical transmission spectra. The technique has been outlined by Swanepoel16 for amorphous silicon films and been applied to III-nitride17,18 and other films. Optical transmission measurements were carried out over the wavelength range of 200–3300 nm using a Cary 5E UV-VIS-NIR spectrophotometer at room temperature and 77 K. The long wavelengths allow the order of the interference fringes to be TABLE I. Fitting parameters in the first-order Sellmeier dispersion formula.
Ordinary index A 0 Ordinary index 0 (nm) Extraordinary index A 0 Extraordinary index 0 共nm兲
2.60⫾0.02 211.4⫾3.7 2.66⫾0.02 214.3⫾5.1
2.37⫾0.003 179.3⫾1.2 2.43⫾0.01 181.5⫾1.6
2.27⫾0.004 168.6⫾0.8 2.32⫾0.01 180.1⫾1.6
unambiguously determined. Rather than using the film thickness obtained by the Swanepoel procedure, more accurate thicknesses obtained from the prism coupling measurements were used to extract the index of refraction from the transmission spectra. The indices of refraction obtained from this technique were consistent with those obtained from the prism-coupling measurements. By linearly fitting the Sellmeier parameters as functions of Mg concentration and using the measured film thickness, absorption coefficients can be found by computing the optical transmission through the Mgx Zn1⫺x O sapphire layered structure with all multiple internal reflections taken into account.19 The refractive indices above the band gap were determined from the reflectance data. Published data20 were used for the refractive index of sapphire as a function of wavelength. The room temperature absorption coefficients of Mgx Zn1⫺x O films with x⫽0.19, 0.27, and 0.36 are shown in Fig. 2. The magnitudes of the absorption coefficients are comparable to ZnS and other II–VI semiconductors.21 Alloy broadening obscures the details of the individual exciton structures. However, the net influence on the absorption peaks is significant and has the spectral line shape predicted by Elliot22 for hydrogenic excitons. We have previously modeled the excitonic absorption of a single crystal ZnO film.10 Briefly, the discrete states of the excitons were modeled with a broadened Lorentzian line shape
␣ 共 E 兲 ⫽Im
兺 m⫽1 兺 n⫽A,B,C
ex A 0n
1 Rn E 0n ⫺ 2 ⫺E⫺i⌫ ex,m m
where n is the index number of the valence band, m is the index number of the excited state of the exciton, R n is the binding energy, ⌫ ex,m is a broadening parameter of the mth ex is excited exciton state, E 0n is the band gap energy, and A 0n an adjustable fitting parameter. This is summed with the continuum absorption above the band gap, which has the form22
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Teng et al.
Appl. Phys. Lett., Vol. 76, No. 8, 21 February 2000 TABLE II. The exciton band gap energies, the exciton binding energies, and exciton broadening parameters of Mgx Zn1⫺x O epitaxial layers. x⫽0 共Ref. 10兲 x⫽0.19 x⫽0.27 x⫽0.36
At room temperature A-exciton energy gap 共eV兲 A-exciton binding energy 共meV兲 A-exciton ⌫ ex,1 共meV兲 B-exciton energy gap 共eV兲 B-exciton binding energy 共meV兲 B-exciton ⌫ ex,1 共meV兲 C-exciton energy gap 共eV兲 C-exciton binding energy 共meV兲 C-exciton ⌫ ex,1 共meV兲
␣共 E 兲⫽
3.40 63.1 1.5 3.45 50.4 4.8 3.55 48.9 8.0
共 E⫺E 0n 兲 1/2
3.76 60.4 48.3 3.82 51.5 69.6 3.92 50.5 73.9
E 2 sinh 1
冑共 E⫺E 0n 兲 /⌫ n
Rn E⫺E 0n
3.92 60.4 67.0 4.00 51.5 104.9 4.16 50.5 103.0
4.19 60.4 79.9 4.27 51.5 94.1 4.38 50.5 80.6
E⫺E 0 , EU
In conclusion, we have investigated the roomtemperature absorption coefficients and refractive indices of Mgx Zn1⫺x O epitaxial layers synthesized by pulsed-laser deposition on 共0001兲 sapphire substrates. The indices of refraction below the band gap were obtained by fitting transmission spectra and by a prism coupling waveguide method. They are well described by the first-order Sellmeier relation. The absorption coefficients, exciton energy gaps, and binding energies were determined from transmission measurements. These results provide important information for the design and modeling of ZnO/MgZnO heterostructure optoelectronic devices. This work was supported in part by DARPA Grant No. N00014-96-1-0738, U.S. Army Research Office Grant Nos. DAAH04-93-D0002 and DAAH04-96-0076, and National Science Foundation Center for Advanced Materials and Smart Structures.
e 冑R n / 共 E⫺E 0n 兲
冉冑 冊 Rn
The last term in brackets is a broadening function with ⌫ n as an additional parameter used to smooth the discontinuity at the band gap. The absorption spectra for films of different Mg compositions were fitted with the above model and are plotted as dotted lines in Fig. 2. The parameters extracted from the data fitting are listed in Table II. As expected, the exciton broadening parameters for these ternary alloys were found to be much larger than those of ZnO and Al0.05Ga0.95N. 23 However, the broadening is compensated by the extremely high binding energy of the exciton, making excitonic effects an important part of optoelectronic device design in this material system. Alloy composition fluctuation makes the absorption edges of MgZnO alloys less distinct than ZnO. The absorption coefficients just below the fundamental gap can be described as
␣ 共 E 兲 ⫽ ␣ 0 exp
where E 0 is the band gap energy and E U is Urbach energy.24 The Urbach energies were fitted within the spectral range where the absorption coefficient-thickness products were greater than unity. Their values range from 55 meV 共x⫽0.19兲 to 90 meV 共x⫽0.36兲 at room temperature. The Urbach energies were measured over a temperature range from 77 to 295 K and displayed variations of less than 4 meV. This weak temperature dependence suggests the main scattering mechanism of optical absorption is from alloy composition fluctuation. The larger Urbach energy for the films of higher Mg incorporation indicates more randomness in these alloys.
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