SCIENCE CHINA Physics, Mechanics & Astronomy • Article •
November 2013 Vol.56 No.11: 2059–2064 doi: 10.1007/s11433-013-5202-6
Temperature dependence of the point defect properties of GaN thin films studied by terahertz time-domain spectroscopy FANG HeNan1, ZHANG Rong1*, LIU Bin1*, LI YeCao1, FU DeYi1, LI Yi1, XIE ZiLi1, ZHUANG Zhe1, ZHENG YouDou1, WU JingBo2, JIN BiaoBing2, CHEN Jian2 & WU PeiHeng2 1
Jiangsu Provincial Key Laboratory of Advanced Photonic and Electronic Materials, School of Electronics Science and Engineering, Nanjing National Laboratory of Microstructure, Nanjing University, Nanjing 210093, China; 2 Research Institute of Superconductor Electronics, School of Electronic Science and Engineering, Nanjing National Laboratory of Microstructure, Nanjing University, Nanjing 210093, China Received June 8, 2012; accepted August 31, 2012; published online September 3, 2013
The dielectric functions of GaN for the temperature and frequency ranges of 10–300 K and 0.3–1 THz are obtained using terahertz time-domain spectroscopy. It is found that there are oscillations of the dielectric functions at various temperatures. Physically, the oscillation behavior is attributed to the resonance states of the point defects in the material. Furthermore, the dielectric functions are well fitted by the combination of the simple Drude model together with the classical damped oscillator model. According to the values of the fitting parameters, the concentration and electron lifetime of the point defects for various temperatures are determined, and the temperature dependences of them are in accordance with the previously reported result. Therefore, terahertz time-domain spectroscopy can be considered as a promising technique for investigating the relevant characteristics of the point defects in semiconductor materials. THz time-domain spectroscopy, GaN film, temperature dependence PACS number(s): 78.20.Ci, 78.20.Bh, 78.30.Fs Citation:
Fang H N, Zhang R, Liu B, et al. Temperature dependence of the point defect properties of GaN thin films studied by terahertz time-domain spectroscopy. Sci China-Phys Mech Astron, 2013, 56: 20592064, doi: 10.1007/s11433-013-5202-6
1 Introduction Gallium nitride (GaN) is one kind of direct, wide bandgap semiconductor which has been intensely studied over the last ten years. It has multiple applications in blue and ultraviolet light-emitting diodes and laser diodes for solid state lighting. Another important area of interest for the study of AlGaN/GaN heterostructures is to fabricate high power electronic devices, owing to their high breakdown fields, large electron saturation velocities, and chemical stability at
*Corresponding author (ZHANG Rong, email:
[email protected]; LIU Bin, email:
[email protected]) © Science China Press and Springer-Verlag Berlin Heidelberg 2013
high temperatures. In addition, it is one of the promising materials for high-frequency transistors operated within the gigahertz and terahertz frequency ranges [1,2]. Recently, terahertz emission has also been reported in InGaN/GaN structures when excited by a blue femtosecond laser [3]. For the successful application of any semiconductor, it is important to understand the behavior of native point defects. The point defects often control, directly or indirectly, compensation, minority carrier lifetime, and luminescence efficiency of the material [4]. For GaN, there are usually six kinds of point defects, which are O impurity, Mg impurity, C impurity, Ga vacancy, negative ion, and vacancy cluster [5]. Obviously, it is necessary to investigate the characteristics of these point defects in GaN. To study the defects, phys.scichina.com
www.springerlink.com
2060
Fang H N, et al.
Sci China-Phys Mech Astron
techniques such as XRD, AFM, positron annihilation, and secondary ion mass spectrometry are usually employed [5,6]. However, XRD and AFM can be only applied to study the dislocations, while the latter two techniques are difficult to implement. With the development of terahertz technology, complex refractive indicies, the dielectric function, and complex conductivities of GaN in range of THz frequencies can be obtained by THz time-domain spectroscopy (THz-TDS) [7–9]. Zhang et al. [10] firstly reported the studies of the complex electric conductivity and dielectric function of n-type freestanding epitaxial GaN in THz frequencies. By applying the simple Drude model, they showed a good theoretical fit to the experimental data and thus determined the plasma frequency and the carrier damping rate. Subsequently, the better agreements between experimental and fitting data of GaN were found when the Kohlrausch stretched exponential model is considered [11]. Nagashima et al. [12] investigated the temperature dependences of both mobility and DC conductivity of several GaN films with various doping levels. It is worthy to note that Nagashima et al. [12] mentioned, without giving the experimental data, that refractive indices contain a small periodic variation with a period of 100–150 GHz. They simply ascribed this phenomenon to a somewhat slight error in the phase shift, which is ambiguous in physics. Recently, the variation of refractive indices and the dielectric function was also found by Fang et al. [13]. In ref. [13], the variation has been ascribed to the defects in the material, and the dielectric function was further well fitted by the combination of the simple Drude model together with the classical damped oscillator model. This indicates that the properties of the defects in GaN may be studied by THz-TDS, which is the aim of this paper. In this paper, we shall investigate the temperature dependences of the point defect properties of GaN films by THz-TDS. First, the dielectric functions of GaN thin films for the temperature and frequency ranges of 10–300 K and 0.3–1 THz are obtained and found to be oscillating at various temperatures. Furthermore, the origination of the oscillation is studied, and the oscillation is attributed to the resonance states of point defects. Considering the influence of the resonance states, the simple Drude model is combined with the classical oscillator model to characterize the oscillating dielectric functions. Finally, according to the values of the fitting parameters, the concentration and electron lifetime of the point defects for various temperatures are determined, and thus the temperature dependences of them are obtained.
November (2013) Vol. 56 No. 11
Figure 1 Schematic of the optical system. Layers 1, 2 and 3 represent air, GaN thin film and substrate, respectively. E0(ω), Er(ω) and Ef (ω) are the incident, reference (substrate only) and signal (with the thin film) THz fields, respectively. d, d1, and d2 are the thicknesses of the thin film, underlying substrate and the bare substrate, respectively.
thickness of the bare substrate used for the reference measurement. Supposing that there is an incident THz radiation field E0(ω) with ω being the frequency. Er(ω) and Ef(ω) will be the corresponding reference field (substrate only) and signal field (with the thin film), respectively. In Figure 1, n and k denote the real refractive index and extinction coefficient of the thin film, respectively; and n1 the real refractive index of the substrate. According to Fresnel’s law, the reference and signal field can be determined as E r t13t31 E0 exp i d d1 d 2 n1 d 2 c ,
E f
(1)
t12 t23t31 E0 exp i n ik d n1 d1 c , (2) 1 r21 r23 exp 2i n ik d / c
where c is the speed of light in vacuum and rij and tij are the reflection and transmission coefficients of the i→j interface (i, j=1, 2, and 3, and i≠j), respectively. So we have E f E r
2 Theoretical background
2( n ik )(n1 1) exp[i ( n ik 1)d / c]exp[i (n1 1)( d1 d 2 ) / c ] . (1 n ik )(n ik n1 ) (1 n ik )(n ik n1 ) exp[2i (n ik )d / c]
An optical system shall be considered as depicted in Figure 1, where d and d1 are the thicknesses of the film and underlying substrate of the sample, respectively, and d2 the
In this complex equation, the refractive indices n and k can be deduced from the real and imaginary parts, and they are the functions of ω. To do so, Ef (ω), Er(ω) and n1 are
(3)
Fang H N, et al.
Sci China-Phys Mech Astron
November (2013) Vol. 56 No. 11
2061
needed. In our work, they will be given by experiment as follows: the Ef (ω) is derived by the fast Fourier transform from the main pulse of E(t), the time-domain signal which transmits through the GaN/Al2O3 sample. Er(ω) will, by contrast, be derived from the main pulse of E(t), the time-domain signal which transmits only through the bare substrate. The zero-padding technique is employed to process the data. As to n1, it also can be obtained by terahertz time-domain spectroscopy. For the sapphire substrate used in our experiment, n1 was found to be around 3.05 for the frequency range 0.3 to 1 THz, while the extinction coefficients were very small and could be neglected at these frequencies. That is in accordance with the result of ref. [14].
3 Experiments The 2.8 μm-thick, unintentionally doped, n-type GaN thin film was grown by metalorganic chemical vapor deposition on a c-plane sapphire substrate. To ensure that the sample is a homogeneous slide with two flat and parallel sides [15], the sapphire substrate used is double-side polished, and thus the optical interfaces are much better than those grown on the single-side polished sapphire. The sample fabricated was wurtzite in structure with its uniaxially optical axis perpendicular to the surface. Time-domain pulses transmitted through the sample were measured from 10 K to 300 K with commercial transmitted THz-TDS system provided by the Ekspla Company. The low temperature grown gallium arsenide antennas were used for the THz emitter and detector. A mode-locked Ti:sapphire laser by the Coherent Company produced optical pulses with a duration width less than 100 fs and a wavelength of 800 nm at a repetition rate of 82 MHz. The THz beam was placed in a closed box purged with dry nitrogen gas which can make the humidity below 4% RH. In addition, the free carrier concentration and mobility of our sample were measured by Hall from 10 K to 300 K.
4 Results and discussion Figure 2 plots the measured time-domain signal E(t) transmitted through the GaN/Al2O3 sample and the reference waveform E(t) which transmitted through only the bare Al2O3 substrate at 300 K. The echo indicated by the arrows is due to multiple reflections of the substrate. When the time-domain signals are transformed to the frequency-domain signals, only the main pulse needs to be taken into account. Thus, the extraction was carried out with the data recorded up to ~15 ps. Figure 3 shows the amplitudes of the frequency-domain signals that are derived by the fast Fourier transform from the main pulse of E(t) (time-domain signal transmitted through the GaN/Al2O3 sample) at various temperatures. As can be seen in Figure 3, the ampli-
Figure 2 Measured THz pulses of the signal and the reference waveform at 300 K. The echo indicated by the arrows is due to multiple reflections of the substrate.
Figure 3 Amplitudes of THz frequency-domain signal transformed from the main pulse of E(t) (time-domain signal transmitted through the GaN/Al2O3 sample) at various temperatures.
tudes of the signals decrease with increasing temperature. This is due to the fact that more free carriers will be frozen up with decreasing temperature, which causes the absorption by the free carriers is weaker at low temperature. It should be noted that the visible oscillations in Figure 3 do not correspond to the reflection echoes in Figure 2, which indicates that the oscillation behavior of the dielectric functions (as shown below) does not originate from the reflection of the substrate. According to the method mentioned above, the indices of refraction n and extinction constants k of the GaN film are obtained, respectively. From n and k, one can obtain the experimental dielectric function =1+i2, where 1=n2k2 and 2=2nk. As shown in Figure 4, there are oscillations of the experimental dielectric function at various temperatures. However, as stated in ref. [13], 1 of the simple Drude model is monotonically increasing and 2 is monotonically decreasing with the rise of the frequency. Therefore, the simple Drude model cannot account for the experimental dielectric function, which is similar to ref. [13].
2062
Fang H N, et al.
Sci China-Phys Mech Astron
November (2013) Vol. 56 No. 11
Figure 4 (Color online) The experimental and fitting dielectric functions of GaN, (a) real part at 10 K, (b) imaginary part at 10 K, (c) real part at 300 K, (d) imaginary part at 300 K.
The oscillation behavior is possibly ascribed to two origins: (a) lattice vibration [16], or (b) defects [13]. Since the frequency of lattice vibration of GaN is much higher than the frequency studied here, the oscillation does not originate from lattice vibrations. Therefore, the oscillation should be ascribed to the defects in the materials. There are mainly two kinds of defects, which are dislocations and point defects. The localized electrons of dislocations cannot have the same resonance frequency, and thus will not give rise to the oscillation of the dielectric function. However, point defects can generate resonance states (sometimes called as virtual bound states) [17], and the electrons at the resonance states will have the same resonance frequency. As a result, the oscillation should be attributed to the resonance states that arose from the point defects. It has been reported that, some emission lines of GaN are observed by high-resolution PL [18,19], which may arise from the excitons bound to defects (electrons at resonance states) [18]. In particular, the differences of energy levels of the emission lines are just in the frequencies studied here, which confirms the existence of the resonance states in THz frequencies. Obviously, the electrons at resonance states will have a contribution to the dielectric function. Since the density distribution of the resonance states is Lorentzian shape, the contribution by the resonance states can be described by the classical damped
oscillator model. If the simple Drude model is combined with the damped oscillator model, the dielectric function (ω) is thus given by
r
At Ne2 2 , * 2 m 0 ( i ) t t 2 i t
(4)
where r denotes the background dielectric constant. Clearly, eq. (4) contains two frequency-dependent terms: (1) the contribution by the free carriers with a concentration N, effective mass m* and damping coefficient . (2) the contribution by the resonance states, where t is the number of the kind of resonance states, At is the oscillator strength, ωt is the resonance frequency, and t is the line width. The experimental dielectric function thus can be fitted by eq. (4), in which the first two terms are from the simple Drude model and the third one describes the contribution by the resonance states. Actually, only the third term needs to be fitted, while the first two terms are determined by the substitution of the value of either the background dielectric constant or the carrier concentration and mobility. For GaN, the first term r (background dielectric constant) is 9.4 [10]. The second term can be determined from the free carrier concentration and mobility, which were derived by Hall measurements. As shown in Figure 5, the Hall measured
Fang H N, et al.
Figure 5
Sci China-Phys Mech Astron
2063
November (2013) Vol. 56 No. 11
(Color online) (a) Measured and actual free carrier concentration versus temperature. (b) Measured and actual mobility versus temperature.
carrier concentration does not monotonically increase with the rise of temperature, as was expected. Therefore, the measured data should be quite different from the actual data in the GaN thin film. This should be ascribed to the influence by the degenerate layer at the GaN/sapphire interface [20]. In order to obtain the actual free carrier concentration and mobility in the GaN thin film, the measured data can be analyzed by a two layer model as described in ref. [20]; the results are shown in Figure 5. Next, the values of the second term were determined by the actual carrier concentration and mobility in the GaN thin film. Finally, the third term was fitted through tuning proper fitting parameters by computer. The fitting dielectric functions at 10 K and 300 K are shown in Figure 4. It can be found that the experimental data agrees quite well with the fitting one, as do the data at other temperatures, which are not shown here. At (oscillator strength), ωt (resonance frequency) and t (line width) can be obtained through the fitting to the experimental dielectric functions. These parameters obtained for experimental dielectric function at 300 K are listed in Table 1. Furthermore, with the variation of temperature, the parameters corresponding to the second resonance frequency are given in Table 2. It indicates that the resonance frequency is nearly a constant at various temperatures, which is reasonable in physics. For the numerical value, At
( N t e 2 ) / (mt* 0 ) , with mt* and Nt being, respectively the
electron effective mass and concentration of the point defects; t is the reciprocal of the electron lifetime τt of the point defects. Consequently, the concentration and electron lifetime of the point defect corresponding to the second resonance frequency can be determined by A2 and 2; the temperature dependences of the concentration and electron lifetime are further obtained, and depicted in Figure 6. As can be seen in Figure 6, the concentration of the point defects decreases with the rise of the temperature. This is in accordance with the result of ref. [21] where the negative temperature dependency is attributed to the charge recombination generated Frenkel defects. Since the point defects will be the recombination centers, the electron lifetime is usually inversely proportional to the concentration of point defects. As a result, the electron lifetime exhibits positive temperature dependence, as shown in Figure 6.
5 Conclusions In summary, we have measured the THz time-domain spectroscopy of GaN thin films, and obtained the oscillating dielectric function at various temperatures within THz fre-
Table 1 Fitting parameters obtained for the experimental dielectric function at 300 K t At (1024 s2) t /2 (THz) t (1012 s1)
Table 2
1 13.504 0.382 0.349
2 16.757 0.543 0.558
3 21.867 0.682 0.63
4 12.174 0.849 0.474
5 9.938 0.986 0.401
6 788.88 1.595 0
240 26.222 0.549 0.548
300 16.757 0.543 0.558
One group of fitting parameters obtained for experimental dielectric functions at various temperatures T (K) A2 (1024 s2) 2 /2 (THz) 2 (1012 s1)
10 52.996 0.533 1.287
60 46.787 0.537 1.115
120 47.938 0.54 1.023
180 37.539 0.543 0.767
2064
Fang H N, et al.
Sci China-Phys Mech Astron
November (2013) Vol. 56 No. 11
1
2
3 4
5
6 7 Figure 6 (a) Concentration and (b) electron lifetime of the point defects (obtained from experimental dielectric functions) versus temperatures.
8 9
quencies. The oscillation behavior is ascribed to the resonance states that originate from the point defects in GaN films. Physically, the resonance states could be characterized by the classical damped oscillator model. Therefore, the experimental data is fitted by the combination of the simple Drude model with the classical damped oscillator model, and shows excellent agreement. Finally, the concentration and electron lifetime of the point defects in GaN thin film are determined, and the temperature dependences of which are obtained. The concentration of the point defects decreases with the rise of temperature, while the electron lifetime shows positive temperature dependence. It indicates that the terahertz time-domain spectroscopy could be considered as a powerful, non-contact and non-destructive tool to study the point defects in semiconductor materials. This work was supported by the Special Funds for Major State Basic Research Project (Grant No. 2011CB301900), the 973 project of the Ministry of Science and Technology of China (Grant No. 2011CBA00107), the Hi-tech Research Project (Grant No. 2011AA03A103), the National Natural Science Foundation of China (Grant Nos. 60990311, 60820106003, 60906025, 60936004, 61176063, 61071009, and 61027008), the Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 20090091110040), the Natural Science of Foundation of Jiangsu province (Grant Nos. BK2011010, BK2010385, and BK2010178), and the Fok Ying-Tong Education Foundation (Grant No. 122028).
10 11
12 13
14
15
16 17 18
19
20
Pearton S J, Zopler J C, Shul R J, et al. GaN: Processing, defects and devices. J Appl Phys, 1997, 86: 1–78 Morkoc H, Strite S, Gao G B, et al. Large-band-gap SiC, III-V nitride, and II-VI ZnSe-based semiconductor device technologies. J Appl Phys, 1994, 76: 1363–1398 Sohn J Y, Yahng J S, Park D J, et al. Nano seismology: Acoustic shock wave geberatin and terahertz emission from InGaN/GaN structures. In: Proceedings of the 28th International Symposium on Compound Semiconductors. Philadelphia, Pa: Taylor & Francis, 2001 Janotti A, Van de Walle C G. Native point defects in ZnO. Phys Rev B, 2007, 76: 165202 Tuomisto F, Saarinen K, Lucznik B, et al. Effect of growth polarity on vacancy defect and impurity incorporation in dislocation-free GaN. Appl Phys Lett, 2005, 86: 031915 Look D C, Fang Z Q, Claflin B. Identification of donors, acceptors and traps in bulk-like HVPE GaN. J Cryst Growth, 2005, 281: 143–150 Tonouchi M. Cutting-edge terahertz technology. Nat Photon, 2007, 1: 97–105 Singh R, Smirnova E, Taylor A J, et al. Optically thin terahertz metamaterials. Opt Express, 2008, 16: 6537 Zhang X C, Beigang R, Tanaka K. Introduction: Terahertz wave photonics. J Opt Soc Am B, 2009, 26: TW1 Zhang W, Azad A K, Grischkowsky D. Terahertz studies of carrier dymamics and dielectric response of n-type, freestanding epitaxial GaN. Appl Phys Lett, 2003, 82: 2841–2843 Tsai T R, Chen S J, Chang C F, et al. Terahertz response of GaN thin films. Opt Express, 2006, 14: 4898–4907 Nagashima T, Takata K, Nashima S, et al. Measurement of electrical properties of GaN thin films using terahertz-time domain spectroscopy. Jpn J Appl Phys, 2005, 44: 926–931 Fang H N, Zhang R, Liu B, et al. Dielectric properties of GaN in THz frequencies. Chin Phys Lett, 2010, 27: 017802 Grischkowsky D, Keiding S, Exter M V, et al. Far-infrared time-domain spectroscopy with terahertz beams of dielectrics and semiconductors. J Opt Soc Am B, 1990, 7: 2006–2015 Duvillaret L, Garet F, Coutaz J L, et al. A reliable method for extraction of material parameters in terahertz time-domain spectroscopy. IEEE J Sel Top Quant Electron, 1996, 2: 739– 746 Guo H C, Zhang X H, Liu W, et al. Terahertz carrier dynamics and dielectric properties of GaN epilayers with different carrier concentrations. J Appl Phys, 2009, 106: 063104 Anderson P W. Localized magnetic states in metals. Phys Rev, 1961, 124: 41–53 Reshchikov M A, Morcok H. Luminescence properties of defects in GaN. J Appl Phys, 2005, 97: 061301 Kornitzer K, Ebner T, Thonke K, et al. Photoluminescence and reflectance spectroscopy of excitonic transitions in high-quality homoepitaxial GaN films. Phys Rev B, 1999, 60: 1471–1473 Look D C, Molnar R J. Degenerate layer at GaN/sapphire interface: Influence on Hall-effect measurements. Appl Phys Lett, 1997, 70: 3377–3379 Tan T Y. Point defects and diffusion mechanisms pertinent to the Ga sublattice of GaAs. Mater Chem Phys, 1995, 40: 245–252
