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Raman scattering spectra of 4H-SiC with different carrier concentrations were measured from 90 K to 660 K. By using the improved empirical formula and the energy-time uncertainty relation, temperature and doping dependence of Raman shift and phonon lifetimes were studied. For the folded transverse acoustic (FTA) and longitudinal optical (FLO) mode with E2 symmetry, the doping process induced the decrease of the c- and a-axis lattice constants which led to the changes of the vibrational frequencies and was the dominant contribution to the difference of the first- and second-order temperature coefficients. And the anharmonic decay of the phonons was established as the dominant mechanism affecting the phonon lifetimes of E2(FTO) mode at all temperatures. It is observed the phonon-carrier interaction directly determines the Raman shift and lifetimes of the folded longitudinal optical (FLO) mode with A1 symmetry.
© 2016 Optical Society of America
1. Introduction
During the past few years, SiC semiconductor material has attracted much attention because of its outstanding features for high voltage, high frequency and high temperature applications. N type SiC substrates are especially important because they are used for power electronic device [1–3]. However, to improve these devices to allow for their mainstream adoption, significant technical challenges remain. One of these challenges is how to improve the device performance and reliability which is mainly affected by the temperature properties, such as phonon-carrier interaction and phonon lifetimes [4,5]. Thus, it is of primary importance to understand and investigate above properties via Raman spectroscopy.
Raman spectroscopy has been widely used as a nondestructive and effective method for various wide-gap semiconductors. It has been used to measure the spatial distribution of the free carrier concentration and carrier mobility of polar semiconductors due to the interaction between longitudinal optical (LO) phonon modes and the plasma oscillation of free carriers which forms LO phonon-plasmon coupled (LOPC) mode [6–10]. At the same time, the temperature dependence of Raman scattering has been investigated for many materials, such as Si [11,12], Ge [12], GaAs [13], ZnO [14], GaN [15–17], AlN [18] and so on. Also, there have been some publications describing the temperature dependence of Raman scattering in SiC. R. Han discussed the detailed Raman scattering in the hexagonal defects and round pit of 4H-SiC [19,20]. Hua yang Sun investigated the temperature dependence of the Raman shift of LOPC mode [21]. However, there have been no reports on temperature and doping dependence of phonon lifetimes in SiC.
In this paper, the temperature and doping dependence of E2(FTA), E2(FTO) and A1(FLO) modes in SiC substrates are presented. By using the improved empirical formula and the energy-time uncertainty relation, the mechanism affecting temperature and doping dependence of Raman shift and the lifetimes are investigated. At the same time, the changes of the intensity of Raman spectrum were also discussed. The papers offer an insight into the temperature properties, phonon-carrier interaction and phonon lifetimes of SiC and are important to the improvement and development of SiC devices.
2. Experiment results
A series of SiC wafers are sliced and processed from SiC boules grown by PVT method. The c axis was normal to the surface of the samples. The carrier concentration of the samples measured by Hall effect is shown in Table 1.
Table 1. The details of the samples
Raman measurements were performed in backscattering geometry by the LabRAM HR system of Horiba Jobin Yvon with the 532 nm solid-state laser as the exciting source. The repeatability is below 0.2 cm−1. A Linkam temperature stage with a transparent window was used to heat the sample from 90 to 660 K in flowing nitrogen.
In Fig. 1, we show typical Raman spectra of sample A at 90 K, 360 K and 660 K in the backscattering z(xx)z¯ geometry, where z is parallel to the c axis of the samples. The changes in Raman shift, FWHM, and intensity are clearly evident.
The Raman shift, FWHM of the E2(FTA), E2(FTO) and A1(FLO) of all samples as functions of temperature are shown in Fig. 2, Fig. 3 and Fig. 4, respectively. The intensities E2(FTA) and A1(FLO), which are normalized by E2(FTO) mode, are shown with solid line and dot line in Fig. 5 and 6, respectively. The present normalization was used to divide out a temperature dependent artifact of the system.
Fig. 2 The Raman shift, FWHM of the E2(FTA) as function of temperature. The solid black line is the fitting result to Eq.Eq. (1).
Fig. 3 The Raman shift, FWHM of the E2(FTO) as function of temperature. The solid black line is the fitting result to Eq.Eq. (1).
3. Analyses of experimental results
The Raman shift, FWHM, intensity of the E2(FTA), E2(FTO) and A1(FLO) of sample A, B, C as function of temperature are quite different, which are indicated different behavior of phonons.
3.1 Temperature dependence of Raman shift
The Raman Shift of E2(FTA) and E2(FTO) decreased with increasing temperature. The peak position of E2(FTA) falls within 2.5 cm−1. The peak position of E2(FTO) falls about 8 cm−1 from 90 K to 660 K.
There is no general and accurate method to describe the temperature dependence of the phonon frequencies in the crystals. W. S. Li and Z. X. Shen proposed an improved empirical formula for GaN [16]. It was found that their formula could be employed to interpret our experiments. Thus temperature dependence of the Raman shift in SiC can be expressed as:
where is the Raman shift when the temperature is extrapolated to 0 K, and and are the first- and second-order temperature coefficients, respectively.
The fitting parameters for Raman shift of E2(FTA) and E2(FTO) are listed in Tables 2 and 3, respectively.
Table 2. Fitting parameter of Raman shift vs Temperature for E2(FTA)
Table 3. Fitting parameter of Raman shift vs Temperature for E2(FTO)
It can be seen from Table 2 that decreases and increases with the increase of carrier concentration. On the other hand, the data in Table 3 show that increases and decreases with the increase of carrier concentration. The underlying cause for this discrepancy of three samples is the difference in doping concentration. It is reported the dependence of Raman shift on temperature can be written as a result of two additive effects, one dominant contribution being the change in the vibrational frequencies due to thermal expansion or volume change [16]. In our samples, the nitrogen atom replaces the carbon atom which causes the decrease of the c-and a-axis lattice constants [22]. Therefore, we deduce the small difference in lattice constants caused the small changes of vibrational frequencies, which led to the above changes of and . However, in Fig. 2, there is almost no shift occurs in two regions, which are 90 K to 210 K and 330 K to 390 K. Equation (1) doesn’t satisfactorily account for no-shift regions because it is an improved empirical formula.
The Raman shifts of A1(FLO) are quite different with different carrier concentration as shown in Fig. 4. At 90 K, Raman shift is 965.7 cm−1, 968.4 cm−1, 970.0 cm−1 for sample A, B, C, respectively. For sample A, red shift of 10.3 cm−1 occurred from 90 K to 660 K. However, for sample B, blue shift is within 0.5 cm−1 from 90 K to 240 K and red shift is 7.4 cm−1 from 240 K to 660 K. For sample C, blue shift is within 1.4 cm−1 from 90 K to 240 K and red shift is 6.8 cm−1 from 240 K to 660 K.
It has generally been accepted that LOPC mode is formed by the coupling between LO phonons and plasma in a polar semiconductor [6–10]. And there is a linear relationship between the carrier concentration and the relative Raman shift of the LOPC mode in SiC which was used as a complement to Hall measurement in the determination of free carrier concentration and mobility [23]. In this study, the carrier concentration increases with temperature. As a result, it leads to the shift of LOPC peak to higher frequency. Coupling between the temperature dependence of LOPC mode and the effect of the carrier concentration results in non-monotonic changes of Raman shift [21].
3.2 Temperature dependence of the phonon lifetimes
Raman FWHM determine the phonon lifetimes through the energy-time uncertainty relation [18, 24]:
where is the Raman FWHM in units of cm−1, and = 5.3 × 10−12cm−1s.
The phonon lifetime is mainly limited by two mechanisms: (i) anharmonic decay of the phonon into two or more phonons, which is called phonon-phonon scattering with a characteristic decay time and (ii) perturbation of the translational symmetry of the crystal by the presence of impurities, which is called phonon-carrier scattering with a characteristic decay time [24]. The phonon lifetime can be written as
It is hard to separate the contribution of both mechanisms. But we can identify the dominant mechanism by recognizing that the phonon-phonon scattering is equivalent in each of the samples and the carrier scattering is different between samples owing the variance in doping concentration [17]. And it should be noted that FWHM discussed in this paper includes the instrumental bandpass broadening. The further studies have been taken to correct the contribution of the instrumental bandpass broadening.
Figures 2, 3 and 4 shows the temperature dependence of the Raman FWHM for each of the three-phonon modes. It can be seen that for all samples, an increase of Raman FWHM is accompanied by an associated decrease in phonon lifetimes. The decrease occurs as the rate of phonon-phonon scattering increase with temperature due to the associated increase in the phonon thermal occupancy and their interaction [17].
However, there are significant qualitative differences of lifetime for different modes. For E2(FTA), the lifetimes of three samples are almost unchanged and the difference between the three samples can hardly be observed .
For E2(FTO), the lifetime of sample A decreases from 1.45 ps to 0.81 ps, whereas the lifetime of sample C decreases from 1.37 ps to 0.79 ps. It is shown the differences of lifetimes among three samples are very small as the carrier concentration increases. In the light of these results, it then becomes apparent that for E2(FTO), the dominant mechanism is the anharmonic decay of the phonon at all temperatures.
For the LOPC mode, the lifetime of sample A decreases from 1.12 ps to 0.62 ps, whereas the lifetime of sample C decreases from 0.40 ps to 0.23 ps. Therefore, the phonon lifetimes inversely vary with the carrier concentration. The similar trend for A1(LO) mode has been reported by Thomas Beechem et al. in GaN [17] and by Leah Bergman et al. in AlN [18]. All these results are shown that the impurity scattering is a shorten mechanism and the denpendency of the lifetime on doping concentration occurs due to an interaction of the phonons with the carrier. At the same time, it is also important to note that the liftimes do not converge at higher temperature. The lack of convergence indicates that phonon-carrier scattering is the dominat machanisms [17].
3.3 Temperature dependence of the intensity
Figure 1, Fig. 5 and Fig. 6 show a strong temperature dependence of the Raman scattering intensity. The intensity of E2(FTA) increases 3 times from 90 K to 660 K. The intensity is proportional to the number of phonons taking part in the scattering process. It means that the acoustic phonon number increases more quickly than the optical phonons as the temperature is increased.
The intensity of LOPC mode is observed to remain unchanged across all temperatures, whereas it decreases with an increase in free carrier concentration. This decrease trend is also exhibited at room temperature. Line shape fitting using classical dielectric function (CDF) shows that the phonon damping, plasmon damping, and plasmon frequency influence the peak intensity [23].
4. Conclusion
By using an improved empirical formula and the energy-time uncertainty relation, the temperature and doping dependence of Raman shift and phonon lifetimes were studied in a series of SiC samples.
For LOPC mode, the results illustrate the phonon-carrier interaction leads to non-monotonic changes of Raman Shift and the phonon lifetimes inversely vary with the carrier concentration. The dominat machanisims affecting lifetime is the phonon-carrier scattering.
In contrast to this, for E2(FTA) and E2(FTO) mode, the different concentration of impurity may cause the changes of vibrational frequencies which lead to very small distinctions of the Raman shift. The dominant mechanism affecting the lifetimes of E2(FTO) mode is the anharmonic decay of the phonon.
Funding
National Natural Science Foundation of China (NSFC) (11404393, 61504075 and 61327808); National High Technology Research and Development Program (2014AA032601 and 2015AA033302); Independent Innovation Project of Shandong Province (2014ZZCX04215); The Fundamental Research Funds for the Central Universities (2014QNA61).
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