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edfas.org 1 1 ELECTRONIC DEVICE FAILURE ANALYSIS | VOLUME 21 NO. 2 photons. This is referred to as Raman scattering, which is an inelastic process. The electron excited in the Raman scattering process decays to a different level than where it started. The energy difference between the initial and final vibrational levels is named Raman shift, expressed in wave numbers (cm -1 ). In terms of the Rayleigh scattering, the Raman shift is equal to zero. It serves as a reference. When the Raman shift is positive (negative), the process is named (anti) Stokes scattering. The Stokes-shifted spectrum always has a higher intensity than the anti- Stokes-shifted spectrum, but both spectra contain the same frequency information (Fig. 1). A Raman spectrum can be composed of peaks depending on the experimental configuration (existence of selection rules), material quality (crystalline or amor- phous phase), and the studied material. Every peak is characterized by three parameters: the Raman shift, the full width at halfmaximum(FWHM), and the intensity. The Raman shift depends on the studied material. It permits its identification. It also depends on themechanical strain and the temperature. FWHM can vary according to the crystal quality of thematerial and also with temperature. Intensity depends on the experimental conditions (config- uration, power andwavelength of the laser, and recording time), and also the material and temperature. Therefore, these threeparameters are temperaturedependent.When temperature increases, FWHM increases while the Raman shift and intensity decrease. DETERMINING TEMPERATURE BY RAMAN SCATTERING There are three different ways to determine the tem- perature by Raman scattering using the temperature dependence of the intensity, FWHM, or the Raman shift. [6] It is possible to determine the temperature from the relative intensity of the anti-Stokes (I aS ) and Stokes (I S ) Raman peaks: (Eq 1) where λ aS and λ S are thewavelength of the anti-Stokes and Stokes shifted scattered light, respectively. h and k B are the Planck and Boltzmann constants, respectively. ω is the phonon frequency at temperature T. This temperature measurement method has the advantage of being rather insensitive to mechanical strain, but is time consuming, requiring long integration periods tomeasure the weaker anti-Stokes Raman line intensity. Thus, it is not widely used for device temperature measurements. It is also possible to obtain the temperature from the linewidth Γ of the Raman peaks, as this is also mainly affected by temperature, but not greatly by strain. [12] (Eq 2) where Γ 0 is the value at the reference temperature T 0 , A andBare fittingparameters. The temperaturedependence of the linewidth is rather small and the signal-to-noise ratio becomes very weak at high temperature. The simplest andmost commonRaman thermography temperature measurement approach uses an empirical expression to describe the phonon frequency shift as shown in Eq 3. [13] (Eq 3) where ω 0 is the phonon frequency at temperature T = 0 K, and A and B are fitting parameters. In this example, only the Stokes Raman line is investigated because its inten- sity is high. Consequently, only a short recording time is needed. The calibration curve is obtained by placing a sample in a temperature-controlled cell and performing Raman scattering measurements as a function of tem- perature. For each material, it is necessary to establish a calibration curve in order to determine the temperature of a biased device. Figure 2(a) shows a typical Raman spec- trum of a GaN-based HEMT on a SiC substrate obtained at room temperature with a 632.8-nm laser wavelength in backscattering geometry. In this configuration, the allowed GaN E 2 h and A 1 (LO) phonon modes are clearly observable, as well as different SiC phonon modes from the substrate. The intensity of the E 2 h phonon mode is higher than the A 1 (LO) phonon mode and is generally used. It is also evident that the intensity of the SiC phonon modes is very high. In addition, this spectrum shows the capability of simultaneously measuring the temperature of the GaN material and the SiC substrate. By using a UV Fig. 1 Typical Raman spectrum showing the different scattering processes.