Nondestructive and Quantitative Evaluation of a GaAs Epitaxial Layer Covered With a Silicon Nitride Insulating Thin Film After a Highly Accelerated Temperature and Humidity Stress With the Use of Photoreflectance Spectroscopy

We demonstrate that photoreflectance spectroscopic measurements of Franz-Keldysh oscillations are applicable to nondestructively quantify the changes in surface Fermi level and surface recombination velocity of semiconductors after reliability stress tests. The present sample, a two-layer homoepitaxial structure consisting of a top undoped GaAs epilayer and a bottom n-type GaAs epilayer, were initially covered with a silicon nitride insulating thin film. This sample was subjected to the highly accelerated temperature and humidity stress. Initially, we estimated the built-in electric field strength from the Franz-Keldysh oscillations. We found that the built-in electric field strength is enhanced after the acceleration stress. Next, we performed the numerical analysis of the built-in electric field strength as a function of probe-light power density. From the above-mentioned numerical analysis, we clarified that the surface recombination velocity of the top undoped GaAs epilayer is enhanced by a factor of two. In contrast, the surface Fermi level is hardly changed. We discuss this phenomenon from the viewpoint of the formation of the surface defects that enhance the surface recombination velocity.


I. INTRODUCTION
I T IS wildly accepted that reliability tests are essential not only for commercial stage devices but also for developmental stage devices because device fabrication processes, which take account of the reliability, enables prompt research and development. For evaluating the reliability of the semiconductor devices, highly accelerated temperature Manuscript [4]. The issue on the insulating film for passivation is not limited with the characteristics of high frequency compound semiconductor devices.
In the solar cell, the insulating film also has a quite important role [5]. For example, LaPierre theoretically demonstrated that the insulating thin films improve current-voltage characteristics and efficiency of GaAs nanowire solar cells [6]. Hsu et al. found that Al 2 O 3 serves as a good passivation layer for Cu(In,Ga)Se 2 -based solar cells [7]. The above-mentioned improvements result from the suppression of surface recombination velocity [8]. The surface recombination velocity is enhanced by the increase in defects at the semiconductor surfaces. We also notice that the defects at the surface influence the phenomenon of the surface Fermi-level pinning [9]. The surface Fermi level relates to turn-on voltage of organic field effect transistors [10]. Accordingly, it is meaningful to test the reliability of the insulating thin film. Transmission electron microscopy (TEM) measurement is a useful tool to observe the interface between the insulating thin film and semiconductor layers after the acceleration stress test; however, it is impossible to quantify the change in the electronic characteristics from the observed TEM image. Accordingly, it is significant to explore how to quantify the change after the acceleration stress test.
In the present work, using photoreflectance spectroscopy [11], [12], [13], we nondestructively and quantitatively evaluated the change caused by the acceleration stress test for a GaAs epi-layer covered with a silicon nitride insulating thin film. In order to investigate whether the silicon nitride insulating thin film sufficiently protects the GaAs epilayer surface, it is fundamental to apply an appropriate monitoring sample. We used a two-layer homoepitaxial structure consisting of a top undoped GaAs epilayer and a bottom n-type GaAs epilayer. In the epitaxial structure, the undoped layer (i-layer) has a uniform built-in electric field that is sensitive to change in power density of probe light used the photoreflectance measurement [14]. We found that, after the highly accelerated temperature and humidity stress test, the surface recombination velocity of the top i-layer is strongly enhanced. In contrast, the surface Fermi level is hardly changed. We discuss the characteristics of the defects formed after the acceleration stress test.

II. SAMPLES AND EXPERIMENTAL PROCEDURES
The present GaAs epitaxial structure consisting of the top i-layer (thicknesses: 200 nm) and the bottom n-layer (thicknesses: 3.0 μm; doping concentration: 3.0×10 18 cm −3 ) grown on a 2 • -off (001)-oriented semi-insulating GaAs substrate by metal organic vapor phase epitaxy. The silicon nitride film, which was deposited on the i-layer, was grown by chemical vapor deposition, and its thickness was 30 nm. The highly accelerated temperature and humidity stress test was performed with the use of the following condition: humidity 70%; temperature: 393 K; total time of the acceleration stress test: 48 hours. We call the sample before the acceleration stress test as sample A and the sample after the acceleration stress test as sample B. Figure 1 shows the surface morphology of the silicon nitride thin film of samples A and B, where the surface image was taken with the use of atomic force microscopy (AMF). The AFM images apparently hardly differ. This means that the silicon nitride thin film itself was not damaged after the acceleration stress test. We estimated the built-in electric field strengths in the i-layer of samples A and B, using photoreflectance spectroscopy at room temperature. The pump light was the laser light with the wavelength of 532 nm chopped at the frequency of 630 Hz. The power density of the pump light was 80 mW/cm 2 . The probe beam was obtained from a tungsten-halogen lamp dispersed by a monochromator with a 1.2-nm resolution. The power density of the probe light was varied from 2.8 to 30 μW/cm 2 . Figure 2(a) shows the photoreflectance spectra of samples A and B in the photon-energy range from 1.36 to 1.78 eV. The probe-light power density was set to be 30 μW/cm 2 . The oscillation patterns, the so-called Franz-Keldysh oscillations, [11], [12], [13] starts from the fundamental transition energy of GaAs at room temperature. The appearance of the Franz-Keldysh oscillations clearly indicates the presence of the built-in electric field in the i-layer. The Franz-Keldysh oscillations appears in the relatively wide photon-energy range. This is because, in the i-layer, the impurities such as ionized donors or accepters, which damps the oscillation [15], [16], hardly exist. In other words, the present epitaxial structure is suitable for monitoring the effects of the acceleration stress test for the passivation ability of the insulating film. In order to highlight the change in the Franz-Keldysh oscillations between the two samples, we show the photoreflectance spectra in the photon-energy range from 1.44 to 1.66 eV in Fig. 2(b). The dashed line at 1.456 eV indicates that, in the two sample, the peak position of the Franz-Keldysh oscillations is located in the same photon energy. In contrast, the dashed line at 1.578 eV indicates the peakposition difference in the Franz-Keldysh oscillations between the two samples. The period of the Franz-Keldysh oscillations connects with the built-in electric field strength, so that the present phenomenon suggests that the built-in electric field strength is changed owing to the acceleration stress test. We reported in [14] that the built-in electric field strength is dominantly influenced both by the surface Fermi level and by the surface recombination velocity. Accordingly, the surface Fermi level or the surface recombination velocity is varied after the acceleration stress test.

III. EXPERIMENTAL RESULTS AND DISCUSSION
In order to evaluate the effects of the acceleration stress test on the surface Fermi level and surface recombination velocity, initially, we estimated the built-in electric field strength of the two samples. We indexed the peaks and/or dips to the integer j from the fundamental transition energy and plotted the photon energy positions of in the spectra as a function of quasi-index ξ j : Here, the quantity φ is the phase term [14], [17], [18], which reflects the interference effect caused by the presence of the insulating thin film. The quantity φ in (1b) is the multiplication of the probe-light wavenumber and the optical path length in the silicon nitride thin film. In the present samples, the silicon nitride film covers the i-layer, so that the interference effect leading to δ is not negligible. The phase term φ, therefore, should be taken into account for precisely estimating the built-in electric field strength. Equation (1a) is equivalent to the theory by Aspnes and Studna [19] in the case where the interference-effect factor δ is zero corresponding to the absence of the interference effect. The applied refractive index of the silicon nitride thin film was 2.05 to derive the interference-effect factor δ [20]. The obtained plots are shown in Fig. 3, where the probe-light power density was 30 μW/cm 2 . The closed and open circles are the peak and dip photon energy of the Franz-Keldysh oscillations of samples A and B, respectively. It is apparent that the plots show a linearity, indicating that the uniform built-in electric field strength is formed in the i-layer of each sample. The slope, the electro-optic constant , is given as a function of built-in electric field strength F [19].
Here, the quantity μ is the reduced effective mass. In GaAs, the value is estimated to be 0.0556 in units of the electron mass in a vacuum [21]. We fitted the following equation to the peak and dip photon energy values ω j (closed and open circles), where the quantity E 0 is the fundamental transition energy of GaAs. The fitting results are depicted as the solid lines. The fitted solid lines agree with the experimental value. In addition, the two solid lines converge at the intercept E 0 of 1.425 eV. The value of 1.425 eV is almost the same as the fundamental transition energy of GaAs (1.424 eV) at room temperature [22]. This indicates that the present fitting analysis has reasonable precision. Finally, we estimate the surface Fermi level E F and surface recombination velocity S, where the reference point of E F is a mid-gap level of GaAs. The built-in electric field strength is enhanced as the probe-light power density is decreased. This  originates from the reduction of the screening effect of the probe light on the built-in surface electric field [14], [23]. The solid lines are obtained by the numerical calculation using the software PC-1D developed on the basis of the theory proposed in [24]. The theory is based on the Boltzmann-Poisson model. The material parameters, which were used in the present calculation, are the same as those in [14]. The solid line has a linear slope in the semi-logarithmic plot in Fig. 4. We reported that this result indicates the surface Fermi level E F is located almost at the mid-gap of GaAs [14]. The estimated surface Fermi levers are +20 meV in both samples A and B. In contrast, the solid line is shifted up in sample B subjected to the acceleration stress test. This means that the surface recombination velocity is enhanced, according to [14]. The surface recombination velocities S are estimated from the numerical calculation to be 1.3×10 5 cm/s for sample A and 2.9×10 5 cm/s for sample B. This indicates that the present acceleration stress test enhances the surface recombination velocity by a factor of two.
Here, we discuss the enhancement of the surface recombination velocity owing to the present highly accelerated temperature and humidity stress test. The surface recombination velocity S is enhanced by the presence of the surface defect states, as pointed out in [14]. As shown in Fig. 1, the silicon nitride thin film is hardly changed after the acceleration stress test. Accordingly, the degradation of the silicon nitride film is not a responsible factor. We, therefore, have reached the following conclusion: The water molecule penetrates the relatively robust silicon nitride film. The water molecule triggers producing the surface defects by the assist of the relatively high temperature. We also note that the surface Fermi level E F hardly is changed. This means that the surface levels formed by the defects are mainly located at the mid-gap of GaAs.

IV. CONCLUSION
We have explored the feasibility that photoreflectance spectroscopy is applicable to quantitatively evaluate the GaAs epilayer covered with the silicon nitride thin film after the highly accelerated temperature and humidity stress test. We have analyzed the Franz-Keldysh oscillations appearing in the photoreflectance spectra and estimated the built-in electric field strength. We have found that the built-in electric field strength in the i-layer is enhanced by the acceleration stress test. We have compared the built-in electric field strength dependence on the probe light power density with the numerical simulation. It has been clarified that the surface recombination velocity of 1.3×10 5 cm/s is enhanced to be 2.9×10 5 cm/s after the acceleration stress test. We have attributed the origin of the present phenomenon to the reasonable assumption that the water molecule penetrates the silicon nitride film and produces the surface defects by the assist of the relatively high temperature. The present findings demonstrate that the photoreflectance spectroscopy is applicable to contactless and quantitative evaluation of the surfaces of semiconductor devices subjected to the acceleration stress test.