Silicon carbide (SiC) is one of the most promising semiconducting materials for the fabrication of high power electronic devices with extremely low loss, owing to its excellent physical properties, such as high breakdown electric field, high saturation electron drift velocity, and high thermal conductivity. Nowadays, some kinds of devices, such as SBDs, JFETs and MOSFETs have been on the market. For the fabrication of SiC devices with high yield rates,
To characterize the distribution of the electrical properties over SiC wafers and homo-epi-wafers, conductivity mapping is often performed . However, the distribution of carrier concentration and mobility cannot provide from the conductivity mapping, because the conductivity depends both on the distribution of dopant concentration and the crystallinity and/or distribution of crystal defects. In order to characterize the distribution of carrier concentration and mobility over epi-layers, electrical measurement techniques such as Hall effect measurements and capacitance-voltage (
Optical measurement techniques such as Raman scattering spectroscopy [2-5], infrared (IR) spectroscopic ellipsometry , optical absorption measurements  have been used to estimate the carrier concentration in SiC wafers as a nondestructive and contactless method. IR reflectance measurements have been used to estimate the electrical properties of GaAs  and SiC . Macmillan
We have developed the method of obtaining the thickness and electrical properties of semiconductor wafers and epi-wafers, simultaneously, by using IR reflectance spectroscopy [11-15]. In this paper, we will summarize the development of the method, and will discuss the validity of the electrical properties derived from the IR reflectance by comparing with those estimated from Hall effect and
2. Characterization method of the electrical properties in SiC wafers using IR reflectance spectroscopy
2.1. Method of obtaining carrier concentration and mobility from IR reflectance spectroscopy [11,12]
The values of dielectric constants of semiconductors in IR spectral region can be calculated as a function of wavelength or frequency using the dispersion equation. For the analysis of IR reflectance spectra, a number of dielectric function models have been proposed [16-20]. The classical dielectric function (CDF) model , which assumes the damping constant of the LO phonon is the same as that of the TO phonon, has been widely used. In the case of wide bandgap semiconductors with an overdamped plasmon system like SiC, the reflectance spectrum is, however, strongly dependent on LO-phonon damping because the plasmon is overdamped and the LO phonon frequency is much higher than the plasma frequency except for heavily doped cases. For these reasons, we have chosen to use the modified classical dielectric function (MDF) model taking into account the contribution of the TO phonon damping constant and the LO phonon damping constant independently . Considering the contributions from phonons and plasmons, the dielectric constant is given as
Assuming that the wafers are uniformed in the depth direction, we used the normal-incidence reflectance of a semi-infinite medium
The carrier concentration and mobility can be determined by fitting the experimental infrared reflectance spectrum with calculated ones. To fit the spectra, we used the least-squares method based on eqs. (1) and (4), where we adopted
2.2. Measurements of IR reflectance spectra of SiC wafers and estimation of electrical properties 
Single crystal wafers of commercially produced
The dotted lines in Figure 1 show the typical infrared reflectance spectra of several 6H-SiC wafers of different carrier concentrations at room temperature. The plasma edges and reststrahlen bands appear in the far-IR and middle-IR regions, respectively. We derived the values of carrier concentration and mobility by the curve fitting of calculated curves to the observed ones. For the curve fitting, we chose
From the curve fitting analysis, we obtained a good fit for each experimental spectrum, which was obtained by measuring nine samples with carrier concentrations in the range of 4×1017~3×1019cm–3. The solid lines in Figure 1 show examples of the fitted curves obtained by fitting to the typical IR reflectance spectra shown as the dotted line in each figure. The free-carrier concentration and drift mobility were derived from the best-fit parameters of
As shown in Figure 1 (c), there is a slight discrepancy at approximately 900 cm–1 between the spectrum observed and that calculated using the MDF model (eq. (1)). This discrepancy increases with increasing carrier concentration in the high 1019 cm–3 range. For heavily doped SiC crystals, the CDF and MDF models would be inappropriate because the MDF model is derived considering the effects of phonons and plasmons independently. In the case of heavily doped SiC crystals, the plasma frequency is closed to the phonon frequency and the LO phonon and plasmon are strongly coupled. Therefore, though the MDF mode can approximately estimate the electrical properties of heavily doped SiC wafer, it is necessary to use another dielectric function mode that takes into account the effect of LO phonon-plasmon coupled modes [19,20] to obtain more accurate values.
2.3. Comparison with the values derived from Hall effect measurements 
For the confirmation of the validity of the values of carrier concentration and mobility derived from IR reflectance spectra, we performed Hall effect measurements for the same samples used for IR reflectance measurements and compared between the values obtained from the optical and electrical methods. The 6H-SiC wafers with a wide variety of carrier concentrations ranging from 3.4×1017 to 2.4×1019cm–3 were used.
We cut the SiC wafers to a size of 5×5 mm2 for the Hall effect measurements using van der Pauw method. After chemical cleaning, ohmic contacts were fabricated at the corners of each sample by the evaporation of nickel and subsequent heat treatment at 1000°C for 10 min. IR reflectance measurement and Hall measurement were carried out at room temperature.
In Figure 2 (a) and (b), the carrier concentrations and mobilities estimated from the IR reflectance spectra are plotted against those obtained from the Hall effect measurements. As the reported Hall scattering factor
The LO phonon damping constant
In Figure 3, the drift mobility and Hall mobility of the 6H-SiC wafers are plotted against the determined free carrier concentration, and against those reported by Karmann
Through comparison, we have ascertained that the electrical characteristics of SiC wafers can be estimated by IR reflectance spectroscopy with high credibility.
2.4. Spatial mapping of the electrical properties over SiC wafers [11,12]
To demonstrate the capability of the method proposed, we performed the spatial mapping of the distribution of the carrier concentration and mobility of a commercially produced 2 inch 6H-SiC wafer. For the spatial mapping, we employed a micro FTIR (JASCO Irtron IRT-30 infrared microscope), which was equipped with a mercury cadmium telluride (MCT) detector. The diameter of the beam was 0.1 mm and the interval between measured points was 5 mm (a total of 120 measurement points). We performed the measurements in the spectral range of 560–2000 cm–1 with a spectral resolution of 4cm–1.
Figure 4 shows an example of the spatial distribution of the free-carrier concentration and mobility of a commercially produced 2-inch 6H-SiC wafer obtained using this technique. This measurement technique needs no prior surface treatment, because the native oxide layer thickness and surface roughness are not more than 3 nm and their influence on the reflectance spectra is negligible in IR region. The uniformity of free-carrier concentration and mobility throughout this wafer except for 5 mm from the edge were estimated to be approximately ±9% and ±15%, respectively. The free-carrier concentration mapping shows that the free-carrier concentration in the central region is greater than that in the edge region. On the other hand, the mobility mapping shows the negative correlation of the mobility distribution with that of carrier concentration. When conductivity mapping is used as the method for the mapping of electrical properties of the wafer, it leads to the misleading conclusion that the electrical uniformity over the wafers is approximately ±5% and the wafer is almost uniform, because the conductivity is determined as the product of carrier concentration and mobility. Therefore, the proposed IR reflectance spectroscopic method is more appropriate for the characterization of the distribution of the electrical properties of SiC wafers.
3. Characterization method of the electrical properties and thickness of epilayers using IR reflectance spectroscopy
3.1. Method of obtaining the carrier concentration, mobility, and thickness of epilayers, simultaneously 
In this section, we propose the method for the simultaneous determination of the electrical properties,
The carrier concentration and mobility of epilayers and substrates, as well as the thickness of the epilayers can be determined simultaneously by fitting the calculated reflectance spectra to measured ones. The reflectance
3.2. Measurements of IR reflectance spectra and derivation of electrical properties and thickness of SiC epi-wafers 
Samples used in this study were nitrogen doped
At first, we estimated the carrier concentration and mobility of
The carrier concentrations and mobilities obtained from the IR reflectance measurements are plotted with respect to those obtained from Hall effect measurements in Figures 6 (a) and (b), respectively. Since the Hall scattering factor
Next, we estimated the values of carrier concentration and mobility for
3.3. Extension of the carrier concentration range down to 1016cm–3 order using Terahertz frequency range 
We have shown that the carrier concentration and mobility of substrate and epilayers as well as the thickness of epilayer are obtained simultaneously from IR reflectance spectra in the frequency range of 80–2000cm–1, and confirmed that the values of the carrier concentration, mobility and epilayer thickness estimated from IR reflectance spectroscopy are valid. However, it was difficult to estimate the electrical properties of homo-epilayers with carrier concentrations less than 1×1017 cm–3 without IR reflectance spectra less than 80 cm–1. Figure 9 is the variation of plasma frequency with carrier concentration calculated from eq.(2) for 4H-SiC. The figure indicates the plasma frequencies are smaller than 100cm–1 for the carrier concentration less than 1017 cm–3. Figure 10 shows the variations of the reflectance spectrum of epilayers with the decrease of carrier concentrations from 3×1018 to 3×1016cm–3. The magnified features of the calculated reflectance spectra for 1×1017cm–3, 5×1016, and 1–5×1015cm–3 in Terahertz frequency range are shown in Figure 11. These figures suggest that it is necessary to measure a spectrum down to around 20cm–1 for extending the carrier concentration down to the order of 1016 cm–1.
From these considerations, we extended the spectral range of the reflectance measurements down to 20 cm–1 (0.6 THz) by using terahertz reflectance spectroscopy to be able to apply the method for epilayers with the carrier concentrations in the range of 1016 cm–3. Also we have compared the free carrier concentrations estimated from reflectance measurements with the net doping concentrations obtained from
Samples used in this study were nitrogen doped
We have estimated the values of carrier concentration and mobility for the samples of
In Figure 13, the free carrier concentrations estimated from the IR reflectance spectra are plotted against the net doping concentrations
4. Characterization of electrical properties and residual crystalline damage in ion-implanted and post-implantation-annealed 4H-SiC epilayers using IR reflectance spectroscopy
4.1. Method of obtaining the electrical properties and crystalline damage in ion-implanted SiC epilayers 
Ion implantation is an indispensable process for selective area doping into crystalline silicon carbide (SiC), because the doping of impurities by thermal diffusion is hard to apply for SiC device process due to very small diffusion constant of impurities in SiC. After the ion implantation, annealing at high temperatures is necessary for activating the dopants electrically as well as recovering the crystallinity of SiC damaged by ion implantation. Hall effect measurements, secondary ion mass spectroscopy (SIMS) and transmission electron microscopy (TEM) have been widely used to characterize the electrical properties, depth profile of the impurities and crystalline damage of implanted layers, respectively. These techniques are, however, inappropriate to use as device process monitoring tools because Hall effect measurement requires the formation of electric contacts, and SIMS and TEM observations result in the destruction of the samples. Recently, the short period and high temperature annealing is used in SiC device process . To make clear the effect of short period high-temperature annealing, we investigated the annealing period dependence at the annealing temperature of 1700°C.
Recently, it has been reported that the crystalline damage induced by ion implantation affects the infrared (IR) reflectance spectra around the reststrahlen region (~800–1000 cm–1) [33,34], and the difference of carrier concentration between epitaxial layer and substrate induces the interference oscillation in the near IR region (1000–4500 cm–1). In this study, we performed the IR reflectance measurements in the spectral range between 600 and 8000 cm–1 for high-dose phosphorus ion implanted and post-implantation-annealed 4H-SiC wafers to characterize both the electrical properties and crystalline damage of the implanted layers without destruction and contactless.
4.2. High-dose phosphorus ion implantation, post-implantation annealing and IR reflectance measurements 
The samples used in this study were 4H-SiC (0001) substrates with
4.3. Analysis of carrier concentration, mobility and crystalline damage from IR reflectance spectra 
Figure 14 shows the annealing temperature dependence of IR reflectance spectrum. For as-implanted samples, the reflectivity maximum and the shape in the reststrahlen band decreases and becomes blunt, respectively, as compared to those of unimplanted samples. After the high temperature annealing, the reflectivity maximum in the reststrahlen band recovers to that of unimplanted samples. This is resulted from the crystalline recovery in implanted layer. In the spectral range above ~2000 cm–1, the evident interference oscillation is observed. It indicates that the implanted dopants are activated and the refractive index of an implanted layer is changed by the change of carrier concentration. We can see the tendencies that the reflectance around 1000 cm–1 becomes larger with increasing the annealing temperature. We analyzed the observed spectra to evaluate the damage of the ion implantation layers assuming that the implanted layers are composed of two phases, recrystallized SiC phase and defective SiC phase. We have derived the effective dielectric constants
4.4. Annealing temperature dependences of electrical activity and re-crystallization 
As an example of curve fitting analysis, the spectrum of the sample annealed at 1400°C for 30 min and the fitted curve are show in Figure 16. We obtained a good fit in the whole spectral region measured. The best-fit parameters derived are also described in the figure. Figure 17 (a) shows the annealing temperature dependence of the volume fraction of the defective phase. By post implantation annealing, the volume fraction of defective SiC drastically decreases from 92 % (as implanted) to 2.9 % (1200°C annealed), and decreases a little with increasing of annealing temperature up to 1400°C. Figure 17 (b) shows the annealing temperature dependence of the carrier concentration (open circle) and the mobility (open triangle) in the re-crystallized phase. For comparison, the electrical properties derived from Hall effect measurements  are also plotted in the figure (filled symbols). We can see a good agreement in the electrical characteristics between IR reflectance spectroscopy and Hall effect measurements. The free carrier concentrations are almost constant in the temperature range studied, as in the case of the volume fraction of defective phase. In contrast, the carrier mobility becomes large with increasing the annealing temperature. These results show that the post implantation annealing at a temperature as low as 1200°C reduces the volume fraction of defective SiC drastically and put the impurities in substitutional lattice sites, but the crystalline recovery of re-crystallized phase is insufficient. In other words, the annealing temperature higher than 1400°C is necessary for improving the mobilities, as well as for activating the impurities.
Figure 18 shows the IR reflectance spectra for the samples annealed for various annealing periods. The spectrum for the sample annealed for 0.5 min is almost the same as that for the sample annealed at 1400°C for 30 min. There is little change with annealing period up to 10 min in the reflectance spectra except for the oscillation periods. Since the oscillation periods are concerned with the thickness of the implanted layer, these changes suggest that the thickness of the implanted layers is changed by evaporation or precipitation in the implanted SiC layer. From the analysis, the thickness of the implanted layer
We proposed the method for estimating the electrical properties, such as, carrier concentration and mobility of semiconductor wafers using IR reflectance spectroscopy. In the method, the observed spectra are fitted with the calculated ones, and the free carrier concentration and mobility are determined from the fitted parameters. In the calculation, we used the modified dielectric function (MDF) model for the dispersion relation of dielectric constants. We demonstrated the estimations of carrier concentrations and mobilities of commercially produced 6H-SiC wafers from observed IR reflectance spectra in the frequency range of 400–2000cm–1. We showed that the free carrier concentration and mobility obtained from IR reflectance measurements agree well with the values obtained from Hall-effect measurements in the carrier concentration range of 1017~1019 cm–3, which suggests that we can estimate the carrier concentration and mobility accurately in a nondestructive and noncontact way. We demonstrated spatial mappings of carrier concentration and mobility in 2-inch 6H-SiC wafers using this method and showed its usefulness to characterize the spatial distribution of the carrier concentration and mobility in SiC wafers.
Next, we applied this method to the simultaneous determination of the carrier concentration, mobility and thickness of homo-epilayers, and the carrier concentration and mobility of substrates. IR reflectance spectra with the frequency range of 80–2000 cm–1 were measured for
Finally, we performed the characterization of both the electrical properties and crystalline damage in high-dose phosphorous implanted and post implantation annealed 4H-SiC layers using IR reflectance spectroscopy. The characterization revealed that the impurities are activated by annealing at a temperature as low as 1200°C for 30 min, though the sufficient recovery of the crystallinity needs higher annealing temperatures than 1200°C. It is also found from the IR reflectance analyses that the annealing at 1700°C activates the impurities and recovers the crystallinity of implanted layer within 1 min. These results suggest that the method can give the information of, not only the electrical properties, but also the crystalline damages of ion-implanted SiC epilayers simultaneously.
In conclusion, the electrical characteristics of SiC wafers and the electrical properties and thickness of SiC epilayers can be obtained simultaneously from the analyses of IR reflectance spectroscopy in nondestructive and contactless manner, which makes possible to obtain the spatial mapping of the electrical characteristics and thickness of SiC epilayers by scanning a probing light beam. Therefore, the method we proposed is a useful technique as a monitoring tool of SiC device-process, i.e., the monitoring of the doping concentration, carrier mobility and thickness, and their uniformity over the wafers in homo-epitaxial growth process, and the recovery of crystallinity and electrical activation of impurities in post-implantation-annealing process.
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