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 [16], 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 3% !z\* #,z/!)%+\* 10+./z3%0\$z\*z+2!. ),! z,(/)+\*z/5/0!)z(%'!z%\_z 0\$!z.!"(!¥ 0\*!z/,!0.1)z%/\_z\$+3!2!.\_z/0.+\*#(5z !,!\* !\*0z+\*zw,\$+\*+\*z ),%\*#z!1/!z0\$!z,(/¥ mon is overdamped and the LO phonon frequency is much higher than the plasma frequency !4!,0z"+.z\$!2%(5z +,! z/!/^z+.z0\$!/!z.!/+\*/\_z3!z\$2!z\$+/!\*z0+z1/!z0\$!z)+ %"%! z(//%¥ Nondestructive and Contactless Characterization Method for Spatial Mapping of the Thickness and Electrical Properties in Homo-Epitaxially Grown SiC Epilayers Using Infrared Reflectance Spectroscopy http://dx.doi.org/10.5772/50749 5

cal dielectric function (MDF) model taking into account the contribution of the TO phonon damping constant and the LO phonon damping constant independently [17]. Considering the contributions from phonons and plasmons, the dielectric constant is given as

fect measurements and capacitance-voltage (*C–V*) measurements have been widely used. These techniques, however, are disadvantageous as a device fabrication process monitoring tool because they require the formation of electrodes on a sample. By using a mercury probe as an electrode, *C–V* measurements can be performed without the formation of electrodes on a sample. However, the problems caused by the contamination with mercury contact have

Optical measurement techniques such as Raman scattering spectroscopy [2-5], infrared (IR) /,!0.+/+,%z!((%,/+)!0.5zeIf\_z+,0%(z/+.,0%+\*z)!/1.!)!\*0/zeJfz\$2!z!!\*z1/! z0+z!/0%¥ mate 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 [8] and SiC [9]. Macmillan *et al*^zeDCfz.!,+.0! z0\$0z0\$!z0\$%'\*!//z+"z\$+)+w!,%04%((5z#.+3\*z%z3¥ fers can be estimated from the interference oscillations in IR reflectance spectra observed both below and upper frequency ranges of the reststrahlen band (800–1000cm–1z"+.z%d^z+3¥ days, the reflectance measurements in near IR spectral range (1000–4000cm–1) is widely used to estimate the thickness of homo-epitaxially grown SiC layers in the SiC device process. As the thickness of epilayers used for power devices are in the range from several to several tens µm, the observation of reflectance spectra in near IR spectral range is suitable to analyze the

oscillation of reflectance caused by the interference effects of light in the epilayers.

damages in the ion-implanted, and post-implantation-annealed SiC epilayers.

using IR reflectance spectroscopy

spectroscopy [11,12]

2. Characterization method of the electrical properties in SiC wafers

2.1. Method of obtaining carrier concentration and mobility from IR reflectance

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 [16], 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 3% !z\* #,z/!)%+\* 10+./z3%0\$z\*z+2!. ),! z,(/)+\*z/5/0!)z(%'!z%\_z 0\$!z.!"(!¥ 0\*!z/,!0.1)z%/\_z\$+3!2!.\_z/0.+\*#(5z !,!\* !\*0z+\*zw,\$+\*+\*z ),%\*#z!1/!z0\$!z,(/¥ mon is overdamped and the LO phonon frequency is much higher than the plasma frequency !4!,0z"+.z\$!2%(5z +,! z/!/^z+.z0\$!/!z.!/+\*/\_z3!z\$2!z\$+/!\*z0+z1/!z0\$!z)+ %"%! z(//%¥

!z\$2!z !2!(+,! z0\$!z)!0\$+ z+"z+0%\*%\*#z0\$!z0\$%'\*!//z\* z!(!0.%(z,.+,!.0%!/z+"z/!)%¥ conductor 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 *C–V* measurements. Finally, we will show the results of applying this method to characterize the electrical activation of impurity and crystalline

been pointed out, recently.

4 Physics and Technology of Silicon Carbide Devices

$$\varepsilon(\omega) = \varepsilon\_{\text{ov}} \left| \frac{\omega\_L \, ^2 - \omega \, ^2 - \text{i}\, \Gamma\_L \, \omega}{\omega\_T \, ^2 - \omega \, ^2 - \text{i}\, \Gamma\_T \, \omega} - \frac{\omega\_p \, ^2}{\omega^2 + \text{i}\, \gamma\_p \omega} \right| \tag{1}$$

where cX is the high frequency dielectric constant, qT and qL are the TO- and LO-phonon frequencies, respectively, \T and \<sup>l</sup> z.!z0\$!zwz\* zw,\$+\*+\*z ),%\*#z+\*/0\*0/\_z.!/,!¥ tively, a<sup>p</sup> is the free-carrier damping constant, and q<sup>p</sup> %/z0\$!z,(/)z".!-1!\*5z+"z0\$!z".!!z.¥ riers, which is given by

$$
\omega\_p = \sqrt{\frac{Ne^2}{m^\* \varepsilon\_\circ}} \tag{2}
$$

where *N*, *e*, and *m*tz.!z0\$!z".!!z..%!.z+\*!\*0.0%+\*\_z!(!0.+\*z\$.#!\_z\* z!""!0%2!z)//\_z.!¥ spectively. The free-carrier damping constant p is the inverse of the scattering time m and therefore the free-carrier mobility can be derived using the following relation,

$$
\mu = \frac{e}{m^\* \mathcal{V}\_p} \tag{3}
$$

//1)%\*#z 0\$0z 0\$!z3"!./z .!z 1\*%"+.)! z%\*z 0\$!z !,0\$z %.!0%+\*\_z3!z 1/! z 0\$!z \*+.)(w%\*%¥ dence reflectance of a semi-infinite medium *R*, which is expressed as

$$R\left(\omega\right) = \frac{\left(n-1\right)^2 + k^2}{\left(n+1\right)^2 + k^2} \tag{4}$$

where *n* and *k* are the optical constants, derived from cSc0=(*n*–*ik*) 2 .

\$!z..%!.z+\*!\*0.0%+\*z\* z)+%(%05z\*z!z !0!.)%\*! z5z"%00%\*#z0\$!z!4,!.%)!\*0(z%\*".¥ red reflectance spectrum with calculated ones. To fit the spectra, we used the least-squares method based on eqs. (1) and (4), where we adopted qp, ap, and \L as adjustable parameters.

#### 2.2. Measurements of IR reflectance spectra of SiC wafers and estimation of electrical properties [12]

Single crystal wafers of commercially produced *n*-type (nitrogen doped) 6H-SiC were used. z .!"(!0\*!z /,!0.z 3!.!z )!/1.! z 1/%\*#z 03+z +1.%!.w0.\*/"+.)z %\*"..! z c dz /,!¥ trometers, JASCO FT/IR–VM7 for the far-infrared region (30–600 cm–1) and JASCO FT/IR 670-PLUS for the middle-infrared region (400–2000 cm–1d\_z .!/,!0%2!(5^z +.z ".w%\*"..! z .!¥ flectance measurements, two light sources (a mercury arc-lamp and nichrome light source), three beam splitters (4, 12, 25 µm thick Mylar films) and a p-DTGS (pyroelectric deuterated triglycine sulfate) detector were used. For middle-infrared reflectance measurements, a high intensity ceramic light source, a KBr beam splitter, and a TGS detector were employed. Each IR reflectance spectrum was measured with 1 cm- spectral resolution. The light diameters were 5 mm for far-infrared measurements, and 3 mm for middle-infrared measurements. The measurements were performed for (0001) Si-faces of 6H-SiC wafers at nearly normal incidence. An Al mirror was used as a reflectance reference.

Figure 1. Infrared reflectance spectra measured for 6H-SiC wafers with various carrier concentrations at room temperature (dotted line). The solid lines show the fitted spectra calculated using MDF model. The values of carrier concentration and mobility obtained from fitting to the measured IR spectra are described in the figure [12].

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 wo, IL Yo as adjustable parameters. For the values of the other parameters, we employed those obtained from Raman scattering measurements, ε..=6.52εω ως=797cm², ωլ=969.4cm²; Γη=2cm²', and m\*=0.35m, for 6H-SiC[2]. Since the light is normally incident on the (0001) face of the samples, these parameters are all for the modes vibrating perpendicular to the c-axis.

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 4×10ºº~3×10ººcm³. 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 freecarrier concentration and drift mobility were derived from the best-fit parameters of ω, and y, using eqs.(2) and (3), mentioned above. The values of free-carrier concentration and mobility obtained are also given in each figure.

As shown in Figure 1 (c), there is a slight discrepancy at approximately 900 cm-' between the spectrum observed and that calculated using the MDF model (eq. (1)). This discrepancy increases with increasing carrier concentration in the high 10" cm3 range. For heavily doped SiC crystals, the CDF and MDF models would be inappropriate because the MDF model is derived considering the ettects 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 [12]

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 2.4×1019cm3 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.

Figure 2. Comparison of (a) carrier concentration and (b) mobility values, NK obtained from IR reflectance spectroscopy measurements with those from Hall effect measurements, Mair The broken lines represent the case of complete agreement with each other [12].

2.4. Spatial mapping of the electrical properties over SiC wafers [11,12]

tral range of 560–2000 cm–1 with a spectral resolution of 4cm–1.

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 3/zHz))zcz0+0(z+"zDECz)!/1.!)!\*0z,+%\*0/d^z!z,!."+.)! z0\$!z)!/1.!)!\*0/z%\*z0\$!z/,!¥

Nondestructive and Contactless Characterization Method for Spatial Mapping of the Thickness and Electrical

Properties in Homo-Epitaxially Grown SiC Epilayers Using Infrared Reflectance Spectroscopy

http://dx.doi.org/10.5772/50749

9

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. \$%/z)!/1.!)!\*0z0!\$\*%-1!z\*!! /z\*+z,.%+.z/1."!z0.!0)!\*0\_z!1/!z0\$!z\*0%2!z+4% !z(5¥ !.z0\$%'\*!//z\* z/1."!z.+1#\$\*!//z.!z\*+0z)+.!z0\$\*zFz\*)z\* z0\$!%.z%\*"(1!\*!z+\*z0\$!z.!"(!¥ tance spectra is negligible in IR region. The uniformity of free-carrier concentration and )+%(%05z0\$.+1#\$+10z0\$%/z3"!.z!4!,0z"+.zHz))z".+)z0\$!z! #!z3!.!z!/0%)0! z0+z!z,,.+4¥ imately ±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 +0\$!.z\$\* \_z 0\$!z)+%(%05z),,%\*#z /\$+3/z 0\$!z\*!#0%2!z +..!(0%+\*z +"z 0\$!z)+%(%05z %/0.%1¥ tion 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.

Figure 4. Spatial mapping of (a) carrier concentration and (b) mobility in a commercially produced 2 inch 6H-SiC wafer

[12].

Figure 3. The variations in drift mobility evaluated from IR reflectance spectroscopy, and Hall mobility measurements plotted against carrier concentration. The reported values of Hall mobility [23] and those calculated theoretically (*N*A/*N*D=0) following reference [24] are also shown for comparison [12].

In Figure 2 (a) and (b), 0\$!z..%!.z+\*!\*0.0%+\*/z\* z)+%(%0%!/z!/0%)0! z".+)z0\$!z z.!"(!¥ tance spectra are plotted against those obtained from the Hall effect measurements. As the reported Hall scattering factor *r*H is approximately unity at room temperature for 6H-SiC [21,22], we assumed *r*H is equal to unity for the calculation. Good agreement was obtained between the electrical characteristics obtained from IR reflectance measurements and those from Hall effect measurements.

The LO phonon damping constant \L\_z3\$%\$z%/z+\*!z+"z0\$!z &1/0(!z,.)!0!./\_z2.%!/z(%\*!¥ .(5z 3%0\$z ..%!.z +\*!\*0.0%+\*^z \$%/z 0!\* !\*5z %/z %\*z #++ z #.!!)!\*0z 3%0\$z 0\$!z .!/1(0/z +¥ tained by Raman scattering spectroscopy [17] in which, as was explained, the interactions between ionized impurity and LO phonon, and free carrier and LO phonon increase with increasing doping concentration.

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 *et al* [23]. The Hall mobilities obtained in the present study are a little higher than those determined by Karmann *et al.* %\*zz\$%#\$w..%!.w+\*!\*0.0%+\*z.!#%+\*^z!z(1(0! z0\$!z .%"0z\* z((z)+%¥ lity at room temperature as functions of dopant concentration following references [24-26], assuming that the compensation ratio *NA/ND*RC\_z\* z+\*/% !.! z"%2!z..%!.z/00!.%\*#z)!\$¥ anisms (acoustic phonon deformation potential scattering, polar optical phonon scattering, %\*0!.2((!5z ,\$+\*+\*z !"+.)0%+\*z ,+0!\*0%(z /00!.%\*#\_z \*!10.(z %),1.%05z /00!.%\*#\_z \* z %+\*¥ ized impurity scattering) as in reference [29]. The values of the mobility obtained in this work are lower than those obtained from the theoretical calculations. This result suggests that the compensation ratio is not 0 but approximately 0.2 in this study and a little higher in the case of Karmann *et al*.

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]

Figure 3. The variations in drift mobility evaluated from IR reflectance spectroscopy, and Hall mobility measurements plotted against carrier concentration. The reported values of Hall mobility [23] and those calculated theoretically

In Figure 2 (a) and (b), 0\$!z..%!.z+\*!\*0.0%+\*/z\* z)+%(%0%!/z!/0%)0! z".+)z0\$!z z.!"(!¥ tance spectra are plotted against those obtained from the Hall effect measurements. As the reported Hall scattering factor *r*H is approximately unity at room temperature for 6H-SiC [21,22], we assumed *r*H is equal to unity for the calculation. Good agreement was obtained between the electrical characteristics obtained from IR reflectance measurements and those

The LO phonon damping constant \L\_z3\$%\$z%/z+\*!z+"z0\$!z &1/0(!z,.)!0!./\_z2.%!/z(%\*!¥ .(5z 3%0\$z ..%!.z +\*!\*0.0%+\*^z \$%/z 0!\* !\*5z %/z %\*z #++ z #.!!)!\*0z 3%0\$z 0\$!z .!/1(0/z +¥ tained by Raman scattering spectroscopy [17] in which, as was explained, the interactions between ionized impurity and LO phonon, and free carrier and LO phonon increase with

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 *et al* [23]. The Hall mobilities obtained in the present study are a little higher than those determined by Karmann *et al.* %\*zz\$%#\$w..%!.w+\*!\*0.0%+\*z.!#%+\*^z!z(1(0! z0\$!z .%"0z\* z((z)+%¥ lity at room temperature as functions of dopant concentration following references [24-26], assuming that the compensation ratio *NA/ND*RC\_z\* z+\*/% !.! z"%2!z..%!.z/00!.%\*#z)!\$¥ anisms (acoustic phonon deformation potential scattering, polar optical phonon scattering, %\*0!.2((!5z ,\$+\*+\*z !"+.)0%+\*z ,+0!\*0%(z /00!.%\*#\_z \*!10.(z %),1.%05z /00!.%\*#\_z \* z %+\*¥ ized impurity scattering) as in reference [29]. The values of the mobility obtained in this work are lower than those obtained from the theoretical calculations. This result suggests that the compensation ratio is not 0 but approximately 0.2 in this study and a little higher in

Through comparison, we have ascertained that the electrical characteristics of SiC wafers

can be estimated by IR reflectance spectroscopy with high credibility.

(*N*A/*N*D=0) following reference [24] are also shown for comparison [12].

from Hall effect measurements.

8 Physics and Technology of Silicon Carbide Devices

increasing doping concentration.

the case of Karmann *et al*.

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 3/zHz))zcz0+0(z+"zDECz)!/1.!)!\*0z,+%\*0/d^z!z,!."+.)! z0\$!z)!/1.!)!\*0/z%\*z0\$!z/,!¥ tral 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. \$%/z)!/1.!)!\*0z0!\$\*%-1!z\*!! /z\*+z,.%+.z/1."!z0.!0)!\*0\_z!1/!z0\$!z\*0%2!z+4% !z(5¥ !.z0\$%'\*!//z\* z/1."!z.+1#\$\*!//z.!z\*+0z)+.!z0\$\*zFz\*)z\* z0\$!%.z%\*"(1!\*!z+\*z0\$!z.!"(!¥ tance spectra is negligible in IR region. The uniformity of free-carrier concentration and )+%(%05z0\$.+1#\$+10z0\$%/z3"!.z!4!,0z"+.zHz))z".+)z0\$!z! #!z3!.!z!/0%)0! z0+z!z,,.+4¥ imately ±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 +0\$!.z\$\* \_z 0\$!z)+%(%05z),,%\*#z /\$+3/z 0\$!z\*!#0%2!z +..!(0%+\*z +"z 0\$!z)+%(%05z %/0.%1¥ tion 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.

Figure 4. Spatial mapping of (a) carrier concentration and (b) mobility in a commercially produced 2 inch 6H-SiC wafer [12].
