3. Characterization method of the electrical properties and thickness of epilayers using IR reflectance spectroscopy

3.2. Measurements of IR reflectance spectra and derivation of electrical properties and

Samples used in this study were nitrogen doped *n*-type 4H-SiC epilayers grown on *n*- and *p*type 4H-SiC substrates supplied from National Institute of Advanced Industrial Science and Technology (AIST). The epilayers were grown on 4H-SiC (0001) Si face 8 off substrates by chemical vapor deposition (CVD). The details of the epilayer growth have been described elsewhere [28]. In the case of the *n*-type epilayers on *p*w05,!z/1/0.0!/\_z0\$!z..%!.z+\*!\*0.¥ tion of the epilayers was in the range between 3×1017 and 2×1018 cm–3\_z \* z 0\$0z+"z 0\$!z/1¥ strates was typically 4×1016 cm–3. On the other hand, in the case of the *n*-type epilayers on *n*type substrates, the net doping concentration (*ND– NA*) of the epilayers was in the range between 1×1017 and 8×1017 cm–3, and that of the substrates was typically 5×1018 cm–3. The thickness of the epilayers were 6~7 µm, measured by scanning electron microscope (SEM) observation of the cleaved facet of the samples. The IR reflectance spectra in the frequency range of 80–2000 cm–1z3!.!z)!/1.! z0z.++)z0!),!.01.!z1/%\*#z/)!z/,!0.+)!0!./z)!\*¥ tioned in Section 2.2. Hall effect measurements were performed at room temperature using van der Pauw method for *n*-type epilayers on *p*w05,!z/1/0.0!/^z\$)%z+\*00/z3!.!z".%¥ 0! z+\*z 0\$!z!,%(5!.z/1."!/z5z 0\$!z!(!0.+\*z!)z!2,+.0%+\*z+"z%z \* z/1/!-1!\*0z \*¥ nealing at 900°C for 30min in N2 atmosphere. *C–V* measurements were performed at room

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

11

0 500 1000 1500 2000 Wave number(cm-1

Figure 5. IR reflectance spectrum of an *n*-type epilayer on a *p*-type substrate at room temperature denoted by dashed line. The solid line shows the fitted curve calculated using the MDF model. The values estimated from this fitting are

)

*<sup>N</sup>*sub = 2.6!1016

 Experiment Fitted curve

sub = 60 cm2

*<sup>N</sup>*epi = 3.2!1017

epi = 296 cm2

*d* = 6.6 µm

cm -3 

/(V·s)

cm -3 

/(V·s)

thickness of SiC epi-wafers [13]

100

80

60

40

Reflectance(%)

20

0

listed in the figure [13].

temperature using a mercury probe as a Schottky contact.

#### 3.1. Method of obtaining the carrier concentration, mobility, and thickness of epilayers, simultaneously [13]

In this section, we propose the method for the simultaneous determination of the electrical properties, *i.e*., free carrier concentration and mobility, and the thickness of epilayers as well /z1('z(5!.z5z z.!"(!0\*!z)!/1.!)!\*0/^z%./0\_z3!z3%((z!4,(%\*z0\$!z,.+! 1.!z+"z+0%\*¥ ing carrier concentration, mobility and thickness of the epilayers on SiC wafers. Then, we will compare the electrical properties derived from the IR reflectance analyses with those from Hall effect measurements for *n*-type epilayers grown on *p*-type substrates, and with those from *C–V* measurements in the case of *n*-type epilayers on *n*-type substrates. Finally we will discuss the validity of the obtained values from the proposed method.

The carrier concentration and mobility of epilayers and substrates, as well as the thickness +"z0\$!z!,%(5!./z\*z!z !0!.)%\*! z/%)1(0\*!+1/(5z5z"%00%\*#z0\$!z(1(0! z.!"(!0\*!z/,!¥ tra to measured ones. The reflectance *R* from an air/ epilayer/substrate structure at normal incidence is given by

$$R = \left| \frac{r\_1 + r\_2 e^{-2\mathcal{S}}}{1 + r\_1 r\_2 e^{-2i\mathcal{S}}} \right|^2, \quad \text{where} \quad \mathcal{S} = \frac{2\pi nd}{\mathcal{A}} \tag{5}$$

where *r*1 and *r*2 are the Fresnel reflection coefficients at the air/epilayer and the epilayer/ substrate interface, respectively, and b is the phase shift of light in the epilayer, *n* and *d* are the refractive index and the thickness of epilayer, respectively, and f %/z32!(!\*#0\$^z\$!z+,¥ 0%(z+\*/0\*0/z+"z%z%\*z z/,!0.(z.\*#!z.!z !.%2! z".+)z0\$!z %!(!0.%z+\*/0\*0/z/zz"1\*¥ tion of the frequency of the incident light, given by eq.(1) both for substrate and epilayer. As in the case of SiC bare wafers written in Section 2, we fitted the calculated spectrum to the measured one by adjusting the values of qp, ap, \T and \L of the epilayer and those of the substrate, and the epilayer thickness *d*^z.+)z0\$!/!z2(1!/\_z3!z\*z+0%\*z0\$!z..%!.z+\*!\*¥ tration *N* and mobility *µ* of the epilayer and substrate using eqs. (3) and (4d^z \*z0\$!z(1(¥ tion, we adopted the values cX=6.56, qT=798cm–1, qL=970cm–1, and *m*\* MG=0.58*m*0, *m*\* MK =0.31*m*0, obtained from the Raman scattering measurements of 4H-SiC [2fz\* z+,0%(z !0!0%+\*z+"z5¥ clotron resonance (ODCR) [27]. Considering that the free carriers distribute themselves in proportion to the square root of each effective mass, the averaged effective mass, *m*\* = (*m*\* MK*m*\* MG) 1/2, and *m*\* =(1/*m*\*MK1/2+1/*m*\*MG1/2)/(1/*m*\*MK3/2+1/*m*\*MG3/2) were used for the calculation of the carrier concentration and mobility, respectively.

#### 3.2. Measurements of IR reflectance spectra and derivation of electrical properties and thickness of SiC epi-wafers [13]

3. Characterization method of the electrical properties and thickness of

3.1. Method of obtaining the carrier concentration, mobility, and thickness of epilayers,

In this section, we propose the method for the simultaneous determination of the electrical properties, *i.e*., free carrier concentration and mobility, and the thickness of epilayers as well /z1('z(5!.z5z z.!"(!0\*!z)!/1.!)!\*0/^z%./0\_z3!z3%((z!4,(%\*z0\$!z,.+! 1.!z+"z+0%\*¥ ing carrier concentration, mobility and thickness of the epilayers on SiC wafers. Then, we will compare the electrical properties derived from the IR reflectance analyses with those from Hall effect measurements for *n*-type epilayers grown on *p*-type substrates, and with those from *C–V* measurements in the case of *n*-type epilayers on *n*-type substrates. Finally

The carrier concentration and mobility of epilayers and substrates, as well as the thickness +"z0\$!z!,%(5!./z\*z!z !0!.)%\*! z/%)1(0\*!+1/(5z5z"%00%\*#z0\$!z(1(0! z.!"(!0\*!z/,!¥ tra to measured ones. The reflectance *R* from an air/ epilayer/substrate structure at normal

we will discuss the validity of the obtained values from the proposed method.

<sup>2</sup> <sup>2</sup>

<sup>2</sup> , <sup>1</sup>

where *r*1 and *r*2 are the Fresnel reflection coefficients at the air/epilayer and the epilayer/ substrate interface, respectively, and b is the phase shift of light in the epilayer, *n* and *d* are the refractive index and the thickness of epilayer, respectively, and f %/z32!(!\*#0\$^z\$!z+,¥ 0%(z+\*/0\*0/z+"z%z%\*z z/,!0.(z.\*#!z.!z !.%2! z".+)z0\$!z %!(!0.%z+\*/0\*0/z/zz"1\*¥ tion of the frequency of the incident light, given by eq.(1) both for substrate and epilayer. As in the case of SiC bare wafers written in Section 2, we fitted the calculated spectrum to the measured one by adjusting the values of qp, ap, \T and \L of the epilayer and those of the substrate, and the epilayer thickness *d*^z.+)z0\$!/!z2(1!/\_z3!z\*z+0%\*z0\$!z..%!.z+\*!\*¥ tration *N* and mobility *µ* of the epilayer and substrate using eqs. (3) and (4d^z \*z0\$!z(1(¥

obtained from the Raman scattering measurements of 4H-SiC [2fz\* z+,0%(z !0!0%+\*z+"z5¥ clotron resonance (ODCR) [27]. Considering that the free carriers distribute themselves in proportion to the square root of each effective mass, the averaged effective mass, *m*\*

<sup>+</sup> = = <sup>+</sup>

*r re nd <sup>R</sup> where*

 

=(1/*m*\*MK1/2+1/*m*\*MG1/2)/(1/*m*\*MK3/2+1/*m*\*MG3/2) were used for the calculation

MG=0.58*m*0, *m*\*

MK =0.31*m*0,

=

(5)

2 1 2

*i i*

 

1 2

*rre*

tion, we adopted the values cX=6.56, qT=798cm–1, qL=970cm–1, and *m*\*

of the carrier concentration and mobility, respectively.

epilayers using IR reflectance spectroscopy

10 Physics and Technology of Silicon Carbide Devices

simultaneously [13]

incidence is given by

(*m*\* MK*m*\* MG)

1/2, and *m*\*

Samples used in this study were nitrogen doped *n*-type 4H-SiC epilayers grown on *n*- and *p*type 4H-SiC substrates supplied from National Institute of Advanced Industrial Science and Technology (AIST). The epilayers were grown on 4H-SiC (0001) Si face 8 off substrates by chemical vapor deposition (CVD). The details of the epilayer growth have been described elsewhere [28]. In the case of the *n*-type epilayers on *p*w05,!z/1/0.0!/\_z0\$!z..%!.z+\*!\*0.¥ tion of the epilayers was in the range between 3×1017 and 2×1018 cm–3\_z \* z 0\$0z+"z 0\$!z/1¥ strates was typically 4×1016 cm–3. On the other hand, in the case of the *n*-type epilayers on *n*type substrates, the net doping concentration (*ND– NA*) of the epilayers was in the range between 1×1017 and 8×1017 cm–3, and that of the substrates was typically 5×1018 cm–3. The thickness of the epilayers were 6~7 µm, measured by scanning electron microscope (SEM) observation of the cleaved facet of the samples. The IR reflectance spectra in the frequency range of 80–2000 cm–1z3!.!z)!/1.! z0z.++)z0!),!.01.!z1/%\*#z/)!z/,!0.+)!0!./z)!\*¥ tioned in Section 2.2. Hall effect measurements were performed at room temperature using van der Pauw method for *n*-type epilayers on *p*w05,!z/1/0.0!/^z\$)%z+\*00/z3!.!z".%¥ 0! z+\*z 0\$!z!,%(5!.z/1."!/z5z 0\$!z!(!0.+\*z!)z!2,+.0%+\*z+"z%z \* z/1/!-1!\*0z \*¥ nealing at 900°C for 30min in N2 atmosphere. *C–V* measurements were performed at room temperature using a mercury probe as a Schottky contact.

Figure 5. IR reflectance spectrum of an *n*-type epilayer on a *p*-type substrate at room temperature denoted by dashed line. The solid line shows the fitted curve calculated using the MDF model. The values estimated from this fitting are listed in the figure [13].

At first, we estimated the carrier concentration and mobility of *n*-type epilayers on *p*w05,!z/1¥ strates from the reflectance measurements, and compared with these values obtained from Hall effect measurements. Figure 5 shows typical IR reflectance spectra measured for the *n*type epilayers on *p*-type substrates. The solid line denotes the calculated values fitted to the experimental one shown as the dashed line. The values *N*epi = 3.2×1017 cm–3, *µ*epi = 296 cm2 /(V s), and *d* = 6.60 µm were obtained by a curve fitting analysis. These values are listed in the figure. In the case of *p*w05,!z/1/0.0!z3\$+/!z..%!.z+\*!\*0.0%+\*z%/z(+3z%\*z#!\*!.(\_z0\$!z.!"(!¥ tance spectrum is almost independent of the electrical properties of the substrate, thus, it is difficult to estimate the carrier concentration and mobility of the substrate. Therefore, we used the values for the *p*w05,!z/1/0.0!z3%0\$+10z!,%(5!.z+0%\*! z".+)z0\$!z((z!""!0z)!/¥ urements. The thickness of the epilayers obtained from the IR reflectance measurements and those measured from the SEM observation coincide with each other within ±1%.

*<sup>n</sup>*(*<sup>T</sup>* ) + *NA* <sup>=</sup> *<sup>N</sup>* (*<sup>h</sup>* )

6 8 1017

400

300

200

FTIR

[13].

[cm2/(V·s)]

100

6 7 8 9 1017

(b)

2

*N*FTIR (cm-3

)

2

(a)

4

1 + {*gn*(*<sup>T</sup>* ) / *NC*}exp ]*E*(*<sup>h</sup>* ) / *kBT* <sup>+</sup>

*NC* =2*MC*( *<sup>m</sup>*\**<sup>d</sup>* .*s*. *kBT*

<sup>2</sup>j§<sup>2</sup> )

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

2 3 4 5 6 7 8 9

100 200 300 400 Hall [cm2

Figure 6. Values of (a) carrier concentration and (b) mobility estimated from IR reflectance measurements and Hall effect measurements. The dotted line in the figures corresponds to the case of complete agreement with each other

/(V·s)]

*<sup>N</sup>*Hall (cm-3)

1018

2 3 4

3/2

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

*N* (*k*)

1 + {*gn*(*<sup>T</sup>* ) / *NC*}exp ]*E*(*k*)/ *kBT* (6)

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

(7)

13

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 *r*Hz%/z.!,+.0! z0+z!z,,.+4%)0!(5z1\*%¥ ty at room temperature for 4H-SiC [27,29] as in the case of 6H-SiC, we directly compared the drift mobilities estimated from the IR reflectance measurements and those of the Hall )+%(%0%!/z+0%\*! z ".+)z 0\$!z((z!""!0z)!/1.!)!\*0/^z\$!z!..+.z./z/\$+3\*z%\*z 0\$!z "%#¥ ures represent the accuracy of the fitting analysis, and the accuracy is about ±4% for both the carrier concentration and the mobility, whereas the accuracy of the values derived from Hall effect measurements is about ±10%. As can be seen from these figures, the electrical ,.+,!.0%!/ z +0%\*! z ".+) z 0\$! z .!"(!0\*! z /,!0. z .! z%\* z #++ z #.!!)!\*0 z3%0\$ z 0\$+/! z +¥ 0%\*! z".+)z0\$!z((z!""!0z)!/1.!)!\*0/^z\$!/!z.!/1(0/z/1##!/0z0\$0z0\$!z,.+,+/! z)!0\$¥ od is valid for obtaining the values of carrier concentration and mobility of the epilayers. +3!2!.\_z.!"1(z+/!.20%+\*z+\*"%.)/z0\$0z0\$!z2(1!/z+"z..%!.z+\*!\*0.0%+\*z\* z)+%(%¥ 05z !.%2! z ".+)z 0\$!z%\*"..! z.!"(!0\*!z)!/1.!)!\*0/z.!z/(%#\$0(5z(+3!.z 0\$\*z 0\$+/!z+¥ tained from the Hall effect measurements. The difference can be explained by the +\*/% !.0%+\*z0\$0z0\$!z,.0z+"z".!!z..%!./z0.,,! z%\*z !"!0/z+.z+1\* ! z5z +,\*0/z\*¥ not follow in the THz frequency range used for the reflectance measurements, unlike in Hall effect measurements, where a direct current is supplied.

Next, we estimated the values of carrier concentration and mobility for *n*-type epilayers on *n*w05,!z/1/0.0!/z".+)z 0\$!z z.!"(!0\*!z/,!0.z)!/1.! ^z%#1.!zJz/\$+3/zz 05,%(z z.!¥ flectance spectrum observed and its fitted curve. The values *N*epi = 1.3×1017 cm–3, *µ*epi = 403 cm2 /(V s) and *d* = 4.45 µm; and *N*sub = 7.1×1018 cm–3, *µ*sub = 53 cm2 /(V s) were obtained by curve fitting analysis as the parameters of the epilayer and substrate, respectively. The accuracy of 0\$!z..%!.z+\*!\*0.0%+\*z\* z)+%(%05z+"z!,%(5!.//z !.%2! z".+)z0\$!z"%00%\*#z+"z0\$!z z.!"(!¥ tance spectrum is about ±10%. In Figure 8, the free carrier concentration estimated from the IR reflectance spectra is plotted with respect to the net doping concentrations *ND– NA* !¥ rived from *C–V* measurements. We calculated the free carrier concentrations *n* from the net doping concentrations using

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 13

$$\text{gn}(T) + N\_A = \frac{N(h)}{1 + \left[\text{gn}(T)/N\_C\right] \text{exp}\left[\Delta E(h)/k\_B T\right]} + \frac{N(k)}{1 + \left[\text{gn}(T)/N\_C\right] \text{exp}\left[\Delta E(k)/k\_B T\right]}\tag{6}$$

At first, we estimated the carrier concentration and mobility of *n*-type epilayers on *p*w05,!z/1¥ strates from the reflectance measurements, and compared with these values obtained from Hall effect measurements. Figure 5 shows typical IR reflectance spectra measured for the *n*type epilayers on *p*-type substrates. The solid line denotes the calculated values fitted to the experimental one shown as the dashed line. The values *N*epi = 3.2×1017 cm–3, *µ*epi = 296 cm2

12 Physics and Technology of Silicon Carbide Devices

s), and *d* = 6.60 µm were obtained by a curve fitting analysis. These values are listed in the figure. In the case of *p*w05,!z/1/0.0!z3\$+/!z..%!.z+\*!\*0.0%+\*z%/z(+3z%\*z#!\*!.(\_z0\$!z.!"(!¥ tance spectrum is almost independent of the electrical properties of the substrate, thus, it is difficult to estimate the carrier concentration and mobility of the substrate. Therefore, we used the values for the *p*w05,!z/1/0.0!z3%0\$+10z!,%(5!.z+0%\*! z".+)z0\$!z((z!""!0z)!/¥ urements. The thickness of the epilayers obtained from the IR reflectance measurements and

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 *r*Hz%/z.!,+.0! z0+z!z,,.+4%)0!(5z1\*%¥ ty at room temperature for 4H-SiC [27,29] as in the case of 6H-SiC, we directly compared the drift mobilities estimated from the IR reflectance measurements and those of the Hall )+%(%0%!/z+0%\*! z ".+)z 0\$!z((z!""!0z)!/1.!)!\*0/^z\$!z!..+.z./z/\$+3\*z%\*z 0\$!z "%#¥ ures represent the accuracy of the fitting analysis, and the accuracy is about ±4% for both the carrier concentration and the mobility, whereas the accuracy of the values derived from Hall effect measurements is about ±10%. As can be seen from these figures, the electrical ,.+,!.0%!/ z +0%\*! z ".+) z 0\$! z .!"(!0\*! z /,!0. z .! z%\* z #++ z #.!!)!\*0 z3%0\$ z 0\$+/! z +¥ 0%\*! z".+)z0\$!z((z!""!0z)!/1.!)!\*0/^z\$!/!z.!/1(0/z/1##!/0z0\$0z0\$!z,.+,+/! z)!0\$¥ od is valid for obtaining the values of carrier concentration and mobility of the epilayers. +3!2!.\_z.!"1(z+/!.20%+\*z+\*"%.)/z0\$0z0\$!z2(1!/z+"z..%!.z+\*!\*0.0%+\*z\* z)+%(%¥ 05z !.%2! z ".+)z 0\$!z%\*"..! z.!"(!0\*!z)!/1.!)!\*0/z.!z/(%#\$0(5z(+3!.z 0\$\*z 0\$+/!z+¥ tained from the Hall effect measurements. The difference can be explained by the +\*/% !.0%+\*z0\$0z0\$!z,.0z+"z".!!z..%!./z0.,,! z%\*z !"!0/z+.z+1\* ! z5z +,\*0/z\*¥ not follow in the THz frequency range used for the reflectance measurements, unlike in

Next, we estimated the values of carrier concentration and mobility for *n*-type epilayers on *n*w05,!z/1/0.0!/z".+)z 0\$!z z.!"(!0\*!z/,!0.z)!/1.! ^z%#1.!zJz/\$+3/zz 05,%(z z.!¥ flectance spectrum observed and its fitted curve. The values *N*epi = 1.3×1017 cm–3, *µ*epi = 403

fitting analysis as the parameters of the epilayer and substrate, respectively. The accuracy of 0\$!z..%!.z+\*!\*0.0%+\*z\* z)+%(%05z+"z!,%(5!.//z !.%2! z".+)z0\$!z"%00%\*#z+"z0\$!z z.!"(!¥ tance spectrum is about ±10%. In Figure 8, the free carrier concentration estimated from the IR reflectance spectra is plotted with respect to the net doping concentrations *ND– NA* !¥ rived from *C–V* measurements. We calculated the free carrier concentrations *n* from the net

those measured from the SEM observation coincide with each other within ±1%.

Hall effect measurements, where a direct current is supplied.

/(V s) and *d* = 4.45 µm; and *N*sub = 7.1×1018 cm–3, *µ*sub = 53 cm2

cm2

doping concentrations using

/(V

/(V s) were obtained by curve

$$N\_C = 2M\_C \left(\frac{m^\*\_{d.s.} \ k\_B T}{2\pi\hbar^2}\right)^{3/2} \tag{7}$$

Figure 6. Values of (a) carrier concentration and (b) mobility estimated from IR reflectance measurements and Hall effect measurements. The dotted line in the figures corresponds to the case of complete agreement with each other [13].

where *kB* is the Boltzmann constant, *T* is the temperature, *NA*z%/z0\$!z+\*!\*0.0%+\*z+"z!,0¥ ors, and *N*(*h*) and *N*(*k*dz.!z0\$!z+\*!\*0.0%+\*/z+"z0\$!z\*%0.+#!\*/z+1,%! z0z\$!4#+\*(z\* z1¥ bic lattice sites, respectively. Since the number of hexagonal sites is equal to those of cubic sites for 4H-SiC, the donor concentration *ND* is given by *N*(*h*) + *N*(*k*). The values of ](*h*) and](*k*) are the ionization energies of the nitrogen donor at hexagonal and cubic lattice sites, respectively, and *g* = 2 is the spin degeneracy factor. Equation (7) gives the effective density of states, where *Mc* = 3 is the number of equivalent conduction band minima, and

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

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

d.s. is the density-of-states effective mass. The values of ](*h*) and ](*k*) were set as 50 meV and 100 meV, respectively, referring to the reported experimental data [30,31f^z\$!z2(¥

were adopted. The solid line in Figure 8 shows the free carrier concentrations calculated as a function of the net doping concentration, where we assumed that *NA/ ND* = 0 or *ND* / (*NA* + *ND*) = 1, because the epilayers we measured are hardly compensated [32f^z \$!z 2(1!/z +¥ tained from the IR reflectance spectra are slightly lower than the calculated values, as in the case for the samples of *n*-type epilaers on *p*w05,!z/1/0.0!/^z\$!z2(1!z+"z .%"0z)+%(%05z(¥

of *NA/ ND* = 0 and *ND* –*NA* =2.7×1017cm–3, which is almost the same as the value obtained from

3.3. Extension of the carrier concentration range down to 1016cm–3 order using Terahertz

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\_z\* z+\*"%.)! z0\$0z0\$!z2(1!/z+"z0\$!z..%!.z+\*!\*0.¥ tion, 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 "+.z0\$!z..%!.z+\*¥ centration 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^z\$!z)#\*%¥ fied 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

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 *C–V* measurements to discuss the validity of this

ML = 0.33*m*0 derived from ODCR measurements [27]

uc/d^z\$%/z.!/1(0z(/+z%\* %0!/z 0\$0z 0\$!z+),!\*/¥

/(Vs), in the case

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

15

*m*\*

ues of *m*\*

= 0.58*m*0, *m*\*

the IR reflectance spectrum, *i.e*., 403 cm2

tion of the sample is low.

frequency range [14]

to the order of 1016 cm–1.

characterization method.

MK = 0.31*m*0, *m*\*

culated in consideration of five carrier scattering mechanisms [24] is 340 cm2

Figure 7. IR reflectance spectrum of an *n*-type epilayer on an *n*-type substrate denoted by dashed line. The solid line shows the fitted curve calculated using the MDF model. The values estimated from this fitting analysis are listed in the figure [13].

Figure 8. Values of the carrier concentration estimated from the IR reflectance for *n*-type epilayers on *n*LQH= KM:s strates as a function of dopant concentration obtained from *C–V* E=9KMJ=E=FLK>GJ=9;@K9EHD=0@=KGDA<DAF=J=HJ=s sents the theoretical carrier concentration for T=300K assuming zero doping concentration (*N*A=0) using eq. (6). The dashed line represents *N*FTIR=*N*D–*N*A [13].

where *kB* is the Boltzmann constant, *T* is the temperature, *NA*z%/z0\$!z+\*!\*0.0%+\*z+"z!,0¥ ors, and *N*(*h*) and *N*(*k*dz.!z0\$!z+\*!\*0.0%+\*/z+"z0\$!z\*%0.+#!\*/z+1,%! z0z\$!4#+\*(z\* z1¥ bic lattice sites, respectively. Since the number of hexagonal sites is equal to those of cubic sites for 4H-SiC, the donor concentration *ND* is given by *N*(*h*) + *N*(*k*). The values of ](*h*) and](*k*) are the ionization energies of the nitrogen donor at hexagonal and cubic lattice sites, respectively, and *g* = 2 is the spin degeneracy factor. Equation (7) gives the effective density of states, where *Mc* = 3 is the number of equivalent conduction band minima, and *m*\* d.s. is the density-of-states effective mass. The values of ](*h*) and ](*k*) were set as 50 meV and 100 meV, respectively, referring to the reported experimental data [30,31f^z\$!z2(¥ ues of *m*\* = 0.58*m*0, *m*\* MK = 0.31*m*0, *m*\* ML = 0.33*m*0 derived from ODCR measurements [27] were adopted. The solid line in Figure 8 shows the free carrier concentrations calculated as a function of the net doping concentration, where we assumed that *NA/ ND* = 0 or *ND* / (*NA* + *ND*) = 1, because the epilayers we measured are hardly compensated [32f^z \$!z 2(1!/z +¥ tained from the IR reflectance spectra are slightly lower than the calculated values, as in the case for the samples of *n*-type epilaers on *p*w05,!z/1/0.0!/^z\$!z2(1!z+"z .%"0z)+%(%05z(¥ culated in consideration of five carrier scattering mechanisms [24] is 340 cm2 /(Vs), in the case of *NA/ ND* = 0 and *ND* –*NA* =2.7×1017cm–3, which is almost the same as the value obtained from the IR reflectance spectrum, *i.e*., 403 cm2 uc/d^z\$%/z.!/1(0z(/+z%\* %0!/z 0\$0z 0\$!z+),!\*/¥ tion of the sample is low.

100

14 Physics and Technology of Silicon Carbide Devices

80

60

40

Reflectance (%)

figure [13].

20

0

dashed line represents *N*FTIR=*N*D–*N*A [13].

6 7 8 9

10<sup>17</sup>

for *N*A/*N*D = 0

2

*N*FTIR (cm-3

)

2

4

0 500 1000 1500 2000 WaveNumber (cm-1)

Figure 7. IR reflectance spectrum of an *n*-type epilayer on an *n*-type substrate denoted by dashed line. The solid line shows the fitted curve calculated using the MDF model. The values estimated from this fitting analysis are listed in the

calculated free carrier concentration

2 3 4 5 6 7 8 9

*<sup>N</sup>*D – *N*<sup>A</sup> (cm-3

Figure 8. Values of the carrier concentration estimated from the IR reflectance for *n*-type epilayers on *n*LQH= KM:s strates as a function of dopant concentration obtained from *C–V* E=9KMJ=E=FLK>GJ=9;@K9EHD=0@=KGDA<DAF=J=HJ=s sents the theoretical carrier concentration for T=300K assuming zero doping concentration (*N*A=0) using eq. (6). The

1018

)

2 3 4

 *<sup>N</sup>*sub = 7.1!1018cm-3 <sup>µ</sup>sub = 53 cm2

 Experiment Fitted Curve

 *<sup>N</sup>*epi = 1.3!1017cm-3 <sup>µ</sup>epi = 403 cm<sup>2</sup>

*d* = 4.45 µm

/(V·s)

/(V·s)

#### 3.3. Extension of the carrier concentration range down to 1016cm–3 order using Terahertz frequency range [14]

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\_z\* z+\*"%.)! z0\$0z0\$!z2(1!/z+"z0\$!z..%!.z+\*!\*0.¥ tion, 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 "+.z0\$!z..%!.z+\*¥ centration 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^z\$!z)#\*%¥ fied 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 *C–V* measurements to discuss the validity of this characterization method.

Samples used in this study were nitrogen doped *n*-type 4H-SiC epilayers grown on *n*-type 4H-SiC substrates by chemical vapor deposition (CVD) [28]. The net doping concentration (*ND– NA*) of the epilayers was in the range between 5×1016 and 1×1018 cm–3, and that of the substrates was typically 5×1018 cm–3. The thickness of the epilayers was 6–7 µm, measured by SEM observation. *C–V* measurements were performed using gold electrodes evaporated on the samples as Schottky contacts. The reflectance spectra were measured at room temperature for the spectral region of 20–100 cm–1, 80–600 cm–1 and 540–2000 cm–1 using terahertz time-domain spectroscopy (THz-TDS) (*Aispec*: pulse IRS 1000/2000), FTIR spectrometers (*JASCO*: IR-VM7) and (*JASCO*: Irtron IRT-30), respectively.

*N*epi=1~10!1015cm-3

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

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

17

*N*epi=1!1017cm-3

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

Wave Number (cm-1)

Figure 11. Calculated reflectance spectra of the SiC epilayers (5eEL@A;COAL@DGO;9JJA=J;GF;=FLJ9LAGFKGF9/AO9s

Figure 12. Measured and calculated reflectance spectra of an *n*-type epilayer on an *n*LQH=KM:KLJ9L=9LJGGEL=EH=Js

We have estimated the values of carrier concentration and mobility for the samples of *n*-type epilayers on *n*-type substrates from the IR reflectance spectra measured. Figure 12 shows the measured and calculated reflectance spectra of the epilayer with a net doping concentration around 5×1016 cm–3z0z.++)z0!),!.01.!^z/z/\$+3\*z%\*z0\$!z"%#1.!\_z.!"(!0\*!z/,!0.1)z)!/¥ 1.! z5z6z.!"(!0\*!z/,!0.+/+,5z.!z3!((z+\*\*!0! z3%0\$z0\$0z)!/1.! z5z z.!"(!¥ tance spectroscopy at around 100 cm–1, and we obtained a good fit between the measured and the calculated spectrum. From the values of fitting parameters, the values *N*epi = 3.2×1016 cm–3,

/(V s) and *d* = 6.14 µm, and *N*sub = 6.8×1018 cm–3, *µ*sub = 63 cm2

In Figure 13, the free carrier concentrations estimated from the IR reflectance spectra are plotted against the net doping concentrations *ND– NA* derived from *C–V* measurements. We calculated the free carrier concentrations *n* from the net doping concentrations using eq.(6). The solid line in the figure shows the free carrier concentrations calculated as a function of net doping concentration. We assumed that *NA/ ND* = 0 or *ND* / (*NA* + *ND*) = 1, because the epilayers we measured are hardly carrier-compensated [32]. The values obtained from the

/(V s) were obtained.

ature. The values estimated from this fitting analysis are listed in the figure [14].

*N*epi=5!1016cm-3

Refrectance (

fer (*N*sub=4×1018cm–3, !sub=50cm2/Vs).

*µ*epi = 562 cm2

! )

**Figure 9.** Variation of plasma frequency ωp with carrier concentration *N.*

**Figure 10.** Calculated reflectance spectra of the SiC epilayers (3μm thick) with various carrier concentrations on a SiC wafer (*N*sub=5.5×1018, μsub=50cm2/Vs).

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 17

Samples used in this study were nitrogen doped *n*-type 4H-SiC epilayers grown on *n*-type 4H-SiC substrates by chemical vapor deposition (CVD) [28]. The net doping concentration (*ND– NA*) of the epilayers was in the range between 5×1016 and 1×1018 cm–3, and that of the substrates was typically 5×1018 cm–3. The thickness of the epilayers was 6–7 µm, measured by SEM observation. *C–V* measurements were performed using gold electrodes evaporated on the samples as Schottky contacts. The reflectance spectra were measured at room temperature for the spectral region of 20–100 cm–1, 80–600 cm–1 and 540–2000 cm–1 using terahertz time-domain spectroscopy (THz-TDS) (*Aispec*: pulse IRS 1000/2000), FTIR spectrometers

1016! 1017! 1018! 1019!

Wavelength! ! (µm) !

103!

*N*epi=3 1016cm-3! *N*epi=1 1017cm-3! *N*epi=3 1017cm-3! *N*epi=1 1018cm-3! *N*epi=3 1018cm-3!

102!

101!

1!

Carrier Concentration *N* (cm-3)!

**Figure 10.** Calculated reflectance spectra of the SiC epilayers (3μm thick) with various carrier concentrations on a SiC

(*JASCO*: IR-VM7) and (*JASCO*: Irtron IRT-30), respectively.

101!

1! 1015!

**Figure 9.** Variation of plasma frequency ωp with carrier concentration *N.*

102!

Plasma Frequency p (cm-1)!

16 Physics and Technology of Silicon Carbide Devices

wafer (*N*sub=5.5×1018, μsub=50cm2/Vs).

103!

Figure 11. Calculated reflectance spectra of the SiC epilayers (5eEL@A;COAL@DGO;9JJA=J;GF;=FLJ9LAGFKGF9/AO9s fer (*N*sub=4×1018cm–3, !sub=50cm2/Vs).

Figure 12. Measured and calculated reflectance spectra of an *n*-type epilayer on an *n*LQH=KM:KLJ9L=9LJGGEL=EH=Js ature. The values estimated from this fitting analysis are listed in the figure [14].

We have estimated the values of carrier concentration and mobility for the samples of *n*-type epilayers on *n*-type substrates from the IR reflectance spectra measured. Figure 12 shows the measured and calculated reflectance spectra of the epilayer with a net doping concentration around 5×1016 cm–3z0z.++)z0!),!.01.!^z/z/\$+3\*z%\*z0\$!z"%#1.!\_z.!"(!0\*!z/,!0.1)z)!/¥ 1.! z5z6z.!"(!0\*!z/,!0.+/+,5z.!z3!((z+\*\*!0! z3%0\$z0\$0z)!/1.! z5z z.!"(!¥ tance spectroscopy at around 100 cm–1, and we obtained a good fit between the measured and the calculated spectrum. From the values of fitting parameters, the values *N*epi = 3.2×1016 cm–3, *µ*epi = 562 cm2 /(V s) and *d* = 6.14 µm, and *N*sub = 6.8×1018 cm–3, *µ*sub = 63 cm2 /(V s) were obtained.

In Figure 13, the free carrier concentrations estimated from the IR reflectance spectra are plotted against the net doping concentrations *ND– NA* derived from *C–V* measurements. We calculated the free carrier concentrations *n* from the net doping concentrations using eq.(6). The solid line in the figure shows the free carrier concentrations calculated as a function of net doping concentration. We assumed that *NA/ ND* = 0 or *ND* / (*NA* + *ND*) = 1, because the epilayers we measured are hardly carrier-compensated [32]. The values obtained from the reflectance spectra are in fairly good agreement with solid line, suggesting that the values of the carrier concentrations estimated from IR reflectance spectra have a sufficient validity. However, a careful look confirms that the values of carrier concentration derived from the .!"(!0\*!z)!/1.!)!\*0/z.!z/(%#\$0(5z(+3!.z 0\$\*z 0\$+/!z!/0%)0! z ".+)z 0\$!z!(!0.%(z)!/¥ urements as in the case of carrier concentrations higher than 1017cm–3. The same tendency was observed in the comparisons with the Hall effect measurements for the samples of *n*type epilayers on *p*-type substrates as shown in Figure 8. This tendency is considered to be partly because of the adoption of inappropriate effective mass values for the calculation of reflectance spectra. It is also considered as a cause that the part of free carriers trapped in the !"!0/z+.z+1\* ! z5z +,\*0/z\*\*+0z "+((+3z%\*z 0\$!z6z ".!-1!\*5z .\*#!z1/! z "+.z 0\$!z .!¥ flectance measurements, as mentioned above.

> Figure 13. The carrier concentration estimated from the reflectance spectra for an *n*-type epilayer on an *n*LQH=KM:s strate as a function of doping concentration obtained from *C–V*E=9KMJ=E=FLK>GJ=9;@K9EHD=0@=KGDA<DAF=J=HJ=s sents the theoretical carrier concentration for *T*=300K assuming zero doping concentration (*N*A=0) using eq. (6). The

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

19

The samples used in this study were 4H-SiC (0001) substrates with *p*-type ~5 µ)z0\$%'z+)¥ mercially produced epitaxial layers. The multi-energy implantations of phosphorus ions at 500°C were carried out through the 10 nm thick oxide film in six steps (40–250 keV) in order to form a box-shaped profile with a thickness of 0.3 µm. The total implanted dose was 7×1015 cm–2. After removing the oxide film by HF, the post implantation annealing was conducted %\*z .z 0)+/,\$!.!^z +z%\*2!/0%#0!z 0\$!z \*\*!(%\*#z 0!),!.01.!z !,!\* !\*!z +"z .5/0((%\*!z .!¥ covery and electrical properties in the implanted layers, the samples were annealed for 30 )%\*z0z %""!.!\*0z0!),!.01.!/z+"zDECC[\_zDFCC[\_z\* zDGCC[^z \*z %0%+\*\_z0+z,,(5z0\$!z z.!¥ flectance analysis to the short-period high-temperature annealing process, we also carried out the post implantation annealing at 1700°C for various periods between 0.5 and 10 min. z .!"(!0\*!z)!/1.!)!\*0/z3!.!z..%! z+10z 0z .++)z 0!),!.01.!z+\*z\*!.(5z\*+.)(z%\*%¥ !\*!z1/%\*#zz)%.+zw z/,!0.+)!0!.zc(%#\$0z!)z %)!0!.z3/zC^Dz))d^z\$!z/,!0.(z.!/¥

4.3. Analysis of carrier concentration, mobility and crystalline damage from IR reflectance

Figure 14 shows the annealing temperature dependence of IR reflectance spectrum. For as- %),(\*0! z /),(!/\_z 0\$!z .!"(!0%2%05z )4%)1)z \* z 0\$!z /\$,!z %\*z 0\$!z .!/0/0.\$(!\*z \* z !¥ creases and becomes blunt, respectively, as compared to those of unimplanted samples. "0!.z0\$!z\$%#\$z0!),!.01.!z\*\*!(%\*#\_z0\$!z.!"(!0%2%05z)4%)1)z%\*z0\$!z.!/0/0.\$(!\*z\* z.!¥ +2!./z0+z0\$0z+"z1\*%),(\*0! z/),(!/^z\$%/z%/z.!/1(0! z".+)z0\$!z.5/0((%\*!z.!+2!.5z%\*z%)¥ planted 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

4.2. High-dose phosphorus ion implantation, post-implantation annealing and IR

dotted line represents *N*FTIR=*N*D–*N*A as a guide to the eye [14].

olution and range were 4 cm–1 and 600–8000 cm–1, respectively.

reflectance measurements [15]

spectra [15]
