Influence of Nitrogen Concentrations on the Lattice Constants and

Article pubs.acs.org/crystal

Influence of Nitrogen Concentrations on the Lattice Constants and Resistivities of n‑Type 4H-SiC Single Crystals Yingxin Cui, Xiaobo Hu,* Kun Yang, Xianglong Yang, Xuejian Xie, Longfei Xiao, and Xiangang Xu* State Key Laboratory of Crystal Materials, Shandong University, Jinan, 250100, People’s Republic of China ABSTRACT: 4H-SiC single crystals with different nitrogen doping concentrations were grown by sublimation method. After processing, the standard 4H-SiC substrates were obtained. The carrier and nitrogen concentrations in 4H-SiC single crystals were measured by Raman spectroscopy and secondary ion mass spectrometry, respectively. The resistivities of 4H-SiC single crystals were measured by a noncontact resistivity testing system. The influence of nitrogen concentration on the resistivity of 4H-SiC single crystal was assessed. In addition, the structural qualities of 4H-SiC single crystals were investigated by high resolution X-ray diffractometry. The 004, 008 symmetric reflection rocking curves and 102, 204 skew symmetric reflection rocking curves of 4H-SiC single crystals were measured and the lattice constants of 4H-SiC single crystals were accurately determined. The effect of nitrogen concentration on the lattice constants was discussed.

1. INTRODUCTION 4H-SiC has a number of superior physical properties that make it a good candidate substrate for the fabrication of high power, high frequency and high temperature devices.1,2 At present, to manufacture the devices with high performance and low loss, the 4H-SiC single crystals with high nitrogen-doping concentration are needed. Also, graphene is a very promising candidate as a robust atomic-scale scaffold in the design of new nanomaterials and devices. It is reported that nitrogen-doped graphene were grown by the thermal decomposition of nitrogen-doped SiC.3,4 However, the nitrogen doping has significant influence on the structure of 4H-SiC single crystal. Furthermore, variations in the lattice constants with nitrogen doping will result in a large residual stress in substrate.5 To ascertain the relationship between the nitrogen doping concentration and the variation of lattice constants, we have accurately measured the lattice constants and resistivities of 4HSiC with different nitrogen doping concentrations. The most widely accepted method for obtaining the absolute lattice constant of a single-crystal is Bond method.6 The Bond method removes some basic errors by virtue of the procedures involved, for instance, the combination of the (n, −n) and the (n, +n) reflection can remove the effect of the zero setting.7 But recently, M. Fatemi8 thought that the diffraction intensities have been decreased about an order of magnitude in the (n, +n) mode. Numerous studies have been carried out on lattice constant changes because of impurities, for example, impurity doping of Si single crystals is known to lead to changes in lattice constants. Impurity atoms (B or P) with atomic radii smaller than the covalent atomic radius of Si cause crystal lattice contraction, while the impurity atoms (Sb) with larger radii cause its expansion.9−11 Several groups have conducted some measurements on the lattice constants of 4H-SiC and 6H-SiC © 2015 American Chemical Society

single crystals with different nitrogen doping concentrations. S. Sasaki et al.12 measured the heavily nitrogen-doped (8 × 1018 cm−3) 4H-SiC (0001) substrates and lightly doped freestanding homoepilayers (100−147 μm) with nitrogen concentrations ranging from 6 × 1014 to 2 × 1019 cm−3. The c-axis lattice constant was determined from the 0008 reflection, while the a-axis lattice constant was determined from the 112̅0 reflection. He found that the c- and a-axis lattice constants of these samples at room temperature are almost identical within the measurement accuracy. Hun Jae Chung5 studied six n-type 4H-SiC crystals with different nitrogen doping concentrations ranging from 9 × 1018 to 4.3 × 1019 cm−3. High-resolution Xray diffraction analysis was conducted with a Philips X’Pert MRD using the ω − 2θ scans of 0008 reflection in triple-axis geometry on multiple locations on each wafer. It was found that within experimental error (±0.0002 Å), the c-axis lattice constant of 4H-SiC did not change over the investigated doping range. Whereas, Tsubasa Matsumoto and Shin-ichi Nishizawa13 calculated the lattice constant of 4H-SiC as a function of impurity concentration with a commercially available software package, CASTEP, using a supercell containing 64 atoms. Nitrogen concentration was fixed in the range from 5 × 1018 cm−3 to 1 × 1020 cm−3. They discovered that the a-axis lattice constant decreases when the nitrogen concentration is above 5 × 1020 cm−3, and the c-axis lattice constant decreases when the nitrogen concentration is above 3 × 1019 cm−3. In this Article, accurate measurements of the c- and a-axis lattice constants of 4H-SiC bulk single crystals with different nitrogen doping concentrations were performed. In addition, Received: August 16, 2014 Revised: May 10, 2015 Published: June 2, 2015 3131

DOI: 10.1021/cg501216d Cryst. Growth Des. 2015, 15, 3131−3136

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Figure 1. Direct X-ray intensity of x- and z-axis scan (x, z direction follow space Cartesian coordinate system). limited by a 1.2 mm standard slit and a 0.3 mm diameter circular aperture slit. In order to obtain the spot size of the direct X-ray, a solid cone was put on the sample stage. The bottom diameter and height of the cone is 10 mm and 30 mm, respectively. Afterward, X and Z direction scanning were carried out on the cone when ω = 2θ = 0°and χ = 90°. Figure 1 shows the direct X-ray intensity variation following the xand z-axis scan. From which, we can speculate approximately the size of the X-ray source. The figure shows that the spot size is gradually reduced with the decrease of the slit size and when the 0.3 mm diameter circular aperture slit is used, the direct X-ray spot area is minimum, 0.6 × 5 mm2. Even in the 004 diffraction peak position, the max X-ray spot area determined by the diffraction geometry is 2 × 5 mm2. Accordingly, the irradiation area on the surface was significantly reduced. In case of small-beam incidence, we can assume that the internal stress will not affect the test results of lattice constants. The samples were placed on a 5 in. vacuum stage, which is a part of an Eulerian Cradle. The purpose of the pumping for the stage is to fix sample on the stage. A scintillation counter was used as the detector to receive the diffraction signal. The angular precision and reproducibility for ω and 2θ of the diffractometer are 0.0001° and 0.0001°, respectively. The penetration depth of X-ray in SiC is about 70 μm for the Cu Kα1 line.15 Accurate lattice parameters c and a are based on multipleorder reflections. Because in single-crystal diffraction experiments, the absolute diffraction angle is generally not accurate due to the uncertainty of the zero point, the zero error can be eliminated by multiple-order reflections. The 004, 008 symmetric reflection rocking curves and 102, 204 skew symmetric reflection rocking curves of 4HSiC single crystals were measured with an angular step of 0.001° per second. All the X-ray measurements started with calibration of the scintillation counter zero position, followed by sample zero point and measurement geometry alignment with the help of XRD Wizard software which contains the sample information such as surface orientation, azimuth angle, crystal system, etc. All tests were conducted in the center of the sample. Considering a general symmetric 00l reflection in a hexagonal structure, Bragg’s law for the wafer is given by

the resistivities of these samples were measured. The influence of nitrogen doping concentrations on the lattice constants and resistivities of 4H-SiC single crystals was discussed.

2. EXPERIMENTAL SECTION The samples used in the experiments are 76.2 mm-diameter 4H-SiC (0001) wafers with different nitrogen concentrations ranging from 1.0 × 1016 to 1.59 × 1019 cm−3 in our laboratory. The 4H-SiC single crystals were grown by the sublimation method. For the n-type 4° offaxis crystals (A, B, C, and D), the dopant source is nitrogen gas (N2). For the nondoped crystal (E), no artificial doping was introduced in the growth process. For the high purity semi-insulating (H−SI) crystal (F), all impurities were minimized in the growth process. To reach a high resistivity for H−SI, a post heat treatment was conducted, that is, the wafer was first heated to 1800 °C and then rapidly cooled to room temperature so as to introduce some point defects. Growth procedure has been described in detail elsewhere.14 After crystal growth, the crystals were ground and then cut into wafers by the diamond wire saw, followed by mechanical lapping and polishing. The wafers were lapped with 5−40 μm B4C-based slurries to achieve planarity. Subsequently, they were mechanically polished by using three finer grades of diamond-based slurries from 6 μm to less 1 μm. To further reduce the roughness and improve the surface quality, chemicalmechanically polishing was used as a final substrate surface processing step on a rotating platform. The final thicknesses of the wafers are in a range of 360−410 μm. The carrier concentrations of 4H-SiC wafers were calculated indirectly from the Raman spectra which were collected in a backscattering configuration by a HR 800 system from Horiba Jobin Yvon. A 532 nm laser was used as excitation source. It was expected that the carrier concentration was lower than the nitrogen doping content due to partial compensation. The resistivities of the wafers (samples A−E) were measured by an EC-80P noncontact resistivity testing system at room temperature and the noncontact resistivity tester is based on Eddy Current technology. The resistivity of sample F was measured by an innovative contactless resistivity measurement system, COREMA-WT. The absolute values of the lattice constants were measured by highresolution X-ray diffractometry (HRXRD) using triple-axis crystal geometry. A Bruker D8 Discover diffractometer with a fixed Cu anode (ceramic tube with long fine focus) operating at 40 kV and 40 mA was used for the measurements. The monochromator, consisting of a Goebel mirror, an attenuator and two-bounce Ge (220) crystals, was placed in the incident beam path to provide monochromatic X-ray from the Cu Kα1 line (λ = 0.154056 ± 0.00005 nm) with a beam divergence of 0.0035°. To exclude the influence of stress on the accuracy of the lattice constant measurement, the X-ray beam was

c λ = 2· · sin θ(00l) l

(1)

In contrast, for a general skew symmetric h′0l′ reflection in a hexagonal structure, Bragg’s law for the wafer is given by −1/2 ⎛ 4 h′ 2 l′ 2 ⎞ λ = 2·⎜ · 2 + 2 ⎟ · sin θ(h ′ 0l ′) ⎝3 a c ⎠

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(2) DOI: 10.1021/cg501216d Cryst. Growth Des. 2015, 15, 3131−3136

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where λ is the wavelength of X-ray, a and c are the lattice constants, and θ(hkl) is the Bragg diffraction angle. If an accurate determination of the Bragg diffraction angle θ(hkl) can be made, the lattice constants a and c can be calculated directly and indirectly by

c=

λ·l 2 sin θ(00l)

a = h′· λ

1 3[sin θ(h ′ 0l ′)2 − (l′/l)2 sin θ(00l)2]

Table 1. Nitrogen Concentration, Carrier Concentration, and Resistivities of Six 4H-SiC Wafers sample A B C D E F

(3)

(4)

However, in a high precision absolute lattice constant measurement, the main error source is the zero error Δθ (zero error is the Bragg angle correction because of the zero setting of instrumental alignment.), which can be eliminated by multiple-order reflections. As we know, there are the 004, 008 reflections from a (00l) 4H-SiC wafer, then according to the Bragg’s law, we can deduce the following equation:

2 sin(θ′004 + Δθ ) = sin(θ′008 + Δθ )

nitrogen concentration (cm−3)

Raman shift (cm−1)

× × × × × ×

1004.0 995.3 977.0 970.9 965.9 964.5

1.59 9.75 5.16 4.02 4.2 1.0

1019 1018 1018 1018 1017 1016

carrier concentration (cm−3)

resistivity (mΩ·cm)

× × × × × ×

12 14 21 36 96 >108

4.9 3.8 1.6 8.4 2.2 4.9

1018 1018 1018 1017 1017 1016

and the resistivity increase with the decrease of nitrogen concentration in 4H-SiC crystal. The resistivity of sample F is drastically higher than those of others is due to the intrinsic defects of SiC such as carbon vacancy pinning the Fermi level deep enough in the bandgap to produce semi-insulating behavior. Figure 3 shows the stress birefringence images of the 4H-SiC wafers which were taken by a Cannon camera from the observation of the stress birefringence of 4H-SiC wafer. From these images, no serious stress was detected at the facet regions of the wafers. The AFM result shows the substrate surface morphology. It is smooth without any scratch and the surface roughness is 0.124 nm. It all implies that the structural qualities of the selected six wafers at facet region are well suited for the determination of the lattice constants because the influence of stress on the structure of the 4H-SiC single crystal is approximately excluded. In our experiments, small-beam incidence was used, the 4H-SiC wafers were treated as homogeneity and the influence of stress on the lattice constant were further lowered. The rocking curves of 004, 008 symmetric and 102, 204 skew symmetric reflections for the sample E are shown in Figure 4. The typical full-width at half-maximum for the 004 reflection was between 10 and 20 arcsec. Accurate lattice constants could be calculated based on formula 3 and 4 and the results are listed in Table 2. However, the size of the beam spot appears to be smaller than the size of the samples. In the center of the samples, with an extent of several mm, the measured repeatability for diffraction peak is 0.0001°and the lattice constant fluctuations are smaller than 5 × 10−5nm with respect to the average value. According to International Standardization Organization, “Guide to the Expression of Uncertainty in Measurement”, the standard uncertainties in the measured lattice constants in Table 2 is 1 × 10−5. For the simplicity, the measurement results for the other samples are not shown here. By comparing the data and lattice constant variation curves in Table 2, it is evident that the lattice constants of 4H-SiC wafers vary with nitrogen concentrations. With an increase of nitrogen concentration, both c- and a-axis lattice constant of 4H-SiC decrease. For a SiC crystal, the values of c/n·a represent a significant criterion for the hexagonal and cubic proportion of the SiC bilayer stacking sequences inside of the different SiC polytypes. The ratio c/(na) deviation from its ideal value in 3C-SiC c/(na) = (2/3)1/2 with increasing nitrogen concentration, indicates that a stronger distortion of the bonding tetrahedral occurs.18 Yokota19 suggested that the change of lattice parameters in semiconductors consists of two components. One comes from the size difference between the dopant and the substituted host atom. The other originates from the hydrostatic deformation potential of the band edge occupied by the free carriers. Unfortunately, neither direct

(5)

Where θ′004, θ′008 are the measured values. Thus, Δθ can be easily obtained from eq 5. Above law is also appropriate for 102, 204 skew symmetric reflection, and then the c- and a-axis lattice constants of 4H-SiC single crystals can be accurately determined.

3. RESULTS AND DISCUSSION Figure 2 shows the Raman shift of the LOPC mode for six 4HSiC wafers with different nitrogen doping concentrations. The

Figure 2. Raman shift of LOPC mode for different nitrogen concentration wafers, taken with 532 nm laser light at room temperature.

carrier concentration of 4H-SiC can be calculated via the Raman shift of the LOPC mode by n = 1.23 × 1017 Δω at room temperature16 and the nitrogen concentrations were measured by secondary ion mass spectrometry. This procedure enabled us to determine the LOPC frequency with the spectral resolution of ±0.05 cm−1 and the change of free carrier concentration by 1 × 1017 cm−3 corresponds to a frequency variation of Δω = 0.8 cm−1.17 The nitrogen concentration, carrier concentration and resistivities are compared in Table 1. From Figure 2 and Table 1, we can see that when the nitrogen concentrations of the 4H-SiC wafer decreases, the peak position of LOPC mode shifts toward the lower wavenumber, the intensity of LOPC mode increases and the full width at half-maximum (FWHM) of LOPC mode is narrowing. In other words, the carrier concentration decreases 3133

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Figure 3. Stress diagram of 4H-SiC wafers, (a) A, (b) B, (c) C, (d) D, (e) E, (f) F, and AFM image of the surface of the sample E.

Figure 4. Rocking curves for sample E showing (a) 004 symmetric reflection, (b) 008 symmetric reflection, (c) 102 skew symmetric reflection, and (d) 204 skew symmetric reflection.

atoms are known to replace the carbon atoms20 and the atomic radius of nitrogen is smaller than that of carbon. At the same time, the molecular hybridization type of the nitrogen-doped SiC transforms from equivalence hybridization of SiC to inequivalence hybridization of SiN, because nitrogen contains one more electron in the outermost shell than carbon, so the bond length and bond angle are changed. Figure 5b is the schematic diagram of the deformed tetrahedron of SiN after a carbon atom is substituted by a nitrogen atom for nitrogen-

experimental data nor calculated values of the absolute hydrostatic deformation potential for the bottom of the conduction band in 4H-SiC were available up to now. For the structure of 4H-SiC, each atom is surrounded by four heterogeneous atoms and each atom is bonded through the directional strong hybridization sp3 bond, which is made up of an s orbital and three p orbitals. The hybrid orbital space configuration is a regular tetrahedron with bond angle of 109° 28′, as shown in Figure 5a. For nitrogen-doped SiC, nitrogen 3134

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Table 2. Lattice Constants and Hexagonality of 4H-SiC Wafers with Different Nitrogen Concentrations

a-axis lattice constants of 4H-SiC decrease with the increase of nitrogen concentration, however, the hexagonality of 4H-SiC increases. Meanwhile, the influence of nitrogen concentration on the resistivity of 4H-SiC single crystal was assessed.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected].

Figure 5. Diagrams of 4H-SiC structure unit (a) for intrinsic 4H-SiC and (b) for nitrogen-doped 4H-SiC. Bond length and bond angle in figure are only schematically represented.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by National Basic Research Program of China under Grant 2011CB301904 and Natural Science Foundation of China under Grants 11134006 and 61327808.

doped SiC. S. A. Reshanov adopted tight-binding theory combining with the Harrison bonding orbital method to estimate theoretically lattice parameter dependence on impurity concentration for substitutive impurities of group III−V compound in β-SiC. The results of the calculation indicated that the length of Si−C bond contracted by 0.038 Å when a part of carbon atoms are replaced by nitrogen atoms in SiC.21 So in the perspective of doped atomic radius and inequivalence molecular hybridization bond length, both c-axis lattice constant and a-axis lattice constant of 4H-SiC should decrease with an increase of nitrogen concentration. Our results are consistent with Tsubasa Matsumoto’s calculation of lattice constant of 4H-SiC as a function of impurity concentration. Accurate determination of lattice constant should meet the following requirements: first of all, small-beam incidence. The influence of stress on the structure of the 4H-SiC single crystal is approximately excluded; second, triple-axis crystal diffraction geometry. This can improve the accuracy of testing peak position; finally, multiple-order reflections. It can rule out the zero error of both instruments and test. Previous researchers found that the c- and a-axis lattice constants of these samples with different nitrogen doping concentrations ranging from 9 × 1018 to 4.3 × 1019 cm−3 at room temperature are almost identical. We attribute it to the low experimental accuracy since the variation of lattice constant was actually in the magnitude order of 10−5 Å.

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REFERENCES

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4. CONCLUSIONS The small-beam incidence is an effective method to rule out the influence of stress. The multiple-order reflections rocking curve scan method can reach the zero error for the measurement of diffraction angle. The combination of the two methods can obtain accurate lattice constants. The experimental data show that the lattice constants exhibit a regular change in 4H-SiC wafers with varying nitrogen concentrations. That is, the c- and 3135

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(19) Yokota, J. J. Phys. Soc. 1965, 19, 1487. (20) Larkin, D. J.; Neudeck, P. G.; Powell, J. A.; Matus, L. G. Appl. Phys. Lett. 1994, 65, No. 1659. (21) Reshanov, S. A.; Parfenova, I. I.; Rastegaev, V. P. Diamond Relat. Mater. 2001, 10, 1278.

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DOI: 10.1021/cg501216d Cryst. Growth Des. 2015, 15, 3131−3136