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High-resolution X-ray diffraction and optical absorption study of heavily nitrogen-doped 4H–SiC crystals
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Journal of Crystal Growth 259 (2003) 52–60
High-resolution X-ray diffraction and optical absorption study of heavily nitrogen-doped 4H–SiC crystals Hun Jae Chung, Marek Skowronski* Department of Materials Science and Engineering, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA 15213, USA Received 25 November 2002; accepted 16 July 2003 Communicated by M.S. Goorsky
Abstract Lattice parameter and optical absorption spectra were measured on heavily nitrogen-doped bulk crystals and epilayers of 4H–SiC. The rate of c-lattice parameter change versus doping concentration in high quality material was ( cm3. In crystals containing high density of double stacking faults, the (0 0 0 8) X-ray reflection less than 3.6 1025 A shifted toward the (2 2 2) reflection in 3C–SiC. Optical absorption measurements in such crystals detected peak at 3.1 eV similar to that reported in 3C–SiC with concomitant decrease of free carrier peak characteristic of 4H–SiC polytype. r 2003 Elsevier B.V. All rights reserved. PACS: 61.10; 61.72.Nn; 78.40.Fy Keywords: A1. Doping; A1. High resolution X-ray diffraction; B2. Semiconducting materials
1. Introduction Low resistivity, highly nitrogen-doped 4H–SiC silicon carbide crystals and epilayers are employed in numerous device structures. Among potential benefits of using such materials are lower on-state losses in high voltage switching devices due to lower substrate resistance as well as lower ohmic contact resistivities. However, there are potential issues in nitrogen doping that need to be clarified. One of them is whether nitrogen doping induces lattice parameter change in hexagonal silicon carbide. The change of lattice parameters with doping would result in the appearance of stress in *Corresponding author. Tel.: +1-412-268-2710; fax: +1412-268-7596. E-mail address: [email protected] (M. Skowronski).
homoepitaxial device structures consisting of differently doped layers. This, in turn, could lead to the degradation of material quality especially in high voltage switching devices. All such structures consist of a thick (10–100 mm) low n-type epilayer (n ¼ 1014 1015 cm3) deposited on a highly doped 4H–SiC substrate (n ¼ 5 1018 cm3). The large thickness of the blocking layers employed could conceivably result in strain relaxation. Yokota [1] suggested that the lattice parameter change in semiconductors consists of two components, one due to the size differences between dopant and the host atom it replaces, and the second to the hydrostatic deformation potential of the band edge occupied by the free carriers. According to the Vegard’s law [2], the lattice parameter change due to the atom size differences shows a linear dependence on composition. This
0022-0248/$ - see front matter r 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0022-0248(03)01584-7
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law was originally proposed for ionic salt pairs, e.g. KCl–KBr, but is widely used in III–V semiconductors [3]. In the case of highly nitrogen-doped SiC crystals, the size effect is expected to decrease the lattice parameter, because nitrogen atoms are known to replace carbon atoms [4] and the atomic radius of nitrogen is thought to be smaller than that of carbon [5]. The magnitude of the size effect in SiC:N has been discussed in a recent paper by Jacobson et al. [6]. The free carrier component can be estimated using a formula proposed by Cardona and Christensen [7]: bcarrier ¼ 7ac;v =3B; where bcarrier is the normalized free carrier-induced lattice strain, ac;v the hydrostatic deformation potential of either conduction or valence band, B is bulk modulus, and (+) sign corresponds to electrons (holes). This formula correctly predicts the sign and magnitude of bcarrier in a number of semiconductor crystals doped with either donors or acceptors [7–11]. The two components, bsize and bcarrier ; are frequently of the same order of magnitude and can either be of the same or opposite sign. In some cases, such as for example Si:As [8] and GaN:Mg [11], the carrier-related component of b results in the net lattice change of the opposite sign to the difference in dopant/host atom size. Several publications reported the experimental results on the lattice parameter measurements versus the nitrogen doping in 4H–SiC [12], 3C– SiC [13,14], and 6H–SiC [15]. Hallin et al. [12] studied epilayers with ND =2.1–3.5 1015 cm3 deposited on a ð1 0 1% 0Þ-oriented substrate with nitrogen doping concentration ND =1 1019 cm3. The reciprocal space maps using ð1 0 1% 0Þ reflection showed two peaks in 2y=o scan which have been interpreted as due to separate reflections from the epilayer and the substrate. The epi/substrate lattice misfit was Da=a ¼ 2 104 : Assuming the proportional change of the c-lattice parameter, one can obtain the normalized misfit parameter ðbexp ¼ Dc=cDnÞ corresponding to the relative change of the clattice parameter (c ¼ cN co where co and cN are the lattice parameters of undoped and nitrogen-
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doped silicon carbide, respectively) divided by the change in doping (Dn ¼ nN no ). In this case, bexp was equal to 2.0 1023 cm3. Nikitina and Nikolaev [13] and Nikolaev et al. [14] studied highly nitrogen-doped 3C–SiC epilayers grown by liquid phase epitaxy on lower ntype doped (2 1018 cm3) 6H–SiC substrates. Doping concentration in the 3C–SiC epilayers ranged from 6 1018 to 7 1020 cm3. Double crystal X-ray diffraction measurements revealed that (2 2 2) interplanar spacing decreased with the nitrogen doping concentration at the rate of bexp ¼ 2 1024 cm3 : Gavrilov et al. [15] investigated the dependence of a- and c-lattice parameters in bulk 6H–SiC crystals with a doping range of 3 1016– 1 1019 cm3. Lattice parameters were measured using the Bond method [16] and it was found that the a-lattice parameter increased with the increase of the nitrogen doping while the c-lattice parameter remained constant. The normalized parameter for the a-lattice parameter was Da=aDn ¼ 1:49 1023 cm3 : The studies cited above did not attempt to separate the electronic effect on the lattice parameters from the dopant size effect. The situation is complicated by the fact that none of these studies monitored structural characteristics of layers and crystals used in the investigations. Recent results indicate that 4H–SiC crystals with free electron concentration above 2 1019 cm3 undergo spontaneous transformation resulting in high density of stacking faults [17]. It is likely that such a transformation affects the X-ray diffraction results and for that reason the structure of heavily doped crystals needs to be monitored independently of the X-ray measurements. This study is focused on the assessment of the c-lattice parameter change versus the nitrogen doping of 4H–SiC bulk crystals and epilayers. The effect of stacking fault formation on basal plane X-ray reflection is discussed.
2. Experimental procedure The data reported in the following sections have been obtained on bulk 4H–SiC crystals as well as
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epilayer structures. Six n-type 4H–SiC crystals with different nitrogen doping concentrations ranging from 9 1018 to 4.3 1019 cm3 were obtained from Cree Inc., Durham, NC. The crystals were grown by the physical vapor transport method and doped with nitrogen during the growth. Doping concentrations were determined by room temperature Hall effect and can be lower than the nitrogen impurity content due to partial compensation. The epilayer structures consisted of B2-mm-thick n+-type (n ¼ 5B9 1019 cm3) 4H– SiC homoepitaxial layers deposited by chemical vapor deposition on substrates with ND =5 1018 cm3 by Acreo AB, Kista, Sweden. High-resolution X-ray diffraction (HRXRD) analysis was conducted with a Philips X’Pert MRD using (0 0 0 8) reflection in triple-axis geometry [18]. The TEM analysis of crystal structure was performed using a Philips EM420 conventional transmission electron microscope (TEM) and a JEOL 4000 high-resolution transmission electron microscope (HRTEM). A Perkin-Elmer Lambda 900 spectrometer was employed for optical absorption measurements.
3. Results and discussion 3.1. Lattice parameter measurement of pure 4H–SiC polytype crystals The absolute values of the c-lattice parameter were measured on a set of bulk crystals by HRXRD analysis using triple-axis geometry. All the X-ray measurements started with calibration of zero 2y position. The o 2y scans of (0 0 0 8) reflection were obtained on multiple locations on each wafer. All the crystals used have been of high quality as ascertained by crossed polarizers test. They were free of low angle grain boundaries with a single narrow (0 0 0 8) peak in o scans. The typical full-width at the half-maximum of (0 0 0 8) reflection was between 18 and 27 arcsec. Also, all the samples have been checked for the presence of polytype inclusions and basal plane stacking faults by the conventional transmission electron microscopy. The samples with an electron concentration below 2 1019 cm3 were free of stacking faults. In
Fig. 1. c-axis lattice parameter versus carrier concentration diagram. Six solid spots correspond to n-type 4H–SiC bulk crystals with different doping concentration. Two hollow spots correspond to annealed samples. Dashed line is obtained from linear fit of the data.
the highest doped sample selected for X-ray diffraction experiment (n ¼ 4:3 1019 cm3), the stacking fault density in as-grown material was below 0.2 mm1. The experimental results are shown on Fig. 1. Filled diamonds denote results of this experiment and empty ones are discussed in the Section 3.2. The error bars correspond to the standard deviation obtained from multiple measurements on the same sample. The error value for ( which each point was approximately 1.9 104 A also corresponds to 1.9 105 error for the relative lattice parameter change Dc=c: Linear fit of filled diamonds has the slope (with ( cm3 and standard error) of 2.577.7 1024 A ( The normathe intercept of 10.085170.0002 A. lized lattice change parameter, bexp is equal to 2.577.0 1025 cm3. Within the experimental error, the c-lattice parameter of 4H–SiC has not changed in the investigated doping range. It should be pointed out that the previous data have the values of much beyond the error of our experiment. In the case of Refs. [13,14], the measured normalized misfit parameter is approximately 8 times higher than the error in this work, while the data published in Ref. [12] have a bexp parameter higher by a factor of 80. At this point it is not clear where does the difference originate from. One possibility is the structure of materials
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investigated. Either the polytype inclusions or the presence of stacking faults affect the lattice parameter X-ray measurements and these factors have to be carefully monitored in the experiment. In the approach described above, part of experimental error originated in the procedure of setting the zero of 2y angle necessary for the measurement of absolute lattice parameter. This error can be eliminated by the measurements of X-ray diffraction on structures consisting of an epilayer deposited on the substrate with a significant different doping concentration. In such experiment, one can directly measure the dopinginduced lattice parameter difference with the sensitivity determined only by the width of reflections. The samples used for this experiment consisted of a heavily nitrogen doped epilayer (nþ ¼ 5 9 1019 cm3) deposited on an n-type substrate with the carrier density of 3.6 1018 cm3. Fig. 2 is the reciprocal space map obtained on the most heavily doped epilayer with the basal plane (0 0 0 8) reflection using triple axis geometry. It shows only one well-defined peak in 2y=o scan with the full-width at half-maximum (FWHM) of 20 arcsec. The conservative estimate of the detection limit for the value of peak splitting is about FWHM/2 what corresponds to the maximum lattice mismatch of Dc=c ¼ 73:1 105 and bexp ¼ 73:6 1025 cm3 : These data
Fig. 2. Reciprocal space map around (0 0 0 8) reflection from the structure consisting of a n-type (n ¼ 9 1019 cm3) 2 mm thick epilayer deposited on n ¼ 3:6 1018 cm3 4H–SiC substrate.
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are in agreement with the results of the lattice parameter measurements on the bulk crystals described above. The lattice parameter change due to the size effect,bsize calc ; predicted from the Vegard’s law and based on interatomic distance data [5] is given by 24 bsize cm3 : calc ¼ 1:570:3 10
With the measured lattice parameter change, bexp , and the estimated size effect, bsize calc ; the lattice parameter change due to free electrons can be estimated by 24 belectron ¼ bexp bsize cm3 : calc ¼ 1:371:0 10
Based on the above, the conduction-band-edge deformation potential should be: ac;v ¼ 3Bbelectron ¼ 2:471:9 eV: Unfortunately, neither direct experimental data nor the calculated values of the absolute hydrostatic deformation potential for the bottom of conduction band in 4H–SiC are available at this time. The magnitude of this parameter was estimated based on the fitting of the mobility data at low temperatures at 10–11.5 eV [19,20]. However, as the acoustic phonon scattering depends on the square of the deformation potential the sign could not be determined. 3C–SiC band structure calculations by Lambrecht et al. [21] can be used as a rough estimate of the effects in 4H–SiC. Their value of ac;v at the bottom of conduction band is about 9 eV which would result in further contraction of the lattice parameter in addition to the nitrogen size effect. This clearly is at variance with our experimental values. The origin of this discrepancy is not known at present. It is worth pointing out, however, that the electron contribution to the lattice parameter change is expected to be significant and should not be neglected. Since the doping differences encountered in most device structures are much lower than the ones used here, it is unlikely that any 4H–SiC epitaxial layers would exceed critical thickness and relax degrading the material quality.
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3.2. Lattice parameter measurement of crystals with stacking faults It has been recently reported that heavily nitrogen doped 4H–SiC spontaneously transforms during annealing at temperatures between 900 C and 1200 C [22]. The transformation occurs through the motion of Shockley partial dislocations resulting in the formation of double stacking faults with six Si–C bilayers in cubic stacking sequence. The density of such faults was reported to be as high as 5 105 cm1 [17]. It is expected that the transformed crystals would have lattice parameter, conductivity, and band structure different from those of perfect 4H–SiC. It is natural to expect that the lattice parameter change is less than the difference between 4H and 3C polytypes. The X-ray (0 0 0 8)4H and (2 2 2)3C 2y=o scan on a 3C epilayer deposited on 4H substrate revealed two peaks with the angular difference of B430 arcsec and the relative difference of the vertical interplanar spacing of Dc=cB1:35 103 : This is in agreement with published data on high quality partially relaxed 3C/4H–SiC films [23]. In order to detect such small changes accurately, we selected the sample that was partially transformed and had a bi-layer structure. The optical image of the sample cross section is shown in Fig. 3. The top layer (marked a in the figure) is approximately 30 mm thick and is visibly lighter in color than the rest of the cross section. The sample has been examined by the cross sectional conventional
Fig. 3. Cross sectional optical image on sample with n ¼ 4:3 1019 cm3. A black arrow marks the sample surface.
Fig. 4. Cross sectional TEM images (taken in the two-beam condition with g ¼ ð1 1% 0 6Þ) of: (a) the area close to the surface; and (b) the area far from the surface of sample shown in Fig. 3.
TEM and the representative microphotographs taken in areas (a) and (b) are shown in Fig. 4(a) and (b), respectively. Fig. 4(a) taken close to the surface shows horizontal thin lines interspersed throughout the image area. The lines correspond to the double stacking faults characteristic of transformed n-type 4H–SiC [17]. The fault density in this part of the sample was about 70 mm1. Fig. 4(b) is a TEM image of the section far from the surface, which corresponds to the area (b) in Fig. 3. The stacking fault density in this part of the sample was more than two orders of magnitude lower than that observed in the transformed layer (B0.2 mm1). The large difference in the stacking fault density is likely due to the difference in available density of nucleation sites producing stacking faults during cooling after crystal growth. The 2y=o scan (0 0 0 8) reflection of the bi-layer sample is shown in Fig. 5. Two peaks separated by 33 arcsec are clearly visible. This corresponds to the relative difference Dc=cB1:0 104 of the
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Fig. 5. High resolution X-ray diffraction 2y=o scan of (0 0 0 8) peak obtained on sample shown in Fig. 3.
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disappears after approximately 21 mm. Concomitantly, the intensity of the low angle peak increases and saturates after the disappearance of high angle peak. It is quite apparent that the high angle peak (corresponding to the smaller c-lattice parameter) is produced by the transformed layer with the high stacking fault density. The results of the above experiment have been confirmed by the X-ray diffraction measurements of the c-lattice parameter on annealed specimens. The pieces from two highest doped crystals used in Fig. 1 have been annealed at 1150 C for 90 min in high purity argon. After annealing, the samples were visibly warped as reported by Skromme et al. [24]. Cross sectional TEM observation revealed presence of stacking faults over the entire cross section of both samples in density of 50 and 80 mm1 in crystals with electron concentrations 3.4 1019 and 4.3 1019 cm3, respectively. The HRXRD 2y=o (0 0 0 8) peaks obtained on the asgrown and annealed sample with ND =4.3 1019 cm3 are shown in Fig. 7. Both samples exhibit only one peak each with the FWHM of 21 arcsec. The reflection from the annealed n ¼ 4:3 1019 cm3 specimen is shifted by 85 arcsec toward higher y angles compared to the as-grown sample. This corresponds to the relative c-lattice parameter change of Dc=c ¼
Fig. 6. Change of 2y=o (0 0 0 8) peak intensity ratio versus thickness of material removed from the surface of sample shown in Fig. 5.
vertical interplanar spacing which is approximately 7.7 percent of the 3C/4H difference. In order to determine which of the two peaks corresponds to transformed layer, the top layer was gradually removed by lapping. Peak shape was monitored by collecting k-space maps after each polishing step. Fig. 6 shows the relative peak intensity as a function of the thickness of material removed. The intensity of the high 2y angle peak decreases as the surface layer is removed and
Fig. 7. 2y=o scan of (0 0 0 8) reflection from the sample with n ¼ 4:3 1019 cm3: (a) before annealing; and (b) after annealing.
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2:7 104 : Similar experiment performed on the second highest doped wafer (nB3:4 1019 cm3) resulted in a smaller peak shift of approximately 25 arcsec which corresponds to Dc=c ¼ 7:8 105 : The results are marked in Fig. 1 with hollow diamonds. Peak position change after annealing is well above experimental error in our measurements. It is likely that the c-lattice parameter within the double stacking faults is different from that of a perfect 4H–SiC crystal (the in-plane lattice parameters are strained to match). However, the mixed structure of 4H–SiC with the stacking faults shows only one sharp peak at the location between that of perfect 4H and 3C polytypes. The peak position appears to shift toward 3C with the increase of stacking fault density. One can consider the faulted 4H structure as a disordered superlattice with two slightly different lattice parameters, c4H and cFAULT : The X-ray reflection from such superlattices consists of a most intense peak located at the position of the average lattice parameter (zero order peak) and satellites surrounding the zero order peak. In disordered superlattice, the satellite peaks disappear and only the zero order reflection remains as has been both predicted theoretically [25] and observed experimentally in certain minerals [26]. Accordingly, the structural transformation of 4H–SiC polytype should result in a small shift of the basal plane reflection towards the 3C peak position. 3.3. Optical absorption measurements From the optical cross sectional image shown in Fig. 3, it is quite apparent that the transparency of a faulted 4H–SiC crystal is different from that of a perfect 4H–SiC. Transformed crystals appear more yellowish compared to greenish-brown color of heavily n-type perfect 4H polytype. A quantitative evaluation of this change is shown in Fig. 8. The room temperature optical absorption spectrum of as-grown sample (n ¼ 4:3 1019 cm3) is marked as a dotted line (b) while the spectrum of the same sample after annealing is shown as continuous line (a). Stacking fault density of this sample was about 50 mm1. Light was propagating
Fig. 8. Optical absorption spectra obtained from heavily doped (n ¼ 4:3 1019 cm3) 4H–SiC bulk crystals: (a) after annealing; and (b) before annealing.
along the c-axis and as a consequence, the electric field vector was perpendicular to c-axis. The spectrum from the as-grown sample (line (b) in Fig. 8) has a peak at B2.7 eV with the intensity of 470 cm1. This peak was observed in n-type 4H–SiC by Biederman [27] and interpreted by Limpijumnong et al. [28] as a transition from the conduction band minimum (c1 ) to the fourth lowest conduction band (c4 ). The optical spectrum from the annealed sample (line (a) in Fig. 8) still has the characteristic peak at B2.7 eV albeit with reduced intensity of 270 cm1 and, in addition, a new peak appeared at B3.1 eV with the intensity of 280 cm1. The 3.1 eV peak is very similar to the one reported in n-type 3C–SiC [29]. The peak was attributed to direct transition from the X1c conduction band minimum to the higher X3c band. The optical spectrum (a) in Fig. 8 with the additional n-type 3C–SiC peak suggests that the conduction band of the stacking faults have similar structure to the conduction band of 3C– SiC. Note that, the 4H–SiC peak after annealing decreases by B50% and the 3C–SiC peak has the higher peak intensity than that of the 4H–SiC peak. This suggests that more than half of free electrons in the 4H–SiC matrix moved to quantum wells induced by stacking faults [17]. Given known
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fault density, this is equivalent to the formation of a depletion region about 5 nm wide on each side of a stacking fault. This figure is in qualitative agreement with the model proposed by Kuhr et al. [30]. The samples with higher stacking fault density can approach the limit in which all electrons from the conduction band are transferred to stacking faults and the 4H matrix is fully depleted. Large electron density modulation along the c-axis should result in interesting transport properties. For example, the conductivity along the basal plane is expected to be much higher than along the c-axis. It is interesting to note that the stacking faults form until a significant fraction of free electrons are removed from the conduction band and the Fermi level drops into the band gap. This correlation indicates that it is the high Fermi energy in heavily doped 4H–SiC that drives the stacking fault formation.
4. Conclusion In 4H–SiC crystals changes of the c-lattice parameter induced by nitrogen doping are smaller than Dc=c ¼ 3:1 105 and are below the detection limit of high-resolution X-ray diffraction in crystals doped up to 1 1020 cm3. It appears unlikely that any epilayer structures would exceed critical layer thickness and relax introducing misfit dislocations. Crystals with the doping-induced high density of stacking faults exhibit the shift of basal plane X-ray reflection toward that of 3C polytype. Optical absorption spectra of faulted 4H material show an additional peak located at 3.1 eV similar to that reported in 3C bulk crystals. Comparison of the free carrier absorption intensities in as-grown and annealed samples indicates the transfer of electrons from the 4H matrix to the stacking fault-induced quantum wells.
Acknowledgements This work was supported in part by NSF Grant No. DMR.9903702 and by ONR Grant No. N00014-00-1-0786.
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Journal of Crystal Growth 259 (2003) 52–60
High-resolution X-ray diffraction and optical absorption study of heavily nitrogen-doped 4H–SiC crystals Hun Jae Chung, Marek Skowronski* Department of Materials Science and Engineering, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA 15213, USA Received 25 November 2002; accepted 16 July 2003 Communicated by M.S. Goorsky
Abstract Lattice parameter and optical absorption spectra were measured on heavily nitrogen-doped bulk crystals and epilayers of 4H–SiC. The rate of c-lattice parameter change versus doping concentration in high quality material was ( cm3. In crystals containing high density of double stacking faults, the (0 0 0 8) X-ray reflection less than 3.6 1025 A shifted toward the (2 2 2) reflection in 3C–SiC. Optical absorption measurements in such crystals detected peak at 3.1 eV similar to that reported in 3C–SiC with concomitant decrease of free carrier peak characteristic of 4H–SiC polytype. r 2003 Elsevier B.V. All rights reserved. PACS: 61.10; 61.72.Nn; 78.40.Fy Keywords: A1. Doping; A1. High resolution X-ray diffraction; B2. Semiconducting materials
1. Introduction Low resistivity, highly nitrogen-doped 4H–SiC silicon carbide crystals and epilayers are employed in numerous device structures. Among potential benefits of using such materials are lower on-state losses in high voltage switching devices due to lower substrate resistance as well as lower ohmic contact resistivities. However, there are potential issues in nitrogen doping that need to be clarified. One of them is whether nitrogen doping induces lattice parameter change in hexagonal silicon carbide. The change of lattice parameters with doping would result in the appearance of stress in *Corresponding author. Tel.: +1-412-268-2710; fax: +1412-268-7596. E-mail address: [email protected] (M. Skowronski).
homoepitaxial device structures consisting of differently doped layers. This, in turn, could lead to the degradation of material quality especially in high voltage switching devices. All such structures consist of a thick (10–100 mm) low n-type epilayer (n ¼ 1014 1015 cm3) deposited on a highly doped 4H–SiC substrate (n ¼ 5 1018 cm3). The large thickness of the blocking layers employed could conceivably result in strain relaxation. Yokota [1] suggested that the lattice parameter change in semiconductors consists of two components, one due to the size differences between dopant and the host atom it replaces, and the second to the hydrostatic deformation potential of the band edge occupied by the free carriers. According to the Vegard’s law [2], the lattice parameter change due to the atom size differences shows a linear dependence on composition. This
0022-0248/$ - see front matter r 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0022-0248(03)01584-7
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law was originally proposed for ionic salt pairs, e.g. KCl–KBr, but is widely used in III–V semiconductors [3]. In the case of highly nitrogen-doped SiC crystals, the size effect is expected to decrease the lattice parameter, because nitrogen atoms are known to replace carbon atoms [4] and the atomic radius of nitrogen is thought to be smaller than that of carbon [5]. The magnitude of the size effect in SiC:N has been discussed in a recent paper by Jacobson et al. [6]. The free carrier component can be estimated using a formula proposed by Cardona and Christensen [7]: bcarrier ¼ 7ac;v =3B; where bcarrier is the normalized free carrier-induced lattice strain, ac;v the hydrostatic deformation potential of either conduction or valence band, B is bulk modulus, and (+) sign corresponds to electrons (holes). This formula correctly predicts the sign and magnitude of bcarrier in a number of semiconductor crystals doped with either donors or acceptors [7–11]. The two components, bsize and bcarrier ; are frequently of the same order of magnitude and can either be of the same or opposite sign. In some cases, such as for example Si:As [8] and GaN:Mg [11], the carrier-related component of b results in the net lattice change of the opposite sign to the difference in dopant/host atom size. Several publications reported the experimental results on the lattice parameter measurements versus the nitrogen doping in 4H–SiC [12], 3C– SiC [13,14], and 6H–SiC [15]. Hallin et al. [12] studied epilayers with ND =2.1–3.5 1015 cm3 deposited on a ð1 0 1% 0Þ-oriented substrate with nitrogen doping concentration ND =1 1019 cm3. The reciprocal space maps using ð1 0 1% 0Þ reflection showed two peaks in 2y=o scan which have been interpreted as due to separate reflections from the epilayer and the substrate. The epi/substrate lattice misfit was Da=a ¼ 2 104 : Assuming the proportional change of the c-lattice parameter, one can obtain the normalized misfit parameter ðbexp ¼ Dc=cDnÞ corresponding to the relative change of the clattice parameter (c ¼ cN co where co and cN are the lattice parameters of undoped and nitrogen-
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doped silicon carbide, respectively) divided by the change in doping (Dn ¼ nN no ). In this case, bexp was equal to 2.0 1023 cm3. Nikitina and Nikolaev [13] and Nikolaev et al. [14] studied highly nitrogen-doped 3C–SiC epilayers grown by liquid phase epitaxy on lower ntype doped (2 1018 cm3) 6H–SiC substrates. Doping concentration in the 3C–SiC epilayers ranged from 6 1018 to 7 1020 cm3. Double crystal X-ray diffraction measurements revealed that (2 2 2) interplanar spacing decreased with the nitrogen doping concentration at the rate of bexp ¼ 2 1024 cm3 : Gavrilov et al. [15] investigated the dependence of a- and c-lattice parameters in bulk 6H–SiC crystals with a doping range of 3 1016– 1 1019 cm3. Lattice parameters were measured using the Bond method [16] and it was found that the a-lattice parameter increased with the increase of the nitrogen doping while the c-lattice parameter remained constant. The normalized parameter for the a-lattice parameter was Da=aDn ¼ 1:49 1023 cm3 : The studies cited above did not attempt to separate the electronic effect on the lattice parameters from the dopant size effect. The situation is complicated by the fact that none of these studies monitored structural characteristics of layers and crystals used in the investigations. Recent results indicate that 4H–SiC crystals with free electron concentration above 2 1019 cm3 undergo spontaneous transformation resulting in high density of stacking faults [17]. It is likely that such a transformation affects the X-ray diffraction results and for that reason the structure of heavily doped crystals needs to be monitored independently of the X-ray measurements. This study is focused on the assessment of the c-lattice parameter change versus the nitrogen doping of 4H–SiC bulk crystals and epilayers. The effect of stacking fault formation on basal plane X-ray reflection is discussed.
2. Experimental procedure The data reported in the following sections have been obtained on bulk 4H–SiC crystals as well as
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epilayer structures. Six n-type 4H–SiC crystals with different nitrogen doping concentrations ranging from 9 1018 to 4.3 1019 cm3 were obtained from Cree Inc., Durham, NC. The crystals were grown by the physical vapor transport method and doped with nitrogen during the growth. Doping concentrations were determined by room temperature Hall effect and can be lower than the nitrogen impurity content due to partial compensation. The epilayer structures consisted of B2-mm-thick n+-type (n ¼ 5B9 1019 cm3) 4H– SiC homoepitaxial layers deposited by chemical vapor deposition on substrates with ND =5 1018 cm3 by Acreo AB, Kista, Sweden. High-resolution X-ray diffraction (HRXRD) analysis was conducted with a Philips X’Pert MRD using (0 0 0 8) reflection in triple-axis geometry [18]. The TEM analysis of crystal structure was performed using a Philips EM420 conventional transmission electron microscope (TEM) and a JEOL 4000 high-resolution transmission electron microscope (HRTEM). A Perkin-Elmer Lambda 900 spectrometer was employed for optical absorption measurements.
3. Results and discussion 3.1. Lattice parameter measurement of pure 4H–SiC polytype crystals The absolute values of the c-lattice parameter were measured on a set of bulk crystals by HRXRD analysis using triple-axis geometry. All the X-ray measurements started with calibration of zero 2y position. The o 2y scans of (0 0 0 8) reflection were obtained on multiple locations on each wafer. All the crystals used have been of high quality as ascertained by crossed polarizers test. They were free of low angle grain boundaries with a single narrow (0 0 0 8) peak in o scans. The typical full-width at the half-maximum of (0 0 0 8) reflection was between 18 and 27 arcsec. Also, all the samples have been checked for the presence of polytype inclusions and basal plane stacking faults by the conventional transmission electron microscopy. The samples with an electron concentration below 2 1019 cm3 were free of stacking faults. In
Fig. 1. c-axis lattice parameter versus carrier concentration diagram. Six solid spots correspond to n-type 4H–SiC bulk crystals with different doping concentration. Two hollow spots correspond to annealed samples. Dashed line is obtained from linear fit of the data.
the highest doped sample selected for X-ray diffraction experiment (n ¼ 4:3 1019 cm3), the stacking fault density in as-grown material was below 0.2 mm1. The experimental results are shown on Fig. 1. Filled diamonds denote results of this experiment and empty ones are discussed in the Section 3.2. The error bars correspond to the standard deviation obtained from multiple measurements on the same sample. The error value for ( which each point was approximately 1.9 104 A also corresponds to 1.9 105 error for the relative lattice parameter change Dc=c: Linear fit of filled diamonds has the slope (with ( cm3 and standard error) of 2.577.7 1024 A ( The normathe intercept of 10.085170.0002 A. lized lattice change parameter, bexp is equal to 2.577.0 1025 cm3. Within the experimental error, the c-lattice parameter of 4H–SiC has not changed in the investigated doping range. It should be pointed out that the previous data have the values of much beyond the error of our experiment. In the case of Refs. [13,14], the measured normalized misfit parameter is approximately 8 times higher than the error in this work, while the data published in Ref. [12] have a bexp parameter higher by a factor of 80. At this point it is not clear where does the difference originate from. One possibility is the structure of materials
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investigated. Either the polytype inclusions or the presence of stacking faults affect the lattice parameter X-ray measurements and these factors have to be carefully monitored in the experiment. In the approach described above, part of experimental error originated in the procedure of setting the zero of 2y angle necessary for the measurement of absolute lattice parameter. This error can be eliminated by the measurements of X-ray diffraction on structures consisting of an epilayer deposited on the substrate with a significant different doping concentration. In such experiment, one can directly measure the dopinginduced lattice parameter difference with the sensitivity determined only by the width of reflections. The samples used for this experiment consisted of a heavily nitrogen doped epilayer (nþ ¼ 5 9 1019 cm3) deposited on an n-type substrate with the carrier density of 3.6 1018 cm3. Fig. 2 is the reciprocal space map obtained on the most heavily doped epilayer with the basal plane (0 0 0 8) reflection using triple axis geometry. It shows only one well-defined peak in 2y=o scan with the full-width at half-maximum (FWHM) of 20 arcsec. The conservative estimate of the detection limit for the value of peak splitting is about FWHM/2 what corresponds to the maximum lattice mismatch of Dc=c ¼ 73:1 105 and bexp ¼ 73:6 1025 cm3 : These data
Fig. 2. Reciprocal space map around (0 0 0 8) reflection from the structure consisting of a n-type (n ¼ 9 1019 cm3) 2 mm thick epilayer deposited on n ¼ 3:6 1018 cm3 4H–SiC substrate.
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are in agreement with the results of the lattice parameter measurements on the bulk crystals described above. The lattice parameter change due to the size effect,bsize calc ; predicted from the Vegard’s law and based on interatomic distance data [5] is given by 24 bsize cm3 : calc ¼ 1:570:3 10
With the measured lattice parameter change, bexp , and the estimated size effect, bsize calc ; the lattice parameter change due to free electrons can be estimated by 24 belectron ¼ bexp bsize cm3 : calc ¼ 1:371:0 10
Based on the above, the conduction-band-edge deformation potential should be: ac;v ¼ 3Bbelectron ¼ 2:471:9 eV: Unfortunately, neither direct experimental data nor the calculated values of the absolute hydrostatic deformation potential for the bottom of conduction band in 4H–SiC are available at this time. The magnitude of this parameter was estimated based on the fitting of the mobility data at low temperatures at 10–11.5 eV [19,20]. However, as the acoustic phonon scattering depends on the square of the deformation potential the sign could not be determined. 3C–SiC band structure calculations by Lambrecht et al. [21] can be used as a rough estimate of the effects in 4H–SiC. Their value of ac;v at the bottom of conduction band is about 9 eV which would result in further contraction of the lattice parameter in addition to the nitrogen size effect. This clearly is at variance with our experimental values. The origin of this discrepancy is not known at present. It is worth pointing out, however, that the electron contribution to the lattice parameter change is expected to be significant and should not be neglected. Since the doping differences encountered in most device structures are much lower than the ones used here, it is unlikely that any 4H–SiC epitaxial layers would exceed critical thickness and relax degrading the material quality.
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3.2. Lattice parameter measurement of crystals with stacking faults It has been recently reported that heavily nitrogen doped 4H–SiC spontaneously transforms during annealing at temperatures between 900 C and 1200 C [22]. The transformation occurs through the motion of Shockley partial dislocations resulting in the formation of double stacking faults with six Si–C bilayers in cubic stacking sequence. The density of such faults was reported to be as high as 5 105 cm1 [17]. It is expected that the transformed crystals would have lattice parameter, conductivity, and band structure different from those of perfect 4H–SiC. It is natural to expect that the lattice parameter change is less than the difference between 4H and 3C polytypes. The X-ray (0 0 0 8)4H and (2 2 2)3C 2y=o scan on a 3C epilayer deposited on 4H substrate revealed two peaks with the angular difference of B430 arcsec and the relative difference of the vertical interplanar spacing of Dc=cB1:35 103 : This is in agreement with published data on high quality partially relaxed 3C/4H–SiC films [23]. In order to detect such small changes accurately, we selected the sample that was partially transformed and had a bi-layer structure. The optical image of the sample cross section is shown in Fig. 3. The top layer (marked a in the figure) is approximately 30 mm thick and is visibly lighter in color than the rest of the cross section. The sample has been examined by the cross sectional conventional
Fig. 3. Cross sectional optical image on sample with n ¼ 4:3 1019 cm3. A black arrow marks the sample surface.
Fig. 4. Cross sectional TEM images (taken in the two-beam condition with g ¼ ð1 1% 0 6Þ) of: (a) the area close to the surface; and (b) the area far from the surface of sample shown in Fig. 3.
TEM and the representative microphotographs taken in areas (a) and (b) are shown in Fig. 4(a) and (b), respectively. Fig. 4(a) taken close to the surface shows horizontal thin lines interspersed throughout the image area. The lines correspond to the double stacking faults characteristic of transformed n-type 4H–SiC [17]. The fault density in this part of the sample was about 70 mm1. Fig. 4(b) is a TEM image of the section far from the surface, which corresponds to the area (b) in Fig. 3. The stacking fault density in this part of the sample was more than two orders of magnitude lower than that observed in the transformed layer (B0.2 mm1). The large difference in the stacking fault density is likely due to the difference in available density of nucleation sites producing stacking faults during cooling after crystal growth. The 2y=o scan (0 0 0 8) reflection of the bi-layer sample is shown in Fig. 5. Two peaks separated by 33 arcsec are clearly visible. This corresponds to the relative difference Dc=cB1:0 104 of the
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Fig. 5. High resolution X-ray diffraction 2y=o scan of (0 0 0 8) peak obtained on sample shown in Fig. 3.
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disappears after approximately 21 mm. Concomitantly, the intensity of the low angle peak increases and saturates after the disappearance of high angle peak. It is quite apparent that the high angle peak (corresponding to the smaller c-lattice parameter) is produced by the transformed layer with the high stacking fault density. The results of the above experiment have been confirmed by the X-ray diffraction measurements of the c-lattice parameter on annealed specimens. The pieces from two highest doped crystals used in Fig. 1 have been annealed at 1150 C for 90 min in high purity argon. After annealing, the samples were visibly warped as reported by Skromme et al. [24]. Cross sectional TEM observation revealed presence of stacking faults over the entire cross section of both samples in density of 50 and 80 mm1 in crystals with electron concentrations 3.4 1019 and 4.3 1019 cm3, respectively. The HRXRD 2y=o (0 0 0 8) peaks obtained on the asgrown and annealed sample with ND =4.3 1019 cm3 are shown in Fig. 7. Both samples exhibit only one peak each with the FWHM of 21 arcsec. The reflection from the annealed n ¼ 4:3 1019 cm3 specimen is shifted by 85 arcsec toward higher y angles compared to the as-grown sample. This corresponds to the relative c-lattice parameter change of Dc=c ¼
Fig. 6. Change of 2y=o (0 0 0 8) peak intensity ratio versus thickness of material removed from the surface of sample shown in Fig. 5.
vertical interplanar spacing which is approximately 7.7 percent of the 3C/4H difference. In order to determine which of the two peaks corresponds to transformed layer, the top layer was gradually removed by lapping. Peak shape was monitored by collecting k-space maps after each polishing step. Fig. 6 shows the relative peak intensity as a function of the thickness of material removed. The intensity of the high 2y angle peak decreases as the surface layer is removed and
Fig. 7. 2y=o scan of (0 0 0 8) reflection from the sample with n ¼ 4:3 1019 cm3: (a) before annealing; and (b) after annealing.
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2:7 104 : Similar experiment performed on the second highest doped wafer (nB3:4 1019 cm3) resulted in a smaller peak shift of approximately 25 arcsec which corresponds to Dc=c ¼ 7:8 105 : The results are marked in Fig. 1 with hollow diamonds. Peak position change after annealing is well above experimental error in our measurements. It is likely that the c-lattice parameter within the double stacking faults is different from that of a perfect 4H–SiC crystal (the in-plane lattice parameters are strained to match). However, the mixed structure of 4H–SiC with the stacking faults shows only one sharp peak at the location between that of perfect 4H and 3C polytypes. The peak position appears to shift toward 3C with the increase of stacking fault density. One can consider the faulted 4H structure as a disordered superlattice with two slightly different lattice parameters, c4H and cFAULT : The X-ray reflection from such superlattices consists of a most intense peak located at the position of the average lattice parameter (zero order peak) and satellites surrounding the zero order peak. In disordered superlattice, the satellite peaks disappear and only the zero order reflection remains as has been both predicted theoretically [25] and observed experimentally in certain minerals [26]. Accordingly, the structural transformation of 4H–SiC polytype should result in a small shift of the basal plane reflection towards the 3C peak position. 3.3. Optical absorption measurements From the optical cross sectional image shown in Fig. 3, it is quite apparent that the transparency of a faulted 4H–SiC crystal is different from that of a perfect 4H–SiC. Transformed crystals appear more yellowish compared to greenish-brown color of heavily n-type perfect 4H polytype. A quantitative evaluation of this change is shown in Fig. 8. The room temperature optical absorption spectrum of as-grown sample (n ¼ 4:3 1019 cm3) is marked as a dotted line (b) while the spectrum of the same sample after annealing is shown as continuous line (a). Stacking fault density of this sample was about 50 mm1. Light was propagating
Fig. 8. Optical absorption spectra obtained from heavily doped (n ¼ 4:3 1019 cm3) 4H–SiC bulk crystals: (a) after annealing; and (b) before annealing.
along the c-axis and as a consequence, the electric field vector was perpendicular to c-axis. The spectrum from the as-grown sample (line (b) in Fig. 8) has a peak at B2.7 eV with the intensity of 470 cm1. This peak was observed in n-type 4H–SiC by Biederman [27] and interpreted by Limpijumnong et al. [28] as a transition from the conduction band minimum (c1 ) to the fourth lowest conduction band (c4 ). The optical spectrum from the annealed sample (line (a) in Fig. 8) still has the characteristic peak at B2.7 eV albeit with reduced intensity of 270 cm1 and, in addition, a new peak appeared at B3.1 eV with the intensity of 280 cm1. The 3.1 eV peak is very similar to the one reported in n-type 3C–SiC [29]. The peak was attributed to direct transition from the X1c conduction band minimum to the higher X3c band. The optical spectrum (a) in Fig. 8 with the additional n-type 3C–SiC peak suggests that the conduction band of the stacking faults have similar structure to the conduction band of 3C– SiC. Note that, the 4H–SiC peak after annealing decreases by B50% and the 3C–SiC peak has the higher peak intensity than that of the 4H–SiC peak. This suggests that more than half of free electrons in the 4H–SiC matrix moved to quantum wells induced by stacking faults [17]. Given known
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fault density, this is equivalent to the formation of a depletion region about 5 nm wide on each side of a stacking fault. This figure is in qualitative agreement with the model proposed by Kuhr et al. [30]. The samples with higher stacking fault density can approach the limit in which all electrons from the conduction band are transferred to stacking faults and the 4H matrix is fully depleted. Large electron density modulation along the c-axis should result in interesting transport properties. For example, the conductivity along the basal plane is expected to be much higher than along the c-axis. It is interesting to note that the stacking faults form until a significant fraction of free electrons are removed from the conduction band and the Fermi level drops into the band gap. This correlation indicates that it is the high Fermi energy in heavily doped 4H–SiC that drives the stacking fault formation.
4. Conclusion In 4H–SiC crystals changes of the c-lattice parameter induced by nitrogen doping are smaller than Dc=c ¼ 3:1 105 and are below the detection limit of high-resolution X-ray diffraction in crystals doped up to 1 1020 cm3. It appears unlikely that any epilayer structures would exceed critical layer thickness and relax introducing misfit dislocations. Crystals with the doping-induced high density of stacking faults exhibit the shift of basal plane X-ray reflection toward that of 3C polytype. Optical absorption spectra of faulted 4H material show an additional peak located at 3.1 eV similar to that reported in 3C bulk crystals. Comparison of the free carrier absorption intensities in as-grown and annealed samples indicates the transfer of electrons from the 4H matrix to the stacking fault-induced quantum wells.
Acknowledgements This work was supported in part by NSF Grant No. DMR.9903702 and by ONR Grant No. N00014-00-1-0786.
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