3. Atomic-scale Ti3SiC2 bilayers embedded in SiC

### 3.1. Atomic structure of the embedded system

Figure 8(a) shows a HAADF image of the annealed TiAl/SiC system, where the SiC substrate is covered entirely by a layered compound, Ti3SiC2, as reported previously. In addition to the formation of this epitaxial and coherent SiC/Ti3SiC2 interface, another interesting feature is that an atomic-scale bilayer is generated in the SiC interior (marked by a square in Fig. 8(a)), which is located approximately 9.5 nm away from the interface. An enlarged image of the region surrounding the bilayer shows that it has a Ti3SiC2-like structure, as shown in Fig. 8(b), where brighter spots represent atomic columns of Ti (smaller circles), while dark ones 0\$+/!z+"z%zc(.#!.z%.(!/d\_z/%\*!z%\*0!\*/%05z+"z\*z0+)%z+(1)\*z%\*z
z%/\_z0+zz#++ z,,.+4%¥ mation, directly proportional to Z1.7 (Z: atomic number) [24].

Figure 8. a) HAADF-STEM image for the Ti3SiC2-like bilayer embedded in 4H-SiC in the annealed TiAl contact system viewed along [11-20] direction. The bilayer sits about 9.5 nm below the SiC/Ti3SiC2 interface. (b) Magnified HAADF image of the region marked in (a) by a dotted square. An overlay is given, where the big circles indicate Si and small ones Ti. (c) The same image as in (b) but has been low-pass filtered to reduce noise. (d) The optimized SiC/Ti3SiC2/SiC multilayer model. The distances between layers around the bilayer are represented by *Lm* (*m*LG9F<L@GK=:=s tween neighboring atoms projected onto the paper plane by *dm*. The atomic layers are labeled 1 through 8. The inset K@GOKLGHNA=OG>9JJ9F?=E=FLG>0A9F<ALKF=A?@:GJAF?/A9F< O@=J=L@=0AG;;MHA=K9LGHL@=;=FL=JG>L@=@=P9s gon composed of Si and C [19].

Evidently, the bilayer is embedded in the SiC in an atomically coherent and ordered fashion with no transitional or intermixing layers (see Fig. 8(c)). In view of bulk structures of 4H-SiC and Ti3SiC2 and the relative stacking sequence of Ti and Si, the image in Fig. 8(c) can be qualitatively fitted by an energetically stable model shown in Fig. 8(d). In this model, the optimal distances between layers around the bilayer (denoted as *L1* to *L5* in Fig. 8(d)) are (1(0! z0+z!zE^HE\_zE^EJ\_zE^EK\_zE^GC\_z\* zE^HJz\_z.!/,!0%2!(5\_z2!.5z(+/!z0+z!4,!.%)!\*0(z2(¥ ues of 2.5, 2.2, 2.3, 2.3, and 2.7 Å estimated via quantitative characterization and averaging +"z %""!.!\*0z/%0!/z%\*z0\$!zz%)#!/^z \*z %0%+\*\_z0\$!z(1(0! z %/0\*!/z!03!!\*z\*!%#\$¥ boring atoms (labeled *d1* to *d5* in Fig. 8(d)) (2.67, 2.44, 2.44, 2.55, and 2.72 Å) also approach the experimental values (2.7, 2.3, 2.4, 2.6, and 2.7 Å). These mean that the model constructed (Fig. 8(d)) matches the HAADF image (Fig. 8(c)) both qualitatively and quantitatively in light of energetics and atomic distances.

### 3.2. Formation of point Fermi surface

both the annealed specimen and the SiCSi model clearly show Ohmic behavior, thereby validating the application of the SiCSi model to describe the Ohmic contacts in the TiAlbased system. In addition to the role of this interface, we also found that an atomic-scale Ti3SiC2-like bilayer can be embedded in the SiC interior, forming an atomically ordered )1(0%(5!.z 0\$0z!4\$%%0/z\*z1\*!4,!0! z!(!0.+\*%z/00!z3%0\$z,+%\*0z!.)%z/1."!^z\$!z2¥ lence charge is confined largely to this bilayer in a spatially connected fashion, serving possibly as a conducting channel to enhance the current flow over the semiconductor.

Figure 8(a) shows a HAADF image of the annealed TiAl/SiC system, where the SiC substrate is covered entirely by a layered compound, Ti3SiC2, as reported previously. In addition to the formation of this epitaxial and coherent SiC/Ti3SiC2 interface, another interesting feature is that an atomic-scale bilayer is generated in the SiC interior (marked by a square in Fig. 8(a)), which is located approximately 9.5 nm away from the interface. An enlarged image of the region surrounding the bilayer shows that it has a Ti3SiC2-like structure, as shown in Fig. 8(b), where brighter spots represent atomic columns of Ti (smaller circles), while dark ones 0\$+/!z+"z%zc(.#!.z%.(!/d\_z/%\*!z%\*0!\*/%05z+"z\*z0+)%z+(1)\*z%\*z
z%/\_z0+zz#++ z,,.+4%¥

Figure 8. a) HAADF-STEM image for the Ti3SiC2-like bilayer embedded in 4H-SiC in the annealed TiAl contact system viewed along [11-20] direction. The bilayer sits about 9.5 nm below the SiC/Ti3SiC2 interface. (b) Magnified HAADF image of the region marked in (a) by a dotted square. An overlay is given, where the big circles indicate Si and small ones Ti. (c) The same image as in (b) but has been low-pass filtered to reduce noise. (d) The optimized SiC/Ti3SiC2/SiC multilayer model. The distances between layers around the bilayer are represented by *Lm* (*m*LG9F<L@GK=:=s tween neighboring atoms projected onto the paper plane by *dm*. The atomic layers are labeled 1 through 8. The inset

Evidently, the bilayer is embedded in the SiC in an atomically coherent and ordered fashion with no transitional or intermixing layers (see Fig. 8(c)). In view of bulk structures of 4H-SiC and Ti3SiC2 and the relative stacking sequence of Ti and Si, the image in Fig. 8(c) can be

O@=J=L@=0AG;;MHA=K9LGHL@=;=FL=JG>L@=@=P9s

3. Atomic-scale Ti3SiC2 bilayers embedded in SiC

mation, directly proportional to Z1.7 (Z: atomic number) [24].

K@GOKLGHNA=OG>9JJ9F?=E=FLG>0A9F<ALKF=A?@:GJAF?/A9F<

gon composed of Si and C [19].

3.1. Atomic structure of the embedded system

160 Physics and Technology of Silicon Carbide Devices

To gain insight into how the embedded layer influences SiC electronically, we present in Fig. 9 band structure and density of states (DOS) of the multilayer system calculated using 0\$!z+,0%)(z0+)%z#!+)!0.5zc%#^zKc dd^z\*!4,!0! (5\_z/!2!.(z\* /z3%0\$zz-1 .0%z %/¥ persion cross the Fermi level (*E* F) at a single point (Fig. 9(a)), rendering conduction bands (CB) and valence band (VB) touch at their tips and hence the multilayer become a gapless /!)%+\* 10+.^z \*/,!0%+\*z0\$.+1#\$+10z0\$!z-.%((%+\*z6+\*!z2!.%"%!/z0\$0z0\$!z!.)%z/1."!z.+//¥ ing is a single point, which determines *E* <sup>F</sup>\_z/z%\*z0\$!z%(5!.z#.,\$!\*!z3%0\$z\*+z!40!.\*(z/0%)¥ uli (bands in graphene extend linearly both to lower and higher energy from point Fermi surfaces, as referred to as "massless Dirac"). This crossing of bands is confirmed in the DOS showing a curious vanishing of states at *E* F for both spins (Fig. 9(b)) and further verified in a surface plot of the two bands proximal to *E* <sup>F</sup> in a small *k* space presenting gapless character 0z0\$!zz,+%\*0z\* zz#,z%\*z0\$!z.!#%+\*z35z".+)z0\$!z.+//%\*#z,+%\*0zc%#^zEcdd^

Figure 9. a) Blowup of band structure around *E*F shown on the *xy* plane with *X* = "/*a*(1, 1¯ ,0) and *M* = "/*a*(1,1,0), where the "*a*" is in-plane lattice constant. Note that the point Fermi surface is at h where bands cross precisely at *E* F. (b) Total DOS and PDOS plots of C, Si, and Ti atom contributions for the optimized SiC/Ti3SiC2/SiC multilayer, showing that bands surrounding *E* F have characters of Ti in the bilayer. (c) "Surface" plot of the two bands that cross the *E* <sup>F</sup> ;=Fs L=J=<KMJJGMF<AF?L@=hHGAFL0@=*E* F position is aligned to zero [19].

In addition, extensive calculations using the LDA and PBE functional corroborate once again the peculiar crossing of the bands (band structure and DOS spectra are almost identical to those calculated using the PW91), which therefore indicates that the crossing at *E* <sup>F</sup> is not an accidental degeneracy arising from the applied functional. This behavior is quite unusual, as it turns up neither in the SiC bulk showing *E* F lying in a gap between states nor in the Ti3SiC2 bulk showing *E* <sup>F</sup>z(5%\*#z%\*z0\$!z)% (!z+"zz\* z+"z!(!0.+\*%z/00!/\_z3\$%\$z\*z!z0¥ tributed to the structural symmetry with Ti atoms sitting exactly atop center of the hexagon composed of Si and C (corresponding to the point in *k* space), as shown in inset of Fig. 8(d). Further calculations reveal that this gapless nature appears in the multilayer consisting of a Ti3SiC2-like monolayer embedded in SiC as well, indicating that the unique state could !z1\* !./0++ z1,+\*z-1\*01)z+\*"%\*!)!\*0z!""!0z\* z 0\$!z%\*0!."!z,\$!\*+)!\*+\*z+),¥ nied by the polarity discontinuity. However, our additional calculations suggest that the point Fermi surface vanishes when a Ti3SiC2 trilayer is hypothetically embedded within SiC, which takes on metallic states with three bands (arise from the three Ti layers) crossing *E* F, similar to what is seen in the band structure of Ti3SiC2 bulk. This transition from the zerogap semiconductor to metal therefore highlight the importance of quantum confinement in %\* 1%\*#z 0\$!z ,+%\*0z !.)%z /1."!\_z /%\*!z %0%+\*(z(5!.z%/z !(%!2! z 0+z .!(%!2!z 0\$!z +\*"%\*!¥ ment effect and produce more states.

undergo a sudden vanishing at *E* F (Fig. 10), which is in stark difference from what is seen in the DOS projected (PDOS) on Ti in bulk Ti3SiC2 presenting continuous states at and around *E* F (lines in Fig. 10). In addition, there are notable electronic states in the forbidden gap of bulk SiC for the C and Si in the multilayer, which is definitely attributable to the embedded bilayer. The presence of the induced gap states, in particular, those below the CB minimum of bulk SiC but close to *E* F, can readily present a trap for CB electrons, which could modify electronic behaviors of the originally insulating SiC and thus be relevant for the current flow +2!.z /!)%+\* 10+.z%\*z 0\$!z%(w !,+/%0! z %z /5/0!)^z
+.!+2!.\_z3!z\*+0!z 0\$0z+2!.((z "!¥ tures of PDOS for identical atom species may even differ from one another, which can be

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163

Figure 11. Contour plot of (a) charge density and (b) density difference for the multilayer system viewed along the (11-20) plane. The difference of charge density gives the redistribution of charge in the system relative to its isolated one. The upper scale denotes the magnitude of charge in (a) and the lower scale that of charge difference in (b). (c) Isosurface and (d) electron density plot along the same plane as in (a) in the energy window (*E*F-0.5 eV, *E*F) [19].

To shed further light on bonding nature and charge distribution in the multilayer, we present contour plots of charge density (Fig. 11(a)) and its difference (Fig. 11(b)) along the (11-20) plane. From the figures, we notice that (i) majority of charge is localized on C atoms with humps distorted toward their neighboring atoms, suggesting that bonds in both SiC and bilayer are of a mixed covalent-ionic nature, (ii) charge distribution on C in SiC exhibits more pronounced lobes than that on C in the bilayer (Fig. 11(a)), indicative of more covalent element for bonds in SiC, and (iii) ionicity originates from the large charge gain on C at an !4,!\*/!z+"z\$.#!z(+//z+\*z%0/z\*!%#\$+.%\*#z0%+\*/z c%#^zDDcdd^z1.0\$!.z!4)%\*0%+\*z+\*z!(!¥ tron distribution around *E* F reveals that valence electrons are confined, to a large extent, to within the bilayer (Fig. 11(c)), in good agreement with the DOS analysis (Fig. 3). These charges are spatially connected and broadly distributed surrounding the bilayer with a small degree of leakage into as far as two atomic layers of SiC (Fig. 11(c)d\_z/z%/z"1.0\$!.z+\*¥ firmed from a slice plot in Fig. 11(d). This implies that the bilayer buried in between the SiC may act as a conducting channel so as to enhance current flow over the semiconductor.

ascribed to their different bonding environments.

Figure 10. DOS projected on selected atomic layers in the multilayer system. Left panel gives the PDOSs of SiC layers and right panel those of Ti3SiC2 layers. The lines show PDOSs of the corresponding atoms in the bulk as a reference. The *E* F is set to zero [19].

#### 3.3. Electronic states

Further investigation of DOS projected on selected atomic layers provides evidence that the bands close to *E* F involve dominantly Ti 3*d* states (layers 4 and 6 in Fig. 8(d)). These states undergo a sudden vanishing at *E* F (Fig. 10), which is in stark difference from what is seen in the DOS projected (PDOS) on Ti in bulk Ti3SiC2 presenting continuous states at and around *E* F (lines in Fig. 10). In addition, there are notable electronic states in the forbidden gap of bulk SiC for the C and Si in the multilayer, which is definitely attributable to the embedded bilayer. The presence of the induced gap states, in particular, those below the CB minimum of bulk SiC but close to *E* F, can readily present a trap for CB electrons, which could modify electronic behaviors of the originally insulating SiC and thus be relevant for the current flow +2!.z /!)%+\* 10+.z%\*z 0\$!z%(w !,+/%0! z %z /5/0!)^z
+.!+2!.\_z3!z\*+0!z 0\$0z+2!.((z "!¥ tures of PDOS for identical atom species may even differ from one another, which can be ascribed to their different bonding environments.

accidental degeneracy arising from the applied functional. This behavior is quite unusual, as it turns up neither in the SiC bulk showing *E* F lying in a gap between states nor in the Ti3SiC2 bulk showing *E* <sup>F</sup>z(5%\*#z%\*z0\$!z)% (!z+"zz\* z+"z!(!0.+\*%z/00!/\_z3\$%\$z\*z!z0¥ tributed to the structural symmetry with Ti atoms sitting exactly atop center of the hexagon composed of Si and C (corresponding to the point in *k* space), as shown in inset of Fig. 8(d). Further calculations reveal that this gapless nature appears in the multilayer consisting of a Ti3SiC2-like monolayer embedded in SiC as well, indicating that the unique state could !z1\* !./0++ z1,+\*z-1\*01)z+\*"%\*!)!\*0z!""!0z\* z 0\$!z%\*0!."!z,\$!\*+)!\*+\*z+),¥ nied by the polarity discontinuity. However, our additional calculations suggest that the point Fermi surface vanishes when a Ti3SiC2 trilayer is hypothetically embedded within SiC, which takes on metallic states with three bands (arise from the three Ti layers) crossing *E* F, similar to what is seen in the band structure of Ti3SiC2 bulk. This transition from the zerogap semiconductor to metal therefore highlight the importance of quantum confinement in %\* 1%\*#z 0\$!z ,+%\*0z !.)%z /1."!\_z /%\*!z %0%+\*(z(5!.z%/z !(%!2! z 0+z .!(%!2!z 0\$!z +\*"%\*!¥

Figure 10. DOS projected on selected atomic layers in the multilayer system. Left panel gives the PDOSs of SiC layers and right panel those of Ti3SiC2 layers. The lines show PDOSs of the corresponding atoms in the bulk as a reference.

Further investigation of DOS projected on selected atomic layers provides evidence that the bands close to *E* F involve dominantly Ti 3*d* states (layers 4 and 6 in Fig. 8(d)). These states

ment effect and produce more states.

162 Physics and Technology of Silicon Carbide Devices

The *E* F is set to zero [19].

3.3. Electronic states

Figure 11. Contour plot of (a) charge density and (b) density difference for the multilayer system viewed along the (11-20) plane. The difference of charge density gives the redistribution of charge in the system relative to its isolated one. The upper scale denotes the magnitude of charge in (a) and the lower scale that of charge difference in (b). (c) Isosurface and (d) electron density plot along the same plane as in (a) in the energy window (*E*F-0.5 eV, *E*F) [19].

To shed further light on bonding nature and charge distribution in the multilayer, we present contour plots of charge density (Fig. 11(a)) and its difference (Fig. 11(b)) along the (11-20) plane. From the figures, we notice that (i) majority of charge is localized on C atoms with humps distorted toward their neighboring atoms, suggesting that bonds in both SiC and bilayer are of a mixed covalent-ionic nature, (ii) charge distribution on C in SiC exhibits more pronounced lobes than that on C in the bilayer (Fig. 11(a)), indicative of more covalent element for bonds in SiC, and (iii) ionicity originates from the large charge gain on C at an !4,!\*/!z+"z\$.#!z(+//z+\*z%0/z\*!%#\$+.%\*#z0%+\*/z c%#^zDDcdd^z1.0\$!.z!4)%\*0%+\*z+\*z!(!¥ tron distribution around *E* F reveals that valence electrons are confined, to a large extent, to within the bilayer (Fig. 11(c)), in good agreement with the DOS analysis (Fig. 3). These charges are spatially connected and broadly distributed surrounding the bilayer with a small degree of leakage into as far as two atomic layers of SiC (Fig. 11(c)d\_z/z%/z"1.0\$!.z+\*¥ firmed from a slice plot in Fig. 11(d). This implies that the bilayer buried in between the SiC may act as a conducting channel so as to enhance current flow over the semiconductor.

Figure 12. A cross-sectional HRTEM image of the contact of the formed Ti3SiC2 to the 4H-SiC substrate viewed from the [11-208<AJ=;LAGF 0@= LOGE9L=JA9DK 9J=<=E9J;9L=<:Q 9RA?R9?DAF= 0=JJ9;=KOAL@N9JQAF?<AE=FKAGFK 9J=G:s served, as indicated by arrows [20].

Figure 13. a) A typical HAADF-STEM image of a small terrace observed from the [11-208<AJ=;LAGF0@=L=JJ9;=AKAF<As cated by a zigzag line. Bigger dotted circles denote Ti and the smaller ones Si. (b) The same image as in (a) but has

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165

Figure 14. A typical HAADF image of an intermediate terrace observed from the [11-208<AJ=;LAGF0@=L=JJ9;=AKAF<As

In general, this contact region contains terraces with a wide variety of dimensions that can be affected by numerous factors. However, to develop an understanding of such a complex contact, it is important to first focus on representative terraces. Here, we choose purposely three species of terraces based on the dimension: small, intermediate, and large terrace. The corresponding HAADF images are presented in Figs. 13–15, which confirm the atomically

cated by a zigzag line. (b) The same image as in (a) but has been filtered to reduce noise [20].

been filtered to reduce noise [20].
