2. Role of coherent SiC/Ti3SiC2 interface

The *p*-type 4H-SiC epitaxial layers (5-µm thick) doped with aluminum (*N* <sup>A</sup> = 4.5 × 1018 cm-3) which were grown on undoped 4H-SiC wafers by chemical vapor deposition (manufactured 5z.!!z!/!.\$\_z \*^dz3!.!z1/! z/z/1/0.0!/^z\$!zGw%z/1/0.0!/z\$ zK~w+""z%w0!.)%¥ nated (0001) surfaces inclined toward a [¯2110] direction because only 4H-type structure of %z3%0\$z,+(5)+.,\$zc!^#^zF\_zG\_zI\_zDHz!0^dz3/z+\*0.+(((!z5z(0!.(z#.+30\$z+"z0\$!z!,%¥ 04%(z(5!./z,.((!(z0+zcCCCDdw+.%!\*0! z/1."!^z"0!.z\$!)%(z(!\*%\*#z+"z0\$!z/1/0.0!z/1.¥ face, a 10 nm-thick sacrificial oxide (SiOx) layer was grown on the SiC substrate by dryoxidation at 1423 K for 60 min. The electrode patterns were made by removing the SiOx (5!./\_z3\$!.!z+\*00z)!0(/z3!.!z !,+/%0! z5z %,,%\*#z%\*zHzMz %(10! z\$5 .+"(1+.%z% z/+(¥ 10%+\*z"+.zDz)%\*z1/%\*#zz,\$+0+(%0\$+#.,\$5z0!\$\*%-1!^z.%+.z0+z0\$!z !,+/%0%+\*z+"z+\*00z)0!¥ rials, the substrates were cleaned by deionized water. Then, Ti and Al stacking layers with high purities were deposited sequentially on the substrate in a high vacuum chamber where the base pressure was below 5 × 10-6 Pa. The thicknesses of the Ti and Al layers investigated in this study are 100 nm and 380 nm, respectively, and these layer thicknesses were chosen 0+z#%2!z0\$!z2!.#!z+),+/%0%+\*z+"z0\$!z%cECz0Mdz\* z(cKCz0Md\_z3\$!.!z0\$!z(5!.z0\$%'\*!//¥ !/z3!.!z)!/1.! z5zz-1.06z+/%((0+.z 1.%\*#z !,+/%0%+\*^z\$!z.!/+\*/z0+z\$++/!z0\$%/z2!.¥ age composition was that aluminum rich (more than 75 at%) in TiAl contacts were empirically found to be essential to yield low contact resistance, resulting from formation of the Ti3SiC2 compound layers. After depositing, the binary TiAl contact layers were annealed at 1273 K for a storage time of 2 min in an ultra-high vacuum chamber where the vacuum pressure was below 1×10-7 Pa.

!4\$\*#!w+..!(0%+\*z"1\*0%+\*(^z\$!z/%\*#(!w,.0%(!z+\$\*w\$)z32!z"1\*0%+\*z3/z!4,\* ¥ ed using plane waves with different cutoff energies depending on the calculated systems. Sampling of irreducible Brillion zone was performed with a regular Monkhorst-Pack grid of special *k* points, and electronic occupancies were determined according to the Methfessel-Paxton scheme. Independent *k*z ,+%\*0z +\*2!.#!\*!z 0!/0/z3!.!z +\* 10! z "+.z %/0%\*0z /1,!.¥ cells. Ground state charge densities were calculated self-consistently using a Pulay-like mixing scheme and the stable blocked Davidson minimization algorithm. Total energies

nates broadening-related uncertainties. All atoms were fully relaxed using the conjugate #. %!\*0z(#+.%0\$)z1\*0%(z0\$!z)#\*%01 !z+"z0\$!z!(()\*\*w!5\*)\*z"+.!z+\*z!\$z0+)z+\*¥

To determine the most stable interface theoretically, one first has to establish feasible models on the basis of the distinct terminations and contact sites and then compare them. However, a direct comparison of total energies of such candidate models is not physically meaningful since interfaces might have a different number of atoms. On the other hand, the adhesion energy (*W* add\_z3\$%\$z%/z'!5z0+z,.! %0%\*#z0\$!z)!\$\*%(z,.+,!.0%!/z+"z\*z%\*0!."!\_z%/z,\$5/%¥ cally comparable. Generally, the *W* ad is defined as the energy required to reversibly separate an interface into two free surfaces, neglecting plastic and diffusion degrees of freedom. The energy needed in actual cleavage experiments is always greater than the *W* ad +3%\*#z0+z,(/¥ tic deformation, but the extent of plastic deformation relies on the *W* ad. Formally, the *W* ad \*z!z!4,.!//! z%\*z0!.)/z+"z/1."!z\* z%\*0!."%(z!\*!.#%!/z+.z5z0\$!z %""!.!\*!z%\*z0+0(z!\*¥

is the surface energy of slab *i*, l 12 is the interface energy, *E* <sup>i</sup>

allowed to optimize fully, yielding an estimation of relaxed *W* ad.

2.1. Atomic-scale structures of the Ohmic contacts

isolated slab *i*, *E* IF is the total energy of the interface system, and *A* is the total interface area. In general, two steps can be taken to estimate the *W* ad^z%./0\_z0\$!z0+0(z!\*!.#%!/z3!.!z(1(0¥ ed for a series of separations as two rigid slabs were brought increasingly closer from a large initial separation. As a consequence, the calculated total energies were found to behave like a parabola, passing through a minimum at the equilibrium separation. The unrelaxed *W* ad was obtained by computing the energy difference between the interface at the equilibrium state and the unrelaxed isolated slab. Next, each isolated slab as well as interfacial slab was

The electric properties for the TiAl contact systems before and after annealing are meaured "%./0z0+z2!.%"5z0\$!z"+.)0%+\*z+"z\$)%z+\*00^z\$!z1..!\*0z()+/0z'!!,/z6!.+z!"+.!z0\$!z\*\*!(¥ %\*#\_z3\$%(!z%\*.!/%\*#z\*!.(5z(%\*!.z3%0\$z0\$!z.%/!z+"z,,(%! z%/\_z3\$%\$z1\*)%#1+1/(5z+\*¥ firms the formation of the Ohmic contacts after annealing. Further XRD analyses demonstrate that a new reaction product, the ternary Ti3SiC2, is generated after annealing, which shows a /0.+\*#(5zcCCCDdw+.%!\*0! z0!401.!^z\$!z%z.!0%\*/zcCCCDdw+.%!\*0! z0!401.!z"0!.z\*\*!(%\*#\_z0\$!.!¥

*W*ad l<sup>1</sup> + l<sup>2</sup> –l<sup>12</sup> = (*E*<sup>1</sup> + *E*<sup>2</sup> –*E*IF) / *A* (1)

(@\$(z +..!0%+\*/\_z3\$%\$z!(%)%¥

http://dx.doi.org/10.5772/50767

153

Physics Behind the Ohmic Nature in Silicon Carbide Contacts

is the total energy of

3!.!z (1(0! z1/%\*#z 0\$!z(%\*!.z 0!0.\$! .+\*z)!0\$+ z3%0\$z-

verged to less than 0.05 eV/Å, yielding optimized structures.

ergy between the interface and isolated slabs [22,23]:

Here l <sup>i</sup>

The surface morphology of the TiAl contact layers on 4H-SiC after annealing was observed using a JEOL JSM-6060 scanning electron microscope (SEM). Microstructural analysis and identification of the Ti3SiC2 layers at the contact layers/4H-SiC interfaces after annealing was ,!."+.)! z1/%\*#zw.5z %"".0%+\*zcdz\* z.+//w/!0%+\*(z
^z+.zz\*(5/%/\_z%#¥ ku RINT-2500 with Cu \_ radiation operated at 30 kV and 100 mA was used. In particular, the interfacial structures and an orientation relationship between the contact layers and the 4H-SiC substrates were characterized by cross-sectional high-resolution TEM observations and selected area diffraction pattern (SADP) analysis, respectively, using a JEOL JEM-4000EX electron microscope operated at an accelerating voltage of 400 kV, where the point-to-point resolution of this microscope was approximately 0.17 nm. Z-contrast images were obtained using a spherical aberration (C*s*dz+..!0! z/\*\*%\*#z0.\*/)%//%+\*z!(!0.+\*z)%¥ .+/+,!zc
dzc zEDCCd\_z3\$%\$z,.+2% !/z\*z1\*,.!! !\*0! z+,,+.01\*%05z0+z%\*2!/0%#0¥ ed atomic-scale structure with a sub-Å electron probe. Thin foil specimens for the TEM and STEM observations were prepared by the standard procedures: cutting, gluing, mechanical grinding, dimple polishing, and argon ion sputter thinning techniques.

Calculations of electronic structure and total energy were carried out using the Vienna *ab initio* simulation package (VASP) within the framework of density functional theory (DFT) [21]. The projector augmented wave method was used for electron-ion interactions, and the generalized gradient approximation of Perdew et al. (PW91) was employed to describe the !4\$\*#!w+..!(0%+\*z"1\*0%+\*(^z\$!z/%\*#(!w,.0%(!z+\$\*w\$)z32!z"1\*0%+\*z3/z!4,\* ¥ ed using plane waves with different cutoff energies depending on the calculated systems. Sampling of irreducible Brillion zone was performed with a regular Monkhorst-Pack grid of special *k* points, and electronic occupancies were determined according to the Methfessel-Paxton scheme. Independent *k*z ,+%\*0z +\*2!.#!\*!z 0!/0/z3!.!z +\* 10! z "+.z %/0%\*0z /1,!.¥ cells. Ground state charge densities were calculated self-consistently using a Pulay-like mixing scheme and the stable blocked Davidson minimization algorithm. Total energies 3!.!z (1(0! z1/%\*#z 0\$!z(%\*!.z 0!0.\$! .+\*z)!0\$+ z3%0\$z-(@\$(z +..!0%+\*/\_z3\$%\$z!(%)%¥ nates broadening-related uncertainties. All atoms were fully relaxed using the conjugate #. %!\*0z(#+.%0\$)z1\*0%(z0\$!z)#\*%01 !z+"z0\$!z!(()\*\*w!5\*)\*z"+.!z+\*z!\$z0+)z+\*¥ verged to less than 0.05 eV/Å, yielding optimized structures.

To determine the most stable interface theoretically, one first has to establish feasible models on the basis of the distinct terminations and contact sites and then compare them. However, a direct comparison of total energies of such candidate models is not physically meaningful since interfaces might have a different number of atoms. On the other hand, the adhesion energy (*W* add\_z3\$%\$z%/z'!5z0+z,.! %0%\*#z0\$!z)!\$\*%(z,.+,!.0%!/z+"z\*z%\*0!."!\_z%/z,\$5/%¥ cally comparable. Generally, the *W* ad is defined as the energy required to reversibly separate an interface into two free surfaces, neglecting plastic and diffusion degrees of freedom. The energy needed in actual cleavage experiments is always greater than the *W* ad +3%\*#z0+z,(/¥ tic deformation, but the extent of plastic deformation relies on the *W* ad. Formally, the *W* ad \*z!z!4,.!//! z%\*z0!.)/z+"z/1."!z\* z%\*0!."%(z!\*!.#%!/z+.z5z0\$!z %""!.!\*!z%\*z0+0(z!\*¥ ergy between the interface and isolated slabs [22,23]:

$$\mathcal{W}\_{\rm ad} \equiv \sigma\_1 + \sigma\_2 - \sigma\_{12} = \left(E\_1 + E\_2 - E\_{\rm IF}\right) / A \tag{1}$$

Here l <sup>i</sup> is the surface energy of slab *i*, l 12 is the interface energy, *E* <sup>i</sup> is the total energy of isolated slab *i*, *E* IF is the total energy of the interface system, and *A* is the total interface area. In general, two steps can be taken to estimate the *W* ad^z%./0\_z0\$!z0+0(z!\*!.#%!/z3!.!z(1(0¥ ed for a series of separations as two rigid slabs were brought increasingly closer from a large initial separation. As a consequence, the calculated total energies were found to behave like a parabola, passing through a minimum at the equilibrium separation. The unrelaxed *W* ad was obtained by computing the energy difference between the interface at the equilibrium state and the unrelaxed isolated slab. Next, each isolated slab as well as interfacial slab was allowed to optimize fully, yielding an estimation of relaxed *W* ad.

#### 2.1. Atomic-scale structures of the Ohmic contacts

2. Role of coherent SiC/Ti3SiC2 interface

152 Physics and Technology of Silicon Carbide Devices

pressure was below 1×10-7 Pa.

.+/+,!zc
dzc

The *p*-type 4H-SiC epitaxial layers (5-µm thick) doped with aluminum (*N* <sup>A</sup> = 4.5 × 1018 cm-3) which were grown on undoped 4H-SiC wafers by chemical vapor deposition (manufactured 5z.!!z!/!.\$\_z \*^dz3!.!z1/! z/z/1/0.0!/^z\$!zGw%z/1/0.0!/z\$ zK~w+""z%w0!.)%¥ nated (0001) surfaces inclined toward a [¯2110] direction because only 4H-type structure of %z3%0\$z,+(5)+.,\$zc!^#^zF\_zG\_zI\_zDHz!0^dz3/z+\*0.+(((!z5z(0!.(z#.+30\$z+"z0\$!z!,%¥ 04%(z(5!./z,.((!(z0+zcCCCDdw+.%!\*0! z/1."!^z"0!.z\$!)%(z(!\*%\*#z+"z0\$!z/1/0.0!z/1.¥ face, a 10 nm-thick sacrificial oxide (SiOx) layer was grown on the SiC substrate by dryoxidation at 1423 K for 60 min. The electrode patterns were made by removing the SiOx (5!./\_z3\$!.!z+\*00z)!0(/z3!.!z !,+/%0! z5z %,,%\*#z%\*zHzMz %(10! z\$5 .+"(1+.%z% z/+(¥ 10%+\*z"+.zDz)%\*z1/%\*#zz,\$+0+(%0\$+#.,\$5z0!\$\*%-1!^z.%+.z0+z0\$!z !,+/%0%+\*z+"z+\*00z)0!¥ rials, the substrates were cleaned by deionized water. Then, Ti and Al stacking layers with high purities were deposited sequentially on the substrate in a high vacuum chamber where the base pressure was below 5 × 10-6 Pa. The thicknesses of the Ti and Al layers investigated in this study are 100 nm and 380 nm, respectively, and these layer thicknesses were chosen 0+z#%2!z0\$!z2!.#!z+),+/%0%+\*z+"z0\$!z%cECz0Mdz\* z(cKCz0Md\_z3\$!.!z0\$!z(5!.z0\$%'\*!//¥ !/z3!.!z)!/1.! z5zz-1.06z+/%((0+.z 1.%\*#z !,+/%0%+\*^z\$!z.!/+\*/z0+z\$++/!z0\$%/z2!.¥ age composition was that aluminum rich (more than 75 at%) in TiAl contacts were empirically found to be essential to yield low contact resistance, resulting from formation of the Ti3SiC2 compound layers. After depositing, the binary TiAl contact layers were annealed at 1273 K for a storage time of 2 min in an ultra-high vacuum chamber where the vacuum

The surface morphology of the TiAl contact layers on 4H-SiC after annealing was observed using a JEOL JSM-6060 scanning electron microscope (SEM). Microstructural analysis and identification of the Ti3SiC2 layers at the contact layers/4H-SiC interfaces after annealing was ,!."+.)! z1/%\*#zw.5z %"".0%+\*zcdz\* z.+//w/!0%+\*(z
^z+.zz\*(5/%/\_z%#¥ ku RINT-2500 with Cu \_ radiation operated at 30 kV and 100 mA was used. In particular, the interfacial structures and an orientation relationship between the contact layers and the 4H-SiC substrates were characterized by cross-sectional high-resolution TEM observations and selected area diffraction pattern (SADP) analysis, respectively, using a JEOL JEM-4000EX electron microscope operated at an accelerating voltage of 400 kV, where the point-to-point resolution of this microscope was approximately 0.17 nm. Z-contrast images were obtained using a spherical aberration (C*s*dz+..!0! z/\*\*%\*#z0.\*/)%//%+\*z!(!0.+\*z)%¥

ed atomic-scale structure with a sub-Å electron probe. Thin foil specimens for the TEM and STEM observations were prepared by the standard procedures: cutting, gluing, mechanical

Calculations of electronic structure and total energy were carried out using the Vienna *ab initio* simulation package (VASP) within the framework of density functional theory (DFT) [21]. The projector augmented wave method was used for electron-ion interactions, and the generalized gradient approximation of Perdew et al. (PW91) was employed to describe the

grinding, dimple polishing, and argon ion sputter thinning techniques.

zEDCCd\_z3\$%\$z,.+2% !/z\*z1\*,.!! !\*0! z+,,+.01\*%05z0+z%\*2!/0%#0¥

The electric properties for the TiAl contact systems before and after annealing are meaured "%./0z0+z2!.%"5z0\$!z"+.)0%+\*z+"z\$)%z+\*00^z\$!z1..!\*0z()+/0z'!!,/z6!.+z!"+.!z0\$!z\*\*!(¥ %\*#\_z3\$%(!z%\*.!/%\*#z\*!.(5z(%\*!.z3%0\$z0\$!z.%/!z+"z,,(%! z%/\_z3\$%\$z1\*)%#1+1/(5z+\*¥ firms the formation of the Ohmic contacts after annealing. Further XRD analyses demonstrate that a new reaction product, the ternary Ti3SiC2, is generated after annealing, which shows a /0.+\*#(5zcCCCDdw+.%!\*0! z0!401.!^z\$!z%z.!0%\*/zcCCCDdw+.%!\*0! z0!401.!z"0!.z\*\*!(%\*#\_z0\$!.!¥ by facilitating development of hetero-epitaxy between reaction products and substrates. The TEM imaging reveals that no any other compounds contact directly the SiC surface, thereby ensuring an exclusive contact of Ti3SiC2 to SiC. Since the carbide itself is metallic in nature, the lowering in Schottky barrier in the TiAl-based contacts is hence attributed qualitatively to the epitaxial and atomically sharp SiC/Ti3SiC2z%\*0!."!^zz.!"1(z%\* !4%\*#z+"z0\$!z/!(!0! z.!z %"¥ fraction pattern (SADP) at the contacts/SiC interface reveals that the formed Ti3SiC2 layers have epitaxial orientation relationships, that is, (0001)Ti3SiC2//(0001)SiC and [0¯110]Ti3SiC2// [0¯110]SiC, with the SiC substrate. These orientation relationships are believed to be beneficial for forming a coherent and well matched interface between SiC and Ti3SiC2\_z/%\*!z0\$!5z+0\$z!¥ long to the hexagonal space group with lattice constants of *a* = 3.081 Å and *c* = 10.085 Å for the SiC and *a* = 3.068 Å and *c* = 17.669 Å for the Ti3SiC2.

transport, we conclude that this clean and coherent SiC/Ti3SiC2 interface should be critical

To clarify the mechanism, it is prerequisite to determine the atomic structure of the SiC/ Ti3SiC2z%\*0!."!z2%z+),(!)!\*0%\*#z 0\$!z+0%\*! zz%)#!z c%#^zDd^z!z\$2!z+\*/% ¥ ered a total of 96 candidate interfacial geometries using bulklike slabs, taking into account termination effect, stacking sequence, and full optimization. From the bulk 4H-SiC and Ti3SiC2 structures and the relative stacking order of Ti and Si, the observed image in Fig. 2(a) can be intuitively fitted by a SiSi model shown in Fig. 2(c). In this model, the interfacial Si atoms of Ti3SiC2 sit above the hollow sites of interfacial Si plane of SiC, where the optimal distance between interfacial Si-Si planes (denoted as *d*1 in Fig. 2(b)dz\* z0\$0z!03!!\*z%\*0!.¥ facial Si-Si atoms projected onto paper plane (denoted as *d*2 in Fig. 2(c)) are calculated to be 2.13 and 2.53 Å, respectively. These distances, however, deviate severely from their average experimental values, 2.5 Å and 2.8 Å, which are obtained by characterizing quantitatively 0\$!zz%)#!zc%#^zEcdd^z \*z %0%+\*\_z\*z!4)%\*0%+\*z+"z%\*0!."!z/0%(%05z5z(1(0¥

the model with interfacial Si of Ti3SiC2 resting straight atop the interfacial Si of SiC (2.58 J/

Figure 2. a) Magnified HAADF image of the SiC/Ti3SiC2 interface. (b) The same image as in (a) but has been low-pass filtered to reduce noise. Relaxed SiC(0001)/Ti3SiC2AFL=J>9;=EG<=DK;OAL@GML/A/A9F<<OAL@/A/AAFL=J>9s cial C atoms. The distance between interfacial Si-Si layers is represented by *d*1 and that between interfacial Si-Si atoms

To resolve these paradoxes, we notice that a possibility might be ignored, that is, the unseen C )%#\$0z!z0.,,! z0z0\$!z%\*0!."!\_z(0!.%\*#z(+(z!\*2%.+\*)!\*0z0\$!.!^z+z0!/0z0\$%/z/!\*.%+\_z3!z!/¥ 0(%/\$! zz\*!3z)+ !(zc\*)! z%%dz5z%\*0.+ 1%\*#zz%\*0+z0\$!z%\*0!."%(z(5!.z".+)z0\$!z+\*¥ sideration of crystal extension and stacking sequences. The calculated *W* ad of this SiCSi model

.0%\*#z^z1.0\$!.z!4)%\*0%+\*z+"z0\$!z.!(4! z0+)%z#!+)!0.5zc%#^zEc ddz.!2!(/z0\$0z0\$!z%\*+.¥ poration of C does not induce a significant structural transformation. Namely, the two Si layers ,.+4%)(z0+z0\$!z%\*0!."!z)%\*0%\*z0\$!z/0'%\*#z/!!\*z%\*z%#^zEcd\_z0\$1/z)0\$%\*#z0\$!zz%)¥ age geometrically. Quantitatively, the *d*1 and *d*Ez %/0\*!/z.!z\*+3zE^HFz\* zE^KDz\_z.!/,!0%2!¥

\_z3\$%\$z%\* %0!/z0\$0z%\*0!."!z%/z%\* !! z/0.!\*#0\$!\*! z/1/0\*0%((5z"0!.z%\*+.,+¥

). It is even less stable than

http://dx.doi.org/10.5772/50767

155

Physics Behind the Ohmic Nature in Silicon Carbide Contacts

ing the *W* ad indicates that this SiSi model is not favored (1.62 J/m2

projected onto the paper plane by *d*2. The interfaces are represented by an arrow [23].

), which contravenes again the observed image.

for the formation of Ohmic contact.

m2

is 6.81 J/m2

Figure 1. A typical HAADF-STEM image of the SiC/Ti3SiC2 interface in the annealed TiAl contact system observed from [11-20] direction. The points at which the phase contrast is no longer periodic in either the Ti3SiC2 or SiC define the interfacial region [23].

A representative HAADF image of the SiC/Ti3SiC2 interface is shown in Fig. 1\_z3\$%\$z+\*¥ firms a clean and atomically sharp contact between the two materials. Since intensity of an atomic column in the Scanning TEM, to good approximation, is directly proportional to the square of atomic number (Z) [24], brighter spots in image represent atomic columns of Ti, 3\$%(!z0\$!z+),.0%2!(5z .'!.z+\*!/z.!z%^z+0z/1.,.%/%\*#(5\_z0\$!z+(1)\*/z+"zz.!z\*+0z/0¥ 0!.! z/0.+\*#(5z!\*+1#\$z0+z!z2%/1(%6! z+3%\*#z0+z%0/z/)((z\_z0\$!.!5z)'%\*#z0\$%/z%)#!z%\*¥ complete. It should be noted that obtaining a signal of pure interfacial carbon is technically very difficult because the specimen can be easily affected by the environmental carbon, thereby precluding the element-selective imaging of carbon. We therefore rely on the firstprinciples calculations instead to discuss the possibility in the presence of C at the interface, as will be described later. To see the interface clearer, we magnify the cross-sectional HAADF image in Fig. 2(a) and further filter it to reduce noise, as shown in Fig. 2(b). The Siterminated Ti3SiC2 is observed intuitively to make a direct contact with the Si-terminated SiC substrate with interfacial Si atoms of Ti3SiC2 sitting above hollow sites of interfacial Si plane of SiC. However, this straightforward interpretation is premature, as will be described later. Since there are no pits, spikes, or dislocations that might act as pathways for current transport, we conclude that this clean and coherent SiC/Ti3SiC2 interface should be critical for the formation of Ohmic contact.

by facilitating development of hetero-epitaxy between reaction products and substrates. The TEM imaging reveals that no any other compounds contact directly the SiC surface, thereby ensuring an exclusive contact of Ti3SiC2 to SiC. Since the carbide itself is metallic in nature, the lowering in Schottky barrier in the TiAl-based contacts is hence attributed qualitatively to the epitaxial and atomically sharp SiC/Ti3SiC2z%\*0!."!^zz.!"1(z%\* !4%\*#z+"z0\$!z/!(!0! z.!z %"¥ fraction pattern (SADP) at the contacts/SiC interface reveals that the formed Ti3SiC2 layers have epitaxial orientation relationships, that is, (0001)Ti3SiC2//(0001)SiC and [0¯110]Ti3SiC2// [0¯110]SiC, with the SiC substrate. These orientation relationships are believed to be beneficial for forming a coherent and well matched interface between SiC and Ti3SiC2\_z/%\*!z0\$!5z+0\$z!¥ long to the hexagonal space group with lattice constants of *a* = 3.081 Å and *c* = 10.085 Å for the

Figure 1. A typical HAADF-STEM image of the SiC/Ti3SiC2 interface in the annealed TiAl contact system observed from [11-20] direction. The points at which the phase contrast is no longer periodic in either the Ti3SiC2 or SiC define the

A representative HAADF image of the SiC/Ti3SiC2 interface is shown in Fig. 1\_z3\$%\$z+\*¥ firms a clean and atomically sharp contact between the two materials. Since intensity of an atomic column in the Scanning TEM, to good approximation, is directly proportional to the square of atomic number (Z) [24], brighter spots in image represent atomic columns of Ti, 3\$%(!z0\$!z+),.0%2!(5z .'!.z+\*!/z.!z%^z+0z/1.,.%/%\*#(5\_z0\$!z+(1)\*/z+"zz.!z\*+0z/0¥ 0!.! z/0.+\*#(5z!\*+1#\$z0+z!z2%/1(%6! z+3%\*#z0+z%0/z/)((z\_z0\$!.!5z)'%\*#z0\$%/z%)#!z%\*¥ complete. It should be noted that obtaining a signal of pure interfacial carbon is technically very difficult because the specimen can be easily affected by the environmental carbon, thereby precluding the element-selective imaging of carbon. We therefore rely on the firstprinciples calculations instead to discuss the possibility in the presence of C at the interface, as will be described later. To see the interface clearer, we magnify the cross-sectional HAADF image in Fig. 2(a) and further filter it to reduce noise, as shown in Fig. 2(b). The Siterminated Ti3SiC2 is observed intuitively to make a direct contact with the Si-terminated SiC substrate with interfacial Si atoms of Ti3SiC2 sitting above hollow sites of interfacial Si plane of SiC. However, this straightforward interpretation is premature, as will be described later. Since there are no pits, spikes, or dislocations that might act as pathways for current

SiC and *a* = 3.068 Å and *c* = 17.669 Å for the Ti3SiC2.

154 Physics and Technology of Silicon Carbide Devices

interfacial region [23].

To clarify the mechanism, it is prerequisite to determine the atomic structure of the SiC/ Ti3SiC2z%\*0!."!z2%z+),(!)!\*0%\*#z 0\$!z+0%\*! zz%)#!z c%#^zDd^z!z\$2!z+\*/% ¥ ered a total of 96 candidate interfacial geometries using bulklike slabs, taking into account termination effect, stacking sequence, and full optimization. From the bulk 4H-SiC and Ti3SiC2 structures and the relative stacking order of Ti and Si, the observed image in Fig. 2(a) can be intuitively fitted by a SiSi model shown in Fig. 2(c). In this model, the interfacial Si atoms of Ti3SiC2 sit above the hollow sites of interfacial Si plane of SiC, where the optimal distance between interfacial Si-Si planes (denoted as *d*1 in Fig. 2(b)dz\* z0\$0z!03!!\*z%\*0!.¥ facial Si-Si atoms projected onto paper plane (denoted as *d*2 in Fig. 2(c)) are calculated to be 2.13 and 2.53 Å, respectively. These distances, however, deviate severely from their average experimental values, 2.5 Å and 2.8 Å, which are obtained by characterizing quantitatively 0\$!zz%)#!zc%#^zEcdd^z \*z %0%+\*\_z\*z!4)%\*0%+\*z+"z%\*0!."!z/0%(%05z5z(1(0¥ ing the *W* ad indicates that this SiSi model is not favored (1.62 J/m2 ). It is even less stable than the model with interfacial Si of Ti3SiC2 resting straight atop the interfacial Si of SiC (2.58 J/ m2 ), which contravenes again the observed image.

Figure 2. a) Magnified HAADF image of the SiC/Ti3SiC2 interface. (b) The same image as in (a) but has been low-pass filtered to reduce noise. Relaxed SiC(0001)/Ti3SiC2AFL=J>9;=EG<=DK;OAL@GML/A/A9F<<OAL@/A/AAFL=J>9s cial C atoms. The distance between interfacial Si-Si layers is represented by *d*1 and that between interfacial Si-Si atoms projected onto the paper plane by *d*2. The interfaces are represented by an arrow [23].

To resolve these paradoxes, we notice that a possibility might be ignored, that is, the unseen C )%#\$0z!z0.,,! z0z0\$!z%\*0!."!\_z(0!.%\*#z(+(z!\*2%.+\*)!\*0z0\$!.!^z+z0!/0z0\$%/z/!\*.%+\_z3!z!/¥ 0(%/\$! zz\*!3z)+ !(zc\*)! z%%dz5z%\*0.+ 1%\*#zz%\*0+z0\$!z%\*0!."%(z(5!.z".+)z0\$!z+\*¥ sideration of crystal extension and stacking sequences. The calculated *W* ad of this SiCSi model is 6.81 J/m2 \_z3\$%\$z%\* %0!/z0\$0z%\*0!."!z%/z%\* !! z/0.!\*#0\$!\*! z/1/0\*0%((5z"0!.z%\*+.,+¥ .0%\*#z^z1.0\$!.z!4)%\*0%+\*z+"z0\$!z.!(4! z0+)%z#!+)!0.5zc%#^zEc ddz.!2!(/z0\$0z0\$!z%\*+.¥ poration of C does not induce a significant structural transformation. Namely, the two Si layers ,.+4%)(z0+z0\$!z%\*0!."!z)%\*0%\*z0\$!z/0'%\*#z/!!\*z%\*z%#^zEcd\_z0\$1/z)0\$%\*#z0\$!zz%)¥ age geometrically. Quantitatively, the *d*1 and *d*Ez %/0\*!/z.!z\*+3zE^HFz\* zE^KDz\_z.!/,!0%2!¥ ly, very close to the experimental values. Therefore, the introduction of interfacial C monolayer resolves the inconsistencies between simulations and experiments.

interfacial Ti *d* and Si *p* states below Fermi level (*E <sup>F</sup>*), which continues well into SiC surface, inducing noticeable gap states in the interfacial C at *E <sup>F</sup>*. This means that the interfacial C (5!.z%/z)!0(%6! \_z%\* %0%2!z+"z,+//%(!z!(!0.%z+\* 10%2%05^z \*z"0\_z0\$!z#,z/00!/z\*z!4¥ tend as far as they can into deeper layers of SiC, as there appear weak but visible peaks at *E <sup>F</sup>* in the PDOSs of the 2nd and 3rdz(5!./z+"z%^z\$!.!"+.!\_zz(+(z3!'z)!0((%%05z)%#\$0z+¥ cur at top few layers of the semiconductor surface, which could enable current flow through the SiC. We also note significant hybridization between the interfacial C *sp* and Si *sp* states,

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Figure 4. Contour plots of charge densities for (a) SiSi and (b) SiCSi interfaces taken along (11-20) plane. The interface is represented by a horizontal line and the atoms that intersect the contour plane are labeled. Corresponding contour

Figure 4 shows contour plots of charge densities and their differences along (11-20) plane for the optimized SiSi and SiCSi interfaces. We notice in Fig. 4(b) that the bonding interaction !03!!\*z%\*0!."%(z%z\* zz"+.z0\$!z%%z%\*0!."!z%/z.!).'(5z/%)%(.z0+z0\$!z%wz%\*0!.¥ tion deeper into SiC: the majority of charge is localized on C with humps directed towards their neighboring Si. We thus conclude that the interfacial bonding for the SiCSi is of mixed +2(!\*0w%+\*%z\*01.!^z\$!z%\*0!."%(z+\* /z"+.z0\$!z%%z%\*0!."!\_z\$+3!2!.\_z\$2!z+2(!\*0z\*¥ ture with a small amount of charge accumulated within the interfacial region (Fig. 4(a)). In addition, the amount of charge accumulated on the interfacial Si-Si bonds of SiSi (Fig. 4(c)) is far less significant than that on the interfacial Si-C bonds of SiCSi (Fig. 4(d)). This heaver charge accumulation in the case of SiCSi, together with its mixed covalent-ionic character at

Although the charge-distribution analysis can reveal valuable information on interfacial bonding, it provides restrained insight into how electrons distribute around *E <sup>F</sup>*\_z3\$%\$z)0¥ ters because density around *E <sup>F</sup>* directly determines the current transmission. Figure 5 %((1/¥ trates an electron-density isosurface and its slice along the (11-20) plane for the optimized

suggestive of covalent bonding at interface.

plots of charge-density differences for (c) SiSi and (d) SiCSi interfaces [23].

2.3. Quantum electron transport properties

interface, accounts for the largest *W* ad associated with the SiCSi interface.

#### 2.2. Electronic structure and bonding

Calculations of *p*-type Schottky barrier height (SBH) reveal that the interface with C (0.60 eV) has much lower SBH than the interface without C (1.05 eV), suggesting that the trapped C assist the lowering of SBH. To shed light on origin of the decrease in SBH and junction strengthening in the SiCSi interface, we characterized thoroughly interfacial electronic states and bonding nature. Figure 3(a) shows a planar-averaged charge-density difference along interface normal, where there appears a more dramatic accumulation of charge within the interfacial region for the interface with C. This indicates that the covalent bonding is /0.!\*#0\$!\*! z%\*z0\$!z%%z/!^z \*z %0%+\*\_z3!z\*+0!z0\$0z0\$!z,(\*.w2!.#! z !\*/%05z %""!.¥ ence for the SiCSi more prominently deviates from zero around interface, reflecting more significant charge transfer between the SiC and Ti3SiC2 slabs. Moreover, charge is observed to be depleted noticeably in both the sub-interfacial SiC and Ti3SiC2 region for the SiCSi, suggesting that the atoms second nearest to the interface contribute to interfacial bonding. These missing charges, to a large extent, make their way onto the more electronegative C ions, indicative of the formation of ionic bonding.

Figure 3. a) Planar-averaged charge-density difference for the relaxed interfaces with and without C along [00018<As J=;LAGF: =FKALQG>KL9L=KHJGB=;L=<GFLGL@=9LGEA;D9Q=JK;DGK=LGL@=J=D9P=</A/AAFL=J>9;=0@=D=>L:GLLGEH9Fs el shows the PDOSs of SiC layers and the right one those of Ti3SiC2 layers. The first layer is the atomic layer proximal to interface. The *E <sup>F</sup>* is set to zero [23].

!z 0\$!\*z,.!/!\*0! z%\*z%#^z Fcdzz,.+&!0! z+\*z /!(!0! z 0+)%z(5!./z+"z 0\$!z %%z%\*0!.¥ face. A key feature in this figure is that a strong interaction is observed between the subinterfacial Ti *d* and Si *p* states below Fermi level (*E <sup>F</sup>*), which continues well into SiC surface, inducing noticeable gap states in the interfacial C at *E <sup>F</sup>*. This means that the interfacial C (5!.z%/z)!0(%6! \_z%\* %0%2!z+"z,+//%(!z!(!0.%z+\* 10%2%05^z \*z"0\_z0\$!z#,z/00!/z\*z!4¥ tend as far as they can into deeper layers of SiC, as there appear weak but visible peaks at *E <sup>F</sup>* in the PDOSs of the 2nd and 3rdz(5!./z+"z%^z\$!.!"+.!\_zz(+(z3!'z)!0((%%05z)%#\$0z+¥ cur at top few layers of the semiconductor surface, which could enable current flow through the SiC. We also note significant hybridization between the interfacial C *sp* and Si *sp* states, suggestive of covalent bonding at interface.

Figure 4. Contour plots of charge densities for (a) SiSi and (b) SiCSi interfaces taken along (11-20) plane. The interface is represented by a horizontal line and the atoms that intersect the contour plane are labeled. Corresponding contour plots of charge-density differences for (c) SiSi and (d) SiCSi interfaces [23].

Figure 4 shows contour plots of charge densities and their differences along (11-20) plane for the optimized SiSi and SiCSi interfaces. We notice in Fig. 4(b) that the bonding interaction !03!!\*z%\*0!."%(z%z\* zz"+.z0\$!z%%z%\*0!."!z%/z.!).'(5z/%)%(.z0+z0\$!z%wz%\*0!.¥ tion deeper into SiC: the majority of charge is localized on C with humps directed towards their neighboring Si. We thus conclude that the interfacial bonding for the SiCSi is of mixed +2(!\*0w%+\*%z\*01.!^z\$!z%\*0!."%(z+\* /z"+.z0\$!z%%z%\*0!."!\_z\$+3!2!.\_z\$2!z+2(!\*0z\*¥ ture with a small amount of charge accumulated within the interfacial region (Fig. 4(a)). In addition, the amount of charge accumulated on the interfacial Si-Si bonds of SiSi (Fig. 4(c)) is far less significant than that on the interfacial Si-C bonds of SiCSi (Fig. 4(d)). This heaver charge accumulation in the case of SiCSi, together with its mixed covalent-ionic character at interface, accounts for the largest *W* ad associated with the SiCSi interface.

#### 2.3. Quantum electron transport properties

ly, very close to the experimental values. Therefore, the introduction of interfacial C monolayer

Calculations of *p*-type Schottky barrier height (SBH) reveal that the interface with C (0.60 eV) has much lower SBH than the interface without C (1.05 eV), suggesting that the trapped C assist the lowering of SBH. To shed light on origin of the decrease in SBH and junction strengthening in the SiCSi interface, we characterized thoroughly interfacial electronic states and bonding nature. Figure 3(a) shows a planar-averaged charge-density difference along interface normal, where there appears a more dramatic accumulation of charge within the interfacial region for the interface with C. This indicates that the covalent bonding is /0.!\*#0\$!\*! z%\*z0\$!z%%z/!^z \*z %0%+\*\_z3!z\*+0!z0\$0z0\$!z,(\*.w2!.#! z !\*/%05z %""!.¥ ence for the SiCSi more prominently deviates from zero around interface, reflecting more significant charge transfer between the SiC and Ti3SiC2 slabs. Moreover, charge is observed to be depleted noticeably in both the sub-interfacial SiC and Ti3SiC2 region for the SiCSi, suggesting that the atoms second nearest to the interface contribute to interfacial bonding. These missing charges, to a large extent, make their way onto the more electronegative C

Figure 3. a) Planar-averaged charge-density difference for the relaxed interfaces with and without C along [00018<As J=;LAGF: =FKALQG>KL9L=KHJGB=;L=<GFLGL@=9LGEA;D9Q=JK;DGK=LGL@=J=D9P=</A/AAFL=J>9;=0@=D=>L:GLLGEH9Fs el shows the PDOSs of SiC layers and the right one those of Ti3SiC2 layers. The first layer is the atomic layer proximal to

!z 0\$!\*z,.!/!\*0! z%\*z%#^z Fcdzz,.+&!0! z+\*z /!(!0! z 0+)%z(5!./z+"z 0\$!z %%z%\*0!.¥ face. A key feature in this figure is that a strong interaction is observed between the sub-

resolves the inconsistencies between simulations and experiments.

2.2. Electronic structure and bonding

156 Physics and Technology of Silicon Carbide Devices

ions, indicative of the formation of ionic bonding.

interface. The *E <sup>F</sup>* is set to zero [23].

Although the charge-distribution analysis can reveal valuable information on interfacial bonding, it provides restrained insight into how electrons distribute around *E <sup>F</sup>*\_z3\$%\$z)0¥ ters because density around *E <sup>F</sup>* directly determines the current transmission. Figure 5 %((1/¥ trates an electron-density isosurface and its slice along the (11-20) plane for the optimized SiCSi interface around *E <sup>F</sup>*. From Fig. 5(a), one can see that charges surrounding interfacial Si .!z+\*\*!0! z\* z.+ (5z %/0.%10! z%\*zz/\$!!0w(%'!z"/\$%+\*\_z3\$%\$z/1##!/0/z,+//%(!z!(!¥ trical conductivity through this region. In addition, there also appear heavily accumulated electrons within the interfacial area, which are connected along the interface and extended as far as several atomic layers into the SiC. These characters can also be confirmed from the /(%!z,(+0z%\*z%#^zHcd\_z)!\*%\*#z0\$0z1..!\*0z)%#\$0z"(+3z+2!.z0+,z"!3z0+)%z(5!./z+"z/!)%¥ conductor, thereby causing Ohmic property. As expected, the electron density at *E <sup>F</sup>* %/z!4¥ tremely high for the Ti3SiC2 (*i.e.*, sea of electrons) but becomes nil for the SiC layers away ".+)z%\*0!."!z c%#^z Hcdd\_z3\$%\$z \*z !z1\* !./0++ z ".+)z 0\$!%.z%\*0.%\*/%z)!0((%z \* z /!)%¥ conducting nature [25].

semi-infinite Ti electrodes are assumed to be the same as those of bulk Ti. On the other hand, the electronic states of scattering region are calculated self-consistently. The scattering region consists of hexagonal SiC and Ti3SiC2 layers and the periodic boundary conditions are imposed along the directions parallel to the interface. The SiC/Ti3SiC2 interface could be either the SiSi or SiCSi, whereas other interfaces are maintained identical for the sandwich systems. In this sense, the difference between the two systems can be mainly attributed to their differing SiC/Ti3SiC2 interfaces. Furthermore, we also calculated the Ti/SiC/Ti system,

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Figure 7. a) Transmission spectra under 0 V and (b) current-voltage characteristics for the sandwich systems involving the interfaces containing direct Si-Si bonding (SiSi), Si-C-Si bonding (SiCSi), and the direct contact of Ti to SiC (SiTi).

Figure 7(a) shows transmission spectra for the relaxed SiSi, SiCSi, and SiTi systems, where one can see that the spectra differ from one another suggesting variations in electronic /0.101.!/z3%0\$z%\*0!."!z#!+)!0.%!/^z\$!z)+/0z%\*0!.!/0%\*#z"!01.!z%/z0\$!z,.!/!\*!z+"z0.\*/¥ mission peaks at *E <sup>F</sup>* for the SiCSi, which is attributable to the electrons distributed around the interface at *E <sup>F</sup>*. Further calculations on electrical properties (*e.g.*, C curve) for 0\$!z 0\$.!!z/5/0!)/z.!2!(z 0\$0z 0\$!z1..!\*0z%\*z 0\$!z%%z/!z%\*.!/!/z)1\$z"/0!.z 0\$\*z!%¥ 0\$!.z0\$!z%%z+.z%%z/!z/z0\$!z,,(%! z%/z2+(0#!z%\*.!/!/zc%#^zJcdd\_z3\$%\$z\*z!z!4¥ plained by its lowest SBH. We further examined how applied bias voltages vary from the interface to the SiC region by analyzing the difference in effective potential along the cDDwECdz,(\*!z!03!!\*z0\$!z%/z2+(0#!z+"zC^Gzz\* z0\$!z+\*!z+"zC^Czz"+.z0\$!z.!(4! z/5/¥ 0!)^z\$!z2+(0#!z%/z"+1\* z0+z .+,z(!//z%\*0!\*/%2!(5z".+)z0\$!z%\*0!."!z0+z0\$!z%z%\*z0\$!z%¥ Si case, suggestive of less Schottky nature. Finally, in comparing the general trend of the calculated C with that of our experimental curve, we find that they agree qualitatively:

wherein the SiTi model was taken as the SiC/Ti interface.

Refer to Fig. 2 for their corresponding interfacial configurations [18].

Figure 5. a) Isosurface and (b) electron density plot along the (11-20) plane in the energy window (*EF*-0.5 eV, *EF*) for the SiCSi interface. The interface is marked by two arrows [18].

Figure 6. Schematic illustration of a two-probe Ti/Ti3SiC2/SiC/Ti3SiC20AIM9FLMELJ9FKHGJLKQKL=E0@=KQKL=E@9KAFs finite extent in the (*x*, *y*) direction and extends to ±g in the *z* direction. The SiC/Ti3SiC2 interfaces shown in Fig. 2 are adopted [18].

To examine electrical conductivity and gain insight into how the interface influences current transport, we devised a two-probe system [26], Ti/Ti3SiC2/SiC/Ti3SiC2/Ti, and investigated nonequilibrium quantum transport properties. Figure 6 schematically shows a model of the /\* 3%\$z 0.\*/,+.0z/5/0!)\_z3\$%\$z\*z!z %2% ! z%\*0+zz(!"0z/!)%w%\*"%\*%0!z!(!0.+ !\_zz/0¥ tering region, and a right semi-infinite electrode. The atomic and electronic structures of the semi-infinite Ti electrodes are assumed to be the same as those of bulk Ti. On the other hand, the electronic states of scattering region are calculated self-consistently. The scattering region consists of hexagonal SiC and Ti3SiC2 layers and the periodic boundary conditions are imposed along the directions parallel to the interface. The SiC/Ti3SiC2 interface could be either the SiSi or SiCSi, whereas other interfaces are maintained identical for the sandwich systems. In this sense, the difference between the two systems can be mainly attributed to their differing SiC/Ti3SiC2 interfaces. Furthermore, we also calculated the Ti/SiC/Ti system, wherein the SiTi model was taken as the SiC/Ti interface.

SiCSi interface around *E <sup>F</sup>*. From Fig. 5(a), one can see that charges surrounding interfacial Si .!z+\*\*!0! z\* z.+ (5z %/0.%10! z%\*zz/\$!!0w(%'!z"/\$%+\*\_z3\$%\$z/1##!/0/z,+//%(!z!(!¥ trical conductivity through this region. In addition, there also appear heavily accumulated electrons within the interfacial area, which are connected along the interface and extended as far as several atomic layers into the SiC. These characters can also be confirmed from the /(%!z,(+0z%\*z%#^zHcd\_z)!\*%\*#z0\$0z1..!\*0z)%#\$0z"(+3z+2!.z0+,z"!3z0+)%z(5!./z+"z/!)%¥ conductor, thereby causing Ohmic property. As expected, the electron density at *E <sup>F</sup>* %/z!4¥ tremely high for the Ti3SiC2 (*i.e.*, sea of electrons) but becomes nil for the SiC layers away ".+)z%\*0!."!z c%#^z Hcdd\_z3\$%\$z \*z !z1\* !./0++ z ".+)z 0\$!%.z%\*0.%\*/%z)!0((%z \* z /!)%¥

Figure 5. a) Isosurface and (b) electron density plot along the (11-20) plane in the energy window (*EF*-0.5 eV, *EF*) for

Figure 6. Schematic illustration of a two-probe Ti/Ti3SiC2/SiC/Ti3SiC20AIM9FLMELJ9FKHGJLKQKL=E0@=KQKL=E@9KAFs finite extent in the (*x*, *y*) direction and extends to ±g in the *z* direction. The SiC/Ti3SiC2 interfaces shown in Fig. 2 are

To examine electrical conductivity and gain insight into how the interface influences current transport, we devised a two-probe system [26], Ti/Ti3SiC2/SiC/Ti3SiC2/Ti, and investigated nonequilibrium quantum transport properties. Figure 6 schematically shows a model of the /\* 3%\$z 0.\*/,+.0z/5/0!)\_z3\$%\$z\*z!z %2% ! z%\*0+zz(!"0z/!)%w%\*"%\*%0!z!(!0.+ !\_zz/0¥ tering region, and a right semi-infinite electrode. The atomic and electronic structures of the

conducting nature [25].

158 Physics and Technology of Silicon Carbide Devices

adopted [18].

the SiCSi interface. The interface is marked by two arrows [18].

Figure 7. a) Transmission spectra under 0 V and (b) current-voltage characteristics for the sandwich systems involving the interfaces containing direct Si-Si bonding (SiSi), Si-C-Si bonding (SiCSi), and the direct contact of Ti to SiC (SiTi). Refer to Fig. 2 for their corresponding interfacial configurations [18].

Figure 7(a) shows transmission spectra for the relaxed SiSi, SiCSi, and SiTi systems, where one can see that the spectra differ from one another suggesting variations in electronic /0.101.!/z3%0\$z%\*0!."!z#!+)!0.%!/^z\$!z)+/0z%\*0!.!/0%\*#z"!01.!z%/z0\$!z,.!/!\*!z+"z0.\*/¥ mission peaks at *E <sup>F</sup>* for the SiCSi, which is attributable to the electrons distributed around the interface at *E <sup>F</sup>*. Further calculations on electrical properties (*e.g.*, C curve) for 0\$!z 0\$.!!z/5/0!)/z.!2!(z 0\$0z 0\$!z1..!\*0z%\*z 0\$!z%%z/!z%\*.!/!/z)1\$z"/0!.z 0\$\*z!%¥ 0\$!.z0\$!z%%z+.z%%z/!z/z0\$!z,,(%! z%/z2+(0#!z%\*.!/!/zc%#^zJcdd\_z3\$%\$z\*z!z!4¥ plained by its lowest SBH. We further examined how applied bias voltages vary from the interface to the SiC region by analyzing the difference in effective potential along the cDDwECdz,(\*!z!03!!\*z0\$!z%/z2+(0#!z+"zC^Gzz\* z0\$!z+\*!z+"zC^Czz"+.z0\$!z.!(4! z/5/¥ 0!)^z\$!z2+(0#!z%/z"+1\* z0+z .+,z(!//z%\*0!\*/%2!(5z".+)z0\$!z%\*0!."!z0+z0\$!z%z%\*z0\$!z%¥ Si case, suggestive of less Schottky nature. Finally, in comparing the general trend of the calculated C with that of our experimental curve, we find that they agree qualitatively: 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.

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

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

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

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>

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

0z0\$!zz,+%\*0z\* zz#,z%\*z0\$!z.!#%+\*z35z".+)z0\$!z.+//%\*#z,+%\*0zc%#^zEcdd^

.%((%+\*z6+\*!z2!.%"%!/z0\$0z0\$!z!.)%z/1."!z.+//¥

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161

;=Fs

light of energetics and atomic distances.

3.2. Formation of point Fermi surface

/!)%+\* 10+.^z \*/,!0%+\*z0\$.+1#\$+10z0\$!z-

L=J=<KMJJGMF<AF?L@=hHGAFL0@=*E* F position is aligned to zero [19].
