*3.2. Determination of Schottky Barrier Height*

Based on the Thermionic Field Emission (TFE) model [21], Equation (10) can be used to determine the Schottky barrier height *φB*, where *k* describes the Boltzmann constant, *h* the Planck constant, *m*∗ the effective tunneling mass (here 0.91 electron masses [22–24]), *ǫ*<sup>0</sup> the vacuum permittivity and *ǫ<sup>S</sup>* the relative permittivity of 4H-SiC (here 9.7 [4,22,23]).

$$\rho\_{\mathbb{C},TFE} \propto \frac{q\phi\_B}{E\_{00}\coth\left(\frac{E\_{00}}{kT}\right)}\text{ with }E\_{00} = \frac{qh}{2\pi}\sqrt{\frac{p}{m^\*\epsilon\_0\varepsilon\_S}}\tag{10}$$

The Schottky barrier height *φ<sup>B</sup>* itself can be calculated by Equation (11), where *E<sup>g</sup>* describes the bandgap of the semiconductor, *φ<sup>M</sup>* the metal workfunction of the ohmic contact material, *χ<sup>S</sup>* the electron affinity of the semiconductor and *V<sup>i</sup>* the built-in voltage [21,25]. It can be seen that the Schottky barrier height decreases slightly with increasing *N* − *A* .

$$\phi\_B = \frac{E\_g}{q} - (\phi\_M - \chi\_S) - \sqrt[4]{\frac{q^3 N\_A^- V\_i}{8\pi^2 \epsilon\_0^3 \epsilon\_S^3}} \tag{11}$$

Figure 2a shows the normalized average specific contact resistances of all sets of samples with an implanted Al surface concentration of 5 <sup>×</sup> <sup>10</sup><sup>19</sup> cm−<sup>3</sup> . It can be observed that all sets of samples show quite similar temperature dependent behavior despite different absolute values of the specific contact resistances (see inset of Figure 2a) and despite the deviation of sample B at temperatures higher than 375 K (indicated by the open red squares). The origin of these deviations is not fully understood. Therefore, these values are not used further.

) Normalized average specific co ∇ re indicated with Δ **Figure 2.** (**a**) Normalized average specific contact resistance (**b**) Determined Schottky barrier heights form this work and literature. Ohmic contacts from literature fabricated on epitaxial regions are indicated with ∇ ([3,4,6,10,11,24]), ohmic contacts from literature fabricated on implanted regions are indicated with ∆ ([22,23,26,27]).

−2 By fitting the theoretical specific contact resistance to the measured ones, the Schottky barrier heights *φ<sup>B</sup>* were determined (see Equation (10)). Figure 2b shows the determined Schottky barrier heights from this work and compares them with Schottky barrier heights known from literature. It can be seen that the determined Schottky barrier heights increase with increasing Al surface concentration, which is in contrast to the theoretically predicted decreasing of the Schottky barrier height with increasing Al surface concentration (see Equation (11)).

−3 −3 In order to investigate this contradiction Secondary Ion Mass Spectrometry (SIMS) analyses were carefully done at the 4H-SiC/Ti3SiC2-interface of sample A by using a CAMECA IMS SC Ultra SIMS tool which allows a sub-nm resolution [28,29]. The sub-nm depth resolution was achieved for O2+ primary ions with an impact energy of 250 eV. The

Al concentration was calibrated using a reference sample consisting of a SiC substrate implanted with Al ions with an energy of 100 keV and a dose of 10<sup>14</sup> cm−<sup>2</sup> .

−3 −3

−2

) Normalized average specific co

∇

re indicated with Δ

Figure 3a shows the measured Al concentration, the measured Ti and Si counts per second (CPS) as well as the implanted Al profile. While no Al could be detected in the Ti3SiC<sup>2</sup> layer, the Al concentration at the 4H-SiC-Ti3SiC2-interface is significantly increased. This additional Al concentration decreases within approx. 3 nm from a peak concentration of approx. 10<sup>21</sup> cm−<sup>3</sup> to the implanted Al concentration (5 <sup>×</sup> <sup>10</sup><sup>19</sup> cm−<sup>3</sup> ). Furthermore no significant amount of Ti could be detected in the 4H-SiC layer. 

**Figure 3.** (**a**) Measured SIMS profiles of Al, Ti and Si on the Ti3SiC<sup>2</sup> -SiC interface (**b**) Approximation of the measured Al profile.

This increase of the Al concentration can be explained by a diffusion of Al during Ti3SiC<sup>2</sup> formation. The total resulting Al profile can be approximated by the superposition of the implanted Al profile *NAl*,*impl*. and the increase of the Al concentration at the 4H-SiC/Ti3SiC2-interface. Equation (12) describes this superposition by using the implanted Al profile *NAl*,*impl*. , the diffused Al dose during high temperature annealing *NAl*,*dose* and the associated diffusion length *LAl*,*di f f* [25]. Figure 3b shows the approximation as well as the associated parameters. It can be seen, that the approximation fits very well with the measured data.

$$N\_{Al}(\mathbf{x}) = N\_{Al,impl.}(\mathbf{x}) + \frac{2}{L\_{Al,diff}\sqrt{\pi}} \exp\left(-\frac{\mathbf{x}^2}{L\_{Al,diff}^2}\right) \tag{12}$$
