**4.1 Photoemission electron spectroscopy for workfunction determination**

The workfunctions of the TCPs were determined using photoemission electron spectroscopy. The photoemission electron yield *Y* is expressed as follows Kane (1962):

$$Y = \alpha (h\nu - E\_t)^n \tag{2}$$

where is a proportional constant, *h* is Planck's constant, is the frequency, *Et* is the threshold energy, and the value of *n* ranges from 1 to 5/2 depending on the system. For metallic materials, an *n* value of 2 is recommended, and the *Et* is consistent with the

Fig. 2. Schematic of TCP/epi.-GaN sample.

photoelectric workfunction. Thus, if we modify Eq. (2) to the following form (Eq. (2)′), we can determine *Et* by extrapolating the linear portion of a Y1/2 vs. *h* plot:

$$Y^{1/2} = \alpha (l\nu - \mathcal{E}\_t) \,. \tag{2}$$

We employed a photoemission yield spectrometer (AC-3, Riken Keiki Co., Ltd.) to determine the workfunctions of the TCPs. The sample, which was prepared as described in section 3.1, was installed in the spectrometer and the photoemission yield was measured in air.
