Electrostatic Potentials at Cu(In,Ga)${\mathrm{Se}}_2$ Grain Boundaries: Experiment and Simulations

In the present Letter, we report on a combined ab initio density functional theory calculation, multislice simulation, and electron holography study, performed on a $\Sigma 9$ grain boundary (GB) in a ${\mathrm{CuGaSe}}_2$ bicrystal, which exhibits a lower symmetry compared with highly symmetric $\Sigma 3$ GBs. We find an electrostatic potential well at the $\Sigma 9$ GB of 0.8 V in depth and 1.3 nm in width, which in comparison with results from $\Sigma 3$ and random GBs exhibits the trend of increasing potential-well depths with lower symmetry. The presence of this potential well at the $\Sigma 9$ GB can be explained conclusively by a reduced density of atoms at the GB. Considering experimental limitations in resolution, we demonstrate quantitative agreement of experiment and theory.

Figure 1

(a) BFTEM image of a $\Sigma 9$ GB in a CGSe bicrystal and (b) corresponding gray-value map of the phase of the object wave function. (c) Measured line profile of differences in the electrostatic potential, extracted from the white box in the phase map. The electrostatic potential in the grain interior was chosen as the zero point.

Figure 2

(a) Crystal model of the CGSe $\Sigma 9$ GB cores after ab initio DFT calculations. (b) Calculated electrostatic potential profile by ab initio DFT calculations across the GB cores. (c) Potential profile from multislice simulations on the fully relaxed crystal model in (a).

Figure 3

(a) Multislice-simulated, electrostatic potential profile from Fig. 2c after application of a fast Fourier transform low-pass filter, corresponding to the objective aperture size during TEM image acquisition. (b) Multislice-simulated, electrostatic potential profiles across the anion and cation GB cores after a tilt of 1.5°, and the measured potential profile from Fig. 1c.