Direct Observation of Dopant Atom Diffusion in a Bulk Semiconductor Crystal Enhanced by a Large Size Mismatch

Diffusion is one of the fundamental processes that govern the structure, processing, and properties of materials and it plays a crucial role in determining device lifetimes. However, direct observations of diffusion processes have been elusive and limited only to the surfaces of materials. Here we use an aberration-corrected electron microscope to locally excite and directly image the diffusion of single Ce and Mn dopants inside bulk wurtzite-type AlN single crystals, identifying correlated vacancy-dopant and interstitial-dopant kick-out mechanisms. Using a 200 kV electron beam to supply energy, we observe a higher frequency of dopant jumps for the larger and heavier Ce atoms than the smaller Mn atoms. These observations confirm density-functional-theory-based predictions of a decrease in diffusion barrier for large substitutional atoms. The results show that combining depth sensitive microscopy with theoretical calculations represents a new methodology to investigate diffusion mechanisms, not restricted to surface phenomena, but within bulk materials.

Figure 1

Selected frames from a sequence of 30 $Z$-contrast images of a $w$-AlN single crystal doped with Ce viewed along the $[11\overline{2}0]$ axis. (a)–(g) Frames 1, 4, 5, 6, 10, 16, 20, respectively, show the locations of a single Ce dopant as marked by the arrowhead in each panel. (h) Frame-averaged $Z$-contrast image. The observed Ce trace is overlaid and the Ce positions in each panel (a)–(g) are indicated. The scale bar in (a) is 3 Å.

Figure 2

The Ce dopant diffusion paths in $w$-AlN (top panels) and the diffusion energy surfaces (bottom panels). (a) Basal-plane diffusion (Al: red, N: blue, and Ce: light blue), (b) pyramidal-plane diffusion (Ce: light green), (c) interstitial diffusion with kick-out mechanism (Ce: yellow, Al interstitial: pink), with the interstitial dopant, substitutional dopant and self-interstitial defects labeled $X_i$, $X_s$, and $I$, respectively. The starting point is not at zero because an interstitial Al is more stable than an interstitial Ce.

Figure 3

Activation energies for Ce pyramidal-plane diffusion via the vacancy-mediated mechanism as a function of volumetric strain. The Ce diffusion barrier increases with increasing volume.

Figure 4

Frame-averaged $Z$-contrast images of Mn-doped $w$-AlN single crystals. The brightest atomic columns in each panel are the location of single Mn dopants as marked by arrowheads in each panel. The scale bars are 3 Å. The crystal orientations are (a) $[11\overline{2}0]$, (b) $[1\overline{1}00]$, (c) [0001] with the corresponding structural models given in (d)–(f), respectively.