One-step fabrication of porous GaN crystal membrane and its application in energy storage

Single-crystal gallium nitride (GaN) membranes have great potential for a variety of applications. However, fabrication of single-crystalline GaN membranes remains a challenge owing to its chemical inertness and mechanical hardness. This study prepares large-area, free-standing, and single-crystalline porous GaN membranes using a one-step high-temperature annealing technique for the first time. A promising separation model is proposed through a comprehensive study that combines thermodynamic theories analysis and experiments. Porous GaN crystal membrane is processed into supercapacitors, which exhibit stable cycling life, high-rate capability, and ultrahigh power density, to complete proof-of-concept demonstration of new energy storage application. Our results contribute to the study of GaN crystal membranes into a new stage related to the elelctrochemical energy storage application.


GaN (s) → Ga(g) + (1-i)N+0.5iN2
(1) where the interaction parameter i varies from 0 to l, depending on the extent to which the nearest nitrogen atoms interact with one another at the instant of decomposition. The morphological reorganization or the corrosion of the GaN material will happen due to the decomposition. The hetero-epitaxy GaN films have high density dislocations, so the decomposition can occur at some dislocation sites to form small V shaped pits. The formation of V shaped pits can be explained by the Cabrera's thermodynamic theory. 2,3 The change in the free energy of V shaped pits on a perfect surface is given by where ΔGs is the change in the surface energy and ΔGv is the change in the volume energy.
In order to form a V shaped pit nucleus at a perfect surface, an energy should be given as where h is the depth of V shaped pits nucleus, γ is the edge free energy, rc is the size of the critical nucleus, Ω is the volume occupied by each atom and Δμ is the potential difference.
The free energy for a V shaped pit nucleation at a dislocation site, ΔGd, consists of the surfaceenergy term ΔGs, the volume-energy term ΔGv, and a dislocation-energy term Edisl. It may be expressed as The dislocation energy outside its core is given as Where G is the shear modulus, b is the Burgers vector of the dislocation, r0 is the radius of the dislocation core outside which the elastic continuum theory is valid, α=1/(1-v) for a clean dege dislocation and α=1 for a clean screw dislocation (where v is Poisson's ration).

Thus we have
ΔGd=ΔGs+ΔGv-(Gb 2 /4π) αln(r/r0) (6) The critical free energy for nucleation of a monomolecular V shaped pit at a dislocation is written as Where rF= αGb 2 /8π 2 γ is Frank's radius. According to these equations, it can be obtained that the ΔGd* is always smaller than ΔGp*. Therefore, the nucleation of V shaped pits occurs preferentially at dislocations.

S2. Characterization Methods
Scanning electron microscopy (SEM) images were taken with a Hitachi S-4800 field emission microscope equipped with a Horiba EX-450 energy-dispersive X-ray spectroscopy (EDS) attachment. The crystalline quality of single-crystal GaN mesoporous membranes (GaNMM) was characterized by high-resolution X-ray diffraction (HRXRD) that utilizes symmetrical (002) and asymmetrical (102)

S3. Electrochemical Tests
CV and GCD curves were collected at −0.55 V to 0.35 V against Hg/Hg2SO4 for the threeelectrode system and 0 V-0.9 V for the two-electrode system by varying the scan rate from 0.1 V s −1 to 100 V s -1 and current density from 1 mA cm -2 to 10 mA cm -2 , respectively.
Alternating current EIS spectra were collected within a frequency range of 10 -2 Hz-10