Lateral epitaxial heterojunctions in single nanowires fabricated by masked cation exchange

Cation exchange is a versatile tool to control the composition of nanocrystals, and recently deterministic patterning could be achieved by combining it with lithography techniques. Regarding single nanocrystal structures, such spatial control of cation exchange enables the design of heterostructures, which can be integrated in functional optoelectronic elements. In this work, we fabricate nanowire CdSe/Cu2Se heterojunctions by masking cation exchange via electron-beam irradiation, such that cation exchange proceeds only in the non-irradiated sections. Interestingly, the heterojunction interfaces are almost atomically sharp, and the adjacent CdSe and Cu2Se domains exhibit epitaxial relationships. We show that the cation exchange at the CdSe/Cu2Se interface is only possible if the displaced Cd2+ ions can radially out-diffuse to the solution phase. If this exit pathway is blocked, the cation exchange cannot occur. Our technique allows one to transform already contacted single nanowires, and the obtained heterojunction nanowires manifest a noticeable gain in conductance.


Supplementary Notes 2: CE experiments with varying cation concentration.
We have performed CE experiments with varying cation concentration to obtain data for the initial process. These experiments have been carried out in solution by adding different amount of Cu + ions. We divide our data in two regimes with low (1) and high (2) Cu + concentration. A detailed HRTEM and STEM-EDS analysis gave the following results: (1) Cu + /Cd 2+ =0.5 to 1: In some of the wires, only a very small amount of Cu + is found distributed all along the wire (Supplementary Figure 3 (a)). For other wires, completely exchanged segments were observed (Supplementary Figure 3 (b, c)); (2) Cu + /Cd 2+ =2 to 4: all the wires were exchanged (Supplementary Figure 3 (d)).
The above results indicate that the transformation in the non-irradiated regions takes place in a way that a short Cu 2 Se section quickly forms and then it expands throughout the whole wire.

Supplementary Notes 3: X-Ray Photoelectron Spectroscopy on Cu 2 Se NWs
X-ray photoelectron spectroscopy (XPS) was performed on (not masked) NWs right after cationexchange ( Supplementary Figure 4a,b) and after exposure to air for 24h (Supplementary Figure  4c,d). After cation-exchange, quantitative analysis gives a Cu:Se ratio of 2.0:1, which suggests that cation-exchange yields fully stoichiometric Cu 2 Se NWs. As expected, the Cu 2p spectrum ( Supplementary Fig. 4a) presents only two peaks for Cu 2p 3/2 and Cu 2p 1/2 at binding energies BE = 932.6 eV +/-0.1 eV and BE = 952.4 eV +/-0.1 eV, typical of Cu(I). 1 The oxidation state of +1 is also confirmed by X-ray-excited Auger Electron Spectroscopy (XAES; Supplementary Fig. 5). Likewise, Se 3d spectrum ( Supplementary Fig. 4b) can be fitted with Se 3d 5/2 and Se 3d 3/2 at BE = 54.0 eV +/-0.1 eV and BE = 54.9 eV +/-0.1 eV typical of Se -2 in Cu 2 Se. 1 We also note a slight contribution from SeO x species at higher BE. As has also been noted by others, 1  First principles calculations were performed using the generalized gradient approximation with PBEsol exchange correlation functional, 3 as implemented in the Quantum Espresso (QE) package. 4 We employed the PAW formalism 5 and datasets 8 available on the website www.quantumespresso.org (Supplementary Table 1).
The Nudged Elastic Band (NEB) calculations to determine the diffusion energy barriers were performed using the neb.x program from the QE package. For CdSe, we used 72-ion supercells composed of 3x3x2 four-atom CdSe unit cells, with a single Cu impurity. The Gamma point branch of the algorithms was used. The energy cutoff was chosen to be 30 Ry. Unit cell vectors were fixed along the NEB to those corresponding to the full relaxation of the initial configuration. Twelve images including the initial and the final ones were used to sample the NEB. The threshold of the force orthogonal to the path was set to 0.1 eV/A, and energy convergence threshold of 10 -8 Hartree was used. The variable elastic constants (k_min and k_max) between 0.2 and 0.3 Bohr were used and climbing image was on in all calculations.
In the estimation of the lower bound on the CE barrier we used a supercell containing the interface between antifluorite Cu2Se and sphalerite CdSe structures. A cubic supercell, shown in Supplementary Fig. 6, was used. It contains 32 Se, 32 Cu, and 19 Cd atoms, plus a Cu and a Cd impurity. The antifluorite and sphalerite structures were matched along the (111) plane of the conventional cubic unit cell, and the impurities were placed in a void in the middle layer of structure to mimick isolated impurities as well as possible. A 4x4x4 Gamma-centered k-point grid, an energy cutoff of 30 Ry and a Gaussian smearing of 0.01 Ry for Brillouin zone integration were used. We performed a full relaxation of the structures, preceded by volume optimizations, in both settings, until the total force on ions reached below 0.0015 Ry/Bohr.

b) Estimation of the diffusion barriers of Cu + in the wurtzite CdSe
First, we analyze the CE in the initial stage in the non-irradiated part of the nanowire, we compare the diffusion rates of Cu + cations in radial and axial directions of NW. The hexagonal c axis of CdSe structure is along the axis of the NW.
We determine the diffusion rate of the impurity according to the transition state theory 6 , that gives an Arrhenius-like dependence of the reaction rate on the free energy difference between the initial configuration and the transition state, defined as the saddle point on the reaction path. Within this scheme, the particle follows the so-called minimum energy path (MEP), which can be defined as a union of steepest descent paths from the saddle point to the minima. The MEP has the property that any point on the path is at an energy minimum in all directions perpendicular to the path 7 . This allows a systematic search for the MEP. We used the Nudged Elastic Band Method 7 implemented in the neb.x program within the Quantum Espresso package to compute the MEP and the reaction rates. S6 In our quest for the local minima representing metastable states involved in diffusion, we identify two interstitial equilibrium positions: A: the impurity lies in the middle of the hexagonal ring in the Cartesian XZ and YZ planes, B: the impurity lies in the middle of the hexagonal ring in the Cartesian XY plane.
There are three possible different diffusion paths in each direction, namely AA, BB and ABAB. We find that the lowest energy diffusion paths for the Cu+ cation link the A and B positions. Through the lowest energy diffusion in radial direction, the lowest energy barrier is 170 meV (labelled as AB). Through the axial direction, we find that the lowest energy barrier is 350 meV (labelled as AB2). The latter is about 2 times larger than the former, so the radial diffusion is roughly 8 times faster than the axial. In addition, we identify two more diffusion paths in axial direction, connecting adjacent A (axial AA) and B points (axial BB). See Supplementary Figure 6

Supplementary Notes 5: Band scheme of Cu 2-x Se/CdSe heterojunction
We have performed Ultraviolet Photoelectron Spectroscopy (UPS) on the original CdSe NWS, as well as on the cation-exchanged, and oxidized, Cu 2-x Se NWs. This technique allows to determine the energy difference between vacuum and Fermi level, and between the valence band and Fermi level. We note that due to the soft increase in signal in (b) the evaluation of the valence band to Fermi energy difference is less precise. This is a well-known limitation of this technique, as for example reported in Supplementary ref. 9.