Optical Properties of Strained Wurtzite Gallium Phosphide Nanowires

Wurtzite gallium phosphide (WZ GaP) has been predicted to exhibit a direct bandgap in the green spectral range. Optical transitions, however, are only weakly allowed by the symmetry of the bands. While efficient luminescence has been experimentally shown, the nature of the transitions is not yet clear. Here we apply tensile strain up to 6% and investigate the evolution of the photoluminescence (PL) spectrum of WZ GaP nanowires (NWs). The pressure and polarization dependence of the emission together with a theoretical analysis of strain effects is employed to establish the nature and symmetry of the transitions. We identify the emission lines to be related to localized states with significant admixture of Γ7c symmetry and not exclusively related to the Γ8c conduction band minimum (CBM). The results emphasize the importance of strongly bound state-related emission in the pseudodirect semiconductor WZ GaP and contribute significantly to the understanding of the optoelectronic properties of this novel material.

NW and place it in the specimen area of the device. Subsequently, NWs were clamped mechanically using electron beam induced deposition of Platinum on both ends of the NW (see Fig.2a in the main text). The free NW length L 0 is typically 5-10um.The test stage is actuated via electrostatic comb drives and enables the application of purely uniaxial tensile strain to the NW. Voltage is applied only across the comb drive while both ends of the NW are grounded. The amount of tensile strain is directly monitored by observing the movement of an indicator cantilever. Mechanical amplification of the test stage movement enables the read-out of the indicator cantilever by means of a microscope and CCD camera. Details on the straining device can be found in ref 2 .

Computational methods:
The ground-state calculations of strained and unstrained wurtzite-GaP are performed using the density functional theory (DFT) as implemented in the Vienna ab initio Simulation Package (VASP). 3 The exchange-correlation (XC) functional is described within the local density approximation (LDA) applying the parametrization of Perdew and Zunger. 4 The Ga4s, Ga4p, Ga3d, P3s, and P4s electrons are treated as valence electrons. The pseudopotentials and wave functions in the core regions are described within the projector-augmented wave (PAW) method. 5 The electronic wave functions between the cores are expanded in plane waves up to a cutoff energy of 500 eV. The Brillouin zone (BZ) integrations are carried out on a Γ-centered 10x10x2 k-point mesh.
The energy gaps and interband distances derived from the eigenvalues of the Kohn-Sham equation of the DFT significantly underestimate the corresponding experimental values because of the missing excitation aspect. 6 In principle, one has to solve a quasiparticle problem. We solve it applying a recently developed approximate quasiparticle scheme, the so-called LDA-1/2 method 7,8 , which however gives reasonable excitation energies and guarantees the correct description of the energy variations with the polytype. This method also allows the natural inclusion of spin-orbit interaction, which is important to describe correctly the valence bands. Its computational effort is similar to that for the DFT-LDA method used in the ground-state calculations. The applicability and the success of the LDA-1/2 method have been demonstrated for all III-V compounds. [9][10][11] GaP doped with N atoms is modeled with a 108 atom wurtzite supercell where one P site is substituted by N. This corresponds to a nominal N doping concentration of 1.8%.
We consider a plane-wave kinetic energy cutoff of 400 eV and PAW pseudopotentials for N atom with valence electronic configuration of 2s2 2p3. The BZ integrations are carried out on a Γ-centered 8x8x1 k-point mesh. The atomic structures are optimized using the LDA functional until the energy and residual forces are smaller than 10-4eV and 0.01 eV/A, respectively. The quasiparticle corrections are also taken into account to simulate the excitation effects. 7,8 Optical characterization: Optical characterization was performed in a low-temperature micro-photoluminescence setup. Details on the optical setup can be found in ref 1 .
The nanotensile testing device was mounted on the cryostat coldfinger and wired to enable the electrostatic actuation. Spectra were collected at 4K in the backscattering geometry, using continuous wave excitation at 405nm or pulsed excitation at 420nm.
Typical excitation power densities were on the order of 0.1-1kW/cm 2 . The excitation spot was either focussed to a diameter of ~1um or elongated along the NW axis by a cylindrical lens in the excitation path.
PL spectra up to 6% strain: Supp. Fig. 1: WZ GaP emission under uniaxial tensile strain. Evolution of the emission spectrum with uniaxial tensile strain up to 6%. The lines α, γ, X, and D are indicated. For the specific NW shown here, an additional line D appears that is proposed to be defect-related.

Reproducibility:
To show the reproducibility of the PL shift, the NW emission was evaluated during several load cycles (see Supp. Fig.2). No hysteretic behavior was found.

Phonon shift:
The energy separation between the α-line and its TO/LO phonon replica was determined from fits to the spectra. Supp. Fig. 3 shows the relative shift of the phonon energy as a function of strain. A linear fit to the data yields a strain rate of -163±7rel.cm -

Electric field along the NW:
To estimate the effect of an electric field, PL spectra were recorded as a function of bias voltage along an unstrained NW (see Supp. Fig. 4). The shift in energy we observed was smaller than 1meV. FWHM is found to increase with field, in agreement with the tendency of exciton emission to broaden upon dissociation in an electric field. 13 The γline suffers remarkably more from broadening than the α-line. The γ-line intensity also quenches at a field of 60-100kV/cm. Integrated intensity for the α-line is less affected by the electric field and the ionization field of α is extrapolated to 450kV/cm. The maximum shift in emission energy before quenching of all lines is extrapolated to <50meV.
The ionization field of an exciton is defined as ξ=E x /a x , with E x the exciton binding energy and a x the exciton Bohr radius. 14

Intensity and width:
Integrated intensities of the lines are shown in Supp. Fig. 5a. The intensities are normalized to the value at 0% strain. Intensity is scattering over a broad range, even for multiple load-cycles on the same wire. Since each measurement is done on a single NW, alignment and stability of the excitation on the wire are the main sources for the observed scatter in intensity. Nevertheless it is evident that the intensity of the γ-line is decaying fast with strain. The bandfilling continuum also quenches at low strain levels around 1%. Due to the spectral shape of the continuum and its cut-off at the γ-line, though, we cannot unambiguously distinguish between a reduction in intensity and a shift towards higher energy.
While each of the line widths exhibits a different strain-slope (Supp. Fig. 5b), the strain dependence of the line energies is similar for all the lines. Thus, broadening due to inhomogeneous strain distribution in the wires can be excluded, since it would affect all lines equally. The α-line is only weakly affected by broadening and intensity quench, while the γ-line is seriously quenched and broadened with strain. To explain the significant broadening, we can speculate that the γ-line is actually composed of a multitude of overlapping lines with slightly different pressure coefficients. 15 Also an unscreened piezoelectric field might lead to broadening and quench of a weakly bound exciton emission 14,16 . Interestingly, the γand X-line exhibit opposing trends in width.
While the γ-line is broadening with strain, the X-line decreases in width.

Excitation power:
Excitation power dependent characterization was performed using a pulsed laser source (repetition rate 80MHz) at 420nm. From fits of the data according to a power law I PL =const.*P exc k , we extract exponents k=1.1-2 (see Supp. Fig. 5c). At low and intermediate excitation densities, PL intensity scales linear to quadratic with excitation power, indicating direct excitonic transitions α, γ and X. The exponents for the X-line transition are slightly higher than for α and γ. Still the exponents for all lines are within the borders 1<k<2 for direct excitonic emission. 17 The slope at lower excitation densities is not significantly altered by strain, thus excitonic properties are maintained under strain. At higher excitation power, the PL intensity clearly saturates for the α transition.
The saturation gives evidence on the origin of the transition being related to states with a finite volume density. 18 The intensity level at which saturation appears varies from wire to wire, indicating a spread in the density of the respective states. For the γand X-line typically no saturation is observed pointing towards a high density of the associated level.