In Situ Spectroscopic Study of the Optomechanical Properties of Evaporating Field Ion Emitters

The possibility of measuring in situ operando photoluminescence spectroscopy within a photonic atom probe allows for the real-time study of the mechanical stress state within a field emitter either statically, as a function of the field-induced tensile stress, or dynamically, as a result of the evolution of the shape of the emitter upon its evaporation. Dynamic evolution results from the relaxation of strain induced by lattice mismatch and by the propagation of stress from the apex, while the morphology of the field emitter changes. Optomechanical information can be interpreted through the three-dimensional atomic scale images of the chemical composition of the emitter obtained through standard atom probe analysis. Here, the photoluminescence signal of a $\mathrm{Zn}\mathrm{O}/(\mathrm{Mg},\mathrm{Zn})\mathrm{O}$ quantum well allows for the local measurement of strain within the well and of the electrostatic field applied to the apex of the nanoscale field emitter.

Figure 1

Schematic representation of the experimental setup and analyzed system. Orientation of the crystal constituting the field emitter is also reported.

Figure 2

(a) Scanning electron micrograph of the tip under analysis. (b) Transmission electron micrograph and crystal orientation of a field emitter extracted from the $\mathrm{Zn}\mathrm{O}/(\mathrm{Mg},\mathrm{Zn})\mathrm{O}$ heterostructure system.

Figure 3

Atom probe tomography analysis. (a) Mass spectrum indicating the main ionic species. (b) Voltage curve and progressive number of detected atoms as a function of the index of the PL spectrum i_PL. (c) Three-dimensionally reconstructed volume of the analyzed field emitter. All $\mathrm{Mg}$ ions are reported in blue; 30% of ${\mathrm{Zn}}^{+}$ and ${\mathrm{Zn}}^{2+}$ ions are reported in red (both classes of detection events are traced with a 0.2 level of transparency). (d) Magnification of the distribution of $\mathrm{Zn}$ and $\mathrm{Mg}$ ions in a 5-nm-thick slice intersecting the axis of the tip at the depth of QW2, (e) II-site fraction map of the slice reported in (d). (f) Magnification of the distribution of $\mathrm{Zn}$ and $\mathrm{Mg}$ ions in a 5-nm-thick slice intersecting the axis of the tip at the depth of QW1. (g) Compositional map of the slice reported in (f). Arrow above the color scale indicates the average value of the $\mathrm{Mg}$ II-site fraction $⟨x_{\mathrm{Mg}}⟩=0.27$ of the $(\mathrm{Mg},\mathrm{Zn})\mathrm{O}$ barrier.

Figure 4

Photoluminescence of the analyzed field emitter during the initial bias ramp. Tip shape does not change, as no evaporation takes place. (a) PL spectra. Inset is a magnification of the QW1 luminescence. (b) Peak energies of emissions of the $(\mathrm{Mg},\mathrm{Zn})\mathrm{O}$ barrier (red squares) and QW1 (black circles) reported as a function of the voltage applied to the tip, V_dc.

Figure 5

(a) Slice extracted from the 3D reconstruction of the positions of $\mathrm{Mg}$ ions. Ions highlighted in orange correspond to those detected during acquisition of the PL spectrum indexed by i_PL. (Notably, only volumes collected during the 10th, 20th, 30th, etc. spectra are shown in this way and serve as a guide to the eye.) (b) Sequence of PL spectra acquired during evaporation of the field emitter. Red bar indicates the spectral region corresponding to the QW1 emission, i.e., to the magnification shown in (c). (d) PL energy of the $(\mathrm{Mg},\mathrm{Zn})\mathrm{O}$ barrier (red squares) and QW1 (black circles) as a function of the spectrum index i_PL.

Figure 6

Strain and stress effects on the exciton energies in $\mathrm{Zn}\mathrm{O}$. (a) Relationship between the in-plane strain tensors of a coherently strained $\mathrm{Zn}\mathrm{O}$ film epitaxially grown on the m plane and the energy shift of the lowest exciton level. Black line represents the strain state of a coherent m-plane $\mathrm{Zn}\mathrm{O}$ layer epitaxially grown on relaxed ${\mathrm{Mg}}_{x}Z{n}_{1-x}\mathrm{O}$ (x < 0.35). Red spot indicates the strain state calculated for the $\mathrm{Zn}\mathrm{O}$ QW contained within the field-emission tip. (b) Energy shifts of three $\mathrm{Zn}\mathrm{O}$ exciton bands as a function of uniaxial stress directed along the m direction $[1\overline{1}00]$. (c) Energy shift of three $\mathrm{Zn}\mathrm{O}$ exciton levels as a function of hydrostatic stress. Gray-shaded regions correspond to compressive stress, which is not applicable in the present experiment.

Figure 7

Strain-stress states related to lattice mismatch and their evolution in the field emitter containing the $\mathrm{Zn}\mathrm{O}/(\mathrm{Mg},\mathrm{Zn})\mathrm{O}$ heterostructure. Field emitter before evaporation: (a) scheme of the materials system, (b) components of the strain tensor, (c) components of the stress tensor and (d) expected shift of the lowest $\mathrm{Zn}\mathrm{O}$ exciton level. (e)–(h) correspond to (a)–(d) for the situation in which the apex of the field emitter is in close proximity to QW1 after partial evaporation. (i) Evolution of strain components at the center of QW1 as a function of the apex position. (h) Evolution of the stress components at the center of QW1 as a function of the apex position.

Figure 8

Energy shifts calculated as a function of the apex position in the evaporating field emitter. Blue dotted line corresponds to the shift related to lattice mismatch, neglecting the effect of the applied field. Red dashed line corresponds to the shift related to the applied bias, neglecting the effect of lattice mismatch. Black solid line corresponds to the shift resulting from the combined effect of lattice mismatch and applied bias.

Figure 9

Strain-stress states related to the application of an electric field at the apex and their evolution in the field emitter containing the $\mathrm{Zn}\mathrm{O}/(\mathrm{Mg},\mathrm{Zn})\mathrm{O}$ heterostructure. Apex stress is set at 1 GPa, while hydrostatic-uniaxial stress transition length L is set at L = 30 nm. Field emitter before evaporation: (a) scheme of the materials system, (b) components of the strain tensor, (c) components of the stress tensor, and (d) expected shift of the lowest $\mathrm{Zn}\mathrm{O}$ exciton level. (e)–(h) correspond to (a)–(d) for the situation in which the apex of the field emitter is in close proximity to QW1 after partial evaporation. (i) Evolution of the strain components at the center of QW1 as a function of apex position. (h) Evolution of the stress components at the center of QW1 as a function of apex position.

Figure 10

Comparison between calculated and experimental energy shifts. (a) Experimental and calculated PL energies during the voltage ramp as a function of applied bias V_dc and (b) as a function of apex position during field-emitter evaporation calculated for different apex stress levels and for a fixed hydrostatic-uniaxial stress transition length L = 150 nm. (c),(d) Same as in (a),(b), but calculations are performed for fixed apex stress σ_F = 1.25 GPa and varying values of L.