Fig. 1. (a) Schematic diagram of field-assisted GaN nanowire array cathodes and (b) geometry structure diagram of two-dimensional field-assisted GaN NWAs cathode (H, d, L, hv, β are respectively wire height, width, distance, and the energy and angle of incident photons. J-side, J-substrate, J-top are the effective emission current density for sides, substrate and top, respectively).

Fig. 2. (a) Model diagram of field-assisted exponential-doping GaN nanowires; (b) Left: the band structure of the nanowires in the x-z direction. Right: the band structure of the nanowires in the x-y direction. EC is the minimum value of the conduction band, EV is the maximum value of the valence band, Evac is the vacuum level, EF is the Fermi level, Eg(z) is the band gap that varies along the z-axis; (c) Upper: carrier concentration of the nanowire in the x-z direction. Lower: carrier concentration of the nanowire in the x-y direction. From left to right: no built-in or external electric field, built-in electric field, external electric field, internal and external electric field; (d) Total QE curve. The illustration is the QE of the top surface of the nanowire. The conditions are: d = 200 nm, H = 400 nm, θ = 0°, Eex=1V/μm.

Fig. 3. Quantum efficiency curves for uniform-doping and exponential-doping GaN nanowire photocathodes with/without field-assistance as a function of (a) wire width, (b) wire height, and (d) incident angle. The QEs of uniform-doping and exponential-doping nanowires without external electric field are expressed as Qu, Qe, the QEs of field-assisted uniform-doping and the exponential-doping nanowires are represented as QE, Qe+E. The QEs at the top surface of the nanowires are denoted as Qu-top, Qe-top, QE-top, Qe+E-top, respectively. (c) Model diagram of field-assisted exponential-doping GaN nanowire photocathodes at different incident angles. The fixing conditions are: Eex = 1 V/μm, and λ = 263.98 nm.

Fig. 4. (a) Model diagram of GaN NWAs under oblique incident beam; (b) Total QE curve. The illustration is the QE of the top surface of NWAs; (c) Upper: carrier concentration of NWAs in the x-z direction. Lower: carrier concentration of NWAs in the x-y direction. From left to right: no built-in or external electric field, built-in electric field, external electric field, internal and external electric field. The conditions are: d = 200 nm, H = 400 nm, L = 400 nm, θ = 20°, Eex=0.5V/μm.

Fig. 5. (a) Three different incident light conditions for an exponential-doping GaN NWAs; (b) The QE and CE of field-assisted exponential-doping NWAs as a function of field intensity at different incident angles. Top: quantum efficiency, bottom: collection efficiency; (c) The trajectory of the exiting electrons of the field-assisted exponential-doping GaN NWAs. Upper: side surface of the nanowire, lower: substrate. The conditions are: d = 200 nm, H = 400 nm, L = 400 nm, λ = 263.98 nm.

Fig. 6. (a) Quantum efficiency and (b) collection efficiency of field-assisted exponential-doping GaN NWAs as a function of electric field intensity under different nanowire spacings. (c) The model of the carrier concentration of a field-assisted exponential-doping GaN NWAs at different nanowire spacings. (d) The QE and CE of the field-assisted exponential-doping GaN NWAs as a function of nanowire spacing. The conditions are: d = 200 nm, H = 400 nm, θ = 50°, and λ = 263.98 nm. Eex=0.5V/μm in (d).

Fig. 7. (a) Quantum efficiency and (b) collection efficiency of a field-assisted exponential-doping GaN NWAs photocathode at different doping concentration of top surface. The conditions are: d = 200 nm, H = 400 nm, L = 335.6 nm, θ = 50°, λ = 263.98 nm.