In a conventional planar solar cell the same distance must both absorb light (needs to be long) and let carriers reach the junction (needs to be short) — a direct trade-off. A vertical nanowire with a radial (core–shell) p–n junction breaks that link: photons travel axially down the wire of length L, while photogenerated electron–hole pairs only travel radially to the shell, a distance bounded by the wire radius r ≪ L.
Absorption (Beer–Lambert, axial path L):
A(L) = 1 − exp(−α_eff · L)
α_eff = α₀ · F_LT(fill) (light trapping from array scattering)
Carrier collection (radial diffusion, junction at r):
η(r, L_D) = 1 / (1 + (r / L_D)²)
Relative short-circuit current:
J_sc ∝ A(L) · η(r, L_D)
- Wire radius r — sets the radial distance minority carriers must diffuse to reach the shell junction; smaller r → higher collection η.
- Array height L — sets the axial optical path; taller wires absorb more of the weakly-absorbed red/near-IR tail of sunlight.
- Diffusion length LD — a material-quality knob (defect/trap density); low-quality material forgives only small r.
- Packing fill fraction — wire density in the array. Light trapping F_LT(fill) peaks at moderate packing (~0.35–0.45): too sparse and light passes through the gaps, too dense and the array reflects like a flat film.
This is the mechanism (radial-junction Si/III–V nanowire and nanopillar solar cells) used in real photovoltaic research to push thin, cheap absorbers past the efficiency ceiling that planar diffusion-length limits impose — the formulas above are a simplified teaching model, not a full drift-diffusion solve.