Nanowire Solar Cell 2D: Radial-Junction Light Trapping

Nanowire Array Geometry

Wire radius r 60 nm

Array height L 4.0 µm

Diffusion length L_D 200 nm

Packing fill fraction 0.35

Live Performance

Light absorbed A

Carrier collection η

Estimated J_sc (relative)

0 mA/cm²

Why it works: absorption depends on the wire's length L (light travels down the long axis — see the side-on panel), while carrier collection depends only on the wire's radius r (carriers only need to diffuse sideways to the shell junction — see the top-down panel). A tall, thin wire can absorb like a thick planar cell yet collect like an ultra-thin one.

How it works

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 (top panel: side-on cross-section), while photogenerated electron–hole pairs only travel radially to the shell, a distance bounded by the wire radius r ≪ L (top panel: top-down view — drag to pan, scroll to zoom).

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 L_D — 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, see the bottom-right curve): 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.

Fixed from the 3D original: the light-trapping factor F_LT is a function of the fill fraction (0–1), peaked near 0.42. The source engine fed it the raw slider value (10–90) instead of the fraction (10–90 ÷ 100), so F_LT silently evaluated to ≈1 everywhere and the "packing peaks light trapping" claim never actually showed up on screen. This build divides by 100 first — verified numerically before shipping (fLT(35 raw) ≈ 1.00 vs fLT(0.35 fraction) ≈ 8.43) — so the curve panel below now really shows the peak.

drag / scroll top-down panel to pan & zoom

Incoming photon Electron (collected) Hole (recombined / lost)

Absorbed: 0
Collected: 0
Recombined: 0