We have designed a diffusion-engineered, singlephoton spectrometer in the optical-UV range using a superconducting tunnel junction. The optical photon is absorbed in a Ta film and creates excess quasiparticles. These trap into an Al tunnel junction. Internal charge multiplication is achieved with backtunneling, which occurs when the residence time of the quasiparticles near the junction is longer than the tunneling time. The collected charge is a multiple of the initially created charge. We implement backtunneling by geometrically constricting the outflow of quasiparticles, with a narrow lead. The outdiffusion time is set by the geometry of the narrow lead. Our geometry optimizes the energy resolution and count rate, while reducing the heating and noise seen with much longer confinement time. Long confinement times produce excess heating and noise, as we observed previously with quasiparticle confinement achieved via bandgap engineering.