We propose a cosmological survey to probe star formation and nuclear activity in galaxies at redshifts of z=2-4 by polycyclic aromatic hydrocarbon (PAH) features using the SPICA mid-infrared instrument (SMI) with a spectral resolution of R=20. We will cover a wavelength range of 20-36 μm that corresponds to z=2-4 for the PAH features (11.3, 7.7, and 6.2 μm). The sensitivity will be 1 X 10-19 W/m2 (5 σ) in case of a reference survey that covers 4 arcmin2 field in a one-hour observation. It corresponds to LIR=2 X 1011 L⊙ at z=3 and will give us more than 10000 galaxies in a 450 hour survey.