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The presence of $\beta$-Cu(In,Ga)$_3$Se$_5$ phase on Cu-poor Cu(In,Ga)Se$_2$ thin film surface could play an important role in the efficiencies of Cu(In,Ga)Se$_2$ thin film solar cells. The $\beta$-Cu(In,Ga)$_3$Se$_5$ with various thicknesses were deposited after a completion of the three-stage co-evaporation process of Cu(In,Ga)Se$_2$ films. The optical absorption measurement is used to obtain their optical band gap energies. The optical band gap energy of the $\beta$-Cu(In,Ga)$_3$Se$_5$ and Cu(In,Ga)Se$_2$ thin films, themselves, are 1.44 and 1.15 eV, respectively. The absorption edges of CIGS thin films with $\beta$-Cu(In,Ga)$_3$Se$_5$ layer shift towards shorter wavelengths. As a result, the band gap energy increases as the thickness of Cu(In,Ga)$_3$Se$_5$ increases. Likewise, the temperature-dependent and excitation power-dependent photoluminescence (PL) spectra for CIGS with various thicknesses of $\beta$-Cu(In,Ga)$_3$Se$_5$ are identified as donor-to-acceptor pairs (DAPs) and free (conduction band) -to-bound (acceptor) transitions. The higher PL transition energy is found with $\beta$-Cu(In,Ga)$_3$Se$_5$ less than 80 nm thick. These minimal defect layers results in larger band gap energy.