We investigate the performance of monolithic copper-indium-gallium-selenide (CIGS)/perovskite tandem solar cells with two different CIGS bottom device absorbers: Cu(In,Ga)Se 2 or Cu(In,Ga)(S,Se) 2 and with three different hole-transporting layers (HTLs): NiO x + SAM, NiO x :Cu + SAM and SAM alone. NiO x (:Cu) is (2 wt% copper-doped) nickel oxide and SAM is the MeO-2PACz ([2-(3,6-dimethoxy-9H-carbazol-9-yl)ethyl]phosphonic acid) self-assembled monolayer. The CIGSe is fabricated by physical-vapor deposition (PVD), has a E g ∼ 1.06 e V, and a σ RMS,PVD ∼ 65 nm, while the CIGSSe is fabricated by rapid-thermal processing (RTP), has a E g ∼ 1.01 e V, and a σ RMS,RTP ∼ 120 nm. While the current certified, 24.2%-efficient, world-record monolithic CIGSe-perovskite tandem solar cell has previously been achieved with SAM as a stand-alone HTL, this work investigates whether SAM can yield similarly high efficiencies also on industrially compatible, very rough RTP CIGSSe absorbers. We find that the devices with SAM as stand-alone HTL suffer from severe FF and V oc losses and that NiO x :Cu is needed to act as a shunt-quenching layer below that SAM, ensuring conformal coverage of the rough bottom sub-cell surface. Within this work the highest-achieved (in-house measured) PCE s for the RTP and PVD CIGS-based tandems are 21.6% and 23.2% respectively, on a cell area of 1.08 cm2, both of which are obtained with NiO x :Cu + SAM as an HTL. • First >20%-efficient monolithic RTP CIGSSe-perovskite tandem on a cell area >1c m2. • RTP CIGSSe is industrially-compatible, but has a very high surface roughness >120 nm. • First integration of low-temperature sputtered NiO x :Cu in CIGSe-perovskite tandems. • NiO x :Cu acts as a shunt-quenching layer below a self-assembled monolayer (SAM). • NiO x :Cu + SAM enables 270 mV and 21.8% higher V oc and FF than the tandems with SAM. [ABSTRACT FROM AUTHOR]