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The relation between the stellar mass and the star formation ratecharacterizes how the instantaneous star formation is determined by the galaxypast star formation history and by the growth of the dark matter structures. Wedeconstruct the M-SFR plane by measuring the specific SFR functions in severalstellar mass bins from z=0.2 out to z=1.4. Our analysis is primary based on aMIPS 24$\mu m$ selected catalogue combining the COSMOS and GOODS surveys. Weestimate the SFR by combining mid- and far-infrared data for 20500 galaxies.The sSFR functions are derived in four stellar mass bins within the range9.5<log(M/Msun)<11.5. First, we demonstrate the importance of taking intoaccount selection effects when studying the M-SFR relation. Secondly, we find amass-dependent evolution of the median sSFR with redshift varying as $sSFR\propto (1+z)^{b}$, with $b$ increasing from $b=2.88$ to $b=3.78$ between$M=10^{9.75}Msun$ and $M=10^{11.1}Msun$, respectively. At low masses, thisevolution is consistent with the cosmological accretion rate and predictionsfrom semi-analytical models (SAM). This agreement breaks down for more massivegalaxies showing the need for a more comprehensive description of thestar-formation history in massive galaxies. Third, we obtain that the shape ofthe sSFR function is invariant with time at z<1.4 but depends on the mass. Weobserve a broadening of the sSFR function ranging from 0.28 dex at$M=10^{9.75}Msun$ to 0.46 dex at $M=10^{11.1}Msun$. Such increase in thescatter of the M-SFR relation suggests an increasing diversity of SFHs as thestellar mass increases. Finally, we find a gradual decline of the sSFR withmass as $log(sSFR) \propto -0.17M$. We discuss the numerous physical processes,as gas exhaustion in hot gas halos or secular evolution, which can graduallyreduce the sSFR and increase the SFH diversity.

Evolution of the specific Star Formation Rate Function at z<1.4 - Dissecting the mass-SFR plane in COSMOS and GOODS