  We investigate the influence of the barrier thickness of
Co$_{40}$Fe$_{40}$B$_{20}$ based magnetic tunnel junctions on the laser-induced
tunnel magneto-Seebeck effect. Varying the barrier thickness from 1nm to 3nm,
we find a distinct maximum in the tunnel magneto-Seebeck effect for 2.6nm
barrier thickness. This maximum is independently measured for two barrier
materials, namely MgAl$_2$O$_4$ and MgO. Additionally, samples with an
MgAl$_2$O$_4$ barrier exhibit a high thermovoltage of more than 350$\mu$V in
comparison to 90$\mu$V for the MTJs with MgO barrier when heated with the
maximum laser power of 150mW. Our results allow for the fabrication of improved
stacks when dealing with temperature differences across magnetic tunnel
junctions for future applications in spin caloritronics, the emerging research
field that combines spintronics and themoelectrics.
