I don't believe that anyone will use blind and burried vias in a 4-layer PCB after considering costs and possible alternatives. Before claiming a specific implementation you should specify your design requirements.
A PCB stackup will be designed from available substrates and prepregs acting as a construction kit. Everything > 0.4-0.5 mm (e.g. 200 µ core + 70 µ prepregs) should be feasible.
Blind and buried on a 4 layer!!!!!
The thickness of the board would depend on the mechanical requirements, best sort them out first then once a thickness is determined talk to the PCB manufacturer about materials.
I don't believe that anyone will use blind and burried vias in a 4-layer PCB after considering costs and possible alternatives. Before claiming a specific implementation you should specify your design requirements.
A PCB stackup will be designed from available substrates and prepregs acting as a construction kit. Everything > 0.4-0.5 mm (e.g. 200 µ core + 70 µ prepregs) should be feasible.
The stated design requirement is 0.4mm, one side of the board has electrodes to the outside world and on the other side of the board opposite the electrodes numerous high density IC's that will require vias. I can probably get away with a combination of blind and through hole vias.
I think your questions have been basically answered, otherwise please elaborate it.
Don't want to keep harping about usefulness of burried vias for a four layer design. It's of course "possible". Ask your favourite PCB manufacturer for the conditions.
The design sounds like it will be a full HDI design (sequential build up, with microvias), I have done similar designs for sensors for automotive designs. Microvias from L1 to L2; L4 to L3 and blind vias between L3 and L4, usually 6 layers are used so you can isolate one side from the other better and have more room for routes.