Hello,
there are some NFC micro-chips, 2mm x 2mm or 3mm x 3mm and I seek for a solution that would enable me to read those chips from a distance of approx. 10cm or at least 7cm.
I bought two ST's eval boards - ST25R3911B and NFC03A1 (1.4W and 250mW) and I wasn't even able to read the smaller chip, and the bigger one - I need to put it directly on the PCB antenna to get a proper readout.
I tried different antennas and also to tune slightly them on the ST25R3911B, but without success.

Is there a possibility to meet my expectations?

 

My first suggestion is to read the manufacturer's data sheets regarding the devices. The reality may not coincide with your expectations. And if you purchased them from amazon, the description may not have been correct, nor even slightly similar to the truth.

 

I know the limitations of the chips - up to 20mm, but I think that this is the matter of the powerful enough transmitter and enough sensitive receiver to be able to read from a longer distance. Or at least I think so.

 

know the limitations of the chips - up to 20mm

You want 10cm. If signal strength reduces with the square of the distance (I don't know if it does for those devices), then you might need a transmitter/receiver with 25 times the normal power/sensitivity.

 

Consider that a big part of the security provided by those tiny chips is a direct result of their very short range.