How can we create a potential barrier? And how does it exactly acts as barrier in electron transfer?
By making a "step" in the potential energy. In the real world that usually means making a "sandwich" of 3 materials, the archtypical example being GaAs/AlGaAs/GaAs where the height of the barrier can be adjusted by varying the amount of aluminium in the middle layer.
This is how e.g. blue laser diodes are made.
Another option is to make a three terminal device where the middle terminal can be used as a gate; the height of the barrier is then set by adjusting the voltage applied to that gate.
Also instead of reflection (as we may think in classical mechanics) how does a particle pass through the barrier (the amplitude of wave actually decreases exponentially,how is this possible)?
In the real world that usually means making a "sandwich" of 3 materials