Formal definition of an empty stack accepting PDA PDA's are usually defined using the 7-tuple convention.

$M=(Q, \Sigma, \Gamma, \delta, q_{0}, Z, F)$

F is the set of accepting states. 

I want to design a PDA accepting by empty stack, so using this notation makes no sense, as I don't need F and I want to make the acceptance condition clear.

How is this usually done? Can I just dismiss F?

$M'=(Q, \Sigma, \Gamma, \delta, q_{0}, Z)$
When the stack is finished you can go to the specified state which shows the empty stack. In addition, when you reach in a state which you found it's a solution but the stack is not empty, iterate over a "pop" action to empty the stack and finally go the empty stack state. 

Hence, you can explain this PD using the defined notation.