I think it is correct. You may want to make some simplifications: Vin = Vctrl = VCC C1 = C2 = ... = Cn If diodes are ideal (Vdn = 0) the open circuit charge pump voltage is

(N+1) Vcc

the current when

Vout = Vcc

is

Cn* f * Vcc

In the real case each stage has a diode forward voltage drop (Vcc -Vdn). This drop is often unacceptable in low voltage designs so alternative solutions are implemented.