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.
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