1. Vin=high, Vout=0, Vx=Vdd-Vt3,
the charge storing in Cs and Cboot is Q1=(Vdd-Vt3)*(Cs+Cboot)
2. Vin=0, Q2=V*Cs+(Vx-Vout)*Cboot
3. cause charge conservation, so Q1=Q2
===> Vx=(Vdd-Vt3)+Vdd*Cboot/(Cs+Cboot)
===> if Cboot >> Cs
===> Vx=2Vdd-Vt3 ................. this is the name of bootstrapping.
4. Ics=ΔQcs/Δt = Cs*ΔVcs/Δt=Cs*[(Vx2-0)-(Vx1-0)]/Δt ≈Cs*Vdd/Δt
5.Icboot=ΔQboot/Δt =Cboot*ΔVboot/Δt=Cboot*[(Vx2-Vx1)-(Vx1-0)]/Δt =Cboot*Vt3/Δt
6. Ics≠Icboot ... different from ur result !??
am I wrong ?