How to analyze this voltage doubler circuitry?
Provided that \$R_1\$ is a pull-up connected to a voltage larger than \$V_{TH,N_2}+V_{D,N_2}\$, this circuit behaves as a charge pump.

At phase one (\$u_1=low\$), \$N_5\$ and \$N_6\$ are off, and \$N_2\$ is on. Hence the capacitor \$C_2\$ is charged to the potential connected to the drain side of \$N_2\$.

Once it is charged, \$u_1\$ can be pulled high (phase two). At this moment, \$N_5\$ and \$N_6\$ are conducting. \$N_5\$ ensures that \$N_2\$ is off, therefore the capacitor cannot discharge through it, and \$N_6\$ grounds one of the plates of the capacitor, forcing it to reverse its polarity and discharge towards the node \$N_3\$.