I drew this schematic years ago before Switchercad III or whatever schematic drawing package was available. It’s a three transistor design; one transistor inverts the photocell’s voltage so it shuts off during the day. The other two transistors make up the V boost circuit. The S9013 is a good transistor for this, but a better one would be the S8050. This S9013 has six gain ranges, from 64 to 300, which isn’t very high. But it will handle a half amp current – about the same as the 2N4401.
The single AA NiCd or NiMH cell needs about 1.4 volts to fully charge. Adding the half volt drop across the D2 diode, the total comes to just under 2 volts, so the solar photovoltaic cell has to put out current at up to 2 volts. That means it must have at least four half volt cells in series.
Someone reckoned that the circuit should not need the CdS photocell because it already had a daylight sensor: the solar photovoltaic cell itself. So many circuits do not have the CdS daylight sensor.
Back to experimenting…