PWM signal drop on low Duty Cycle
To answers you question completely, some missing information is needed.  It depends if the load is connected when this waveform is generated and what value is.  Is it resistive.  The value of the base resistor is also needed to understand what is going on.  The first thing you need to verify is the transistor turn on isn't causing the the solar cell voltage to drop.  If this is the case, no transistor choice is going to make a difference.  If the solar sell is not dropping when the transistor is turned on, try more base current.  Do this by reducing the size of the base resistor.  If you can't reduce the size of the base resistor, try adding a little capacitance across it.