Augment battery-run device power with 100mA solar cell?
Where on earth will this be used?

A 100 mA x 5V PV (= photovoltaic = solar) cell is not a small item compared to many items of portable equipment. 

A modern highish efficiency crystalline PV panel will give you about 10 mW/cm^2 actually delivered in full sun.

So for 5V x 100 mA = 500 mW output you will need about 50 cm^2.

You can connect this via a diode directly across a suitable battery, or via a regulator to a load of your choice. If you connect directly to a battery then you may wish to provide overvoltage regulation. This is easy and cheap and can be discussed if your application sounds like that approach may be useful.

A 9V Alkaline "PP3"size (transistor radio type) battery is NOT intended to be recharged. You could arrange the panel so that it sup[plies load current when it is able to do so, but does not do so, or you could arrange it so it can power the equipment directly when illuminated adequately and the load is active BUT can also charge the battery. Alkaline batteries are NOT intended by their manufacturers to be recharged in most cases BUT a degree of recharging is in fact possible. Charging efficiency is limited, lifetime cycles are poor compared to eg NimH, and overcharge control would be needed. This is a nonstandard application so you would need to be aware of possible problems. 

Use of a small rechargeable battery in combination  with the main battery could be useful. Charge control is easy and cheap.