It's actually enough to actuate a relay.
Um, no. Show me a relay that can actuate at 100 microWatts. Electromechanical relays require much more current and voltage than this betavoltaic cell can source. Solid state relays also need more drive current and voltage to light the LED in them. There isn't a relay on the planet that can work at the low level of power this battery can supply. If you know of one that will, please link the data sheet for it.
Menlo Micro MM5600 switch uses .08mw
Um, mw is milliWatts not microWatts. That's a long way off still. A quick look at the product data sheet for the MM5130 device that you linked shows that the Gate Bias Voltage is 88 volts. This battery definitely will not be outputting that level of voltage. You'd need a metric shit tonne of them in series to get that kind of voltage.
not true, with a capacitor it could actuate a relay that is neither normaly open or closed but rather the gate flops like it had a broken spring. the device could send an IR lazer blast across a distance for a long range doorbell that can last 28000 years.
You're going to have to wait a very long time for enough charge to build up in a capacitor to get it to click the relay. Once actuated, the capacitor will drain rapidly and the relay will open again. Sure there are latching relays, as you sort of described, but what good is switching a relay if you still don't have enough power to do anything else with it and you can only actuate that relay once every year or so? 100 microWatts is nothing. You can't get usable work out of it. Capacitors aren't magic and this battery isn't useful. The video I linked covers this well.
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