Diode behavior when reverse biased with small voltage

Question

I'm designing a simple circuit to use a lithium-metal coin battery as a backup power supply, and I'm considering something simple like this:

^{simulate this circuit – Schematic created using CircuitLab}

However, during normal operation, \$V+\$ is expected to be at a higher voltage than the coin cell, so I expect some reverse current through D2. According to this source, this absolutely can damage the coin cell if it is too high - coin lithium batteries can't be guaranteed to work after subject to a total reverse charge of 3% total capacity, and a 1μA current will do that in a few months.

My question is, how can I find out how much current will go through D2? Most diode datasheets are completely uninterested at the currents going through the diodes when a small reverse bias is applied, mentioning only maximum reverse current when operating very close to the maximum voltage of the diode. Others have graphs like this, that show reverse current growing roughly exponentially, but don't show any details when close to the origin:

So my question is, is there a good model for how diodes behave when subject to a small reverse voltage bias? Can I have a better estimate of reverse current than simply using the maximum value?

(before you mention, assuming I take Shockley's diode law seriously, the reverse current would be close to the saturation current \$I_S\$ for a large range of negative voltages, but if that were the case I'd expect datasheet graphs as the one provided to look a lot different, and for \$I_S\$ to be mentioned in every single diode datasheet. Since this is not the case, I am assuming the diode law doesn't hold very well for reverse bias)

Answer 1

One of the best simple models I've seen is here:

This shows that the reverse current quickly enters a predictable saturation region with mainly the temperature effects to be aware of. However there is a much higher resistive leakage current that impacts the total reverse current.

This diagram shows both Is (the saturation reverse current) and Il (the resistive surface and bulk leakage).

It's worth noting that the resistive leakage value can be permanently changed (increased) by overheating the device during soldering. This makes it very difficult to predict total reverse current in any simplified model. Resistive reverse leakage may be in the 10 - 1000 MOhms range.

Note: If your goal is to provide BBU for something low current like an RTC chip with a CR2302 battery, then you don't need to use diodes at all. You can use a transmission gate to switch from one supply to the other. For example the Philips 74LVC1G3157 is capable of up to 12mA with off state leakage below 1 uA maximum.

Answer 2

Make sure to factor in the self-discharge of the cell (maybe 1% per year) as well as leakage currents on the PCBA...you may very well be leaking that 1uA away elsewhere on the board. Another option is to put a tantalum capacitor in line with your cell. The leakage of that capacitor will be enough to ensure you don't damage the cell.