The essence of what you are looking for is a circuit like this:

^{simulate this circuit – Schematic created using CircuitLab}

Here, I've indicated a circuit that will work if you are willing to stack up a few solar cells. I've tried to design this for lowest operating voltage, so it's probably okay starting at around \$2.5\:\text{V}\$ (red LED only, obviously, though with larger source voltages other LEDs would then work.) I know this isn't a single cell. But there it is.

The basic idea is to let \$C_1\$ charge up slowly. At some point the voltage trigger (middle section with \$Q_1\$) will fire off the SCR that is made up of \$Q_2\$, \$Q_3\$ and \$D_9\$. The SCR dumps the accumulated charge on \$C_1\$ through the LED (\$D_7\$). \$Q_2\$ and \$D_9\$ form a current mirror with a gain very much less than one. And \$Q_3\$ forms up the rest of the SCR. A little tickler positive feedback is provided via \$C_2\$ and \$R_7\$ (both essential for clean operation) to make this a reliable circuit.

That's about it.

But this provides a "flavor" of what a discrete circuit might look like. As you can see, it's non-trivial. And it only does part of what you want. There's no boosting here. And that's yet another stage.

The essence of what you are looking for is a circuit like this:

^{simulate this circuit – Schematic created using CircuitLab}

Here, I've indicated a circuit that will work if you are willing to stack up a few solar cells. I've tried to design this for lowest operating voltage, so it's probably okay starting at around \$2.5\:\text{V}\$ (red LED only, obviously, though with larger source voltages other LEDs would then work.) I know this isn't a single cell. But there it is.

The basic idea is to let \$C_1\$ charge up slowly. At some point the voltage trigger (middle section with \$Q_1\$) will fire off the SCR that is made up of \$Q_2\$, \$Q_3\$ and \$D_9\$. The SCR dumps the accumulated charge on \$C_1\$ through the LED (\$D_7\$). \$Q_2\$ and \$D_9\$ form a current mirror with a gain very much less than one. And \$Q_3\$ forms up the rest of the SCR. A little tickler positive feedback is provided via \$C_2\$ and \$R_7\$ (both essential for clean operation) to make this a reliable circuit.

That's about it.

But this provides a "flavor" of what a discrete circuit might look like. As you can see, it's non-trivial. And it only does part of what you want. There's no boosting here. And that's yet another stage.

Spice shows, at \$3\:\text{V}\$, that this delivers \$10\:\text{mA}\$ pulses into a red LED and draws an average current of about \$1.5\:\mu\text{A}\$. And there remain a variety of adjustments that can be made to the circuit to tailor it to specifications, if you have them.

The essence of what you are looking for is a circuit like this:

^{simulate this circuit – Schematic created using CircuitLab}

Here, I've indicated a circuit that will work if you are willing to stack up a few solar cells. I've tried to design this for lowest operating voltage, so it's probably okay starting at around \$2.5\:\text{V}\$. I know this isn't a single cell. But there it is.

The basic idea is to let \$C_1\$ charge up slowly. At some point the voltage trigger (middle section with \$Q_1\$) will fire off the SCR that is made up of \$Q_2\$, \$Q_3\$ and \$D_9\$. The SCR dumps the accumulated charge on \$C_1\$ through the LED (\$D_7\$). \$Q_2\$ and \$D_9\$ form a current mirror with a gain very much less than one. And \$Q_3\$ forms up the rest of the SCR. A little tickler positive feedback is provided via \$C_2\$ and \$R_7\$ (both essential for clean operation) to make this a reliable circuit.

That's about it.

The essence of what you are looking for is a circuit like this:

^{simulate this circuit – Schematic created using CircuitLab}

Here, I've indicated a circuit that will work if you are willing to stack up a few solar cells. I've tried to design this for lowest operating voltage, so it's probably okay starting at around \$2.5\:\text{V}\$ (red LED only, obviously, though with larger source voltages other LEDs would then work.) I know this isn't a single cell. But there it is.

The basic idea is to let \$C_1\$ charge up slowly. At some point the voltage trigger (middle section with \$Q_1\$) will fire off the SCR that is made up of \$Q_2\$, \$Q_3\$ and \$D_9\$. The SCR dumps the accumulated charge on \$C_1\$ through the LED (\$D_7\$). \$Q_2\$ and \$D_9\$ form a current mirror with a gain very much less than one. And \$Q_3\$ forms up the rest of the SCR. A little tickler positive feedback is provided via \$C_2\$ and \$R_7\$ (both essential for clean operation) to make this a reliable circuit.

That's about it.

But this provides a "flavor" of what a discrete circuit might look like. As you can see, it's non-trivial. And it only does part of what you want. There's no boosting here. And that's yet another stage.