Fred McKenzie wrote:

Bianca-

If you look at the characteristic curves of an FET, you will see lines that
maintain a nearly constant current over a wide voltage range. One of those
lines corresponds to the case of zero volts between gate and source.

In other words, an FET with gate tied to its source, becomes a constant-current
diode. You just have to try several to find one that meets your requirement.
(In fact, such a device is available with the leads tied together internally.)

Fred -

You are exactly right. And if you put a resistor in the source lead
(between the source and the connection to the gate), you can change the
value of the constant current. Start with FET that delivers a bit too
much current. Connect a variable resistor, and dial the current down to
where you want it. Then replace the variable resistor with a fixed one.
Easy!

Bill