In the class earlier this week, I had shown students the I vs. V plot from the datasheet for the orange LED WP710A10ND (which is not the LED they will be using—I want them to look up the specs for the LEDs they will have available, and not rely on the worked example in class). I had also made the claim that the current is roughly exponential with voltage around the voltage at which the diode starts conducting, but there was no evidence in the data sheet to support this claim, and the plot did not look particularly exponential. Of course, people are terrible at recognizing the shape of rapidly increasing functions—straight lines are about all we can understand visually for graphs.
Tonight, I decide to actually measure the I-vs-V graph to see whether I could demonstrate the exponential. The circuit was simple: the LED in series with a current-sense resistor, driven by my FG085 function generator with a very slow triangle wave (about a 9 second period), with the two voltages monitored by a Teensy 3.1 board running PteroDAQ. I added a 10µF capacitor across the output of the function generator, to get rid of some of the high-frequency noise from the steps in the function generator output. I didn’t use differential inputs to the Teensy, but did the subtraction to get the voltage across the LED in gnuplot.
The linear plot is reasonably similar to the plot in the data sheet, which shows around 14mA at 2V and a fairly straight-line increase from 1.8V to 2.05V (where it reaches 20mA). In this plot one can see the crude quantization of the bad DAC in the FG085 function generator, as banding in the line. One can add a straight-line fit for 1.9V and up can get that the current is about 75 mA/V (VF–1.8V). That is, the LED can be treated almost like a 13.4Ω resistor in series with a 1.8V voltage source at high voltages (and an open circuit at low voltages).
The log scale opens up the region where the LED is turning on or turning off, and we can see the subthreshold exponential behavior that I had told the class to expect. Below about 0.3µA, the plot is very noisy—I could probably get cleaner results by using a still larger sense resistor in this range. (I trimmed out of the plot the similarly noisy part of the plot below 30µA for the 30Ω sense resistor.)
The subthreshold exponential growth of current with voltage is about what I would expect, but the current grows a little more slowly than I had expected above the threshold. I thought it would grow proportional to (VF–1.8V)2 rather than linearly.