The Light-Emitting Diode

A diode under forward bias pushes electrons from the n side and holes from the p side into the same region. When one meets the other they recombine, and the electron drops from the conduction band to the valence band. It has to give up the energy difference somewhere. IN SILICON it gives it up as heat, and this is not a small effect or a matter of purity. Silicon has an INDIRECT bandgap: the bottom of the conduction band and the top of the valence band sit at different crystal momenta, so an electron cannot simply drop across. It has to change momentum at the same time, which means a lattice vibration must participate, which means a three-body event, which is rare. So the electron waits, and long before its number comes up it has found some other way down. Silicon diodes do not glow and no amount of engineering makes them. IN GALLIUM ARSENIDE the two band edges sit at the SAME momentum. It is a DIRECT gap. The electron drops straight across, emits a photon, and does it in nanoseconds. That single band-structure difference is why every LED is made from a compound semiconductor and none is made from silicon, and it is why the LED had to wait for III-V materials to be grown well. THE PHOTON ENERGY IS THE GAP. E = hc over lambda, so: gallium arsenide 1.42 eV 873 nm infrared gallium arsenide phosphide, Holonyak's alloy, tunable through the red gallium phosphide 2.26 eV 549 nm green, but indirect and therefore dim indium gallium nitride, tunable 2.6 to 3.4 eV, blue through ultraviolet TO GET A COLOUR YOU CHOOSE AN ALLOY. Gallium arsenide phosphide is GaAs with some of the arsenic replaced by phosphorus, and the gap slides continuously from 1.42 eV at zero phosphorus upward as you add more. Holonyak picked a composition that landed at 655 nm. Craford at Monsanto added nitrogen a decade later to reach yellow. Nothing else about the diode changes. WHERE THE BLUE PROBLEM CAME FROM, and this is worth knowing because it is the reason for a Nobel Prize in 2014. Getting a wide gap is easy; gallium nitride has a gap of 3.4 eV and was grown in the 1970s. Getting a wide-gap material to be P-TYPE is the hard part, because the dopant levels sit too deep to ionise. Gallium nitride simply would not go p-type for twenty years. Isamu Akasaki and Hiroshi Amano cracked it in 1989 — the magnesium acceptors were being passivated by hydrogen, and an electron beam or a thermal anneal drove the hydrogen out. Shuji Nakamura at Nichia then made it manufacturable and bright. Blue arrived last, and once it did, white followed immediately: a blue die under a yellow phosphor. SO WHITE LEDs ARE NOT LEDs of a white colour. They are a blue LED plus a phosphor, and that matters for the next step, because a white LED has the forward voltage of a BLUE one and emits nothing like a single wavelength. Do not put one in the dataset.

You could take the wavelength off the datasheet. Do not. Half the point of this experiment is that both quantities are measured, and a transmission grating measures wavelength to a couple of percent with a ruler. WHAT YOU NEED. A transmission grating sheet — 1000 lines per millimetre is the common one, so the line spacing d is 1.000 micrometre. A metre rule. A dark room. And a way to make a narrow source: run the LED behind a slit cut in card, 0.5 mm wide, or simply use the LED die itself at a distance, which is small enough. THE GEOMETRY. Mount the grating vertically. Put the LED behind it at distance L, on the axis, so you look through the grating at the LED. You will see the LED straight ahead — that is the zero order — and a copy of it to each side, which is the first order. Measure the distance x from the centre to the first-order copy, along a rule held across the field at the LED's distance. Then sin(theta) = x over the square root of (x squared plus L squared), and the grating equation for first order is simply lambda = d sin(theta). MEASURE IT PROPERLY. Take x on BOTH sides and average them; that cancels any misalignment of the grating, and it is the single biggest source of error. Get L with a tape, not by estimating. Keep L large — half a metre or more — because the angle error falls as L grows. WHAT YOU SHOULD GET, roughly, so you know when something is wrong: red 620 to 640 nm amber 600 to 610 nm yellow 585 to 595 nm green 560 to 570 nm for the traditional gallium phosphide sort blue 465 to 475 nm AND HERE IS THE TRAP, stated plainly because it will otherwise wreck your result. GREEN LEDs COME IN TWO COMPLETELY DIFFERENT KINDS. The traditional green is gallium phosphide, emits near 565 nm, and has a forward voltage around 2.2 V. The modern bright green — the one in traffic lights and in most LED assortments sold today — is indium gallium nitride, the SAME material family as blue, emits near 525 nm, and has a forward voltage around 3.2 V. It is a blue-technology device tuned green. If you put a modern InGaN green in this dataset it will sit far off the line and you will conclude your measurement is broken. It is not. You are measuring two different device families and pretending they are one. HOW TO TELL THEM APART without a datasheet: measure the forward voltage first. Below about 2.4 V it is a traditional gallium-phosphide or gallium-arsenide-phosphide part. Above about 2.7 V it is a nitride part. Sort them into two groups before you plot anything. DO NOT USE A WHITE LED at all, for the reason in step 1. Do not use an infrared LED unless you have a phone camera to see it with; most phone cameras will, and it is a good addition to the dataset because it sits at the far end of the line.