Photonics and optoelectronics
Silicon detects light very well and hardly emits it: its band gap is indirect. That is why solar cells are made of silicon and LEDs of gallium.
01Photons and bands
A photon with energy greater than the band gap can be absorbed and create an electron-hole pair; a pair that recombines can emit a photon with the energy of the band gap. All of optoelectronics comes from those two sentences and from the relationship between energy and wavelength:
The difference between absorbing and emitting lies in the type of band gap. In direct band gap semiconductors (GaAs, GaN, InP) the electron can fall into the hole emitting just a photon, and it does so in nanoseconds. In indirect ones, such as silicon, the transition also needs a lattice vibration, it is very improbable, and the electron almost always recombines through defects without emitting light, the mechanism of the transport unit. That is why silicon is good for detecting light and for solar cells, but not for making LEDs or lasers.
02The photodiode
The pairs that light generates inside the depletion region of a PN junction, or within one diffusion length of it, are separated by the field and produce a current in the reverse direction proportional to the optical power. The constant is the responsivity:
| Mode or type | How it is used | Advantage |
|---|---|---|
| Photovoltaic, unbiased | Into a transimpedance amplifier, with zero voltage | No dark current: the lowest noise, for measuring weak light |
| Photoconductive, reverse biased | With reverse voltage, which widens the depletion region | Less capacitance and more speed |
| PIN | A wide intrinsic layer between the P and the N | Almost all absorption occurs in a region with field: fast and efficient |
| Avalanche (APD) | Near breakdown, with internal multiplication | Gain of tens to hundreds, for very weak signals |
03The solar cell
A solar cell is a large photodiode that works in the fourth quadrant: light generates current and the junction, forward biased, delivers power to the load. Its curve is that of the diode shifted downward by the photocurrent:
The efficiency of a single-junction cell has a theoretical ceiling, the Shockley–Queisser limit: photons with less energy than the band gap are not absorbed, and those with more lose the excess as heat. The optimum, near 1.34 eV, gives 33.7 %; for silicon the limit is about 29 %, and the best laboratory cells exceed 26 %. Multijunction cells with stacked layers of different band gaps pass 40 % and are used on satellites.
A 156 × 156 mm silicon cell with 9 A short-circuit current and 0.64 V open-circuit voltage at 1000 W/m² and 25 °C, ideality factor 1.2 and 4 mΩ series resistance. You choose the irradiance and the cell temperature: the current and the power are plotted against the voltage, with the maximum power point, which is where a good controller makes it work.
04The LED
In an LED the junction is forward biased, carriers are injected on each side and, in a direct band gap material, a good part of the recombinations emit light with the energy of the band gap. That is why the color is set by the material, and the forward voltage is approximately the band gap divided by the electron charge:
| Color | Material | Wavelength | Typical forward voltage |
|---|---|---|---|
| Infrared | GaAs, AlGaAs | 850 to 940 nm | 1.2 to 1.5 V |
| Red and amber | AlGaInP | 590 to 630 nm | 1.8 to 2.2 V |
| Green | InGaN | 520 to 530 nm | 2.8 to 3.4 V |
| Blue | InGaN | 450 to 470 nm | 2.8 to 3.4 V |
| White | Blue LED with a yellow phosphor | Broad spectrum | 2.8 to 3.4 V |
The gallium nitride blue LED, which made the white LED possible and with it solid-state lighting, earned the 2014 Nobel Prize in Physics for Akasaki, Amano and Nakamura. Like a diode, the LED is driven by current: its exponential curve means that a fixed voltage gives a very uncertain current, and that is why it always has a series resistor or a current source.
05The semiconductor laser
If so much current is injected that there are more electrons up than down in the junction (population inversion), a passing photon stimulates the emission of another identical one, in phase and in the same direction. With two mirrored faces forming a cavity, the light goes back and forth being amplified, and above a threshold current the emission becomes coherent and very narrow in wavelength. Below the threshold, the laser is a mediocre LED.
Semiconductor lasers are found in optical drives, in printers and, above all, in fiber-optic communications, which use the three windows where the fiber loses little: 850, 1310 and 1550 nm. VCSELs, which emit through the surface of the wafer, light up the short links in data centers and the face sensors of phones.
06The optocoupler
An infrared LED and a phototransistor facing each other inside an opaque package transmit a signal with no electrical connection: the isolation is thousands of volts. The parameter that defines it is the current transfer ratio (CTR), the output current over the input current: in the PC817 it ranges from 50 to 600 % depending on the class. It separates the control side from the power side in switching power supplies, in motor drives and in PLC inputs.
07Where it appears in electronics
| Case | Device |
|---|---|
| Photovoltaic installation | Silicon cell panels and an inverter with maximum power point tracking |
| Remote control and presence sensor | Infrared LED and a photodiode with a filter |
| Fiber-optic link | Laser, fiber and a PIN or avalanche photodiode |
| Isolated switching power supply | Optocoupler in the feedback loop |
| Digital camera | Millions of photodiodes in a CMOS sensor |
| Pulse oximeter | Red and infrared LEDs and a photodiode that compares how much the blood absorbs |
08In the lab
Measure the voltage at which LEDs of four colors begin to conduct and plot it against \( 1/\lambda \). The slope is \( h c / q \): solve for \( h \).
With a cell or a small panel in the sun, measure voltage and current across a variable load from short circuit to open circuit. Plot the curve and the power, locate the maximum power point and calculate the fill factor.
With a PC817, measure the collector current for LED currents from 1 to 20 mA with 5 V at the output, and plot the CTR. Verify the class against the datasheet.
09Common mistakes
- Connecting an LED directly to a voltage. Without limiting the current, it is destroyed.
- Expecting light from a silicon junction. Its indirect band gap hardly emits at all.
- Making a solar cell work at an arbitrary fixed voltage. Power is lost; the maximum power point has to be tracked.
- Forgetting that the cell loses output with heat. The open-circuit voltage drops about 2 mV per degree.
- Reading responsivity as efficiency. 0.6 A/W is not 60 %: it depends on the wavelength.
10Self-assessment
Up to what wavelength does a 1.42 eV material absorb?
\( 1240 / 1.42 \approx 873 \) nm.
Why are silicon LEDs not made?
Because its band gap is indirect: recombination with emission of a photon is very improbable and the carriers recombine through defects, without emitting light.
A photodiode with \( \eta = 0.8 \) at 850 nm, what responsivity does it have?
\( 0.8 \times 850 / 1240 \approx 0.55 \) A/W.
If the irradiance drops by half, what happens to \( I_{sc} \) and \( V_{oc} \)?
\( I_{sc} \) drops by half; \( V_{oc} \) drops only \( n V_T \ln 2 \), about 20 mV.
What does the CTR of an optocoupler measure?
The ratio between the output current of the phototransistor and the LED current.
11Further reading
- E. Fred Schubert. Light-Emitting Diodes. 2nd ed., Cambridge University Press, 2006. The reference on the LED: materials, efficiency, color and packaging.
- Jenny Nelson. The Physics of Solar Cells. Imperial College Press, 2003. The solar cell from the physics of the junction, with the Shockley–Queisser limit explained.
- Bahaa E. A. Saleh and Malvin Carl Teich. Fundamentals of Photonics. 3rd ed., Wiley, 2019. Photodetectors, semiconductor lasers and fibers in a single text, in great detail.