Photodetectors, Solar Cells and Light Emitting Diodes

By the end you should be able to: Describe junction and PIN photodiodes qualitatively, interpret the solar cell I-V characteristic and calculate fill factor and efficiency, explain how cells are strung into a panel, and describe LED operation and the choice of material.

The syllabus marks photonic devices qualitative treatment only, so the detectors are described rather than derived. Solar cell efficiency and fill factor are calculated, because the syllabus asks for them explicitly.

The junction converts between photons and carriers in both directions: absorb light and generate current, or pass current and emit light.

Photodetectors

The junction photodiode. An ordinary p-n junction, reverse biased, with a window admitting light.

A photon of energy greater than $E_g$ absorbed in or near the depletion region creates an electron-hole pair. The built-in field, reinforced by the reverse bias, immediately sweeps the two apart — electron to n, hole to p. The result is a photocurrent proportional to the light intensity, adding to the small dark current.

Two features make it useful:

The current is linear in incident power over many decades.
It is nearly independent of reverse voltage, exactly as the reverse saturation current is: every generated carrier is already collected, so pulling harder achieves nothing.

The reverse bias is not there to collect carriers — the built-in field would do that — but to widen the depletion region and reduce the junction capacitance, both of which make the device faster.

The PIN photodiode. An intrinsic layer is inserted between the p and n regions. Since the intrinsic layer is undoped, it is fully depleted and the field extends across the whole of it.

This fixes two limitations at once.

Sensitivity. In an ordinary photodiode, a photon absorbed outside the thin depletion region generates a pair that must diffuse to the field before recombining, and many do not. Making the depleted region thick means most photons are absorbed where the field already is.

Speed. Carriers generated in the field drift, which is fast; carriers generated outside it diffuse, which is slow and smears the response. Eliminating the diffusion component sharpens it. A thicker region also lowers the capacitance, further reducing the RC time constant.

There is a trade-off: too thick and the transit time itself becomes the limit. The optimum balances absorption depth against transit time, and PIN photodiodes are the standard receiver in optical fibre systems.

Solar cells

The same photovoltaic effect with no external bias — the cell generates the power rather than consuming it. A large-area junction with a very shallow top layer, so light reaches the depletion region.

Reading the characteristic. The illuminated I-V curve is the ordinary diode curve shifted downwards by the photocurrent, so the operating region lies in the fourth quadrant, where voltage is positive and current negative — the sign convention that means the device delivers power.

Three quantities describe it:

$I_{SC}$ , short circuit current — at $V = 0$ , the full photocurrent, proportional to illumination.
$V_{OC}$ , open circuit voltage — at $I = 0$ , about 0.5–0.6 V for silicon. Limited by the band gap, so it barely depends on illumination and never approaches $E_g/e$ .
$P_{max}$ at the maximum power point, the knee where the rectangle $V \times I$ under the curve is largest.

Fill factor measures how square the curve is:

FF = \frac{V_{mp}I_{mp}}{V_{OC}I_{SC}} = \frac{P_{max}}{V_{OC}I_{SC}}

Typically 0.7–0.85. A perfect cell would have $FF = 1$ ; series resistance and shunt leakage round the knee and reduce it.

Efficiency:

\eta = \frac{P_{max}}{P_{in}} \times 100\% = \frac{V_{OC}I_{SC}\,FF}{G \times A} \times 100\%

where $G$ is irradiance, standardised at $1000\ \text{W m}^{-2}$ , and $A$ is cell area. Commercial silicon cells reach 18–22%.

Why not higher? Photons below $E_g$ pass straight through unabsorbed; photons well above $E_g$ are absorbed but their excess energy is lost as heat within picoseconds. A single band gap cannot suit the whole solar spectrum, and that alone caps a single-junction cell near 33% — the Shockley–Queisser limit.

Stringing cells into a panel

One cell gives about 0.6 V, useless by itself. Cells are connected in series into a string: voltages add, current stays the same. Sixty cells in series give roughly 36 V open circuit, enough to charge a 12 V battery or feed an inverter. Strings may then be paralleled to raise current.

The consequence that matters practically. In a series string the same current flows through every cell, so the worst cell limits the whole string. One shaded cell throttles the output of all sixty, and worse, it is then reverse biased by the others and dissipates their power as heat — a hot spot that can crack the cell or start a fire.

The cure is a bypass diode across each group of cells (typically one per 20). Under normal operation it is reverse biased and does nothing. When a cell is shaded, current diverts through the diode instead, and the panel loses that group's output rather than everything. This is why a leaf on a panel costs a fraction of the output rather than all of it.

Light emitting diodes

The reverse process: forward bias, and electrons injected across the junction recombine with holes, each releasing a photon of energy approximately $E_g$ .

\lambda\,(\text{nm}) \approx \frac{1240}{E_g\,(\text{eV})}

Colour is set by the band gap, not by any coating. As with the laser diode, a direct gap material is required, so LEDs are III–V compounds — GaAsP and AlGaInP for red through yellow, GaP for green, InGaN for blue. Silicon LEDs do not exist.

Blue was the hard one. It needs a gap above 2.6 eV, and gallium nitride resisted growth as good crystal for decades — the eventual solution won the 2014 Nobel Prize in Physics, because it completed the set. Red and green existed already; blue made white light possible, and white LEDs made general lighting possible.

White light is not a single LED. Either a blue LED excites a yellow phosphor and the mixture appears white, which is how nearly all white LEDs work, or red, green and blue emitters are combined.

An LED differs from a laser diode in being spontaneous emission only: incoherent, broad-spectrum (tens of nanometres), and emitted in all directions. There is no threshold current and no optical cavity — the same junction physics, without the feedback.

Advantages: high efficiency, long life (tens of thousands of hours), low voltage, instant switching, no mercury, and mechanical robustness. Applications: general lighting, displays and backlights, indicators, remote controls (infrared), traffic signals and automotive lighting, and short-range optical communication.