Photovoltaic Cells

Introduction

A solar cell uses semiconductor absorption to create electron–hole pairs and selective contacts to collect them as electrical work. The p–n junction's field helps separate carriers near its depletion region, but light supplies the energy. Good design must absorb a broad solar spectrum, prevent premature recombination, and deliver carriers to contacts with small resistance. The gap that makes absorption possible also creates unavoidable spectral tradeoffs.

Core explanation

A photon with sufficient energy can promote an electron into an accessible conduction state, leaving a hole. Pairs generated in or near the junction can be separated by the built-in field; pairs generated farther away may diffuse toward the junction before collection. Electrons and holes flow to selective contacts and through an external load. The device is under illumination and is not in thermal equilibrium; electron and hole quasi-Fermi levels can separate, giving a terminal voltage. With no illumination, a built-in junction potential alone does not furnish sustained external power. MIT's photovoltaics course connects junction formation to the ideal diode equation used for solar-cell models.

An ideal illuminated diode can be approximated by I(V) = I₀[exp(eV/(ηk BT)) − 1] − I ph , using one sign convention where delivered photocurrent is negative. I ph represents generated and collected current under the assumed illumination; actual devices can have voltage-dependent collection. At short circuit V = 0, output current magnitude is approximately I ph in this ideal model. At open circuit I = 0, the terminal voltage is set by the balance of photogeneration and recombination. The maximum power point is where VI is greatest in the operating quadrant, not at either endpoint. Fill factor equals P max/(V oc I sc) using magnitudes, and power conversion efficiency equals P max divided by incident optical power.

Single-junction spectral losses include transmission of photons below the gap and thermalisation of energy above the gap: one absorbed high-energy photon generally yields one collected electron–hole pair, while excess energy quickly becomes heat in an ordinary cell. Radiative recombination is an unavoidable part of ideal detailed-balance analysis, and nonradiative recombination further lowers actual voltage. Resistive losses, reflection, incomplete absorption and contact shading reduce delivered power. The US Department of Energy's multijunction research overview explains the gap-related single-junction limit and the use of stacked absorbers.

Material selection balances electronic gap, carrier diffusion length, defect tolerance, abundance, stability, processability and environmental constraints. Silicon is a dominant practical absorber; III–V compounds can make highly efficient multijunction cells in applications where their costs are justified. A multijunction stack uses different gaps to collect different portions of the spectrum, relaxing some single-junction losses at the cost of greater complexity. The precise efficiency limit depends on spectrum, concentration, temperature and assumptions; quoting a universal percentage without them is misleading.

Step-by-step reasoning

1. Identify which incident photons are absorbed and generate mobile pairs. 2. Trace carrier separation and diffusion to selective contacts. 3. Locate short-circuit current, open-circuit voltage and maximum-power point on I–V axes. 4. Calculate fill factor and efficiency with incident power and consistent units. 5. Assign losses to optical absorption, recombination or electrical resistance.

Visual explanation

Draw sunlight entering a p–n cell. One low-energy photon passes through; one suitable photon creates a pair collected at opposite contacts; one high-energy photon makes a pair and releases excess energy as heat. Beside the cell, draw an illuminated I–V curve and mark I sc, V oc and the rectangle of maximum power.

Real-world analogy

A sorting conveyor accepts packages only above a minimum size. Packages below threshold pass through unused; oversized packages are trimmed, wasting the extra material. Accepted packages must still reach an exit before being lost. This conveys spectral loss and recombination, while the actual photovoltaic conversion involves electronic energies rather than package dimensions.

Real-world example

A rooftop silicon panel combines many cells in series and parallel to reach useful voltage and current. Shading, temperature and wiring affect output in addition to cell chemistry. As temperature rises, increased recombination-related dark current often lowers open-circuit voltage, even if photocurrent changes modestly. Therefore a panel's rated power under a standard test condition is not the power delivered at every time of day.

Why?

Why can a solar cell have voltage while an unilluminated equilibrium junction cannot supply continuous power? Illumination creates nonequilibrium carriers and separates their electrochemical potentials. The external circuit can then extract work as carriers recombine through the load. Without the light-driven generation process, drift and diffusion balance and the equilibrium Fermi level is flat through the complete system.

Common misconception

“Every photon above E g becomes electrical energy hν” ignores thermalisation and collection losses. “The built-in field does all the work” ignores the incoming photon energy. “A higher band gap is always better” misses the lost subgap photons; a lower gap reduces attainable voltage and increases thermalisation losses.

Worked example

A cell under incident power 0.100 W has V oc = 0.60 V, I sc = 0.030 A and fill factor 0.75. Maximum output power is P max = 0.75(0.60)(0.030) = 0.0135 W . Efficiency is 0.0135/0.100 = 13.5% . Multiplying V oc by I sc alone would overestimate useful power because those two values occur at different points on the operating curve.

Quick check

1. What happens to an ordinary single-junction cell when a photon has less energy than the relevant absorption gap? Answer: It is generally not absorbed by the intended band-to-band process and does not generate a useful pair through that mechanism.

Exam focus

Describe generation, separation and collection as separate steps. Use the maximum-power point in efficiency calculations. State a sign convention before writing an illuminated diode equation. Tie voltage to nonequilibrium carrier populations and identify transmission and thermalisation as the two basic gap-related spectral losses.

Advanced insight

The detailed-balance limit treats radiative emission as the reverse of absorption and connects open-circuit voltage to entropy and recombination. Tandem cells can reduce spectral mismatch by assigning high-energy photons to larger-gap top cells and lower-energy photons to smaller-gap cells beneath. Practical design also requires current matching and transparent interconnections in series-connected stacks.

Summary

Photovoltaic cells convert absorbed photons into separated and collected carriers. Junctions and selective contacts enable extraction, while light establishes the nonequilibrium potential difference. The band gap creates a tradeoff between subgap transmission and above-gap thermalisation; recombination and resistance impose additional losses.

Practice questions

1. Why is P max less than V oc I sc for an ordinary cell? Answer: V oc occurs at zero current and I sc at zero voltage; the maximum-power point has neither endpoint value. 2. Name one optical and one electronic loss mechanism. Answer: Reflection is an optical loss; nonradiative recombination is an electronic loss. 3. If P max = 12 W under 80 W incident light, what is efficiency? Answer: 12/80 = 0.15, or 15%. 4. Does a dark p–n junction's built-in potential alone deliver continuous external power? Answer: No. Equilibrium drift and diffusion balance, with no sustained external energy source.