# Solar cell A **solar cell**, or photovoltaic cell, is a [[Semiconductor_device|semiconductor device]] that turns light directly into electricity. A [[Photon|photon]] carrying more energy than the material's [[Band_gap|band gap]] is absorbed, lifting an electron across the gap and leaving a hole behind; the built-in field of a junction sweeps the two apart before they recombine, and the result appears at the terminals as a current with a voltage behind it. Nothing boils and nothing spins — and, unlike every device in this portal's Part V so far, the [[Carnot_cycle|Carnot]] limit does not apply. Andrea Mitofsky is explicit: Carnot efficiency governs heat-to-other-energy converters, and photovoltaic devices are not among them.[^mitofsky-carnot] In the microsim below the reader moves two controls — irradiance from 0 to 1,000 W/m² and cell temperature from −20 to 80 °C — across the single-diode model, `I = I_L − I_0·[exp(q·V/(n·k·T)) − 1]`, in which the light-generated current I_L rises in proportion to irradiance and the dark saturation current I_0 rises steeply with temperature. Two curves are drawn, the I–V curve and the power curve P = I·V that hangs beneath it, and three numbers are read off them: the open-circuit voltage `V_oc = (n·k·T/q)·ln(I_L/I_0 + 1)`, the maximum-power point where P peaks, and the fill factor `FF = P_mpp/(I_sc·V_oc)`, the fraction of the rectangle I_sc × V_oc that the cell actually delivers. A band-gap selector sets I_0(T), with [[Silicon|silicon]] at 1.12 eV as the home position; that dependence is a model fit and is marked ILLUSTRATIVE in the sim's heads-up display.[^spec-e38] On the [[Energy]] flagship this article serves *Solar cells* in Part V — Transformation, the section that hands the portal its direct light-to-electricity converter; it places the silicon variant used by the Elements programme. ## Applications A solar cell on its own produces about half a volt, so cells are almost never used singly. They are wired in series into modules, modules into panels and panels into arrays, each series string adding voltage and each parallel string adding current, until the array matches what an inverter or a battery bank wants. Because the series current is set by the weakest cell, shading one cell throttles a whole string — the reason bypass diodes are built into modules, and the reason array layout is a design problem rather than a wiring problem. The engineering above the cell is the subject of the [[Photovoltaic_system|photovoltaic system]].[^mitofsky-pv] ### Space Photovoltaics reached maturity in orbit before they were affordable on the ground, for arithmetic rather than sentimental reasons. Above the atmosphere there is no cloud, no dust and, in a sun-synchronous orbit, no night, and the alternative — carrying chemical fuel for years — is impossible. Cost per watt matters far less than watts per kilogram, the trade that favours the expensive, high-efficiency multijunction devices described below, and that inversion is why space cells and rooftop cells have been different products for sixty years.[^murphy-solar] ## History The photovoltaic effect belongs to a family of nineteenth-century observations that light does electrical work, and its theoretical key is the [[Photoelectric_effect|photoelectric effect]]: light arrives in quanta, and only quanta above a threshold free an electron. That threshold is why a cell cares about the colour of light and not merely its brightness, and why `E_eV = 1.24/λ_µm` is the first equation in the subject.[^murphy-99] Visible light spans 0.4 to 0.7 µm and so 3.1 to 1.8 eV, comfortably above silicon's 1.12 eV gap; infrared beyond 1.107 µm falls below it and passes through unabsorbed.[^murphy-99][^derived-sc] ### Improved manufacturing methods post 1960s The modern cell is a child of the semiconductor industry rather than of power engineering. Once the [[Czochralski_method|Czochralski method]] could pull metre-long single crystals of [[Silicon|silicon]], and [[Doping_(semiconductor)|doping]] could be controlled to parts per billion, a solar cell became a large, cheap, low-specification version of something the electronics industry already made to a far tighter one. Every subsequent cost reduction has come from that inheritance: bigger wafers, thinner kerfs, faster [[Semiconductor_device_fabrication|fabrication]] lines, better [[Passivation_(chemistry)|surface passivation]].[^mitofsky-pv] ## Declining costs and exponential capacity growth Photovoltaic capacity has grown for decades at rates that only look modest annually. The arithmetic is worth doing once. A technology compounding at 30 % a year multiplies by 1.3 each year, so climbing from 1 % to 100 % of some target takes ln(100)/ln(1.3) = 17.6 years; at 40 % a year it takes 13.7.[^derived-sc] Kerlin runs exactly this calculation for the wind fleet, growing 0.013 quad to 1 quad at 30 % a year, and the same exponential governs any young generating technology.[^kerlin-growth] Such a source therefore looks negligible for a long time and then, over about a decade, stops being negligible — without the growth rate having changed at all. The price series that accompanies this growth is not tabulated in any Portal Book on this page's shelf, so it is left to the pair; what the shelf supplies instead is the land arithmetic under *Deployment*. ### Subsidies and grid parity Grid parity is the point at which electricity from a cell costs no more than electricity from the wire, and it arrives at different dates in different places because it depends on the local price of the alternative as much as on the cell. Subsidy policy moves that date without changing any of the physics on this page. The durable observation is structural: photovoltaics is a capital-cost technology with a near-zero fuel cost, so its economics are dominated by the discount rate and the [[Capacity_factor|capacity factor]], and comparisons that quote only the installed price per watt are incomplete.[^theis-098] ## Theory Three things must happen in sequence for a cell to work, and the single-diode model is the accounting of all three. Absorption comes first. A photon above E_g creates an electron–hole pair; a photon below E_g is not absorbed at all; a photon well above E_g creates a pair and dumps the excess as heat within picoseconds. Silicon's 1.12 eV gap puts the cutoff at 1.24/1.12 = 1.107 µm.[^murphy-99][^derived-sc] Separation comes second: the [[Depletion_region|depletion region]] of a p–n junction carries a built-in [[Electric_field|electric field]] that sweeps electrons one way and holes the other, turning excited carriers into a current I_L proportional to photon flux, and therefore to irradiance.[^mitofsky-pv] Collection comes third, and it is a race — carriers reaching a contact deliver charge, carriers recombining on the way deliver heat. The cell is then a current source I_L in parallel with the junction's own diode, which conducts backwards as soon as a voltage appears across it: `I = I_L − I_0·[exp(q·V/(n·k·T)) − 1]` with q the elementary charge, k the [[Boltzmann_constant|Boltzmann constant]] — 1.381×10⁻²³ J/K — and n the ideality factor, between 1 and 2.[^mitofsky-pv][^mitofsky-kb] At V = 0 the diode is off and the current is I_sc ≈ I_L. At open circuit the diode passes back exactly what the light drives forward, giving the sim's second equation, `V_oc = (n·k·T/q)·ln(I_L/I_0 + 1)`. The thermal voltage k·T/q is 25.7 mV at 25 °C, so for a typical silicon cell at 1,000 W/m² — I_L = 35 mA/cm², I_0 = 1×10⁻¹² A/cm², n = 1 — the logarithm is 24.3 and V_oc = 0.624 V.[^derived-sc] The asymmetry between the two controls is the lesson of the sim. I_sc is linear in irradiance, V_oc only logarithmic: cutting irradiance tenfold, from full sun to overcast, cuts the current by 90 % but the voltage by (k·T/q)·ln(10) = 59 mV, from 0.624 V to 0.565 V.[^derived-sc] A shaded cell is a weak current source at nearly full voltage — which is why a panel's voltage says almost nothing about the power it is making. ## Efficiency Power is the product of the two curves, and the maximum-power point sits where the I–V knee is sharpest. The fill factor measures that sharpness. For the silicon cell above, the empirical relation `FF = (v_oc − ln(v_oc + 0.72))/(v_oc + 1)`, with v_oc = V_oc·q/(n·k·T) = 24.3, gives FF = 0.833 — a display fit rather than a derived law, marked ILLUSTRATIVE wherever the sim uses it.[^derived-sc][^spec-e38] Delivered power is then FF·I_sc·V_oc = 0.833 × 35 mA/cm² × 0.624 V = 18.2 mW/cm², which against 1,000 W/m² = 100 mW/cm² of sunlight is an efficiency of 18.2 %.[^derived-sc] The ceiling above that number is set by the band gap, not by workmanship. A gap that is too small wastes energy as heat, since every photon above it delivers only E_g and the remainder warms the lattice; a gap that is too large wastes photons entirely, since everything below it passes through. The optimum for the solar spectrum falls near 1.1 to 1.4 eV — which is why silicon, [[Gallium|gallium]] arsenide and cadmium telluride all cluster there — and the resulting single-junction limit is a little over 30 %.[^mitofsky-pv][^murphy-solar] Temperature moves the whole curve the wrong way. Warming a cell raises I_0 far faster than I_L, so V_oc falls; differentiating the open-circuit expression at fixed band gap gives dV_oc/dT ≈ −1.9 mV/K for silicon, a relative loss of about −0.31 % per kelvin.[^derived-sc] At the top of the sim's range a cell at 80 °C has lost 0.106 V of the 0.624 V it had at 25 °C — a seventh of its voltage, from nothing but being hot. That is the counter-intuitive result the sim exists to show: a black panel in still desert air can make less power than the same panel in cool wind under the same sun. Series resistance in the fingers and busbars adds the other loss, an ordinary `P = I²·ρ·L/A` [[Electrical_resistivity_and_conductivity|resistive]] tax that flattens the knee and cuts the fill factor.[^mitofsky-joule] ## Materials Nearly all the world's cells are silicon; the interesting minority is defined by what it trades away. ### Crystalline silicon Silicon's band gap of 1.12 eV is close to optimal in energy but indirect, and so poor in absorption: an indirect transition needs a lattice vibration as well as a photon, so a silicon cell must be of order 100 µm thick to absorb what a direct-gap material absorbs in one. That thickness is the source of both silicon's cost — it is mostly material, purified and sawn from a boule — and its durability, since a thick, inert [[Crystal_structure|crystal]] under glass degrades very slowly.[^mitofsky-pv] ### Thin film Direct-gap absorbers — cadmium telluride, copper indium gallium selenide, amorphous silicon — absorb sunlight in a micrometre or two and deposit straight onto glass or foil, skipping the ingot, the wafer and the saw. They use grams of [[Tellurium|tellurium]], [[Indium|indium]], [[Gallium|gallium]], [[Selenium|selenium]] or [[Cadmium|cadmium]] where silicon uses kilograms. They pay in efficiency, in the scarcity of some of those elements, and in end-of-life handling. ### Multijunction cells Stacking cells of decreasing band gap, widest on top, lets each layer take the photons it converts best and pass the rest downward, defeating the single-gap compromise at the root. Three- and four-junction devices pass 40 % under concentrated light, and are the most expensive cells made — so they are used where mass matters more than money: in orbit, and under concentrating optics that buy area in mirrors instead of silicon.[^murphy-solar] ## Research in solar cells Most current research attacks one of the three steps of the theory above. Light-trapping work — surface texturing, antireflection coatings, bifacial cells that also collect ground-reflected light — improves absorption without changing the absorber. Passivation and contact engineering improve collection by giving carriers fewer places to recombine. Intermediate-band, upconversion and [[Quantum_dot|quantum-dot]] schemes attack the spectral mismatch itself, harvesting sub-gap photons or splitting high-energy ones, which is the only route past the single-junction limit that does not require stacking whole cells. Encapsulation research is unglamorous and decisive: a cell that degrades in five years is worthless whatever its first-day efficiency.[^mitofsky-pv] ### Perovskite solar cells Metal-halide perovskites absorb strongly, tolerate defects that would kill a silicon cell, process from solution at low temperature, and have a band gap tunable by composition — which makes them the natural top cell for a silicon tandem, taking the blue photons and passing the red ones down. Their unsolved problem is not efficiency but lifetime: the ionic softness that makes them easy to make also makes them sensitive to moisture, heat and the light they are there to absorb. ## Manufacture Silicon cell manufacture is a purification chain. Quartz is reduced to metallurgical silicon, refined to polysilicon, grown into a single crystal, sawn into wafers, doped to form the junction, coated with an antireflection layer, printed with metal contacts, sorted by measured output and laminated into modules. Each step throws away material and energy, and the industry's history is a history of throwing away less: thinner wafers, narrower saw kerfs, [[Silicon_dioxide|silica]] feedstock used more completely.[^mitofsky-pv] Modules are flash-tested and sorted because cells in a series string must be matched, and certification testing — damp heat, thermal cycling, mechanical load, hail — exists because the product carries a twenty-five-year warranty. ### Materials sourcing Silicon is the second most abundant element in the crust, so a silicon cell has no resource ceiling worth discussing; its constraint is the energy and capital of purification. Thin films are the opposite case. [[Tellurium|Tellurium]] and [[Indium|indium]] are recovered as by-products of [[Metallurgy|copper and zinc refining]], so their supply responds to the price of a different metal entirely, and [[Neodymium|rare-earth]]-style supply concentration becomes a policy question rather than a geological one. ## Deployment The land question has a clean answer on this shelf. Kerlin computes that one quad per year of photovoltaic electricity needs about 330,000 acres of collector at 15 % efficiency, falling to about 165,000 at 30 % — area scales as 1/η, so doubling cell efficiency halves the land.[^kerlin-land] Against Arizona's 73 million acres, a quad is about 0.45 % of one state; the roughly 100 quads the United States uses annually would be 33 million acres at 15 %.[^kerlin-land][^derived-sc] Those figures are for collector area, not the fenced site, and say nothing about where the demand sits relative to the sun; that gap is what [[Electric_power_transmission|transmission]] and [[Energy_storage|storage]] exist to close. The deployment story by country — China's manufacturing dominance, the United States' utility-scale build-out, and the growth in Latin America, the Middle East and Africa — rests on capacity statistics this page's Portal Books do not tabulate, and the pair carries it. ## Disposal A module is mostly glass and aluminium by mass, with a few hundred grams of silicon, a little silver in the contacts and a polymer encapsulant deliberately hard to take apart. That last property is the whole difficulty: the lamination keeping water out for twenty-five years also resists separation at end of life. ### Recycling Recovery is therefore a delamination problem before it is a materials problem. Glass and frame recover easily and are most of the mass; silicon, silver and the thin-film absorbers are the valuable fraction and the hardest to reach. For [[Cadmium|cadmium]]-bearing thin films recovery is not optional, which made their manufacturers the earliest operators of take-back schemes. Because deployment grew exponentially, the waste stream lags the installed base by the module lifetime and then grows at the same rate — the retirement wave of a technology installed over one decade arrives, compressed, over the next.[^derived-sc][^theis-098] ## See also - [[Photovoltaic_system]] — the array above the cell: kWh per kWp-year - [[Solar-cell_efficiency]] — the fill factor and the band-gap ceiling in detail - [[Solar_power]] - [[Growth_of_photovoltaics]] - [[Band_gap]] — the quantity the selector sets - [[Doping_(semiconductor)]] — how the junction is made - [[Silicon]] — the placed element variant - [[Photoelectric_effect]] ## References [^mitofsky-pv]: Mitofsky, Andrea M. (2018). *Direct Energy.* Part I, "Survey of Energy Conversion Devices" (pp. 33–254), Photovoltaics (pp. 111–148): the photovoltaic effect, junction devices and the cell as a current source in parallel with a diode (page to pin within the chapter). https://open.umn.edu/opentextbooks/textbooks/direct-energy [^mitofsky-carnot]: Mitofsky, Andrea M. (2018). *Direct Energy*, Chapter 8 "Thermoelectrics" (pp. 183–210), pp. 199–200: the Carnot efficiency `eta = 1 - T_c/T_h` applies to heat-to-other-energy converters but not to photovoltaic or piezoelectric devices. [^mitofsky-kb]: Mitofsky, Andrea M. (2018). *Direct Energy*, p. 186: the Boltzmann constant k_B = R/N_A = 1.381×10⁻²³ J/K. [^mitofsky-joule]: Mitofsky, Andrea M. (2018). *Direct Energy*, Chapter 8, p. 201: Joule heating `P = I^2·rho·l/A`, the form the series-resistance loss of a cell takes. [^murphy-99]: Murphy, Thomas (2021). *Energy and Human Ambitions on a Finite Planet*, Chapter 5 "Energy and Fossil Fuels" (pp. 87–182), p. 99: photon energy `E = h·nu = h·c/lambda` (Eq. 5.4) and `E_eV = 1.24/lambda_um` (Eq. 5.5); visible light from 0.4 to 0.7 µm carries 3.1 to 1.8 eV. https://open.umn.edu/opentextbooks/textbooks/energy-and-human-ambitions-on-a-finite-planet [^murphy-solar]: Murphy, Thomas (2021). *Energy and Human Ambitions on a Finite Planet*, Chapter 13, "Solar", within Chapter 6 "Alternative Energy" (pp. 183–322): the solar resource, cell efficiency ceilings and concentrator and space applications (page to pin). [^kerlin-land]: Kerlin, Thomas (2013). *Future Energy: Opportunities & Challenges*, Chapter 3 (pp. 169–191), pp. 185 and 188: photovoltaic land requirement of about 330,000 acres per quad per year at 15 % efficiency and about 165,000 acres at 30 %, against Arizona's 73 million acres. https://open.umn.edu/opentextbooks/textbooks/future-energy-opportunities-challenges [^kerlin-growth]: Kerlin, Thomas (2013). *Future Energy: Opportunities & Challenges*, Chapter 5 (pp. 217–231), p. 229: the exponential-growth arithmetic applied to a generating fleet, growing 0.013 quad to 1 quad at 30 % a year. The book prints "≈15 years"; the expression gives 16.4 years (computed; see sub-manual 10 §A.2). [^theis-098]: Theis, Tom; Tomkin, Jonathan, eds. (2015). *Sustainability: A Comprehensive Foundation.* Chapter "Sustainable Energy Systems" (page to pin; the extraction index does not resolve this book's chapter page ranges): renewable generation as a capital-cost technology with near-zero fuel cost, and end-of-life material flows. https://open.umn.edu/opentextbooks/textbooks/sustainability-a-comprehensive-foundation [^derived-sc]: Computed for this article from the equations on this page: the silicon cutoff wavelength 1.24/1.12 = 1.107 µm; the thermal voltage k·T/q = 25.69 mV at 298.15 K; with I_L = 35 mA/cm², I_0 = 1×10⁻¹² A/cm² and n = 1, V_oc = 0.624 V, v_oc = 24.3, FF = 0.833, P_mpp = 18.2 mW/cm² and η = 18.2 %; the irradiance decade costing (k·T/q)·ln(10) = 59 mV; dV_oc/dT = −(E_g/q − V_oc + 3·k·T/q)/T = −1.9 mV/K = −0.31 %/K, giving −0.106 V over 55 K; the doubling times ln(100)/ln(1.3) = 17.6 yr and ln(100)/ln(1.4) = 13.7 yr; and 100 quads at 15 % = 33 million acres from [^kerlin-land]. The I_L, I_0 and n values are representative single-diode parameters for the sim's silicon preset, not measurements, and are marked ILLUSTRATIVE. [^spec-e38]: Matter & Energy Cluster contract, `_registry/plans/ENERGY_SECTIONS.md` row E38: sim concept (`solar.diode`), single-diode `I = I_L - I_0[exp(qV/(nkT)) - 1]` with `I_L ∝ G` and `V_oc = (nkT/q)ln(I_L/I_0 + 1)`; controls irradiance 0–1,000 W/m² and cell temperature −20 to 80 °C; maximum-power point, `FF = P_mpp/(I_sc·V_oc)` and efficiency read off the I–V and P–V curves; a band-gap select (Si 1.12 eV) sets I_0(T), marked ILLUSTRATIVE. ## Bibliography - Mitofsky, Andrea M. (2018). *Direct Energy.* Part I, Survey of Energy Conversion Devices, pp. 33–254, with Photovoltaics at pp. 111–148 and Relating Energy Conversion Processes at pp. 279–300. https://open.umn.edu/opentextbooks/textbooks/direct-energy - Murphy, Thomas (2021). *Energy and Human Ambitions on a Finite Planet.* Chapter 5, pp. 87–182 (units and the photon), and Chapter 6, Alternative Energy, pp. 183–322 (the solar chapter). https://open.umn.edu/opentextbooks/textbooks/energy-and-human-ambitions-on-a-finite-planet - Kerlin, Thomas (2013). *Future Energy: Opportunities & Challenges.* Chapter 3, pp. 169–191, for collector and photovoltaic land requirements. https://open.umn.edu/opentextbooks/textbooks/future-energy-opportunities-challenges - Theis, Tom; Tomkin, Jonathan, eds. (2015). *Sustainability: A Comprehensive Foundation.* https://open.umn.edu/opentextbooks/textbooks/sustainability-a-comprehensive-foundation ## External links - [*Direct Energy*](https://open.umn.edu/opentextbooks/textbooks/direct-energy), Mitofsky (2018) — the photovoltaics chapter behind this page's theory section - [*Energy and Human Ambitions on a Finite Planet*](https://open.umn.edu/opentextbooks/textbooks/energy-and-human-ambitions-on-a-finite-planet), Murphy (2021) - The Wikipedia pair's *External links* section lists manufacturer, certification and capacity-statistics sources, which this page's shelf does not carry. <!-- MATTERSIM:BEGIN g33 — Matter & Energy Cluster microsim (framework build, specs/sims/Solar_cell.json); do not hand-edit inside --> **Microsim — three.js (Wikitube framework):** *Solar cell* <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/matter/Solar_cell.html" data-title="Solar cell"></div> *Built from `MICROSIM_GUIDE/specs/sims/Solar_cell.json`; part of the [[PORTAL_Matter|Matter portal]] spine (section sims and See-also variants).* <!-- MATTERSIM:END --> ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Solar_cell) : [Wikitube](https://en.wikitube.io/wiki/Solar_cell) · pinned revision [1373990572](https://en.wikipedia.org/w/index.php?oldid=1373990572) · 2026-09-11 ## Previous hub tags Hubs: `Life_Physics`. Portals: [[PORTAL_Energy]]. --- *Matter & Energy Cluster child articles, wave 1 · 2026-09-11 · drafted · Energy row E38 · sim pending (matter/Solar_cell).*