Solar, wind, and batteries: physics, scaling, and supply

A photovoltaic (PV) cell is a semiconductor diode that converts incident photons into an electric current. The conversion has three steps:

1. A photon hits the semiconductor and is absorbed if its energy exceeds the material's bandgap $E_g$.
2. The absorbed photon excites an electron from the valence band to the conduction band, creating an electron-hole pair.
3. The pair is separated by the built-in electric field of the p-n junction, driving current through an external circuit.

The physics implies two structural inefficiencies:

• Photons with $E < E_g$ are not absorbed at all. Their energy passes through the cell.
• Photons with $E > E_g$ are absorbed but the excess energy $E - E_g$ is wasted as heat.

The Shockley–Queisser limit (1961) computes the maximum efficiency of a single-junction PV cell under standard sunlight as a function of bandgap. The optimum bandgap is around 1.34 eV; the resulting limit is ~33.7%.

Real single-junction silicon cells reach ~26–27% in production today, with laboratory records pushing higher. The remaining gap to Shockley-Queisser comes from imperfect light trapping, recombination losses, and series resistance.

To exceed Shockley-Queisser, multi-junction cells stack semiconductors with different bandgaps, each absorbing a different part of the spectrum. Multi-junction cells reach ~47% efficiency under concentrated sunlight in laboratory measurements, but the manufacturing complexity confines them to specialized applications (satellites, concentrator PV). Commercial flat-panel PV remains single-junction or close to it.

About 95% of installed PV capacity worldwide uses crystalline silicon as the absorber, in two variants:

• Monocrystalline silicon (c-Si). Single-crystal wafers, ~26–27% maximum cell efficiency. Higher cost per wafer, higher efficiency per area.
• Polycrystalline silicon (mc-Si). Many small crystals fused, ~22% maximum. Lower wafer cost, slightly lower efficiency.

Manufacturing steps:

1. Mine and refine silicon to electronic-grade purity (~99.9999%).
2. Form into ingots (Czochralski for mono, casting for poly).
3. Slice into wafers ~150 μm thick.
4. Add dopants and form the p-n junction.
5. Apply electrical contacts, anti-reflective coating, encapsulation.
6. Assemble into modules of 60–144 cells.

The industry has consolidated significantly over the past 15 years:

• Cell efficiency has risen from ~14% in 2010 to ~22–24% in 2025 in production modules.
• Module costs have fallen from ~$2/W to ~$0.10–0.20/W over the same period.
• Annual production has grown from a few GW in 2005 to several hundred GW in 2025.
• Manufacturing is geographically concentrated, with much of polysilicon, wafer, cell, and module capacity in China; some specialty positions remain in Korea, Japan, US, Europe.

Alternative PV technologies (thin-film CdTe, CIGS, perovskite, organic) occupy specific niches (large utility scale, building-integrated, specialty applications) but have not overtaken crystalline silicon's combination of efficiency, durability, and manufacturing maturity.

Wind power comes from the kinetic energy of moving air. The available power per unit rotor swept area is

$P/A = \frac{1}{2}\rho v^3,$

where $\rho$ is air density (~1.2 kg/m³ at sea level) and $v$ is wind speed.

The cubic dependence on velocity is the dominant structural feature of wind:

• Doubling wind speed eight times the available power.
• A 10 m/s wind has $1000 \cdot 1.2 / 2 = 600$ W/m².
• A 7 m/s wind (~typical good site annual mean) has $0.49 \cdot 600 = 294$ W/m² of available power.

Not all the wind's kinetic energy can be extracted. The Betz limit (1919) shows that no turbine can extract more than $16/27 \approx 59.3\%$ of the available power. The physics: extracting too much slows the air so much that less of it passes through the rotor, reducing power. The optimum slows the air to about 1/3 of upstream speed.

Real turbines achieve about 35–45% of available wind power at their rated wind speed — somewhat below Betz because of rotor blade, gearbox, and generator losses. Capacity factors (annual energy divided by rated power × 8760 h) are typically 25–40% onshore and 35–55% offshore, reflecting the average wind speeds and how often the turbine operates near rated conditions.

The cubic-velocity scaling explains:

• Why turbine height matters so much (wind speed rises with height above ground; doubling the height can raise mean speed by 30%, raising available power by ~2.2×).
• Why offshore wind has higher capacity factors (steady, faster wind).
• Why a moderately good site is worth ~3× as much energy as a marginally-good one, for the same nameplate.

A modern utility-scale wind turbine has:

• Rotor diameter 120–250 m (commercial offshore now exceeds 200 m).
• Hub height 100–170 m (taller for higher wind speeds aloft).
• Rated power 4–15 MW.
• Blade material mostly fiberglass-reinforced epoxy with some carbon fiber for very long blades.
• Gearbox or direct-drive generator depending on design philosophy.
• Control system that pitches blades, yaws the nacelle, and adjusts torque to maximize power and protect against extreme winds.

Size scales structurally. Power $\propto$ rotor area $\propto$ diameter². Mass and material cost scale with diameter to a higher power (~2.5–3 depending on design). The economic question is whether the larger turbine's higher capacity factor and lower installation cost per unit power justify the higher unit cost. Industry trajectories of the past two decades have answered yes — turbine sizes have grown roughly 1 MW per generation, and energy cost has fallen monotonically.

Offshore wind has different scaling. Foundation costs (fixed-bottom monopiles, jackets, or floating platforms for deep water) push toward larger turbines per foundation. Service costs are higher (boat or helicopter access), so reliability investments pay back differently. Offshore turbines are typically 1–2 generations larger than concurrent onshore.

Wind has structural limits other than physics:

• Land use. A wind farm needs space; transmission to demand centers must follow.
• Site quality distribution. Best sites (high mean wind speed, accessible) fill up first; marginal sites are progressively less economic.
• Capacity-value asymmetry. Wind correlates poorly with summer demand peaks in many regions. The system value of additional wind depends on how much wind is already on the grid (a saturation effect).

Lithium-ion batteries dominate electric vehicles and grid storage. The basic operation: a lithium cation shuttles between two electrodes through an electrolyte, while electrons flow through an external circuit.

The cathode chemistry determines most of the cell's energy density, cost, and cycle life. Common cathode materials in production:

• LFP (lithium iron phosphate, LiFePO₄). Lower energy density (~150–180 Wh/kg), lower cost, longer cycle life, no cobalt or nickel. Dominant in stationary storage and increasingly in standard-range EVs.
• NMC (lithium nickel manganese cobalt oxide). Higher energy density (~220–280 Wh/kg), higher cost, contains cobalt and nickel. Dominant in long-range EVs.
• NCA (lithium nickel cobalt aluminum oxide). Similar to NMC, used in some Tesla cells.
• LMFP (lithium manganese iron phosphate). Intermediate; emerging.

The anode is most commonly graphite, with silicon additions (5–10% by mass) emerging in newer cells to boost capacity. The electrolyte is typically a lithium salt in organic solvents.

Cell formats:

• Cylindrical (e.g., 18650, 21700, 4680). Standardized sizes; production-friendly.
• Prismatic. Rectangular cans; better volumetric packaging.
• Pouch. Flexible packaging; thinner and lighter but more vulnerable to swelling.

A modern lithium-ion EV pack of 70–100 kWh contains hundreds to thousands of cells (depending on format) wired in series and parallel, with thermal management, electronics for cell balancing, and a battery management system.

Solar PV and lithium-ion battery costs have fallen by remarkably steady percentage rates per doubling of cumulative production. The relationship is called Wright's law (after T.P. Wright, 1936) or, equivalently, the learning curve.

For solar PV modules:

• Learning rate ~24% per doubling of cumulative production over 1976–2024.
• Module cost has fallen from ~$100/W (1976) to ~$0.10–0.20/W (2024).
• Cumulative production has doubled roughly 18 times over this period.

For lithium-ion battery packs:

• Learning rate ~18% per doubling, slightly slower than solar.
• Pack cost has fallen from ~$1200/kWh (2010) to ~$120/kWh (2024).
• Continued at a roughly steady rate despite chemistry transitions.

The structural lesson: learning rates appear to be properties of the industry (how it expands, learns, and competes) rather than specific to a generation of technology. Solar PV chemistry has changed substantially (poly to mono, larger wafers, PERC and TOPCon and HJT cell architectures), and the learning rate has been roughly maintained. Lithium-ion chemistries have shifted (LCO to NMC to LFP and back to NMC for high-density), and the pack-level learning rate has held.

Forecasting future costs by extrapolating the learning curve has worked well for solar and batteries from 2010 to 2024. The key uncertainty for any near-term projection is whether cumulative production will continue to double, and how soon. Learning rates are statistical properties; they describe the average over many doublings, not necessarily the next year.

When solar penetration reaches a significant share of a regional grid, the net load (demand minus solar generation) takes on a characteristic shape over the daily cycle.

In the morning, demand rises and solar ramps up; net load stays modest. Midday, solar dominates and net load drops sharply — sometimes to near zero or negative (excess supply curtailed). In the evening, solar falls off as demand peaks for cooking and air conditioning, and net load spikes sharply.

The resulting net-load curve resembles a duck — flat back, deep belly, rising neck — hence 'duck curve.' California's ISO popularized the term in the 2010s.

The duck curve has structural consequences:

• Midday curtailment. Excess solar generation has nowhere to go without storage, transmission, or flexible demand. Curtailed energy is lost.
• Evening ramp. The grid must rapidly increase generation as solar falls; conventional plants designed for slow ramps strain to follow.
• Diminishing solar value. Each additional solar GW at midday displaces less avoided fuel cost than the previous one. The marginal value of solar falls as penetration rises.
• Increasing storage value. A battery that charges at midday and discharges in the evening captures the energy price spread; its value rises with the depth of the duck.

Grid-scale battery deployment has tracked this exactly: California, Texas, Australia, and other regions with high solar penetration have built tens of GW of battery storage primarily to manage the duck curve, with 2–4 hour discharge duration matching the typical solar-to-peak gap.

Longer-duration storage (8+ hours, multi-day) is structurally different — it addresses weather-week and seasonal variability rather than daily cycles, and the technology economics differ accordingly (pumped hydro, compressed air, iron-air, hydrogen).

Each of solar, wind, and batteries depends on specific materials supply chains that concentrate differently.

Solar PV. Polysilicon, glass, silver paste, encapsulant, frames. Polysilicon production concentrates in China, Russia, US, Germany, Malaysia. Silver consumption is non-trivial at scale; alternatives (copper-silver alloys, full-copper) are in development.

Wind turbines. Steel, fiberglass, copper, rare earth permanent magnets (neodymium-iron-boron in direct-drive generators). Rare earth supply concentrates in China; direct-drive turbines that don't use rare-earth magnets (some Vestas, Enercon designs with electromagnetic excitation) trade lower power density for supply-chain independence.

Lithium-ion batteries. Lithium, nickel, cobalt, manganese, graphite, copper, aluminum, electrolyte solvents.

• Lithium is currently sourced primarily from Australia (hard-rock mining), Chile and Argentina (brine extraction), with growing production in Canada, the US, China, and elsewhere. The 'lithium triangle' of Argentina-Bolivia-Chile holds large reserves; processing capacity is more concentrated in China.
• Cobalt is concentrated in the Democratic Republic of Congo (~70% of global production). Refining is concentrated in China. LFP chemistries avoid cobalt entirely.
• Nickel mining concentrates in Indonesia, the Philippines, Russia, Australia. High-purity sulfate-grade nickel for batteries is a more constrained category.
• Graphite (natural and synthetic) both have concentrated supply; China dominates synthetic production.

The broader pattern: each clean-energy supply chain has its own choke points, often in materials processing rather than ore mining. The structural questions for the energy transition concentrate not in whether the reserves exist (they generally do) but in whether processing capacity, recycling, and substitution can keep pace with demand. The next lesson moves these supply considerations into the grid context where they ultimately apply.