Photovoltaic Materials, Devices and Conversion Theory

Introduction and Context

A photovoltaic (PV) device converts optical radiation directly into electrical power. The conversion is enabled by a semiconductor whose electronic structure permits photons to create mobile electron–hole pairs and by an internal electric field that separates these carriers. A practical solar cell therefore combines materials science, semiconductor physics, optical engineering, electrical circuit theory, and thermal analysis.

The most widely deployed technology is crystalline silicon, although thin-film materials such as cadmium telluride (CdTe), copper indium gallium diselenide (CIGS), amorphous silicon, and emerging perovskites are important alternatives. Regardless of material, the central engineering questions are similar: how much sunlight is absorbed, how efficiently carriers are collected, how much recombination occurs, and how closely the device approaches its theoretical voltage and current limits.

Learning Objectives

By the end of this chapter, the reader should be able to:

1. Explain intrinsic and extrinsic semiconductor behavior and the operation of a p–n junction.
2. Describe photon absorption, carrier generation, recombination, and collection in a solar cell.
3. Interpret spectral response, external quantum efficiency, and internal quantum efficiency.
4. Derive and apply the ideal and practical single-diode equations.
5. Interpret I–V and P–V characteristics and calculate [[MATH:P_{max}], fill factor, and efficiency.
6. Predict the effects of irradiance, temperature, series resistance, and shunt resistance.
7. Evaluate a PV cell or module using measured electrical and environmental data.

1. Semiconductor Foundations

1.1 Energy bands and the band gap

In an isolated atom, electrons occupy discrete energy levels. In a crystalline solid, interaction among many atoms produces nearly continuous allowed energy bands. The valence band is normally occupied by bonding electrons, while the conduction band contains mobile electrons. The energy separation between them is the band gap, E_g, measured in electron-volts (eV).

A photon of wavelength λ has energy

where h is Planck’s constant, ν is frequency in hertz, c is the speed of light in vacuum, and λ is wavelength in metres. For convenient solar calculations, E_ph(eV) ≈ 1240/λ(nm). A photon can generate an electron–hole pair only when its energy is approximately equal to or greater than E_g. Excess energy above the band gap is initially converted mainly into lattice heat through thermalisation.

A semiconductor differs from an electrical insulator because its conductivity can be controlled by temperature, impurities, light, and electric fields. Its conductivity is

where σ is conductivity in siemens per metre, q is the elementary charge, n and p are electron and hole concentrations, and μ_n and μ_p are their mobilities.

1.2 Intrinsic and doped semiconductors

An intrinsic semiconductor contains no intentional electrically active impurity. Thermal equilibrium requires equal electron and hole concentrations, n = p = n_i, where n_i is the intrinsic carrier concentration.

Doping introduces controlled impurities. Donor atoms produce n-type material, in which electrons are majority carriers. Acceptor atoms produce p-type material, in which holes are majority carriers. Under nondegenerate equilibrium conditions, the mass-action law is

This relation assumes thermal equilibrium and nondegenerate semiconductor statistics. In an n-type region, approximately n ≈ N_D and p ≈ n_i²/N_D, provided donor concentration N_D is sufficiently larger than n_i and compensation is negligible. Analogous relations apply to p-type material with acceptor concentration N_A.

2. The p–n Junction and Photovoltaic Action

2.1 Junction formation

When p-type and n-type materials are joined, electrons diffuse from the n side into the p side, while holes diffuse in the opposite direction. Their recombination leaves behind fixed ionised donors and acceptors. This charged region, depleted of mobile carriers, is the depletion region.

The resulting electric field points from the positively charged donor ions toward the negatively charged acceptor ions. It opposes further diffusion and establishes a built-in potential. For an abrupt junction at equilibrium,

where k is Boltzmann’s constant, T is absolute temperature in kelvin, and the doping concentrations are in consistent units. This equation assumes an abrupt, nondegenerate junction in thermal equilibrium.

A simplified depletion width is

where ε_s is semiconductor permittivity. Under applied bias, the potential term is modified; forward bias narrows the depletion region and reverse bias widens it.

2.2 Separation of photogenerated carriers

When sunlight enters the absorber, photons with adequate energy create electron–hole pairs. Carriers generated within or near the depletion region are separated by the electric field. Carriers generated outside that region must diffuse toward the junction before recombining. Selective contacts then extract electrons and holes to opposite electrodes, producing current through an external load.

The direction of conventional current is opposite to electron motion. Under illumination, the cell behaves approximately as a current source in parallel with a diode. It can deliver power because the light-generated current shifts the operating point away from the dark diode characteristic.

2.3 Materials and device architectures

Crystalline silicon has an indirect band gap of about 1.12 eV at room temperature and therefore requires relatively thick absorbers. It offers high stability, abundant raw material, and a mature manufacturing base. CdTe has a near-optimal direct band gap of about 1.5 eV and uses thin absorber layers, but cadmium management and tellurium availability require responsible materials governance. CIGS has a tunable band gap and strong absorption, while perovskites offer highly promising efficiencies and low-temperature processing but face challenges involving long-term stability, lead management, and scalable encapsulation.

A conventional crystalline-silicon cell includes a light-receiving front surface, antireflection coating, textured surface, emitter, base, rear surface field or passivation, and metallic contacts. Modern passivated-contact cells reduce recombination at interfaces and improve voltage.

3. Optical Absorption and Spectral Response

3.1 Absorption and generation

The absorption coefficient, α(λ), describes how rapidly optical intensity decreases with depth. In a uniform material, intensity approximately follows

where x is depth and I₀ is incident intensity at the surface. The reciprocal 1/α is an approximate absorption depth. Direct-band-gap materials generally absorb strongly near the band edge; indirect materials require phonon-assisted transitions and often thicker layers.

If the incident spectral photon flux is Φ(λ) photons per square metre per second per unit wavelength, the ideal generated current density is related to the collected fraction of those photons. A general expression is

where the integration covers the relevant solar spectrum, EQE(λ) is external quantum efficiency, and J_sc is short-circuit current density. The formula assumes steady illumination and that each collected electron contributes charge q.

3.2 Quantum efficiency

External quantum efficiency (EQE) is the ratio of collected charge carriers to incident photons at a specified wavelength:

Internal quantum efficiency (IQE) uses absorbed photons rather than incident photons. Thus, approximately,

where R(λ) is front-surface reflectance, assuming transmission and parasitic absorption are negligible or separately accounted for. EQE includes optical losses such as reflection; IQE focuses more directly on carrier generation and collection.

The spectral response, measured in amperes per watt, is related to EQE by

Here SR is spectral response. If wavelength is expressed in nanometres, the numerical conversion must include the factor 10^-9 to convert nanometres to metres.

A falling short-wavelength response may indicate front-surface reflection, dead layers, or emitter recombination. A falling long-wavelength response may indicate insufficient absorber thickness, weak rear reflection, or poor minority-carrier diffusion length.

4. Carrier Transport and Recombination

4.1 Drift and diffusion

Carrier motion occurs by drift in an electric field and diffusion down a concentration gradient. For electrons, a one-dimensional current-density expression is

and for holes,

where E is electric field, D_n and D_p are diffusion coefficients, and signs follow the conventional current convention. The Einstein relation connects mobility and diffusion coefficient under near-equilibrium conditions:

4.2 Recombination mechanisms

Recombination removes electrons and holes before collection. Important mechanisms include:

• Radiative recombination: an electron recombines with a hole and emits a photon.
• Shockley–Read–Hall recombination: defects or impurities provide intermediate energy states in the band gap.
• Auger recombination: energy from recombination is transferred to a third carrier; it becomes important at high carrier concentration.
• Surface and interface recombination: dangling bonds and imperfect passivation accelerate loss near surfaces and contacts.

The minority-carrier diffusion length is

where τ is the effective carrier lifetime. Collection is generally improved when the relevant diffusion length is comparable to or greater than the distance carriers must travel.

The open-circuit voltage is reduced by recombination. In an idealised diode under illumination,

where n is the ideality factor, I_ph is photocurrent, and I₀ is reverse saturation current. This equation assumes the single-diode model and steady-state operation.

5. The Single-Diode Model

5.1 Ideal model

The illuminated ideal cell equation is

where I is terminal current, V is terminal voltage, and all currents refer to the chosen terminal sign convention. For an ideal cell, n = 1, no series resistance exists, and shunt leakage is absent.

At short circuit, V = 0, so I_sc ≈ I_ph. At open circuit, I = 0, giving the expression for V_oc.

5.2 Practical model with parasitic resistances

A practical single-diode equation is

where R_s is series resistance, R_sh is shunt resistance, and V_T = kT/q is thermal voltage. At 25 °C, V_T is approximately 25.7 mV. The equation is implicit because I appears on both sides and is commonly solved numerically.

Series resistance represents bulk resistance, contact resistance, and interconnect resistance. It mainly reduces the slope near the high-voltage portion of the I–V curve and lowers the fill factor. Shunt resistance represents leakage paths across the junction; low R_sh reduces current near short circuit and also lowers fill factor.

5.3 I–V, P–V, and performance parameters

Power delivered to an external load is

The maximum-power point is defined by (V_mp, I_mp), and

The fill factor is

and conversion efficiency is

where P_in is incident optical power. Current is conventionally positive in the power-producing quadrant; the precise sign may differ among instruments.

The I–V curve is nearly horizontal in its current-source region, bends through a knee near maximum power, and becomes nearly vertical in its voltage-source region. The P–V curve is zero at short circuit and open circuit and has a maximum between them. Maximum-power-point tracking (MPPT) adjusts the operating voltage so that the system remains near this peak as irradiance and temperature vary.

Figure: Representative I–V curve with short-circuit and open-circuit limits, and corresponding P–V curve with its maximum-power point.

6. Effects of Operating Conditions

6.1 Irradiance

Short-circuit current is approximately proportional to irradiance over the normal operating range:

where G is irradiance in W/m². Open-circuit voltage varies approximately logarithmically with photocurrent:

This approximation assumes constant temperature and unchanged recombination behavior. Increasing irradiance generally increases P_max, while voltage rises only modestly.

6.2 Temperature

As temperature increases, reverse saturation current rises strongly because intrinsic carrier concentration increases. Consequently, V_oc and usually P_max decrease, while I_sc increases slightly. A manufacturer’s temperature coefficient is commonly expressed in %/°C or A/°C. For a parameter X,

where β_X is the temperature coefficient and the approximation is valid over a specified temperature range.

6.3 Partial shading and mismatch

Cells connected in series carry the same current. A shaded cell can therefore limit a string and become reverse biased, creating a hot spot. Bypass diodes reduce the risk by allowing current to bypass a shaded group, although they also reduce available voltage. In parallel strings, unequal voltage conditions can cause circulating currents unless properly controlled.

7. Worked Example: Cell Performance

A cell operates under a test condition with V_oc = 0.62 V, I_sc = 5.0 A, V_mp = 0.50 V, and I_mp = 4.4 A. Incident optical power is 1000 W/m² over an active area of 0.015 m². Determine maximum power, fill factor, and efficiency.

Maximum power:

Incident power:

Fill factor:

Efficiency:

The result indicates that the cell converts about one-seventh of incident radiant power into electrical power under the stated conditions. Losses include below-band-gap transmission, thermalisation, recombination, reflection, resistance, and nonideal contacts.

8. Applied Case: Diagnosing a Low-Power PV Module

Background

This illustrative case concerns a 60-cell silicon module rated at 300 W under standard test conditions (STC: 1000 W/m², 25 °C cell temperature, and a specified reference spectrum). After installation, its measured output is only 245 W on a clear day.

Problem

The engineer must determine whether the reduction arises from temperature, irradiance, shading, wiring losses, or module degradation.

Analysis and approach

The module backsheet temperature is measured at 55 °C. If the module power temperature coefficient is −0.40%/°C, the temperature increase above 25 °C is 30 °C. The approximate power reduction is

Thus, temperature alone predicts approximately 300 × 0.88 = 264 W, before accounting for wiring and spectral effects. Inspection then finds a partially shaded lower-row cell group and a loose connector. Thermal imaging shows a warm bypass-diode region, consistent with activation under shading. After removing the obstruction and repairing the connector, measured output rises to 258 W, which is consistent with the remaining temperature-related reduction and measurement uncertainty.

Outcome and learning points

The diagnosis demonstrates that nameplate power is not a guaranteed field output. Engineers should record irradiance, cell temperature, I–V curves, shading geometry, connector condition, and module mismatch. Comparing only ambient temperature with STC can mislead because cell temperature is often substantially higher than ambient temperature. I–V tracing and infrared inspection are complementary: the former identifies electrical parameter changes, while the latter can locate hot spots and abnormal current paths.

9. Losses, Limitations, and Best Practices

The principal loss mechanisms are reflection, incomplete absorption, transmission of sub-band-gap photons, thermalisation of excess photon energy, bulk and surface recombination, resistive loss, optical shading by contacts, and mismatch between cells. Laboratory efficiency does not automatically imply field reliability; encapsulation, thermal cycling, ultraviolet exposure, humidity, mechanical stress, and potential-induced degradation must also be considered.

Good engineering practice includes using calibrated reference cells, controlling spectral and temperature conditions during testing, reporting active area and measurement uncertainty, applying four-wire measurements where appropriate, and distinguishing cell, module, and array ratings. Models should be fitted to measured data only within their validity range. A single-diode model is valuable for design and simulation, but it does not fully represent spatially distributed shading, dynamic capacitance, hysteresis, or complex degradation.

PV design also has governance responsibilities. Hazardous materials should be managed through compliant manufacturing, worker protection, recycling, and end-of-life pathways. Electrical installations must follow applicable standards for insulation, grounding, overcurrent protection, rapid shutdown where required, and safe connection of DC equipment. AI-assisted diagnostics can identify abnormal I–V curves or thermal images, but training-data quality, explainability, cybersecurity, and human verification remain essential.

Contemporary Developments

Current research focuses on tandem cells that combine absorbers with different band gaps, passivated and interdigitated contacts, bifacial modules, advanced light trapping, and durable perovskite–silicon tandems. Tandem designs reduce thermalisation and transmission losses by assigning different spectral regions to different subcells. Their engineering challenges include current matching, interface recombination, long-term stability, manufacturability, and reliable outdoor certification.

Chapter Summary

Photovoltaic conversion begins when photons with energy at least equal to the semiconductor band gap generate electron–hole pairs. A p–n junction creates an electric field that separates carriers, while diffusion, drift, and selective contacts enable extraction. Optical absorption and carrier collection determine spectral response and quantum efficiency. Recombination through bulk, surface, radiative, defect-assisted, and Auger processes reduces current and voltage.

The single-diode model represents a PV cell as a photocurrent source, diode, series resistance, and shunt resistance. Its I–V curve provides I_sc, V_oc, and the maximum-power point; the P–V curve shows the operating peak used by MPPT controllers. Irradiance mainly affects current, whereas temperature strongly affects voltage. Series resistance, shunt leakage, mismatch, shading, and thermal conditions explain much of the difference between laboratory ratings and field performance.

Key Terms

Band gap: Energy separation between the valence and conduction bands.

Photovoltaic effect: Direct conversion of light into electrical energy.

Electron–hole pair: A mobile electron and the corresponding vacancy left in the valence band.

Doping: Intentional introduction of impurities to control carrier concentration.

p–n junction: Interface between p-type and n-type semiconductor regions.

Depletion region: Junction region depleted of mobile carriers and containing fixed ionised dopants.

Built-in potential: Equilibrium electrostatic potential across a p–n junction.

Photocurrent: Current generated by absorbed light and collected carriers.

Recombination: Process in which an electron and hole cease to be available as mobile carriers.

Carrier lifetime: Effective average time before a carrier recombines.

Diffusion length: Average distance a minority carrier travels before recombination.

External quantum efficiency: Collected carriers per incident photon at a wavelength.

Internal quantum efficiency: Collected carriers per absorbed photon.

Spectral response: Photocurrent generated per unit incident optical power at a wavelength.

Single-diode model: Equivalent circuit containing a photocurrent source, diode, and parasitic resistances.

Fill factor: Ratio of maximum power to the product of open-circuit voltage and short-circuit current.

Series resistance: Effective resistance causing internal voltage and power loss.

Shunt resistance: Effective parallel leakage resistance across a cell.

Maximum-power point: Operating point at which the product of voltage and current is greatest.

MPPT: Control method that maintains operation near the maximum-power point.

Review Questions

Short Answer Questions

1. Why does a photon with energy below the band gap generally fail to generate a useful electron–hole pair?
2. Distinguish external quantum efficiency from internal quantum efficiency.
3. What physical processes produce the depletion region in a p–n junction?
4. Why does increasing irradiance affect short-circuit current more strongly than open-circuit voltage?
5. State the effects of high series resistance and low shunt resistance on a PV I–V curve.

Long Answer Questions

1. Explain the operation of a p–n junction solar cell from photon absorption to current extraction.
2. Derive the principal performance parameters from the single-diode model and discuss its assumptions.
3. Explain radiative, Shockley–Read–Hall, Auger, and surface recombination and their effects on device performance.
4. Discuss how wavelength-dependent absorption, reflection, and collection determine spectral response.
5. Compare the effects of irradiance, cell temperature, partial shading, and mismatch on module output.

Analytical / Application Questions

1. A cell has V_oc=0.65 V, I_sc=6 A, V_mp=0.52 V, and I_mp=5.4 A. Calculate P_max and fill factor.
2. A module rated at 400 W has a power temperature coefficient of −0.35%/°C. Estimate its power at a cell temperature of 60 °C when irradiance remains at the reference value and the reference temperature is 25 °C.
3. An I–V curve shows a strong reduction in current near short circuit but nearly normal open-circuit voltage. Identify the most likely parasitic or environmental causes and propose two diagnostic tests.

Multiple Choice Questions with Answers

Question 1

Which condition is required for a photon to generate an electron–hole pair in an ideal semiconductor absorber?

A. Its energy must be less than the band gap.

B. Its energy must be approximately equal to or greater than the band gap.

C. Its wavelength must be independent of the band gap.

D. Its frequency must be zero.

Correct Answer: B. Its energy must be approximately equal to or greater than the band gap.

Question 2

What is the principal electrical effect of increasing irradiance at constant temperature?

A. A strong increase in short-circuit current

B. A strong decrease in short-circuit current

C. A complete loss of open-circuit voltage

D. No change in photocurrent

Correct Answer: A. A strong increase in short-circuit current

Question 3

Which expression represents the photovoltaic fill factor?

A. V_oc/I_sc

B. P_in/P_max

C. P_max/(V_ocI_sc)

D. I_sc/V_oc

Correct Answer: C. P_max/(V_ocI_sc)

Question 4

A low shunt resistance primarily represents which condition?

A. A parallel leakage path

B. An ideal insulated junction

C. A reduction in photon energy

D. An increase in band-gap energy

Correct Answer: A. A parallel leakage path

Question 5

At open circuit, which terminal condition applies?

A. V=0

B. I=0

C. P=0 and I=0 only because the cell is shorted

D. I=I_sc and V=0

Correct Answer: B. I=0

Question 6

For the worked cell with V_mp=0.50 V and I_mp=4.4 A, what is maximum power?

A. 0.11 W

B. 2.20 W

C. 4.90 W

D. 9.40 W

Correct Answer: B. 2.20 W

Question 7

Which recombination mechanism uses defect or impurity energy levels in the band gap?

A. Radiative recombination

B. Auger recombination

C. Shockley–Read–Hall recombination

D. Thermal reflection

Correct Answer: C. Shockley–Read–Hall recombination

Question 8

What is the usual effect of increasing cell temperature on silicon-cell open-circuit voltage?

A. It increases substantially.

B. It decreases.

C. It becomes exactly zero.

D. It is unaffected under all conditions.

Correct Answer: B. It decreases.

Question 9

What is the purpose of an MPPT controller?

A. To maintain operation near the maximum-power point

B. To eliminate all semiconductor recombination

C. To increase the band gap during operation

D. To short-circuit the module continuously

Correct Answer: A. To maintain operation near the maximum-power point

Question 10

A cell has V_oc=0.62 V, I_sc=5.0 A, and P_max=2.20 W. What is its approximate fill factor?

A. 35.5%

B. 50.0%

C. 71.0%

D. 88.0%

Correct Answer: C. 71.0%