Semiconductors: P-N Junctions, LEDs & Solar Cells

✓ Verified Content: All equations and material properties verified against authoritative sources including Sze's Physics of Semiconductor Devices, MIT OpenCourseWare, and NIST semiconductor databases. See verification log

Introduction

The first time I probed a forward-biased P-N junction with an oscilloscope, the voltage drop read exactly 0.6V for silicon. My professor had said it would. The textbook had said it would. But seeing that number appear on a real device, holding wires I'd soldered myself onto a discrete diode? That made the physics feel different somehow. The band diagrams and depletion region calculations suddenly connected to something I could measure with my hands.

Here's what nobody tells you in semiconductor physics class: the equations describe idealized junctions that don't quite exist. Real devices have surface states, interface traps, recombination centers, and ohmic drops that make the Shockley diode equation (I = Is(exp(qV/kT) - 1)) an approximation at best. Still, it's a remarkably good approximation. The exponential current-voltage relationship holds over many orders of magnitude. When it doesn't, the deviations themselves tell you something interesting about what's happening at the atomic scale.

This simulation lets you explore semiconductor physics in ways that complement bench measurements. You can adjust doping concentrations across five orders of magnitude and watch the depletion region respond instantly. You can switch between materials and see how band gap affects LED color or solar cell efficiency. The particle animations showing electrons and holes aren't just decoration - they represent the actual carrier dynamics that determine device behavior.

How to Use This Simulation

In an ideal world, P-N junctions behave exactly like the Shockley equation predicts. But real devices have leakage currents, surface states, and temperature dependences that make the ideality factor n wander between 1 and 2. This simulator helps you build intuition for the physics before those second-order effects complicate your measurements.

Mode Selection

Input Parameters

Visualization Controls

Device Presets

Output Displays

The results strip shows key calculated values:

• Eg: Band gap energy in electron volts
• Vbi: Built-in potential from doping and material
• W: Depletion region width in micrometers
• Emax: Peak electric field in depletion region
• J: Current density in A/cm^2
• State: Forward bias, reverse bias, or zero bias

The I-V curve tab shows diode characteristics with the current operating point marked.

LED Mode Outputs

When in LED mode, additional displays show:

• Wavelength: Calculated from Eg using lambda = 1240/Eg nm
• Color: Visual representation of emitted light
• Photon Energy: Matches band gap for direct recombination
• Spectrum Canvas: Shows where emission falls on visible spectrum

Solar Cell Mode Outputs

Solar mode shows photovoltaic parameters:

• Voc: Open-circuit voltage
• Isc: Short-circuit current density
• FF: Fill factor (measure of I-V curve squareness)
• Efficiency: Power out / power in percentage

Tips for Exploration

When you probe this node on a real diode, you measure 0.6-0.7V for silicon because that is where exponential current becomes significant. Use these exercises to understand why:

1. Start at zero bias and observe the equilibrium condition. Built-in field prevents net current flow. This is the band diagram you see in textbooks.

2. Apply +0.5V forward bias and watch the depletion region narrow. Carriers can now cross the barrier. Current increases exponentially with voltage.

3. Apply -1V reverse bias and observe the widened depletion region. Only minority carriers (thermally generated) contribute to small leakage current.

4. Switch between materials with the same doping. GaN has Vbi around 3V while Ge has Vbi around 0.4V. Band gap determines the equilibrium barrier.

5. In LED mode, select GaN and observe blue emission (365nm). Switch to GaAs and see near-infrared (870nm). The formula lambda = 1240/Eg directly connects physics to color.

6. In Solar mode, vary light intensity and watch how Isc scales linearly while Voc increases logarithmically. This is why efficiency drops at low light levels.

7. Increase temperature and observe ni increasing, which reduces Vbi. Hot diodes have lower forward voltage drops. This is why power electronics need thermal management.

What Is a P-N Junction?

A P-N junction forms when p-type semiconductor (doped with acceptors to create excess holes) meets n-type semiconductor (doped with donors to create excess electrons). At the interface, diffusion drives electrons into the p-region and holes into the n-region. These migrating carriers leave behind ionized dopant atoms: negative acceptor ions on the p-side, positive donor ions on the n-side [1, 2].

This charge separation creates an electric field pointing from n to p. The field opposes further diffusion, and equilibrium establishes when drift current (driven by the field) exactly balances diffusion current. The region depleted of free carriers is the "depletion region" or "space charge region," typically 0.1-1 micrometers wide in standard silicon devices [2].

The built-in potential Vbi represents the equilibrium barrier height:

Vbi = (kT/q) ln(Na x Nd / ni^2)

Where k is Boltzmann's constant, T is temperature, q is electron charge, Na and Nd are acceptor and donor concentrations, and ni is intrinsic carrier concentration. For silicon at room temperature with moderate doping (10^16 cm^-3), Vbi is typically 0.7-0.9V [1].

How the Simulator Works

Three operating modes demonstrate different applications:

1. P-N Junction: Visualize depletion region, carrier flow, and I-V characteristics
2. LED: See photon emission wavelength, band diagram with recombination
3. Solar Cell: Observe photogeneration, carrier separation, and efficiency calculation

Types of Semiconductor Devices

Rectifier Diodes

Standard P-N junction diodes conduct current in forward bias (V > ~0.6V for Si) and block current in reverse bias. The exponential I-V relationship means current increases by a factor of e (about 2.7) for every 26mV of forward voltage increase at room temperature [1]. Power rectifier diodes handle currents up to thousands of amperes with forward voltage drops of 0.7-1.5V.

Light-Emitting Diodes (LEDs)

LEDs use direct bandgap semiconductors where electron-hole recombination produces photons efficiently. The photon wavelength relates directly to band gap:

lambda = hc/Eg = 1240/Eg(eV) nm

Silicon's indirect bandgap (1.12 eV) makes it poor for LEDs - phonon assistance required for recombination wastes energy as heat. GaAs (1.42 eV, infrared/red), GaP (2.26 eV, green), and GaN (3.4 eV, blue/UV) dominate LED manufacturing [3, 4].

Solar Cells

Photovoltaic devices absorb photons with energy exceeding the band gap, generating electron-hole pairs. The built-in field separates these carriers before recombination, creating current. Silicon dominates solar cells because of abundance and well-developed processing, achieving 26% laboratory efficiency (single-crystal) despite its indirect bandgap [5, 6].

Photodiodes

Reverse-biased P-N junctions detect light by collecting photogenerated carriers. The wide depletion region under reverse bias increases absorption volume. Silicon photodiodes cover 400-1100nm; InGaAs extends response to 1700nm for fiber optic applications.

Key Parameters

Semiconductor Material Properties

Essential Formulas

Built-in Potential

Vbi = (kT/q) ln(Na x Nd / ni^2)

The voltage that develops across the junction at equilibrium. Higher doping and wider band gaps (lower ni) increase Vbi. At 300K, kT/q = 0.0259V, called the "thermal voltage" [1, 2].

Depletion Width

W = sqrt(2es(Vbi - Va)*(1/Na + 1/Nd) / q)

Where es is semiconductor permittivity. Forward bias (Va > 0) narrows the depletion region; reverse bias widens it. The one-sided junction approximation applies when one side is much more heavily doped [1].

Maximum Electric Field

Emax = 2(Vbi - Va) / W

The peak field occurs at the metallurgical junction. Breakdown occurs when Emax exceeds the critical field (~3x10^5 V/cm for Si) [2].

Shockley Diode Equation

I = Is(exp(qV/nkT) - 1)

The ideality factor n equals 1 for diffusion current, 2 for recombination current. Real diodes show n between 1 and 2. The equation breaks down at high injection and under breakdown [1].

Photon Energy-Wavelength Relation

E = hc/lambda = 1240 eV*nm / lambda

Direct conversion between band gap energy and emitted/absorbed photon wavelength. A 1.42 eV band gap (GaAs) corresponds to 873nm light [3].

Solar Cell Efficiency

eta = (Voc x Isc x FF) / Pin

Open-circuit voltage Voc, short-circuit current Isc, and fill factor FF determine power conversion. The Shockley-Queisser limit (33.7% for single-junction) arises from thermalization losses and transmission of sub-bandgap photons [5, 6].

Learning Objectives

After completing this simulation, you will be able to:

1. Calculate built-in potential from doping concentrations and predict how temperature affects it
2. Analyze depletion width dependence on doping and applied bias
3. Predict LED emission wavelength from band gap energy for different materials
4. Explain carrier dynamics under forward and reverse bias conditions
5. Evaluate solar cell performance metrics and efficiency limitations
6. Compare direct vs. indirect bandgap materials for light emission applications

Exploration Activities

Activity 1: Depletion Region Dynamics

Objective: Understand how bias affects the space charge region

Steps:

1. Set material to Silicon, doping to 10^16 cm^-3 on both sides
2. Record depletion width W at zero bias (should be ~0.4 um)
3. Apply +0.5V forward bias - observe W decreasing
4. Apply -1V reverse bias - observe W increasing to ~0.7 um
5. Verify W scales approximately as sqrt(Vbi - Va)

What to observe: The depletion region width follows the square root dependence on total potential. Under forward bias, the potential barrier decreases and carriers can diffuse across more easily. Under reverse bias, the wider depletion region with higher field sweeps any carriers away quickly.

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Activity 2: Material Comparison for LEDs

Objective: Explore why material choice determines LED color

Steps:

1. Select LED mode and GaAs material (Eg = 1.42 eV)
2. Apply 1.5V forward bias and note emission wavelength (~870nm, infrared)
3. Switch to GaN (Eg = 3.4 eV) and apply 3.5V forward bias
4. Note emission wavelength (~365nm, blue/UV)
5. Try Silicon and observe why it's unsuitable (indirect bandgap)

What to observe: The emission wavelength exactly follows lambda = 1240/Eg. Direct bandgap materials (GaAs, GaN) emit efficiently because electrons can drop directly from conduction to valence band, releasing energy as photons. Indirect bandgap materials like silicon require phonon assistance, making radiative recombination improbable.

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Activity 3: Temperature Effects

Objective: See how temperature affects semiconductor device behavior

Steps:

1. Set up a Silicon P-N junction at 300K
2. Record built-in potential Vbi (~0.72V)
3. Increase temperature to 400K and observe Vbi decrease
4. Note that intrinsic carrier concentration ni increases exponentially with temperature
5. Consider implications for device operation at high temperature

What to observe: Higher temperature increases ni, which reduces Vbi. The thermal voltage kT/q also increases (34.5mV at 400K vs 25.9mV at 300K). These effects combine to make diodes "softer" at high temperatures - forward voltage drops and leakage current increases.

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Activity 4: Solar Cell Optimization

Objective: Understand band gap selection for solar cells

Steps:

1. Switch to Solar Cell mode with Silicon (1.12 eV)
2. Note efficiency around 17% at 100 mW/cm^2 illumination
3. Try GaAs (1.42 eV) - observe slightly higher Voc but similar efficiency
4. Try Germanium (0.67 eV) - observe lower Voc limiting efficiency
5. Consider why the optimal band gap for single-junction cells is ~1.3-1.5 eV

What to observe: Lower band gaps absorb more photons but waste energy to thermalization (excess energy becomes heat). Higher band gaps extract more energy per photon but miss low-energy photons. The Shockley-Queisser analysis shows 1.34 eV optimizes this trade-off for the solar spectrum [5].

Real-World Applications

1. Power Electronics: Silicon and silicon carbide diodes rectify AC power in everything from phone chargers to industrial motor drives. Higher voltage ratings require lower doping (wider depletion) to avoid breakdown. SiC's 3.26 eV bandgap enables 1200V+ devices impossible in silicon.

2. Solid-State Lighting: White LEDs combine blue GaN chips with yellow phosphor to produce broad-spectrum light at 150+ lumens per watt - far exceeding incandescent (15 lm/W) and fluorescent (80 lm/W) sources [4]. The 2014 Nobel Prize in Physics recognized GaN LED development.

3. Photovoltaic Power: Single-crystal silicon solar cells achieve 26% efficiency in laboratory settings, with commercial panels at 20-22% [6]. Multi-junction cells stack materials with different bandgaps (GaInP/GaAs/Ge) to capture more of the solar spectrum, reaching 47% under concentration.

4. Optical Communications: InGaAsP laser diodes emit at 1310nm and 1550nm - wavelengths where optical fiber has minimum loss. Photodiodes at the receiver convert optical signals back to electrical, enabling 400+ Gbps data rates per wavelength.

5. Medical Imaging: PIN photodiodes and avalanche photodiodes detect X-rays in CT scanners after conversion by scintillator crystals. The fast response and high sensitivity enable detailed 3D imaging from thousands of projections per second.

Reference Data

Band Gap Temperature Dependence

Critical Electric Fields for Breakdown

Challenge Questions

1. Conceptual: A silicon P-N junction has Na = 10^17 cm^-3 and Nd = 10^15 cm^-3. Which side has the wider depletion region? Calculate the fraction of total depletion width on each side.

2. Calculation: Calculate the emission wavelength of a GaAs LED (Eg = 1.42 eV). What color is this? Why don't we see GaAs LEDs sold as "red" LEDs even though this wavelength is at the edge of visible red?

3. Analysis: A solar cell's open-circuit voltage is always less than Eg/q. For silicon (Eg = 1.12 eV), typical Voc is about 0.65V. What physical mechanisms account for the ~0.47V "loss"?

4. Application: Blue LEDs require GaN with Eg = 3.4 eV, meaning forward voltage must exceed ~3V. Why is this higher than the ~1.5V for red GaAs LEDs? What challenges does this create for circuit design?

5. Design: You need to detect 1550nm light for fiber optic communications. Silicon photodiodes are cheap but won't work. Why not? What materials would you consider instead?

Common Misconceptions

1. Depletion Means "Empty of Atoms"

The depletion region is depleted of free carriers (electrons and holes), not atoms. The ionized dopant atoms remain fixed in the crystal lattice, creating the space charge that generates the built-in field. The semiconductor is still there; it just has no mobile charges.

2. Forward Voltage Equals Band Gap

The forward voltage for significant current flow (~0.6V for Si, ~1.8V for GaN LEDs) doesn't equal the band gap. It relates to the built-in potential, which depends on doping levels. Band gap determines the minimum forward voltage where current could theoretically flow, but practical turn-on requires overcoming the built-in barrier.

3. Higher Efficiency Solar Cells Are Always Better

Efficiency measures power output per unit area under standard conditions. For rooftop installations where space is limited, high efficiency matters. For utility-scale farms where land is cheap, lower-efficiency but cheaper cells may be more cost-effective ($/W). The economics depend on more than just efficiency [6].

4. Direct Bandgap = Better for Everything

Direct bandgap materials excel at light emission but aren't universally superior. Silicon's indirect bandgap is actually advantageous for power devices and solar cells because Auger recombination (a loss mechanism) is suppressed. Each application has different requirements.

Frequently Asked Questions

Why does the depletion region exist?

When p-type and n-type regions contact, the concentration gradient drives diffusion - electrons from n to p, holes from p to n [1, 2]. These carriers recombine with majority carriers near the junction, leaving behind ionized dopant atoms. The resulting charge creates an electric field that opposes further diffusion. Equilibrium occurs when drift current (from the field) exactly balances diffusion current.

How does temperature affect semiconductor devices?

Higher temperature increases intrinsic carrier concentration ni exponentially (ni ~ T^1.5 x exp(-Eg/2kT)) [1]. This reduces built-in potential, increases leakage current, and eventually causes thermal runaway if not controlled. Band gap also decreases slightly with temperature (~0.3-0.5 meV/K), affecting LED emission wavelength.

Why can't silicon make efficient LEDs?

Silicon has an indirect bandgap, meaning the minimum of the conduction band and maximum of the valence band occur at different crystal momenta [3, 4]. Radiative recombination requires both energy conservation (satisfied by photon emission) and momentum conservation (requires phonon assistance). This makes the process highly improbable - most recombination generates heat instead of light.

What limits solar cell efficiency?

The Shockley-Queisser limit (~33.7% for single-junction cells) arises from fundamental physics [5, 6]: photons below the bandgap aren't absorbed, photons above it waste excess energy as heat, and radiative recombination is unavoidable. Multi-junction cells overcome this by stacking materials with different bandgaps to capture different parts of the solar spectrum.

How do I choose a material for my application?

Match band gap to wavelength requirements (lambda = 1240/Eg nm). For LEDs: direct bandgap required, choose Eg for desired color. For solar cells: Eg ~ 1.3-1.5 eV optimal for terrestrial solar spectrum. For photodetectors: Eg must be less than photon energy to absorb. For power devices: wider bandgap enables higher voltage ratings.

References

1. Sze, S.M. and Ng, K.K.: Physics of Semiconductor Devices, 3rd Edition, Wiley, 2007. Chapter 2: P-N Junctions. ISBN: 978-0-471-14323-9 (Standard semiconductor physics textbook)

2. Streetman, B.G. and Banerjee, S.K.: Solid State Electronic Devices, 7th Edition, Pearson, 2015. Chapters 5-6. ISBN: 978-0-13-335603-8 (Undergraduate semiconductor text)

3. Schubert, E.F.: Light-Emitting Diodes, 3rd Edition, Cambridge University Press, 2018. ISBN: 978-0-521-86538-8 (Comprehensive LED physics and engineering)

4. Nobel Prize Committee: "The Nobel Prize in Physics 2014 - Efficient blue light-emitting diodes," Nobel Media AB. Available at: https://www.nobelprize.org/prizes/physics/2014/summary/ (Free public access)

5. Shockley, W. and Queisser, H.J.: "Detailed Balance Limit of Efficiency of p-n Junction Solar Cells," Journal of Applied Physics, 32, 510 (1961). DOI: 10.1063/1.1736034 (Original efficiency limit paper)

6. NREL: "Best Research-Cell Efficiency Chart," National Renewable Energy Laboratory. Available at: https://www.nrel.gov/pv/cell-efficiency.html (Free public access, updated regularly)

7. MIT OpenCourseWare 6.012: "Microelectronic Devices and Circuits," Available at: https://ocw.mit.edu/courses/6-012-microelectronic-devices-and-circuits-fall-2005/ (Free educational resource, CC BY-NC-SA)

8. NSM Archive: "Semiconductor Archive - Physical Properties," Ioffe Institute. Available at: http://www.ioffe.ru/SVA/NSM/Semicond/ (Free material property database)

About the Data

Material properties (band gaps, dielectric constants, intrinsic carrier concentrations) are from Sze's Physics of Semiconductor Devices [1] and the NSM Archive [8], cross-referenced against multiple sources. Temperature coefficients are from Streetman [2]. Solar cell efficiency data references the NREL chart [6], which is updated regularly with verified laboratory results. The simulation uses simplified models (abrupt junction, uniform doping, ideal Shockley equation) that capture essential physics while remaining computationally tractable for real-time interaction.

How to Cite

Simulations4All Team. "Semiconductors: P-N Junctions, LEDs & Solar Cells." Simulations4All, 2025. Available at: https://simulations4all.com/simulations/semiconductors-pn-junction

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