LEDs, Laser Diodes & VCSELs

Semiconductor light emitters. Learn electroluminescence by radiative recombination in direct-gap materials, LED structures (double heterostructure, quantum wells, InGaN/GaN blue and phosphor-converted white, AlGaInP red), wavelength and colour, internal/extraction/external quantum efficiency and wall-plug efficiency, forward voltage, luminous efficacy, thermal effects and efficiency droop, LED drivers; then lasers: stimulated emission, population inversion, optical gain and the cavity, threshold current, slope efficiency and L–I curves, longitudinal modes, temperature sensitivity (T₀), modulation speed, edge emitters (Fabry-Pérot, DFB) and VCSELs — with Python computing emission wavelengths, EQE/WPE, LED resistors, laser output power and threshold vs temperature.

Forward-biasing a direct-gap PN junction injects electrons and holes that recombine and emit photons with energy close to the bandgap: an LED. Confine carriers and light in a resonant cavity and drive it hard enough, and stimulated emission takes over: a laser.

LEDs revolutionised lighting and displays; laser diodes carry the internet over fibre, read optical discs, sense depth in phones and cut materials.

An analogy

An LED is a crowd clapping at random — lots of sound but no rhythm (incoherent light). A laser is the same crowd clapping in perfect unison because each clap prompts the neighbours (stimulated emission) — once enough people join (threshold), the sound becomes a single powerful beat.

LED physics and efficiency

Efficiency chain:

White LEDs and drivers

White light usually comes from a blue InGaN LED plus a yellow (YAG:Ce) or multi-phosphor coating; RGB and violet-pumped designs improve colour rendering. Because LED current rises exponentially with voltage and V_F falls with temperature, LEDs are driven by current sources: resistors for indicators, linear constant-current drivers, or switching (buck/boost) LED drivers with PWM or analogue dimming.

Laser diodes

Lasing needs population inversion (more carriers in upper states than lower), optical gain exceeding cavity losses, and feedback. Below threshold the device behaves like an LED (spontaneous emission); above, output rises linearly with slope efficiency and spectrum narrows to cavity modes. Fabry-Pérot lasers emit several longitudinal modes; DFB lasers use a grating for a single mode (telecom); VCSELs emit vertically from a short cavity between DBR mirrors — low threshold, circular beam, wafer testable, arrays (3D sensing, datacom).

Dynamics and reliability

Direct modulation bandwidth is set by relaxation oscillations (∝ √(I − I_th)) — tens of GHz for datacom VCSELs/DFBs. Chirp and relative intensity noise matter for long links. Lasers degrade by facet damage (COD at high power), dark-line defects and thermal ageing; LEDs by phosphor and package degradation. Eye safety (IEC 60825) governs laser power levels.

Formulas

Worked example: Colour

Given: E_g 2.0 eV

Find: λ.

Answer: 620 nm (orange-red)

Worked example: Slope efficiency

Given: η_d 0.5, 850 nm

Find: mW/mA.

Answer: 0.73 mW/mA

Worked example: Mode spacing

Given: λ 1310 nm, n_g 3.6, L 300 µm

Find: Δλ.

Answer: ≈ 0.79 nm

Double-heterostructure LED/laser

   p-AlGaAs (wide gap, cladding) │ GaAs/InGaAs quantum well (active) │ n-AlGaAs (cladding)
   E_c ‾‾‾‾‾‾‾‾‾‾‾╲___ well ___╱‾‾‾‾‾‾  electrons and holes confined together → efficient recombination
   E_v ___________╱‾‾‾‾‾‾‾‾‾╲_______  lower refractive index cladding also guides the light
  Laser: add mirrors (cleaved facets, DFB grating, or DBR stacks for VCSELs) → optical feedback

Wide-gap cladding layers confine injected carriers in a thin active region (and, having lower refractive index, also guide the light). Quantum wells tune the wavelength and reduce threshold. Mirrors turn an LED structure into a laser once gain exceeds losses.

Wavelength, efficiency, LED resistor and laser L–I

import math
# LED and laser-diode numbers: wavelength, efficiencies, series resistor, laser L-I and threshold vs temperature
for name, eg in (("GaAs IR", 1.42), ("AlGaInP red", 1.95), ("InGaN blue", 2.7)):
    print(f"{name:12s}: Eg {eg:.2f} eV -> lambda ~ {1240/eg:.0f} nm")
I, V, P_opt, lam = 0.35, 3.0, 0.45, 450e-9          # blue LED at 350 mA
h, c, q = 6.626e-34, 3e8, 1.602e-19
photons = P_opt / (h * c / lam)
print(f"blue LED: wall-plug efficiency {P_opt/(V*I)*100:.0f}%, EQE = photons/electrons = {photons/(I/q)*100:.0f}%")
Vs, Vf, If = 5.0, 2.0, 20e-3
print(f"series resistor for a red LED at 20 mA from 5 V: R = {(Vs-Vf)/If:.0f} ohm, dissipating {(Vs-Vf)*If*1e3:.0f} mW")
Ith, eta_d, lam_l = 20e-3, 0.6, 1310e-9
for Ia in (10e-3, 30e-3, 50e-3):
    P = eta_d * (h * c / lam_l) / q * max(0, Ia - Ith)
    print(f"laser at {Ia*1e3:.0f} mA: optical power {P*1e3:.2f} mW")
T0 = 60.0
for dT in (0, 40, 60):
    print(f"threshold at +{dT} K (T0 = 60 K): {Ith*math.exp(dT/T0)*1e3:.1f} mA")
# GaAs IR     : Eg 1.42 eV -> lambda ~ 873 nm
# AlGaInP red : Eg 1.95 eV -> lambda ~ 636 nm
# InGaN blue  : Eg 2.70 eV -> lambda ~ 459 nm
# blue LED: wall-plug efficiency 43%, EQE = photons/electrons = 47%
# series resistor for a red LED at 20 mA from 5 V: R = 150 ohm, dissipating 60 mW
# laser at 10 mA: optical power 0.00 mW
# laser at 30 mA: optical power 5.68 mW
# laser at 50 mA: optical power 17.05 mW
# threshold at +0 K (T0 = 60 K): 20.0 mA
# threshold at +40 K (T0 = 60 K): 39.0 mA
# threshold at +60 K (T0 = 60 K): 54.4 mA

Bandgap sets colour: 1.42 eV GaAs emits near-IR at 873 nm, InGaN at 2.7 eV emits blue. A modern blue power LED converts ~43% of electrical power to light (EQE ~47%). A red indicator LED on 5 V needs a 150 Ω resistor. The 1310 nm laser emits nothing useful below its 20 mA threshold, then ~0.57 mW/mA; its threshold nearly triples when heated by 60 K (T₀ = 60 K) — why telecom lasers use thermoelectric coolers or automatic power control.

Common mistakes

Applications

Key takeaways

Going further