Carrier confinement

Carrier confinement is the spatial localization of injected carriers (electrons and holes) within a designed active region of a semiconductor device, achieved by bandgap discontinuities at the active-cladding interfaces. Effective carrier confinement is essential for high-efficiency LEDs and lasers because it concentrates injected carriers where the optical mode is located, maximizing the local carrier density and hence the optical gain or radiative recombination rate.

Heterojunction band offsets. When two semiconductors with different bandgaps form a heterojunction, the difference in bandgap is partitioned between conduction band offset ($\Delta E_c$) and valence band offset ($\Delta E_v$):

$$\Delta E_g \;=\; \Delta E_c + \Delta E_v.$$

The partition ratio $Q = \Delta E_c / \Delta E_g$ depends on the material pair:

Heterojunction	$\Delta E_g$	$\Delta E_c$	$\Delta E_v$	$Q$
GaAs / Al₀.₃Ga₀.₇As	374 meV	240 meV	134 meV	0.64
GaAs / AlAs	1.1 eV	0.95 eV	0.15 eV	0.86
InGaAs / InP (LM)	611 meV	220 meV	391 meV	0.36
InGaAsP (1.55) / InP	590 meV	230 meV	360 meV	0.39
GaN / Al₀.₂Ga₀.₈N	600 meV	420 meV	180 meV	0.70
InGaN / GaN (5% In)	200 meV	130 meV	70 meV	0.65
Si / Si₀.₇Ge₀.₃	250 meV	30 meV	220 meV	0.12

For lasers, balanced confinement (both electrons and holes confined) requires sufficient $\Delta E_c$ and $\Delta E_v$ at both heterojunctions of the double heterostructure.

Required barrier height. For confinement to be effective at temperature $T$, the barrier must significantly exceed the thermal energy:

$$\Delta E_{barrier} \;\gtrsim\; (5 - 10) \, k_B T.$$

At room temperature ($k_B T = 25.9$ meV), barriers of 150 – 250 meV provide reasonable confinement. At elevated temperatures (e.g., 85 °C for telecom transceiver operation, $k_B T = 31$ meV), barriers need to be proportionally larger.

Three confinement geometries.

1. Bulk double heterostructure. Active region thickness 0.1 – 0.5 μm; carriers occupy 3D bulk states. Standard 1970s-era laser design; superseded by QW structures in the 1980s.

2. Quantum well (QW). Active region 5 – 20 nm; carriers occupy 2D subbands. Most modern semiconductor lasers and LEDs use multi-quantum-well (MQW) active regions:

• Number of wells: typically 3 – 8
• Well width: 5 – 10 nm (tuned to lase at desired wavelength)
• Barrier between wells: 5 – 15 nm; chosen to allow carrier transport between wells while maintaining individual-well confinement

3. Quantum dot (QD). Active region 5 – 30 nm 3D nanostructures; carriers fully confined in 0D. Used in some specialized lasers (very low threshold, broad spectrum, temperature-insensitive operation).

Carrier capture and escape. Injected carriers must be captured into the active QWs and then re-emitted at a much slower rate. Carrier capture in MQWs:

• Capture time $\tau_\text{cap}$: typically 1 – 10 ps for electrons, 1 – 10 ps for holes
• Escape time $\tau_\text{esc}$: depends on barrier height; for $\Delta E_c = 200$ meV and $T = 300$ K, $\tau_\text{esc} \sim$ many ns (>> recombination time of $\sim 1$ ns)

Effective confinement requires $\tau_\text{esc} \gg \tau_\text{recomb}$ — easily satisfied at room temperature with 200 meV barriers but becomes marginal at high temperatures.

Cladding thickness. The cladding layers must be:

• Thick enough to provide optical confinement (typically 1 – 2 μm for InGaAsP at 1.55 μm)
• Thin enough that series resistance remains acceptable
• Doped sufficiently for low contact resistance (typically 10¹⁸ cm⁻³)

Heavy doping introduces free-carrier absorption ($\alpha_{fc} \propto N$), so there is a tradeoff between low series resistance (favoring high doping) and low optical loss (favoring low doping). Standard solution: doping profile that is heaviest near the contacts and graded to lower doping toward the active region.

Why GaN-based LEDs struggle with hole confinement. GaN/InGaN/GaN MQWs have asymmetric band offsets:

• $\Delta E_c \approx 70\%$ of $\Delta E_g$ — large electron barrier
• $\Delta E_v \approx 30\%$ of $\Delta E_g$ — small hole barrier

The small valence-band offset means holes are poorly confined in the InGaN wells, leading to non-uniform carrier distribution across the MQW stack and reduced internal quantum efficiency. The "electron blocking layer" (EBL) — an AlGaN layer between the active region and the p-cladding — is added to compensate, although it introduces a large valence-band barrier that impedes hole injection. This is a major design challenge for GaN LEDs and a primary reason for their lower wall-plug efficiency compared to AlGaAs/GaAs structures.

Confinement and carrier overflow. At high injection, the carrier density approaches the available state density in the QWs. Above this:

• Higher subbands become populated
• Carriers spill over into the barriers
• Effective gain saturation occurs

This "carrier overflow" limits maximum CW power. Mitigations:

• Increase number of QWs to spread carriers
• Use deeper barriers
• Strain-engineer to modify the DOS

Confinement vs optical confinement. Carrier confinement and optical confinement are separate physical effects:

• Carrier confinement: bandgap discontinuity localizes electrons and holes
• Optical confinement: refractive index step localizes the optical mode

A heterostructure typically provides both, since lower-bandgap materials usually have higher refractive index. The two confinement profiles need not be identical — separate confinement heterostructure (SCH) designs deliberately use different geometries for carrier and optical confinement:

• Thin QWs for carrier confinement
• Thicker waveguide for optical confinement

This SCH design is standard in modern 1310/1550 nm DFB lasers.

Diffusion within the active region. Within the confined region, carriers can still diffuse laterally:

$$L_D \;=\; \sqrt{D \tau},$$

where $D$ is the diffusion coefficient and $\tau$ is the lifetime. For InGaAsP: $L_D \approx 1 - 3$ μm. This sets the minimum lateral dimension for efficient devices — narrower stripes lose carriers to lateral surface recombination.

References: Saleh & Teich, Fundamentals of Photonics (3rd ed., 2019), Ch. 17; Coldren, Corzine & Mašanović, Diode Lasers and PICs (2nd ed., 2012), Ch. 5 — comprehensive treatment of heterostructure confinement; Piprek, Semiconductor Optoelectronic Devices (2003) for the device-physics derivations; Yu & Cardona, Fundamentals of Semiconductors (4th ed., 2010) for the band-offset theory.