Non-radiative recombination

Non-radiative recombination encompasses all processes by which an electron-hole pair recombines without emitting a photon. The released energy goes into heat (phonons) or to a third carrier (Auger). Non-radiative recombination is a major loss mechanism in semiconductor light emitters and a fundamental constraint on internal quantum efficiency.

Three principal mechanisms.

1. Shockley-Read-Hall (SRH) recombination. Carriers recombine through defect-related energy levels in the bandgap. The recombination rate:

$$R_\text{SRH} \;=\; \frac{n p - n_i^2}{\tau_p (n + n_1) + \tau_n (p + p_1)},$$

where $n_1, p_1$ depend on the trap energy level and $\tau_n, \tau_p$ are the capture lifetimes for electrons and holes. For high injection ($n \approx p \gg n_i$):

$$R_\text{SRH} \;\approx\; \frac{\Delta n}{\tau_\text{SRH}},$$

with $\tau_\text{SRH}^{-1} = A$ in the ABC model. Typical lifetimes:

Material quality	$\tau_\text{SRH}$
Defect-free GaAs (state of the art)	$> 1$ μs
Standard GaAs laser-grade epi	0.1 – 1 μs
InGaAsP laser-grade epi	0.05 – 0.5 μs
Standard InGaN	5 – 50 ns
Polycrystalline Si	$< 1$ ns
Amorphous Si	$< 0.1$ ns
Highly defective heteroepitaxy	$< 0.01$ ns

Defects providing SRH centers include:

• Vacancies, interstitials, antisites (point defects)
• Dislocations from lattice mismatch in heteroepitaxy (line defects)
• Impurity atoms (Fe in InP, Cu in Si, etc.)
• Stacking faults (planar defects)
• Threading dislocations at the wafer surface

2. Auger recombination. A three-particle process where the energy of an electron-hole recombination is given to a third carrier (electron or hole), boosting it to a higher energy state. The third carrier then loses energy to phonons. The rate:

$$R_\text{Auger} \;=\; C_n n^2 p + C_p n p^2 \;\approx\; C \Delta n^3 \quad \text{(intrinsic)}.$$

Auger coefficients:

Material	$C$ (cm⁶/s)
Si	$\sim 4 \times 10^{-31}$
GaAs	$\sim 7 \times 10^{-30}$
InP	$\sim 4 \times 10^{-29}$
InGaAs (1.55 μm)	$1 - 5 \times 10^{-28}$
InGaAsP (1.55 μm)	$1 - 5 \times 10^{-28}$
Type-II superlattice (mid-IR)	$> 10^{-26}$
InGaN	$\sim 5 \times 10^{-31}$

Auger recombination dominates at high carrier densities and especially in narrow-bandgap (long-wavelength) materials. This is why 1.55 μm InGaAsP lasers have higher temperature sensitivity than 850 nm GaAs lasers — Auger losses are 4 – 5 orders of magnitude larger.

3. Surface recombination. Surfaces and interfaces have high defect densities (broken bonds, oxidation states) that act as efficient SRH centers. The surface recombination velocity $S$ characterizes:

$$\text{boundary condition}: D \frac{\partial \Delta n}{\partial z}\bigg|_\text{surface} \;=\; -S \cdot \Delta n_\text{surface},$$

where $D$ is the diffusion coefficient. Typical $S$ values:

Surface	$S$ (cm/s)
GaAs, untreated	$10^6$
GaAs, sulfide-passivated	$10^4$
Si, native oxide	$10^4 - 10^5$
Si, thermal SiO₂	$\sim 10$
InGaAs, native oxide	$10^4 - 10^5$
InGaAs, dielectric-passivated	$10^2 - 10^3$

Why surface recombination matters for narrow devices. When the active region's lateral dimension approaches the carrier diffusion length, surface recombination becomes a major loss path. This is the "narrow-stripe lateral leakage" problem in edge-emitting lasers — for stripe widths < 2 – 3 μm, surface recombination at the etched sidewalls dominates non-radiative losses.

The standard solution is to bury the active stripe in a wide-bandgap material (the "buried heterostructure" geometry) or to use ridge-waveguide geometry with the active material extending beyond the optical mode.

Temperature dependence. Most non-radiative mechanisms accelerate with temperature:

• SRH: weakly temperature-dependent if traps are deep; can have characteristic activation energy if shallow
• Auger: strongly temperature-dependent, $\propto \exp(-E_\text{th}/k_B T)$ where $E_\text{th}$ is the threshold energy for the third-carrier promotion
• Surface: depends on temperature-dependence of $S$, generally mild

The temperature sensitivity of laser threshold (characterized by $T_0$) reflects which mechanism dominates:

• Direct narrow-gap materials (InGaAsP at 1.55 μm): $T_0 \sim 50 - 80$ K (Auger-dominated)
• Direct wide-gap materials (GaAs at 0.85 μm): $T_0 \sim 150 - 250$ K (weak Auger)
• Strained QWs: improved $T_0$ via band-structure engineering to suppress Auger

Strategies to suppress non-radiative recombination.

Strategy	Targets
High-purity growth	SRH (defect density)
Lattice matching	SRH (dislocations from mismatch)
Surface passivation	Surface recombination
Strain engineering	Auger (band offsets)
Wide-bandgap cladding	Carrier confinement, reduces surface effects
Quantum confinement	Reduces effective Auger by modifying band states
Type-II band alignment	Spatial separation suppresses Auger
Cooling	All thermally-activated mechanisms

Non-radiative dark current. In photodetectors, non-radiative thermal generation produces dark current. The same defect levels that act as SRH centers in light emitters act as thermal generation sites in detectors. Reducing dark current and improving radiative efficiency are dual problems — both demand defect-free, well-passivated material.

Auger vs free-carrier absorption. Both are concentration-dependent losses in lasers. At high carrier densities:

• Auger: $\propto n^3$, intrinsic to the band structure
• Free-carrier absorption: $\propto n$, optical loss from inverse-bremsstrahlung-like process

Both contribute to laser threshold rollover and limit maximum CW output power.

Why Si emits poorly. Si has $B \sim 10^{-15}$ cm³/s (radiative) but $A \sim 10^7 - 10^9$ s⁻¹ (typical SRH). At any practical carrier density, non-radiative recombination dominates: internal quantum efficiency $\eta_i \ll 0.01$. This single fact is why every commercial semiconductor laser uses III-V (not Si) gain material.

References: Saleh & Teich, Fundamentals of Photonics (3rd ed., 2019), Ch. 16 (semiconductors); Coldren, Corzine & Mašanović, Diode Lasers and PICs (2nd ed., 2012), Ch. 2 — definitive ABC-model treatment; Piprek, Semiconductor Optoelectronic Devices (Academic Press, 2003) for detailed non-radiative mechanism analysis; Sze & Ng, Physics of Semiconductor Devices (3rd ed., 2007) for SRH statistics.