Glossary entry

Threshold current density (J_th)

The threshold current of a semiconductor laser normalized to active region area, with units of A/cm². The intrinsic figure of merit for laser-material quality, independent of device geometry.

Threshold current density is the threshold current $I_\text{th}$ divided by the active-region area $A$ :

J_\text{th} \;=\; \frac{I_\text{th}}{A} \;=\; \frac{I_\text{th}}{W \cdot L},

where $W$ is the stripe width and $L$ is the cavity length. Units are A/cm² in academic literature, sometimes mA/μm² in foundry process documents.

$J_\text{th}$ is the intrinsic figure of merit for laser material quality — it removes the trivial scaling of $I_\text{th}$ with device size. Two devices with identical $J_\text{th}$ but different areas will have proportionally different $I_\text{th}$ .

Why $J_\text{th}$ matters more than $I_\text{th}$ for process development. Threshold current scales with area, so a "low threshold" device may just be small. Threshold density is the parameter that distinguishes well-grown epitaxy from poor epitaxy. Comparing $J_\text{th}$ between epi runs at fixed temperature is the standard wafer acceptance metric for III–V laser foundries.

Typical room-temperature values.

Active region	Wavelength	$J_\text{th}$
AlGaAs/GaAs DH bulk	850 nm	1 – 2 kA/cm²
AlGaAs/GaAs SQW	850 nm	200 – 400 A/cm²
InGaAs/GaAs SQW (strained)	980 nm	60 – 150 A/cm²
InGaAsP/InP MQW (5–8 wells)	1310 nm	600 – 1200 A/cm²
InGaAsP/InP MQW (5–8 wells)	1550 nm	800 – 1500 A/cm²
InGaAlAs/InP MQW	1550 nm	500 – 1000 A/cm²
Quantum-dot 1300 nm	1300 nm	30 – 100 A/cm²
GaN/InGaN MQW	405 – 470 nm	1 – 5 kA/cm²
VCSEL active region	850 / 980 nm	100 – 300 A/cm²

The wavelength dependence within a material system is dominated by Auger recombination, which scales steeply at longer wavelengths due to smaller bandgap. The decade-scale variation between material systems comes primarily from differences in Auger and intervalence band absorption.

Length dependence. $J_\text{th}$ is not strictly length-independent: longer cavities require less round-trip gain (lower $g_\text{th}$ , lower carrier density at threshold), so $J_\text{th}$ decreases asymptotically toward the transparency current density $J_\text{tr}$ as $L \to \infty$ . The exact relationship:

J_\text{th}(L) \;=\; J_\text{tr} \exp\!\left[ \frac{\alpha_i + (1/L)\ln(1/R)}{\Gamma g_0} \right],

where the bracketed exponent contains internal loss $\alpha_i$ , mirror loss, and modal gain parameters. Extrapolating $J_\text{th}(L)$ to infinite length isolates $J_\text{tr}$ — a fundamental material property.

Temperature dependence. $J_\text{th}$ follows the same Arrhenius-like temperature dependence as $I_\text{th}$ :

J_\text{th}(T) \;=\; J_0 \exp(T / T_0),

with characteristic temperature $T_0$ . The 50–70 K $T_0$ typical of telecom InGaAsP lasers is driven by Auger; AlGaAs/GaAs devices reach 120–160 K because Auger is much weaker.

References: Coldren et al. Diode Lasers, 2nd ed., Ch. 2; Piprek, Semiconductor Optoelectronic Devices, Ch. 3 for the underlying carrier-density vs current relationship.