Threshold current density (J_th)

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

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.

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 toward $J_{\text{tr}}{e}^{{\alpha }_i\mathrm{/}(\mathrm{\Gamma }{g}_0)}$ as $L\to \mathrm{\infty }$, which equals the transparency current density $J_{\text{tr}}$ only when the internal loss is negligible. The exact relationship:

where the bracketed exponent contains internal loss ${\alpha }_i$, mirror loss, and modal gain parameters. Plotted against $1\mathrm{/}L$, $\ln J_{\text{th}}$ is a straight line: its slope gives $\mathrm{\Gamma }{g}_0$, and its intercept at $1\mathrm{/}L=0$ is $\ln J_{\text{tr}}+{\alpha }_i\mathrm{/}(\mathrm{\Gamma }{g}_0)$, so with ${\alpha }_i$ measured separately it isolates $J_{\text{tr}}$, a fundamental material property.

Temperature dependence. $J_{\text{th}}$ follows the same empirical exponential temperature dependence as $I_{\text{th}}$:

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.