Glossary entry

Characteristic temperature (T₀)

The empirical parameter that quantifies how fast a semiconductor laser's threshold current rises with temperature, through I_th(T) = I₀ exp(T/T₀). A larger T₀ means a less temperature-sensitive laser: 50 to 70 K for InGaAsP telecom lasers, 120 to 160 K for GaAs-based devices, and effectively unbounded over limited ranges for p-doped quantum dot lasers.

Lasers & gain Lab practiceUpdated October 2026

Nearly every semiconductor laser needs more current to reach threshold as it warms up (a VCSEL below its gain-cavity alignment temperature and some p-doped quantum dot lasers are exceptions), and the characteristic temperature $T_{0}$ is the single number that says how much more. It is defined by the empirical fit

I_{t h} (T) = I_{0} \exp ⁣ (\frac{T}{T_{0}})

where $I_{t h} (T)$ is the threshold current at active-region temperature $T$ and $I_{0}$ is a constant with units of current. Because only temperature differences enter, $T$ can be in kelvin or degrees Celsius so long as $I_{0}$ is fitted consistently, and $T_{0}$ itself is always quoted in kelvin. Two lasers with the same threshold at 20 °C but $T_{0}$ of 60 K and 150 K reach 23 mA and 14 mA at 70 °C from 10 mA: over a 50 K rise the threshold grows by $\exp (50 / T_{0})$ , a factor 2.3 in the first case and 1.4 in the second. Since the fit is exponential, $T_{0}$ is also the reciprocal logarithmic slope, $T_{0} = (d \ln I_{t h} / d T)^{- 1}$ , and a measured threshold curve rarely follows a single exponential over a wide range: $T_{0}$ is higher below room temperature and falls above 50 to 70 °C as the loss mechanisms below switch on, so a quoted value should come with the temperature range it was fitted over.

Typical values

System	Wavelength	$T_{0}$
AlGaAs / GaAs	750–850 nm	120–160 K
InGaAs / GaAs	900–1100 nm	100–140 K
InGaAsP / InP	1300–1550 nm	50–70 K
InGaAlAs / InP	1300–1550 nm	70–90 K
GaN / InGaN	405–470 nm	90–150 K
InAs / GaAs quantum dots, p-doped	1300 nm	160 K and above, and effectively unbounded over ranges of several tens of kelvin

The ordering has physical causes. Threshold rises with temperature for three reasons that add: the carriers spread over more states as the Fermi distributions broaden, so a higher carrier density is needed for the same peak gain; Auger recombination, which grows roughly as $n^{3}$ with a thermal activation energy, consumes an increasing share of the current in narrow-gap materials; and carriers leak over the heterobarriers into the cladding. InGaAsP on InP suffers most because its bandgap is small and its conduction-band offset is only about 40 % of the gap difference, so both Auger loss and electron leakage are strong, which is why the aluminum quaternary InGaAlAs, with about 70 % of the offset in the conduction band, gives 20 K more. GaAs-based lasers have a larger gap, weaker Auger recombination, and deep wells. Quantum dot lasers separate the levels by more than $k T$ , and p-doping the dots keeps holes from thermally spreading among their closely spaced states, which is what removes the temperature dependence over a limited range.

The companion parameter T₁

The slope efficiency falls with temperature as well, and the same exponential form is used: $η_{d} (T) = η_{d 0} \exp (- T / T_{1})$ , with $T_{1}$ typically several times $T_{0}$ . Together the two parameters describe how the whole LIV curve shifts with temperature, and they are what a datasheet's "operating temperature range" is built on: at the upper end the threshold has risen, the slope has fallen, and the drive current for a given power may have doubled, with the extra dissipation raising the junction temperature further; the Junction Temperature Calculator works that rise out from the thermal resistance and the dissipated power.

Measuring it

$T_{0}$ is extracted from threshold currents measured at several stage temperatures, usually 20 to 80 °C in steps of 10 K, by fitting a line to $\ln I_{t h}$ against $T$ . Two precautions decide whether the number is meaningful. The measurement should be pulsed, or the threshold corrected for self-heating, because under continuous drive the junction sits above the stage by $R_{t h} (I V - P)$ and that offset grows with the threshold itself; a CW fit against stage temperature therefore returns a $T_{0}$ that is too low. And the threshold must be defined the same way at every temperature, by the second derivative of the LI curve or a linear fit above threshold, since the knee softens as the temperature rises and an eyeballed threshold drifts. The procedure and the fitting are worked in Characteristic temperature extraction from LIV measurements, and the T₀ Extraction Calculator fits $T_{0}$ and $I_{0}$ from pasted threshold-versus-temperature data and reports the $R^{2}$ of the fit.

Temperature moves the wavelength as well as the threshold; the rates for gain-peak and grating-defined lasers are tabulated in the wavelength temperature coefficient entry.

Common questions

What does a T₀ of 60 K mean in practice?

That the threshold current grows by a factor $e$ for every 60 K of temperature rise, or about 1.7 % per kelvin near room temperature. A 1550 nm DFB with a 10 mA threshold at 25 °C will need about 20 mA at 65 °C and 30 mA at 90 °C, which is why uncooled telecom lasers are specified to 85 °C with generous current headroom, and why lasers that must hold a wavelength are placed on a thermoelectric cooler.

Is a higher T₀ always better?

For temperature stability, yes; but $T_{0}$ says nothing about the absolute threshold or the efficiency. A laser with a high threshold and a high $T_{0}$ can still dissipate more heat at 85 °C than a low-threshold device with a modest $T_{0}$ , and the slope-efficiency parameter $T_{1}$ matters as much for the drive current at the operating power.

References: L. A. Coldren, S. W. Corzine, and M. L. Mašanović, Diode Lasers and Photonic Integrated Circuits, 2nd ed. (Wiley, 2012), sections 2.7 and 4.6. G. P. Agrawal and N. K. Dutta, Semiconductor Lasers, 2nd ed. (Van Nostrand Reinhold, 1993), chapter 3, on the temperature dependence of threshold in InGaAsP lasers. C. E. Zah et al., "High-performance uncooled 1.3-μm AlₓGaᵧIn₁₋ₓ₋ᵧAs/InP strained-layer quantum-well lasers for subscriber loop applications," IEEE Journal of Quantum Electronics 30, 511 (1994). O. B. Shchekin and D. G. Deppe, "1.3 μm InAs quantum dot laser with T₀ = 161 K from 0 to 80 °C," Applied Physics Letters 80, 3277 (2002).