LIV curve

The LIV curve of a semiconductor laser diode is the record of its optical output power L and its forward voltage V against the drive current I, both taken in the same current sweep; it is also written L–I–V or P–I–V. It is the first measurement made on a new laser and the source of most of the numbers on its datasheet: the threshold current, the slope efficiency, the series resistance and the wall-plug efficiency at any operating point. The 1310 nm Fabry-Perot laser with a high-reflection rear coating used as the example in this site's LIV articles has a threshold of 8.0 mA and a slope efficiency of 0.55 W/A when measured with short pulses, and driven continuously at 50 mA it emits 22.66 mW with 1.200 V across it, a wall-plug efficiency of 37.8%.

Reading the curve

A continuous-wave sweep of that laser on a 25 °C heatsink gives:

Below threshold the laser behaves as a light-emitting diode. Its output is spontaneous emission, microwatts spread over many directions and wavelengths, and it grows slowly with current, while the voltage climbs steeply through the diode's turn-on.

At threshold the gain reaches the cavity loss, stimulated emission takes over and the L–I curve turns sharply upward. The carrier density stops rising at that point, and with it the separation of the quasi-Fermi levels, so the junction voltage clamps. Above threshold only the resistive drop keeps growing, and the differential resistance $dV\mathrm{/}dI$ falls by the junction's own contribution, $n{k}_{B}T\mathrm{/}(q{I}_{\text{th}})$ for an ideality factor $n$: 3 to 6 Ω at a threshold of 8 mA for $n$ between 1 and 2. That step gives an electrical measure of threshold that needs no optical detector.

Above threshold the output rises in proportion to the current above threshold, $P={\eta }_s(I-I_{\text{th}})$, and the voltage follows $V\approx V_0+I{R}_s$, which for the example laser is 0.95 V + 5 Ω × $I$. The intercept $V_0$ lies close to the photon energy divided by the electron charge, 0.95 V at 1310 nm, because lasing requires the quasi-Fermi-level separation to exceed the photon energy. At high current the L–I curve bends over as self-heating raises the threshold and lowers the slope, and abrupt changes of slope, kinks, mark changes in the lasing mode.

Parameters taken from it

• Threshold current $I_{\text{th}}$, most often from a straight line fitted to the lasing part of the L–I curve and extended to zero power. The second-derivative peak and the other methods compared in Threshold extraction methods place it slightly differently, so the method is reported with the value.
• Slope efficiency ${\eta }_s=dP\mathrm{/}dI$ above threshold, in W/A. Multiplied by $q\mathrm{/}h\nu$ it gives the external differential quantum efficiency: 0.55 W/A at 1310 nm, where $h\nu \mathrm{/}q$ = 0.946 V, is 58.1% from the front facet.
• Series resistance $R_s$, the slope of V against I well above threshold, where the junction voltage is clamped: 5 Ω in the example. Power dissipated in it heats the device, and the voltage it adds is the main reason the efficiency falls at high current.
• Operating voltage, the voltage at the working current, which the driver must be able to supply.
• Wall-plug efficiency ${\eta }_{\text{WPE}}=P\mathrm{/}(IV)$ at each point. For the example it peaks at 37.8% at 46 mA, 5.7 times its CW threshold of 8.05 mA, and stays within one percentage point of the peak from 34 to 66 mA (Wall-plug efficiency from LIV data).

Sweeps at several heatsink temperatures give the characteristic temperatures, $T_0$ for the threshold and $T_1$ for the slope efficiency: 59.6 K and 143 K for the example laser (Extracting T₀ from LIV measurements, Pulsed vs CW LIV measurement).

Measurement

Four-wire sensing keeps the resistance of the leads and probe contacts out of the measured series resistance. The detector has to capture the whole beam: an edge-emitting laser's beam spreads by 25 to 40° (full width at half maximum) perpendicular to the junction (far-field divergence), and a detector that clips part of it understates the slope efficiency.

Continuous drive heats the active region. In the example the junction runs 4.8 K above the heatsink at 100 mA, and the output there is 4% below its isothermal value. Pulsed drive, commonly 1 µs pulses at 1 kHz, a duty cycle of 0.1%, keeps the junction close to the heatsink temperature and gives nearly isothermal curves, which is checked by halving and doubling the pulse width; Pulsed vs CW LIV measurement quantifies the difference for each parameter, and Laser characterization bench setup describes the bench.

What the curve shows about a device

A single sweep also screens the laser. A soft, rounded knee points to a high spontaneous emission factor or to parts of the device reaching threshold at different currents. A series resistance well above the design value points to poor contacts. Kinks point to a mode hop, a change of lateral mode or filamentation, as explained in Why laser diode L-I curves kink, and early rollover points to poor heat sinking. Sweeps before and after burn-in show whether the threshold has drifted, the usual first sign of degradation. In packaged lasers the current of the back-facet monitor photodiode is recorded in the same sweep, and its ratio to the front-facet power over temperature gives the tracking error.

Common questions

What does LIV stand for?

Light, current (I) and voltage: the laser's optical output power and forward voltage recorded against the drive current in one sweep.

How is the threshold current found from an LIV curve?

Usually by fitting a straight line to the lasing part of the L–I curve and extending it to zero output. The peak of the second derivative $d^{2}P\mathrm{/}d{I}^2$ and the step in $dV\mathrm{/}dI$ are alternatives; the methods that locate the transition should agree to within about its width, a few tenths of a milliampere for an ordinary edge emitter.

Why measure the LIV curve pulsed?

To remove self-heating. Under continuous drive the junction warms with current, which raises the threshold, lowers the slope and bends the curve over at high current. Pulses of about a microsecond at a low duty cycle keep the junction close to the heatsink temperature, so the curve shows the laser's isothermal behavior.

What is a kink in an LIV curve?

An abrupt change in the slope of the L–I curve, usually caused by a change in the lasing mode. It shows most clearly in $dL\mathrm{/}dI$ plotted against current, and datasheets specify a kink-free power or current below the first one.

References: L. A. Coldren, S. W. Corzine, and M. L. Mašanović, Diode Lasers and Photonic Integrated Circuits, 2nd ed. (Wiley, 2012). J. Piprek, Semiconductor Optoelectronic Devices: Introduction to Physics and Simulation (Academic Press, 2003).