Forward voltage (V_f)

The forward voltage $V_f$ is the voltage across a diode's terminals while it conducts current in the forward direction. For a laser the junction must be biased so that the separation of the electron and hole quasi-Fermi levels exceeds the photon energy, the condition for gain, and an LED needs a similar bias to inject a large current, so the voltage at operating current is close to the photon energy divided by the electron charge, plus the drop across the series resistance:

$$V_f \approx \frac{h\nu}{q} + I R_s .$$

A 1550 nm laser diode has a photon energy of 0.80 eV; with $R_s = 5$ Ω at 50 mA the resistive term adds 0.25 V and $V_f \approx 1.05$ V. Red light-emitting diodes typically run near 2 V (the photon energy at 630 nm is 1.97 eV) and blue and white InGaN LEDs near 3 V (2.76 eV at 450 nm), with the excess over the photon energy depending on the device's heterojunctions and contacts.

The I–V curve

At low current the junction follows the Shockley equation with an ideality factor $n$,

$$I = I_0\left[\exp\!\left(\frac{qV_j}{nkT}\right) - 1\right],$$

so the junction voltage $V_j$ rises by $n \times 59.5$ mV for each tenfold increase in current at 300 K, where $kT/q$ = 25.85 mV. The terminal voltage is $V_j + IR_s$, and as the current grows the linear resistive term overtakes the logarithmic one. In a laser above threshold the carrier density, and with it the junction voltage, is clamped, so the measured curve becomes nearly a straight line whose slope, the differential resistance, approaches $R_s$. The physics of the junction itself is described under p-n junction.

Measurement

Forward voltage is recorded together with optical power in the LIV curve, usually with a source-measure unit forcing current and sensing voltage with four wires at the device, so that lead and contact resistance in the fixture is not counted. Datasheets quote $V_f$ at a stated current and heatsink temperature; with a two-wire reading, a few tenths of an ohm of cable and probe-contact resistance adds tens of millivolts at 100 mA, enough to distort a series-resistance fit.

Temperature coefficient and junction thermometry

At fixed current the forward voltage falls as the temperature rises, typically by about 1–2 mV/K for III-V laser junctions at a small sense current; the exact value depends on the device and the current and is measured rather than assumed. Calibrated against heatsink temperature at a sense current of about 1 mA, where self-heating is negligible, $V_f$ becomes a thermometer for the active region itself: if the calibration slope is $-1.5$ mV/K and the voltage read at the sense current immediately after switching from the operating current is 30 mV lower than the calibration value at the same heatsink temperature, the junction was 20 K above the heatsink. This is the forward-voltage method for junction temperature, and dividing the rise by the dissipated power gives the thermal resistance. The procedure, including the switching transient, is described in Measuring Laser Diode Junction Temperature and Thermal Resistance.

Forward voltage and efficiency

The electrical input is $IV_f$, so every millivolt above $h\nu/q$ is spent as heat. The ratio $h\nu/(qV_f)$, sometimes called the voltage efficiency, bounds the wall-plug efficiency of a laser from above: for the 1550 nm example it is 0.80/1.05 = 76%, before any loss of carriers or photons is counted. At high current the resistive loss $I^2R_s$ grows quadratically while optical output grows at most linearly, which is one reason wall-plug efficiency peaks several times above threshold and then declines.

Pitfalls

A forward voltage much above the expected value at low current usually points to a poor contact or a barrier at a heterointerface; one much below it, or a soft knee, points to leakage through a shunt resistance. Comparing $V_f$ between devices or over time is meaningful only at the same current and temperature, since a few kelvin of self-heating moves it by several millivolts.

Common questions

What is the forward voltage of a laser diode?

At its operating current it is typically the photon energy in eV plus a few tenths of a volt: around 1.0–1.5 V for 1310 and 1550 nm InP lasers and somewhat more for shorter-wavelength GaAs-based lasers, which have larger photon energies.

Why does forward voltage decrease with temperature?

At constant current a warmer junction needs less voltage, because the bandgap shrinks and thermally generated carriers make injection easier. The coefficient, roughly $-1$ to $-2$ mV/K, is close to linear over tens of kelvin, which is why it serves as a thermometer.

Is a lower forward voltage better?

For efficiency, yes, provided the current and output are unchanged: the excess voltage above $h\nu/q$ times the current is dissipated as heat in the chip and raises the junction temperature.

References: S. M. Sze and K. K. Ng, Physics of Semiconductor Devices, 3rd ed. (Wiley, 2007); L. A. Coldren, S. W. Corzine and M. L. Mašanović, Diode Lasers and Photonic Integrated Circuits, 2nd ed. (Wiley, 2012); E. F. Schubert, Light-Emitting Diodes, 2nd ed. (Cambridge University Press, 2006).