Glossary entry

Series resistance

Total Ohmic resistance in series with a diode's active junction, including contact, bulk, and metallization contributions. Limits high-current performance and contributes to self-heating.

Lasers & gain Lab practiceUpdated October 2026

Series resistance $R_{s}$ is the total Ohmic resistance in the current path of a diode, including:

Contact metal traces and wirebonds
Metal-semiconductor contact (specific contact resistivity ÷ contact area)
Doped cladding layers above and below the junction
Series-coupled passive elements in the package

It excludes the junction itself, whose I-V relationship is exponential (described by the ideality factor equation), and any shunt-leakage paths in parallel (described by the shunt resistance).

Where it appears in the diode equation. The modified diode equation including series resistance:

V = \frac{n k T}{q} \ln ⁣ (\frac{I}{I_{0}} + 1) + I R_{s} .

At low currents, $I R_{s} ≪ n k T / q$ and the equation reduces to the ideal diode form. At high currents the logarithmic term grows slowly while $I R_{s}$ grows linearly, so the curve approaches a straight line with $d V / d I \to R_{s}$ .

Distinction from differential resistance. Differential resistance $R_{d} = d V / d I$ at a specified operating point. For a laser above threshold (where carrier density is clamped and the junction voltage is constant), $R_{d} = R_{s}$ in the limit. Below threshold, $R_{d}$ includes the junction's exponential contribution, while $R_{s}$ is the linear (Ohmic) portion only.

Components of $R_{s}$ in a typical InP DFB laser.

Component	Typical value (Ω)
Top contact metallization (Ti/Pt/Au)	0.1 – 0.5
Top contact resistance (specific contact resistivity ÷ area)	0.1 – 1
p-InP cladding (3 μm thick, $5 \times 10^{17}$ cm $^{- 3}$ )	2 – 5
Active region and confinement layers (MQW, undoped)	0.5 – 2
n-InP cladding (3 μm, $5 \times 10^{18}$ cm $^{- 3}$ )	0.3 – 1
Bottom contact + submount metallization	0.1 – 0.5
Wire bonds	0.05 – 0.2
Total $R_{s}$	3 – 10 Ω

The p-cladding usually dominates. Hole mobility in p-InP is more than an order of magnitude below electron mobility in n-InP at the same doping, and the p-side is doped more lightly: zinc, the usual acceptor in MOVPE-grown InP (beryllium in MBE growth), diffuses into the active region at high concentrations, and holes add free-carrier absorption where the mode overlaps the cladding.

Why $R_{s}$ matters.

Self-heating. Power dissipated in $R_{s}$ is $P = I^{2} R_{s}$ , not delivered to the optical output. For a laser at $5 \times I_{th}$ ( $\sim 100$ mA) with $R_{s} = 8$ Ω: $P = 80$ mW dissipated as heat, comparable to the optical output power. The heat lowers the slope efficiency and raises the threshold, so a laser with higher $R_{s}$ needs more current for the same output power, which heats it further.
Modulation bandwidth. Combined with package capacitance, $R_{s}$ limits the laser drive bandwidth: $f_{R C} = 1 / (2 π R_{s} C_{p})$ . For $R_{s} = 5$ Ω, $C_{p} = 1$ pF: $f_{R C} \approx 32$ GHz. Keeping this pole above 50 GHz with $R_{s} = 5$ Ω takes $C_{p}$ below 0.64 pF, which is why fast directly modulated lasers use small bond pads and low-capacitance ridge structures.
Impedance matching to drivers. Above threshold a laser presents only a few ohms, $R_{s}$ plus a small junction term, to a driver and transmission line built for 50 Ω. An 8 Ω load on a 50 Ω line reflects 52% of the incident power, so packages usually add a series resistor on the submount to bring the load closer to the line impedance, at the cost of drive power dissipated in that resistor.
Operating voltage at high current. Above threshold $V = V_{j} + I R_{s}$ , where $V_{j}$ , the junction voltage, is clamped slightly above the photon energy divided by $q$ . For $V_{j} = 1$ V, $I = 100$ mA and $R_{s} = 8$ Ω: $V = 1.8$ V. Driver ICs run from supplies of 1.8 to 3.3 V, so at high current the laser's drop takes most of the headroom.

Reducing $R_{s}$ .

Larger contact area: contact resistance is the specific contact resistivity divided by the contact area
Lower contact resistivity: a heavily doped p⁺ InGaAs cap layer under the contact rather than InP, with a high-work-function first metal such as Pt
Lower cladding resistance: a thinner or more heavily doped p-cladding, limited by optical loss: the mode must stay clear of the contact metal, and holes add free-carrier absorption

Measurement. On an LIV curve, a straight line fitted to the V-I data well above threshold has a slope equal to $R_{s}$ to good approximation, because the junction voltage is clamped there and contributes little to $d V / d I$ .

References: Coldren, Corzine, Mašanović, Diode Lasers, Ch. 2; Sze, Physics of Semiconductor Devices, 2nd ed. (Wiley, 1981), Ch. 5 (specific contact resistivity).