Shunt resistance

Shunt resistance $R_{\text{sh}}$ is the parallel resistance across a p-n junction that allows current to flow around the junction rather than through it. In an ideal diode, $R_{\text{sh}}=\mathrm{\infty }$ (no leakage path). In a real device, $R_{\text{sh}}$ is finite due to physical leakage paths, surface conduction, or process defects.

Modified diode equation including shunt resistance:

$$I=I_0[\exp \text{\hspace{0.17em}⁣}\left(\frac{q(V-I{R}_s)}{nkT}\right)-1]+\frac{V-I{R}_s}{R_{\text{sh}}},$$

where $R_s$ is series resistance and the second term is shunt current. At low forward bias (or any reverse bias), shunt current can dominate over diode current.

Origins of finite shunt resistance. The paths act in parallel, so the lowest-resistance one sets $R_{\text{sh}}$, and which one dominates varies from device to device:

• Surface conduction at the facets and along etched mesa sidewalls
• Bulk defects in or near the junction, such as dislocations and point defects
• Direct paths between the contacts through the substrate or the doped layers
• Pinholes in the passivation
• Leakage from the bond pads to ground through the dielectric beneath them

For a high-quality InP DFB laser, total $R_{\text{sh}}$ is typically $>1$ MΩ. For a research-grade photodetector with optimized passivation, $R_{\text{sh}}$ can exceed 10 GΩ.

Why $R_{\text{sh}}$ matters.

1. Dark current floor in photodetectors. A photodetector at zero or small reverse bias has:

$$I_{\text{dark}}\approx \frac{V_{\text{bias}}}{R_{\text{sh}}}\mathrm{.}$$

For $V_{\text{bias}}=-1$ V and $R_{\text{sh}}=1$ GΩ: $I_{\text{dark}}=1$ nA. For $R_{\text{sh}}=10$ MΩ: $I_{\text{dark}}=100$ nA. Leakage through an ohmic shunt carries the thermal noise of $R_{\text{sh}}$, $\sqrt{4kT\mathrm{/}{R}_{\text{sh}}}$ (4.1 fA/√Hz for 1 GΩ at 300 K), while dark current generated in the junction carries shot noise, $\sqrt{2q{I}_{\text{dark}}}$ (17.9 fA/√Hz at 1 nA). Either sets the receiver noise floor only when the amplifier's own input noise is lower, as in slow, high-impedance receivers; a transimpedance amplifier with a few pA/√Hz of input noise hides both.

2. Leakage at sub-threshold in lasers. A laser biased below threshold should be off; if $R_{\text{sh}}$ is finite, current flows around the active region without producing optical output. For very-low-threshold lasers (sub-mA), this can be a significant fraction of total injected current.

3. Solar cell efficiency. Solar cells with low $R_{\text{sh}}$ leak photogenerated current through the shunt path instead of delivering it to the load. The fill factor (a measure of solar cell efficiency) drops sharply when $R_{\text{sh}}$ becomes comparable to the cell's load resistance.

4. Forward-bias leakage. Even at typical operating forward bias, a shunt path can carry significant current. For a laser at $V=0.8$ V (below threshold) and $R_{\text{sh}}=1$ MΩ: leakage = 800 nA. Compared to typical $I_{\text{th}}=5-20$ mA, this is negligible. For $R_{\text{sh}}=1$ kΩ: leakage = 800 μA, non-negligible and indicating a bad device.

Extraction. Shunt resistance is extracted from the reverse-bias I-V slope:

$$R_{\text{sh}}\approx {\frac{dV}{dI}\mid }_{\text{reverse bias, low |I|}},$$

evaluated at a reverse bias where breakdown has not occurred but the diode is fully off. For a photodetector, this is typically $V=-0.5$ to $-2$ V. The slope of the reverse-bias I-V curve is approximately $1\mathrm{/}{R}_{\text{sh}}$.

Diagnostic value.

• Sudden drop in $R_{\text{sh}}$: process defect at fabrication, or in-service damage (ESD event, mechanical damage)
• Gradual drop in $R_{\text{sh}}$: progressive defect growth, contact migration, or passivation degradation
• $R_{\text{sh}}$ thermally activated: indicates a thermally-driven leakage mechanism (e.g., generation-recombination at deep traps)
• $R_{\text{sh}}$ unaffected by light: bulk or interface defect, not photogenerated
• $R_{\text{sh}}$ drops in light: photoconductive shunt path; e.g., light absorption in unintended region

Improving $R_{\text{sh}}$.

• High-quality passivation: SiNₓ or SiO₂ cap layers reduce surface conduction
• Mesa etching: separate physically separated devices reduce contact-to-contact leakage
• Block current paths: lateral oxidation (in VCSELs), proton implantation, or regrowth of semi-insulating Fe-doped InP around the mesa (in buried-heterostructure lasers) confines the current to the intended path

References: Pierret, Semiconductor Device Fundamentals, Ch. 6; Sze, Physics of Semiconductor Devices, Ch. 13 for the photodetector dark current treatment.