Photodetector Characterization: Responsivity, NEP, and Bandwidth

Scope

This article describes the procedures for measuring the three primary parameters of photodetectors used in photonics: wavelength-dependent responsivity $\mathcal{R}(\lambda)$, noise-equivalent power (NEP), and 3-dB electrical bandwidth $f_\text{3dB}$. Coverage focuses on PIN photodiodes for the visible through near-IR (400–1700 nm) range, with brief discussion of avalanche photodiodes (APDs) and high-speed devices. Pyroelectric, thermopile, and bolometric detectors used at longer wavelengths are outside scope.

The three core parameters

A photodetector converts incident optical power into a measurable electrical signal (current or voltage). Three parameters describe this conversion:

For most applications, all three parameters are required. A detector with high responsivity but poor NEP is unable to measure weak signals; a detector with adequate NEP but slow bandwidth cannot resolve high-speed modulation.

Typical values for commercial photodetectors:

Responsivity measurement

Responsivity is the ratio of generated photocurrent to incident optical power:

$$\mathcal{R}(\lambda) \;=\; \frac{I_\text{photo}}{P_\text{in}(\lambda)}.$$

The fundamental quantum-limited responsivity is:

$$\mathcal{R}_\text{quantum}(\lambda) \;=\; \frac{q \lambda}{h c} \;=\; \frac{\lambda \text{ [}\mu\text{m]}}{1.24 \text{ V}} \text{ A/W},$$

corresponding to one electron generated per incident photon. The internal quantum efficiency $\eta_\text{IQE}$ accounts for incomplete carrier generation:

$$\mathcal{R}(\lambda) \;=\; \eta_\text{IQE}(\lambda) \cdot (1 - R_\text{fac}(\lambda)) \cdot \mathcal{R}_\text{quantum}(\lambda),$$

where $R_\text{fac}$ is the facet reflectance.

For an ideal InGaAs PIN at 1550 nm, $\mathcal{R}_\text{quantum} = 1.25$ A/W; with $\eta_\text{IQE} = 0.85$ and AR-coated facet, the measured responsivity is approximately 1.0 A/W. Practical InGaAs PIN devices achieve 0.85–0.95 A/W at peak.

Procedure

The responsivity measurement uses a calibrated reference power meter:

Procedure:

1. Inject the source through the beam splitter. One arm goes to the calibrated reference meter; the other goes to the DUT.
2. Calibrate the splitting ratio at each measurement wavelength by swapping the meter and DUT positions.
3. Sweep the source wavelength across the detector's operating range in small steps (typically 1–5 nm).
4. At each wavelength, record the optical power $P_\text{ref}$ at the reference meter and the photocurrent $I_\text{DUT}$ at the DUT.
5. Compute responsivity: $\mathcal{R}(\lambda) = I_\text{DUT} / (P_\text{ref} \cdot \text{splitter ratio})$.

For accurate responsivity measurement, the optical power at the DUT must be well-known. The dominant uncertainty sources:

• Reference meter calibration uncertainty (typically $\pm 2{-}5\%$)
• Beam splitter ratio uncertainty
• Coupling efficiency variation between the DUT and the reference path
• Detector linearity (DUT must operate in linear range; verify by varying power)

Polarization-dependent responsivity

Many detectors exhibit polarization-dependent responsivity, particularly waveguide-coupled devices and devices with anti-reflection coatings optimized for a specific polarization. Polarization-dependent responsivity (PDR) is the ratio of maximum to minimum $\mathcal{R}$ as polarization is varied:

$$\text{PDR} \;=\; 10 \log_{10} \left(\frac{\mathcal{R}_\text{max}}{\mathcal{R}_\text{min}}\right) \text{ [dB]}.$$

Typical PDR for free-space coupled InGaAs PIN: $<0.1$ dB. For fiber-coupled WG-PIN: 0.5–2 dB depending on design.

Noise-equivalent power (NEP)

NEP is the input optical power that produces a signal-to-noise ratio of 1 (S/N = 1) at the detector output, per unit bandwidth. It is the minimum detectable optical signal:

$$\text{NEP} \;=\; \frac{S_I^{1/2}}{\mathcal{R}},$$

where $S_I$ is the noise current power spectral density (in A$^2$/Hz) and $\mathcal{R}$ is the responsivity. Units: W/$\sqrt{\text{Hz}}$.

NEP has three contributions for typical operating conditions:

Shot noise. From the photocurrent itself (signal-induced) and from any DC photocurrent under DC illumination:

$$S_I^\text{shot} \;=\; 2 q I_\text{photo}.$$

Dark current shot noise. When no light is incident, the detector still produces a "dark" current from thermally generated carriers:

$$S_I^\text{dark} \;=\; 2 q I_\text{dark}.$$

Thermal (Johnson) noise. From the load resistance $R_L$:

$$S_I^\text{thermal} \;=\; \frac{4 k_B T}{R_L}.$$

For low-noise InGaAs PINs at room temperature with 10 nA dark current and 50 Ω load:

The thermal noise dominates for unamplified detection on 50 Ω. With a low-noise transimpedance amplifier (effective transimpedance $\sim 10$ kΩ to 1 MΩ), thermal noise is reduced and the detector can approach the shot-noise-limited NEP.

Procedure

Measurement of NEP requires:

Procedure:

1. With the detector covered (no light), measure the noise spectrum across the frequency range of interest. This is the dark noise floor.
2. With a known optical power $P$ illuminating the detector, measure both the signal and the noise spectrum.
3. NEP at frequency $f$: $\text{NEP}(f) = P \cdot \sqrt{S_\text{dark}(f)} / \sqrt{S_\text{signal}(f) - S_\text{dark}(f)}$, normalized to a 1 Hz bandwidth.

For DC-coupled measurements, NEP is reported at the frequency where it is minimum (typically the mid-band of the detector). For AC-coupled measurements, NEP is reported as a function of frequency.

The reciprocal of NEP — the detectivity $D^* = (A \cdot \Delta f)^{1/2} / \text{NEP}$, normalized by detector area $A$ and bandwidth — is more commonly reported for thermal detectors and IR imaging sensors. For PIN photodiodes the NEP is the standard figure.

3-dB bandwidth

The 3-dB bandwidth $f_\text{3dB}$ is the modulation frequency at which the detector's response (electrical power per unit incident optical modulation) falls 3 dB below its DC value.

Three contributions limit detector bandwidth:

RC time constant. The detector capacitance $C_d$ and load resistance $R_L$ form an RC low-pass filter:

$$f_\text{RC} \;=\; \frac{1}{2 \pi R_L C_d}.$$

For an InGaAs PIN with 1 pF capacitance and 50 Ω load: $f_\text{RC} = 3.2$ GHz. For a 0.1 pF high-speed device with 50 Ω load: $f_\text{RC} = 32$ GHz.

Transit time. Photogenerated carriers must traverse the depletion region to reach the electrodes. The transit time depends on the depletion width $w$ and the carrier saturation velocity $v_s$:

$$f_\text{transit} \;\approx\; \frac{0.45 \, v_s}{w}.$$

For InGaAs PIN with 1 μm depletion and $v_s \approx 6 \times 10^4$ m/s: $f_\text{transit} \approx 27$ GHz.

Diffusion time. Carriers generated outside the depletion region (in the substrate or contact regions) must diffuse to the depletion region before they contribute to the photocurrent. For deep-IR penetration depths, this can extend the impulse response significantly and limit bandwidth.

The total bandwidth is approximately the harmonic combination:

$$\frac{1}{f_\text{3dB}^2} \;=\; \frac{1}{f_\text{RC}^2} + \frac{1}{f_\text{transit}^2} + \frac{1}{f_\text{diff}^2}.$$

For most modern detectors, either RC or transit time dominates; diffusion is mitigated by structure design.

Procedure

Bandwidth measurement uses a modulated optical source:

Procedure:

1. Configure the modulated source. For a small-signal frequency response measurement, the optical modulation depth should be small (typically $\leq 10\%$) to remain in the linear regime.
2. Calibrate the modulator + RF source response using a known reference detector. The reference response is removed from subsequent DUT measurements.
3. Sweep the modulation frequency from low (typically 100 kHz) to high (twice the expected DUT bandwidth). At each frequency, record the DUT photocurrent RF amplitude.
4. Plot the DUT response (in dB) versus frequency. Identify $f_\text{3dB}$ as the frequency at which the response is 3 dB below the low-frequency value.

For high-bandwidth detectors ($f_\text{3dB} > 50$ GHz), pulse-based measurements using a femtosecond pulse train are more practical than frequency-domain VNA measurements. The detector's impulse response is reconstructed from the pulse autocorrelation, and the frequency response is obtained by Fourier transform.

Cross-coupling between parameters

The three parameters are interconnected; design tradeoffs require choosing among them:

For application selection:

• Power meter applications: prioritize $\mathcal{R}$ and PDR; bandwidth is irrelevant
• High-speed communications: prioritize $f_\text{3dB}$ and PDR; modest $\mathcal{R}$ acceptable
• Single-photon counting: prioritize NEP and dark current; bandwidth depends on count rate
• Spectroscopy / sensing: prioritize NEP; modest bandwidth and reasonable responsivity

Sources of error

Light not fully on the active area. If part of the beam misses the active area, the apparent $\mathcal{R}$ is artificially low. Verify beam alignment and beam diameter $\leq$ active area diameter for free-space measurements; verify good fiber coupling for fiber-coupled detectors.

Detector saturation. At high optical power, the detector response becomes non-linear (the photocurrent does not scale linearly with optical power). Verify operation in the linear range by varying input power and checking that photocurrent scales linearly.

Amplifier noise dominating NEP. Many detectors are sold with integrated amplifiers. The NEP of the detector + amplifier system is set by whichever has the lowest noise, and is typically dominated by the amplifier rather than the detector. Specify NEP for the system as deployed, not for the detector alone.

Bandwidth measurement reference uncertainty. The reference detector calibration uncertainty propagates to the DUT bandwidth measurement. Use a reference detector with bandwidth substantially exceeding the DUT (typically 3×) so that the reference response is essentially flat across the measurement range.

Polarization-dependent response interpreted as $\mathcal{R}$ variation. For polarized sources, polarization drift can be mistaken for responsivity variation across wavelength or time. Use polarization scrambling at the input or specify the polarization state.

References

For the textbook treatment of photodetector physics and the design tradeoffs across detector classes, see Saleh and Teich (2007), Fundamentals of Photonics, chapters 17 and 18. For the modern high-speed InGaAs PIN devices used in datacom and telecom, see Kato (1999) on ultrawide-band photodetectors. For NEP measurement standards and the methodology recommended by NIST, see NIST Special Publication 250-39 on photometric and radiometric measurements. For polarization-resolved detector characterization, see IEC 61290-1 on optical amplifier test methods (the same approach applies to receiver characterization).