How to Read an HgCdTe (MCT) Noise Spectrum

Core idea: An ideal MCT spectrum can be organized into \(1/f\), generation-recombination, and Johnson contributions. Independent noise powers add, so their amplitude spectral densities combine in quadrature.

A noise spectrum does not divide into three perfectly isolated bands. The contributions overlap, and the apparent boundaries move with detector resistance, temperature, bias, geometry, material quality, contacts, passivation, and the measurement chain. The regions are therefore useful interpretive limits—not rigid material constants.

Power spectral density versus amplitude spectral density

MCT noise is commonly plotted as voltage power spectral density \(S_V(f)\) in \(\mathrm{V^2/Hz}\), or as voltage amplitude spectral density \(e_n(f)=\sqrt{S_V(f)}\) in \(\mathrm{V}/\sqrt{\mathrm{Hz}}\). A lock-in frequency sweep or spectrum analyzer commonly presents amplitude spectral density.

The distinction matters when reading slopes. If \(S_V\propto 1/f^\alpha\), then \(e_n\propto 1/f^\beta\) with \(\beta=\alpha/2\). The direct NASD model above squares each component, adds the resulting noise powers, and then takes the square root.

How to interpret the model

The direct NASD equation combines a low-frequency power law, one GR Lorentzian, and the Johnson-Nyquist amplitude. Two frequencies should not be conflated: \(f_\times\) is the \(1/f\)-to-GR crossover where those contributions are equal, while \(f_{-3\mathrm{dB}}\) is the GR component's own rolloff.

Reading the spectrum

The low-frequency \(1/f\) region

The exponent \(\beta\) describes the ASD slope. The corresponding PSD term is \(S_{1/f}=e_{1/f}^2\propto 1/f^{2\beta}\), so the common PSD notation \(S_{1/f}\propto1/f^\alpha\) uses \(\alpha=2\beta\). In MCT photoconductors, a broad distribution of trap and relaxation times can produce approximate power-law behavior. Contacts, surfaces, passivation, carrier-number fluctuations, mobility fluctuations, nonuniform current flow, bias instability, and slow thermal drift can produce similar low-frequency excess.

The crossover \(f_\times\) is defined by \(e_{1/f}(f_\times)=e_{\mathrm{GR}}(f_\times)\). It marks a change in the dominant noise contribution; it is not generally the GR \(-3\ \mathrm{dB}\) frequency.

The reference-frequency amplitude \(A_{1/f}\) becomes more physically useful when tracked against bias, current, resistance, area, temperature, contact geometry, processing history, and passivation state. One spectrum at one operating point rarely identifies a unique cause.

The generation-recombination region

A single relaxation process gives a Lorentzian PSD. In ASD form, the amplitude equals \(e_{\mathrm{GR},0}/\sqrt{2}\) at \(f_{-3\mathrm{dB}}\). This is distinct from the lower-frequency \(1/f\)-to-GR crossover. For a genuine first-order relaxation,

The word effective matters. In HgCdTe, Auger-1, Auger-7, Shockley-Read-Hall recombination, deep levels, and transport effects can contribute overlapping time scales. Several processes can produce multiple Lorentzians or one broadened feature, so the observed rolloff need not equal one uncomplicated bulk minority-carrier lifetime.

The Johnson region

In the ideal MCT spectrum, the high-frequency detector floor is Johnson-Nyquist noise from thermal carrier motion through the detector resistance:

The Johnson region is frequency independent over the classical measurement band. Its level changes with the detector's operating temperature and resistance, so both values must be recorded at the same bias point used for the noise sweep.

A useful Johnson-region check compares the measured high-frequency floor with \(\sqrt{4k_{\mathrm B}TR}\), then repeats the acquisition with a known resistor and a shorted input through the same readout chain.

When a GR rolloff is not a lifetime

The equation \(\tau_{\mathrm{eff}}=1/(2\pi f_{-3\mathrm{dB}})\) is correct for a first-order relaxation. The difficult part is proving that the measured rolloff belongs to that relaxation.

The strongest interpretation comes from agreement among independent measurements. The noise rolloff, modulated-responsivity rolloff, and time-domain rise or decay should produce compatible time constants under the same temperature, bias, and optical condition.

Why the 1–10 kHz range is often useful

A 1–10 kHz range is often practical for MCT noise testing because it can lie above the strongest low-frequency excess while remaining well below a typical GR rolloff. That makes the measured value more representative of the GR plateau rather than the \(1/f\) rise or the high-frequency Johnson region.

This range is not universal. A detector with a lower GR rolloff, different lifetime, different bias, or significant instrumentation limits may require another frequency window. The correct test frequency is established from the measured spectrum and responsivity transfer function—not from a fixed convention alone.

A practical fitting workflow

1. Confirm the units. Determine whether the data are PSD in \(\mathrm{V^2/Hz}\) or ASD in \(\mathrm{V}/\sqrt{\mathrm{Hz}}\), and verify that ENBW normalization has been applied exactly once.
2. Record the MCT operating point. Include temperature, resistance, bias, current, device dimensions, optical condition, and stabilization time.
3. Establish the system floor. Measure a shorted input, open input, and known resistor through the same preamplifier, cabling, gain, and acquisition settings.
4. Check the Johnson prediction. Calculate \(e_J=\sqrt{4k_{\mathrm B}TR}\) from the measured detector resistance and temperature, then compare it with the high-frequency ASD plateau.
5. Fit Lorentzian structure. Estimate \(e_{\mathrm{GR},0}\) and \(f_{-3\mathrm{dB}}\), then inspect residuals for additional corners or broadening.
6. Fit the low-frequency term last. Estimate \(A_{1/f}\) and \(\beta\), then calculate \(f_\times\) from the intersection of the fitted \(1/f\) and GR components.
7. Repeat across operating conditions. Bias, temperature, resistance, area, contact geometry, and passivation provide the scaling needed for physical interpretation.
8. Inspect the time series. Random-telegraph switching, intermittent contacts, thermal drift, and microphonics can be hidden by a smooth averaged spectrum.

What the fitted quantities mean

Common interpretation mistakes

• Adding amplitude spectral densities directly instead of adding independent noise powers.
• Using a PSD slope and ASD slope as though they were the same exponent.
• Calling every low-frequency increase “trap noise” without checking drift, contacts, passivation, or bias heating.
• Calling the \(1/f\)-to-GR crossover and the GR \(-3\ \mathrm{dB}\) rolloff the same corner frequency.
• Assuming the three regions must appear as clean, nonoverlapping bands.
• Extracting a lifetime from the first visible rolloff without de-embedding electrical and instrument response.
• Calling a flat high-frequency region Johnson noise without comparing it with \(4k_{\mathrm B}TR\) and the measured system floor.
• Fitting a stationary model to a record containing random-telegraph switching or slow drift.

What to report

A reproducible MCT noise-spectrum result should include detector temperature, resistance, bias, current, device dimensions, optical condition, preamplifier and gain, acquisition method, frequency points or sample rate, record length, averaging, ENBW, and system-floor measurements. Report fitted uncertainties and the frequency interval used for each fit.

The final interpretation should distinguish three levels of confidence:

• Observed: the measured MCT slope, GR plateau, crossover, rolloff, or high-frequency floor.
• Modeled: the mathematical component used to fit that feature.
• Interpreted: the physical mechanism proposed after independent checks.