Photodetector, PV, TFT and Statistical Analyses

When you take a measurement with an instrument you are left with a pile of numbers (time, current, voltage columns); this section turns that raw table into meaningful physical answers such as "how fast is this photodetector?" or "what is the efficiency of this solar cell?". Just as a blood test analyzer extracts individual values (sugar, iron, cholesterol) from a blood sample, each analysis module computes a specific quantity from the CSV file you load and tells you whether the result is trustworthy.

How it works: Most of the modules in this section interpret the characteristic curve of a device (time response, J-V, transfer, noise spectrum...), because the shape of that curve directly carries the physics within it (exponential rise = RC/trap, J-V series = diode+resistors, sub-threshold line = switching sharpness). Each module extracts the physical parameters from the curve, compares the result against standards (IEC/IEEE/GUM) and against example "ground truth" values, and marks it with a reliability badge. In the module boxes below, the physical meaning, typical range and common interpretation pitfall of each metric are explained one by one.

• Why it is done: a raw signal has no meaning on its own; to make a decision you must convert it into standard, comparable metrics (speed, efficiency, noise, quality).
• What it teaches / measures: dozens of physical quantities for photodetectors, solar cells (PV), thin-film transistors (TFT) and statistics; plus how reliable each result is (the badge).
• Where it is used: device comparison in research labs, quality control in production, result interpretation in classroom/lab experiments, and failure analysis.

When you suddenly switch the light on and off at a light detector, its output does not jump instantly; it rises and decays with some delay. This module turns the question "how quickly does it respond?" into a number. Just like measuring how many seconds a car takes to go from 0 to 100 km/h — it shows how fast the detector reaches the light and how fast it stops.

Physical background: When the light turns on, photons are absorbed and carriers are generated, but those carriers accumulate charge in the device capacitance (and load resistance); the system behaves like an RC circuit and carries the output to its saturation level not instantaneously but exponentially. That is why the time series is not a sharp step but a smooth "rising-exponential / decaying-exponential" shape; the 10%→90% transition takes exactly ln(9)·τ ≈ 2.197·τ in a single-pole system. When the light turns off the same RC discharges; if the material contains traps, the fall/recovery is noticeably slower than the rise (asymmetry = trapping fingerprint).

• Why it is done: to understand whether the detector can follow fast signals (e.g. high-speed communication, pulsed light) without distorting/missing them.
• What it teaches / measures: rise_time_s = the time for the output to climb from 10% to 90% when the light turns on (turn-on speed); fall_time_s = the time to drop from 90% to 10% when the light turns off (turn-off speed); recovery_time_s = the time to return to the baseline (baseline+5%), capturing persistent effects; the t_fall/t_rise ratio indicates symmetry (≈1 clean, ≫1 trapping); n_cycles is the number of on/off cycles averaged.
• Typical values and interpretation: fast Si PIN photodiodes ns–µs; phototransistors µs; a-Si / organic / perovskite photoconductors are considered "slow" at the ms–s scale. t_fall ≈ t_rise is ideal; if t_fall is much larger, there are deep traps / persistent photoconductivity.
• Common mistake / caution: if sampling is too sparse (Nyquist: if t_r ≥ 1/f_s is not satisfied) the rise time is measured larger than it is — check the nyquist_ok flag. On a noisy signal the baseline/peak may be misestimated and the thresholds may shift; if no transition is found, review the threshold percentages.
• Where it is used: optical communication receiver selection, sensor design validation, fast photo-switch characterization, and trap/persistence diagnosis in materials.

A light detector produces a small "dark current" even when there is no light; when light arrives the current grows much larger. This module computes the ratio of the two and how clearly the signal is distinguished relative to the noise (SNR). Like being able to hear a whisper in a quiet room — the lower the ambient noise, the more confidently you can pick out the real signal.

Physical background: Dark current arises from thermally generated carriers without light and from leakage (generation-recombination, surface leakage, reverse-bias leakage); this is the detector's "baseline". When light arrives, photo-generated carriers ride on top of it and carry the current upward, so in the time series you see two stable plateaus (dark and light); the height of the jump in between is I_photo. The small fluctuation on the dark plateau is the noise (σ); whether you can confidently read the signal as "on/off" depends on how many times this jump exceeds the noise.

• Why it is done: to measure whether the detector can distinguish weak light from the background (dark current + noise) and how "clean" an on/off contrast it provides.
• What it teaches / measures: i_dark = lightless baseline current (the smaller the better); i_photo = the net current increase with light; photo_dark_ratio = I_photo/I_dark = contrast (large = good); noise_sigma = standard deviation of the dark region; snr_db = 20·log10(|I_photo|/σ) = how many dB the signal is above the noise.
• Typical values and interpretation: for a good photodiode a ratio of 10³–10⁶ and SNR of tens of dB (e.g. ~60 dB is very clean) is expected; if the ratio is <10 the signal is drowned in the background. Dark current rises exponentially with temperature, so low I_dark = low noise and the ability to see weaker light.
• Common mistake / caution: reading SNR linearly instead of in log (dB) and misinterpreting it; not measuring the dark plateau long enough (σ is poorly estimated); if the light region hits saturation/compliance, I_photo comes out smaller than it is. The ratio and SNR are different: one measures contrast, the other distinguishability relative to noise.
• Where it is used: low-light-level detection, sensor quality control, material comparison, and temperature-dependent dark-current diagnosis.

When you turn the light off, the signal of some detectors does not reset immediately but stays "stuck" for a while; this is because traps in the material release the charge carriers late. This module models that slow decay and extracts how long it lasts. Like a glow-in-the-dark toy that keeps glowing for a while after the light is switched off.

Physical background: Some of the carriers generated under light are captured at defect/trap levels; when the light turns off these traps release the charge thermally late, so the current does not drop to zero instantly (persistent photoconductivity, PPC). If there is a single trap depth the decay is single-exponential (exp(−t/τ)); if the traps are distributed the curve bends into a "stretched exponential" (stretched, β<1) or a double-exponential with two separate time scales. That is why it is typical to see a fast initial drop followed by an extended tail; the module turns the character of this tail into a number by selecting the model with the highest R².

• Why it is done: to understand the defect/trap density in the material and whether the device exhibits a "memory effect" (slow reset).
• What it teaches / measures: persistence_tau_s = the characteristic time constant τ of the decay (large = long memory/deep trap); persistence_model = the selected model (single/stretched/double); persistence_beta = the stretching exponent β (close to 1 = single time scale, <1 = wide trap distribution); persistence_r2 = how well the model fits the data.
• Typical values and interpretation: τ µs–ms in fast crystalline detectors; τ can be seconds–minutes in trap-heavy a-Si/oxide/perovskite/organic devices. β≈1 clean single-trap; β≈0.3–0.7 distributed traps; if R²<0.95 a single model is insufficient and the module suggests an alternative.
• Common mistake / caution: a wrong detection of the light-off instant ruins the entire fit; if the window is chosen too short the long tail is not seen and τ comes out small. Forcing a single-exponential misreports the physics of a double-exponential decay — read R² and the model selection together.
• Where it is used: new-material research, defect/trap diagnosis, suitability assessment for applications requiring fast repetition (high frame-rate imaging, etc.).

It converts how fast a detector responds (rise time) directly into the answer to "what is the highest-frequency signal it can follow, in Hz?". Like computing how many steps per minute a runner can take from their stride speed — speed and frequency are two faces of the same coin.

Physical background: A system that is "slow" in the time domain is "narrow-band" in the frequency domain; the same RC/single-pole behavior locks these two faces together. For a single-pole low-pass there is a fixed relation between the corner frequency at which the gain falls to -3 dB (half the power) and the 10%–90% rise time: BW·t_r ≈ 0.35. That is, you can invert the measured rise time to estimate the highest frequency that the device can pass with less than 30% attenuation; this is why you read the speed limit without performing a separate frequency sweep.

• Why it is done: to know whether the detector can pass a signal (modulation, pulse train) at a given frequency without attenuation, without performing a separate frequency sweep.
• What it teaches / measures: rise_time_s = the 10%–90% rise time used (from temporal_response if not provided); bandwidth_3db_hz = the -3 dB bandwidth derived from it (large = fast device). Relation BW = 0.35/t_r.
• Typical values and interpretation: ms rise → kHz band; µs → hundreds of kHz–MHz; ns → GHz scale. The 0.35 coefficient is a single-pole/Gaussian approximation; in multi-pole or trap-dominated devices the real bandwidth may deviate, and the result should be read as an order-of-magnitude estimate.
• Common mistake / caution: if the rise time was measured with sparse sampling that violates Nyquist, the derived bandwidth is also wrong; also, if the fall time is much larger than the rise time (trapping), the bandwidth derived from a single t_r overstates the true repetition rate.
• Where it is used: high-speed optical link design, sensor specification validation, and speed-limit (modulation band) estimation.

It tells you how much current the detector produces for each watt of light falling on it — that is, the device's "sensitivity to light". Like how much electricity a solar panel produces under the same sun; a detector that produces more current under the same light is more responsive.

Physical background: Each absorbed photon produces at most one electron-hole pair (in the absence of gain), so the current is directly proportional to the optical power and the slope gives the responsivity (R = I_photo/P). Since the energy of a photon is E = hc/λ, at constant power there are more photons at long wavelengths; therefore R tends to increase linearly with λ even if the quantum efficiency stays constant (R = EQE·qλ/hc) until the material's band gap is exceeded and absorption drops. This is why the R(λ) curve peaks and then falls: surface loss at short λ, band-gap cutoff at long λ.

• Why it is done: to compare the efficiency of different detectors under the same light, to calibrate the measurement chain, and to find which color it is most sensitive to.
• What it teaches / measures: responsivity_a_w = responsivity in A/W (the slope); i_photo = net photocurrent; p_detector_w = the power that actually falls on the detector, with active/spot area scaling; in spectral mode responsivity_peak_a_w and peak_wavelength_nm = the peak of R(λ) and its wavelength. The implied EQE = R·1239.84/λ also shows the per-photon yield.
• Typical values and interpretation: for a Si photodiode R ~0.3–0.6 A/W in the visible–near IR (peak ~0.6 at ~900 nm); for InGaAs ~0.8–1.0 A/W (1550 nm). R exceeding the qλ/hc limit (EQE=1) is only possible with internal gain (APD, phototransistor); otherwise it indicates a measurement/power error.
• Common mistake / caution: the most critical input is the incident power p_in_w; a wrong/uncalibrated power scales the entire R. If the spot area is larger than the active area, part of the light does not fall on the detector — if area scaling is not entered, R comes out smaller than it is. If you see EQE>100% (and gain is not expected), first check the power and area.
• Where it is used: detector selection, spectral characterization, calibration, and production quality control.

It tells you, as a percentage, how many out of every 100 light particles (photons) striking the device are converted into electric charge. Like inviting 100 guests and counting how many came in — EQE is based on all the photons that strike, while IQE accounts for those that turn back at the door (reflected light) to give the "true" fraction of those that came in.

Physical background: While responsivity ties the current to watts, quantum efficiency normalizes the count per photon: since a photon's energy is hc/λ, EQE = R·(hc/qλ) = R·1239.84/λ[nm]. EQE includes all losses — reflected + unabsorbed + recombined — so it can understate the true collected-charge efficiency. IQE is based only on the photons that enter (are absorbed): IQE = EQE/(1−R_refl). Therefore IQE is always greater than (or equal to) EQE and tells you "how well the material collects what it absorbs, reflection aside".

• Why it is done: to see how hard the device pushes the fundamental limit of converting light into load (each photon → one charge) and to separate whether the loss is from reflection or from collection/recombination.
• What it teaches / measures: eqe_pct = the percentage of charge collected per incident photon (external); iqe_pct = the efficiency per absorbed photon after reflection is removed (internal); responsivity_a_w and wavelength_nm = the inputs of the calculation. The eqe_needs_reflection_correction flag indicates that reflection data is required for IQE.
• Typical values and interpretation: for a good Si detector/cell, peak EQE can be 80%–95% and IQE >90%; an anti-reflection coating brings EQE closer to IQE. EQE or IQE exceeding 100% (with no gain mechanism) is suspicious and the module issues a warning.
• Common mistake / caution: entering a wrong λ scales EQE directly (the formula is inversely proportional to λ); mistaking IQE for "internal efficiency" without entering reflection (R_refl); mistaking EQE>100% for gain when it is usually a power/area/λ error.
• Where it is used: solar cell/detector research, material and anti-reflection coating optimization, efficiency comparison.

When you double the light, does the current double too? This module measures how "honestly proportional" the detector is to the incident power and over what brightness range it stays reliable. Like a scale being able to weigh both one gram and one kilogram accurately — proportionality must not break over a wide range.

Physical background: In an ideal detector the photocurrent is one-to-one proportional to the incident power (I ∝ P¹), because twice the photons produce twice the carriers. In reality the proportionality breaks when traps saturate at low power or recombination increases at high power; the relationship is summarized by the power law I = C·P^α, which becomes a straight line on a log-log plot with slope α. α=1 is perfectly linear; α<1 (sub-linear) charge trapping/recombination; α>1 (super-linear) indicates a gain mechanism. The span between the smallest and largest power over which the device preserves proportionality is the linear dynamic range (LDR).

• Why it is done: to find over what light range the detector's measurement can be trusted and where it enters saturation/trapping/gain.
• What it teaches / measures: linearity_alpha = the power-law exponent α (regime indicator); powerlaw_coeff = the coefficient C (scale); linearity_r2 = the quality of the log-log fit; ldr_db = 20·log10(P_max/P_min) = the linear dynamic range; p_min_w/p_max_w = the ends of the range.
• Typical values and interpretation: in a good detector 0.95 ≤ α ≤ 1.05 and LDR is tens–100+ dB (several decades); values like α=0.5 indicate a strong trapping regime. If R²<0.999, the whole range does not obey a single linear law (curvature at the ends).
• Common mistake / caution: assessing linearity "by eye" on a normal (linear) axis — it must be viewed log-log; claiming a wide LDR with only a few points; mistaking the detector saturating at the brightest point and lowering α for a material defect. LDR is converted to dB with 20·log10, not with the number of decades (1 decade = 20 dB).
• Where it is used: measurement instrument calibration, sensor operating-range definition, and detection of gain/trapping behavior.

What is the "weakest light" a detector can detect? This module measures the device's own noise and computes the light power that produces a signal equal to that noise (NEP) and a size-independent quality figure (D*). Like determining the faintest sound you can hear in a noisy environment — the quieter the device, the weaker the signal it can catch.

Physical background: There is always random current fluctuation at the baseline of a detector (shot noise from the dark current √(2qIΔf) and Johnson/thermal noise from the shunt resistance √(4k_BTΔf/R)). You have "seen" a signal only when you can lift it above this noise floor; the optical power that produces a current equal to the noise is the noise-equivalent power (NEP = i_noise/R). Since a larger area or wider band collects more noise, the specific detectivity D* = R·√(A·Δf)/i_noise is defined to normalize these for fair comparison of devices — the larger D*, the more sensitive the device.

• Why it is done: to determine the detector's sensitivity limit (the weakest detectable light) and to fairly compare devices of different size/band/technology.
• What it teaches / measures: nep_w_sqrthz = band-normalized noise-equivalent power (small = sensitive); nep_total_w = total NEP over the whole band; detectivity_jones = area/band-normalized D* (large = good); noise_density_a_sqrthz = current noise density; shot_noise_a/thermal_noise_a and noise_dominant = which noise mechanism dominates.
• Typical values and interpretation: for room-temperature Si/InGaAs D* ~10¹¹–10¹³ Jones is realistic; cooled IR detectors are on the order of 10¹⁰–10¹². D*>10¹⁴ Jones (with no gain) is physically suspicious and the module issues a warning; the smaller the NEP, the weaker the light the device can pick out.
• Common mistake / caution: R (responsivity) is a REQUIRED input; a wrong R scales NEP and D* directly. If the bandwidth Δf and area A are not entered, the comparison becomes meaningless. NEP (W/√Hz) must not be confused with NEP_total (W); very small D* values are preserved with significant-figure rounding (decimal rounding would have shown 0).
• Where it is used: low-light/infrared detector selection, performance ranking, and noise-source (shot vs thermal) diagnosis.

Every device has noise, but this noise is not uniform; it comes from different sources at different frequencies. This module breaks the noise down by frequency and tells you which mechanism dominates (1/f flicker, shot, thermal). Like listening to the hum of an orchestra and separating "is this coming more from the bass drum or the violins?".

Physical background: When you transform the dark-current time series into frequency (PSD), different noise mechanisms leave different signatures. Shot and thermal noise give a flat "white" floor at all frequencies (frequency-independent); in contrast, flicker noise arising from the trap capture-release dynamics is large at low frequency and decreases with frequency as 1/f^γ. That is why on a log-log PSD plot you see a sloped (1/f) region at low frequency and a flat floor at high frequency; the "corner frequency" where the two cross is the point at which flicker submerges into the white floor. Operating above the corner minimizes the noise.

• Why it is done: to find the root cause of the noise (trap-dominated, or fundamental shot/thermal) so the right improvement can be made (filtering, choice of operating frequency, material/process).
• What it teaches / measures: flicker_gamma = the low-f slope γ (close to 1 means classic 1/f); corner_freq_hz = the corner frequency where flicker drops to the white floor; white_floor_a2_hz = the white noise floor; shot_level_a2_hz/thermal_level_a2_hz = the theoretical shot/thermal levels; low_freq_fit_r2 and noise_dominant = fit quality and the dominant mechanism.
• Typical values and interpretation: γ≈1 pure 1/f flicker (trap/defect dominated); γ≈0 white (shot/thermal dominated). A low corner frequency = clean, low-trap material; a high corner = defect-heavy device where operating at low frequencies is difficult. The measured white floor being close to the theoretical shot level indicates the device has reached the fundamental limit.
• Common mistake / caution: if the sampling frequency (sampling_hz) is wrong the entire frequency axis shifts; a too-short series cannot resolve low frequencies (the corner is not seen). Reading the PSD on a linear axis hides the 1/f region; interpret γ not on its own but together with the corner frequency and the fit R².
• Where it is used: low-noise detector/circuit design, material/process quality diagnosis, and operating-band optimization.

Light sources such as LEDs are often driven with a very fast on-off (PWM) signal; the frequency of this flicker invisible to the eye, how much of it is "on" (duty cycle) and how clean it is all matter. This module measures the drive signal and, if a detector response is present, finds the delay between them. Like reading the rate and rhythm of a heart with an ECG.

Physical background: In PWM the average brightness is proportional to how much of a constant-amplitude pulse is "on" (the duty cycle); the eye perceives this as continuous light, but the signal is actually a square wave. The module extracts the frequency from the time between rising edges, the duty from the on-fraction, and the ripple from the peak-to-peak variation at the on level; an ideal square wave consists of a fundamental frequency and its harmonics in the FFT, and as distortion increases (sloped edges, ringing) the harmonic content (THD) grows. If a detector response is also present, the time shift between drive and response gives the system's response delay/phase.

• Why it is done: to verify that the drive signal is at the correct frequency/brightness and undistorted, and to measure the drive→detector system delay.
• What it teaches / measures: frequency_hz (±frequency_std_hz stability) = the pulse frequency; duty_cycle = the on-fraction (average brightness); ripple_pp = the peak-to-peak ripple at the on level; thd = harmonic distortion (the "cleanliness" of the signal); v_high/v_low = the levels; if a response is present response_delay_s/response_phase_deg = delay/phase.
• Typical values and interpretation: for flicker-free visible lighting a frequency ≳ a few hundred Hz–kHz is preferred; the duty maps to the desired brightness (e.g. 30% = dim); low ripple and low THD mean a clean drive. A large frequency_std means an unstable drive (jitter).
• Common mistake / caution: if the thresholds (v_high/v_low) are auto-detected incorrectly on a noisy signal the duty/frequency shifts; if the sampling is too sparse relative to the pulse width the duty and THD become unreliable. When measuring the response delay, the drive and response must be on the same time axis.
• Where it is used: LED driver verification, optical-system timing, and control-electronics quality control.

It takes how the power produced by a solar cell varies with voltage and quickly answers "at which point does it deliver the most power and what is its efficiency?". Like finding the most efficient gear/pedal speed of a bicycle — a particular point delivers the highest power.

Physical background: A solar cell is a diode in parallel with a light-fed current source; as the voltage rises the diode turns on and swallows part of the current it produces internally. Since power is P = V·I, the power is zero at V=0 (I=I_sc) and again zero at I=0 (V=V_oc); somewhere in between a peak forms — this is the maximum power point (MPP). That is why the P-V curve is a single-peaked hill and you always want to operate the cell at this peak. The fill factor tells you how closely this real peak approaches the ideal "rectangular" power (V_oc·I_sc); the sharper the knee of the J-V curve, the higher the FF.

• Why it is done: to see the cell's maximum power point and overall quality at a quick glance, without going into the detailed engine.
• What it teaches / measures: p_max_w, v_mpp_v, i_mpp_a = the power at the MPP and the voltage/current that deliver it; v_oc_v/i_sc_a = open-circuit voltage and short-circuit current; fill_factor = P_max/(V_oc·I_sc) = the rectangularity of the curve; pce_pct = P_max/(P_in·A)·100 = the power conversion efficiency.
• Typical values and interpretation: in a healthy cell FF is 0.7–0.85 (high = low Rs, high Rsh); FF<0.5 indicates high series resistance or low shunt resistance. V_mpp is always below V_oc; FF>1 is physically impossible and indicates that V_oc/I_sc is wrong (the module issues a warning).
• Common mistake / caution: this is the "quick" core — use the detailed pv_metrics for Rs/Rsh, the STC badge, and a fine-grid MPP. If the sign convention is wrong, the power peak stays in the negative quadrant and P_max cannot be found; if the incident power p_in_w and area are not entered, the efficiency for PCE is not computed.
• Where it is used: quick solar cell screening, production-line sorting, and educational/lab demonstration.

It computes the entire standard performance report card extracted by applying a voltage to a solar cell and measuring its current (a J-V sweep). Like deriving all of a student's course grades from a single exam — a single sweep gives the cell's full performance table.

Physical background: The illuminated J-V curve is the dark diode curve shifted down by the photocurrent; that is why it takes its characteristic "knee" shape in the fourth quadrant (positive V, negative I — i.e. the power-generating region). The sharpness of the knee depends on two parasitic resistances: the series resistance Rs (contact/grid losses) flattens the slope near V_oc, while the shunt resistance Rsh (leakage/short paths) prevents the slope near V=0 from being steep. The module reads Rs and Rsh from these regional slopes; with the J_sc normalized by area and the PCE computed from the incident power, the result becomes comparable under STC (1000 W/m², 25 °C).

• Why it is done: to document a cell's efficiency and quality in a standards-compliant (IEC), area-normalized and comparable way.
• What it teaches / measures: v_oc_v = the voltage at which light generation equals the diode loss; j_sc_ma_cm2 = the short-circuit current density divided by area; fill_factor = the rectangularity of the knee; pce_pct = efficiency; r_s_ohm = series resistance from the slope above V_oc (low is good); r_sh_ohm = shunt resistance from the slope near V=0 (high is good); metrics_resolved = the reliability flag.
• Typical values and interpretation: in a good lab Si cell V_oc ~0.6–0.7 V, J_sc ~30–40 mA/cm², FF 0.75–0.83, PCE ~15%–22%; Rsh should be high (kΩ–MΩ·cm²) and Rs low (<a few Ω·cm²). Low FF + low Rsh = leakage; low FF + high Rs = contact/conduction loss.
• Common mistake / caution: if irradiance/temperature/active_area are not entered, the badge becomes non_stc and the PCE cannot be compared; if the sign convention is wrong, V_oc/I_sc are found inverted (even though the module auto-detects, do check). Under 1000 W/m², the identity PCE[%] = J_sc·V_oc·FF is a quick way to verify consistency.
• Where it is used: solar cell research, pre-certification measurement, and production quality control.

If you sweep the same solar cell in the forward and reverse directions, the two curves usually do not overlap exactly; the difference between them is "hysteresis" and is often a sign of instability. This module converts this difference into a numerical index. Like getting tired differently going up and coming down a hill — if behavior changes with direction, something is shifting.

Physical background: Hysteresis arises from the presence of a slow internal process (especially ion migration in perovskites, plus trap filling/emptying and interface capacitance) that cannot keep up with the sweep. Because these slow charges "catch" the curve at a different place depending on the sweep direction, the forward and reverse J-V curves diverge and an area remains between them; usually the reverse (V_oc→0) sweep gives a better (higher) PCE. The hysteresis index measures this divergence: the PCE-based index quantifies the relative difference between the two efficiencies, while the area-based index quantifies the whole area between the two curves.

• Why it is done: to understand whether the measured efficiency is "real/stable" or misleadingly dependent on the sweep direction and speed, and to assess the device's stability.
• What it teaches / measures: pce_fwd_pct/pce_rev_pct = the forward and reverse sweep efficiencies; hysteresis_index = the PCE-based index (PCE_rev−PCE_fwd)/PCE_rev; hysteresis_index_area = the normalized area between the two curves.
• Typical values and interpretation: in stable Si/inorganic cells HI ≈ 0%–a few %; in perovskites it can be tens of %. A positive and small HI is tolerable; a large HI is a warning that the reported efficiency may be inflated by a single-direction sweep. Ideally, cross-validate with stabilized power output (MPP tracking).
• Common mistake / caution: loading a single-direction sweep and thinking there is "no" hysteresis (the module expects a single bidirectional file); a wrong detection of the turning point distorts the segment split; treating HI as absolute truth without reporting the sweep rate — hysteresis depends on the rate, so devices should not be compared without fixing the rate.
• Where it is used: perovskite/next-generation cell research, stability assessment, and measurement-protocol validation.

By measuring the cell in the dark (no light) and examining its diode-like behavior, it answers "what kinds of losses are inside it?". The ideality factor n is a fingerprint of the recombination mechanism in the cell. Like diagnosing a fault by listening to the engine idle without driving.

Physical background: In the dark the cell is a pure diode and its forward current rises exponentially with voltage: I = I0·[exp(qV/nkT)−1]. When you plot ln(I) against V, this exponential region turns into a straight line; the slope of the line gives the ideality factor q/(nkT) and the intercept gives the saturation current I0. That is why the mid-voltage region of a semilog J-V should be straight; at very low voltage shunt leakage (Rsh) bends this line from below, and at very high voltage series resistance (Rs) flattens the curve. The module performs the fit exactly in this clean middle window.

• Why it is done: to see the cell's fundamental diode quality and the dominant recombination/loss mechanism independently of light effects.
• What it teaches / measures: ideality_factor = n, the conduction/recombination fingerprint; saturation_current_a = I0, how much the diode "leaks"; r_s_ohm = series resistance at high V; r_sh_ohm = shunt resistance at low V; fit_r2 = the quality of the semilog line fit.
• Typical values and interpretation: n≈1 diffusion (band-band) dominated, ideal; n≈2 depletion-region (SRH/trap) recombination dominated; 1<n<2 mixed. n>2 indicates a serious defect/interface problem or a poor fit. Low I0 = good diode. The module warns when n∉[0.8,10] or R²<0.98.
• Common mistake / caution: if we move the fit window (v_fit_min/v_fit_max) into the Rsh-bent or Rs-flattened region, n grows artificially; entering the wrong temperature corrupts the slope→n conversion (the kT/q scale). Read n not on its own but together with R². For physical consistency this module uses the DiodeAnalysisEngine, so there is no metric drift relative to the Diode/Schottky modules.
• Where it is used: cell quality diagnosis, identifying loss sources in the production process, and material comparison.

It represents a solar cell with a simple circuit of five fundamental electrical components (a current source, a diode, two resistors) and fits the whole I-V curve to this model simultaneously to find the values of the components in one go. Like redrawing the internal schematic of a complex device from external measurements.

Physical background: The single-diode model describes the cell as follows: light produces a current source Iph, a parallel diode (I0, n) swallows part of it, a shunt resistance Rsh leaks, and a series resistance Rs lowers the output. These five components shape different regions of the same J-V curve (the height of Iph, the diode knee, the Rsh low-V slope, the Rs V_oc slope). Instead of taking regional slopes one by one, the module nonlinearly fits the whole curve to a single equation with the Lambert-W closed-form solution; this way the parameters correctly account for each other's effects and the 1σ uncertainty of each comes out from the fit covariance.

• Why it is done: to explain the cell's behavior not piece by piece (regional slope) but with a holistic and more accurate model, and to know the uncertainty of each parameter.
• What it teaches / measures: iph_a = the photocurrent source; saturation_current_a (j0_a_cm2) and ideality_factor = diode quality; r_s_ohm/r_sh_ohm (area-normalized *_cm2) = the parasitic resistances; in two-diode mode i02_a/n2 = the second recombination path; for each parameter *_sigma_* = the 1σ uncertainty; fit_r2/rmse_a/nrmse_pct/reduced_chi2 = fit quality.
• Typical values and interpretation: in a successful fit R²≈1 and the nRMSE is small; if the uncertainties (σ) are small next to the value the parameter is reliable, if large that parameter is not well-constrained by the curve (e.g. at very high Rsh the Rsh σ comes out large — this is normal). It is far more accurate than the slope/ln(I) methods.
• Common mistake / caution: if the initial guess is poor or the data is noisy the fit may get stuck in a local minimum; in that case enable the robust (global search) option. Forcing a two-diode model on a single curve makes the parameters over-uncertain; read the circuit_resolved flag and the σ values together. If the sign convention is wrong the sign of Iph comes out inverted.
• Where it is used: advanced cell modeling, simulation (SPICE) parameter extraction, and loss analysis.

It collects in a single package nearly every analysis that can be done from a single J-V file: basic performance, hysteresis, sweep-rate-dependent dynamic effects, diode parameters and shape-distortion (kink/S-curve) diagnostics. Like a vehicle's full inspection report — a check from every angle in one pass.

Physical background: A J-V curve carries not only efficiency but also the charge accumulated during the sweep and the device's internal dynamics. If a time axis is present, the sweep rate comes from the voltage-time slope, and the swept charge and apparent capacitance come from the current-time integral; these dynamic metrics reveal the source of the hysteresis (capacitive/ionic). Furthermore, if there is a step (kink) below the "knee" of the curve or a reverse bend before the MPP (S-shape), this usually indicates that charge extraction is being impeded at an interface (energy barrier, unbalanced transport). Because the module calls the same jv_engine core as the live PV measurement, the report is one-to-one consistent with the real-time measurement.

• Why it is done: to comprehensively document a cell in a single pass and to ensure consistency by using exactly the same engine as the live measurement.
• What it teaches / measures: basic: v_oc_v, j_sc_ma_cm2, p_max_mw_cm2, fill_factor, pce_pct, window-fitted r_s_a_ohm_cm2/r_sh_a_ohm_cm2; hysteresis package hi_pce/hi_area_jscvoc/delta_voc_v; dynamic sweep_rate_v_s/charge_density_c_cm2/apparent_cap_mean_f_cm2; diode ideality_factor/j0_a_cm2; diagnostics rr_at_1v (rectification ratio), j_leak_1v_ma_cm2 (leakage), kink_score, s_shape_index.
• Typical values and interpretation: in a healthy cell kink_score and s_shape_index ≈0, a high rectification ratio and low leakage are expected; a large s_shape_index/kink indicates a charge-extraction barrier (poor contact/transport layer). The dynamic metrics should shrink at low sweep rate; large apparent capacitance + high HI = ionic/capacitive source.
• Common mistake / caution: feeding a dark curve into the light report makes the metrics "Unreliable" — set the is_dark flag correctly (the example dataset is precisely the corrected version of this mistake). The dynamic metrics require a time axis (t) or sweep_rate_v_s; otherwise charge/energy/capacitance are not computed.
• Where it is used: a detailed research report, problem diagnosis (S-shape, kink, leakage), and full characterization.

It tracks a cell's performance over time and answers "how long does it last?"; it finds the time it takes to drop to a certain percentage of the initial value (T80/T90). Like a phone battery losing capacity over time — the answer to "when does it drop to 80%?".

Physical background: Solar cells degrade over time: moisture/oxygen ingress, light-induced defect formation, ion migration or contact corrosion slowly lower the performance. This decline is often close to an exponential decay; the times to drop to 80% (T80) and 90% (T90) of the initial value are standard lifetime metrics. If the measurement window ends before the device drops to these thresholds, the module uses the slope of the last 30% (if negative) to estimate the threshold by extrapolation — this is why the slope of the observed tail in the plot determines the predicted lifetime.

• Why it is done: to estimate the device's real operating lifetime and to fairly compare the durability of different materials/encapsulations/coatings.
• What it teaches / measures: initial_value = the mean of the first n_initial points (the reference y0); t80/t90 = the times to drop to 80%/90% of y0; retention_pct = the ratio of the last value to y0 (remaining performance); final_value = the last measured value; the t80_extrapolated flag indicates that the threshold was not measured but estimated.
• Typical values and interpretation: in commercial Si modules T80 is decades (~0.5%–1% loss per year); in immature perovskite/organic devices it can be hours–hundreds of hours. High retention = stable device; if t80_extrapolated=True the number was not measured but estimated — be cautious about inferring a long lifetime from a short test.
• Common mistake / caution: presenting an extrapolated T80 as precisely as if it were measured; if n_initial falls on noisy first points, y0 and therefore all thresholds shift; in non-exponential (stepwise/abrupt) degradation the closed-form τ assumption is misleading. Mind the time unit (s/h).
• Where it is used: stability tests (ISOS protocols), product lifetime/warranty estimation, and accelerated aging studies.

By varying the gate voltage of a thin-film transistor it answers "how good a switch is it?": when does it turn on, how large is the difference between on/off current, how sharply does it switch on. Like measuring at what point a tap starts to flow when you open it, and the difference between fully open and fully closed.

Physical background: The gate voltage Vgs controls the charge density in the channel through the insulating oxide. Below the threshold voltage Vth the channel has not yet formed, so the current flows only by thermal emission and increases exponentially with Vgs — that is why the sub-threshold region of the semilog transfer curve is a straight line and its slope (SS) gives the sharpness of the switching. Above Vth the channel fills and the current now grows linearly/quadratically; this is why the curve settles onto the "on" plateau. The steeper the sub-threshold slope (smaller SS), the fewer the traps; when swept bidirectionally, the shift of the curve (ΔVth) indicates trap filling/emptying hysteresis.

• Why it is done: to quantify the switching quality of the transistor and the electronic properties of the channel/interface material.
• What it teaches / measures: on_off_ratio = the on/off current ratio (contrast); vth_v = the threshold at which the channel turns on (max-gm tangent extrapolation); ss_mv_dec = the Vgs required to change the current by 10× (switching sharpness/trap indicator); mu_fe_cm2_vs = the field-effect mobility (how easily the carriers flow); dit_cm2_ev = the interface trap density (from SS); vth_y_v/mu0_y_cm2_vs = the Rs-free Y-function extraction; delta_vth_v/hysteresis_window_v = the bidirectional hysteresis.
• Typical values and interpretation: for a good TFT on/off ≳10⁶–10⁸; SS ~60–100 mV/dec is near-perfect (60 mV/dec is the room-temperature theoretical limit), >300 mV/dec dense interface traps; mobility varies by technology (a-Si ~1, metal-oxide/IGZO ~10, poly-Si tens of cm²/V·s). A small ΔVth = a stable interface.
• Common mistake / caution: trying to read on/off and SS on a linear axis (it must be semilog); if W/L/C_ox are not entered, mobility and Dit are not computed (but Vth/SS/on-off still come out); reading Ioff from the noise/leakage floor and overstating the on/off (use ioff_robust_a); missing hysteresis by sweeping a single direction.
• Where it is used: display/sensor transistor characterization, evaluation of new semiconductor/dielectric materials, and process quality control.

With the transistor on, it examines how much current it can drive as the drain voltage is increased and where the current "saturates" and stabilizes. Like measuring how much flow a water pump can deliver as the pressure increases and where it hits the ceiling.

Physical background: At low Vds the channel is conductive everywhere and the current increases linearly with Vds (linear/triode region, slope ≈ 1/Ron). As Vds grows the channel is "pinched off" at the drain end (pinch-off); beyond this point the extra Vds mainly drops across the pinched region and the current is nearly constant — the saturation region. This is the reason for the gentle plateau of the curve. The plateau is not perfectly flat: due to channel-length modulation (λ) it rises slightly; this slope is read as the output resistance r_o = 1/(I_dsat·λ) and the Early voltage V_A = 1/λ. For multiple Vgs, this family of curves also gives the saturation mobility.

• Why it is done: to understand the current the transistor can drive, the output resistance and the gain potential as an amplifier (intrinsic gain).
• What it teaches / measures: ron_ohm = the linear-region on-resistance (low-Vds slope); idsat_a = the saturation current; lambda_per_v = channel-length modulation; output_resistance_ohm = the output resistance r_o in saturation; va_v = the Early voltage (1/λ); av = the intrinsic gain g_m·r_o; knee_v = the linear→saturation knee voltage; if multiple Vgs are present mu_sat_cm2_vs = the saturation mobility; n_curves/vgs_used_v = the number of curves in the family.
• Typical values and interpretation: low Ron = good drive capability; high r_o / high V_A (large 1/λ) = a flat plateau, a good current source and high gain; low V_A (steep plateau) = a short-channel effect. The knee voltage is roughly around Vgs−Vth.
• Common mistake / caution: the saturation mobility cannot be extracted from a single curve (single Vgs) (µ_sat = N/A); fitting λ from the linear region instead of the plateau ruins r_o; reading Ron from the saturation region. r_o, λ and V_A are different expressions of the same physics and must be consistent.
• Where it is used: transistor modeling for circuit design, sizing the driver/amplifier stage, and performance validation.

When you measure the same thing repeatedly the results do not come out exactly identical; this module computes from those repetitions the mean, the spread and the scientific answer to "how much can I trust the mean?" (the uncertainty). Like shooting the same arrow at a target many times and looking at how scattered the shots are — if the spread is narrow your confidence is high. This is a pure statistics module; it has no device-specific physics.

• Why it is done: to quantify the repeatability of a measurement and to report the result with a standard uncertainty (GUM).
• What it teaches / measures: mean/median = central tendency; std_sample = spread; u_mean = s/√N = the standard uncertainty of the mean; expanded_u_mean = k·u = the expanded uncertainty; rel_std_pct = the relative scatter.
• Common mistake / caution: with few repetitions (2 ≤ N < 10) the uncertainty is weak; with a single measurement (N=1) the uncertainty is undefined (the badge is unreliable). Do not confuse the standard deviation (spread) with the uncertainty of the mean (smaller by √N).
• Where it is used: measurement uncertainty budget, calibration report, quality-control statistics.

If there is a straight proportionality between two quantities (e.g. if current increases as light increases), this module draws the "best line" through the points and gives the slope/intercept along with their reliability. Like passing the most suitable line through the middle of scattered points with a ruler — but with mathematics, not by eye. This is a pure statistics (OLS) module; it has no device-specific physics.

• Why it is done: to quantify the relationship between two variables, to extract a calibration line, or to derive a physical quantity from a slope.
• What it teaches / measures: slope/intercept = the slope and intercept of the line (each with a Type-A u_* and expanded uncertainty); r_squared = the fit quality; residual_std = the scatter of the residuals.
• Common mistake / caution: with few points (N < 8) the uncertainties are wide; mistaking a high R² for "proof of linearity" (a curve can also give a high R² — look at the residuals); in a perfect fit (R²=1) the uncertainty comes out 0, which is a sign of synthetic data.
• Where it is used: sensor calibration, trend analysis, experimental-law validation.

How many "write-erase" cycles can a resistive-switching memory (memristor) cell withstand? This module tracks the high and low resistance states in each cycle and finds when the "window" between them begins to close (failure). Like switching a light switch on and off thousands of times and counting when it starts to stick.

Physical background: An RRAM cell stores "1" and "0" by forming (SET → low resistance, LRS) or rupturing (RESET → high resistance, HRS) a conductive filament inside it. To read the data the resistances of the two states must be clearly different; this difference is the "memory window" ratio R_HRS/R_LRS. As the cycles repeat, the filament material fatigues (ion depletion, thermal damage): LRS rises or HRS drops and the window narrows. When the window falls below a certain threshold the two states can no longer be safely distinguished — this is the endurance failure. That is why the cycle-resistance plot is drawn semilog and the moment the two series approach each other is sought.

• Why it is done: to assess the lifetime of a memory cell (number of cycles) and its ability to reliably distinguish the states.
• What it teaches / measures: window_ratio_initial/window_ratio_final/window_ratio_min = the start, end and worst of the window ratio R_HRS/R_LRS; first_failure_cycle = the first cycle where the window drops below the threshold (none if no failure); r_lrs_final_ohm/r_hrs_final_ohm = the final state resistances; n_cycles_analyzed = the number of cycles analyzed; endurance_pass = the decision of no failure AND worst window ≥ threshold.
• Typical values and interpretation: in a robust cell the window ratio is ≳10 (usually 10–100+) and stays stable across the cycles; the first cycle that drops below failure_window_ratio (default 5) is the end of life. A high and narrowly-distributed window is good; a window that drops or scatters heavily with cycling is a sign of fatigue/instability.
• Common mistake / caution: mind the role overloading — here i = R_LRS, v = R_HRS, t = the cycle number (not current/voltage); if R_HRS is not loaded only LRS is computed and a missing-HRS note is left (the window ratio is not produced). Looking linear instead of semilog hides small LRS changes.
• Where it is used: next-generation memory (RRAM/memristor) research, reliability/endurance testing, and material/structure comparison.