Scanning photocurrent microscopy and ultrafast transient photovoltage field dependence data with simulation programs

Becerra Silva, Rodrigo 1 ; Yi, Xiang2; Song, Ziyi1; Yu, Dong 1

Research facility: Center for Nano-MicroManufacturing

Published Sep 29, 2026 on Dryad. https://doi.org/10.5061/dryad.z08kprrx6

Data files

Sep 29, 2026 version files 12.57 MB

Files.zip

12.53 MB
README.md

35.66 KB

Abstract

Photogenerated carriers in Sb-doped Bi₂Se₃ can travel unusually long distances, possibly due to the formation of an exciton condensate in the material. This study contains the measurements and models we used to study how an applied electric field alters that transport to resolve the charge nature of carriers. We measured the photovoltage of Bi₂Se₃ devices with lock-in detection while sweeping an in-plane electric field, at temperatures from 12 to 150 K and laser powers from 5 to 100 µW. We mapped the photocurrent across the device with scanning photocurrent microscopy for a series of field values of both polarities, and we recorded pump–probe time traces of the photovoltage as a function of field at four temperatures and four pump powers, from which carrier recovery times, mobilities, diffusion coefficients, and Einstein ratios were extracted. To interpret the measurements, we developed a two-dimensional drift–diffusion simulation of field-dependent carrier flux and a one-dimensional exciton transport model with field-dependent dissociation. The results show that the long-range photoresponse is not carried by free charge but by a charge-neutral correlated state.

Measurements, processed results, analysis scripts, and simulation code behind Figures 1- 4 of the article. The experiments are electrically detected optical measurements on Sb-doped Bi2Se3 nanoribbon devices under an in-plane electric field: lock-in photovoltage versus field, scanning photocurrent microscopy, and pump-probe photovoltage time traces. Two models accompany them: a 2D drift-diffusion simulation of field-dependent carrier flux and a 1D exciton transport model with field-dependent dissociation.

The deposit is organized by figure. Each leaf folder has its own README that documents the file format, the processing steps and parameters, and the command that regenerates that folder's results. This file is the map, and it also carries the data dictionary for every variable used anywhere in the deposit.

Layout

Files.zip/
|-- README.md                                   <- this file
|
|-- Figure 1 data/
|   |-- PV signal vs Electric field at fixed location/
|   |       photovoltage vs field at 20 K, both polarities (raw sweeps,
|   |       processed curve, script)                          -> README.md
|   |-- SPCM under Electric field/
|   |       photocurrent maps at 20 K for 10 field values of each polarity,
|   |       with reflection images, line cuts, script          -> README.md
|   `-- Simulation/
|           2D drift-diffusion solver, sweep data, figure     -> README.md
|
|-- Figure 2 data/
|       1D multiple-pass exciton transport model, the 20 K measurement it is
|       fitted to, figure and plotted curves          -> README_multipass_v2.md
|
|-- Figure 3 data/
|   `-- Temperature and Fluence analysis sweep Vt/
|       |-- Temperature dependence/   photovoltage vs field, 25-150 K, 5 uW
|       |                                                      -> README.md
|       `-- Fluence dependence/       photovoltage vs field, 45 K, 5-100 uW
|                                                              -> README.md
`-- Figure 4 data/
    `-- Temperature analysis TT/
            pump-probe time traces at 12, 20, 80, 120 K and four pump powers;
            fitted recovery times; mobility, diffusion coefficient and
            Einstein ratio                                     -> README.md

Reproducing the figures

Python >= 3.9 with numpy, scipy, pandas, and matplotlib. Every script locates its data relative to its own file, so it can be run from any working directory. Run times are in seconds, except where noted.

Figure	Command (from the folder that holds the script)
1, photovoltage vs field	`python "Transverse electrode lockin method.py"`
1, photocurrent maps	`python spcm_efield.py`
1, simulation	`python drift_diffusion_solver.py` (about 30 s)
2, multiplepass sim	`python multipass_model_v2.py`
3, temperature	`python "Transverse electrode lockin method.py"` in `Temperature dependence/`
3, fluence	`python "Transverse electrode lockin method.py"` in `Fluence dependence/`
4	`python code/run_all_fits.py` then `python code/einstein_ratio.py`; add `--refit` to redo the fits from the raw traces (1-2 min per dataset)

Processed outputs are shipped alongside the raw data in every folder, so the published curves can be inspected without running anything.

Conventions shared by all folders

Raw measurements are plain-text .dat files (tab-separated) with a short header. Part of the metadata lives only in the file name; see the filename tokens table below.
Lock-in readings are stored in instrument units, not volts. The scripts convert them to physical units using the sensitivity encoded in the file name; the two conversions are given in the data dictionary.
The in-plane field is the transverse bias divided by the electrode gap of that device, E = Vt / gap. The gap is not the same in every folder: 5 um for Figures 1 and 2, 15 um for Figures 3 and 4. The value used is a constant at the top of each script (GAP_UM).
There are no missing values anywhere in the deposit except in mu_D_einstein.csv, where einstein_ratio and einstein_ratio_err are left empty for the single dataset (20 K, 25 uW) in which the mobility could not be determined, and note is empty for the fifteen datasets that need no flag. Empty means "not defined".
Processed results are .csv files with labelled column headers; figures are .png and .svg.

Data dictionary

Every variable in the deposit is listed once below, with units. Variables that recur in several files are described at their first appearance and cross-referenced afterwards.

1. Metadata carried in file names

Some quantities are recorded only in the file name, and the scripts parse them from there. A typical pump-probe name:

03, 690, 12K, TT, 218-270UpDown, 1vel, 3900acc, 0Vg, 0.0025mWPr, 0.015mWPu, BH, 30uV, 40x, VbDG=101.12mV.dat

Token	Meaning	Units
leading integer	acquisition index, used only for ordering	-
`690`	excitation wavelength	nm
`12K`, `20K` ...	sample temperature	K
`TT`	measurement type (time trace)	-
`218-270UpDown`	delay-stage travel range and that it sweeps out and back	mm
`1vel`, `2vel`	delay-stage velocity	mm/s
`3900acc`	delay-stage acceleration	mm/s²
`0Vg`	back-gate voltage	V
`0.0025mWPr`	probe power (0.0025 mW = 2.5 uW)	mW
`0.015mWPu`	pump power	mW
`BH`	electrode pair used for detection	-
`30uV`, `sen=100uV`	lock-in full-scale sensitivity	uV
`40x`	objective magnification	-
`VbDG=101.12mV`	transverse bias applied across the electrode gap	mV
`10^-7`, `10^-6`	current-preamplifier sensitivity, full scale	A
`power=5uW`	incident laser power	uW
`positive bias` / `negative bias`	polarity of the transverse bias	-
`pos 2`, `pos=3`	laser position on the device	-
`x axis`	In-phase axis for lock-in	-

2. Raw data files

2a. Lock-in bias sweeps

Figure 1 data/PV signal vs Electric field at fixed location/Raw data/*.dat and both Raw data/ folders under Figure 3 data/. Tab-separated, one header line, one row per sample.

Column	Description	Units
`V(V)`	DC voltage across the device; 0 in every deposited file	V
`Lockin(V)`	Lock-in output as a percentage of full scale, despite the header. Convert with `PhotoV (uV) = Lockin(V) * sensitivity(uV) * sqrt(2) * pi / 4 / 100`, which takes percent to fraction, RMS to amplitude, and the square-wave fundamental to its peak	% of full scale
`Vg(V)`	back-gate voltage; 0 in every deposited file	V
`Time(sec)`	elapsed time from the start of the sweep	s
`Vt(mV)`	transverse bias across the electrode gap, magnitude only; the polarity is in the file name	mV

2b. Scanning photocurrent maps

Figure 1 data/SPCM under Electric field/20K/{Positive,Negative}/*.dat. Nine header lines of the form key: value, then a tab-separated matrix with one row per scan line (y) and one column per scan point (x).

Header key	Description	Units
`Ouput rate (Hz)`	DAC update rate (spelling as written by the instrument)	Hz
`Input rate (Hz)`	ADC sampling rate	Hz
`Y Scan Size (um)`	scan extent along y	um
`X Scan Size (um)`	scan extent along x	um
`Scan Rate (Hz)`	line rate	Hz
`Scan Points`	samples per line, i.e. number of matrix rows	count
`Scan Lines`	number of lines, i.e. number of matrix columns	count
`Average Over`	hardware averages per point	count
`Bias/Gate`	instrument bias field; unreliable, use `VbDG` from the file name	V

Matrix	Description	Units
`*-cur.dat` values	photocurrent as a fraction of the preamplifier full scale. Convert with `I (nA) = value * 10^(9+n)` where `10^n` is the sensitivity in the file name	fraction of full scale
`*-ref.dat` values	simultaneously recorded reflected optical power, used only to locate the device	arbitrary

2c. Pump-probe delay scans

Figure 4 data/Temperature analysis TT/data/<T>K/<power>uW/*.dat.
Same five-column layout as 2a, but the last column means something different:

Column	Description	Units
`V(V)`, `Vg(V)`	as in 2a; both 0 throughout	V
`Lockin(V)`	as in 2a; converted to photovoltage the same way	% of full scale
`Time(sec)`	elapsed time. The delay axis is derived from this and the stage velocity in the file name, then re-zeroed at t0	s
`Vt(mV)`	instrument readback, not the applied bias. The bias for these files is the `VbDG` value in the file name; the analysis ignores this column	mV

3. Processed data files

3a. `processed_pv.csv`

Figures 1 and 3, one row per bias bin. Produced by
Transverse electrode lockin method.py.

Column	Description	Units
`temperature_K`	sample temperature of the sweep	K
`power_uW`	incident laser power	uW
`sign`	polarity of the transverse bias: `positive` or `negative`	-
`vt_mV`	signed bin-centre transverse bias, bin width 1 mV	mV
`electric_field_mV_per_um`	`vt_mV / GAP_UM`; gap is 5 um in Figure 1 and 15 um in Figure 3	mV/um
`pv_averaged_uV`	photovoltage after binning and a 10-bin centred moving average	uV
`pv_averaged_std_uV`	1 sigma of the raw samples, pooled over the smoothing window (RMS of the per-bin standard deviations). With `ERROR_KIND="sem"` the column is named `pv_averaged_sem_uV` and holds the standard error instead	uV
`pv_averaged_zeroE_normalized`	`pv_averaged_uV / zeroE_reference_uV`; equals 1 at E ~ 0	dimensionless
`pv_averaged_zeroE_normalized_std`	the band above, in normalized units	dimensionless
`zeroE_reference_uV`	photovoltage at the smallest measured \|Vt\| for that temperature, averaged over the two polarities where both reach it	uV

3b. `20K_{Positive,Negative}_cross_sections.csv`

Figure 1 data/SPCM under Electric field/output/. One row per scan point along x; one column per bias.

Column	Description	Units
`x_um`	position along the channel	um
`I_nA_at_<bias>V`	Photocurrent in the cross section at that bias, dark-offset subtracted and averaged over an 11 (y) x 3 (x) pixel window at y = 14.9 um. The bias appears in the column name in volts, e.g. `I_nA_at_-0.2513V`	nA

3c. `right_flux_sweep.csv`

Figure 1 data/Simulation/data/. Raw solver output, one row per (mobility, field). All fluxes are percentages of the total optical generation rate, so they are independent of the absolute laser power.

Column	Description	Units
`mobilityCm2Vs`	carrier mobility used for that solve	cm²/Vs
`eFieldMvUm`	applied field across the slab thickness, signed	mV/um
`diffusionUm2Ns`	diffusion constant, from the Einstein relation `D = mu kB T / e`	um²/ns
`interfaceRightPct`	carrier flux crossing the internal interface into the right field-free buffer, at x = +W/2. This is the simulated signal	% of generation
`interfaceLeftPct`	same at the left interface, x = -W/2	% of generation
`topContactPct`	flux absorbed by the top contact	% of generation
`bottomContactPct`	flux absorbed by the bottom contact	% of generation
`farLeftPct`	flux leaving the far left numerical edge	% of generation
`farRightPct`	flux leaving the far right numerical edge	% of generation
`recombinedPct`	carriers lost to bulk recombination	% of generation
`balancePct`	sum of all boundary fluxes and recombination; a closure check that should equal 100 (it does, to 1e-11)	% of generation

3d. `right_flux_normalized.csv`

Same folder. One row per field, one column per mobility. This is the file that is plotted.

Column	Description	Units
`eFieldMvUm`	Applied field, signed	mV/um
`mu_<value>_cm2Vs`	`interfaceRightPct` divided by its value at E = 0, for the mobility named in the column (100, 1000, 10000, 100000 cm^2/Vs)	dimensionless

3e. Figure 2 files

File and column	Description	Units
`Normalized_PV_vs_E_t_20K_D1.csv` : `Efield_exp`	transverse field, the measurement the model is fitted to (20 K, device D1; the same sweep as Figure 1, unbinned)	mV/um
`Normalized_PV_vs_E_t_20K_D1.csv` : `Lockin_exp`	measured photovoltage normalized to its low-field plateau	dimensionless
`Fig2a_profiles.csv` : `x_um`	laser position along the 275 um channel	um
`Fig2a_profiles.csv` : `I_sT0`, `I_sT0p5`, `I_sT1`, `I_sT5`, `I_sT10`, `I_sT50`	simulated photocurrent profile, normalized to max\|I\| of the zero-field profile. The suffix is the sink strength in units of 1e-4 um^-1, with `p` for the decimal point (`I_sT0p5` is s_T = 0.5e-4 um^-1)	dimensionless
`Fig2b_sT_vs_Et_points.csv` : `Et_mV_per_um`	transverse field, binned	mV/um
`Fig2b_sT_vs_Et_points.csv` : `sT_per_um`	sink strength of the biased transverse contact pair, obtained by inverting the measured suppression through the model	um^-1^
`Fig2b_PF_fit.csv` : `Et_mV_per_um`, `sT_per_um`	the Poole-Frenkel fit line `ln s_T = 1.2425 sqrt(E_t) - 14.978`, sampled for plotting	mV/um, um^-1^

3f. `recovery_times.csv`

Figure 4 data/Temperature analysis TT/results/. One row per pump-probe trace. L and R denote the negative-delay and positive-delay branches of the trace.

Column	Description	Units
`T_K`	sample temperature	K
`pump_uW`	pump power	uW
`bias_mV`	transverse bias, from `VbDG` in the file name	mV
`E_mV_per_um`	`bias_mV / 15 um`	mV/um
`tau_L_ps`	recovery time of the delay < 0 branch, from a single-exponential fit. This is the one used in step 2	ps
`tau_L_err_ps`	1 sigma on `tau_L_ps` from a moving-block residual bootstrap	ps
`tau_R_ps`, `tau_R_err_ps`	the same for the delay > 0 branch	ps
`A_L`, `A_R`	fitted baseline photovoltage of each branch	uV
`B_L`, `B_R`	fitted amplitude of each branch; negative, since the signal dips	uV
`dV_over_V_L`, `dV_over_V_R`	relative dip depth, `100 * B / A`	%

3g. `mu_D_einstein.csv`

Same folder. One row per (temperature, pump power) dataset, from a weighted straight-line fit of 1/tau_L against field: 1/tau = A + B E, with
D = A W0^2 / 4 and mu = B W0, using W0 = 0.85 +- 0.05 um and a
15 +- 1 um gap.

Column	Description	Units
`T_K`	sample temperature	K
`pump_uW`	pump power	uW
`fluence_uJcm2`	pump fluence	uJ/cm^2
`n_points`	number of traces entering the line fit	count
`intercept_A`	intercept A of `1/tau` versus field	1/ns
`intercept_err`	1 sigma on the intercept	1/ns
`slope_B`	slope B of `1/tau` versus field	1/ns per (mV/um)
`slope_err`	1 sigma on the slope	1/ns per (mV/um)
`D_cm2s`	diffusion coefficient	cm²/s
`D_err`	1 sigma on D, from the fit only	cm²/s
`mu_cm2Vs`	mobility	cm²/Vs
`mu_err`	1 sigma on mu, from the fit only	cm²/Vs
`einstein_ratio`	`(D/mu) / (kB T / q)`; equals 1 if the Einstein relation holds. Empty where the slope is unresolved and the ratio is therefore undefined	dimensionless
`einstein_ratio_err`	1 sigma, from the fit only; empty on the same row. A further +-9 % geometric systematic from W0 and the gap is not included	dimensionless
`note`	free text, empty unless the dataset needs a flag. The only entry is on 20 K / 25 uW: "slope of 1/tau vs E not resolved mobility and R undefined". On that row `mu_cm2Vs` = -26.4 with `mu_err` = 408 is the raw fit output and should not be used as a mobility; `D_cm2s`, which comes from the intercept, is unaffected	-

3h. `fit_param_<power>uW.dat`

Figure 4 data/Temperature analysis TT/results/fits/<T>K/<power>uW/.
Tab-separated with a header line, one row per bias. These are the per-dataset
fits that recovery_times.csv collects.

Column	Description	Units
`A_left`, `A_left_err`	baseline of the delay < 0 branch and its 1 sigma	uV
`B_left`, `B_left_err`	amplitude of the delay < 0 branch and its 1 sigma	uV
`tau_left`, `tau_left_err`	recovery time of the delay < 0 branch and its 1 sigma	ps
`A_right`, `A_right_err`	baseline of the delay > 0 branch and its 1 sigma	uV
`B_right`, `B_right_err`	amplitude of the delay > 0 branch and its 1 sigma	uV
`tau_right`, `tau_right_err`	recovery time of the delay > 0 branch and its 1 sigma	ps
`vg`	back-gate voltage	V
`PPr`	probe power	uW
`PPu`	pump power	uW
`lamb`	excitation wavelength	nm
`T`	sample temperature	K
`DeltaV_V_l`, `DeltaV_V_r`	relative dip depth of each branch, `100 * B / A`	%
`Vt`	transverse bias	mV

4. Figures included as files

File	Content
`*_maps.png`	photocurrent maps, one panel per bias, symmetric +-1000 nA colour scale
`*_cross_sections.png`	the line cuts in 3b, coloured by bias
`right_flux_normalized_xlog.png`	normalized simulated flux versus field, one curve per mobility
`Multipass.png`	Figure 2 panels (a) and (b)
`overlay_deltaVoverV.svg`	every pump-probe trace of a dataset as dV/V versus delay, with the fitted branches
`tau_vs_V.png`	fitted tau_L and tau_R versus bias, with error bars

Relations between folders

The measurement fitted in Figure 2 (Normalized_PV_vs_E_t_20K_D1.csv) is the same 20 K sweep as in Figure 1 data/PV signal vs Electric field at fixed location/, exported unbinned and normalized. Both therefore use the 5 um electrode gap.
The temperature and fluence sweeps of Figure 3 use the same script and the same processing as the Figure 1 photovoltage data, on a device with a 15 um gap.
Figure 4 uses the same 15 um gap as Figure 3.