Chemicals

Mercury chloride (HgCl₂, Strem Chemicals, 99%), Mercury compounds are highly toxic. Handle them with special care. Tellurium powder (Te, Sigma-Aldrich, 99.99%), trioctylphosphine (TOP, Alfa, 90%), oleylamine (OLA, Acros, 80–90%), dodecanethiol (DDT, Sigma-Aldrich, 98%), methanol (VWR, 98.5%) acetone (VWR rectapur), ethanol (absolute VWR), toluene (VWR, 99.8%), hexane (VWR), dimethylformamide (DMF, VWR, 99.9%), mercaptoethanol (MpOH, Merck, >99%). All chemicals are used without any further purification.

1M TOP:Te precursor

2.54 g of Te powder is mixed in 20 mL of TOP in a three-neck flask. The flask is kept under vacuum at room temperature for 5 min and then the temperature is raised to 100 °C. Furthermore, degassing of flask is conducted for the next 20 min. The atmosphere is switched to nitrogen and the temperature is raised to 275 °C. The solution is stirred until a clear orange coloration is obtained. The flask is cooled down to room temperature and the color switches to yellow. Finally, this solution is transferred to an N₂ filled glove box for storage.

HgTe NCs synthesis with band edge at 4000 cm⁻¹

513 mg of HgCl₂ was added to 50 mL of oleylamine in a 100 mL three-neck flask. The solution was degassed under vacuum for 1 h at 110 °C. Then, the temperature is decreased to 80 °C and solution is placed to nitrogen atmosphere. 1.9 mL of TOP:Te (1 M) with 10 mL of oleylamine is added to the mercury solution. The solution color gradually turns to dark brown and the reaction is stopped at 3 min. A solution made of 1 mL of dodecanethiol and 9 mL of toluene is quickly added to quench the reaction. The nanocrystals are then precipitated with methanol. After centrifugation, the nanocrystals are redispersed in toluene. The washing step is repeated two more times with ethanol. The solution is filtered with a 0.2 µm filter and redispersed in toluene to reach a 50 mg.mL⁻¹ concentration.

HgTe ink and thin film preparation

15 mg of HgCl₂, 1 mL of MpOH and 9 mL of DMF are mixed. At 1 mL of this solution is added 6 mL of hexane and 500 µL of a HgTe solution (at 50 mg mL⁻¹ in toluene). After stirring the QDs migrate from the top phase (hexane) to the bottom DMF phase, showing an efficient ligand exchange. After 3 washing steps with hexane, few drops of EtOH are added and the solution is centrifuged at 4427 × g for 3 min. The supernatant is discarded and the pellet is redispersed in 130 µL of DMF. 35 µL of this solution is used to prepare the film by spin-coating. The nanotrench electrodes are plasma-cleaned for 5 min. Then 35 µL of the ink are deposited on the substrate. The spin-coating steps are 1200 rpm (acceleration 200 rpm s⁻¹) for 180 s and 3000 rpm (200 rpm s⁻¹) for 120 s. The obtained film thickness is about 300 nm.

Electron microscopy

For transmission electron microscopy (TEM) pictures, a drop of the CQD solution is drop-casted onto a copper grid covered with an amorphous carbon film. The grid is degassed overnight to reduce future contamination. A JEOL 2010F is used for acquisition of pictures and operated at 200 kV.

For scanning electron microscopy (SEM) pictures, a Zeiss Supra 40 scanning electron microscope is used. The acceleration bias is set at 7 kV and the aperture at 15 µm.

Infrared spectroscopy

Infrared spectroscopy is conducted using a Fisher IS50 Fourier transform Infrared spectrometer (FTIR). To measure NC absorption, we use the spectrometer in ATR configuration. A drop of NC solution is dried on the diamond cell. The source is a globar, the beamsplitter is an extended-KBr and the detector is a DTGS ATR. Spectra are typically acquired between 8000 cm⁻¹ and 400 cm⁻¹ with a 4 cm⁻¹ resolution and averaging over 32 spectra. Photocurrent spectra are acquired as the sample is biased using a Femto DLPCA 200 current amplifier which role is also to magnify the current. The signal is then fed into the FTIR acquisition board. Spectra are typically acquired between 8000 cm⁻¹ and 2000 cm⁻¹ with a 4 cm⁻¹ resolution and averaging over 64 spectra.

Nanotrench fabrication

The nanogap electrodes are made using the procedure described by Dayen et al.³⁰. The electrodes are prepared using a two-steps lithography procedure. Starting from a cleaned Si/SiO₂ wafer (400 nm of oxide), AZ5214 resist is spin coated and baked for 90 s at 110 °C on a hot plate. The first pattern is then exposed for 2 s using a UV light (Süss microtec MJB4). The wafer is further baked for 2 min at 125 °C. Then a flood exposure is conducted for 40 s. Development is then made using AZ326 developer for 25 s and then rinsed in water. A O₂ plasma cleaning is then conducted for 5 min. Metal deposition (Plassys MEB550S) is operated by deposing 6 nm of Cr and 54 nm of gold. The lift off is made by dipping the substrate overnight in acetone. Another step of plasma cleaning and acetone washing is generally performed to obtain a better success ratio. For the second electrodes, the pattern needs to overlap with the first electrodes and the nanotrench will be formed at the interface (see Supplementary methods). The second lithography is done as described before. For the second metal deposition, the evaporation is made under a tilted angle, typically from 50° to 65° depending on the expected nanotrench size. It is worth pointing that evaporation has to be as directive as possible and that sample holder does not rotate during the evaporation. The second deposition is conducted while depositing 5 nm of Ti and 50 nm of gold. The lift-off is also conducted by dipping the samples in acetone overnight.

Nanotrench characterization

DC transport

The sample is connected to a Keithley 2634b, which controls the drain bias (V_DS) and measures the associated current (I_DS). This measure is carried out in the dark or under illumination using 1.55 µm laser diode or a blackbody at 980 °C.

Transistor measurement

The sample is connected to a Keithley 2634b, which sets the drain source bias (V_DS), controls the gate bias (V_GS) and measures the associated currents (I_DS and I_GS). A scheme of the device is given is Supplementary methods.

Responsivity measurement

The source is a laser diode at 1.55 µm or a blackbody at 980 °C placed at 40 cm of the sample. The laser-diode spot size is 1.6 mm². The flux can be chopped form 1 Hz to 10 kHz. The photocurrent is measured using Zurich Instruments MFLI lock-in amplifier at 1 V bias. When the black body is used, a germanium filter is utilized to suppress the high energy part of the blackbody spectrum. The total power calculated according to the formula: \(P = A_{\mathrm{D}}.\pi .{\it{{\mathrm{cos}}}}\left( \beta \right). {\it{{\mathrm{sin}}}}^2\left( \alpha \right).{\int}_{\lambda _{{\it{min}}}}^{\lambda _{{\it{max}}}} {\frac{{hc^2}}{{\lambda ^5}}} .\frac{1}{{e^{hc/\lambda kT}}}d\lambda\) where α is the solid angle illuminated, β is the angle of the sample (0° corresponds to sample perpendicular to the light illumination), A_D is the device area, h is the Planck constant, c the light velocity, k is the Boltzmann constant and T the temperature. The light is chopped form 1 Hz to 1 kHz. The photocurrent is measured using Zurich Instruments MFLI lock-in amplifier under 1 V of applied bias. The sample is mounted on the cold finger of a close cycle cryostat. As scheme of the set-up is given in Supplementary methods.

EQE calculation

The external quantum efficiency (EQE) is the ratio of the generated photoelectron flux over the flux of incident photon. For a monochromatic wavelength it is simply given by: \({\mathrm{EQE}} = R.\frac{{h\nu }}{e}\), with R the responsivity and hv the photon energy of the incident light and e the elementary charge.

Noise measurement

Current from the device (at 1 V bias, kept in the dark) is amplified by a Femto DLPCA-200, then fed into a SRS SR780 signal analyzer. The sample is mounted on the cold finger of a close cycle cryostat.

Specific detectivity determination

The specific detectivity (in Jones) of the sample is determined using the formula: \(D^ \ast = \frac{{R\sqrt A }}{{S_I}}\), where R (in A W⁻¹) is the responsivity, S_I is the noise (A Hz^−1/2A the area of the device (cm²).

Electrostatic simulation

Calculations have been achieved using COMSOL Multiphysics software with AC/DC module and electric currents physics. For quantum dots, electrical conductivity and relative permittivity are set to 5 × 10⁻⁴ S m⁻¹ and 4, respectively. The mesh is made of triangular elements whose maximum size has been refined is the nanotrench area and is set to 1 nm. Outside the nanotrench, maximum element size is 5 nm. These values are more than sufficient to properly describe the electrostatic phenomenon for this geometry.

Electromagnetic simulation

Calculations have been achieved with Matlab library based on rigorous coupled-wave analysis (RCWA)³⁷. The Maxwell equations are solved in each layer and interface conditions are applied to find the final solution of the whole structure. We considered incoming plane wave under normal incidence, either with transverse magnetic or transverse electric polarization, i.e., with the magnetic field or electric field parallel with the slits of the grating s, respectively. Grating is supposed to be invariant along y direction, and repeated infinitely along x direction with a period of 10 µm. Inputs needed for this simulation are the device structure and the optical index of the different materials (see Supplementary note 7).

Schrödinger equation resolution

To probe the effect of the electric field on the bandgap and wave functions, we solve the 1D time-independent Schrödinger equation in spherical geometry: \(\left[ { - \frac{{\hbar ^2}}{{2m \ast }}\left( {\frac{2}{r}\frac{\partial }{{\partial r}} + \frac{{\partial ^2}}{{\partial r^2}}} \right) + V(r)} \right]\psi (r) = E\psi (r)\) Where ħ is the reduced Planck constant, m^* the effective mass profile, V(r) the energy band profile, E the eigen energy and ψ(r) the wavefunction. V(r) here accounts for a constant part, relative to confinement for which we add on top of which a linear contribution that mimic the effect of electric field. Using spherical geometry in presence of an electric field can only be valid in the regime where electric field is a small perturbation (e.F.R << E_G), which actually corresponds to the operating bias range of our nanotrench electrodes. At large electric field, quantitative results become inaccurate but the charge localization effect remains valid. The equation is solved using a shooting method⁴¹. Material input parameters are the effective masses of electrons (m*_HgTe = 0.035m₀^42,43) and holes (m*_HgTe = 0.5m₀^42,43) and the position of the valence band maximum of the two materials.

Tight binding simulations

We used the tight-binding model of ref. ⁴⁴ to calculate the electronic structure of the HgTe NCs. Each Hg or Te atom is described by a double set of sp³d⁵s* orbitals, one for each spin orientation. Surfaces are saturated by pseudo-hydrogen atoms characterized by a single s orbital. Tight-binding parameters, i.e., on-site energies, nearest-neighbor hopping matrix elements and spin-orbit coupling terms were determined to provide a very good description of the band structure of bulk HgTe (at 300 K). For all NCs, we calculated 60 (1200) conduction (valence) states and we computed dipolar matrix elements between them as described in ref. ⁴⁴. More information on the overlap definition are given in Supplementary note 8.