Mid- and Long-Wave Infrared Optoelectronics via Intraband Transitions in PbS Colloidal Quantum Dots

Optical sensing in the mid- and long-wave infrared (MWIR, LWIR) is of paramount importance for a large spectrum of applications including environmental monitoring, gas sensing, hazard detection, food and product manufacturing inspection, and so forth. Yet, such applications to date are served by costly and complex epitaxially grown HgCdTe quantum-well and quantum-dot infrared photodetectors. The possibility of exploiting low-energy intraband transitions make colloidal quantum dots (CQD) an attractive low-cost alternative to expensive low bandgap materials for infrared applications. Unfortunately, fabrication of quantum dots exhibiting intraband absorption is technologically constrained by the requirement of controlled heavy doping, which has limited, so far, MWIR and LWIR CQD detectors to mercury-based materials. Here, we demonstrate intraband absorption and photodetection in heavily doped PbS colloidal quantum dots in the 5–9 μm range, beyond the PbS bulk band gap, with responsivities on the order of 10–4 A/W at 80 K. We have further developed a model based on quantum transport equations to understand the impact of electron population of the conduction band in the performance of intraband photodetectors and offer guidelines toward further performance improvement.


METHODS
QD synthesis and ligand exchange procedure. The PbS QDs were synthesized by a previously reported multi-injection method with modifications. 1 The injection temperature and concentration of hexamethyldisilathiane [(TMS)2S] in 1-octadecene (ODE) were adjusted according to the final desired size of QDs. The QDs were washed with acetone/ethanol and were finally dispersed in toluene at a concentration of 30 mg/ml and bubbled with N2.
PbS CQD films were deposited using a layer-by-layer spin-coating process under ambient conditions. For each layer, the CQD solution was deposited on either the substrate (Si, Si/SiO2 or CaF2) at 2500 r.p.m. Solid-state ligand exchange was performed by flooding the surface with (I) 1-ethyl-3-methylimidazolium iodide in methanol (EMII, 7 mg/ml) or (II) 1,2-Ethanedithiol (EDT) in acetonitrile (ACN) (0.01% v/v) 30 s before spin-coating dry at 2500 r.p.m. Two washes with (I) methanol or (II) acetonitrile were used to remove unbound ligands.
Atomic Layer Deposition. Al2O3 deposition was performed in a GEMStar XT Thermal ALD system. High-purity trimethylaluminium (TMA), purchased from STREM Chemicals Inc., was used as Al precursor. Pure H2O was used as O precursor. The deposition was carried out at 80 ºC. The TMA and H2O manifolds were maintained at 150 ºC during gas supply. Each layer of Al2O3 was formed by applying a 15-ms pulse of H2O, followed by a 50-ms pulse of TMA. The waiting time between pulses was 15 s and 20 s, respectively.
Sample and device fabrication. For transmission measurements, films consisting of 3 to 8 layers of QDs exchanged with either EMII or EDT were spin-coated on lowly doped (1-10 ohm·cm) silicon substrates. After film formation, 3 to 5 nm of Al2O3 were deposited by ALD on some of the samples.
For photoconductivity measurements, interdigitated gold electrodes were evaporated onto CaF2 substrates patterned using standard photolithography methods. The area of the interdigitated devices is 1x1 mm 2 . The width of the metal fingers is 10 µm. The distance between fingers is either 10 or 20 µm. Devices were completed by depositing 4 to 6 layers of EMII-exchanged dots followed by ALD deposition of 3 to 5 nm of Al2O3. For FET measurements, gold electrodes were evaporated onto p-Si/SiO2 substrates patterned using standard photolithography methods. The p-type Si layer acted as the gate electrode. The length of the FET channel was in the 10-25 µm range. Fabrication was completed by depositing 2 layers of EMII-exchanged dots followed by ALD deposition of 3 to 5 nm of Al2O3. In all cases, the second derivative of the absorption spectrum was used to determine the central energy of the intraband and interband peaks. In some cases, raw data was subjected to a smoothing process so that reliable fits could be done. Gaussian fits to the second derivative of the spectra yielded more consistent and reliable results than fits to the absorption spectra. This is due to the difficulty of removing the baseline from some the absorption measurements of the films. with adequate diffraction gratings and second-order filters, was used to monochromatize and modulate light, generated using either a halogen lamp or a Nernst IR source. Light exiting the monochromator was directed onto the sample using gold mirrors, in order to avoid chromatic aberration effects. A Standford Research low-noise trans-impedance amplifier was used to bias the devices and amplify the measured current. Final signal detection was made using standard lock-in techniques. The chopping frequency was 11 Hz. In order to correct the measured photo-      The peaks at around 0.14 eV in the low-temperature measurement are an artifact due to the temperature shift of the signature of the native SiO2 present in the silicon substrate used in the QD sample, while the silicon reference sample was measaured at room temperature.

TRANSPORT MODEL
Our model evaluates as a function of : (I) the steady-state conductance under a given applied bias prior to illumination, ̅ ; and (II) the change in conductance, ∆ , caused by intraband absorption in the QDs. The ratio ∆ ̅ ⁄ will provide a qualitative indication of the potential detectivity of our devices, since detectivity is proportional to ∆ and inversely proportional to the noise, which, in turn, increases with ̅ . The model relies on the following assumptions: i) transport in the weak coupling regime, which is usually the case for semiconductor CQD films 3 ; ii) the conductance of a matrix of QDs is assumed to be proportional to the conductance between two adjacent quantum dots, which is in turn analyzed in the framework of quantum transport; iii) conductance between QDs and the metallic contacts is left out of the analysis, since we want to focus solely on the intrinsic material properties.
At 0K, conductance through the different possible channels between nanostructures is is the Fermi function and determines the electron occupancy factor (from 0 to 1) at levels of energy . Equation (S2) will be the starting point of our model and will allow us to evaluate how conductance is affected by small variations of . Note that in our experiments the light power density employed was low (in the 10 -5 -10 -4 W/cm 2 range) so that it would modify only slightly, in relative terms, the carrier populations of our highly doped (~10 19 cm -3 ) samples.
Let us now consider our case of study. Figure S8 illustrates the transport scheme of our model.
1Se is the eight-fold degenerate ground state, with energy ES; and 1Pe is the first excited state, with energy EP. For the moment, the degeneracy of 1Pe is disregarded; it will be included in the model later. In general, we can say that conduction will take place either through 1Se channels ( ) or 1Pe channels ( ). We assume a homogenous CQD ensemble with narrow (< intraband energy) intrinsic absorption line shapes, so that tunneling between 1Se and 1Pe channels is not possible. Since conductance through parallel channels add up, = + . Prior to illumination, 1Se is partially populated through doping. 1Pe is not populated, since the intraband energy (150-250 meV) is much greater than (~7 meV at 80K). This is represented in proportional to ∆ ; hence, the detectivity, * , of our detectors is proportional to it as well.
However, * is inversely proportional to the dark current of the device and, therefore, to ̅ .
Provided that ∆ → 0, the model holds for any value of and , and therefore, of .
Equations (S9) and (S10) are general for any given QD material. For an eight-fold degenerated 1Se, we can define the occupancy factor of the 1Se states as = 8/ . Hence, we can rewrite Equations (S9) and (S10) as Equations (S11), (S12) and (S13): Nevertheless, it is valid to analyze the impact of doping for the range in which dark current due to population of 1Se is the main source of noise. The sensitivity of Equation (S13) to ( , ) -related to the difference in degeneracy of 1Pe and 1Se, and the different transmission probability of their respective propagating modes-is evaluated in Figure S9. In all cases, high detectivity can only be achieved by closely approaching the occupancy limit of 1Se.