# HgTe Nanocrystals Carrier Density and Its Tuning

Mariarosa Cavallo, Dario Mastrippolito, Clément Gureghian, Erwan Bossavit, Huichen Zhang, Albin Colle, Tommaso Gemo, Alexandre Neyret, Adrien Khalili, Debora Pierucci, et al.

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## ► To cite this version:

Mariarosa Cavallo, Dario Mastrippolito, Clément Gureghian, Erwan Bossavit, Huichen Zhang, et al. HgTe Nanocrystals Carrier Density and Its Tuning. Small Structures, 2025, 10.1002/sstr.202400576. hal-05091694

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# HgTe Nanocrystals Carrier Density and Its Tuning

Mariarosa Cavallo, Dario Mastrippolito, Clément Gureghian, Erwan Bossavit, Huichen Zhang, Albin Colle, Tommaso Gemo, Alexandre Neyret, Adrien Khalili, Debora Pierucci, and Emmanuel Lhuillier*

HgTe nanocrystals (NCs) are now an established material for colloidal opto-electronics. In the mid- and far-infrared range, there is to date no viable colloidal alternative material that can emit or detect light with such a high efficiency. Advancements have been rapid, primarily concentrating on the direct application of the narrow bandgap material spectrum in devices. However, certain material properties, such as carrier density, have been suboptimally addressed, despite their critical importance to device design. Therefore, this review aggregates most of the recent developments related to the determination and control of the carrier density with HgTe NCs. The manuscript is organized along three scales: the intrinsic properties that mostly relate to the inorganic core of the NCs, the nanoscale functionalization that relates to the surface modification of the NCs, and the device scale mostly driven by gating methods. The review provides a systematic discussion on strategies and technologies to control the carrier density and their use for optoelectronics. Finally, a discussion is done on the directions to be developed to push even further the efficiency of devices based on this material.

2D nanoplatelets[7,8] (roughly 1 nm thick), up to the THz[9,10] range, reached by micro-crystals with sizes that largely exceed the material Bohr radius[11] (40 nm). In addition to offering comparable performances to PbS in the short-wave infrared, HgTe stands out as the most mature platform for the mid- and far-infrared. It is the only colloidal material that exhibits electroluminescence in the 2–7 µm range,[12,13] the only one with demonstrated emission in the THz range,[14] and the only material to have been integrated into mid-wave infrared cameras.[15]

In spite of these successes, the knowledge about the connection between material properties and device performances remains far less advanced than it is for PbS. For example, the facets of lead chalcogenide NCs (mostly (100) and (111)) are well identified,[16,17] including how the ratio of these two types of facets changes

with size.[18] In contrast, shape control for HgTe has been the object of numerous studies over the recent years. Branched objects are classically obtained, making the expressed facet far less defined compared to a well-defined truncated cube. Recent efforts have enabled the growth of quasi spherical objects,[19–21] presenting the benefit of denser packing (and thus potentially higher optical index and higher carrier mobility) but also some drawbacks such as a broader exciton linewidth[20] that still makes unclear which shape is optimal for application such as detection.[22]

HgTe NCs present a unique and somewhat paradoxical situation in optoelectronic devices. On one hand, they have seen advanced integration into high-performance detectors and light-emitting diodes (LEDs). On the other hand, much of this success has been driven by empirical approaches rather than a comprehensive understanding of their fundamental properties, particularly the control of carrier density. The best-performing devices, especially those relying on vertical stack diode configurations, assume the formation of a pn or p-i-n junction,[23] yet the control over doping within HgTe NCs is often partial and inconsistent.

The aim is to review the existing knowledge on the carrier density of HgTe NCs and explore the strategies developed to tune this key parameter, both at the nanoscale and meso-scale (typically at the device level). The discussion will attempt to bridge the gap between the intrinsic material properties of HgTe NCs and their influence on device design, offering insights into how these relationships can be better understood and controlled.

## 1. Introduction

Among nanocrystals (NCs), HgTe material[1–6] occupies a special place as a versatile platform capable of addressing the whole infrared spectrum, see **Figure 1a**. This range extends from the visible region, achieved by the most confined forms that are

M. Cavallo, D. Mastrippolito, C. Gureghian, E. Bossavit, H. Zhang,

A. Colle, T. Gemo, A. Neyret, A. Khalili, D. Pierucci, E. Lhuillier

Sorbonne Université

CNRS

Institut des NanoSciences de Paris

75005 Paris, France

E-mail: el@insp.upmc.fr

E. Bossavit

Synchrotron SOLEIL

L'Orme des Merisiers, Départementale 128, 91190 Saint-Aubin, France

A. Neyret

Institut Supérieur de l'Aéronautique et de l'Espace (ISAE-SUPAERO)

Université de Toulouse

31055 Toulouse, France

The ORCID identification number(s) for the author(s) of this article can be found under https://doi.org/10.1002/sstr.202400576.

© 2025 The Author(s). Small Structures published by Wiley-VCH GmbH. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

DOI: 10.1002/sstr.202400576
<figure><img src="image_3.png" /><figcaption>**Figure 1.** Size effect. a) Absorbance spectra of HgTe NCs with increasing sizes, ranging from 1 nm (most confined material) to above 100 nm (weakest confined). The feature at around 80 µm (125 cm⁻¹) is due to the optical phonon. Adapted with permission.[1] Copyright 2021, American Chemical Society.
b) Valence and conduction bands of HgTe NCs with varying sizes, with the Fermi energy taken as reference. Typical particle sizes are indicated in gray. Adapted with permission.[26] Copyright 2018, American Chemical Society.</figcaption></figure>

The review is organized as follows: 1) Intrinsic Properties of HgTe NCs: This section explores how fundamental factors such as size, temperature, and pressure influence the carrier density in HgTe NCs. The quantum confinement effect, which is particularly pronounced in smaller NCs, alters the energy band structure and thus affects the carrier concentration. Additionally, external factors such as temperature and pressure can further modulate these properties, making HgTe a highly tunable material; 2) Nanoscale Tuning of Carrier Density: Strategies at the nanoscale primarily involve modifying the surface chemistry of HgTe NCs. The native surface dipole plays a crucial role in the carrier density, and modifying this dipole through ligand exchange or surface functionalization can drastically change the electronic properties. Surface ligands, typically organic molecules, can either donate or withdraw electrons, impacting the NC's carrier density. Furthermore, these strategies can also help stabilize NCs and prevent oxidation or degradation, which is essential for maintaining device performance; 3) Device-Level Tuning of Carrier Density: At the meso-scale, carrier density can be actively tuned by integrating the NCs into device structures. The use of external electric fields (gating) is one of the most effective methods for tuning carrier density. This section reviews recent technological developments that go beyond traditional single-gate dielectric structures. Innovations include using high-capacitance materials to enhance field effects, as well as employing multi-gate architectures that enable more precise control over the spatial distribution of carriers within a device.

## 2. Intrinsic Properties of the Quantum Confined Material

### 2.1. Effect of Size

HgTe NCs, due to their semimetal nature, exhibit a unique and wide spectral tunability. The absence of a bulk bandgap means that the optical transitions in HgTe NCs are largely governed by quantum confinement effects, allowing the energy of the

electronic transitions to be tuned down to the order of thermal energy (k_bT). This tunability leads to significant shifts in the band edge, without drastic changes in the nature of the lowest-energy electronic transitions.

For small HgTe particles (<12 nm in diameter), absorption spectra exhibit a sharp onset—starting at a threshold energy, characteristic of interband transitions. This behavior is expected when quantum confinement dominates, preventing low-energy transitions. However, as the particle size increases, the absorption spectra change significantly. For larger particles, instead of a sharp onset, a pronounced absorption peak appears before a higher-energy edge. This peak is attributed to intraband absorption,[24] indicating that the system is degenerately doped (with the Fermi level inside the conduction band), even in a steady-state condition.

The relationship between the band structure and the Fermi level is better understood by studying the electronic spectra in absolute energy scales, which can be probed using techniques like electrochemistry[25] or X-ray photoemission spectroscopy (XPS),[26,27] as shown in Figure 1b. In small HgTe NCs, the bandgap increases due to quantum confinement. However, the conduction and valence bands respond differently due to the large disparity in the effective masses of electrons and holes in HgTe[28] (a factor of 25). The conduction band experiences much stronger dispersion, meaning the observed increase in bandgap value with reduced size is mainly due to electron confinement.[28,29]

XPS data show that strongly confined HgTe NCs have a Fermi level located within the bandgap, typically near the bottom, suggesting p-type behavior. This p-type nature has been corroborated by field-effect transistor (FET) measurements.[30,31] However, due to the aforementioned difference in effective masses between charge types, the conduction band rises faster than the valence band as the particle size increases and confinement decreases, causing HgTe NCs to gradually shift toward n-type behavior. Once the bandgap decreases below ≈250 meV, the Fermi level enters the conduction band, resulting in a degenerate doping, a phenomenon often referred to as self-doping. This
self-doping[32-35] is intrinsic to HgTe NCs and does not require the introduction of external impurities.

Interestingly, this self-doping[34] behavior is not exclusive to HgTe. It has been previously observed in other NC systems such as Ag₂Se,[36,37] HgS,[35] HgSe,[38,39] and later in PbS[40,41] NCs. As the bandgap closes, the Fermi level descends deeper into the conduction band, occupying higher-energy states (S, then P, and beyond). Despite this, the carrier relaxation times in HgTe NCs remain relatively slow (on the order of a few picoseconds), compared to plasmonic systems where relaxation typically occurs within tens of femtoseconds (≈50 fs). This suggests that the carrier density, though elevated, remains below the threshold for plasmonic behavior.

## 2.2. Impact of Temperature and Pressure

The narrow bandgap nature of the HgTe NCs leads to a significant thermally activated carrier density. This situation is not specific to HgTe but common to any semiconductor operating in the infrared range. The reduction of the thermally activated carrier density is the main motivation for lowering the operating temperature in these semiconductors, as it helps to minimize dark current flow and its associated noise.

For the sake of illustration, an intrinsic HgTe NC with a 5 µm cutoff wavelength (250 meV, ≈12 nm in size) at room temperature has 1 thermally activated carrier per thousand NCs.[42] As the NC size increases to about 20 nm (bandgap at around 10 µm or 150 meV), the number increases to around 2 electrons per NC. This situation contrasts with wider bandgap II-VI materials, such as CdSe with a 2 eV bandgap, where the thermally activated carrier density is negligible (10⁻¹⁷ carriers per NC). Tuning the temperature drastically impacts the carrier density following the equation:

$$n = 2 \cdot \exp(-E_a/k_b T) \quad (1)$$

where the factor 2 relates to the degeneracy of the 1S state (extra term will apply if further bands get filled), E_a is the activation energy, k_b is the Boltzmann constant, and T is the actual

temperature. This activation energy directly relates to the presence of traps within the bandgap, which typically result from the imperfect passivation of the surface dangling bonds. Assuming that we remain in the non-degenerate doping regime (i.e., small size regime), E_a should be smaller than the interband gap, assuming a band-to-band recombination. However, in practice, in HgTe NCs the value for E_a is generally below half of the bandgap[43] value, suggesting that deep traps close to the middle of the gap actually drive the carrier generation. This leads to:

$$n(T) = 2 \cdot \exp(-E_G(T)/2k_bT) \quad (2)$$

In this expression, the bandgap (E_G) itself can depend on the temperature, see Figure 2a. In bulk and large HgTe NCs, the bandgap decreases upon cooling.[44] Though a second-order effect, this behavior goes against the carrier reduction. However, the bandgap's temperature dependence also appears to rest on NC size. Smaller NCs present a reduced temperature dependence, and the most confined ones can even exhibit an inverted trend[28] (i.e., an increase of the bandgap upon cooling). A reduction of the activation energy below half the bandgap can be observed if the material is not intrinsic, as depicted in Figure 2b. This lower activation energy is often an issue in practice, since it implies that the decrease of the carrier density upon cooling becomes less effective. To date, the effect of temperature on carrier density is mostly probed through transport measurement and direct determination on how the electronic structure is affected is still missing, mostly due to instrumental challenges. Electrochemistry is difficult to conduct at cryogenic temperature due to the freezing of the electrolyte generally used to induce gating, while the effort for in situ temperature-controlled photoemission measurement is just missing.

Pressure is a complementary way to temperature to induce a large modification of the electronic structure.[28,45,46] Upon the application of hydrostatic pressure, it has been observed that the interband gap increases (Figure 2c), while the intraband gap decreases[46] (though to a lower extent). Application of 4 GPa of pressure can lead to a large increase in bandgap of

<figure><img src="image_4.png" /><figcaption>**Figure 2.** Temperature and pressure effect. a) Absorption spectra for a HgTe NCs film with a band edge around 0.8 eV at room temperature, measured at various temperatures down to 10 K. b) Current, normalized by its value at room temperature, as a function of the inverse of temperature for two HgTe NCs sizes (0.8 eV interband bandgap and 50 meV intraband gap). (b) Adapted with permission.[45,92] Copyright 2021, American Chemical Society. c) Absorption spectra of HgTe NPLs under varying applied pressure. (a,c) Adapted with permission.[28] Copyright 2020, American Chemical Society.</figcaption></figure>
the order of 400 meV. According to Equation (2), this means that an increased pressure is expected to reduce the carrier density. Again, the quantification of the change in the electronic structure is hindered by experimental issues. Indeed, since pressure is applied using a diamond anvil cell, the sample environment becomes incompatible with electrochemistry or soft X-ray photoemission. It is worth pointing out that the application of an even larger pressure can induce an even greater change in the carrier density, resulting from a structural phase change. The semimetal zinc blende phase of HgTe at room pressure transforms toward a semiconductor phase with a cinnabar lattice under a few GPa of pressure (1.4–4 GPa threshold, depending on NC size) and into a metallic phase with a rock salt lattice at even higher pressure (8–10 GPa threshold, depending on NC size[28]).

It appears that size, temperature and pressure are key parame-
ters driving the carrier density. This results in a dramatic change in
the material behavior, shifting from reasonably insulating charac-
teristics at small sizes, low temperatures and room pressure to a
quasi-metallic behavior for larger objects and a truly metallic nature
under high pressure. In turn, integration of NCs into devices
requires this ability to achieve some degree of tunability in carrier
density. For use as a photoconductor, the material needs to be
made as intrinsic as possible, while diodes require the formation
of p- and n-doped layers, possibly spaced by an intrinsic absorbing
layer. Lasers can instead benefit from quasi-degenerate doping as a
pathway to reduce the population inversion threshold.[47]

**3. Modification at the Nanoscale Level**

**3.1. Ligand Exchange**

Following the work done on PbS NCs, ligand exchange can be
used not only as a strategy to increase interparticle coupling

but also as a way to induce a surface dipole.[48,49] These dipoles
bend the bands on the NC surface, tuning their relative energy
with respect to the Fermi level. Chu et al. screened various short
ligands with lengths compatible with electrical conduction and
observed, thanks to X-ray photoemission, the shift of the band
for 0.8 eV bandgap HgTe NCs, see **Figure 3a**. They demonstrated
that the Fermi level can be displaced from the lower part of the
bandgap with short thiol capping (i.e., p-type behavior) to the
upper part of the bandgap (i.e., n-type behavior) in the presence
of an amine. Nevertheless, this work did not demonstrate the
formation of a pn junction through the stacking of such layers.

To succeed in this endeavor, Tang's group developed a
method inspired by the c-ALD procedure.[50] The method was
initially proposed as a low-temperature method to grow a shell
on fragile colloidal materials such as 2D nanoplatelets.[8] The
concept was then extended to mercury chalcogenides as a way
to grow shells. Here Chen et al. applied this technique to care-
fully tune the ligands on the surface of HgTe NCs. On HgS NCs,
it was observed that excess mercury or sulfide induced n- and
p-type doping, respectively.[35] On HgTe, Chen et al. demon-
strated that a careful tuning of the HgCl₂ or (NH₄)₂S precursors
used to conduct ligand exchange through the method mentioned
previously is a viable strategy to induce n-type, p-type or even
intrinsic behavior in HgTe layers with a bandgap in the short
or mid-wave infrared,[23,51] as pointed out by transport measure-
ments probed in a FET geometry, see Figure 3b. In these meas-
urements, carriers are accelerated under a constant drain source
bias, while the gate bias is tuned. In a classic FET, the charge Q
generated at the surface of the gate dielectric is proportional to
the applied gate bias (VGS) according to Q = C · VGS, where C is
the gate capacitance, which is highly technology-dependent, as
discussed later in this review. Under negative gate bias, holes
are injected, while electrons are injected upon positive gate bias

<figure><img src="image_5.png" /><figcaption>**Figure 3.** Impact of ligands. a) Reconstructed energy diagram (valence and conduction bands, and vacuum level with respect to the Fermi level used as reference) for HgTe NCs with an initial band edge of 0.8 eV and capped with various ligands. Adapted with permission.[30] Copyright 2019, American Chemical Society. b) Transfer curves for HgTe NCs (band edge at around 0.8 eV) capped with various ligands. n-type behavior is induced by excess mercury on surface while excess sulfide generates a p-type nature. In the middle an intrinsic behavior can be obtained. c) Schematic of a p-i-n junction obtained by stacking HgTe NCs capped with suited ligands. d) I-V curve in the dark and under illumination for the diode made of an homojunction as depicted in part c. The IV curve is rectifying in the dark, with a clear open-circuit voltage upon light illumination. (b-d) Adapted with permission.[23] Copyright 2023, Wiley.</figcaption></figure>
application. If the current rises under injection of only one type of carrier, the material is unipolar. This is the case for the p-type material capped with sulfide (bottom graph of Figure 3b). If the current rises under both types of carrier injection, the material is described as ambipolar (middle graph of Figure 3b). The gate bias under which the current switches from hole to electron injection is considered as the neutrality point. The closer this bias is to zero, the more intrinsic the material is. Here we additionally observe a non-monotonous rise of the conduction in the electron branch that is attributed to Pauli blockade. The mobility has a local maximum when the 1S state is half filled and then drops for band filling from 1 to 2, before rising again when the 1P state starts to take part in the conduction process. Thanks to this ligand exchange process, Chen et al. were able to develop a p-i-n stack[23,51] (Figure 3c) that exhibits a rectifying electrical characteristic and that displays an open-circuit voltage under infrared light illumination, see Figure 3d.

A clear limitation of the conventional ligand exchange process is its lack of post-fabrication tunability. Furthermore, it couples the mobility magnitude and doping, as both are driven by the choice of capping ligands. The latter with large dipoles may not be suited for charge conduction. Therefore, reconfigurable ligands, presenting a tunable dipole moment, appear relevant. This concept is inspired from molecular motors, in which a molecule presenting two isomers can be activated by light. This is the case of azobenzene, which presents both *cis* and *trans* configurations (**Figure 4a,b**) and the transformation from one to another can be activated by light or temperature. To use them as ligands,

Martinez et al. further functionalized the azobenzene group with a thiol,[52] which serves as an anchor to the HgTe NCs surface thanks to the strong affinity of thiol for mercury. Under UV illumination, the azobenzene switches to its *cis* configuration, which is associated with a dipole. This induces a shift of the valence band toward the Fermi level (see Figure 4c,d), increasing the p-type nature of the material and resulting in a change in the sample's conductivity. This change is reversible after a pulse of blue light that returns the azobenzene to its *trans* configuration. However, the practical use of this approach has been held back by the limited cyclability of the process.

## 3.2. Surface Functionalization

As pointed out earlier, one key bottleneck of the ligand exchange as a strategy to control the carrier density is this coupling between carrier density and mobility. Therefore, it is highly appealing to develop methods where the dipole does not result from the ligand. In surface science, alkali functionalization of semiconductor surfaces is a well-known method to tune the material work function.[53–56] Recently, the concept has been applied to HgTe NCs by Mastrippolito et al.[57] Authors bring evidence that upon K deposition, the work function is strongly reduced, see **Figure 5a,c**, by 0.6 eV. This kind of shift is promising for the design of diodes, offering a way to replace expensive metal electrodes (Au, Pt) with alternatives that have a reduced work function, though it will also raise questions regarding a possible amalgam formation.[58] It may also offer more flexibility

<figure><img src="image_6.png" /><figcaption>**Figure 4.** Light reconfigurable ligands. a) (resp b)) Schematic of a NC capped with an azobenzene ligand in trans (resp cis) configuration. c) (resp d)) Energy diagram in absolute energy scale (Fermi level as reference) for HgTe NCs capped with the two configurations of the azobenzene. Reproduced with permission.[52] Copyright 2019, American Chemical Society.</figcaption></figure>
<figure><img src="image_7.png" /><figcaption>Figure 5. Functionalization by alkali atoms. a) XPS spectra relative to the cut-off of the secondary electrons for HgTe NCs with a band edge at around 0.8 eV after various durations of K evaporation. b) Photoemission spectra relative to the low binding energy region of the spectrum for the same film as in a. The energy range displays valence band, Hg and K core levels. c) Work function from the same film as a function of the amount of K deposited. Adapted with permission.[57] Copyright 2024, American Chemical Society.</figcaption></figure>

regarding the choice of relevant charge transport layers used to surround the optically active material. Authors also note a key difference with the ligand-induced dipole, which is that the energy of the valence band and the core level remains unchanged during deposition, see Figure 5b. This means that the carrier density remains unchanged during this process and that the alkali does not generate any free charge, acting purely as a dipole. In this sense, ligand exchange and alkali deposition may be complementary methods. Further confirmation that the effect (work function shift) can be maintained at the device level also needs to be demonstrated.

# 4. Device Scale Modification of the Carrier Density

## 4.1. From Gate Effect to Advanced Gating to Shape Carrier Density Landscape

Previous approaches aimed at tuning the carrier density rely on nanoscale modifications of the material and mostly lack post-fabrication tunability. In the next part of the review, we focus on device-scale strategies to achieve a change in the carrier density, with the central method based on gating. As already mentioned, gating traditionally relies on the formation of a capacitor. The latter is made of a dielectric layer. Applying bias ($V_{GS}$) across this dielectric generates charges $Q$ on its surface according to

$$Q = C \cdot V_{GS} \qquad (3)$$

with $C$ the capacitance, of which the value per unit area ($S$) is given as the ratio of the dielectric constant over the dielectric thickness ($d$), so that

$$C = \frac{\epsilon_0 \epsilon_r S}{d} \qquad (4)$$

where $\epsilon_0$ the vacuum permittivity. If a semiconductor is brought into contact with the dielectric as gate bias is applied, charges will be injected by the electrode into the semiconductor to maintain

charge neutrality, resulting in a change of its carrier density, and therefore a modulation of the current magnitude, see Figure 6a and 7b.

In the context of NCs, this type of gate is used to design FETs, which are three-electrodes devices[59] commonly employed to determine the carrier mobility (related to the derivative of the transfer curve) and the nature of the carriers, as discussed in part 3.1.

With HgTe NCs, Kim et al.[60] reported the first FET, see Figure 6a. This device was a dual-gated FET with both a bottom and a top gate. The material displays a p-type behavior and early reported mobility values were modest. The most basic way to design this sort of transistor is to start from an oxidized doped silicon wafer with a thin silica layer on the top. This approach has the benefit of being commercially available and is schematized in Figure 7a. Oxides prepared by dry methods (as opposed to wet methods) tend to offer higher robustness toward electrical breakdown, and are better suited to operate the gate under large bias (Figure 7d). Silica nevertheless presents the drawback of limited dielectric constant ($\epsilon_r = 3.9$) and hence alternative materials with larger dielectric constants ($Al_2O_3$, $HfO_2$) are also suited to design gates. In particular, the ease of conformal deposition through atomic layer deposition (ALD) makes these two oxides well adapted to the design of complex gating strategies to shape the carrier density landscape. Chee et al. have reported the design of a gate-induced planar pn junction thanks to a dual-gated transistor,[22] see Figure 6b. If the two gates are operated with the same bias, the device acts as a conventional FET, presenting a symmetric IV curve, see Figure 6c. Conversely, when the two gates are operated with opposite polarization, the induced carrier densities have opposite signs leading to the formation of a planar pn junction.[61] The latter is evidenced by the emergence of a rectifying IV curve, as shown in Figure 6d.

When trying to integrate HgTe NCs, devices based on conventional dielectrics quickly become limited by their relatively low capacitance. At room temperature, a non-negligible amount of thermally activated charges are generated due to the narrow bandgap nature of HgTe. The gate-induced charges have to compete with the thermally activated carrier density and thus the
<figure><img src="image_8.png" /><figcaption>**Figure 6.** Gating to shape carrier density landscape. a) Transfer curve (T = 300 K) from the first reported HgTe NCs field-effect transistor, as presented by Kim et al. Adapted with permission.[60] Copyright 2006, AIP. b) Schematic of a dual-gated FET with a channel made of HgTe NCs. The color gradient in the channel illustrates the ability to generate both n and p domains, forming a planar pn junction. c) IV curve of the dual-gated transistor when operated as a FET (V<sub>G1</sub> = V<sub>G2</sub>; T = 250 K). d) IV curve of the dual-gated transistor when operated as a diode (V<sub>G1</sub> = -V<sub>G2</sub>; T = 250 K). Parts (c) and (d) are adapted with permission.[93] Copyright 2021, American Chemical Society.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>**Figure 7.** High-capacitance gating strategies. a) Schematic of field-effect transistor made of silica gate and a HgTe NC channel. b) Schematic of field-effect transistor made of ion gel electrolyte gate and a HgTe NC channel. c) Schematic of field-effect transistor made of STO gate and a HgTe NC channel. d–f) are the transfer curves (current vs gate bias under constant drain source bias) associated with device (a–c) respectively. Adapted with permission.[80] Copyright 2019, American Chemical Society.</figcaption></figure>

modulation from the gate is generally restricted. A possible way to remedy this issue is to operate at low temperature. As temperature is lowered, the residual carrier density at the neutrality point is strongly reduced and the on/off ratio (magnitude of the current modulation) is strongly increased. As pointed out by Equation (3), an alternative strategy would be to increase

the gate capacitance. Thick dielectrics (200–300 nm) are commonly used but only offer capacitances on the order of 10 nF cm⁻². Reducing the oxide thickness down to the 50–100 nm increases the capacitance but also increases the likelihood of breakdowns. Therefore, in the next section, we discuss developments relative to the use of high-capacitance gates.
## 4.2. Beyond Traditional Dielectric

Traditional dielectric gates, whose capacitance directly relates to their geometrical size, face a tradeoff between the amount of leakage and the number of gate-induced charges. To illustrate this problem, one can estimate the surface charge induced by a dielectric gate. For 300 nm of silica, corresponding to a typical commercial gate thickness, this corresponds to $6 \times 10^{11}$ charges cm$^{-2}$ under 10 V. Assuming a square shape for the particle with an 8 nm edge, the packing density of NCs will be $1.6 \times 10^{12}$ NCs cm$^{-2}$, therefore a gate should be able to generate ≈0.5 charges per nanocrystal. However, in practice, a significant fraction of the sheet charge is not injected within the NCs, but is rather used to passivate the surface of the gate oxide. This explains why, to date, intraband absorption has never been reported based on dielectric gating. To overcome this limitation, electrolytes[62,63] offer an interesting alternative. With electrolytes, the capacitance is no longer determined by the electrolyte thickness but rather by the size of the ions, or more accurately, the size of the ionic double layer. This results in typical sheet capacitance values in the order of $1–10 \mu F$ cm$^{-2}$,[64,65] which are 100–1000 times larger than those found in dielectrics. In the case of electrolytes, surface charge can reach the $10^{14}$ electrons.cm$^2$, which corresponds to multiple charges per NC and enables the observation of intraband transitions.[24] This massively increased sheet capacitance is nevertheless mitigated by the reduced range of gate bias that can be applied, which must remain within the electrochemical stability window of the electrolyte matrix (few volts). Electrolyte operation relies on the displacement of ions within a matrix, which can be a liquid,[24] a gel[7,31,66] or even a solid.[67] The nature of the matrix drives how fast the ions can diffuse, thereby affecting the sweep rate that can be used to drive the transistor. To operate, the electrolyte needs to be above the freezing point of the matrix. With ion gels, this freezing point can be quite close to room temperature. If ever a wider temperature range is required, a liquid matrix is better suited. Conversely, liquid electrolytes generally require strict air-free conditions to operate, while ion gels and solid electrolytes can even function in room conditions. Freezing of the electrolyte also prevents the low-temperature tuning of the carrier density. However, the material can be charged at room temperature and then frozen, so that it maintains its charge under cryogenic conditions.

In the context of HgTe NCs, electrolyte gating brings several advantages compared to dielectric gating. First, it enables room temperature operation, see Figure 7b,e, which show effective gating at 300 K using an electrolytic gate. Second, electrolyte gating allows for high carrier densities leading to the emergence of intraband features. Using an electrolyte, Liu et al. succeeded in inducing both degenerate n- and p-type doping in HgTe NCs, monitored by infrared spectroscopy through the emergence of intraband absorption.[24] Finally, electrolyte gating ensures that gating effect is not limited to the film's surface (Figure 7b). Ions from electrolytes have the ability to percolate within the array of NCs. This makes intercalation within the HgTe lattice possible if small ions are used, but this is generally not an objective, since it brings an irreversibility in the device operation. However, ion percolation also grants the ability to gate

thick films[68] which is particularly promising in the perspective of a phototransistor design. There is usually a trade-off for NC-based phototransistors. On one hand, gating is usually only a surface effect and hence the dark current is modulated only close to the dielectric interface, while on the other hand, the absorption occurs in film thicknesses larger than 1 µm.[44] With electrolyte gating, the carrier density tuning can be obtained over a range of sizes compatible with a large absorption of the incident light.

A complementary approach to electrolyte gating relies on ionic glasses, which can be seen as solid electrolytes. This expands the range of available materials beyond those inspired by batteries (such as Li garnet[67]). Shukla's group initially observed that ions in a glass slide appear mobile at high temperatures.[69,70] In this case, glass is used as a high-freezing-point electrolyte capable of generating high carrier densities in 2D materials. However, for HgTe NCs, the operating temperature of this glass is too high, as they tend to be damaged upon exposure to elevated temperatures.[71] Other ionic glasses, such as LaF₃, present mobilities from F⁻ vacancies.[72,73] The second advantage of this kind of glasses is their initial use as an infrared window, thus allowing for potential backside illumination,[74] which is generally not compatible with most gates. The operating temperature range of LaF₃ glass (180–300 K) is quite close to the one from liquid electrolytes, with the added benefit of being entirely solid. Furthermore, this temperature range typically matches the expected operating temperature for short- and mid-wave detectors. The use of these gates for phototransistor has been proposed by Gréboval et al.[75,76] In this device, the gate bias is chosen to minimize the dark current, while the gate-induced modulation is expected to be larger for the photocurrent than for the dark current.

With strategies based on ion displacement, the sheet capacitance is maximized by reducing the dielectric thickness down to an equivalent value of 1 nm, see Equation (4). Maximizing the capacitance can also be achieved by increasing the dielectric constant. As previously mentioned, high-k materials such as Al₂O₃ or HfO₂ can serve this purpose, but their dielectric constants remain modest $\epsilon_r \approx 7.5$ and below 20, respectively. An alternative approach to explore even higher dielectric constants is to switch to ferroelectric materials. In the vicinity of their Curie temperature, the dielectric constant diverges. This divergence occurs on both sides of the paraelectric/ferroelectric transition. On the paraelectric side, the behavior is similar to that of a dielectric with a high dielectric constant. The concept has been proposed using ferroelectric polymers such as the derivative of polyvinylidene fluoride (PVDF). With proper functionalization of the polymer chains, values of $\epsilon_r$ above 50 have been reported.[77] While this type of gating has been applied to PbS NCs,[78,79] it has not yet been explored for HgTe NCs. A possible reason is the above-room-temperature Curie temperature of this polymer. Therefore to benefit completely from the dielectric constant divergence, high temperatures should be targeted. This is in contradiction with the typical use of these materials for infrared sensing, where low temperatures are preferred. Therefore, materials with lower Curie temperatures should be investigated. An interesting case is SrTiO₃ (STO), a well-known oxide with a perovskite structure, see Figure 7c. Its Curie temperature is negative, but quantum fluctuations lead to divergences of the dielectric constant below 100 K, reaching values of $\epsilon_r = 30 000$.
at 4 K. In addition to its exceptionally high dielectric constant, STO is also a classic substrate for epitaxial growth, making substrates of this material available in reasonably large formats. The large dielectric constant is balanced by the thickness of the layer, which is on the order of a hundred micrometers. Nevertheless, the large bandgap of STO, prevents breakdowns in these substrates, even under very large applied biases (up to 200 V, see Figure 7f). This concept was demonstrated by Gréboval et al. who fabricated a phototransistor made of HgTe NC channel on a STO substrate and further designed the electrode to trap light as a strategy to enhance film absorption.[80]

### 4.3. Ferroelectric Gating

In practice, the design of phototransistors using any of the aforementioned gate technologies continues to face noise issues. On one hand, the gate is used to reduce the dark current and its associated noise. On the other hand, the addition of an extra electrode can act as an antenna, bringing extra noise, especially related to the 50/60 Hz power lines. This is the reason why operating ferroelectrics below the Curie temperature becomes relevant, since their polarization can act as a steady-state gate, which does not require a connection to a power supply. This approach foregoes the tunability of the carrier density, but keeps the benefit of having a modified carrier density. Cavallo et al. have explored the interaction of ferroelectric domains with HgTe NCs used for

infrared optoelectronics.[81,82] In this work, ferroelectric domains are first patterned at the surface of PbZrTiO₃ (PZT), see **Figure 8a,b**. They designed two domains of opposite polarization in the area between two electrodes that were later used to probe transport. This patterning requires a piezoelectric force microscope, which is certainly a limitation for later scaling up this approach. The HgTe NCs film is then coated onto the functionalized substrate. Using soft X-ray photoemission imaging (**Figure 9b** provides a schematic of the experiment), they tracked how the binding energy of a mercury core level (Hg 5d) was affected by the underlying polarization, see Figure 8c. They noticed a clear shift of the binding energy over the area corresponding to the ferroelectric domains. This shift is ≈150 meV (Figure 8d), which is about a quarter of the optical bandgap value of the HgTe NCs used here. This shift is large enough to generate a rectifying IV curve, whereas the reference sample built on a single polarization presents an ohmic IV curve. To address the limited area resulting from the microscopy-based definition of the domains, it is again relevant to look around in the direction of optical materials. For non-linear optics, periodically poled LiNbO₃ (PPLN) substrates are used to achieve the phase matching condition. In these substrates, slabs of LiNbO₃ with opposite polarization are stacked next to each other. Cavallo et al. proposed to use this kind of substrate in a way similar to the previously discussed PZT, and designed the electrodes in such a way that each one overlaps the opposite polarization domain,[73]

<figure><img src="image_10.png" /><figcaption>**Figure 8.** Ferroelectric gating. a) Schematic of a HgTe NCs channel coupled with two ferroelectric domains defined at the surface of PZT. b) Piezoelectric force microscopy phase image of the two ferroelectric domains with opposite polarization defined on a PZT substrate. c) Intensity of the Hg 5d state determined from photoemission imaging from a HgTe NC film coating the two ferroelectric domains observed in part b. d) XPS spectra relative to the Hg 5d state for HgTe on top of P+ and P− polarized domain. (a–d) Adapted with permission.[81] Copyright 2023, Wiley. e) Schematic of a PPLN (periodically poled LiNbO₃) substrate on which graphene electrodes have been fabricated, knowing that each electrode is built on opposite polarization domains. f) IV curves under various irradiances at 1.55 µm for the device of part e. (e,f) Adapted with permission.[82] Copyright 2023, AIP.</figcaption></figure>
<figure><img src="image_11.png" /><figcaption>**Figure 9.** Remote doping. a) Schematic of a planarized diode stack in which the active layer is the top layer, coupled to both electron and hole transport layers. b) Schematic of photoemission imaging: a soft X-ray beam is focused on a sub µm scale thanks to a Fresnel lens on the sample. The latter is scanned in the plane and for each point a photoelectron spectrum is collected by the electron analyzer. c) Photoemission spectra of the Hg 5d state for HgTe NCs on top of the hole transport layer (Ag₂Te) and atop the electron transport layer (SnO₂). (a–c) Adapted with permission.[84] Copyright 2023, American Chemical Society.</figcaption></figure>

see Figure 8e. Again, the capacity to generate a planar pn junction was validated through the observation of a diode behavior in the electrical characteristic, see Figure 8f.

### 4.4. Remote Doping

Following the concept of inducing carrier density modifications via polarization, doping can be induced by a functionalized substrate. Conventional insulating substrates used for devices can be locally functionalized using charge transport layers to induce a modification on the HgTe NC film. This concept is actually directly inspired by the design of photodiodes, in which the absorbing layer is coupled to electron and hole transport layers. By favoring the extraction of one carrier, the carrier density in the optically active layer is modified. The same concept can be applied to locally shape the carrier density landscape. Specifically, HgTe NCs can be coupled to a textured substrate made of SnO₂ that is locally functionalized with an Ag₂Te layer. These two materials have been previously used for photo-diode design, acting as electron and hole transport layers, respectively.[83]

Again, photoemission microscopy (Figure 9b) appears as a relevant tool to directly image the modified energy landscape with a sub µm spatial resolution.[27,84] The method is well suited

to provide a direct measurement of the built-in potential of a diode stack, which otherwise is only determined through modeling, for example, of capacitive measurements.

Here, a planar version of a diode stack is used, as depicted in Figure 9a, to be compatible with the surface origin of the photo-electrons. Once coupled with SnO₂ and Ag₂Te layers, the energy shift reaches ≈150–200 meV (Figure 9c), depending on the exact bandgap of the HgTe NCs considered. Compared to non-spatially resolved photoemission, this technique has the benefit of being insensitive to calibration errors. The method appears quite suited to systematically screen potential combinations of electron and hole transport layers to maximize charge dissociation.

### 5. Conclusion

Table 1 summarizes the properties of the various gate technologies that have been developed in interaction with HgTe NCs. Given the broad range of operating conditions (temperature, size, presence of intrinsic doping), a single-gate technology could not address all requirements. Therefore, these technologies are complementary to each other. Clear efforts have been made to enhance carrier density control at the material scale, surface chemistry and device level, ensuring robust p-n junction formation in this material. This being said, current shifts of the

<table><caption>**Table 1.** Typical ranges of use for solid-state gating of HgTe NC-based field-effect transistor.</caption><thead><tr><th>Gate technology</th><th>Dielectric</th><th>Ionic glass</th><th>Electrolyte</th><th>Quantum paraelectric</th><th>Ferroelectric</th></tr></thead><tbody><tr><td>Material</td><td>SiO<sub>2</sub>, Al<sub>2</sub>O<sub>3</sub>, HfO<sub>2</sub></td><td>LaF<sub>3</sub></td><td>Liquid, ion gel, or solid</td><td>SrTiO<sub>3</sub></td><td>PbZrTiO<sub>3</sub>, LiNbO<sub>3</sub></td></tr><tr><td>Temperature range</td><td>4–300 K</td><td>180–260 K</td><td>300 K for solid<br>Down to 160 K for liquid</td><td>4–100 K</td><td>Up to Curie temperature<br>(generally above room temperature)</td></tr><tr><td>Mechanism generating the charges</td><td>Surface charges (fast)</td><td>Ion displacement</td><td>Ion displacement<br>(speed depends<br>on electrolyte viscosity)</td><td>(fast)</td><td>Remanent polarization</td></tr><tr><td>Gate voltage range</td><td>&lt;60 V (dielectric breakdown)</td><td>Up to 10 V at 200 K</td><td>&lt;3 V (electrochemical stability<br>of the electrolyte)</td><td>No breakdown<br>even at 200 V</td><td>—</td></tr><tr><td>References</td><td>[60,94–96]</td><td>[74–76]</td><td>[7,24,31,66,80]</td><td>[80]</td><td>[81,82]</td></tr></tbody></table>
quasi-Fermi level remain of the order of ¼ of the bandgap, pushing for the development of new solutions. The increase of the built-in potential is however not limited to how strong doping can be, but also directly relates to the presence of traps and their associated non-radiative pathways, which will be another subject to develop in parallel with the carrier density control.

Two methods prevail for the moment when it comes to carrier density characterization: FETs, which give information on the amount of charge, and spectroscopy techniques (photoemission, electrochemistry), which offer insights into the energy landscape and the relative shifts of bands with respect to the Fermi level. A proper connection between charges and their impact on the energy landscape is still missing. This certainly relates to a significant portion of the charges being lost in the imperfections of the system (traps on a dielectric surface, NC defects...).

As the field matures, we are entering a phase where proof-of-concept methods are increasingly being integrated into more complex systems that potentially combine several carrier density techniques within a single device. A second challenge relates to the fact that the carrier density control is not the only factor that contributes to the device efficiency. The introduction of photonic cavities has proven very beneficial for both detection[85-89] and light emission.[90,91] Therefore, a clear challenge will be the combination of carrier density control and light management strategies within the same device. This will raise expectations on the material stability (thermal, chemical...), but such challenges are a necessary part of moving from lab-scale research to real-world applications.

## Acknowledgements

The project is supported by ERC grants blackQD (no. 756225) and AQDtive (grant no. 101086358). This work was supported by French state funds managed by the Agence Nationale de la Recherche through the grant Bright (ANR-21-CE24-0012), Operatwist (no. ANR-22-CE09-0037-01), MixDFerro (ANR-21-CE09-0029), Quicktera (ANR-22-CE09-0018), E-map (ANR-23-CE50-0025), DIRAC (ANR-24-ASM1-0001), camIR (ANR-24-CE42-2757), Piquant (ANR-24-CE09-0786) and NanoSaclay (ANR-10-LABX-0035).

## Conflict of Interest

The authors declare no conflict of interest.

## Author Contributions

**Mariarosa Cavallo**: conceptualization (lead); writing—original draft (lead); writing—review & editing (lead). **Dario Mastrippolito**: writing—review & editing (equal). **Clément Gureghian**: writing—original draft (equal); writing—review & editing (equal). **Erwan Bossavit**: writing—original draft (equal); writing—review & editing (equal). **Huichen Zhang**: writing—review & editing (equal). **Albin Colle**: writing—review & editing (equal). **Tommaso Gemo**: writing—review & editing (equal). **Alexandre Neyret**: writing—review & editing (equal). **Adrien Khalili**: writing—review & editing (equal). **Debora Pierucci**: funding acquisition (equal); writing—original draft:supporting; writing—review & editing (equal). **Emmanuel Lhuillier**: conceptualization (lead); funding acquisition (lead); writing—original draft (lead); writing—review & editing (lead).

## Keywords

carrier density, doping, HgTe, nanocrystals, pn junction

Received: October 28, 2024

Revised: December 16, 2024

Published online:

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<figure><img src="image_12.png" /></figure>

**Mariarosa Cavallo** is a third-year Ph.D. student at Institut des Nanosciences de Paris, under the supervision of Emmanuel Lhuillier. She received her master's degree in nanotechnologies and quantum devices from Politecnico di Torino and Université Paris Cité. Her research focuses on the characterization of colloidal NC-based devices by nanobeam photoemission microscopy.

<figure><img src="image_13.png" /></figure>

**Dario Mastrippolito** is a postdoctoral researcher at the Institut des Nanosciences de Paris, CNRS-Sorbonne University. He holds a Ph.D. in Physical and Chemical Sciences from the University of L'Aquila. His current research investigates the optoelectronic properties of 2D/0D materials, ranging from fundamental studies to device integration.
<figure><img src="image_14.png" /></figure>

**Clément Gureghian** has an engineering degree in physics and nanoscience for optics. Graduated from his PhD at Office National d'Études et de Recherche Aérospatiales on nanostructured long wave infrared photodetectors based on Type II superlattices and heavily doped semiconductor in 2024. Currently occupying a CNRS Postdoc position at Sorbonne Université on short-wave infrared photodetection based on semiconductor NCs.

<figure><img src="image_15.png" /></figure>

**Erwan Bossavit** is a Ph.D. student in a joint project between the INSP laboratory of Sorbonne Université and the SOLEIL synchrotron, supervised by Emmanuel Lhuillier and Mathieu G. Silly. His research interests revolve around the integration of infrared-active NCs into novel infrared-emitting devices, from light-emitting diodes to photonic structures.

<figure><img src="image_16.png" /></figure>

**Huichen Zhang** is a Ph.D. student at Sorbonne University, supervised by Emmanuel Lhuillier. Her research interest involves the synthesis of NCs for infrared optoelectronic devices.

<figure><img src="image_17.png" /></figure>

**Albin Colle** graduated from Chimie ParisTech, member of PSL University, in 2024. He did his master thesis at the Institut des NanoSciences de Paris working on HgTe quantum dots-based photodiodes. Since that he initiated PhD thesis in the same group.

<figure><img src="image_18.png" /></figure>

**Tommaso Gemo** did his undegraduate study at Politecnico di Torino in Physics Engineering and Nanotechnologies. He is now graduate student at Sorbonne université designing mid-wave infrared NC-based detector.

<figure><img src="image_19.png" /></figure>

**Alexandre Neyret** is a first year Ph.D. student at ISAE-Supaéro, in collaboration with Institut des Nanosciences de Paris. He received an engineering degree in aerospace technologies and microelectronics at ISAE-Supaéro in 2023. His current research focuses on radiation effects on CQDs-based camera.
<figure><img src="image_20.png" /></figure>

**Adrien Khalili** is a post-doc at Institut des Nanosciences de Paris. He received his master's degree in applied physics from Ecole Normale Supérieur Paris-Saclay and completed his Ph.D. at Sorbonne Université supervised by Emmanuel Lhuillier, focusing on the optoelectronics of infrared NCs. His current research is centered on advancing NC-based infrared camera technology.

<figure><img src="image_21.png" /></figure>

**Debora Pierucci** is a CNRS researcher at Sorbonne University, France. She earned her Ph.D. from Université Pierre et Marie Curie in 2013. Her research focuses on the electronic properties of heterostructures made from low-dimensional materials, employing advanced photoemission techniques.

<figure><img src="image_22.png" /></figure>

**Emmanuel Lhuillier** did his Ph.D. at Onera, the French aerospace lab, under the supervision of Emmanuel Rosencher working on quantum well-based infrared detectors. He then joins Guyot-Sionnest's group as a post-doctoral scholar at University of Chicago working on HgTe NC and their mid-infrared photoconductive properties. Since 2015, he is a CNRS researcher and drives a group at Sorbonne Université dedicated to the optoelectronics of confined nanomaterials, with a clear focus on NC-based infrared applications.