Two-dimensional hole gas in organic semiconductors

A highly conductive metallic gas that is quantum mechanically confined at a solid-state interface is an ideal platform to explore nontrivial electronic states that are otherwise inaccessible in bulk materials. Although two-dimensional electron gas (2DEG) has been realized in conventional semiconductor interfaces, examples of two-dimensional hole gas (2DHG), which is the counter analogue of 2DEG, are still limited. Here, we report the observation of a 2DHG in solution-processed organic semiconductors in conjunction with an electric double-layer using ionic liquids. A molecularly flat single crystal of high mobility organic semiconductors serves as a defect-free interface that facilitates two-dimensional confinement of high-density holes. Remarkably low sheet resistance of 6 k$\Omega$ and high hole gas density of 10$^{14}$ cm$^{-2}$ result in a metal-insulator transition at ambient pressure. The measured degenerated holes in the organic semiconductors provide a broad opportunity to tailor low-dimensional electronic states using molecularly engineered heterointerfaces.

A metallic gas confined in semiconductor heterostructures, which is also known as a twodimensional electron gas (2DEG) or two-dimensional hole gas (2DHG), is one of the most intriguing platforms not only for exploring the fundamentals of condensed matter 1, 2 but also for developing high performance devices 3,4 . Over the past four decades, the discovery of 2DEGs at the interface between compound semiconductors 5,6 as well as at the interface between oxide insulators 7,8 has provided an in-depth understandings of the nontrivial electronic states that are otherwise inaccessible in a bulk material 9 . Although 2DEGs with a remarkably high sheet conductivity at n-type interfaces have been discovered and are widely used in various high frequency devices (high-electron-mobility transistors are the most representative example), the use of its counter analogue, i.e., 2DHGs, at p-type interfaces, are still limited 10,11 . The lack of these 2DHGs is rooted in the physics of conventional semiconductor heterointerfaces; wide-gap semiconductors generally lead to heavy valence bands, resulting in low mobility holes and deep valence bands 11 . In addition, extra attention should be paid to lattice continuity with respect to atomic scale precision, establishment of polar discontinuity, and extreme elimination of dangling bond, whose excess electrons often suppress hole transport 10 .
Metallic phases under high carrier densities have been extensively studied in the field of organic semiconductors (OSCs) [12][13][14][15][16][17][18][19][20] . Recent studies have shown that self-assembled molecules without any dangling bonds can construct highly periodic electrostatic potential, and a coherent band hole system is realized, even in van der Waals bonded molecular crystals [21][22][23] . Despite the recent success in the field of materials science or in the developments in printing technologies for the single-crystalline forms of OSCs 24 , an apparent metallic gas state has not been observed 3 in OSCs. This is clearly because both static as well as dynamic disorders result in the carrier localization .i.e.,. large fluctuations in the intermolecular transfer integrals caused by thermal molecular motions are negligible even in the single crystals of OSCs.
Here, we demonstrate solution-processed, organic 2DHGs in which the metallic gas can be confined electrostatically within a monolayer of the OSCs. OSCs have been studied extensively as frontier materials for the development of new generation electronics. Recently, improvements in synthetic routes and device fabrication techniques have led to the development of small-molecule OSCs with high carrier mobility of 10 cm 2 V −1 s − 1 22, 25-29 . We unambiguously demonstrate a metal-insulator transition (MIT) in the solution-processed, single-crystalline OSC at ambient pressure. In this, an extremely high carrier density of approximately 1 × 10 14 cm −2 (approaching 0.25 holes per molecule) can be confined two-dimensionally at the OSC/electric double-layer (EDL) interface. An apparent metallic signature, i.e., the positive temperature coefficient of the resistance (dR/dT > 0), is observed concomitantly with a minimum resistance of 6 kΩ (below the two-dimensional quantum value h/e 2 , e is the elementary charge and h is the Planck constant) down to a temperature of T = 15 K. This has not yet been demonstrated in a single component of OSCs. This observation is in striking contrast to the localized nature of the electronic states in OSCs and is manifested such that the degenerated electronic states are realized in OSCs.
As an ideal organic two-dimensional system, we employ an alkyl-substituted small molecule.
A truly single-crystalline form of 3,11-dioctyldinaphtho [2,3- Figs. 1a and b) is deposited on a flexible substrate via the continuous edge-4 casting method 26,28,30 (Fig. 1c). The continuous edge-casing method allows a one-shot crystal growth of layer-controlled thin films of C 8 -DNBDT-NW with an areal coverage of up to at least 1 cm 2 26, 28 . This is large enough to cover an entire channel (Fig. 1d). Technically, this oneshot printing method allows the fabrication of defect-free, single-crystalline nanosheets with large areal-coverage of up to 100 cm 2 28 onto any given substrate 31 . The single crystallinity across the C 8 -DNBDT-NW thin film has been confirmed by X-ray diffraction and electron diffraction measurements 29,31 . A uniform optical intensity in polarized microscopy images confirms the existence of a molecularly flat surface without molecular steps. A single-crystalline bilayer is prepared selectively by controlling the substrate temperature 26,32 . A plastic substrate (polyethylene naphtalate: PEN) coated with a parylene layer is a better alternative with regard to the thermal expansion coefficient of OSCs, i.e., less crystal cracks are induced during low temperature measurements.
Gold/chromium electrodes are deposited gently on the surface of the bilayer C 8 -DNBDT-NW to form source and drain electrodes (a photograph of the device is shown in Fig. 1d). The channel direction is along the c-axis of C 8 -DNBDT-NW . In this work, we use an ion gel as an electrolyte, Previous studies have revealed that the EDL formed particularly at the surface of the OSC causes an unavoidable dissolution/damage 33 . In contrast, an insulating alkyl side chain of C 8 -5 DNBDT-NW with a thickness of 1 nm can separate the conducting layer of C 8 -DNBDT-NW from the IL (Fig. 1f). It is possible that the alkyl side chains provide indirect contact of the IL with the C 8 -DNBDT-NW molecules and suppress the electrical potential fluctuation, which is an origin of the carrier localization 34 .
To assess the formation of the EDL at the surface of C 8 -DNBDT-NW , charging/discharging properties are investigated based on the standard EDLT characteristics. Figure 2a  between IL and C 8 -DNBDT-NW is is 8.5 µF cm −2 , which is consistent with the literature value 35 .
These results lead to the conclusion that the carriers are induced electrostatically, i.e., the contribution of electrochemical doping is negligible. µ Hall at T =180 K increases from 5.0 cm 2 V −1 s −1 at (Fig. 2e), which is slightly smaller than those obtained for FETs with solid-state dielectrics 26 . The decrease in mobility for the two-dimensional electron systems has been often observed, particularly when a high electric field (normal to twodimensional sheet) is applied 36 . It is possibly because not only ordinary phonon scattering but also other scattering such as scattering by ionized impurity may contribute to the carrier transport 2, 10, 11 .
Temperature-dependence of sheet resistance R sheet = σ sheet −1 was investigated after the introduction of holes into the channel at T = 260 K with various V G (Fig. 3a).
V, a typical semiconducting behaviour is observed, in which the temperature-dependence changes    can be clearly attributed to the strong carrier localization, which could not be overcome for any of the existing OSCs. materials [12][13][14][15][16][17][18][19][20] . We emphasize that high-quality crystals even in the absence of surface crystal steps would be essential for the emergence of a 2DHG system at the heterointerfaces. Figure 3b shows the σ sheet of sample 2 normalized by conductivity quantum e 2 /h as a function of V G . The temperature-independent crossing point can be seen at a well-defined V G = −2.5 V (n Hall = 4 × 10 13 cm −1 , equivalently 0.1 holes per molecule), which clearly segregates the metallic and insulating phases 37 . The emergence of metallic ground state in highly doped is the Fermi wave vector and l e =hk F σ/ (e 2 n 2D ) is the mean free path of the charge carriers) 38 , suggesting that the two-dimensional hole gas can be realized at the interface between single-crystal C 8 -DNBDT-NW and IL.
The observation of metallic states in C 8 -DNBDT-NW EDLTs can be associated with the strongly correlated two-dimensional (2D) hole gas. As carriers induced by EDLT are confined in two dimension, the Coulomb interaction between holes result in a large r S , which is the ratio of the hole-hole interaction E C and Fermi energy E F : where n v is the degenerate valley, m * is the effective mass of carriers, ε is the dielectric constant of the semiconductor, and n 2D is the carrier density. Generally, when r S is larger than 1, the Coulomb interaction is not negligible and causes two-dimensional metal-insulator transition (2D MIT). Given the n v = 1, m * = 1.51 m 0 (m 0 is the mass of free holes) as an average effective mass in bc-plane of C 8 -DNBDT-NW , typical dielectric constant of OSCs 39 ε = 3 and carrier density obtained in this work n 2D = 4 × 10 13 cm −2 , we evaluate r S to be ∼ 8.5, which is comparable to those obtained for inorganic 2D systems (for example, r S ∼ 8 for Si metal-oxide-semiconductor  /(k B T )), which is small enough to activate from shallow trap states to valence band and is consistent with the weak temperature dependence of Hall carrier density n Hall at low temperatures (Fig. 3b). In contrast, µ Hall measured above n Hall ∼ 4.0 × 10 13 cm −2 increases monotonically as T decreases (Fig. 3b), where µ Hall is estimated to be 7 cm 2 V −1 s −1 at 180 K, and increases up to 26 cm 2 V −1 s −1 at 10 K.
The temperature-dependence of µ Hall can be fitted with the power law behaviour µ ∝ T −q (q > 0).
The exponent q in the power-dependence is estimated to be q = 0.24 at n Hall n Hall is estimated to be 1 × 10 14 cm −2 at 200 K and 4 × 10 13 cm −2 at 15 K. Remarkably high carrier density approaching 1 × 10 14 cm −2 at room temperature corresponds to 0.25 holes per molecule, which is the highest carrier density observed in OSCs to the best of our knowledge, and clearly shifts the Fermi energy below the top of the valence band, leading the Fermi degeneracy.
The decrease in n Hall as temperature decreases does not imply a decrease in the actual carrier density because EDL can electrostatically confine the net of holes at the interface. In fact, this trend has been often observed for many of 2D electron/hole gasses and is interpreted as the crossover in different carrier scattering mechanism, most likely the cross over from phonon scattering at higher temperature to ionized impurity scattering at lower temperatures. This interpretation does not contradict to the mobility saturation at lower temperatures (Fig. 3d). Alternatively, it is envisaged that the strong hole-hole interaction may induce a soft gap at the Fermi energy, resulting in a reduction of density-of-states. Although further researches will be necessary to fully understand electronic properties in 2DHG in OSCs interface, the presence of degenerated hole systems concomitantly with the signature of metal-insulator transition has been demonstrated for the first time in the OSC heterointerface.
This study unambiguously demonstrates a metal-insulator transition in OSCs at ambient pressure for the first time. The metallic gas state with high a carrier density of 0.25 holes per molecule and remarkably low sheet resistance of 6 kΩ is experimentally observed. In a striking contrast with the localized nature of electronic states in OSCs, the observation of 2DHGs manifests itself, such that the static disorder inevitably found in OSCs is overcome. One-shot printing of semiconductor ink at room temperature allows for the ideal production of self-assembled, two-14 dimensional molecular nanosheets with a large areal coverage, up to 100 cm 2 . The technique employed in this study to achieve remarkably high carrier density can act as framework for the exploration of electronic phase transitions in strongly correlated electronic systems in OSCs.

Sample preparation
The

Determination of Fermi level
The observation of metallic states in single-crystal C 8 -DNBDT-NW with a high carrier density exceeding 4 × 10 13 cm −2 in this work is accompanied by Fermi degeneracy. To investigate the relationship between the carrier density n and Fermi level µ ′ , we estimate the Fermi level of C 8 -DNBDT-NW from the following equation:   is observed over a wide temperature range, which is in a good agreement with the well-established Lorentz magnetoresistance. In weak magnetic fields, the magnetotransport can be described via the semiclassical Boltzmann transport framework; the positive magnetoresistance is expected with a parabolic dependence to the applied magnetic field, i.e., (R(B) − R(0))/R(0) = µ MR 2 B 2 . Here, the mobility µ MR is the only fitting parameter that can reproduce the magnitude of the positive magnetoresistance (shown in black curves). We summarize the temperature-dependence of the two mobilities determined from the Hall effect (µ Hall ) and longitudinal magnetoresistance (µ MR ) in Fig. (b). While the temperature-dependence µ Hall exhibits a saturation behaviour as temperature decreases, which is interpreted as a crossover in hole transports from phonon scattering to ionized impurity scattering, µ MR increases monotonically as temperature decreases with µ MR ∝ T −q (q = 0.87). This discrepancy can be explained by the difference in scattering mechanisms.