Amorphous Indium Oxide Films Research Articles

Nucleation and grain growth in low-temperature rapid solid-phase crystallization of hydrogen-doped indium oxide

Nucleation and grain growth are discussed as a means of clarifying the mechanism of the rapid solid-phase crystallization (SPC) process of H2-doped amorphous indium oxide (InO x :H) films. H2-doping in InO x :H films reduced nucleation density at 250 °C from 4.1 to 1.1 μm−2, resulting in an increase in grain size and Hall mobility of the polycrystalline (poly)-InO x :H films. Lateral growth rate from the nucleus was estimated to be 220 nm min−1 for the InO x :H film at 250 °C. Thus, an amorphous InO x :H film could be converted to a poly-InO x :H film within 3 min owing to a fast lateral growth rate from the nucleus. Almost the same grain size, Hall mobility, and carrier density could be obtained from the poly-InO x :H films after annealing at 250 °C for only 3 min irrespective of the ramp rate. The results demonstrated the wide range of the processing window for SPC for poly-InO x :H films.

1/f Noise During Thermal Treatment of Amorphous Films

Flicker noise is a sensitive tool for probing the dynamics of two‐level systems. Herein, this technique is employed to study the dependence of conductance noise on disorder for two versions of amorphous indium oxide films. The disorder in these substances may be tuned by thermal treatment that is manifested by enhanced conductivity. Structural studies reveal that this is mainly due to densification of the material. A similar reduction of volume has been achieved in glasses when subjected to high pressures. Both protocols, pressure and heat treatment, initiate nonequilibrium state that slowly relaxes. This relaxation is reflected in the sample conductivity and its optical transmission as a monotonic change. The magnitude of 1/f noise during these events turns out to fluctuate appreciably following changes in the sample conductance caused by thermal treatment. This may overshadow the tendency of the noise level to increase with disorder. Possible reasons for the fluctuations of noise levels in highly disordered systems are discussed.

Relation between disorder and homogeneity in an amorphous metal

Disorder and homogeneity are two concepts that refer to spatial variation of the system potential. In condensed-matter systems disorder is typically divided into two types; those with local parameters varying from site to site (diagonal disorder) and those characterized by random transfer-integral values (off-diagonal disorder). Amorphous systems in particular exhibit off-diagonal disorder due to random positions of their constituents. In real systems diagonal and off-diagonal disorder may be interconnected. The formal depiction of disorder as local deviations from a common value focuses attention on the short-range components of the potential-landscape. However, long range potential fluctuation are quite common in real systems. In this work we seek to find a correlation between disorder and homogeneity using amorphous indium-oxide films with different carrier-concentrations and with different degree of disorder. Thermal treatment is used as a means of fine tuning the system disorder. In this process the resistance of the sample decreases while its amorphous structure and chemical composition is preserved. The reduced resistivity affects the Ioffe-Regel parameter that is taken as a relative measure of disorder in a given sample. The homogeneity of the system was monitored using inelastic light-scattering. This is based on collecting the Raman signal from micron-size spots across the sample. The statistics of these low-energy data are compared with the sample disorder independently estimated from transport measurements. The analysis establishes that heterogeneity and disorder are correlated.

Microstructure and the boson peak in thermally treated InxO films

We report on the correlation between the boson-peak and structural changes associated with thermally-treating amorphous indium-oxide films. In this process, the resistance of a given sample may decrease by a considerable margin while its amorphous structure is preserved. In the present study, we focus on the changes that result from the heat-treatment by employing electron-microscopy, X-ray, and Raman spectroscopy. These techniques were used on films with different stoichiometry and thus different carrier-concentration. The main effect of heat-treatment is material densification, which presumably results from elimination of micro-voids. The densified system presents better wavefunction-overlap and more efficient connectivity for the current flow. X-ray, and electron-beam diffraction experiments indicate that the heat-treated samples show significantly less spatial heterogeneity with only a moderate change of the radial-distribution function metrics. These results are consistent with the changes that occur in the boson-peak characteristics due to annealing as observed in their Raman spectra.

Electron glass effects in amorphous NbSi films

We report on non equilibrium field effect in insulating amorphous NbSi thin films having different Nb contents and thicknesses. The hallmark of an electron glass, namely the logarithmic growth of a memory dip in conductance versus gate voltage curves, is observed in all the films after a cooling from room temperature to 4.2~K. A very rich phenomenology is demonstrated. While the memory dip width is found to strongly vary with the film parameters, as was also observed in amorphous indium oxide films, screening lengths and temperature dependence of the dynamics are closer to what is observed in granular Al films. Our results demonstrate that the differentiation between continuous and discontinuous systems is not relevant to understand the discrepancies reported between various systems in the electron glass features. We suggest instead that they are not of fundamental nature and stem from differences in the protocols used and in the electrical inhomogeneity length scales within each material.

Structural Dynamics in Thermal Treatment of Amorphous Indium Oxide Films

Thermal treatment of amorphous indium oxide (InxO) films is used in various basic studies as a means of tuning the disorder perceived by the electronic system. In this process, the resistance of a given sample decreases, whereas its amorphous structure and chemical composition is preserved. The main effect of the process is an increase in the system density, which, in turn, leads to improved interatomic overlap manifested as improved conductivity. A similar effect has been observed in studies of other amorphous systems that were subjected to pressure. Herein, the Raman spectra of amorphous InxO change in response to thermal treatment in a similar way as in pressure experiments performed on other disordered and amorphous systems. A study of how thermal treatment changes the system dynamics is presented by monitoring the resistance versus time of InxO films following various stages of thermal treatment. The time dependence of the sample resistance fits the stretched exponential law with parameters that change systematically with repeated thermal treatment cycles. The implications of these results to slow dynamics phenomena that are governed by the Kohlrausch's law are discussed.

Screening the Coulomb interaction and thermalization of Anderson insulators

Long range interactions are relevant for a wide range of phenomena in physics where they often present a challenge to theory. In condensed matter, the interplay of Coulomb interaction and disorder remains largely an unsolved problem. In two dimensional films the long-range part of the Coulomb interaction may be screened by a nearby metallic overlay. This technique is employed in this work to present experimental evidence for its effectiveness in limiting the spatial range of the Coulomb interaction. We use this approach to study the effects of the long-range Coulomb interaction on the out-of-equilibrium dynamics of electron-glasses using amorphous indium-oxide films. The results demonstrate that electronic relaxation times, extending over thousands of seconds, do not hinge on the long-range Coulomb interaction nor on the presence of a real gap in the density of states. Rather, they emphasize the dominant role played by disorder in controlling the slow thermalization processes of Anderson insulators taken far from equilibrium.

Infinite-randomness fixed point of the quantum superconductor-metal transitions in amorphous thin films

The magnetic-field-tuned quantum superconductor-insulator transitions of disordered amorphous indium oxide films are a paradigm in the study of quantum phase transitions, and exhibit power-law scaling behavior. For superconducting indium oxide films with low disorder, such as the ones reported on here, the high-field state appears to be a quantum-corrected metal. Resistance data across the superconductor-metal transition in these films are shown here to obey an activated scaling form appropriate to a quantum phase transition controlled by an infinite randomness fixed point in the universality class of the random transverse-field Ising model. Collapse of the field-dependent resistance vs. temperature data is obtained using an activated scaling form appropriate to this universality class, using values determined through a modified form of power-law scaling analysis. This exotic behavior of films exhibiting a superconductor-metal transition is caused by the dissipative dynamics of superconducting rare regions immersed in a metallic matrix, as predicted by a recent renormalization group theory. The smeared crossing points of isotherms observed are due to corrections to scaling which are expected near an infinite randomness critical point, where the inverse disorder strength acts as an irrelevant scaling variable.

Collective energy gap of preformed Cooper pairs in disordered superconductors

In most superconductors the transition to the superconducting state is driven by the binding of electrons into Cooper-pairs. The condensation of these pairs into a single, phase coherent, quantum state takes place concomitantly with their formation at the transition temperature, $T_c$. A different scenario occurs in some disordered, amorphous, superconductors: Instead of a pairing-driven transition, incoherent Cooper pairs first pre-form above $T_c$, causing the opening of a pseudogap, and then, at $T_c$, condense into the phase coherent superconducting state. Such a two-step scenario implies the existence of a new energy scale, $\Delta_{c}$, driving the collective superconducting transition of the preformed pairs. Here we unveil this energy scale by means of Andreev spectroscopy in superconducting thin films of amorphous indium oxide. We observe two Andreev conductance peaks at $\pm \Delta_{c}$ that develop only below $T_c$ and for highly disordered films on the verge of the transition to insulator. Our findings demonstrate that amorphous superconducting films provide prototypical disordered quantum systems to explore the collective superfluid transition of preformed Cooper-pairs pairs.

Low-temperature anomaly in disordered superconductors near B c2 as a vortex-glass property.

Strongly disordered superconductors in a magnetic field display many characteristic properties of type-II superconductivity—except at low temperatures, where an anomalous linear temperature dependence of the resistive critical field Bc2 is routinely observed. This behavior violates the conventional theory of superconductivity, and its origin has posed a long-standing puzzle. Here we report systematic measurements of the critical magnetic field and current on amorphous indium oxide films with various levels of disorder. Surprisingly, our measurements show that the Bc2 anomaly is accompanied by mean-field-like scaling of the critical current. Based on a comprehensive theoretical study we argue that these observations are a consequence of the vortex-glass ground state and its thermal fluctuations. Our theory further predicts that the linear-temperature anomaly occurs more generally in both films and disordered bulk superconductors, with a slope that depends on the normal-state sheet resistance, which we confirm experimentally.

Quantum Criticality at the Superconductor-Insulator Transition Probed by the Nernst Effect.

The superconductor-insulator transition (SIT) is an excellent example of a quantum phase transition at zero temperature, dominated by quantum fluctuations. These are expected to be very prominent close to the quantum critical point. So far, most of the experimental studies of the SIT have concentrated on transport properties and tunneling experiments that provide indirect information on criticality close to the transition. Here we present an experiment uniquely designed to study the evolution of quantum fluctuations through the quantum critical point. We utilize the Nernst effect, which has been shown to be effective in probing superconducting fluctuation. We measure the Nernst coefficient in amorphous indium oxide films tuned through the SIT and find a large signal on both the superconducting and the insulating sides, which peaks close to the critical point. The transverse Peltier coefficient α_{xy}, which is the thermodynamic quantity extracted from these measurements, follows quantum critical scaling with critical exponents ν∼0.7 and z∼1. These exponents are consistent with a clean X-Y model in 2+1 dimensions.

Transition to exponential relaxation in weakly disordered electron glasses

The out-of-equilibrium excess conductance of electron-glasses typically relaxes with a logarithmic time-dependence. Here it is shown that the log(t) relaxation of a weakly-disordered amorphous indium-oxide films crosses-over asymptotically to an exponential dependence. This allows assigning a well-defined relaxation-time t' for a given system-disorder (characterized by the Ioffe-Regel parameter). Near the metal-insulator transition, t' obeys the scaling relation with the same critical disorder where the zero-temperature conductivity of this system vanishes. The latter defines the position of the disorder-driven metal-to-insulator transition (MIT) which is a quantum-phase-transition. In this regard the electron-glass differs from classical-glasses such as the structural-glass and spin-glass. The ability to experimentally assign an unambiguous relaxation-time allows us to demonstrate the steep dependence of the electron-glass dynamics on carrier-concentration.

Instability of Insulators near Quantum Phase Transitions.

Thin films of amorphous indium oxide undergo a magnetic field driven superconducting to insulator quantum phase transition. In the insulating phase, the current-voltage characteristics show large current discontinuities due to overheating of electrons. We show that the onset voltage for the discontinuities vanishes as we approach the quantum critical point. As a result, the insulating phase becomes unstable with respect to any applied voltage making it, at least experimentally, immeasurable. We emphasize that unlike previous reports of the absence of linear response near quantum phase transitions, in our system, the departure from equilibrium is discontinuous. Because the conditions for these discontinuities are satisfied in most insulators at low temperatures, and due to the decay of all characteristic energy scales near quantum phase transitions, we believe that this instability is general and should occur in various systems while approaching their quantum critical point. Accounting for this instability is crucial for determining the critical behavior of systems near the transition.

Nonequilibrium restoration of duality symmetry in the vicinity of the superconductor-to-insulator transition

The magnetic field driven superconductor to insulator transition in thin films was theoretically analyzed via a vortex-charge duality transformation applied to the Hamiltonian. Vortices condensation was conjectured as the underline physical mechanism of the insulating phase. Experimental evidence supported duality symmetry across the magnetic-field driven superconductor to insulator transition in amorphous Indium Oxide films. Counterintuitively, duality symmetry is broken at low temperatures where the insulating phase develops strongly non linear current-voltage characteristics. Here, we follow the breakdown of duality symmetry down to very low temperatures and demonstrate the restoration of duality symmetry out of equilibrium.

Memory versus irreversibility in the thermal densification of amorphous glasses

We report on dynamic effects associated with thermally-annealing amorphous indium-oxide films. In this process the resistance of a given sample may decrease by several orders of magnitude at room-temperatures, while its amorphous structure is preserved. The main effect of the process is densification - increased system density. The study includes the evolution of the system resistivity during and after the thermal-treatment, the changes in the conductance-noise, and accompanying changes in the optical properties. The sample resistance is used to monitor the system dynamics during the annealing period as well as the relaxation that ensues after its termination. These reveal slow processes that fit well a stretched-exponential law, a behavior that is commonly observed in structural glasses. There is an intriguing similarity between these effects and those obtained in high-pressure densification experiments. Both protocols exhibit the "slow spring-back" effect, a familiar response of memory-foams. A heuristic picture based on a modified Lennard-Jones potential for the effective interparticle interaction is argued to qualitatively account for these densification-rarefaction phenomena in amorphous materials whether affected by thermal-treatment or by application of high-pressure.

Low temperature, solution-processed ambipolar field-effect transistors based on polymer/self-assembled monolayer modified InOx hybrid structures for balanced hole and electron mobilities exceeding 1 cm2 V−1 s−1

Ambipolar field-effect transistors (FETs) based on solution-processed organic-inorganic bilayer structures were investigated. An amorphous indium oxide (InOx) film, as the n-type semiconducting layer, was prepared with an environmentally friendly method and annealed at a low temperature; and a low band-gap (LBG) donor–acceptor (D–A) conjugated polymer, FBT-Th4(1,4), was spin-coated on the InOx film as the p-type semiconducting layer. To improve the p-type mobility, a self-assembled monolayer (SAM) of octadecyl-phosphonic acid was introduced to modify the surface of InOx. The ambipolar FETs showed high and well-balanced hole and electron mobilities of 1.1 and 1.5 cm2 V−1 s−1, respectively. Furthermore we found that ambipolar FETs could be integrated into functional complementary metal oxide semiconductor (CMOS)-like inverters.

Self-duality and a Hall-insulator phase near the superconductor-to-insulator transition in indium-oxide films

We combine measurements of the longitudinal (ρxx) and Hall (ρxy) resistivities of disordered 2D amorphous indium-oxide films to study the magnetic-field tuned superconductor-to-insulator transition (H-SIT) in the T --> 0 limit. At the critical field, Hc, the full resistivity tensor is T independent with ρxx(Hc) = h/4e(2) and ρxy(Hc) = 0 within experimental uncertainty in all films (i.e., these appear to be "universal" values); this is strongly suggestive that there is a particle-vortex self-duality at H = Hc. The transition separates the (presumably) superconducting state at H < Hc from a "Hall-insulator" phase in which ρxx --> ∞ as T --> 0 whereas ρxy approaches a nonzero value smaller than its "classical value" H/nec; i.e., 0 < ρxy < H/nec. A still higher characteristic magnetic field, Hc* > Hc, at which the Hall resistance is T independent and roughly equal to its classical value, ρxy ≈ H/nec, marks an additional crossover to a high-field regime (probably to a Fermi insulator) in which ρxy > H/nec and possibly diverges as T --> 0. We also highlight a profound analogy between the H-SIT and quantum-Hall liquid-to-insulator transitions (QHIT).

High-field termination of a Cooper-pair insulator

We conducted a systematic study of the disorder dependence of the termination of superconductivity, at high magnetic fields $(B)$, of amorphous indium oxide films. Our lower disorder films show conventional behavior where superconductivity is terminated with a transition to a metallic state at a well-defined critical field, ${B}_{\mathrm{c}2}$. Our higher-disorder samples undergo a $B$-induced transition into a strongly insulating state, which terminates at higher $B$'s forming an insulating peak. We demonstrate that the $B$ terminating this peak coincides with ${B}_{\mathrm{c}2}$ of the lower disorder samples. Additionally, we show that, beyond this field, these samples enter a different insulating state in which the magnetic field dependence of the resistance is weak. These results provide crucial evidence for the importance of Cooper-pairing in the insulating peak regime.

Thermalization processes in interacting Anderson insulators

This paper describes experiments utilizing a unique property of electron-glasses to gain information on the fundamental nature of the interacting Anderson-localized phase. The methodology is based on measuring the energy absorbed by the electronic system from alternating electromagnetic fields as function of their frequency. Experiments on three-dimensional (3D) amorphous indium-oxide films suggest that, in the strongly localized regime, the energy spectrum is discrete and inelastic electron-electron events are strongly suppressed. These results imply that, at low temperatures, electron thermalization and finite conductivity depend on coupling to the phonon bath. The situation is different for samples nearing the metal-insulator transition; in insulating samples that are close to the mobility-edge, energy absorption persists to much higher frequencies. Comparing these results with previously studied 2D samples [Ovadyahu, Phys. Rev. Lett., 108, 156602 (2012)] demonstrates that the mean-level spacing (on a single-particle basis) is not the only relevant scale in this problem. The possibility of de-localization by many-body effects and the relevance of a nearby mobility-edge (which may be a many-body edge) are discussed.

Electron glass in a three-dimensional system

We report on non-equilibrium transport features observed in experiments using three-dimensional amorphous indium-oxide films. It is demonstrated that all the features that characterize intrinsic electron-glasses which heretofore were seen in two-dimensional samples are also observed in field-effect measurements of systems that exhibit three-dimensional variable-range-hopping. In particular, a memory-dip is observed in samples configured with gate. The memory-dip width and magnitude support models that associate the phenomenon with the Coulomb-gap. The memory-dip and the glassy effects disappear once the quenched disorder in the system is reduced and the system becomes diffusive. This happens when the Ioffe-Regel dimensional parameter k_{F}l exceeds 0.3 which is the critical value for the metal-to-insulator transition in all versions of the amorphous indium-oxides [Phys. Rev. B 86, 165101 (2012)]. This confirms that being in the Anderson localized phase is a pre-requisite for observing the memory-dip and the associated glassy effects. The results of the gating experiments suggest that the out-of equilibrium effect caused by inserted charge extend over spatial scales considerably larger than the screening length.