Hopping In Band Tails Research Articles

Fabrication of electrical semi-conductive SiCN ceramics by vat photopolymerization

The emergence of additive manufacturing (AM) enables ceramics to be fabricated with customized geometry, and polymer-derived ceramics (PDCs) has attracted growing attention owing to their irreplaceable advantages. The combination of 3D printing and PDCs endows the resultant ceramics with both precision and performance. However, AM of ceramics from preceramic polymers is still challenging, and insufficient investigation of functionality also limits the versatility of precursor and its derived ceramics. Herein, we propose a novel paradigm for 3D printing dense silicon carbonitride ceramic and study its electrical semi-conducting properties. The formulated photosensitive precursor inks could achieve self-polymerization and cross-linking under the radiation of UV light (405 nm). The green body with intricate structures is fabricated by digital light processing (DLP). Lightweight (1.79–2.08 g cm–3) and low porosity (< 5%) amorphous ceramics were obtained after thermal treatments. Processes of cross-linking, decomposition, and ceramization are monitored and analyzed. Furthermore, the semi-conducting behaviors of resultant ceramics are identified where the conductivity (10–5–10–1 S m–1) has a monotonic correspondence with the testing temperatures (25–1000 °C). The numerical relationship is fitted by exponential functions, and its conducting mechanism could be interpreted by the band tail hopping (BTH) model. This work could provide alternative solutions for the fabrication of PDCs and potentials for sensing applications.

Semiconductor‐conductor transition of pristine polymer‐derived ceramics SiC pyrolyzed at temperature range from 1200°C to 1800°C

AbstractThis paper studies the effect of pyrolysis temperature on the semiconductor‐conductor transition of pristine polymer‐derived ceramic silicon carbide (PDC SiC). A comprehensive study of microstructural evolution and conduction mechanism of PDC SiC pyrolyzed at the temperature range of 1200°C‐1800°C is presented. At relatively lower pyrolysis temperatures (1200°C‐1600°C), the carbon phase goes through a microstructural evolution from amorphous carbon to nanocrystalline carbon. The PDC SiC samples behave as a semiconductor and the electron transport is governed by the band tail hopping (BTH) mechanism in low pyrolysis temperature (1300°C); by a mixed mechanism driven by band tail hopping and tunneling at intermediate temperature (1500°C). At higher pyrolysis temperatures (1700°C‐1800°C), a percolative network of continuous turbostratic carbon is formed up along the grain boundary of the crystallized SiC. The samples demonstrate metal‐like conductive response and their resistivity increases monotonically with the increasing measuring temperature.

Electrical transport in transverse direction through silicon carbon alloy multilayers containing regular size silicon quantum dots

Electrical transport in the transverse direction has been studied through a series of hydrogenated silicon carbon alloy multilayers (SiC-MLs) deposited by plasma enhanced chemical vapor deposition method. Each SiC-ML consists of 30 cycles of the alternating layers of a nearly amorphous silicon carbide (a-SiC:H) and a microcrystalline silicon carbide (μc-SiC:H) that contains high density of silicon quantum dots (Si-QDs). A detailed investigation by cross sectional TEM reveals preferential growth of densely packed Si-QDs of regular sizes ∼4.8nm in diameter in a vertically aligned columnar structure within the SiC-ML. More than six orders of magnitude increase in transverse current through the SiC-ML structure were observed for decrease in the a-SiC:H layer thickness from 13nm to 2nm. The electrical transport mechanism was established to be a combination of grain boundary or band tail hopping and Frenkel–Poole (F-P) type conduction depending on the temperature and externally applied voltage ranges. Evaluation of trap concentration within the multilayer structures from the fitted room temperature current voltage characteristics by F-P function shows reduction up-to two orders of magnitude indicating an improvement in the short range order in the a-SiC:H matrix for decrease in the thickness of a-SiC:H layer.

Eco-friendly all-carbon paper electronics fabricated by a solvent-free drawing method

Here we report the fabrication of high-performance all-carbon temperature and infrared (IR) sensors with a solvent-free multiwalled carbon nanotube (MWCNT) trace as the sensing element and commercial graphite pencil trace as the electrical contact on recyclable and biodegradable cellulose filter paper without using any toxic materials or complex procedures. The temperature sensor shows a large negative temperature coefficient of resistance (TCR) in the range of −3100 ppm K−1 to −4900 ppm K−1, which is comparable to available commercial temperature sensors, and an activation energy of 34.85 meV. The IR sensor shows a high responsivity of 58.5 V W−1, which is greater than reported IR sensors with similar dimensions. A detailed study of the conduction mechanism in MWCNTs with temperature and the photo response with IR illumination was done and it was found that the conduction is due to thermally assisted hopping in band tails and the photo response is bolometric in nature. The successful fabrication of these sensors on cellulose filter paper with a comparable performance to existing components indicates that it is possible to fabricate high-performance electronics using low-cost, eco-friendly materials without the need for expensive clean-room processing techniques or harmful chemicals.

Frequency-dependent conductive behavior of polymer-derived amorphous silicon carbonitride

The AC conductive behavior of a polymer-derived amorphous silicon carbonitride ceramic was systemically studied. The conductivity exhibited a frequency-dependent switch: at low frequencies, the conductivity is constant and independent of frequency; while at high frequencies, the conductivity increases with frequency, showing a strong relaxation process. Both the frequency-independent conductivity and the characteristic frequency for the relaxation follow the Arrhenius relation with respect to the annealing temperature and follow a band-tail hopping process with respect to the testing temperature. XPS analysis revealed that a sp3–sp2 transition took place in the free-carbon phase of the material with increasing annealing temperature. The activation energy of the transition is similar to those for the Arrhenius relations. The following conductive mechanisms were proposed to account for the observed behaviors: the frequency-independent conductivity in the low frequency region is dominated by a long-distance transport of charge carriers via matrix-free carbon path, enhanced by an electric-field concentration effect; while the frequency-dependent conductivity in the high frequency region is dominated by a interfacial polarization process governed by charge carrier relaxation within the free-carbon phase.

Low‐temperature transport of charge carriers in InGaN/GaN multiple quantum well light‐emitting diodes

AbstractThe results of experimental investigation of forward current‐voltage characteristics of InGaN/GaN multiple quantum well light‐emitting diodes are presented. A new model for explaining the complex current dependence on voltage is proposed. The model is based on the assumption of space charge limited current, and ballistic overflow of electrons through the multiple quantum well region. It is shown that electrons are captured in the shallow traps while transferring through the active region. The results of measurements indicate that the activation energy of traps decreases with a temperature decrease, which corresponds to the theory of hopping in exponential band tails.

The effect of grain boundaries and adsorbates on the electrical properties of hydrogenated ultra nano crystalline diamond

The results of a comprehensive study on the temperature dependence of the electrical properties of hydrogenated and air exposed undoped UNCD layers following heating/cooling cycles are presented. The results clearly show that, in contrast to hydrogenated and air exposed single crystal type IIa diamond, which exhibits a clear highly conductive p-type surface layer, the electrical properties of hydrogen and H 2O exposure of UNCD are determined by the properties of the entire layer. The changes in the electrical conductivity of UNCD as a result of heating are governed by two different processes: (i) Loss of water from the external surface that takes place at about 150 °C. This process is reversible, reviving the electrical properties upon exposure to humidity, just like in single crystalline diamond.(ii) Modification of the inter-grain material, which occurs at higher temperatures possibly due to H diffusion and passivation of some dangling bonds in the inter-grain material. This increases the resistivity in an irreversible manner. The conduction mechanism in the inter-grain material is characterized by variable range hopping in band tails thus indirectly proving that the material between the grains is some kind of amorphous carbon.

Clustering in Amorphous Carbon Films Probed by the Charge Transport and Structural Studies

The influence of deposition energy on the electron transport character in amorphous carbon films containing silicon and oxygen was studied. It is shown that the dominant mechanism of the conductivity over the entire range of deposition energies at the applied electric fields up to 5·105 V/cm is a bandtail hopping of the charge carriers along the transport energy level. The role of sp2 clustering enhancement at high deposition energies in the electron transport modification is considered.

Scaling analysis of field‐enhanced bandtail hopping transport in amorphous carbon nitride

AbstractHopping transport within a bandtail distribution of localized electronic states has been investigated in amorphous carbon nitride (a‐C1–x Nx :H, x = 0.23) as a function of temperature T and electric field F. The conductivity σ follows Mott's law in the ohmic regime, i.e. ln (σohmic) varies linearly with T–1/4, while at higher field, a scaling law, ln (σ /σohmic) = φ [FS /T ] with S = 0.67 (±0.05), is found. Data are fully consistent with a field‐enhanced bandtail hopping (FBTH) model in which the effective temperature concept describes the non‐equilibrium occupation probability of tail states. A “filling rate” method, considering forward non‐activated hopping transitions, is developed to analyze the high field regime of FBTH. For an exponential distribution with disorder energy E0, increasing F shifts the transport energy EDL towards shallower tail states, with a density of states N (EDL) ∼ (F)3 (E0)–4. In this model, FBTH is parametrized using ln σ (T, F) vs T–1/4 plots, which provide field‐dependent apparent values of prefactor (ln σ00) and slope (T01/4). As F increases, both parameters strongly decrease. This behavior (observed in a‐C1–x Nx :H, x = 0.23, for F &gt; 5 × 104 V cm–1) is a signature of band tail hopping transport. Our FBTH model predicts a minimum value $ \sigma^{00}_{\rm min} $ of σ00(F), which is indeed observed in a‐C1–x Nx :H (x = 0.23) for T &lt; 70 K ($ kT^*_{\rm eff} $ ≈ 10–6 S cm–1 at Fmin ≈ 3 × 105 V cm–1). Near Fmin, kT *eff = (1/kTeff – 1/E0)–1 is parametrized by kT *eff ∼ Fq. The value of q that best reproduces the experimental results, q = 0.7 ± 0.1, is consistent with the scaling exponent S = 0.67 and with the density of states parameters deduced from the Ohmic regime. Hence, this “filling rate” method applied to FBTH transport appears to be very useful to analyze the apparent prefactor σ00(F) and to derive the effective temperature Teff(T, F) which governs bandtail states occupation and FBTH conductivity. (© 2007 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Disorder and localization in bandtail hopping transport: experiments and concepts

This review describes the main transport experiments (including Ohmic and nonlinear transport in both dc and ac regimes) and related concepts which can be used to derive quantitative information on the localized electronic states above the Fermi level and in the bandtails, in low carrier mobility materials governed by hopping conductivity. For bandtail hopping, a model based on the filling rate of electronic states near the preferred transport path shows a sharp decrease of the hopping mobility with increasing bandtail disorder. While the slope T 1/4 0, derived from lnσ vs T −1/4 plots, is weakly sensitive to the shape of the DOS distribution, the prefactor σ ∘; ∘; values are extremely sensitive to bandtail disorder; uniform and exponential distributions can be discriminated experimentally (σ ∘; ∘; ≫ 102 S.cm−1 for bandtail hopping). As an illustration, the localized π states distribution in amorphous carbon nitride a-C1−x N x :H (x=0.23) is investigated in sandwich devices. Using a wide range of temperatures, electric fields and ac frequencies, several methods are proposed to derive some DOS parameters: density of states at the Fermi level, localization radius and disorder energy of the exponential bandtail distribution. In the field-enhanced bandtail hopping and in the activationless regimes, both apparent slope T 1/4 0 and prefactor σ ∘; ∘; values are also properly described. An analytical model, based on the filling rate of localized states near the preferred transport energy, shows that the (F S /T) scaling properties of nonlinear conductivity σ(F, T) (with S ≈; 2/3 in a-C1−x N x :H) are related to the field-dependent effective temperature describing the non-equilibrium distribution of π; ∗; electrons in the bandtail. In ac transport, the characteristic response time τ(F, T) shows a linear lnτ vs T −1/4 behaviour, with a smaller T-dependence as the field strength increases, closely related to the filling rate obtained from the dc hopping transport.

IMPEDANCE CHARACTERIZATION OF DIELECTRIC AND SEMICONDUCTING MATERIALS WITH ORGANIC CAPACITORS FOR ORGANIC TRANSISTORS

A new characterization method based on impedance frequency response analysis at different temperatures has been developed to assess and identify the dielectric and semiconductor materials for organic field-effect transistors (OFET). This method can not only characterize simultaneously dielectric and conductive behaviors of materials but also distinguish individual contributions to electrical conduction or to polarization from layers such as dielectric layer, semiconductor layer, and interfaces in OFET. Two kinds of materials, Urathan and DuPont 5018A as dielectric materials have been used to make a multilayer organic capacitor. It has been observed that Urathan, due to its lower conductivity, non-metallic conduction behavior at high temperature, and lower interfacial resistance, is more suitable as dielectric layer for OFET. Urathan appears an enhancement in conductivity by heating following an Arrhenius law with an activation energy transition from 0.002 to 0.24 eV at ~307 K, which originates from band tail hopping that occurs around the Fermi edge. At ~314 K, a dielectric transition also occurs, which is interpreted as a combination of electron polarization associated to the band tail hopping. The materials were used to fabricate OEFT, which performance was in agreement with that obtained from impedance analysis of the organic capacitor.

Optical and electronic properties of plasma-deposited hydrogenated amorphous carbon nitride and carbon oxide films

A comparative investigation of the nanostructural vs. electronic properties of DECR plasma deposited carbon nitride and carbon oxide alloys provides new insights in the changes of the sp 2-clusters and sp 3 matrix resulting from the decrease in the average coordination number, as N and O atoms are increasingly incorporated. This review emphasizes the similar incorporation efficiency of N and O atoms in the carbon matrix as a function of the gas phase mixture (C 2H 2, N 2) or (C 2H 2, O 2), the decrease in the alloy density deduced from Nuclear Reaction Analysis and optical measurements, and the better ordering of the sp 2-hybridized carbon phase evidenced by Raman studies. Opposite variations in the ohmic conductivity σ( T), apparent activation energy E ACT and hopping transport parameters (related to the localization parameter N( E F) γ −3) are found as a function of the (N/N+C) and (O/O+C) stoichiometries. This surprising result gives evidence of some competition between the improved ordering of the sp 2 phase shown by Raman spectra in both alloys (stronger in a-C 1− x N x :H with a large influence of aromatic clusters) and the increasing polymer-like character of the sp 3 matrix, dominant in a-C 1− x O x :H films where the weaker connectivity of the sp 3 matrix is attributed to two-fold bonded oxygen atoms C–O–C and terminating C O groups. The role of π and π* states localization is discussed in the context of bandtail hopping conductivity.

Analytical derivation of the effective temperature for field-dependent hopping conductivity

The electric-field enhancement of hopping conductivity in amorphous solids can be described in terms of an effective temperature T eff given by for hopping, at a temperature T and field F, within a uniform distribution of electronic states with localization length γ−1. We have derived this expression analytically and find at low fields a value for C of 1/21/2, which is consistent with the F-independent value C = 0.67 previously obtained numerically for band-tail hopping. With increasing electric field, the decrease in C(F) matches the hopping transport characteristics in amorphous semiconductors (hydrogenated amorphous silicon and hydrogenated amorphous carbon nitride) better than previous numerical simulations.

Field-enhanced electrical transport mechanisms in amorphous carbon films

In order to investigate the localized electronic states in hydrogenated amorphous carbon (a-C : H) films, the temperature and electric field dependences of the current density have been measured in low-field coplanar (Al/a-C : H/Al) and in high-field transverse (TiW/a-C : H/TiW) geometries. The very-low-field conductivity σ = σ00 exp[−(T 0/T)1/4] reveals a band-tail hopping transport mechanism in an Ohmic regime (at least for films above 20 nm thickness) while, for electric field values F > 4 × 103 V cm−1, a different behaviour is evidenced of the form with a transition in the exponent value from n = 2 at low fields (F<3 × 104 V cm−1) towards n ⩾̸ 1/2 at high fields (F > 3 × 105 V cm−1). This field enhancement of electrical transport can be interpreted as arising from either a three-dimensional Poole–Frenkel effect for charged empty defects, or field-assisted hopping out of neutral empty defects (the Apsley–Hughes hopping model). Although a clear discrimination between both models would require very high electric fields (F > 8γkT/e, where γ −1 is the localized wavefunction radius), the Apsley–Hughes model describes accurately the experimental temperature-dependent and field-enhanced transport within localized states (scaling as eF/2γkT with γ −1 = 2.8 ± 0.4 nm) and is also consistent with the variable-range hopping mechanism observed in the Ohmic regime.

Dielectric relaxation and transition of porous silicon

Dielectric impedance measurements of porous silicon within the frequency range of 50 Hz–1.0 MHz and temperature range of 298–798 K revealed three semicircles in a Cole–Cole plot when the temperature is raised to 773 K; they are thought to correspond to contributions from the grain interior, grain boundary, and electrode/film interface, respectively. The enhancement in conductivity by heating follows an Arrhenius law with an activation energy transition from 0.07 to 0.79 eV at ∼565 K, which originates from band tail hopping that occurs around the Fermi edge. At a critical temperature, a high degree of dispersion in the real and imaginary parts of the permittivity also occurs at low frequencies. This dispersion behavior is interpreted as a combination of electron-lattice polarization associated to the band tail hopping and the crystal field weakening due to thermal expansion.

Physics of bandtail hopping in disordered carbons

Electrical transport data in disordered forms of carbon are reviewed and compared with the bandtail hopping characteristics obtained from a modeling of phonon-assisted tunneling within an exponential density of states distribution. In the weak electric field limit, the dependence of the effective carrier mobility and the ohmic conductivity on the localization parameter N( E F)γ −3 and the disorder parameter E 0 are computed using the filling rate method and the Kubo formula. Most of the data for amorphous carbon-based alloys and ion-implanted diamond match the bandtail hopping predictions and the changes in the localization parameter can thus be investigated as a function of the synthesis conditions. For nanotube mats or cluster beam deposited films, the situation is more complex and transport data probably reflect the heterogeneity of the microstructure.

Effect of the RF power and deposition temperature on the electrical and vibrational properties of carbon nitride films

We present a detailed investigation of the effect of the radio frequency (RF) power and substrate temperature on the electrical and vibrational properties of amorphous carbon nitride films prepared by radio frequency magnetron sputtering using pure N 2 gas and a graphite target. A combination of electrical conductivity, visible transmission, infrared and Raman spectroscopy measurements is applied to fully characterise the films. The optical gap decreases with increasing temperature or RF power to a minimum value almost equal to zero. An important increase in the room electrical conductivity by approximately ten orders of magnitude (5×10 −9–10 2 Ω −1 cm −1) is also observed in the same range of RF power and temperature. The dependence on temperature of the conductivity is better explained in terms of bandtail hopping mechanism rather than a thermally activated process. The results as a whole are discussed in comparison with the earlier ones in the field.

Electronic Localization and Bandtail Hopping Charge Transport

Our previous modeling of hopping in localized bandtails has improved the description of electrical transport in amorphous carbon films and elemental amorphous semiconductors. This model is further developed to understand the role of the wavefunction localization radius γ -1 and density of states (DOS) distribution N(E) on the T dependence of the conductivity and the thermopower in disordered solids. Using values of the localization parameter LP = N(E F ) γ -3 in the range from 10 -4 to 1 eV -1 , our simulations show that: (i) The assumption of extremely low LP values made in previous works is often irrelevant for comparison with experiments. (ii) For low temperatures or large LP values, a linear relation holds between the dominant transport energy (E t - E F ) and temperature (with a stronger dependence as LP decreases) while a logarithmic dependence is obtained in the high-T range for small LP values. (iii) In the weak localization condition, a T-independent thermopower S(T) is predicted with an absolute value of eS/k (LP) -1/3 . (iv) The relationship σT 1/2 = σ 00 exp (-(T 0 /T) 1/4 holds, as expected for 3D hopping, over a wide temperature range (50-500 K); using the LP value as a parameter, the positive linear correlation between In (σ 00 ) and T 1/4 0 is a signature of an exponential localized bandtail distribution, clearly incompatible with Mott's hypothesis for 'Variable Range Hopping' in an energy-independent DOS distribution near the Fermi level.

Dynamics of Carrier Hopping in Exponential Band Tails of Quasi‐One‐Dimensional Systems in Electric Field

AbstractThe dynamics of carrier hopping in band tails of a quasi‐one‐dimensional (QOD) system is studied in the presence of temperature and electic field. A method is used in which it is assumed that localized states are distributed randomly in both space and energy coordinates and the hopping of carriers occurs in both coordinates. The exponential form of the density of states for band tails is considered. The hopping rate and the time dependent demarcation energy are calculated in the activated and nonactivated relaxation regimes. The hopping rate varies with the electric field as (1  β2)−1/γ and exp [(1  β2)] for the AR and the NAR regions, respectively. Here β and γ are directly proportional to the electric field and the temperature, respectively. Numerical calculations are performed for the hopping rate and the demarcation energy as a function of β and γ for both regions.

Electric-field dependence of low-temperature recombination in a-Si:H.

Detailed results on the quenching of photoluminescence (PL) by electric fields in hydrogenated amorphous silicon (a:Si:H) are presented. Applying a modulated voltage to films with a sandwich structure results in a typical quenching value of 40% at an electric field of ${10}^{5}$ V/cm and a temperature of 80 K. By analyzing the photocurrent transients we observe a non-exponential dielectric relaxation. We measure the field quenching as a function of excitation intensity and temperature. Below a generation rate of \ensuremath{\sim}${10}^{19}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$ ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$ the field quenching is constant, whereas above this value it gradually decreases. This phenomenon is interpreted in terms of a transition from geminate to nongeminate recombination. Considering the temperature dependence of the PL quenching we observe almost identical dependence on electric field above \ensuremath{\sim}80 K. Below 80 K the quenching is weak. The experimental data are discussed on the basis of various models, including the Poole-Frenkel effect, carrier separation in extended states, and field induced hopping in tail states (the effective temperature approach). Good agreement between experiment and theory is provided by the latter model with a linear dependence of the effective temperature on electric field and temperature, in contrast to the relationship previously derived by Marianer and Shklovskii. We also performed time resolved PL measurements as a function of electric field. We observe a shift of the peak of the lifetime distribution around 10 \ensuremath{\mu}s at 80 K with electric field to shorter times, indicating an enhancement of nonradiative recombination processes. At 10 K the millisecond lifetime, which is attributed to a mostly radiative transition, shows a slight increase with field. This is supposed to be due to separation of electrons and holes by field induced hopping in band tails, thereby increasing the electron-hole distance.