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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Unconventional Error Cancellation Explains the Success of Hartree–Fock Density Functional Theory for Barrier Heights

Energy barriers, which control the rates of chemical reactions, are seriously underestimated by computationally efficient semilocal approximations for the exchange-correlation energy. The accuracy of a semilocal density functional approximation is strongly boosted for reaction barrier heights by evaluating that approximation non-self-consistently on Hartree–Fock electron densities, which has been known for ~30 years. Here, the conventional explanation is that the Hartree–Fock theory yields the more accurate density. This work presents a benchmark Kohn–Sham inversion of accurate coupled-cluster densities for the reaction H 2 + F → HHF → H + HF and finds a strong, understandable cancellation between positive (excessively overcorrected) density-driven and large negative functional-driven errors (expected from stretched radical bonds in the transition state) within this Hartree–Fock density functional theory. This confirms earlier conclusions (Kaplan, A. D., et al. J. Chem. Theory Comput. 2023, 19, 532–543) based on 76 barrier heights and three less reliable, but less expensive, fully nonlocal density functional proxies for the exact density.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Temperature dependent barrier height and ideality factor of electrodeposited n-CdSe/Cu Schottky barrier diode

This article reports the measurement of temperature-dependent barrier height and ideality factor of n-CdSe/Cu Schottky barrier diode. The Cadmium Selenide (CdSe) thin films have been deposited by simple electrodeposition technique. The XRD measurements ravels the deposited single phase CdSe films are highly oriented on (002) plane and the average particle size has been calculated to be ~18 nm. From SEM characterization, it is clear that the surface of CdSe thin films are continuous, homogeneous and the film is well adhered to the substrate and consists of fine grains which are irregular in shape and size. Current-Voltage characteristics have been measured at different temperatures in the range (298 K – 353 K). The barrier height and ideality factor are found to be strongly temperature dependent. The inhomogenious barrier height increases and ideality factor decreases with increase in temperature. The expectation value has been calculated and its value is 0.30 eV.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Reducing the Barrier Height in Organic Transistors

Abstract Reducing the Schottky barrier height and Fermi level de‐pinning in metal‐organic semiconductor contacts are crucial for enhancing the performance of organic transistors. The reduction of the Schottky barrier height in bottom‐contact top‐gate organic transistors is demonstrated by adding 1 nm thick atomic layer deposited Al 2 O 3 on the source and drain contacts. By using two different donor‐acceptor copolymers, both p‐ and n‐ type transistors are investigated. Temperature‐dependent current–voltage measurements from non‐treated, self‐assembled monolayer treated, and Al 2 O 3 treated Au source‐drain contact field‐effect transistors with varying channel lengths are carried out. The drain current versus drain voltage near zero gate voltage, which may be described by the thermionic emission model at temperatures above 150 K, allows the estimation of the Schottky barrier height ( φ B ). The Al 2 O 3 contact‐treated transistors show more than 40% lower φ B compared with the non‐treated contacts in the p ‐type transistor. Similarly, an isoindigo‐based transistor, with n ‐type transport, shows a reduction in φ B with Al 2 O 3 treated contacts suggesting that such ultrathin oxide layers provide a universal method for reducing the barrier height.

Ghobadi, Arash↗
DOE OSTI2015

Barrier height inhomogeneity in electrical transport characteristics of InGaN/GaN heterostructure interfaces

We have grown InGaN/GaN heterostructures using plasma-assisted molecular beam epitaxy and studied the temperature dependent electrical transport characteristics. The barrier height (φ{sub b}) and the ideally factor (η) estimated using thermionic emission model were found to be temperature dependent. The conventional Richardson plot of ln(J{sub s}/T{sup 2}) versus 1/kT showed two temperature regions (region-I: 400–500 K and region-II: 200–350 K) and it provides Richardson constants (A{sup ∗}) which are much lower than the theoretical value of GaN. The observed variation in the barrier height and the presence of two temperature regions were attributed to spatial barrier inhomogeneities at the heterojunction interface and was explained by assuming a double Gaussian distribution of barrier heights with mean barrier height values 1.61 and 1.21 eV with standard deviation (σ{sub s}{sup 2}) of 0.044 and 0.022 V, respectively. The modified Richardson plot of ln(J{sub s}/T{sup 2}) − (q{sup 2}σ{sub s}{sup 2}/2k{sup 2}T{sup 2}) versus 1/kT for two temperature regions gave mean barrier height values as 1.61 eV and 1.22 eV with Richardson constants (A{sup ∗}) values 25.5 Acm{sup −2}K{sup −2} and 43.9 Acm{sup −2}K{sup −2}, respectively, which are very close to the theoretical value. The observed barrier height inhomogeneities were interpreted on the basis of the existence of a double Gaussian distribution of barrier heights at the interface.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Investigating the effect of aluminum oxide fixed charge on Schottky barrier height in molybdenum oxide-based selective contacts

A tunneling atomic layer deposited (ALD) AlO x layer was inserted in a Si|SiO x |AlO x |MoO x |metal tunnel diode structure to investigate the impact of fixed interface charge on Schottky barrier height. ALD AlO x provides a synthesis-tunable fixed charge and can provide excellent field effect passivation at the SiO x |AlO x interface. A large (>1 × 10 12 q.cm –2 ) negative fixed charge density was expected to decrease Schottky barrier height on p-type silicon and increase Schottky barrier height on n-type silicon by up to 0.4 eV based on an electrostatic model. Fixed charge density and interface trap state density were measured using a thick layer of AlO x in metal oxide semiconductor capacitor structures (MOSCAPs); Schottky barrier height and specific contact resistivity were measured using a tunneling-active layer of AlO x in contacted structures with MoO x . In some samples, HfO x interface layers were inserted between AlO x and silicon to quench the fixed negative charge. The Schottky barrier height was found to vary with processing conditions but did not have a strong correlation with expected fixed charge density. Here, while fixed charge may play a role in determining the Schottky barrier height, other parameters also have significant affect. Further work is needed to minimize contact resistivity and elucidate other factors impacting the Schottky barrier height.

14 SOLAR ENERGY↗
DOE OSTI2024

The rise and fall of stretched bond errors: Extending the analysis of Perdew–Zunger self-interaction corrections of reaction barrier heights beyond the LSDA

Incorporating self-interaction corrections (SIC) significantly improves chemical reaction barrier height predictions made using density functional theory methods. We present a detailed orbital-by-orbital analysis of these corrections for three semi-local density functional approximations (DFAs) situated on the three lowest rungs of Jacob’s ladder of approximations. The analysis is based on Fermi–Löwdin Orbital Self-Interaction Correction (FLOSIC) calculations performed at several steps along the reaction pathway from the reactants (R) to the transition state (TS) to the products (P) for four representative reactions selected from the BH76 benchmark set. For all three functionals, the major contribution to self-interaction corrections of the barrier heights can be traced to stretched bond orbitals that develop near the TS configuration. The magnitude of the ratio of the self-exchange–correlation energy to the self-Hartree energy (XC/H) for a given orbital is introduced as an indicator of one-electron self-interaction error. XC/H = 1.0 implies that an orbital’s self-exchange–correlation energy exactly cancels its self-Hartree energy and that the orbital, therefore, makes no contribution to the SIC in the FLOSIC scheme. For the practical DFAs studied here, XC/H spans a range of values. Here, the largest values are obtained for stretched or strongly lobed orbitals. We show that significant differences in XC/H for corresponding orbitals in the R, TS, and P configurations can be used to identify the major contributors to the SIC of barrier heights and reaction energies. Based on such comparisons, we suggest that barrier height predictions made using the strongly constrained and appropriately normed meta-generalized gradient approximation may have attained the best accuracy possible for a semi-local functional using the Perdew–Zunger SIC approach.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Exploiting Fixed Charge to Control Schottky Barrier Height in Si|Al 2 O 3 |MoO x – based Tunnel Diodes

The insertion of a tunneling atomic layer deposited (ALD) Al 2 O 3 film between MoO x and p-type Si has been studied to investigate Schottky barrier height tunability with varied negative fixed charge density. This work seeks to increase the hole-selectivity of MoO x -based contacts through manipulation of interface fixed charge. Fixed charge density and interface trap state densities are determined as a function of alumina processing conditions in metal-oxide-semiconductor capacitors (MOSCAPs). Schottky barrier heights were determined from Mott-Schottky analysis of tunnel diodes. An alumina deposition temperature of 80°C and post-deposition annealing at 425°C yielded the highest magnitude of negative fixed charge density (-3.5 × 10 12 q . cm –2 ). High deposition temperature and/or post-deposition annealing produced the lowest interface trap state density (1 × 10 12 eV -1 . cm –2 ). On p-type silicon, Schottky barrier height minimization was not clearly correlated with increasing fixed charge density. However, on n-type silicon, a significant increase in Schottky barrier height was evident (~0.8 eV to > 1 eV) and is attributed to the large negative fixed charge. Here, the findings from this work indicate that Schottky barrier height in carrier selective contacts can be tuned by electrostatic engineering of the SiO x |Al 2 O 3 interface.

aluminum oxide↗
DOE OSTI2015

Correlation between amplitude of spin accumulation signals investigated by Hanle effect measurement and effective junction barrier height in CoFe/MgO/n{sup +}-Si junctions

Correlation between the amplitude of the spin accumulation signals and the effective barrier height estimated from the slope of the log (RA) - t{sub MgO} plot (RA: resistance area product, t{sub MgO}: thickness of MgO tunnel barrier) in CoFe/MgO/n{sup +}-Si junctions was investigated. The amplitude of spin accumulation signals increases with increasing effective barrier heights. This increase of the amplitude of spin accumulation is originated from the increase of the spin polarization (P{sub Si}) in Si. The estimated absolute values of P{sub Si} using three-terminal Hanle signals are consistent with those estimated by four-terminal nonlocal-magnetoresistance (MR) and two-terminal local-MR. To demonstrate large spin accumulation in Si bulk band and enhance the local-MR through Si channel, these results indicate that the increase of the effective barrier height at ferromagnet/(tunnel barrier)/n{sup +}-Si junction electrode is important.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2015

Study of barrier height and trap centers of Au/n-Hg{sub 3}In{sub 2}Te{sub 6} Schottky contacts by current-voltage (I-V) characteristics and deep level transient spectroscopy

The temperature-dependent electrical characteristics of the Au/n-Hg{sub 3}In{sub 2}Te{sub 6} Schottky contact have been studied at the temperature range of 140 K–315 K. Based on the thermionic emission theory, the ideality factor and Schottky barrier height were calculated to decrease and increase from 3.18 to 1.88 and 0.39 eV to 0.5 eV, respectively, when the temperature rose from 140 K to 315 K. This behavior was interpreted by the lateral inhomogeneities of Schottky barrier height at the interface of Au/n-Hg{sub 3}In{sub 2}Te{sub 6} contact, which was shown by the plot of zero-bias barrier heights Φ{sub bo} versus q/2kT. Meanwhile, it was found that the Schottky barrier height with a Gaussian distribution was 0.67 eV and the standard deviation σ{sub 0} was about 0.092 eV, indicating that the uneven distribution of barrier height at the interface region. In addition, the mean value of Φ{sup ¯}{sub b0} and modified Richardson constant was determined to be 0.723 eV and 62.8 A/cm{sup 2}K{sup 2} from the slope and intercept of the ln(I{sub o}/T{sup 2}) – (qσ{sub 0}{sup 2}/2k{sup 2}T{sup 2}) versus q/kT plot, respectively. Finally, two electron trap centers were observed at the interface of Au/n-Hg{sub 3}In{sub 2}Te{sub 6} Schottky contact by means of deep level transient spectroscopy.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2016

Investigation of significantly high barrier height in Cu/GaN Schottky diode

Current-voltage (I-V) measurements combined with analytical calculations have been used to explain mechanisms for forward-bias current flow in Copper (Cu) Schottky diodes fabricated on Gallium Nitride (GaN) epitaxial films. An ideality factor of 1.7 was found at room temperature (RT), which indicated deviation from thermionic emission (TE) mechanism for current flow in the Schottky diode. Instead the current transport was better explained using the thermionic field-emission (TFE) mechanism. A high barrier height of 1.19 eV was obtained at room temperature. X-ray photoelectron spectroscopy (XPS) was used to investigate the plausible reason for observing Schottky barrier height (SBH) that is significantly higher than as predicted by the Schottky-Mott model for Cu/GaN diodes. XPS measurements revealed the presence of an ultrathin cuprous oxide (Cu{sub 2}O) layer at the interface between Cu and GaN. With Cu{sub 2}O acting as a degenerate p-type semiconductor with high work function of 5.36 eV, a high barrier height of 1.19 eV is obtained for the Cu/Cu{sub 2}O/GaN Schottky diode. Moreover, the ideality factor and barrier height were found to be temperature dependent, implying spatial inhomogeneity of barrier height at the metal semiconductor interface.

36 MATERIALS SCIENCE↗
DOE OSTI2016

Schottky barrier heights at the interfaces between pure-phase InAs nanowires and metal contacts

Understanding of the Schottky barriers formed at metal contact-InAs nanowire interfaces is of great importance for the development of high-performance InAs nanowire nanoelectronic and quantum devices. Here, we report a systematical study of InAs nanowire field-effect transistors (FETs) and the Schottky barrier heights formed at the contact-nanowire interfaces. The InAs nanowires employed are grown by molecular beam epitaxy and are high material quality single crystals, and the devices are made by directly contacting the nanowires with a series of metals of different work functions. The fabricated InAs nanowire FET devices are characterized by electrical measurements at different temperatures and the Schottky barrier heights are extracted from the measured temperature and gate-voltage dependences of the channel current. We show that although the work functions of the contact metals are widely spread, the Schottky barrier heights are determined to be distributed over 35–55 meV, showing a weak but not negligible dependence on the metals. The deduced Fermi level in the InAs nanowire channels is found to be in the band gap and very close to the conduction band. The physical origin of the results is discussed in terms of Fermi level pinning by the surface states of the InAs nanowires and a shift in pinned Fermi level induced by the metal-related interface states.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Voltage-Dependent Barrier Height of Electron Transport through Iron Porphyrin Molecular Junctions

Electron transport through iron porphyrin (FeP) molecules self-assembled on a gold (Au) substrate was investigated using conductive atomic force microscopy (AFM) to measure current–voltage (I–V) characteristics. In the direct tunneling region (|V| ≤ 0.1 V), the Simmons model was used to characterize the electron transport. Furthermore, the energy barrier between the Fermi energy level of Au and the highest occupied molecular orbital (HOMO) level of the FeP molecule was determined to be between 0.3 and 0.6 eV; the range of the electron attenuation coefficient was 0.6–0.8 Å–1. Instead of a constant barrier height, a voltage-dependent barrier height was adapted to simulate the experimental I–V curves over the entire voltage range (|V| ≤ 2 V) using the Simmons model for the intermediate case. The voltage-dependent barrier height is supported by a previously predicted response of molecular-projected self-consistent Hamiltonian orbitals. The dependence showed that the HOMO level relative to the Fermi energy level of the Au electrode decreased as the bias voltage increased. To verify the deposition of the FeP on the Au substrate, Raman spectroscopy and AFM analysis were performed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Study of self-interaction-errors in barrier heights using locally scaled and Perdew-Zunger self-interaction methods

We study the effect of self-interaction errors on the barrier heights of chemical reactions. For this purpose we use the well-known Perdew-Zunger [J. P. Perdew and A. Zunger, Phys. Rev. B,23, 5048 (1981)] self-interaction-correction(PZSIC), as well two variations of the recently developed, locally scaled self-interaction correction (LSIC) [Zope et al.,J. Chem. Phys.151, 214108 (2019)] to study the barrier heights of the BH76 benchmark dataset. Our results show that both PZSIC and especially the LSIC methods improve the barrier heights relative to the local density approximation(LDA). The version of LSIC that uses the iso-orbital indicator z as a scaling factor gives a more consistent improvement than an alternative version that uses an orbital-dependent factor based on the ratio of orbital densities to the total electron density. We show that LDA energies evaluated using the self-consistent and self-interaction-free PZSIC densities can be used to assess density-driven errors. Furthermore, the LDA reaction barrier errors for the BH76 set are found to contain significant density-driven errors for all types of reactions contained in the set, but the corrections due to adding SIC to the functional are much larger than those stemming from the density for the hydrogen transfer reactions and of roughy equal size for the non-hydrogen transfer reactions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Interfacial Chemistry-Induced Modulation of Schottky Barrier Heights: In Situ Measurements of the Pt–Amorphous Indium Gallium Zinc Oxide Interface Using X-ray Photoelectron Spectroscopy

A method to modulate the Schottky barrier heights for platinum and amorphous indium gallium zinc oxide (a-IGZO) interfaces is demonstrated through thermal processing and background ambient pressure control. The interfacial chemistries that modulate barrier heights for the Pt/a-IGZO system were investigated using in-situ X-ray photoelectron spectroscopy. A significant reduction of indium, from In 3+ to In 0 , occurs during deposition of Pt on to the a-IGZO surface in ultra-high vacuum. Post-annealing and controlling the background ambient O 2 pressure allows tuning the degree of indium reduction and the corresponding Schottky barrier height between 0.17 to 0.77 eV. Understanding the detailed interfacial chemistries at Pt/a-IGZO interfaces may allow for improved electronic device performance, including Schottky diodes, memristors, and metalsemiconductor field-effect transistors.

Environmental Molecular Sciences Laboratory↗
DOE OSTI2019

The Most Reliable and Precise Model to Determine Schottky Barrier Height and Photoelectron Yield Spectroscopy

Schottky barrier height (SBH), φ, plays a crucial role in the design of electronic and photo-electronic devices. In order to reckon SBH via internal photoemission (IPE), the technique is through extrapolating square root of IPE yield-and cube root of IPE yield-photon energy plots to zero before this work, this work was motivated by the most reliable and precise model to determine the SBH via IPE. A phenomenological model for connection IPE quantum yield and photon energy has been successfully established based on Fermi–Dirac distribution. The results of experimental observations fitted via the model indicate that the modeled quantum yield agrees well with experimental data. This model emphasizes the threshold of photon energy for calculating SBH, and the SBH of InN/GaN, p-type GaP/p-type Si, Pt/GaP, Au/GaAs, Si/SiO{sub 2} and Cu/SiO{sub 2} were obtained with high reliability after the method had been applied.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Barrier Heights for Diels–Alder Transition States Leading to Pentacyclic Adducts: A Benchmark Study of Crowded, Strained Transition States of Large Molecules

Theoretical characterization of reactions of complex molecules depends on providing consistent accuracy for the relative energies of intermediates and transition states. Here we employ the DLPNO-CCSD(T) method with core–valence correlation, large basis sets, and extrapolation to the CBS limit to provide benchmark values for Diels–Alder transition states leading to competitive strained pentacyclic adducts. We then used those benchmarks to test a diverse set of wave function and density functional methods for the absolute and relative barrier heights of these transition states. Our results show that only a few of the tested density functionals can predict the absolute barrier heights satisfactorily, although relative barrier heights are more accurate. The most accurate functionals tested are ωB97M-V, M11plus, ωB97X-V, PBE-D3(0), M11, and MN15 with MUDs from best estimates less than 3.0 kcal. Furthermore, these findings can guide selection of density functionals for future studies of crowded, strained transition states of large molecules.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗