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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 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 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 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↗
DOE OSTI2023

Interface formation and Schottky barrier height for Y, Nb, Au, and Pt on Ge as determined by hard x-ray photoelectron spectroscopy

Development of a robust, thin, hole-blocking (n+) contact on high purity germanium (HPGe) has been the main challenge in the development of Ge-based radiation sensors. Yttrium has been reported to be a viable hole-blocking contact on HPGe, and detectors with low leakage have been fabricated. Niobium has also been considered as a potential hole-blocking contact due to its low work function. Here, we investigate interface chemistry and the Schottky barrier height of Y and Nb, as well as electron-blocking contacts Au and Pt, on Ge(100) surfaces using hard x-ray photoelectron spectroscopy. We find a barrier height of 1.05 ± 0.10 eV for Y/HPGe, confirming the formation of a hole-blocking barrier. For Nb/HPGe, the barrier height of 0.13 ± 0.10 eV demonstrates that the interface is not hole-blocking. The Schottky barrier of Au and Pt was found to be 0.45 ± 0.10 and 0.51 ± 0.10 eV, respectively.

36 MATERIALS SCIENCE↗
DOE OSTI2016

How Accurate Are the Minnesota Density Functionals for Noncovalent Interactions, Isomerization Energies, Thermochemistry, and Barrier Heights Involving Molecules Composed of Main-Group Elements?

The 14 Minnesota density functionals published between the years 2005 and early 2016 are benchmarked on a comprehensive database of 4986 data points (84 data sets) involving molecules composed of main-group elements. The database includes noncovalent interactions, isomerization energies, thermochemistry, and barrier heights, as well as equilibrium bond lengths and equilibrium binding energies of noncovalent dimers. Additionally, the sensitivity of the Minnesota density functionals to the choice of basis set and integration grid is explored for both noncovalent interactions and thermochemistry. By and large, the main strength of the hybrid Minnesota density functionals is that the best ones provide very good performance for thermochemistry (e.g., M06-2X), barrier heights (e.g., M08-HX, M08-SO, MN15), and systems heavily characterized by self-interaction error (e.g., M06-2X, M08-HX, M08-SO, MN15), while the main weakness is that none of them are state-of-the-art for the full spectrum of noncovalent interactions and isomerization energies (although M06-2X is recommended from the 10 hybrid Minnesota functionals). Similarly, the main strength of the local Minnesota density functionals is that the best ones provide very good performance for thermochemistry (e.g., MN15-L), barrier heights (e.g., MN12-L), and systems heavily characterized by self-interaction error (e.g., MN12-L and MN15-L), while the main weakness is that none of them are state-of-the-art for the full spectrum of noncovalent interactions and isomerization energies (although M06-L is clearly the best from the four local Minnesota functionals). Finally, as an overall guide, M06-2X and MN15 are perhaps the most broadly useful hybrid Minnesota functionals, while M06-L and MN15-L are perhaps the most broadly useful local Minnesota functionals, although each has different strengths and weaknesses.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2017

Origin of discrepancies in the experimental values of the barrier height at metal–semiconductor junctions

A possible explanation is suggested for discrepancies between experimental values obtained by different authors for the barrier height at the same metal–semiconductor junction. It is supposed that the problem is caused primarily by the structural inhomogeneity of the metal. As a result, the junction behaves as an assembly of a large number of subjunctions connected in parallel. To determine the effect of metal inhomogeneity on the properties of a junction, the dependence of the barrier height in a Schottky diode on the junction area is investigated under the assumption that, with an increase in the area of a junction between a singlecrystal semiconductor and a polycrystalline metal, the degree of inhomogeneity and, thus, the number of subjunctions, increases.

36 MATERIALS SCIENCE↗
DOE OSTI2019

Buffer/absorber interface recombination reduction and improvement of back-contact barrier height in CdTe solar cells

Electronic properties of a CdTe solar cell are reported using temperature-dependent capacitance spectroscopy and current-voltage characteristics, the latter in dark and illuminated conditions. The baseline solar cell material stack investigated is comprised of soda-lime-glass/SnO 2 :F/SnO 2 /CdS:O-buffer/CdTe-absorber/Cu/Au. Properties are compared with CdTe solar cells in which the back surface was hydroiodic acid etched, before the back-contact formation, and a CdTe device in which Mg-doped ZnO (MZO) replaces buffer layer CdS. Reduced back-contact barrier height and grain boundary barrier height are observed in the HI treated CdTe cell. As a result, improved device performance in the MZO-based CdTe device is attributed to reduced emitter/absorber interface recombination when using the MZO window layer.

14 SOLAR ENERGY↗
DOE OSTI2017

Accurate barrier heights using diffusion Monte Carlo

Fixed node diffusion Monte Carlo (DMC) has been performed on a test set of forward and reverse barrier heights for 19 non-hydrogen-transfer reactions, and the nodal error has been assessed. The DMC results are robust to changes in the nodal surface, as assessed by using different mean-field techniques to generate single determinant wave functions. Using these single determinant nodal surfaces, DMC results in errors of 1.5(1) kcal/mol on barrier heights. Using the large data set of DMC energies, we attempted to find good descriptors of the fixed node error in this study. It does not correlate with a number of descriptors including change in density but does show some correlation with the gap between the highest occupied and lowest unoccupied orbital energies in the mean-field calculation.

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

Influence of the Pore Structure on the Electron Barrier Height of Metal-Ceramic Nanomaterials Based on Gold-Anodic Aluminum Oxide

The influence of the of the pore structure on the electron barrier height of Au–Al{sub 2}O{sub 3} structures is experimentally studied. The porous structures of anodic aluminum oxide of two types with through pores and pores in the form of a well are investigated. It is shown that, depending on the shape of the pore profile, the deposited thin gold film creates a different height of the electron barrier at the metal-insulator interface. The method of linear optical spectroscopy showed that the height of the barrier for structures with through pores is higher by 2.0 eV.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2022

Temperature-dependent charge barrier height of amorphous germanium contact detector

The exploration of germanium (Ge) detectors with amorphous Ge (a-Ge) contacts has drawn attention to the searches for rare-event physics such as dark matter and neutrinoless double-beta decay. The charge barrier height (CBH) of the a-Ge contacts deposited on the detector surface is crucial to suppress the leakage current of the detector in order to achieve a low-energy detection threshold and high-energy resolution. The temperature-dependent CBH of a-Ge contacts for three Ge detectors is analyzed to study the bulk leakage current (BLC) characteristics. The detectors were fabricated at the University of South Dakota using homegrown crystals. The CBH is determined from the BLC when the detectors are operated in the reverse bias mode with a guard-ring structure, which separates the BLC from the surface leakage current (SLC). Here the results show that CBH is temperature dependent. The direct relation of the CBH variation to temperature is related to the barrier inhomogeneities created on the interface of a-Ge and crystalline Ge. The inhomogeneities that occur at the interface were analyzed using the Gaussian distribution model for three detectors.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗