^{1,a)}

### Abstract

Empirical branch-point energies of Si, the group-III nitrides AlN,GaN, and InN, and the group-II and group-III oxides MgO, ZnO, Al_{2}O_{3} and In_{2}O_{3} are determined from experimental valance-band offsets of their heterostructures. For Si, GaN, and MgO, these values agree with the branch-point energies obtained from the barrier heights of their Schottky contacts. The empirical branch-point energies of Si and the group-III nitrides are in very good agreement with results of previously published calculations using quite different approaches such as the empirical tight-binding approximation and modern electronic-structure theory. In contrast, the empirical branch-point energies of the group-II and group-III oxides do not confirm the respective theoretical results. As at Schottky contacts, the band-structure lineup at heterostructures is also made up of a zero-charge-transfer term and an intrinsic electric-dipole contribution. Hence, valence-band offsets are not equal to the difference of the branch-point energies of the two semiconductors forming the heterostructure. The electric-dipole term may be described by the electronegativity difference of the two solids in contact. A detailed analysis of experimental Si Schottky barrier heights and heterostructure valence-band offsets explains and proves these conclusions.

I. INTRODUCTION

II. INTERFACE-INDUCED GAP STATES

III. EMPIRICAL BRANCH-POINT ENERGIES

A. Heterostructures

B. GaNSchottky contacts

C. MgO Schottky contacts

IV. DISCUSSION

V. CONCLUSIONS

### Key Topics

- III-V semiconductors
- 42.0
- Semiconductors
- 42.0
- Heterojunctions
- 32.0
- Schottky barriers
- 29.0
- II-VI semiconductors
- 17.0

## Figures

and data of Si heterostructures as a function of the branch-point energies of the semiconductors. The dashed and dash-dotted lines, respectively, are the linear least-squares fits to the respective data points. The solid line is the prediction of the IFIGS theory using Tersoff’s (Ref. 9) *p*-type branch-point energy 0.36 eV.

and data of Si heterostructures as a function of the branch-point energies of the semiconductors. The dashed and dash-dotted lines, respectively, are the linear least-squares fits to the respective data points. The solid line is the prediction of the IFIGS theory using Tersoff’s (Ref. 9) *p*-type branch-point energy 0.36 eV.

data of AlN, GaN, and InN heterostructures as a function of the branch-point energies of the semiconductors. The dashed lines are the linear least-squares fits to the respective data points. YSZ stands for yttria-stabilized zirconia.

data of AlN, GaN, and InN heterostructures as a function of the branch-point energies of the semiconductors. The dashed lines are the linear least-squares fits to the respective data points. YSZ stands for yttria-stabilized zirconia.

data of MgO and ZnO heterostructures as a function of the branch-point energies of the semiconductors. The dashed lines are the linear least-squares fits to the respective data points.

data of MgO and ZnO heterostructures as a function of the branch-point energies of the semiconductors. The dashed lines are the linear least-squares fits to the respective data points.

data of Al_{2}O_{3} and In_{2}O_{3} heterostructures as a function of the branch-point energies of the semiconductors. The dashed lines are the linear least-squares fits to the respective data points.

data of Al_{2}O_{3} and In_{2}O_{3} heterostructures as a function of the branch-point energies of the semiconductors. The dashed lines are the linear least-squares fits to the respective data points.

Flat-band barrier heights as a function of temperature and effective barrier heights as a function of the ideality factors at different temperatures between 300 and 480K of one Pt/*n*-GaN diode. Data from Ref. 149. The dashed lines are the linear least-squares fit to the corresponding data points.

Flat-band barrier heights as a function of temperature and effective barrier heights as a function of the ideality factors at different temperatures between 300 and 480K of one Pt/*n*-GaN diode. Data from Ref. 149. The dashed lines are the linear least-squares fit to the corresponding data points.

Barrier heights of laterally homogeneous GaN Schottky contacts as a function of the difference of the metal and GaN electronegativities. □, , , and data points represent *I/V*, *C/V*, XPS, and IPEYS results, respectively. The dashed line is the linear least-squares fit to the experimental data. The MIGS line is drawn with = 2.37 eV (♦ data point), from Ref. 12, and *S* _{X} = 0.29 eV/Miedema-unit.

Barrier heights of laterally homogeneous GaN Schottky contacts as a function of the difference of the metal and GaN electronegativities. □, , , and data points represent *I/V*, *C/V*, XPS, and IPEYS results, respectively. The dashed line is the linear least-squares fit to the experimental data. The MIGS line is drawn with = 2.37 eV (♦ data point), from Ref. 12, and *S* _{X} = 0.29 eV/Miedema-unit.

Barrier heights of laterally homogeneous MgO Schottky contacts as a function of the difference of the metal and MgO electronegativities. , , , and □ data points are from Ref. 180, Ref. 181, Ref. 113 and Refs. 182–184, respectively. The dashed line is the linear least-squares fit to the experimental data. The MIGS line is drawn with = 3.92 ± 0.31 eV (♦ data point), see Table I, and *S* _{X} = 0.66 eV/Miedema unit.

Barrier heights of laterally homogeneous MgO Schottky contacts as a function of the difference of the metal and MgO electronegativities. , , , and □ data points are from Ref. 180, Ref. 181, Ref. 113 and Refs. 182–184, respectively. The dashed line is the linear least-squares fit to the experimental data. The MIGS line is drawn with = 3.92 ± 0.31 eV (♦ data point), see Table I, and *S* _{X} = 0.66 eV/Miedema unit.

Valence-band offsets of Si heterostructures as a function of the branch-point energies of the semiconductors. The dashed line is the linear least-squares fit to the data points. The dash-dotted line is the prediction of the IFIGS theory without the electric-dipole term using Tersoff’s (Ref. 9) *p*-type branch point energy 0.36 eV.

Valence-band offsets of Si heterostructures as a function of the branch-point energies of the semiconductors. The dashed line is the linear least-squares fit to the data points. The dash-dotted line is the prediction of the IFIGS theory without the electric-dipole term using Tersoff’s (Ref. 9) *p*-type branch point energy 0.36 eV.

## Tables

Empirical slope parameters *ϕ* _{vbo} and values determined from Figs. 1–4 and *p*-type branch-point energies calculated by Tersoff (Ref. 9), Mönch (Ref. 12 and 188) Schleife *et al.* (Ref. 17), Höffling *et al.* (Ref. 18) and Robertson *et al.* (Ref. 14–16).

Empirical slope parameters *ϕ* _{vbo} and values determined from Figs. 1–4 and *p*-type branch-point energies calculated by Tersoff (Ref. 9), Mönch (Ref. 12 and 188) Schleife *et al.* (Ref. 17), Höffling *et al.* (Ref. 18) and Robertson *et al.* (Ref. 14–16).

Empirical slope parameters *S* _{X} and values from Ref. 6 and Figs. 1–4, 7, and 8.

Empirical slope parameters *S* _{X} and values from Ref. 6 and Figs. 1–4, 7, and 8.

Empirical and calculated *p*-type branch point energies of insulators in eV.

Empirical and calculated *p*-type branch point energies of insulators in eV.

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