^{1}, R. M. Feenstra

^{1,a)}, M. P. Semtsiv

^{2}and W. T. Masselink

^{2}

### Abstract

Scanning tunneling microscopy and spectroscopy are used to study heterojunctions with InGaAs-like interfaces. Band offsets are probed using conductance spectra, with tip-induced band bending accounted for using three-dimensional electrostatic potential simulations together with a planar computation of the tunnel current. Curve fitting of theory to experiment is performed. Using an InGaPband gap of , which is appropriate to the disordered InGaP alloy, a valence band offset of is deduced along with the corresponding conduction band offset of (type I band alignment).

This work was supported by the National Science Foundation under Grant No. DMR-0503748, and by the Deutsche Forschungsgemeinschaft. Discussions with M. Hybertsen and A. Zunger are gratefully acknowledged. We also thank R. Duca and S. Gaan for their careful readings and criticism of this manuscript. We are grateful to the Undergraduate Physics Laboratories at Carnegie Mellon University for providing the computer resources used in this work.

I. INTRODUCTION

II. EXPERIMENTAL

III. RESULTS

A. STM imaging

B. Spatially resolved spectroscopy

IV. ANALYSIS

A. Computation of tunneling spectra

B. Spectra far from the heterojunction

C. Spectra across the heterojunction

D. Additional parameters

V. DISCUSSION

VI. CONCLUSION

### Key Topics

- III-V semiconductors
- 58.0
- Heterojunctions
- 24.0
- Scanning tunneling microscopy
- 17.0
- Semiconductors
- 17.0
- Contact potential
- 14.0

## Figures

(A) STM image of the heterostructure at sample voltage of . The image is displayed with a gray scale of . (B) [(a)–(c)] STM topography line scans, acquired at the sample voltages indicated. [(d)–(f)] Solid lines show the average of the experimental curves from (a) to (c), respectively. Dashed lines show theoretical predictions, assuming (d) 0.06% compressive strain only in the InGaP layer, (e) strain only at InGaAs-like interfaces with a single bilayer of 3.36% compressive strain, and (f) strain both in the InGaP layer (0.02% compressive) and at InGaAs-like interfaces [same condition as curve (e)].

(A) STM image of the heterostructure at sample voltage of . The image is displayed with a gray scale of . (B) [(a)–(c)] STM topography line scans, acquired at the sample voltages indicated. [(d)–(f)] Solid lines show the average of the experimental curves from (a) to (c), respectively. Dashed lines show theoretical predictions, assuming (d) 0.06% compressive strain only in the InGaP layer, (e) strain only at InGaAs-like interfaces with a single bilayer of 3.36% compressive strain, and (f) strain both in the InGaP layer (0.02% compressive) and at InGaAs-like interfaces [same condition as curve (e)].

(A) Atomic resolution STM image of InGaP-on-GaAs interface. The image was acquired with sample voltage of and is displayed with a gray scale of . White circles represent positions where spectra are taken. The dashed line in the image labels the interface, with the InGaP layer being on the left side of the interface and the GaAs layer on the right. (B) Tunneling spectra across the interface. For comparison purposes, spectrum (a) is overlaid as a dashed line on spectrum (h).

(A) Atomic resolution STM image of InGaP-on-GaAs interface. The image was acquired with sample voltage of and is displayed with a gray scale of . White circles represent positions where spectra are taken. The dashed line in the image labels the interface, with the InGaP layer being on the left side of the interface and the GaAs layer on the right. (B) Tunneling spectra across the interface. For comparison purposes, spectrum (a) is overlaid as a dashed line on spectrum (h).

Example of a potential distribution obtained from the theoretical computations, for a tip-sample separation of , tip radius of , and tip position inside the InGaP layer. The tip potential energy is relative to a point far inside the semiconductor (achieved in this case with a contact potential of between tip and sample and zero applied voltage between them). Contours of constant potential energy, as labeled, are shown in (a). The variation in the potential energy along the surface is shown in (b).

Example of a potential distribution obtained from the theoretical computations, for a tip-sample separation of , tip radius of , and tip position inside the InGaP layer. The tip potential energy is relative to a point far inside the semiconductor (achieved in this case with a contact potential of between tip and sample and zero applied voltage between them). Contours of constant potential energy, as labeled, are shown in (a). The variation in the potential energy along the surface is shown in (b).

(a) Semiclassical variation (band bending) of energy levels in a semiconductor dues to a varying electrostatic potential, showing the VB maximum at , the CB minimum at , and some representative state at energy . The sample Fermi level is denoted by with the tip Fermi level at , where is the sample voltage. The band bending at the surface is denoted by , with and both being negative in this diagram. Quantum effects within the semiconductor are illustrated in (b) and (c) for wavefunction tailing through a depletion region and for localized state formation, respectively.

(a) Semiclassical variation (band bending) of energy levels in a semiconductor dues to a varying electrostatic potential, showing the VB maximum at , the CB minimum at , and some representative state at energy . The sample Fermi level is denoted by with the tip Fermi level at , where is the sample voltage. The band bending at the surface is denoted by , with and both being negative in this diagram. Quantum effects within the semiconductor are illustrated in (b) and (c) for wavefunction tailing through a depletion region and for localized state formation, respectively.

Comparison of theory and experiment for tunneling spectra acquired at a point in the GaAs located from the heterointerface. (a) Computed band bending as a function of sample voltage, for various parameters sets. (b) Computed conductance (symbols), compared with a measured spectrum (solid line). The same experimental curve is shown three times, and compared with various theoretical curves for different values of tip radius of curvature and contact potential , as listed. A tip-sample spacing of is used, together with a VB offset of .

Comparison of theory and experiment for tunneling spectra acquired at a point in the GaAs located from the heterointerface. (a) Computed band bending as a function of sample voltage, for various parameters sets. (b) Computed conductance (symbols), compared with a measured spectrum (solid line). The same experimental curve is shown three times, and compared with various theoretical curves for different values of tip radius of curvature and contact potential , as listed. A tip-sample spacing of is used, together with a VB offset of .

Comparison of theory and experiment for tunneling spectra acquired at a point in the InGaP located from the heterointerface. (a) Computed band bending as a function of sample voltage, for various parameters sets. (b) Computed conductance (symbols), compared with a measured spectrum (solid line). The same experimental curve is shown three times, and compared with various theoretical curves for different values of tip radius of curvature and contact potential , as listed. A tip-sample spacing of is used, together with a VB offset of except for the theory shown by × marks that has a VB offset of .

Comparison of theory and experiment for tunneling spectra acquired at a point in the InGaP located from the heterointerface. (a) Computed band bending as a function of sample voltage, for various parameters sets. (b) Computed conductance (symbols), compared with a measured spectrum (solid line). The same experimental curve is shown three times, and compared with various theoretical curves for different values of tip radius of curvature and contact potential , as listed. A tip-sample spacing of is used, together with a VB offset of except for the theory shown by × marks that has a VB offset of .

Tunneling spectra acquired across an InGaP-on-GaAs interface, showing the same data as Fig. 2 but plotted as conductance at constant tip-sample separation. Experiment is shown by solid lines and theory by circles. Consecutive pairs of experimental and theoretical curves are displaced by an order of magnitude, for ease of viewing. Parameter values for the theory are listed, with being the tip-sample separation, the tip radius, the tip-sample contact potential, and the VB offset. A single amplitude parameter is used for the entire set of spectra. The inset shows the negative voltage side of spectrum (d), with the × marks showing a theoretical result in which the current from evanescent states is neglected.

Tunneling spectra acquired across an InGaP-on-GaAs interface, showing the same data as Fig. 2 but plotted as conductance at constant tip-sample separation. Experiment is shown by solid lines and theory by circles. Consecutive pairs of experimental and theoretical curves are displaced by an order of magnitude, for ease of viewing. Parameter values for the theory are listed, with being the tip-sample separation, the tip radius, the tip-sample contact potential, and the VB offset. A single amplitude parameter is used for the entire set of spectra. The inset shows the negative voltage side of spectrum (d), with the × marks showing a theoretical result in which the current from evanescent states is neglected.

(a) Measured constant-current contour across the InGaP-on-GaAs interface pictured in Fig. 2(a). (b) Computed constant-current contour across the heterointerface, for the parameters listed in Fig. 7. (c) Computed elastic strain of the surface, from curve (f) of Fig. 1(b). The zero of tip height for each curve is arbitrary (some curves have been shifted in height, for ease of viewing). The arrows at the top of the plot indicate the locations at which the spectra of Figs. 2 and 7 were measured.

(a) Measured constant-current contour across the InGaP-on-GaAs interface pictured in Fig. 2(a). (b) Computed constant-current contour across the heterointerface, for the parameters listed in Fig. 7. (c) Computed elastic strain of the surface, from curve (f) of Fig. 1(b). The zero of tip height for each curve is arbitrary (some curves have been shifted in height, for ease of viewing). The arrows at the top of the plot indicate the locations at which the spectra of Figs. 2 and 7 were measured.

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