Off-axis electron holographic potential mapping across AlGaAs/AlAs/GaAs
heterostructures
Suk Chung, Shane R. Johnson, Yong-Hang Zhang, David J. Smith, and Martha R. McCartney
Citation: Journal of Applied Physics 105, 014910 (2009); doi: 10.1063/1.3062449
View online: http://dx.doi.org/10.1063/1.3062449
View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/105/1?ver=pdfcov
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JOURNAL OF APPLIED PHYSICS 105, 014910 共2009兲

Off-axis electron holographic potential mapping across AlGaAs/AlAs/GaAs
heterostructures
Suk Chung,1,a兲 Shane R. Johnson,2 Yong-Hang Zhang,2 David J. Smith,3 and
Martha R. McCartney3
1

School of Materials, Arizona State University, Tempe, Arizona 85287, USA
Department of Electrical Engineering, Arizona State University, Tempe, Arizona 85287, USA
3
Department of Physics, Arizona State University, Tempe, Arizona 85287, USA
2

共Received 24 September 2008; accepted 20 November 2008; published online 13 January 2009兲
The electrostatic potential profile across AlGaAs/AlAs/GaAs heterostructures containing
1-␮m-thick n-doped 共or p-doped兲 AlGaAs layers is measured using off-axis electron holography.
Simulations of the potential profiles assuming no unintentional impurities in the undoped regions of
the samples show small discrepancies with experiment. Revised simulations reproduce the
measurements accurately, when a p-layer with an 8.4⫻ 1011 cm−2 acceptor density is included at the
buffer/substrate interface to simulate the presence of unintentional carbon impurities. © 2009
American Institute of Physics. 关DOI: 10.1063/1.3062449兴
I. INTRODUCTION

AlGaAs/GaAs heterostructures have attracted intense interest for both fundamental studies in solid state physics and
optoelectronic applications, such as laser diodes, lightemitting diodes, and high electron mobility transistors, ever
since Esaki and Tsu1,2 suggested the possible novel properties of these heterostructures. However, impurities located at
the epilayer/substrate interface have often been reported to
degrade the expected performance of GaAs heterostructure
devices.3,4 Studies to determine the nature of these interfacial
impurities have been conducted using a range of techniques
including photoreflectance spectroscopy,5,6 capacitanceversus-voltage
measurements,7
deep-level
transient
8
spectroscopy, and secondary ion mass spectroscopy.9,10 According to these studies, it has been shown that the presence
of interfacial carbon impurities shifts the threshold voltage of
field-effect transistors due to changes in band structure,3
which reduces the electron mobility and density in the channel as the thickness of the buffer layer between the substrate
and active channel decreases.10 It has also been found that
p-type conducting interfacial layers of carbon at the epilayer/
substrate interface cause side gating.4
As the dimensions of semiconductor devices decrease,
determining the electrostatic potential distribution within
deep-submicron heterostructures represents an imposing
challenge. Electron holography in the electron microscope is
an interferometric technique that can measure the phase
change in an electron wave passing through a specimen with
nanometer-scale resolution.11 Since this phase change depends on the local electrostatic potential, the technique has
proven to be a powerful tool for mapping out potential variations caused by charges such as activated dopants.12 In this
research, off-axis electron holography is used to determine
the electrostatic potential profile across AlGaAs/AlAs/GaAs
heterojunctions. The electrostatic potential drop at the

epilayer/substrate interface and the corresponding sheet concentrations of charge due to interfacial impurities are determined and compared with previous studies.

II. EXPERIMENTAL DETAILS

Two different samples grown by molecular beam epitaxy
in a VG V80H solid-source system were studied. The first
sample was n-doped and consisted of a semi-insulating 共SI兲
GaAs 共001兲 substrate followed by a 100-nm-thick undoped
GaAs buffer layer, an 80-nm-thick undoped AlAs layer, a
n = 2.3
1000-nm-thick
n-type
共NSi = 2 ⫻ 1018 cm−3,
17
−3
⫻ 10 cm 兲 Al0.65Ga0.35As layer, and a 10-nm-thick
n+ GaAs cap, as illustrated in Fig. 1. The second sample was
similar to the first except that it was p-doped and consisted
of a SI GaAs 共001兲 substrate followed by a 40-nm-thick undoped GaAs buffer, a 30-nm-thick undoped AlAs layer, a
p = 1.5
1000-nm-thick
p-type
共NBe = 2 ⫻ 1018 cm−3,
18
−3
⫻ 10 cm 兲 Al0.65Ga0.35As layer, and a 10-nm-thick p
GaAs cap. The carrier densities of the n- and p-type AlGaAs
layers were determined using Hall effect measurements.
Samples suitable for observation by transmission electron microscopy 共TEM兲 and electron holography were prepared using a Multiprep™ wedge-polishing apparatus

a兲

Electronic mail: suk.chung@asu.edu.

0021-8979/2009/105共1兲/014910/4/$23.00

FIG. 1. Schematic of n-doped heterostructure.
105, 014910-1

© 2009 American Institute of Physics

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014910-2

Chung et al.

J. Appl. Phys. 105, 014910 共2009兲

FIG. 2. Annular-dark-field scanning TEM image showing cross section of
p-doped heterostructure. Note the faint line of brighter contrast indicated by
arrows at buffer/substrate interface.

共wedge angle of 2°兲, followed by gentle argon ion milling for
a few minutes at 3.5 keV, with a current of 13 ␮A and a
milling angle of ⫾5°.
Off-axis electron holograms were recorded using a Philips CM200 FEG 共field-emission gun兲 TEM operated at 200
keV.13 An electrostatic biprism was inserted in the selectedarea aperture plane, and a positive voltage was applied to the
biprism. This arrangement caused the vacuum or reference
wave to overlap with the object wave that passes through the
sample. A typical biprism voltage of 130 V resulted in an
interference fringe spacing of 5 nm, and a typical primary
image magnification of 15 000⫻ resulted in an effective

FIG. 4. 共Color online兲 共a兲 Reconstructed phase image of n-doped heterostructure; 共b兲 comparison of simulated and experimental potential profiles
along line indicated in 共a兲. Region I: n-doped AlGaAs; region II: AlAs;
region III: GaAs buffer; and region IV: GaAs substrate.

pixel size of 10 nm in the reconstructed phase image. An
additional weak Lorentz minilens located just beneath the
bore of the lower objective-lens pole-piece was used to provide an enlarged field of view of ⬃1 ␮m for holographic
analysis; as compared to a smaller field of view for imaging
with the normal objective lens switched on.13 During the
holography observations, the samples were typically tilted by
⬃5° away from the 关110兴 zone axis about the substrate normal to minimize dynamical diffraction.14
III. RESULTS AND DISCUSSION

FIG. 3. 共Color online兲 共a兲 Reconstructed amplitude image of n-doped heterostructure; 共b兲 corresponding thickness line profile.

Figure 2 shows a typical cross section of the p-doped
heterostructure recorded in the annular-dark-field imaging
mode. The separate AlGaAs and AlAs layers are clearly visible. A faint line of brighter contrast can also be seen at the
buffer/substrate interface, suggesting the presence of an unintentional delta-doped layer.
Figure 3共a兲 is an amplitude mage of the n-doped heterostructure, obtained after reconstruction of the off-axis electron hologram. A line profile was taken from the region indicated by the arrow in Fig. 3共a兲, taking into account the
different values for the inelastic mean-free-path of GaAs 共67
nm兲, AlAs 共77 nm兲, and Al0.65Ga0.35As 共an interpolated value
of 73 nm was used兲.15 The resulting thickness profile is
shown in Fig. 3共b兲, and indicates a gentle thickness increase
away from the specimen edge. This image confirms a welldefined specimen geometry and indicates minimum diffracting conditions within the analyzed area.
Figure 4共a兲 shows a reconstructed phase image of the

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J. Appl. Phys. 105, 014910 共2009兲

Chung et al.

n-doped heterostructure. The electrostatic potential profile is
extracted from the thickness and phase images in Figs. 3共a兲
and 4共a兲 using the following expression:16
⌽=

E0 + E
2␲e
⫻
V 0t = C EV 0t
␭E
2E0 + E

共1兲

where e and ␭ are the charge and wavelength of the incident
electron, E is the kinetic energy, E0 is the rest energy, CE is
an energy-related constant 共0.007 28 rad V−1 nm−1 for 200
keV electrons兲, and V0 is the mean inner potential. The result
is shown in Fig. 4共b兲 for the line profile indicated. The
sample thickness t in the analyzed area is estimated using the
relationship between the incident electron-beam intensity
and the reduced intensity caused by inelastic scattering.17
The electrostatic potential profile across the heterostructure is simulated using a 1D Poisson solver,18 and compared
to the experimental result in Fig. 4共b兲. The experimental
measurements provide the electrostatic potential profile
within an arbitrary voltage offset, which is chosen so that
both the experimental and simulated potential profiles
are zero in the AlGaAs layer. The values for the mean
inner potential difference 共⌬V0兲 used in the simulation
are 共i兲 the published value of 1.9 V for the AlAs/GaAs
interface15 and 共ii兲 an interpolated value of 0.7 V for the
Al0.65Ga0.35As/ AlAs interface, assuming a linear relationship
between ⌬V0 and composition. In comparing the experimental and simulated profiles, the change in the experimental
potential is more than that predicted by the simulation in the
AlAs layer. Most notably, the measured potential shows a
substantial decrease in the GaAs buffer, a minimum at the
buffer/substrate, and an increase in the substrate, which are
not predicted by the simulation.
In order to improve the agreement with experiment, the
simulation is revised to include a negative electrostatic sheet
charge caused by unintentional impurities at the buffer/
substrate interface. The calculated band-edge energy diagram
for the n-doped sample is shown in Fig. 5共a兲, where a p-type
impurity sheet with an 8.4⫻ 1011 cm−2 accepter concentration is included at the buffer/substrate interface. The electrostatic potentials for the experimental measurements and the
simulations with and without the acceptor impurities are
compared in Fig. 5共b兲. Further improvements between experiment and simulation are realized by adjusting ⌬V0 on
each side of the AlAs layer. The revised values are 0.87 V at
the AlGaAs/AlAs interface and 1.85 V at the AlAs/GaAs
interface, which are reasonable when uncertainties in the
electrostatic potential measurements and the alloy composition are considered. Furthermore, both the experimental profile and the simulation with impurities show a potential decrease of 0.5 V at the buffer/substrate interface relative to the
constant potential in the substrate, as indicated by the arrow.
This potential drop corresponds to an electric field of 3.8
⫻ 104 V cm−1 and compares well with previously reported
potential drops of 0.45V,19 and electric fields on the order of
104 V cm−1 in GaAs epilayer/GaAs substrate structures.20
The negative sheet charge can be explained by the presence of impurities on the surface of the substrate. Impurities
such as carbon, silicon and oxygen at the epilayer/substrate
interface have been reported in the literature,3,20 and the im-

FIG. 5. 共Color online兲 Band-edge energy diagram and electrostatic potential
of n-doped heterostructure; region I: n-doped AlGaAs; region II: AlAs; region III: GaAs buffer; and region IV: GaAs substrate. 共a兲 Band-edge energy
simulation that includes a negative sheet charge due to impurities at buffer/
substrate interface. 共b兲 Electrostatic potential comparisons between measurement and simulations with and without impurities at buffer/substrate
interface.

purity concentrations have been reported to be growthcondition dependent8 and to range from a fraction to one
monolayer.3 Carbon and silicon impurities can act as shallow
acceptors and donors, respectively, for GaAs, while oxygen
can be a deep-level impurity for nonradiative recombination
centers.3,21 Reynolds and Geva10 have shown that there is a
relationship between carrier depletion near the interface and
net interface impurity 共关C兴-关Si兴 cm−3兲, suggesting that the
amount of accumulated sheet charge is a function of
关C兴-关Si兴cm−3 at the interface.
Similarly, the simulated and experimental electrostatic
potentials are compared for the p-doped heterostructure. The
band-edge energy diagram is shown in Fig. 6共a兲 and the electrostatic potential profile is shown in Fig. 6共b兲. The simulation with impurities again includes a sheet layer of 8.4
⫻ 1011 cm−2 acceptors at the buffer/substrate interface. The
values used for ⌬V0 are 0.7 V at the AlGaAs/AlAs interface
and 1.8 V at the AlAs/GaAs interface. As before, the agreement with experiment is improved when the electrostatic potential simulation includes the presence of acceptor impurities at the buffer/substrate interface. Once again, the
experiment and the simulation with impurities show a poten-

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014910-4

J. Appl. Phys. 105, 014910 共2009兲

Chung et al.

erostructures. Electrostatic potential drops were observed at
the epilayer/substrate interface of both n- and p-doped heterostructures and were attributed to ionized carbon acceptors.
The measured potential profiles in the region of the buffer/
substrate interface were accurately simulated by adding an
accepter impurity layer with a sheet concentration of 8.4
⫻ 1011 cm−2 at the buffer/substrate interface. The holography technique could also be used to determine the sheet concentration of charge for the interface states at oxide/
semiconductor interfaces.
ACKNOWLEDGMENTS

This work was partially supported by the Department of
Energy 共Grant No. DE-FG02-04ER46168兲. We acknowledge
the use of facilities in the John M. Cowley Center for High
Resolution Electron Microscopy at Arizona State University.
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FIG. 6. 共Color online兲 Band-edge energy diagram and electrostatic potential
of p-doped heterostructure; region I: p-doped AlGaAs; region II: AlAs; region III: GaAs buffer; and region IV: GaAs substrate. 共a兲 Band-edge energy
simulation that includes a negative sheet charge due to impurities at buffer/
substrate interface. 共b兲 Electrostatic potential comparisons between measurement and simulations with and without impurities at buffer/substrate
interface.

tial decrease of 0.5 V at the buffer/substrate interface relative
to the constant potential in the substrate, as indicated by the
arrow.
IV. CONCLUSIONS

Off-axis electron holography has been used to map the
electrostatic potential profile across AlGaAs/AlAs/GaAs het-

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