Optimization of AlAs/AlGaAs quantum well heterostructures on on-axis andmisoriented GaAs (111)B

F. Herzog,1 M. Bichler,1 G. Koblmuller,1,a) S. Prabhu-Gaunkar,2 W. Zhou,2

and M. Grayson2,a)

1Walter Schottky Institut and Physik Department, Technische Universitat Munchen, Garching 85748, Germany2Electrical Engineering and Computer Science, Northwestern University, Evanston, Illinois 60208, USA

(Received 16 March 2012; accepted 19 April 2012; published online 8 May 2012; corrected

15 May 2012)

We report systematic growth optimization of high Al-content AlGaAs, AlAs, and associated

modulation-doped quantum well (QW) heterostructures on on-axis and misoriented GaAs (111)B

by molecular beam epitaxy. Growth temperatures TG> 690 �C and low As4 fluxes close to group

III-rich growth significantly suppress twin defects in high-Al content AlGaAs on on-axis GaAs

(111)B, as quantified by atomic force and transmission electron microscopy as well as x-ray

diffraction. Mirror-smooth and defect-free AlAs with pronounced step-flow morphology was

further achieved by growth on 2� misoriented GaAs (111)B toward ½0�11� and ½2�1�1� orientations.

Successful fabrication of modulation-doped AlAs QW structures on these misoriented substrates

yielded record electron mobilities (at 1.15 K) in excess of 13 000 cm2/Vs at sheet carrier densities

of 5� 1011 cm�2. VC 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4711783]

Aluminum arsenide (AlAs) semiconductors have gained

significant attention due to their bulk three-fold degeneracy

of the X-conduction band valleys and their heavy and aniso-

tropic conduction band effective masses, providing for large

exchange effects.1 With near-perfect lattice-match to GaAs,

this multivalley semiconductor is further an excellent system

for fabrication of high-mobility, modulation-doped quantum

wells (QWs), where large progress was recently achieved in

(001) and (110)-oriented AlAs/AlGaAs two-dimensional

electron systems (2DES) with mobilities in excess of

105 cm2/Vs.2–4 The three-fold valley degeneracy is broken

due to strain and quantum confinement effects in these biax-

ially strained AlAs/AlGaAs QW heterostructures, leading to

either double [in (001)-oriented QWs] or single [in (110)-ori-

ented QWs] valley degeneracy.2–4,8 In addition, a transition

between double and single valley degeneracy was observed

in piezoelectrically strained (001) AlAs QWs and as a func-

tion of QW width,1 facilitating dynamic control of valley oc-

cupancy and tuning of valley effective mass.5,6

In contrast, the symmetrical (111)-oriented AlAs QWs

should preserve the three-fold valley degeneracy as found

from systematic strain tensor calculations in biaxially

strained multivalley AlAs QW heterostructures.7,8 This per-

fect SU(3) symmetry is expected to add an extra valley

degree of freedom as compared to (001)-oriented AlAs

QWs, allowing for ultimate exploration of interaction effects

such as anisotropic composite Fermion mass and possible

SU(3) valley skyrmions8–10 or related valley textures.11,12

Accessing these interesting properties in (111) AlAs

QWs demands growth of high-quality electrically active sili-

con (Si) modulation-doped AlAs/AlGaAs heterostructures on

(111)-oriented substrates. Ideally, growth is performed on a

GaAs (111)B substrate due to the negligible lattice mismatch

and preferential donor activity of remote Si dopants along this

orientation, as opposed to the p-type nature of Si dopants

along the other polar GaAs (111)A orientation.13 As seen in

previous literature, epitaxial growth on exactly oriented, i.e.,

on-axis GaAs (111)B substrates, has been notoriously diffi-

cult, where a high propensity of twin defect and surface py-

ramidal mound formation limited device-quality thin films

and heterostructures.14–17 Improvements in thin film quality

with smooth step-flow growth and reduced defect formation

were achieved by using vicinal substrates, i.e., misoriented by

0.5–4� against the exact (111)B orientation.18–21

However, as most of the previous work concentrated on

the growth of binary GaAs thin films, very little attention has

been addressed toward fabrication of ternary high-Al content

AlxGa1�xAs or binary AlAs layers on GaAs (111)B substrates.

Hayakawa et al.19 were able to fabricate (Al,Ga)As hetero-

structures for QW lasers on 0.5� misoriented (111)B substrates

by molecular beam epitaxy (MBE), using an Al content up to

80% and very high growth temperatures of 720 �C. Smith

et al.22 demonstrated AlAs multi-QW structures on GaAs

(111)B with electron mobilities of up to 8 000 cm2/Vs. How-

ever, critical dependencies on growth conditions and doping

efficiencies have not been elucidated, though they are instru-

mental for optimizing Al(Ga)As-based QW heterostructures,

and single AlAs QWs have not been attempted.

In this letter, we systematically investigate the growth

of high Al-content AlGaAs thin films and AlAs/AlGaAs

QW heterostructures on both on-axis and misoriented GaAs

(111)B substrates. In particular, we demonstrate a comple-

mentary methodology of combining atomic force micros-

copy (AFM), transmission electron microscopy (TEM), and

x-ray diffraction (XRD) to quantitatively probe the presence

of twin defect domains and surface mounds in the as-grown

films as a function of growth parameters. Optimized growth

conditions resulting in minimum defect densities were then

employed for successful growth of single modulation-doped

AlAs QW heterostructures on 2� misoriented GaAs (111)B

toward the ½2�1�1� orientation, yielding record electron

a)Authors to whom correspondence should be addressed. Electronic addresses:

Gregor.Koblmueller@wsi.tum.de and m-grayson@northwestern.edu.

0003-6951/2012/100(19)/192106/5/$30.00 VC 2012 American Institute of Physics100, 192106-1

APPLIED PHYSICS LETTERS 100, 192106 (2012)

mobilities exceeding 13 000 cm2/Vs at low-temperature of

1.15 K.

All growths were performed in a solid-source Veeco,

Gen-II MBE system equipped with standard group-III ele-

mental sources (Ga, Al, In), a Veeco valved cracker source

supplying uncracked As4, and solid dopant sources for sili-

con (Si) and carbon (C). Two-inch semi-insulating GaAs

(111)B wafer substrates were used (AXT Inc.), either ori-

ented on-axis within 60.5� uncertainty or slightly misor-

iented (1) miscut 2� toward ½2�1�1� and (2) 2� toward ½0�11�.Growth temperatures in the range of TG¼ 630–720 �C were

employed, as measured by an optical pyrometer calibrated to

the onset temperature of native oxide desorption from the

GaAs (111)B wafer surface. For all GaAs and AlGaAs

growth experiments, the total group-III flux was kept con-

stant, i.e. /(Ga)¼ 2.7 A/s for GaAs, /(Ga)¼ 1.48 A/s and

/(Al)¼ 1.22 A/s for AlxGa1�xAs (x� 0.45), respectively,

while for binary AlAs growths /(Al)¼ 1.22 A/s was applied.

The As4 beam equivalent pressure (BEP) was varied between

0.8� 10�5 mbar and 2.0� 10�5 mbar. Details on Si doping

are further described below.

After-growth imaging of the surface morphology was

carried out using an Asylum Research MFP-3D AFM. Addi-

tionally, cross-section and plan-view TEM (200-keV Hitachi

H8100) as well as XRD (Huber 4-circle diffractometer) were

performed on selected samples to correlate surface morpho-

logical features with the underlying defect structure. Plan-

view specimens were prepared by standard polishing, dim-

pling, and Arþ ion milling. Subsequent magnetotransport

characterization of the modulation-doped AlAs/AlGaAs QW

heterostructures was carried out in a pumped He4 cryostat at

1.15 K, where samples were contacted in van der Pauw ge-

ometry using In contacts. Magnetotransport measurements

up to 15 T were performed using standard low-frequency

lock-in measurement techniques.

Prior to growth of high Al-content AlGaAs and AlAs/

AlGaAs heterostructures, initial growth optimization was

conducted for on-axis GaAs (111)B buffer layers. For con-

ventional (001)-GaAs growth conditions (T¼ 630 �C,

/(Ga)¼ 2.7 A/s, As4 BEP¼ 1.2� 10�5 mbar), AFM mor-

phologies on (111)B GaAs substrates evidenced large

triangular-shaped pyramids (mounds of few lm-wide lateral

extension with height of few tens of nm) as well as relatively

deep (several tens of nm) triangular surface pits (not shown,

but similar to AlGaAs as in Fig. 1(a)). The large triangular

pyramids are described by facets consisting of inclined

(�1–3�) surfaces stepping down toward ½2�1�1� and equivalent

directions. These are intersected by triangular surface pits

which have been commonly associated with dense twin

defect complexes in on-axis GaAs (111)B films.14–17 These

observations are further consistent with the typical 2� 2,

i.e., As-rich, surface reconstruction obtained under these

conditions.14,23,24 Increased growth temperature (up to

660 �C) and decreased As4 flux (<1.0 E-5 mbar, close to the

transition boundary to Ga-rich growth) resulted in elimina-

tion of surface pits and significantly reduced pyramidal facet

angle (hF< 1�). Furthermore, under these optimized (111)B

GaAs growth conditions, �0.5 -lm-thick Si-doped (bulk)

GaAs buffer layers were grown side-by-side on co-loaded

(001) and (111)B GaAs substrates to compare and evaluate

the Si doping efficiency via standard van-der Pauw measure-

ments. Both (001) and (111)B GaAs:Si layers showed nearly

identical n-type carrier concentration and electron mobility,

confirming the excellent doping efficiency of Si and high-

quality buffer layer growth along (111)B.

In contrast, growth of high Al-content AlxGa1�xAs

(x� 0.45) layers showed a much higher propensity for twin

defect formation under identical growth conditions as opti-

mized for GaAs (111)B buffer layer growth. Fig. 1 shows

representative AFM surface morphologies together with cor-

responding plan-view TEM bright field images taken along

the (111) zone axis for thick (350 nm) Al0.45Ga0.55As layers

grown on on-axis (111)B substrates at growth temperatures

of TG¼ 650 �C and 690 �C, respectively. As observed in

GaAs (111)B buffer layer growth, the AFM images exhibit

again the characteristic triangular pyramidal surface mounds

with inclined surfaces stepping down toward the {211} fam-

ily of facets where facet angles decrease continually from

hF¼ 0.7� (TG¼ 650 �C) to 0.3� (690 �C). Note further the

extremely regular step terrace distribution within the inclined

FIG. 1. AFM surface morphologies of 350-nm thick Al0.45Ga0.55As grown

on on-axis GaAs (111)B substrate at (a) 650 �C and (b) 690 �C (inset:

1� 1 lm2 AFM image showing distinct step-terrace structure). Growth

fluxes were /(Ga)¼ 1.48 A/s, /(Al)¼ 1.22 A/s, and As4(BEP)¼ 0.8� 10�5

mbar. Corresponding plan-view TEM images of the same films taken along

the (111) zone axis are shown for growths at 650 �C (c) and 690 �C (d). (e)

Cross-sectional dark-field TEM image of a 800-nm thick Al0.45Ga0.55As

layer on GaAs (111)B grown at 650 �C taken along the ð�312Þ zone axis. The

image shows the nucleation of twins (inclined line defects) at the substrate

interface and their propagation to the layer surface.

192106-2 Herzog et al. Appl. Phys. Lett. 100, 192106 (2012)

pyramid facets as shown in the inset of Fig. 1(b). The meas-

ured average step terrace width of 50–60 nm together with a

facet angle of merely hF¼ 0.3� results in a step height of

�3 A, corresponding to exactly one monolayer (ML) of

GaAs (111) (i.e., 1 ML¼ 3.26 A).

Unlike GaAs, the high Al-content AlGaAs layer grown

at TG¼ 650 �C is interspersed with deep (>20 nm)

triangular-shaped pits with edges aligned along f110g direc-

tions (Fig. 1(a)). Identical features were identified as twin

defect complexes from TEM investigations on GaAs (111)B

by Rajkumar et al.15 and were further explained by the

according twin formation model. In this respect, twin defects

are planar stacking faults in zincblende (ZB) crystals which

easily form on (111) planes interrupted by insertion of one

monolayer of wurtzite structure. This leads to a 60� rotation

about the (111) plane normal to the subsequent ZB layers,

and these defects result on any of the available (111) planes.

For the AlGaAs layer grown at TG¼ 650 �C, the correspond-

ing plan-view TEM image (Fig. 1(c)) thus reveals a high

density of straight black lines arranged at 120� to each other

which were attributed to lateral twin boundaries. These are

twin defects formed with ð1�1�1Þ, ð�11�1Þ, and ð�1�11Þ planes,

respectively, with total densities ndef> 109 cm�2. Since these

planes are inclined with respect to the (111) zone axis, they

appear thick in the plan-view TEM image. We find that as

the planes terminating these triangular twin boundaries are

propagating to the surface, they are replicated as triangular-

shaped surface pits in the AFM surface morphologies.

Hence, AFM imaging is a very straightforward method of

determining the presence of underlying twin defects within

the as-grown layers. The propagation of twin defects was

further confirmed by the cross-sectional dark-field TEM

image of a representative (800-nm thick) Al0.45Ga0.55As

layer grown at TG¼ 650 �C (Fig. 1(e)). The micrograph

shows twin defects as inclined lines, delineating lateral bor-

ders which separate crystal domains of different twinning. It

is apparent that these twin defects nucleate at the GaAs

(111)B substrate interface itself and propagate through the

layer to the top AlGaAs surface. In contrast to highly

twinned Al0.45Ga0.55As growth at intermediate temperatures,

high growth temperatures of TG¼ 690 �C and above resulted

in a remarkable reduction of both surface pits (Fig. 1(b)) and

related twin defect density (Fig. 1(d)).

These observations are further corroborated by XRD

measurements of the asymmetric 60�-rotated (220) twin-

related reflections.24 By tilting the sample by v¼ 35.26�

away from the ½�1�1�1� surface normal, three strong (220) sub-

strate reflections (separated by 120�) appeared in a 360� u-

scan which were superimposed by three twin-related reflec-

tions (shifted by 60�) (Fig. 2(a)). Normalizing the twin peak

intensity to the bulk (220) peak intensity thus provided a

measure of the twin defect densities formed with the (111)

plane as present inside the film. This is directly illustrated by

the high-resolution u-scans recorded for three 350-nm thick

Al0.45Ga0.55As layers grown on GaAs (111)B at different

growth temperatures (Fig. 2(b)). Since all peaks were cen-

tered at u¼ 0, their intensities can be compared directly

among the different AlGaAs layers. As expected, the

AlGaAs layer grown at the highest growth temperature

(TG¼ 690 �C) evidences the lowest XRD peak intensity and

thus lowest twin defect density. Table I summarizes the val-

ues of twin defect density determined by plan-view TEM

and XRD twin peak intensities measured for the 350-nm

thick Al0.45Ga0.55As layers as a function of growth tempera-

ture. Note that the twin defect density from the TEM images

(see Figs. 1(c) and 1(d)) was estimated from the total number

of long straight black lines arranged at 120� to each other, i.e.,

twin defects formed with ð1�1�1Þ, ð�11�1Þ, and ð�1�11Þ planes,

except for the (111) plane which lies parallel to the imaging

direction in plan-view TEM. In XRD, however, the bulk of

crystal domains rotated by 60� with respect to the (111) plane

is measured, independent of the crystal domain size. This dif-

ference may limit determination of direct proportionality

between TEM- and XRD-measured twin defect densities

given in Table I. Nevertheless, both methods consistently

reveal the improvement of AlGaAs layer quality by reduction

of twin defect density using higher growth temperatures.

The need for higher growth temperatures of high Al-

content AlGaAs as compared to binary GaAs to obtain simi-

lar low defect density layers can be attributed to the reduced

surface migration lengths of Al adatoms. On the on-axis

(111) facets, readily adsorbed adatoms (as in the case of Al

adatoms) are able to rotate about the available single chemi-

cal bond, promoting the formation of twin defects. Under

FIG. 2. (a) 360� XRD u-scan of 350-nm thick Al0.45Ga0.55As on GaAs

(111)B grown at 650 �C. The sample was tilted 35.26� away from the ½�1�1�1�surface normal. Three intense reflections (grey) separated by 120� corre-

spond to the substrate’s h220i reflections, while additional peaks (black, less

intense) shifted by 60� from the bulk reflections are due to twin defects

formed with the ð�1�1�1Þ plane inside the grown layer; (b) High-resolution u-

scans of 350-nm thick Al0.45Ga0.55As on GaAs (111)B for different growth

temperatures. All peaks are centered at u¼ 0 for comparison.

192106-3 Herzog et al. Appl. Phys. Lett. 100, 192106 (2012)

high adatom migration (as in the case of Ga adatoms), how-

ever, adatoms can easily migrate to existing terrace edges

where more than one dangling bond is present, suppressing

twin defect formation effectively.

This situation of low Al adatom diffusion becomes even

more evident for the growth of binary AlAs films on GaAs

(111)B substrates. Fig. 3(a) shows the AFM surface mor-

phology of a 350-nm-thick AlAs layer grown on on-axis

GaAs (111)B at TG¼ 720 �C under otherwise optimized V/

III ratio. Pyramidal mounds appear smaller in size and their

appearance can be due to the reduced adatom mobility of Al,

and many surface pits and trenches are present despite the

higher growth temperature. These surfaces indicate again a

high amount of twin boundaries, manifested also in a 60�

rotation of some of the triangular pyramids separating indi-

vidual crystal domains. Achievement of twin defect-free

AlAs films would thus require extremely high growth tem-

peratures, far beyond the limits of thermal decomposition of

the underlying GaAs substrate.

Similar to earlier observations for GaAs (111)B

growth,18–21 enormous improvement of surface morphology

and reduction in surface structural defects was achieved for

AlAs growth on slightly misoriented GaAs (111)B sub-

strates. Results of two representative 350-nm-thick AlAs

layers grown on GaAs (111)B substrates with miscut angles

of 2� toward ½2�1�1� and 2� toward ½0�11�, respectively, are

exemplified in Figs. 3(b) and 3(c). Both layers exhibit an

atomically flat step terrace structure without any trace of

twin-defect related surface pits. While the steps follow an

irregular, zig-zag structure (average step height �15 A) for

the layer grown on misoriented substrate toward ½0�11�,extremely straight, shallow steps [step height �7.5 A, equiv-

alent to 2-ML of GaAs (111)] were obtained for the layer

grown on the misoriented substrate toward ½2�1�1�. The latter

direction of misorientation also coincides with the preferred

orientation of the pyramidal facets observed on on-axis

(111)B-grown layers. These results are consistent with the

miscut orientation dependency of step terrace structure found

by Yang and Schowalter16 for GaAs (111)B. For consecutive

AlAs/AlGaAs heterostructures, growth on substrates with

miscut toward ½2�1�1� was selected due to two distinct advan-

tages: (1) decreased step height providing for smoother inter-

faces and less interface scattering of electrons and (2)

narrower terrace width alleviating demands for high Al ada-

tom migration lengths. The latter may enable selection of

even smaller miscut angles (closer to the exact (111)B orien-

tation) while maintaining twin-defect free step-flow growth

morphology.

Using optimized growth conditions for bulk

Al0.45Ga0.55As and AlAs layers (i.e., TG¼ 690 �C (AlGaAs),

690 �C, and 720 �C (AlAs), As4(BEP)¼ 0.8� 10�5 mbar),

we fabricated a full modulation-doped AlAs/AlGaAs QW

structure with both layer sequence and band diagram

depicted in Fig. 4(a). Specifically, a 15-nm wide double-

sided doped AlAs QW layer is sandwiched between the

Al0.45Ga0.55As matrix, where symmetric Si-doping layers d2

and d3 provide electrons to the QW while d1 was imple-

mented near the surface to pin the conduction band down to

the Fermi level and to satisfy mid-gap surface states. The Si

doping levels for the individual layers were selected such

that d1¼ 3d2¼ 3d3, as adopted from our earlier optimized

(001) AlAs/AlGaAs QW structures.2 In detail, we used Si

source current of 11.4 A and 15 s of doping time for d2 and

d3, corresponding to a Si sheet density of nSi� 2� 1012 cm�2

based on GaAs bulk doping calibration. This full structure

was grown both on on-axis GaAs (111)B substrates and

misoriented substrates with 2� miscut toward ½2�1�1�. The sur-

face morphologies represented in Fig. 4(b) show large pits

and trenches with overall high surface roughness for the

structure grown on on-axis GaAs (111)B. This demonstrates

that even very thin (15-nm wide) AlAs combined with the

highest selected growth temperature poses detrimental

TABLE I. Growth temperature dependence of twin defect related quantities,

i.e., two-dimensional twin defect densities as determined by plan-view TEM

and /-integrated XRD intensities of the asymmetric twin peaks as normal-

ized to the substrate (220) reflection for 350-nm thick Al0.45Ga0.55As grown

on on-axis GaAs (111)B.

AlGaAs growth

temperature ( �C)

Twin defect density by

plan-view TEM (cm�2)

Twin peak intensity of

(220) XRD reflection (a. u.)

650 >109 2 600

670 3� 108 2 200

690 6� 107 24

FIG. 3. AFM surface morphologies of 350-nm thick AlAs grown on (a) on-axis GaAs (111)B and mis-oriented GaAs (111)B with 2� miscut toward ½0�11� (b) and 2�

miscut toward ½2�1�1� (c), respectively. The in-plane image orientation pointing along the ½2�1�1� direction is identical for all images. All growth conditions were identical

for the three AlAs layers (T¼ 720 �C, /(Ga)¼ 1.48 A/s, /(Al)¼ 1.22 A/s, and As4(BEP)¼ 0.8� 10�5 mbar).

192106-4 Herzog et al. Appl. Phys. Lett. 100, 192106 (2012)

effects on twin defect formation, and surface morphology

cannot be recovered by successive thick Al0.45Ga0.55As layer

growth. Due to the large amount of twin defects present in

the active region of this structure, electrical measurements

revealed insulating behavior (room–temperature two-point

resistance >10 MX).

In contrast, smooth step-flow like morphology was pre-

served for the entire layer structure grown on the misoriented

substrate (Fig. 4(c)), indicating high-quality growth free of

twin defects. As expected, the modulation-doped AlAs QW

structure conducts well at both room temperature (two-point

resistance �50–100 kX) and low temperatures as revealed

from classical Hall and van der Pauw measurements. A typi-

cal magnetoresistivity trace (Rxx, Rxy) taken at 1.15 K is

shown in Fig. 4(d), evidencing well developed Shubnikov–

de Haas oscillations which persist to fields as low as B� 3 T

and filling factors as high as �¼ 7. The presence of filling

factors different from integer multiples of 3 indicates a lifting

of the expected three-fold valley degeneracy at high

magnetic fields, and SU(3)-symmetry is not observed within

this sample. Possible valley-splitting mechanisms such as

interaction effects and the role of substrate misorientation

angle will be investigated in future ultra-low-T magnetotran-

sport measurements.

For the selected Si doping in our structure, we obtained

low-temperature (1.15 K) 2DES mobilities of l¼ 5 000 cm2/

Vs in dark at sheet carrier densities of n¼ 2.6� 1011 cm�2

and record l¼ 13 200 cm2/Vs (n¼ 5.3� 1011 cm�2) when

illuminated with a red LED and post-illumination annealing

at 30 K.2 To our knowledge, these values are the highest-

ever reported electron mobilities for slightly miscut (111)-

oriented AlAs/AlGaAs QW heterostructures.

This work was supported by NSF grant DMR-0748856,

the NSF MRSEC program DMR-0520513 and DMR-

1121262 at the Materials Research Center of Northwestern

University, with work conducted at the Electron Probe

Instrumentation Center (EPIC) of Prof. Dravid and the J. B.

Cohen X-ray Diffraction Facility of Prof. Bedzyk at

Northwestern University. The authors thank Jinsong Wu,

Shu-You Li, and J. Carsello for assistance with TEM and

XRD measurements (Materials Science and Engineering,

NU) as well as J. Becker, K. Chen, and S. Bolte for help

with AFM and transport measurements (WSI-TUM).

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FIG. 4. (a) Energy band diagram and layer sequence of the entire AlAs/

AlGaAs QW heterostructure (c denotes the growth direction, and both X

(solid) and U (dashed) conduction bands are depicted). (b),(c) AFM surface

morphologies of the entire QW heterostructure grown on (b) on-axis

GaAs (111) B (As4(BEP)¼ 0.8� 10�5 mbar, TG(Al0.45Ga0.55As)¼ 690 �C,

TG(AlAs)¼ 720 �C) and (c) misoriented GaAs (111) B with 2� miscut to-

ward ½2�1�1� (As4(BEP)¼ 0.8� 10�5 mbar, TG(Al0.45Ga0.55As)¼TG(AlAs)

¼ 690 �C). (d) Longitudinal Rxx and transversal Rxy resistances of the full

QW structure grown on GaAs (111)B with 2� miscut towards ½2�1�1� taken at

T¼ 1.15 K up to B¼ 15 T. Electron densities were determined from the min-

ima in the Rxx data, with prominent filling factors �¼ nh/eB.

192106-5 Herzog et al. Appl. Phys. Lett. 100, 192106 (2012)