The impact of heavy Ga doping on superconductivity in germanium
We report new experimental results on how superconductivity in gallium-doped germanium (Ge:Ga) is influenced by hole concentration and microstructure. Ion implantation and subsequent flash-lamp annealing at various temperatures have been utilized to prepare highly p-doped thin films consisting of na...
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| Cite this: | The impact of heavy Ga doping on superconductivity in germanium / R. Skrotzki, T. Herrmannsdörfer, V. Heera, J. Fiedler, A. Mücklich, M. Helm, J. Wosnitza // Физика низких температур. — 2011. — Т. 37, № 9-10. — С. 1098–1106. — Бібліогр.: 44 назв. — англ. |
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Skrotzki, R. Herrmannsdörfer, T. Heera, V. Fiedler, J. Mücklich, A. Helm, M. Wosnitza, J. 2017-05-31T08:38:50Z 2017-05-31T08:38:50Z 2011 The impact of heavy Ga doping on superconductivity in germanium / R. Skrotzki, T. Herrmannsdörfer, V. Heera, J. Fiedler, A. Mücklich, M. Helm, J. Wosnitza // Физика низких температур. — 2011. — Т. 37, № 9-10. — С. 1098–1106. — Бібліогр.: 44 назв. — англ. 0132-6414 PACS: 74.10.+v, 74.78.–w https://nasplib.isofts.kiev.ua/handle/123456789/118783 We report new experimental results on how superconductivity in gallium-doped germanium (Ge:Ga) is influenced by hole concentration and microstructure. Ion implantation and subsequent flash-lamp annealing at various temperatures have been utilized to prepare highly p-doped thin films consisting of nanocrystalline and epitaxially grown sublayers with Ga-peak concentrations of up to 8 at.%. Successive structural investigations were carried out by means of Rutherford-backscattering spectrometry in combination with ion channelling, secondaryion-mass spectrometry, and high-resolution cross-sectional transmission electron microscopy. Hole densities of 1.8·10²⁰ to 5.3·10²⁰ cm⁻³ (0.4 to 1.2 at.%) were estimated via Hall-effect measurements revealing that only a fraction of the incorporated gallium has been activated electrically to generate free charge carriers. The coincidence of a sufficiently high hole and Ga concentration is required for the formation of a superconducting condensate. Our data reflect a critical hole concentration of around 0.4 at.%. Higher concentrations lead to an increase of Tc from 0.24 to 0.43 K as characterized by electrical-transport measurements. A short mean-free path indicates superconductivity in the dirty limit. In addition, small critical-current densities of max. 20 kA/m² point to a large impact of the microstructure. We acknowledge the support of F. Arnold, K.-H. Heinig, H. Hortenbach, M. Posselt, B. Schmidt, W. Skorupa, S. Teichert, M. Voelskow, and C. Wündisch for technical assistance and helpful discussion. Part of this work was supported by Deutsche Forschungsgemeinschaft under Contract No. HE 2604/7 and by EuroMagNET II under EU contract No. 228043. en Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України Физика низких температур Сверхпроводимость и сверхтекучесть The impact of heavy Ga doping on superconductivity in germanium Article published earlier |
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The impact of heavy Ga doping on superconductivity in germanium |
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The impact of heavy Ga doping on superconductivity in germanium Skrotzki, R. Herrmannsdörfer, T. Heera, V. Fiedler, J. Mücklich, A. Helm, M. Wosnitza, J. Сверхпроводимость и сверхтекучесть |
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The impact of heavy Ga doping on superconductivity in germanium |
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The impact of heavy Ga doping on superconductivity in germanium |
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The impact of heavy Ga doping on superconductivity in germanium |
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The impact of heavy Ga doping on superconductivity in germanium |
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impact of heavy ga doping on superconductivity in germanium |
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Skrotzki, R. Herrmannsdörfer, T. Heera, V. Fiedler, J. Mücklich, A. Helm, M. Wosnitza, J. |
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Skrotzki, R. Herrmannsdörfer, T. Heera, V. Fiedler, J. Mücklich, A. Helm, M. Wosnitza, J. |
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Сверхпроводимость и сверхтекучесть |
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Сверхпроводимость и сверхтекучесть |
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2011 |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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We report new experimental results on how superconductivity in gallium-doped germanium (Ge:Ga) is influenced by hole concentration and microstructure. Ion implantation and subsequent flash-lamp annealing at various temperatures have been utilized to prepare highly p-doped thin films consisting of nanocrystalline and epitaxially grown sublayers with Ga-peak concentrations of up to 8 at.%. Successive structural investigations were carried out by means of Rutherford-backscattering spectrometry in combination with ion channelling, secondaryion-mass spectrometry, and high-resolution cross-sectional transmission electron microscopy. Hole densities of 1.8·10²⁰ to 5.3·10²⁰ cm⁻³ (0.4 to 1.2 at.%) were estimated via Hall-effect measurements revealing that only a fraction of the incorporated gallium has been activated electrically to generate free charge carriers. The coincidence of a sufficiently high hole and Ga concentration is required for the formation of a superconducting condensate. Our data reflect a critical hole concentration of around 0.4 at.%. Higher concentrations lead to an increase of Tc from 0.24 to 0.43 K as characterized by electrical-transport measurements. A short mean-free path indicates superconductivity in the dirty limit. In addition, small critical-current densities of max. 20 kA/m² point to a large impact of the microstructure.
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0132-6414 |
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https://nasplib.isofts.kiev.ua/handle/123456789/118783 |
| citation_txt |
The impact of heavy Ga doping on superconductivity in germanium / R. Skrotzki, T. Herrmannsdörfer, V. Heera, J. Fiedler, A. Mücklich, M. Helm, J. Wosnitza // Физика низких температур. — 2011. — Т. 37, № 9-10. — С. 1098–1106. — Бібліогр.: 44 назв. — англ. |
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© R. Skrotzki, T. Herrmannsdörfer, V. Heera, J. Fiedler, A. Mücklich, M. Helm, and J. Wosnitza, 2011
Low Temperature Physics/Fizika Nizkikh Temperatur, 2011, v. 37, Nos. 9/10, p. 1098–1106
The impact of heavy Ga doping on superconductivity
in germanium
R. Skrotzki1,2, T. Herrmannsdörfer1, V. Heera1, J. Fiedler1, A. Mücklich1,
M. Helm1, and J. Wosnitza1
1Dresden High Magnetic Field Laboratory (HLD) and Institute of Ion Beam Physics and Materials Research, Helm-
holtz-Zentrum Dresden-Rossendorf (HZDR), D-01314 Dresden, Germany
E-mail: j.wosnitza@hzdr.de
2Department of Chemistry and Food Chemistry, TU Dresden, D-01062 Dresden, Germany
Received April 11, 2011
We report new experimental results on how superconductivity in gallium-doped germanium (Ge:Ga) is influ-
enced by hole concentration and microstructure. Ion implantation and subsequent flash-lamp annealing at vari-
ous temperatures have been utilized to prepare highly p-doped thin films consisting of nanocrystalline and epi-
taxially grown sublayers with Ga-peak concentrations of up to 8 at.%. Successive structural investigations were
carried out by means of Rutherford-backscattering spectrometry in combination with ion channelling, secondary-
ion-mass spectrometry, and high-resolution cross-sectional transmission electron microscopy. Hole densities of
1.8·1020 to 5.3·1020 cm–3 (0.4 to 1.2 at.%) were estimated via Hall-effect measurements revealing that only a
fraction of the incorporated gallium has been activated electrically to generate free charge carriers. The coinci-
dence of a sufficiently high hole and Ga concentration is required for the formation of a superconducting con-
densate. Our data reflect a critical hole concentration of around 0.4 at.%. Higher concentrations lead to an in-
crease of Tc from 0.24 to 0.43 K as characterized by electrical-transport measurements. A short mean-free path
indicates superconductivity in the dirty limit. In addition, small critical-current densities of max. 20 kA/m2 point
to a large impact of the microstructure.
PACS: 74.10.+v Occurrence, potential candidates;
74.78.–w Superconducting films and low-dimensional structures.
Keywords: superconducting semiconductors, heavily gallium-doped germanium, thin films.
Introduction
Notably, not more than one decade has passed since the
sudden scientific ascent of superconductivity in covalent-
bound materials [1,2]. Highly doped diamond [3], silicon
[4], and germanium [5] — classic group-IV semiconduc-
tors — surprisingly turned out to be low-temperature su-
perconductors. However, to achieve this, doping concen-
trations beyond the metal-to-insulator transition (MIT) had
to be incorporated.
Motivated by the first observations of ambient-pressure
superconductivity in boron-doped diamond (BDD), silicon
(Si:B), and gallium-doped germanium, methods of increas-
ing the critical temperature (Tc) had soon been sought af-
ter. Thus, new state-of-the-art nonequilibrium preparation
techniques were applied to realize even higher doping le-
vels. Replacing high-pressure high-temperature synthesis
by chemical vapor deposition successfully increased Tc of
BDD from around 4 to more than 7 K [3,6]. Alternatively,
improved gas-immersion laser doping (rising Tc from 0.4
to 0.6 K in Si:B) [4,7] and enhanced ion implantation ac-
companied by flash-lamp or rapid thermal annealing (ris-
ing Tc from 0.5 to 1.2 K in Ge:Ga) [5,8] have been demon-
strated.
However, a thorough analysis is required in order to
find out which key features really tend to trigger supercon-
ductivity in covalent-bound materials. Of course, most in-
sight is expected studying the role of the dopant concentra-
tion, i.e., in particular the charge-carrier density. It was
found that above a certain concentration, usually tagged as
critical doping level, superconductivity emerges. Close to
this point, Tc rises steeply and seems to saturate at higher
concentrations [7,9,10].
Achieving a comprehensive picture is complicated when
considering a general lack of comparability among sample
series prepared differently. For instance, crystal orientation
The impact of heavy Ga doping on superconductivity in germanium
Low Temperature Physics/Fizika Nizkikh Temperatur, 2011, v. 37, Nos. 9/10 1099
during doping processes have been reported to play a cru-
cial role [11]. Since nonequilibrium preparations almost
inevitably introduce disorder down to the atomic scale, its
impact on superconductivity — which up to now remains
uncertain — must be considered. While most reports un-
veil critical fields in the Tesla range, thus obviously indi-
cating type-II superconductivity, recent investigations on
more homogeneously doped Si:B samples give rise to a
possible intrinsic type-I character that may artificially be
hidden due to mean-free path and Ginzburg–Landau cohe-
rence-length restrictions, respectively [7]. Further physical
properties may change when extraordinarily high dopant
concentrations of often more than 10 at.% are incorpo-
rated. That is why further insight in microstructure and
local analysis is highly desirable. Most important recent
work include angle-resolved photo-emission spectroscopy
[12] and low-temperature scanning tunnelling microscopy
(STM) [13–15]. The former indicated that diamond va-
lence-band holes establish the Fermi surface of BDD, thus
rendering a possible impurity-band scenario unlikely. STM
data revealed that Si:B epilayers exhibit BCS-like super-
conductivity [13] while in nanocrystalline BDD the prox-
imity effect has been found [14,15]. A distinct carbon but
less clear boron isotope effect has further unraveled the
phonon-mediated nature of superconductivity in BDD
[16,17]. All these findings favor conventional superconduc-
tivity which is well confirmed within a theoretical approach
pronouncing similarities of Cooper pairing in heavily doped
diamond, silicon, and germanium to superconductivity in
magnesium diboride [18].
Focussing on heavily gallium-doped germanium, the most
recently discovered hence least explored of the above-men-
tioned superconductors, we will present new results on the
evolution of Tc with charge-carrier concentration. By stud-
ying a large number of samples prepared differently, fur-
ther light is shed on the impact of microstructure, i.e., Ga
distribution and crystallinity. Moreover, critical-field and crit-
ical-current density measurements unravel the underlying
character of superconductivity.
Preparation methods
In order to incorporate high charge-carrier densities in
semiconductors, dopants with large solid solubilities are
favorable. Unlike for diamond and silicon, boron doping,
so far, has failed to establish superconductivity in germa-
nium [19]. Gallium — adjacent to germanium in the peri-
odic table of elements — is a better choice. Because of its
similar covalent radius it allows for the highest charge-car-
rier activation in germanium among all possible elements
[20]. Thus, the solubility limit of gallium in germanium
(4.9·1020 cm–3) is almost two orders of magnitude larger
than reported for boron (5.5·1018 cm–3) [21]. Due to high-
mobility Ge valence-band holes, the metal-to-insulator
transition in Ge:Ga occurs already at 1.9·1017 cm–3 [22].
In contrast, concentrations of more than 1020 cm–3 are re-
quired for the MIT in BDD [3].
Ion implantation, known as the standard process for se-
lected-area doping in silicon-based microelectronic tech-
nology [23], may be also a key process in the fabrication of
future germanium-based electronic devices [24]. It allows
for a very reproducible and well controllable realization of
dopant profiles ranging from several μm down to some nm
in depth. For that reason, it provides a versatile tool that
can be utilized for nonequilibrium high-dose doping
processes as required for Ge:Ga. However, high-dose ion
implantation causes severe lattice damages as well. The
latter, noticeable as substrate amorphization in Ge:Ga, has
to be annealed subsequently to the implantation process.
Therefore, a short-time thermal treatment at temperatures
close to but still below the melting point is applied. Fur-
thermore, this step is necessary to activate the implanted
atoms electrically, i.e., to adapt them to substitutional lat-
tice positions. Though, one has to consider that depending
on the annealing temperature, there is an exposure-time
window, defined as the time when solid-phase epitaxy
(SPE) or random-nucleation and growth (RNG) has taken
place, but dopant diffusion, thus possible segregation, has
not yet started. Approaching the melting temperature, this
favorable window becomes narrow, though still being ac-
cessible via novel annealing processes like flash-lamp an-
nealing (FLA) providing high-intensity infrared to optic
light pulses in the ms range.
In our previous investigations, flash-lamp or rapid
thermal annealing (RTA) were accompanied by an emerg-
ing dopant diffusion and, finally, a loss of dopant atoms
through out-diffusion at higher temperatures [5,8]. As a
consequence, superconductivity has been excluded or at
least shifted to lower temperatures in the samples where a
loss of dopants has been observed. This has motivated the
present work where the annealing — restricted to FLA
here — is varied in small steps throughout a series of seven
samples. Causing slight, hence less dramatic changes in the
electronic and structural properties, we have been able to
study the impact on superconductivity in more detail.
Measurement technique
We have used commercial <100>-oriented 2′′ Ge wafers
as substrates. The wafers had initially been slightly n dop-
ed by antimony (1014 cm–3) to keep leakage currents low
due to the formation of a space-charge zone upon p doping.
To prevent surface degradation during implantation, an ad-
ditional 30 nm SiO2 capping has been sputtered on top of
the wafers. Implantation has been carried out with 100 keV
Ga+ ions at a total dose of 2·1016 cm–2, equal to our pre-
vious investigations [5,8]. Though, further samples with a
lower dose, 0.6·1016 cm–2, have been prepared for compar-
ison. After implantation, the samples were cut into 1×1 cm
pieces. As second processing step, FLA in flowing Ar gas
R. Skrotzki, T. Herrmannsdörfer, V. Heera, J. Fiedler, A. Mücklich, M. Helm, and J. Wosnitza
1100 Low Temperature Physics/Fizika Nizkikh Temperatur, 2011, v. 37, Nos. 9/10
at 3 ms constant light-pulse duration and total energy den-
sities, i.e., fluences of 46–60 J/cm2 has been applied. Dur-
ing the pulses, the surface of the samples heats up to tem-
peratures ranging from 700°C (lowest fluence) to slightly
below the melting temperature of Ge (highest fluence). An
estimate of the thermal evolution and distribution during
FLA — sensitively depending on the optical and thermal
properties of the sample — is given in Ref. 20. Finally, the
samples were etched in fluoric acid to remove the SiO2
cover which is necessary for electrical transport measure-
ments.
The structure of Ge:Ga has been analyzed by means of
Rutherford-backscattering spectrometry with 1.7 MeV He+
ions in combination with ion channelling (RBS/C). Fur-
ther, the Ga-depth distribution has been measured via sec-
ondary ion mass spectrometry (SIMS) using an O2+ ion
beam. In addition, high-resolution cross-sectional transmis-
sion electron microscopy (XTEM) has been carried out to
study the morphology of Ge:Ga using an image-corrected
FEI Titan 80-300 transmission electron microscope. Se-
lected-area diffraction patterns were taken to search for
Ga-related precipitates.
Hall-effect measurements have been performed at tem-
peratures between 2 and 400 K by using a commercial sys-
tem (Lakeshore Model 9709A). The charge-carrier density
and mobility were determined via the “Van-der-Pauw” me-
thod, while low-temperature transport measurements were
carried out in the usual four-terminal geometry. For the
latter, a self-built insert making use of adiabatic demagne-
tization of a paramagnetic salt installed in a commercial
magnet-cryostat system allowed for reaching minimum
temperatures of around 80 mK. Ohmic contacts have either
been realized by use of silver glue and indium or via suffi-
cient mechanical pressure.
Crystal structure and the normal state
Ion implantation at 2·1016 cm–2 results in a Gaussian
Ga-depth profile with a maximum concentration of 8 at.%
(3.6·1021 cm–3) and a FWHM of roughly 60 nm situated at
a depth of around 20 nm as revealed by SIMS measure-
ments (Fig. 1). These findings match well with the predic-
tion of simulations [25]. Due to the implantation damage, a
120 nm thick layer beneath the surface becomes amorph-
ous. This feature is reflected by a clear TEM contrast
(Fig. 1) and a near-surface RBS/C peak reaching the inten-
sity of the spectrum that has been measured in random
orientation (Fig. 2). While in this case RBS/C is not sensi-
Fig. 1. High-resolution cross-sectional transmission electron micrographs revealing the microstructure of Ge:Ga. The bright-colored
implantation-induced amorphous surface region becomes nanocrystalline upon flash-lamp annealing. Further, a gradual solid-phase epi-
taxial regrowth starting from the dark single crystalline substrate takes place. The diffraction patterns of the displayed regions support
these findings. In addition, Ga-depth profiles have been measured via secondary ion mass spectrometry.
Fig. 2. (Color online) Depth-calibrated spectra of Rutherford
backscattering on Ge and Ga atoms using ion channelling (meas-
ured prior to the SiO2 etching). The backscattering rate is propor-
tional to the amount of local lattice misorientation in respect to
the single crystalline substrate (virgin). Near-surface peaks reach
the maximum scattering rate as referenced by the random orienta-
tion spectrum, though having different origins (Fig. 1) as anneal-
ing forms a nanocrystalline layer out of the previously amorphous
region (as-implanted). A gradual epitaxial regrowth starting from
the substrate occurs with increasing FLA fluence.
–40 0 40 80 120 160
0
4
8
60 50 48
virgin
as-impl.
random
Ge:Ga
Depth, nm
SiO2
Fluence, J/cm
2
R
B
S
/C
c
o
u
n
ts
,
ar
b
.
u
n
it
s
The impact of heavy Ga doping on superconductivity in germanium
Low Temperature Physics/Fizika Nizkikh Temperatur, 2011, v. 37, Nos. 9/10 1101
tive to distinguish between polycrystalline and amorphous
areas, broad rings in the selected-area diffraction pattern
give rise to an amorphous structure. However, deeper-lying
(depth > 120 nm) Ge layers remain single crystalline indi-
cated by characteristic Ge diffraction patterns. Flash-lamp
annealing changes the morphology. On the one hand, the
previously amorphous near-surface region transforms into
a polycrystalline layer with grain sizes of 5 to 15 nm re-
sulting in thin TEM diffraction rings (Fig. 1). These grains
grow with increasing fluence and are visible as dark XTEM
spots (Fig. 1). On the other hand, we observe a gradual
solid-phase epitaxial regrowth from the substrate towards
the surface which reduces the polycrystalline area to a min-
imum thickness of approximately 60 nm at 60 J/cm2. The
high amount of Ga and intermixed atoms from the SiO2
capping most probably act as nucleation spots for a cata-
lyzed crystallization which prevents a full epitaxial re-
growth. The latter has been observed for an implantation
dose of 0.6·1016 cm–2 [20]. Remarkably, the Ga distribu-
tion did not change significantly during FLA (Fig. 1). Al-
though a closer look reveals an evolving kink in the pro-
files located at the boundary between poly- and single
crystalline regions. This may be explained by different
diffusion rates. Additionally, a Ga loss through the surface
is observed affecting the maximum concentration that is
reduced to 6.2 at.% at 60 J/cm2. To exclude possible for-
eign phases, an extensive XTEM search via sample tilting
and spatial Fourier transformation has been carried out.
Since the binary phase diagram of Ge:Ga features only an
eutectic mixture of almost pure Ga (with 0.006 at.% Ge),
solely clusters of the latter and no further intermetallic
phases would be expected [26]. After all, in none of our
samples clusters have been found. However, segregations
of less than 3 nm cannot be excluded within our micro-
scopic resolution.
As one may expect, also the electronic properties are
clearly affected by each preparation step. Temperature-
dependent resistivity measurements of the virgin Ge sub-
strate, as-implanted Ge:Ga, and FLA Ge:Ga are presented
in Fig. 3. Upon cooling, the virgin substrate’s resistivity
first decreases due to a rising charge-carrier mobility, but
finally exhibits a typical semiconducting behavior. The as-
implanted sample shows a more complicated dependence
as leakage currents through the substrate have to be taken
into account at higher temperatures. Towards low tempera-
tures, the resistivity increases indicating a potential hop-
ping conductivity. This is a striking evidence for insuffi-
cient dopant activation in the amorphous surface region.
Upon annealing, Ge:Ga finally shows metallic conductivity
and, furthermore, a reasonable low-temperature resistivity
of about 10–3–10–4 Ω·cm before the superconducting tran-
sition at around 0.5 K sets in. The double-logarithmic scale
in Fig. 3 emphasizes how dramatic the transport behavior
can be influenced by controlled preparation methods. As
will be outlined below, the transport and especially the
superconducting properties of annealed Ge:Ga depend sen-
sitively on the applied FLA fluences. At temperatures of
around 260 to 270 K, the annealed Ge:Ga samples reveal a
crossover from electron- to hole-like conductivity. This
indicates that leakage currents through the n-doped sub-
strate are dominating the electronic transport at higher
temperatures. Thus, Hall-effect measurements for estimat-
ing the charge-carrier density and mobility have been per-
formed at 3 K. Since the magnetoresistance does not ex-
ceed 10% at fields of 9 T, a one-band interpretation of the
Hall-effect proves to be reasonable within the uncertainties
that are implicated by electrical transport through a multi-
layered system. As already shown in Fig. 3, annealed
Ge:Ga exhibits a substantial small residual resistivity ratio
(RRR) of the order 1 indicating that Ge:Ga is a “bad” met-
al. Low hole mobilities of around 40 cm2/(V·s) in all an-
nealed samples reflect the short mean-free paths originat-
ing from the disordered and mainly nanocrystalline
structure. Increasing the annealing fluence from 48 to
60 J/cm2 results in a gradual drop of the low-temperature
resistivity by a factor of 4 (Fig. 4). This may rather be
caused via an increasing charge-carrier density (Fig. 5)
than reflecting the slight improvement of sample crystallin-
ity. Obviously, the hole activation turns out to be crucially
affected upon FLA. As our Hall-effect measurements
show, the latter increases nearly monotonously within our
sample series, resulting in hole concentrations per area
ranging from 1.9 to 4.8·1015 cm–2. The spatial activation,
i.e., the hole-depth distribution remains unknown. As the
thickness of the epitaxially grown layer, where — from a
qualitative point of view — higher activation ratios may be
expected, and the Ga profile change only slightly upon
FLA, we can translate the rising sheet-carrier concentration
into an increase of the spatial hole concentration. Further,
Fig. 3. (Color online) Temperature dependence of the resistance
for different preparation steps. While the virgin substrate reveals
a typical semiconducting behavior and as-implanted Ge:Ga is
highly resistive at low temperatures, annealed Ge:Ga shows me-
tallic conductivity and superconductivity below approximately
0.5 K.
0.1 1 10 100
10
4
10
3
10
2
10
1
10
0
10
–1
Ge:Ga
as-implanted
Ge virgin
Ge:Ga annealed (60 J/cm )
2
T , K
R
,
Ω
R. Skrotzki, T. Herrmannsdörfer, V. Heera, J. Fiedler, A. Mücklich, M. Helm, and J. Wosnitza
1102 Low Temperature Physics/Fizika Nizkikh Temperatur, 2011, v. 37, Nos. 9/10
we do not know whether one layer favors the occurrence of
superconductivity more than the other. That is why we
point out two estimates disregarding the local crystallinity.
On the one hand, a spatial activation proportional to the
Ga-depth profile may be conceivable. On the other hand,
the formation of a hole-concentration plateau over an ef-
fective length within the implanted region renders another
possible scenario. Since the latter takes into account that
regions containing less Ga are activated much better in
respect to their Ga concentration, it seems to be a reasona-
ble approach. Following the latter, we derive an effective
plateau length of 80–100 nm with hole densities nvol =
= (1.8–5.3)·1020 cm–3 (0.4 to 1.2 at.%). Considering Ga
peak concentrations between 6 and 8 at.% (Fig. 1) this re-
sults in minimal local activation ratios of 5–20%. In
Ref. 20, this important issue is addressed in more detail.
Superconducting properties
The low-temperature resistivity of Ge:Ga is presented
in Fig. 4. The measurements were performed in zero mag-
netic field with excitation currents of 1 μA. The results
were reproduced with currents of 100 nA indicating that no
influence of the critical current density has to be consi-
dered at these measurement currents.
After annealing with a fluence of 48 J/cm2, no super-
conductivity is found. As the annealing temperature is in-
creased, superconductivity emerges at 0.24 K and gradual-
ly rises to higher temperatures. A maximum Tc of 0.43 K is
reached at 60 J/cm2 (taking the resistive midpoint as crite-
rion). Further, the relative height of the resistivity drop also
increases monotonously. In more detail, a large remnant
resistivity in the superconducting state remains after FLA
at 50 J/cm2, whereas zero resistivity has been observed
after FLA at 60 J/cm2. While we attribute the rising Tc to
an increase of the hole concentration, the remaining resi-
dual resistivity may be explained in terms of laterally in-
homogeneous activation ratios which could result in less
doped, thus nonsuperconducting regions. The evolution of
the critical temperature (10, 50, and 90% of the resistance
drop) and corresponding sheet-carrier concentration nsheet
with applied FLA fluence is shown in Fig. 5. Since crystal-
linity and Ga profile differ only slightly among the sam-
ples, we suggest a direct correlation between Tc and hole
concentration. This would mean that the dependence out-
lined in the introduction seems to be valid not only for
BDD and Si:B but also for Ge:Ga since we observe the
following. The critical temperature of Ge:Ga rises steeply
at a critical sheet concentration of about 2·1015 cm–2 or a
corresponding spatial density of 0.4 at.% (inset Fig. 5). For
this concentration no sign of superconductivity is found
down to 80 mK after FLA at 48 J/cm2, whereas for
50 J/cm2 superconducting traces emerge at 0.24 K. Tc in-
creases further with hole concentration though less steeply.
The transition width fluctuates nonsystematically between
0.1 and 0.2 K. As mentioned above, we further investi-
gated a series of equally flash-lamp annealed Ge:Ga sam-
ples having an implantation dose of 0.6·1016 cm–2. We
have found similar or even higher hole concentrations but
no superconductivity. This means that nonactivated gal-
lium that may be situated at interstitial lattice places, seems
to be another necessary parameter (besides the charge-
carrier concentration) for the occurrence of superconduc-
tivity. Whether this originates from corresponding lattice
distortions, i.e., chemically induced pressure or modifica-
tions of the phonon spectra remains an open question.
After the discussion of the influence of the preparation
parameters, we now focus on the properties of the super-
Fig. 4. (Color online) Low-temperature resistivity of Ge:Ga that
has been annealed at different FLA fluences measured with an
applied current of 1 μA. Rising the annealing temperature results
in a higher Tc and an increased relative resistivity drop upon en-
tering the superconducting state. Zero resistivity at T < Tc has
only been observed after FLA at 60 J/cm2.
0.1 1
0
10
20
40
T, K
48
50
52
54
56
58
60
Fluence, J/cm
2
R
,
Ω
Fig. 5. (Color online) Critical temperature (left axis) and sheet-
carrier concentration (right axis) of Ge:Ga plotted vs. the anneal-
ing fluence. The filled circles and open triangles mark the tem-
peratures at 50, 10, and 90% superconducting resistivity drop (as
derived from Fig. 4). A direct correlation between the concentra-
tion and Tc is assumed and plotted in the inset.
48 50 52 54 56 58 60
0
0.2
0.4
0.6
0.8
0
5
10
15
0 2 4 6
0.4
n
sh
ee
t,1
0
cm
1
5
–
2
nsheet,10 cm
15 –2
T
c
,
K
T
c
,
K
Fluence, J/cm
2
The impact of heavy Ga doping on superconductivity in germanium
Low Temperature Physics/Fizika Nizkikh Temperatur, 2011, v. 37, Nos. 9/10 1103
conducting state. We have performed electrical-transport
measurements at various applied magnetic fields and with
different excitation currents. In Fig. 6,a, the temperature-
dependent resistivity of the sample with the highest Tc
(60 J/cm2) is shown for in-plane fields up to 400 mT. The
broadening of the transition may be attributed to a so-
called vortex-liquid state which is well known for type-II
superconductors [27]. The resulting field-temperature
phase-diagram of this and three other samples is drawn in
Fig. 6,b. Here, the 10% resistivity drop of various R(T)
curves at constant in-plane magnetic fields has been taken
as criteria for Bc2||(T). If we extrapolate the linear depen-
dence for T → 0, we find Bc2|| ≈ 0.8 T for the sample an-
nealed at 60 J/cm2. A linear dependence of Bc2|| down to
0.1 Tc has been revealed within our previous investigations
of Ge:Ga [5]. The theory of Werthamer, Helfand, and Ho-
henberg describes Bc2(T) for superconductors in the dirty
limit, i.e., where the Ginzburg–Landau coherence length
is restricted by short electronic mean-free paths [28–30].
This condition is fulfilled for heavily Ga-doped Ge. An
estimate of the electronic mean-free path is given via
eff* / 7Fl v m e= μ ≈ nm, with 2 1/3
eff vol( / )(3 )Fv m nπ= as
the Fermi velocity for the maximum spatial hole density
nvol = 5.3·1020 cm–3, μ = 40 cm2/(V·s) the charge carrier
mobility, and meff the effective hole mass [31]. This esti-
mate appears reasonable as the mean-free path matches
well with the grain size of the nanocrystalline Ge:Ga layer.
Although we have found a small anisotropy [5], the critical
fields parallel and perpendicular to the layer are roughly of
the order of Bc2 ≈ 0.5 T. This leads to a Ginzburg–Landau
coherence length of ξGL = [φ0/(2π Bc2)]0.5 ≈ 26 nm, where
φ0 = h/2e = 2.068·10–15 Wb is the flux quantum. Thus, ξGL
is restricted by the mean-free path according to ξGL(l*) =
= (ξGL(l* = ∞)l*)0.5 as l* < ξGL(l* = ∞) [32]. With this
formula, we are able to estimate the coherence length in
the clean limit ξGL(l* = ∞) ≈ 100 nm. Unfortunately, there
was no sign of field screening detectable via ac-suscep-
tibility measurements as possible supercurrents are strong-
ly limited (see below). The expected Meissner signals are
also below the resolution limit of our dc-susceptibility
measurements. Most likely, this is related to a strong re-
duction of field expulsion which is common for structures
smaller than or of the order of the London penetration
depth λL [33]. Thus, λL and the Ginzburg–Landau parame-
ter κGL = λL/ξGL remain unknown. However, as the mean-
free path modifies the latter via ( *) ( * )GL GLl lκ ≈ κ = ∞ ×
( * )/ *GL l l×ξ =∞ [32], we see that ( *)/ ( * ) 14GL GLl lκ κ =∞ >
which indicates a significant structure-induced shift of su-
perconductivity towards type-II character. Together with
the high critical fields, this confirms type-II superconduc-
tivity in our samples, while in cleaner Ge:Ga this character
may be less distinct.
Finally, we discuss the impact of the current density on
superconductivity in Ge:Ga. Notably, even small excitation
currents of 20 μA are sufficient to depress superconducti-
vity almost completely in the sample annealed at 50 J/cm2
(Fig. 7). The occurrence of possible heating effects can be
excluded as thermometry has been checked thoroughly.
Moreover, we observe a pronounced transition broadening
in all samples as the current is increased from 1 to 5 μA. A
possible qualitative understanding may be given in terms
of an inhomogeneous lateral doping which could lead to
weak links along the current paths. Thus, Josephson junc-
tions through poorly conducting or through still nonsuper-
conducting but low resistive Ge grains could modify the
transport behavior. However, we do not find explicit evi-
dence for Josephson coupling as has been revealed, e.g.,
for superconductivity in granular cuprates [34]. There, an
increase of resistivity towards lower temperatures at over-
Fig. 6. (Color online) (a) Temperature dependence of the resis-
tance at various in-plane magnetic fields (measured with a current
of 1 μA) for the sample annealed at 60 J/cm2. (b) In-plane field-
temperature phase diagram of four differently annealed Ge:Ga
samples. Bc2||(T) has been derived from the temperatures at which
the resistivity drops by 10% at constant magnetic fields.
0.1 1
0
5
10
0 0.5
0.5
b
300
200
100
400
0
�0 ||H , mT
60 J/cm
2
a
52 56
54 60
T , KT , K
Fluence, J/cm
2
B
c
||,
T
0.5 1.00
10
20
20 5 1
60 J/cm
2
54 J/cm2
T, K
50 J/cm
2
Excitation, �A
R
,
�
Fig. 7. (Color online) Temperature dependence of the resistance
for differently annealed samples and different excitation currents.
For the sample annealed at 50 J/cm2 a current of around 20 μA
(equivalent to a current density of about 20 kA/m2) is sufficient
to suppress the superconducting transition.
R. Skrotzki, T. Herrmannsdörfer, V. Heera, J. Fiedler, A. Mücklich, M. Helm, and J. Wosnitza
1104 Low Temperature Physics/Fizika Nizkikh Temperatur, 2011, v. 37, Nos. 9/10
critical currents indicates thermal blocking of quasiparticle
tunnelling. This behavior has not been observed in Ge:Ga.
Further, we find that higher annealing fluences result in
slightly larger critical currents. A comparison with other
Ge:Ga samples unveiled that this is not a consequence of
the rising Tc, but may rather be explained by the increasing
crystallinity (i.e., larger grain sizes and further epitaxial
regrowth) and a possibly more homogeneous dopant acti-
vation. Generally, we find very low critical-current densi-
ties down to Jc ≈ 20 μA/(100 nm·1 cm) = 20 kA/m2 that
further need to be probed locally for better quantitative
understanding.
Discussion
Triggered by our findings, ab initio supercell calcula-
tions based on the density-functional theory have been
published recently [35]. Starting with the assumption of
perfectly doped, i.e., activated Ge:Ga with a Ga concentra-
tion of 6.25 at.%, the crystal lattice has been found to be
only slightly altered compared to undoped Ge while the
band structure becomes significantly modified and exhibits
a shift of the Fermi level to 0.6 eV below the valence-band
maximum. This results in the formation of a Fermi surface
emerging around the Brillouin-zone center. Consequently,
the optical-phonon spectrum becomes softened and new
gallium-associated modes arise. These findings are well
confirmed by a second approach that further includes an
investigation of the electron–phonon coupling and its im-
pact on Tc [36]. The latter has been evaluated using the
Allen–Dynes modification [37] of McMillan’s solution of
the Eliashberg equation [38]. In accordance to BDD and
Si:B, the main contribution to the electron–phonon coup-
ling (λ = 0.35) is assigned to optical-phonon modes (75%).
While these are attributed to the Ge lattice, the acoustic
modes are associated with the incorporated gallium con-
tent. Most interestingly, the latter account for 25% of the
coupling featuring a significant impact of the dopant atom
on the BCS-like superconductivity identified for Ge:Ga.
We now want to discuss our experimental results in the
context of superconductivity in heavily doped group-IV
semiconductors. We find that the qualitative doping de-
pendence of Ge:Ga is in good agreement with previous
observations in BDD and Si:B [7,9]. Also the critical hole
concentrations of 0.5 at.% (0.9·1021 cm–3) [9] in BDD and
2 at.% (1·1021 cm–3) [7] in Si:B are comparable to our
finding of 0.4 at.% (0.2·1021 cm–3) in Ge:Ga. However, a
quantitative description in terms of an universal under-
standing requires further knowledge about the role of the
dopants. Theoretical investigations which focus roughly on
treating the latter as source of charge carriers lead to an
underestimation of critical temperatures as the predicted
crucial doping levels lie above those which have been
found experimentally [18]. Within this work, we have
shown that especially for Ge:Ga the activation ratio of do-
pants may play an important though previously unconsi-
dered role. A critical charge-carrier concentration of about
0.4 at.% has been found in the vicinity of a maximum Ga
concentration of 8 at.%. This reflects the presence of main-
ly electrically nonactivated gallium. Furthermore, in case
of an implantation dose about three times smaller, similar
and even higher hole concentrations did not result in su-
perconductivity. This obviously calls for a more sophisti-
cated influence of the incorporated gallium.
As we are facing a large amount of nonactivated gal-
lium and are dealing with concentrations above the solubil-
ity limit, the issue of possible Ga segregation has to be
discussed seriously, although no traces of Ga clusters have
shown up in our XTEM investigations. Several supercon-
ducting Ga phases are known. The standard α phase has a
Tc of 1.08 K. Further crystalline phases reveal critical tem-
peratures between 6.07 and 7.85 K [39]. Amorphous Ga
reveals a more complex behavior as superconductivity in
disordered thin films depends sensitively not only on film
thickness but also on chemical surrounding, i.e., the sub-
strate used for film growth [40,41]. Furthermore, the nor-
mal-state low-temperature thin-film sheet resistance seems
to play a crucial role, as Rq ≈ 6.45 kΩ/sq. manifests as ma-
terial-independent universal upper threshold for the occur-
rence of superconductivity [42]. Approaching Rq, quantita-
tive differences have been found as Tc can decrease
considerably. However, all these critical temperatures are
well above those which we have found in Ge:Ga. One
should further mention that amorphous Ga with a diameter
smaller than 1.3 nm — which could not have been detected
via XTEM — was classified as nonsuperconducting [40].
Most conclusively, recent studies on Ga-implanted silicon
have shown that amorphous Ga-rich precipitates can form
upon subsequent rapid thermal annealing [43]. Exceeding
Rq or not, they remain resistive or reveal superconductivity
with an invariable Tc of 7 K. We deduce that Ga clusters
prepared under such comparable though less favorable
doping conditions (lower solubility of Ga in Si, higher im-
plantation dose, longer annealing time) do not feature low-
temperature superconductivity setting in at around 0.5 K
which thus can be considered as intrinsic property of
Ge:Ga.
Conclusion
In summary, we have unraveled the evolution of Tc
with hole concentration in heavily Ga-doped germanium.
In addition to a high hole concentration (> 0.4 at.%) pro-
vided by Ga acceptors the presence of a sufficiently high
total Ga concentration in the range of several at.% is essen-
tial for the occurrence of superconductivity in Ge. The
disordered and mainly nanocrystalline structure of Ge:Ga,
as revealed by RBS/C, SIMS, and XTEM, has a decisive
impact on superconductivity as the critical currents are
strongly reduced. Moreover, this structure enhances the
type-II character with comparably large critical fields. So
far, electrical-transport measurements have been the only
The impact of heavy Ga doping on superconductivity in germanium
Low Temperature Physics/Fizika Nizkikh Temperatur, 2011, v. 37, Nos. 9/10 1105
way to characterize the superconducting state in thin-film
Ge:Ga.
Although this work sheds light on the underlying fun-
damental physics, the application potential of covalent-
bound superconductors is worth mentioning. Due to the
preparation being fully compatible with state-of-the-art
semiconductor processing thin-film Ge:Ga could easily be
patterned into custom-designed devices where combined
semi- and superconducting circuits may be integrated
close-by [8]. Besides the small critical temperatures, first
achievements concerning BDD have been reported and
may stimulate further progress [44].
We acknowledge the support of F. Arnold, K.-H. Hei-
nig, H. Hortenbach, M. Posselt, B. Schmidt, W. Skorupa,
S. Teichert, M. Voelskow, and C. Wündisch for technical
assistance and helpful discussion. Part of this work was
supported by Deutsche Forschungsgemeinschaft under
Contract No. HE 2604/7 and by EuroMagNET II under EU
contract No. 228043.
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