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RESEARCH ARTICLE
|
APRIL 22 2024
Investigation of cryogenic current–voltage anomalies in
SiGe HBT
s: Role of base–emitter junction inhomogeneities
Nachiket R. Naik
;
Bekari Gabritchidze
;
Justin H. Chen
;
Kieran A. Cleary
;
Jacob Kooi
;
Austin J. Minnich
J. Appl. Phys.
135, 164501 (2024)
https://doi.org/10.1063/5.0210218
24 April 2024 18:51:36
Investigation of cryogenic current
–
voltage
anomalies in SiGe HBTs: Role of base
–
emitter
junction inhomogeneities
Cite as: J. Appl. Phys.
135
, 164501 (2024);
doi: 10.1063/5.0210218
View Online
Export Citation
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k
Submitted: 25 March 2024 · Accepted: 2 April 2024 ·
Published Online: 22 April 2024
Nachiket R. Naik,
1
Bekari Gabritchidze,
2
Justin H. Chen,
1
Kieran A. Cleary,
2
Jacob Kooi,
3
and Austin J. Minnich
1
,
a)
AFFILIATIONS
1
Division of Engineering and Applied Science, California Institute of Technology, Pasadena, California 91125, USA
2
Cahill Radio Astronomy Lab, California Institute of Technology, Pasadena, California 91125, USA
3
NASA Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California 91109, USA
a)
Author to whom correspondence should be addressed:
aminnich@caltech.edu
ABSTRACT
The deviations of cryogenic collector current
–
voltage characteristics of SiGe heterojunction bipolar transistors (HBTs) from ideal drift-diffu-
sion theory have been a topic of investigation for many years. Recent work indicates that direct tunneling across the base contributes to the
non-ideal current in highly scaled devices. However, cryogenic discrepancies have been observed even in older-generation devices for which
direct tunneling is negligible, suggesting that another mechanism may also contribute. Although similar non-ideal current
–
voltage charac-
teristics have been observed in Schottky junctions and were attributed to a spatially inhomogeneous junction potential, this explanation has
not been considered for SiGe HBTs. Here, we experimentally investigate this hypothesis by characterizing the collector current ideality
factor and built-in potential of a SiGe HBT vs temperature using a cryogenic probe station. The temperature dependence of the ideality
factor and the relation between the built-in potential as measured by capacitance
–
voltage and current
–
voltage characteristics are in good
qualitative agreement with the predictions of a theory of electrical transport across a spatially inhomogeneous junction. These observations
suggest that inhomogeneities in the base
–
emitter junction potential may contribute to the cryogenic non-idealities. This work helps to iden-
tify the physical mechanisms limiting the cryogenic microwave noise performance of SiGe HBTs.
© 2024 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license
(
https://creativecommons.org/licenses/by/4.0/
).
https://doi.org/10.1063/5.0210218
I. INTRODUCTION
Silicon
–
germanium heterojunction bipolar transistors (HBTs)
are widely used in microwave applications such as high-speed com-
munications and radar systems owing to their competitive micro-
wave performance, low cost, and ease of integration compared with
III
–
V compound semiconductor devices.
1
Technological advances
such as reduced emitter widths, decreased base resistances and
extrinsic capacitances, and advanced epitaxial techniques have
enabled microwave noise performance approaching that of III-V
high electron mobility transistors.
2
,
3
As a result, cryogenic SiGe
HBTs have recently been considered for applications in quantum
computing and radio astronomy.
4
–
6
The cryogenic microwave performance of SiGe HBTs has been
investigated following their initial development in the 1980s
7
as
various performance metrics such as transconductance and noise
figure improve with cooling. However, below
77 K, these
improvements are observed to plateau with decreasing
temperature,
8
–
10
corresponding to a temperature-dependent collec-
tor current ideality factor
n
(
T
) that greatly exceeds unity at cryo-
genic temperatures.
11
,
12
This behavior differs markedly from the
predictions of drift-diffusion theory for fabricated p
–
n junctions
for which
n
is close to unity and independent of temperature, and
the transconductance increases inversely with temperature.
13
,
14
Because the minimum noise temperature is directly proportional to
n
(
T
) in the limit of
f
=
f
t
1 and low base resistance (see Eq. 5.1 in
Journal of
Applied Physics
ARTICLE
pubs.aip.org/aip/jap
J. Appl. Phys.
135,
164501 (2024); doi: 10.1063/5.0210218
135,
164501-1
©Author(s)2024
24 April 2024 18:51:36
Ref.
10
), identifying the physical origin of the discrepancies is nec-
essary to improve the cryogenic microwave noise performance of
SiGe HBTs.
The cryogenic non-ideal behavior has been attributed to
various mechanisms including quasiballistic transport,
9
,
10
direct
tunneling,
11
or trap-assisted tunneling.
15
However, a theoretical
study has reported that quasiballistic electron transport cannot
explain the observed collector cryogenic non-idealities.
16
Recent
works indicate that direct tunneling across the base can account for
the non-idealities in highly scaled devices.
5
,
11
,
12
,
17
At the same
time, non-idealities have been observed in devices with base widths
of
100 nm
5
,
9
for which direct tunneling is negligible. This obser-
vation suggests that, in addition to tunneling, another mechanism
may contribute to cryogenic non-ideal current
–
voltage characteris-
tics in SiGe HBTs.
In a different context, similar anomalies have been observed
and extensively investigated in Schottky diodes,
18
–
21
and they were
ultimately attributed to spatial inhomogeneities in the built-in
potential
Φ
BI
.
22
–
25
Although semiconductor junctions are often
modeled as uniform across their lateral area, in fact various imper-
fections exist, which affect the local electronic structure of the junc-
tion, a point that was recognized as early as 1950.
26
Even at
epitaxial interfaces, it was found that different crystallographic
orientations
27
–
29
or the presence of dislocations
30
,
31
can lead to
potential barrier height variations on the order of hundreds of mV.
In Schottky junctions, these inhomogeneities have been directly
observed using ballistic electron emission microscopy.
32
,
33
Various
theories and numerical analyses of the electrical characteristics of
inhomogeneous junctions have been reported and lead to compati-
ble conclusions.
22
–
24
In particular, the theory of Werner and
Güttler makes several predictions regarding the temperature depen-
dence of the ideality factor and the relation between the built-in
potential as measured by different methods.
23
,
34
,
35
However, an
experimental test of these predictions for SiGe HBTs has not yet
been reported.
Here, we perform this experimental investigation by character-
izing the collector current ideality factor and built-in potential of a
SiGe HBT from room to cryogenic temperatures. We find that the
measured temperature dependence of the ideality factor and the
relation between built-in potential as determined by capacitance
–
voltage and current
–
voltage characteristics are compatible with the
theoretical predictions. This observation suggests that inhomogene-
ities in the base
–
emitter junction potential could be a mechanism
affecting the cryogenic current
–
voltage characteristics in SiGe
HBTs. We discuss how the existence of barrier inhomogeneities
could be further confirmed. Our work advances efforts to improve
the cryogenic electrical characteristics and, hence, microwave noise
performance of SiGe HBTs.
II. THEORY AND METHODS
A. Overview
The theory of Werner and Güttler describes electrical trans-
port over the lateral area of a Schottky junction with a spatially
inhomogeneous barrier characterized by a mean barrier height and
a variance.
23
The distribution of the barrier heights is taken to be
Gaussian, an assumption that is supported by local measurements
of the barrier heights (Fig. 19.12 in Ref.
13
). The variance in the
distribution is assumed to decrease with increasing junction bias
due to the pinch-off of low-barrier patches of dimension less than
the depletion length, a concept that was originally introduced in
Ref.
24
and later developed in Ref.
22
.
The theory makes several predictions regarding the trends of
electrical characteristics with temperature and other parameters in
junctions exhibiting voltage-independent ideality factors
n
(
T
). In
particular,
n
(
T
), as determined from the slope of
I
V
characteris-
tics, is predicted to vary with temperature according to
n
(
T
)
1
1
¼
ρ
2
þ
ρ
3
2
kT
=
q
,
(1)
where
k
is Boltzmann
’
s constant,
q
is the electric charge, and
ρ
2
and
ρ
3
are constants describing a linear variation in the mean
barrier height,
f
B
, and variance,
σ
2
s
, with junction voltage
U
[c.f.
Eq. (23) in Ref.
23
]
Δ
f
B
¼
ρ
2
U
,
(2a)
Δ
σ
2
s
¼
ρ
3
U
:
(2b)
A plot of
n
(
T
)
1
1vs
T
1
should, therefore, yield a line
over some range of temperatures if any temperature-dependence of
ρ
2
and
ρ
3
is negligible.
In addition, the effective built-in potential
Φ
BI
can be mea-
sured in two ways. From
C
BE
V
BE
characteristics,
Φ
BI
(
CV
) can be
obtained by fitting the variation in depletion capacitance with junc-
tion voltage using
C
BE
(
V
BE
)
¼
C
BE
,0
(1
V
BE
=
Φ
BI
)
m
, where
C
BE
,0
is the zero-bias junction capacitance and
m
is an exponent that
depends on the doping profile at the junction.
14
On the other hand, from
I
C
V
BE
characteristics, the poten-
tial barrier for transport,
Φ
BI
(
IV
), relative to its value at some tem-
perature, can be obtained by extrapolating the measured collector
current to zero bias using the diode expression,
I
C
¼
I
S
exp
qV
BE
nkT
1
,
(3)
where
I
S
¼
A
exp(
q
Φ
BI
(
IV
)
=
kT
) is the transport saturation
current and
A
is a constant prefactor that depends on
device-specific characteristics (Sec. 4.2.1 in Ref.
1
). From this
expression,
Φ
BI
(
IV
) can be extracted relative to
Φ
BI
,
T
RT
(
CV
), the
value determined by C
–
V measurements at
T
RT
¼
300 K, using
I
S
(
T
)
I
S
(
T
RT
)
¼
exp
Φ
BI
(
IV
)
=
kT
ðÞ
exp
Φ
BI
,
T
RT
(
CV
)
=
kT
RT
ðÞ
:
(4)
We have neglected the polynomial temperature-dependence of
the prefactor as it only makes a log-scale correction to the built-in
potential that does not alter our conclusions.
The inhomogeneous junction theory predicts that the barrier
measured in these two ways should differ in magnitude and tem-
perature dependence owing to the fact that current depends on
V
BE
exponentially, while the capacitance varies with
V
BE
with a weaker
Journal of
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135,
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©Author(s)2024
24 April 2024 18:51:36
polynomial dependence. The barrier as determined through
C
–
V
characteristics is, therefore, typically interpreted as the mean
barrier height, while that determined from
I
–
V
characteristics is
often less than the mean value due to the larger contribution from
low-barrier regions.
23
,
36
The theory gives a relation between these
barrier heights as [c.f. Eq. (14) in Ref.
23
]
Φ
BI
(
IV
)
¼
Φ
BI
(
CV
)
σ
2
s
2
kT
=
q
:
(5)
Considering the form of
n
(
T
)inEq.
(1)
,thisrelationiscompat-
ible with the empirical observation that
Φ
BI
(
CV
)
n
(
T
)
Φ
BI
(
IV
)
37
(see also Sec. V in Ref.
23
).
These predictions can be tested on SiGe HBTs of interest in
this work using a cryogenic probe station to measure the
I
C
–
V
BE
and
C
BE
–
V
BE
characteristics. Although the inhomogenous junction
theory and measurement approach were developed for Schottky
junctions, it is applicable to the base
–
emitter junction of an HBT
due to the following considerations. First, the theory does not make
any specific assumption that the junction is a Schottky junction,
but rather only that an inhomogeneous barrier to current transport
exists that is characterized by a Gaussian height distribution.
Second, the temperature dependence of the junction saturation
current is exponential in both cases as the key transport mechanism
is thermal charge injection, with the exponent being proportional
to the effective barrier height for charge injection,
Φ
BI
(
IV
).
Therefore, analysis of the current
–
voltage characteristics as
described above will yield
Φ
BI
(
IV
) equally well for SiGe HBTs as
for Schottky junctions. We note that this charge injection approach
to model the current
–
voltage characteristics is relatively simple
compared to generalized-integral charge-control relation (GICCR)
models employed for HBTs.
38
However, GICCR models also
exhibit discrepancies with experiment below 100 K (Fig. 6.5(a) in
Ref.
39
), suggesting that the physical origin of current
–
voltage dis-
crepancies is not due to the simplicity of the charge injection
model.
Finally, for the
C
BE
–
V
BE
characteristics, although the mecha-
nisms of current transport in the forward active regime differ
between Schottky junctions and HBTs, the electrostatics of the
space charge region and the associated depletion capacitance are
identical between the devices (Chaps. 6 and 7 in Ref.
40
).
Therefore, the built-in potential can be determined by the depen-
dence of
C
BE
on
V
BE
at reverse or low-forward biases, in which
case
C
BE
is dominated by the depletion capacitance. This procedure
was recently applied to determine the built-in potential of SiGe
HBTs.
12
B. Experimental methods
We extracted
Φ
BI
from
C
BE
–
V
BE
and
I
C
–
V
BE
characteristics
from 20 to 300 K on a SiGe HBT (SG13G2, IHP). The discrete tran-
sistors were probed in a custom-built cryogenic probe station.
41
,
42
We employed nickel/tungsten probes (40A-GSG-100-DP, GGB
Industries) that are suitable for probing Al pads.
I
C
–
V
BE
characteris-
tics were performed at a constant collector voltage
V
CE
¼
1V to
provide a collector current above the minimum resolution of our
measurement setup (10 nA). The current range used for this fitting
is limited to 0.2 mA, below the high-injection regime, to exclude
effects of series resistance, self-heating, and the Early and reverse
Early effects. Inclusion of the reverse Early effect in the extraction of
the built-in potential was found to alter the extracted
Φ
BI
(
IV
)by
only a few percent as it makes only a log-scale correction. Due to the
difficulty in distinguishing periphery from area currents, we assumed
that the area current is dominant following other studies of cryogenic
SiGe HBTs.
5
,
10
–
12
,
17
Following standard procedure,
12
,
13
C
BE
–
V
BE
characteristics
were obtained using a vector network analyzer (VNA, Keysight
E5061B). In reverse-bias and low-forward bias regimes, the
Y
-parameters are given by
Y
11
¼
g
BE
þ
j
ω
(
C
BE
þ
C
BC
) and
Y
12
¼
j
ω
C
BC
, where
C
BC
is the base
–
collector depletion capaci-
tance. The base
–
emitter capacitance can, therefore, be expressed as
C
BE
¼
(
=
(
Y
11
þ
Y
12
))
=
2
π
f
.
V
BE
was restricted to [
0
:
5V,
þ
0
:
5V]
to ensure that the measured capacitance was dominated by the
depletion capacitance.
V
BC
¼
0 V was held constant to ensure
C
BC
was constant while
V
BE
was swept. The
Y
parameters were mea-
sured in 1
–
3 GHz, and the extractions were performed at 2.4 GHz.
At these frequencies, it was observed that the imaginary part
of
Y
11
was linear in frequency, indicating purely capacitive behav-
ior. Short-Open-Load-Through calibration was performed on a
CS-5 calibration standard at each temperature, and the shunt para-
sitic capacitance at the input of the device was de-embedded using
an OPEN structure. The intermediate-frequency bandwidth
(1 kHz) and frequency points (every 0.2 GHz) were selected to limit
the total sweep time to less than 15 s to avoid drift. At each bias,
Y-parameters were swept across frequency and ensemble-averaged
10 times.
Φ
BI
was extracted from a sweep of
C
BE
vs
V
BE
by fitting
the parameters
Φ
BI
,
C
BE
,0
, and
m
using a trust region reflective
algorithm from the SciPy library.
43
Φ
BI
was constrained to [0.5 V,
1.2 V],
C
BE
,0
was constrained between the minimum and maximum
values of the sweep, and
m
was constrained to [0, 1].
III. RESULTS
Figure 1(a)
shows the collector current
I
C
vs
V
BE
at various
temperatures between 20 and 300 K. Consistent with prior find-
ings,
5
,
10
,
11
the measurements exhibit deviations from drift-diffusion
theory at cryogenic temperatures, with the current
–
voltage charac-
teristic plateauing to a temperature-independent curve below
60 K. We plot the extracted
n
(
T
)as
T
eff
¼
n
(
T
)
T
phys
vs
T
phys
in
Fig. 1(b)
.
T
eff
is observed to plateau to
100 K due to
n
(
T
)
.
1at
cryogenic temperatures, as has been reported previously.
10
We next examine the
C
BE
V
BE
characteristics.
Figure 2(a)
plots
=
(
Y
11
þ
Y
12
)
=
ω
vs
f
for various
V
BE
at 300 K, where
ω
¼
2
π
f
. A narrowed frequency range from the 1
–
3 GHz measure-
ments is plotted to aid in distinguishing the curves. The
de-embedded base
–
emitter capacitance
C
BE
is directly obtained
from this plot by averaging across the frequency range.
Figure 2(b)
plots the resulting
C
BE
vs
V
BE
at seven representative temperatures
vs voltage along with the fitted curves. The error bars, representing
the 2
σ
error in
C
BE
, are obtained from the 10
C
BE
–
V
BE
sweeps per-
formed at each temperature.
The magnitudes of the measured capacitances are on the same
order as other reports on the same device type (SG13G2) used
here.
12
We note a non-monotonic trend in the capacitance data of
Journal of
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Fig. 2(b)
with temperature. This trend was also observed in Fig. 4
(a) in Ref.
12
, and it can be attributed to variations in parasitic pad
capacitances on landing, which overwhelm any intrinsic tempera-
ture dependence of the capacitances. However, the magnitude of
the capacitance is not used to determine
Φ
BI
(
CV
), and hence the
parasitics have no effect on our conclusions.
These data are next analyzed to obtain
Φ
BI
from the
I
C
–
V
BE
and
C
BE
V
BE
characteristics according to the methods in
Sec.
II A
. At 300 K,
Φ
BI
(
CV
) is found to be 0.83 V, in good agree-
ment with Ref.
12
. This value is specified as the room temperature
value for
Φ
BI
(
IV
).
Figure 3(a)
plots the
Φ
BI
from both measure-
ments vs
T
phys
.For
Φ
BI
(
CV
), the error bars represent the 2-
σ
error, obtained by performing fits to 100
C
BE
–
V
BE
sweeps with
errors randomly determined based on a normal distribution
defined by the uncertainty in the measured
C
BE
. The extracted
Φ
BI
(
CV
) is observed to weakly increase with decreasing tempera-
ture, consistent with observations for similar HBT devices
12
and
Schottky diodes.
37
In contrast,
Φ
BI
(
IV
) demonstrates a qualitatively
stronger dependence on temperature than
Φ
BI
(
CV
), exhibiting a
lower magnitude at cryogenic temperatures as previously observed
in Schottky diodes
13
,
37
(also compare to
Fig. 3
in Ref.
34
). The vari-
ation in
Φ
BI
(
IV
) with temperature is significantly stronger than
that of the emitter and base bandgaps,
14
suggesting that another
mechanism is responsible for the observed temperature trend.
We now examine the agreement between the data and the pre-
dictions from the inhomogeneous junction theory of Ref.
23
,as
summarized in Sec.
II A
. First, qualitatively,
Φ
BI
(
CV
) and
Φ
BI
(
IV
)
are predicted to differ, with
Φ
BI
(
IV
) expected to exhibit a stronger
temperature dependence and be smaller in magnitude than
Φ
BI
(
CV
). This behavior is observed in
Fig. 3(a)
. More quantita-
tively, for the predicted temperature-dependence of
n
(
T
)from
the theory, it is expected that
Φ
BI
(
CV
)
n
(
T
)
Φ
BI
(
IV
) (Sec. V in
Ref.
23
). The product
n
(
T
)
Φ
BI
(
IV
) is also plotted in
Fig. 3(a)
,
demonstrating good agreement with
Φ
BI
(
CV
).
FIG. 2.
(a) Measured
=
(
Y
11
þ
Y
12
)
=
ω
(symbols) vs
f
at 300 K for various
V
BE
in steps of 0.1 V. The lines are guides to the eye. (b) Measured (symbols) and
fitted (solid lines) intrinsic
C
BE
capacitance vs
V
BE
from 20 to 300 K. Parasitic
capacitances are de-embedded from the Y-parameter measurements as detailed
in Sec.
II B
. As a representative example, the fit for 300 K yields
Φ
BI
¼
0
:
83 V
and
m
¼
0
:
10.
FIG. 1.
(a) Measured
I
C
vs
V
BE
for various temperatures. The characteristics
become independent of temperature at cryogenic temperatures. (b)
T
eff
¼
n
(
T
)
T
phys
vs
T
phys
from measurements (symbols) and diode theory
(line), indicating the non-ideality of the base
–
emitter junction at cryogenic
temperatures.
Journal of
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135,
164501-4
©Author(s)2024
24 April 2024 18:51:36
Second, Eq.
(1)
predicts that
n
(
T
)
1
1vs
T
1
should be a
straight line over some range of temperatures, assuming
ρ
2
and
ρ
3
to be independent of temperature.
Figure 3(b)
plots this quantity
for the present device and other devices with data obtained from
Fig. 5.8 in Ref.
10
. For all the devices, the expected trend is
observed over a temperature range that is comparable in relative
width to that in Fig. 9 in Ref.
23
, confirming the prediction.
Two regimes of deviation from the linear trend are observed
at high and low temperatures. At high temperatures
300 K,
n
(
T
)
1
1 plateaus to zero for all the devices, corresponding to an
ideal junction with
n
¼
1. This deviation was also observed in
Fig. 8 in Ref.
23
and is expected since
n
1 for fabricated junc-
tions, meaning
n
(
T
)
1
1
0. It could be explained by a
temperature dependence of
ρ
2
and
ρ
3
, which was neglected in this
work and in Ref.
23
.
The SG13G2 also exhibits a deviation from the linear trend at
low temperature (
20 K). This discrepancy could be attributed to
the presence of a direct tunneling current that has been previously
reported to exist in highly scaled devices.
11
,
12
The present device
has a base width less than 20 nm,
44
and so direct tunneling could
occur. The older-generation devices exhibit the linear trend down
to 20 K, which is compatible with the absence of tunneling current
in these devices with larger base widths. Despite these deviations,
overall the experimental trends are in good qualitative agreement
with the theoretical predictions of the inhomogeneous barrier
theory.
Semi-quantitative information regarding the variation of the
barrier height variance with bias for the present device can be
obtained from the linear fit in
Fig. 3(b)
.If
ρ
2
þ
ρ
3
=
(2
kT
=
q
)
1,
the theory of Ref.
23
described in Sec.
II A
reduces to the
T
0
model
for non-ideal junctions, which has been extensively studied in the
Schottky junction literature.
19
,
22
,
23
In this case, the slope of the
linear fit in
Fig. 3(b)
is simply
T
0
. Performing this fit for the
present data yields
T
0
30 K, a value that is generally compatible
with values for Schottky diodes compiled in Ref.
23
.
T
0
, in turn,
can be linked to
ρ
3
as (Eq. 33 in Ref.
23
)
T
0
ρ
3
2
k
=
q
:
(6)
We obtain a value
ρ
3
¼
5
:
2 mV. The magnitude of this
value indicates that changes in standard deviation of the potential
barrier height distribution with base
–
emitter bias of less than a
percent of the mean barrier height are sufficient to account for the
observed electrical anomalies.
IV. DISCUSSION
The agreement of our data with the predictions of the inho-
mogeneous barrier theory suggests that lateral inhomogeneities in
the base
–
emitter junction potential could contribute to the cryo-
genic electrical anomalies. Additional evidence for the barrier inho-
mogeneity hypothesis could be obtained using techniques such as
ballistic emission electron microscopy (BEEM), which directly mea-
sures the spatial profile of the built-in potential.
33
However, apply-
ing this method to SiGe HBTs would require specialized samples to
be prepared, which are compatible with the measurement tech-
nique. Other methods that would be applied without requiring spe-
cialized samples might include transmission electron microscopy or
a combination of device physics simulations and electrical measure-
ments. However, none of these methods give as direct evidence as
BEEM.
The materials-scale origin of the inhomogeneities in HBTs
could be crystal defects such as dislocations, Ge clusters,
45
or elec-
trically active carbon defects.
46
Non-uniform Ge content over a few
nanometers in SiGe p-wells with Ge concentration
30% has been
reported to lead to the degradation of electrical properties such as
hole mobility.
45
Trap states associated with C impurities have also
been detected in modern HBTs.
46
In the SG13G2, the peak Ge con-
centration in the base is 28%,
47
and the value in the vicinity of the
FIG. 3.
(a) Built-in potential
Φ
BI
vs physical temperature from
C
BE
V
BE
(black circles) and
I
C
V
BE
(orange triangles) measurements. Also plotted is
n
(
T
)
Φ
BI
(
IV
) (green squares), which is predicted to agree with
Φ
BI
(
CV
).
23
Good
agreement is observed. (b)
n
(
T
)
1
1 vs inverse physical temperature
T
1
for
measured data on the SG13G2 (base width
,
20 nm) with a linear fit to the
data in 40
–
100 K following the prediction in Ref.
23
. Data obtained from older-
generation devices (Fig. 5.8 in Ref.
10
) are also shown.
Journal of
Applied Physics
ARTICLE
pubs.aip.org/aip/jap
J. Appl. Phys.
135,
164501 (2024); doi: 10.1063/5.0210218
135,
164501-5
©Author(s)2024
24 April 2024 18:51:36
base
–
emitter junction is, therefore, expected to be in the tens of
percent based on the SIMS profile of similar device reported in
Fig. 1.17 in Ref.
44
. These concentrations are sufficiently high for
Ge clusters to potentially form. Additionally, the C doping is on
the order of 10
20
cm
-3
,
1
and electronic trap states associated with
the doping have been previously identified.
46
These defects could
be the origin of an inhomogeneous base
–
emitter junction potential.
If the presence of spatial inhomogeneities across the emitter
area is verified, a less aggressive Ge doping concentration and
profile, especially in narrow-base SiGe HBTs, could decrease the
concentration of these imperfections and thereby lead to a more
uniform base
–
emitter junction potential. However, care would
need to be taken to avoid negatively impacting the high-frequency
properties of the device. Additionally, direct tunneling may pose a
fundamental obstacle to improve the cryogenic electrical ideality of
highly scaled devices. Further study is needed to distinguish the
various mechanisms and identify the limits to cryogenic electrical
ideality and, hence, microwave noise performance.
V. CONCLUSION
We have reported a characterization of the collector-current
ideality factor and built-in potential vs temperature of a SiGe HBT.
The observed trends with temperature and between measurement
techniques agree with a theory of electrical transport across a spa-
tially inhomogeneous junction, suggesting that barrier inhomoge-
neities may contribute to cryogenic electrical non-idealities in these
devices. This work advances efforts to improve the cryogenic
microwave noise performance of SiGe HBTs.
ACKNOWLEDGMENTS
The authors thank Akim Babenko, John Cressler, Nicolas
Derrier, Xiaodi Jin, Pekka Kangaslahti, Holger Rücker, Michael
Schröter, and Sander Weinreb for useful discussions. This work
was supported by NSF Award No. 1911926 and by JPL PDRDF
Project No. 107978.
AUTHOR DECLARATIONS
Conflict of Interest
The authors have no conflicts to disclose.
Author Contributions
Nachiket R. Naik:
Conceptualization (equal); Data curation
(equal); Investigation (equal); Methodology (equal); Writing
–
original draft (equal); Writing
–
review & editing (equal).
Bekari
Gabritchidze:
Data curation (equal); Methodology (equal).
Justin
H. Chen:
Data curation (supporting); Writing
–
review & editing
(equal).
Kieran A. Cleary:
Project administration (equal);
Writing
–
review & editing (equal).
Jacob Kooi:
Funding acquisi-
tion (equal); Methodology (equal); Writing
–
review & editing
(equal).
Austin J. Minnich:
Conceptualization (equal); Data cura-
tion (equal); Funding acquisition (equal); Methodology (equal);
Project administration (equal); Supervision (equal); Writing
–
original draft (equal); Writing
–
review & editing (equal).
DATA AVAILABILITY
The data that support the findings of this study are available
from the corresponding author upon reasonable request.
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