Close-packed arrays of transition-edge x-ray microcalorimeters with high spectral
resolution at
5.9
keV
N.
Iyomoto, S.R. Bandler, R.P. Brekosky, A.-D. Brown,
J.A.
Chervenak, F.M.
Finkbeiner,
R.L.
Kelley, C.A. Kilbourne, F.S. Porter, J.E. Sadleir, and S. J. Smith
NASA/Goddard Space Flight Center, Greenbelt, MD 20771*
E. Figueroa-Feliciano
Department
of
Physics, Massachusetts Institute
of
Technology, Cambridge, MA 02139
(Dated:)
We present measurements of high fill-factor arrays of superconducting transition-edge x-ray mi-
crocalorimeters designed to provide rapid thermalization of the x-ray energy. We designed an x-ray
absorber that is cantilevered over the sensitive part of the thermometer itself, making contact only
at normal metal-features. With absorbers made of electroplated gold, we have demonstrated an
energy resolution between
2.4
and 3.1 eV at
5.9
keV on 13 separate pixels. We have determined the
thermal and electrical parameters of the devices throughout the superconducting transition, and,
using these parameters, have modeled all aspects of the detector performance.
PACS
numbers:
The requirements of the X-ray Microcalorimeter Spec-
trometer on NASA's Constellation-X mission include a
full-width-at-half-maximum (FWHM) energy resolution
AE
of 2.5 eV at count rates up to 1000 s-' per pixel and
at least 95% quantum efficiency (QE) at an x-ray en-
ergy
E
of
6
keV. In order to cover a 5-arcminute field of
view with spatial sampling matched to the performance
of the optics, a
64x64
array of 0.25-mm pixels wit11
i3
high
fill
fBc-tor is required. We report significant progress in
the development of superconducting transition-edge sen-
sor (TES) microcalorimeterl arrays for missions such as
Constellation-X.
The TES thermometers in our arrays consist of bilayers
of
Mo
and Au with a superconducting transition temper-
ature
T,
of
N
0.1 K. Each 0.13-mm square TES is cen-
tered on a
0.5-pm silicon-nitride membrane, which is the
thermal link with thermal conductance
G
to the solid sil-
icon frame at
Tb
w
50 mK. The TES pixels are arrayed
on a 0.25-mm pitch. To achieve high QE and fill fac-
tor requires thick-film x-ray absorbers that fill the space
above and between each TES. Our original approach to
this requirement was to construct
Bi/Cu absorbers that
make contact to the entire area of the TES, but extend
cantilevered over the surrounding area. However, we de-
termined that the need for good thermal contact to the
TES and fast thermal equilibration of the absorber
(to
a\.oitl variwtioil
of
pulst:
sl~apt:
with posilio~~
ill
tlw
ill)-
5orl)rr) conflicts with the requirement that the absorber
not alter the superconducting transition of the
sens~r.~
We have developed absorbers that are cantilevered over
the sensitive regions of the
TES's themselves as well as
the surrounding area, making contact to the TES only at
ing the properties of the TES thermometer, even when a
normal metal is used as the absorber.
In order to avoid shunting the TES bias current
through the absorber, the absorber and TES may make
contact at only one region along the direction of current
flow. This constraint limits the size of the contact area
within the TES. To ensure mechanical stability of the
cantilevered structure, we extend the contact region onto
the membrane. In this letter we present results from elec-
troplated Au absorbers of two basic designs, one limiting
the absorber-TES contact to the device edges and one
making contact to the interdigitated stripes, as shown in
Figure la. A photograph of a portion of an 8x8 array
containing such pixels is shown in Figure lb.
jcads
Banks
!i
J
I
L,-
contact
e!n-
f
Le-,
Interdigitated
stri~
normal metal features that are already part of its design.
We deposit
Au along the edges parallel to the current
FIG.
1: (a) Schematics of the cantilevered absorbers. The
flow, to ensure a reproducible boundary condition, and
square gray outline marks the edge of the absorbers, which
on the surface, in interdigitated stripes perpendicular to
are supported only at the contact areas shown shaded in black.
the current flow,
to reduce detector noise3. Limiting the
(b) Photograph of TES array with electroplated Au absorbers.
absorber contacts to these normal regions avoids alter-
The area where the absorber touches the membrane
potentially provides a path to the heat sink that does
not go through the TES. In order to achieve high spec-
tral resolution in such a design, the equilibration time
teq
in the absorber must be much shorter than the time for
energy loss
tl,,,. The ratio t,q/tl,,, needs to be of order
AEIE. Applying the Wiedemann-Franz law to the low-
temperature electrical conductivity of our Au absorbers,
we estimate that
teq is approximately 30 ns at 0.09
K.
We further estimate that tloss, the time for energy de-
posited in one of the on-membrane supports to be lost
to the heat sink, is of order 1 ms, based on the heat ca-
pacity of the contact region and the conductance from
it. Therefore, we expect no significant energy loss from
the on-membrane support in either geometry.
Also.
wc>
cx1)cc.t rin sigliifioalit variatioll
of
pulst:
~1litl)i'.
thdriks
to
the
fasl
t,,.
-40
J
5880
5885
5890
5895
5900 5905
5910kV
Energy [eV]
I
1.8
2.0 2.2 2.4 2.6
2.8
3.0 3.2
Energy resolution
[eV]
FIG.
2:
(a) Optini,illy
filtc~~t~l
p~ll>c
Ii(~ifil>t
hr)(~tl.l~nl
with
Mn
K,
lines. The solid line shows the least-squares best fit,
and the dotted line shows the natural line shape, from Holzer
et with correction and extension provided by Holzer via
private communication. (b) Distribution of
AEb
and
AEbln
(FWHM) of
13
devices. The bin size of
0.2
eV is compara-
ble to typical statistical errors associated with the individual
spectral fits.
We have fabricated two wafers of TES arrays with elec-
troplated Au absorbers
with
:L
fill
f;lc.tur
of
!EW.
They
had 5.3 and 3.7
pm-thick absorbers, with QE at 6 keV of
99% and
95%, respectively. In the following discussion,
we present the performance of one pixel from the first
wafer
(T,
N
77 mK) and 12 pixels from the second wafer
(T,
-
88
mK). These pixels represent both absorber con-
tact geometries, and the results are sufficiently similar
to warrant discussion of the ensemble without specify-
ing type. On one of the devices from the second wafer,
we obtained a resolution of 2.37% 0.17
eV FWHM at 5.9
keV in a spectrum of Mn
K,
lines with 2900 counts as
shown in Figure 2a. The FWHM was determined from a
least-squares fit of the convolution of a Gaussian of that
width with the known profile of the Mn
K,
lines4. The
quoted error is one standard deviation, assuming statisti-
cal errors only. The baseline energy resolution
AEb was
2.3310.03 eV FWHM, where AEb is determined from
measurement of the noise. Therefore, there was no signif-
icant degradation of the resolution due to energy loss via
the absorber supports or
tluo
to
vi~ridtior~ of 1)1115~ ~lli~l)('
In Figure 2b, we summarize the results of the 13 pixels.
The bias points for these measurements ranged from
7%
to 26% of RIR,, where R, is the normal state resistance
of
8
mR, and were not rigorously optimized for each
device. Their
AEb is distributed around 2.5 eV FWHM,
while
AEMn is distributed around 2.7 eV FWHM. This
difference is unlikely to be fundamental since repeated
spectral acquisitions on the same pixel have resulted in
differences in
AEMn on the same scale, likely due to sys-
tematic errors in the measurement such as from thermal
and electrical gain instability. We have achieved spectral
resolution comparable to the state of the art for TES
calorimeters6, but in a close-packed array that can be
scaled to the focal-plane requirements of Constellation-
X.
Tt~c
response
wits
fairly lincar: thc ratio
of
thc
Jln
I<
,
aricl 1111 pulscl hcigllts after opti111al filtc.r~rlg'
wiis
1.087+
0.007.
w11erc:ts thc c<orrcsl)o~lding ~atio
1x1
(:rlc~gv
is
1.103.
In order to construct a physical model for these devices,
we measured the complex impedance7
Z
of one of the
pixels from the second wafer at twelve bias points from
11
to 91% of RIR,. The impedance curves of the pixel
trace semi-circles in the
Im[Z] vs. Re[Z] plane between
10 Hz and
1
kHz. Such data are well fit by a simple
calorimeter model equivalent to a single heat capacity
C
connected to the heat sink through
G.
We fit the
12 sets of data simultaneously to determine
cr
and
P
(5
d log Rld log
T
and d log R/d log
I,
respectively, where R,
TI
and
I
are the resistance, temperature, and current of
the TES) of the individual bias points.
IYv
lct
C'
vary.
constraining its
\;tlue
to
11~'
sanic
at
all
12
l)i:~s
points.
Although the TES heat capacity may change through
the transition, this is a valid approximation since
the'
i)t)tninc~d tvt<>l
boat
c~;cpnc,itv
of
I
..t4
I)J
K
is more than
an order of magnitude higher than the maximum TES
heat capacity. We fixed
G at 149 pW K-' as determined
from measuring the power required to bias the detector
over a range in
Tb
.
With this simple model, we are able
to reproduce the data well.
We also accumulated noise spectra at the same bias
points and compared these to the noise predicted by
our model. The parameters determined from fitting the
impedance curves reproduce the low-frequency portion of
the noise spectra, where noise from thermal fluctuations
between the calorimeter and the heat sink dominate. At
frequencies corresponding to time scales faster than the
pulse recovery time constant
7,
Johnson noise and excess
white noise dominate. For the purpose of this paper, we
define Johnson noise
as
voltage noise with power 4kBRT
V2/Hz, where kB is Boltzmann's constant, and ignore
any corrections for non-Ohmic resistances. Thus, we de-
fine excess white noise as the quadrature difference be-
tween the measured noise and Ohmic Johnson noise. We
fit the noise spectra by fixing all the parameters deter-
mined from the impedance fits and varying only the ratio
of the excess noise to the Johnson noise.
TI]
tht. rnotlcl.
the>
.lol~i~su~~ am1
c~c
t,ss rloi\o
,ire
<~pplicci
:IS
voltagc llois(1
.so111
c
ill sorit~\ with
11
100-30-
80.24.
60.18.
0
a
40.12.
20.06.
o-oo-
o
Excess noise
0
20
4
60
80
100
R~as
RRn
[%]
FIG.
3:
(a) Circles, squares, and diamonds show
a,
P,
and
excess noise, respectively, vs. bias point. The dotted line, to
be read using the excess-noise axis, shows using the
P
determined at each bias point. (b and
c)
Circles, squares, and
diamonds show
AE,
7,
and
raw
pulse height, respectively, vs.
bias point. Filled markers are actual data and open markers
are simulations.
Figure 3a shows the resulting best fit values of
a,
3
and excess noise through the transition. The
CY
and
3
values are well correlated. Their relationship is a mani-
festation of the surface in R-I-T space that describes this
particular superconducting transition. The excess noise
also follows
a
and
3.
Irwins estimated that the voltage
noise power of a non-Ohmic resistor near equilibrium is
4kBRT(1
+
2P)
V2/Hz and our measurement is consis-
tent with that estimate, despite the fact that the devices
are operated far from equilibrium.
From the detector parameters determined
from
our
fits, we calculated the theoretical energy resolution
AEmodel
at each point in the transition. As seen in Fig-
ure
3b, the values of
AEmOdel
follow
AEb
fairly well,
although the latter suffers from systematic and statisti-
cal errors. (Note that the
AEb
values in Figure 2b were
determined from data records with better statistics.) At
the same bias points, we also averaged signal pulses from
Mn
K,
x-rays and compared them to pulses simulated
using the parameters determined in the impedance fit.
As shown in Figure
3c, the values for
T
of the actual
and simulated pulses are in good agreement through the
transition. To first order,
T
is proportional to
(C/a)/G.
A
non-zero
p
suppresses changes in R, which increases
T.
Our use of
a
relatively large bias resistance,
R,,
of
0.5
mR weakens electrothermal feedback1 in the lower part
of the transition, also lengthening
T.
These additional
effects are reproduced by the simulation. The depen-
dence of the raw pulse heights on the bias point is also
explained well by the simulation, as shown in Figure
3c.
The depel~dente
of'
A
E.
raw
pulsr
height.
and
T
on
bias
point
w,lb
qui~litittivcly sirnildr for thc othc>r
12
pixclls.
k)~
~t
t
hc~o
w;t.:
d
sligllt svstk~rrl<ltic. tliff(.rc.nc.o bc't~~cc~i tl1t1
two ,~l)soll)cjr c,olltucSt titlsigris.
In
urdcr tu rc~tlliccl
r
anti
AEl,,
wc.
plan
to
rccil~ce
C'
by 'illk)stitutillg
PI<:(
troplat(~i Hi for
d
fraction of
th~
wlii(
11
will dlso
result
iri (it~,l(\as(d lillearity itntl inc.rc<lscd
f,>,
ill
tlith
,~l)st~ll)cr.
'I
lit,
ol)tlrrlitl
I)~~uIIc~:
I)CI
LVCCII
thest'
ciftbcts
rll11,t
hc
tlct crniiimcl.
\\i'
<llso pl<jn
to
rcciucc
I?,
and
increast.
C;
to
1t3tluce
r.
In summary, we have achieved high spectral resolution
in arrays of close-packed TES x-ray calorimeters in a de-
sign scalable for use in astrophysics applications. More-
over, we have characterized these devices and have mod-
eled all aspects of their performance.
The authors are grateful to Kent Irwin's group at NIST
Boulder for providing the SQUID amplifiers used for
these measurements. They are also grateful to Mark
Lindeman at the University of Wisconsin and Tarek
Saab at the University of Florida for useful discussions.
This work was supported in part by an appointment to
the NASA Postdoctoral Program (S.J. Smith and A.-D.
Brown) at Goddard Space Flight Center, administered
by Oak Ridge Associated Universities through a contract
with NASA.
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