metallic magnetic calorimeters for spectrometry applications
TRANSCRIPT
1
Matias RODRIGUES DRTBT09 11/05/2009
Metallic Magnetic Calorimeters for spectrometry applications
Matias RodriguesCEA-Saclay LNHB
DRTBT09 : 6ième école thématiquePerspectives des détecteurs cryogéniques
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Matias RODRIGUES DRTBT09 11/05/2009
Metallic magnetic calorimeter
• Physical principle
• Choice of the paramagnetic sensor
• The calculation of signal size
• Intrinsic sources of noise
• Detector read out
• SQUID read out and performances
• SQUID-detector coupling
• Optimizations
• Signal to noise ratio
• Fabrication and experimental set-up
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Matias RODRIGUES DRTBT09 11/05/2009
• Applications
•External sources
• X ray spectrometry
• Gamma ray spectrometry
• Embedded source in the detector
• Activity measurement
• Beta spectrometry
• MARE project
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Matias RODRIGUES DRTBT09 11/05/2009
Physical principle of metallic
magnetic calorimeters
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Matias RODRIGUES DRTBT09 11/05/2009
Physical principle of calorimetersEParticle
Gbath
AbsorberSensor or
thermometer
Cabsorber = CElectron T (Metal)CPhonon T3 (Dielectric crystal, superconductor)
A photon with an energy E interacts in the absorber
Temperature rise : ΔT = E / Ctotal
The detector is weakly thermally coupled to a thermal bath
Return to the equilibrium temperature :td = Ctotal / Gbath
DT maximised at low Tbath
ttd
ΔT
PulseT
t
Tbath < 100 mK
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Matias RODRIGUES DRTBT09 11/05/2009
Physical principle of magnetic calorimeters
Tbath < 100 mK
EParticle
SensorV
SQUID loop
xxB
expressed in units of the magnetic flux quantum, Ф0 = 2.07x10-15 A/m
The sensor is a paramagnetic material, magnetized by an external magnetic field B
The sensor magnetization M is strongly dependent on the temperature
Absorption of a particle with the energy E leads to a temperature rise and a change of M
A magnetization change induces a flux variation DФ in the SQUID loop
absorbersensor
particle
sensor
looploop CC
E
T
MV
r
Gm
r
G
0
Magnetic coupling factor
Thermodynamic quantities of paramagnetic materialf (B, T , Vsensor , x )
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Matias RODRIGUES DRTBT09 11/05/2009
Thermodynamics quantities for free magnetic moments
Calculation of thermodynamics quantities using statistical physics
Example for localized spin of 1/2 interacting with B
Zeeman Hamiltonian
Two eigen energies
Partition function of a canonical ensemble
Internal energy
Magnetization
Spin heat capacity
B
J
Jn
kTn
eZ
D E
BH Zeeman
DD
Tk
EEN
T
ZTNkNU
BB
B2
tanhln2
sensorTkE
B
Bspin
V
spin CeTk
EkN
T
UC
B
D
D 22
2
cosh
1
2
DD
Tk
E
B
E
V
N
B
U
V
NM
Bsensor
spin
sensor
spin
2tanh
2
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Matias RODRIGUES DRTBT09 11/05/2009
Magnetization
TkE BD
0
500
1000
1500
2000
0 1 2 3 4 5 6 7
M (A
/m)
JgV
NM BJ
s
13
22
JJTk
Bg
V
NM
B
BJ
s
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Matias RODRIGUES DRTBT09 11/05/2009
0,0E+00
1,0E-03
2,0E-03
3,0E-03
4,0E-03
0 1 2 3 4 5
cs
pin
(J
/K/m
ole
)Thermodynamics quantities for the signal
0E+00
2E+04
4E+04
6E+04
8E+04
0 1 2 3 4 5
dM
/dT
(A
/m/K
)
ETkB D
2
2
T
B
TkE BeD
Specific heat Schottky anomaly
0,0
0,2
0,4
0,6
0,8
1,0
1,2
0 1 2 3 4 5
Sig
nal
siz
e (
U.A
.)
(Ex. with Cabsorber fixed)
absorberspinspin
sensorCcN
E
T
MVm
Signal
Possibility to use large Cspin and
couple absorber with large Cabsorber
0E+00
2E+04
4E+04
6E+04
8E+04
0 1 2 3 4 5
dM
/dT
(A
/m/K
)
∂M
/ ∂
T
ETkB D
0,0E+00
1,0E-03
2,0E-03
3,0E-03
4,0E-03
0 1 2 3 4 5
cs
pin
(J
/K/m
ole
)
c spin
TkE BeD
2
2
T
B
Magnetization
Signal
m
(U.A
.)
ETkB D
cste1
spinspin
sensorcNT
MV
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Matias RODRIGUES DRTBT09 11/05/2009
Ideal magnetic calorimeters for spectrometry
Tbath ~ 30 mK
Each application requires a detection efficiency which fixes the absorber heat capacity.
One has to calculate the parameters B, Tbath, x, Vsensor,that maximize the Signal/Noise ratio.
For spectrometry applications one needs a fast rise time and high energy resolution.
Ideal magnetic calorimeters :- Large signal strong dependence of the magnetization on the temperature
No interaction between magnetic momentsNo additional heat capacities
- Fast rise time Strong coupling between spins and the absorber heat capacity
Csensor = Cspin
large Gsensor-absorber
Csensor
~ Cspin
Cabsorber
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Matias RODRIGUES DRTBT09 11/05/2009
Different choices of magnetic ions and host• Dielectric host
– TmAG:Er, YAG:Er
– CMN, CDPHigh sensitivity but very long rise time due to a weak coupling between magnetic moments and phonons
• Metallic host– LaB6:Er (large additional heat capacity at low T)
– Au:Er (well known, stable)
– Ag:ErReduced sensitivity due to exchange interaction between magnetic moments but fast rise time due to strong coupling between magnetic magnetics moments and conduction electrons
• Semi metallic host (unstudied)
• Semiconductor (unstudied)– Bi2Te3 (Eg = 0,15 eV) doped with Er
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Matias RODRIGUES DRTBT09 11/05/2009
Signal size forMetallic Magnetic Calorimeter
using Au:Er sensor
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Matias RODRIGUES DRTBT09 11/05/2009
Magnetic properties of AuEr. Er in cubic symmetry
• Electronic Zeeman interaction
J = 15/2 gJ = 6/5
• Crystal field interaction
JBgH BJ
Zeeman
5s, 5p
Au
Er3+
4f
o
5
o
4
621110
A 1
A 3.0
5544Kr
p
f
r
r
psfd
Γ7
Γ8
8.6~ g
2/1~
S
64 VVJBgH BJ
SBgH B
~~
isotrope
At T < 1 K
eV 1 ~~2 D BgSE B
mT 1 B
B
M
Quantum energy :
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Matias RODRIGUES DRTBT09 11/05/2009
Exchange interactions
• Dipole – Dipole interaction
Coupling between two localized magnet
• RKKY interaction (Ruderman - Kittel - Kasuya - Yosida)
Interaction between two localized magnetic moments mediates through
the conduction electrons and their magnetic moment (itinerant electrons).
GRKKY = 5.GDipole
RKKY interaction leads to spin glass transition at ~ 1 mK with 300 ppm erbium
minimal Tbath ~ 10 mK
3
320
2
~~3
~~
2~
4ijF
ijjijiji
FB
Dipole
ijrk
rSrSSS
kgH
Interaction between two localized spins Si and Sj
332
4*2
2
222
2
2sin212cos~~
2
41~
ijF
ijFijFijF
ji
Fep
J
Jsf
RKKY
ijrk
rkrkrkSS
kmV
g
ggJH
GRKKY
GDipole
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Matias RODRIGUES DRTBT09 11/05/2009
Thermodynamic quantities for the signal
ETkB D
∂M
/ ∂
T (
A/m
/K)
ETkB D
c AuE
r(J
/K/m
ole
)
0E+00
1E+04
2E+04
3E+04
4E+04
0 0,5 1 1,5 2
dM
/dT
(A
/m/K
)
0E+00
1E-03
2E-03
3E-03
4E-03
0,0 0,5 1,0 1,5 2,0
Sp
ec
ific
he
at
(J/K
/mo
le)
0,0
0,2
0,4
0,6
0,8
1,0
1,2
0 0,5 1 1,5 2S
ign
al siz
e (
U.A
.)
Specific heat
868 ppm
9,7 mT
ETkB D
Exchange interactions lead to
a reduced of the signal size
AuEr with exchange
AuEr w/o exchange
TkE BD
M (
A/m
)
0
500
1000
1500
2000
0 1 2 3 4
M (
A/m
)
868 ppm
9,7 mT
absorberspinspin
sensorCcN
E
T
MVm
Signal
m
(U.A
.)
Magnetization
Signal
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Matias RODRIGUES DRTBT09 11/05/2009
T (mK)
c AuE
r(1
04
J m
ol
1 K
1 )
T1 (K 1)
M(A
/m)
Thermodynamic properties of AuEr can be calculated by mean field
approximations or with Monte Carlo simulations.
We can predict the signal size as a function of all the parameters
Magnetization Specific heat
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Matias RODRIGUES DRTBT09 11/05/2009
Time structure of the signal
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Cadd
CAu
If we use a gold absorber
•
• Cspin electronic magnetic moments (Zeeman+exchange)
• Cel conduction electrons of Au:Er (~ 1% of Cspin)
• Cadd : interaction of the nuclear quadrupole moments
of gold with the electric field gradient due to the
presence of Er3+
• CEr168 : hyperfine interactions of the nuclear magnetic
moments of Er168. Using of enriched Er166 or Er167
Heat capacities and thermal conductances
Cel
EParticle
3
234D
aBAu
TNkTNC
/moleJ/K 10.29.7 24
K 4,162D
CEr168
Cspin
Celectron Cspin
Csensor
Tbath ~ 30 mK
Tbath ~ 30 mK
(with enriched Er166)
x = 900 ppm
B ~ 5 mTcAu
mJ/K/mole
cspin
mJ/K/mole
cadd
mJ/K/mole
20 mK 0.015 1.8 ~1/4 cspin
30 mK 0.022 1.4 ~1/5 cspin
Cadd
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Matias RODRIGUES DRTBT09 11/05/2009
Thermalisation of the particle energy and pulse shape
Cspin
Zeeman+exchange
CaddCelectron
EParticle
tadd ~ 100-300 s
td = Ctotal / GGKapitza ~ 10 nW/K/mm² at 20 mK
Gmetal-metal preferable, >> GKapitza
tspin-e = 0.25 s at 30 mKKorringa relation, tspin-e = k/T, k = 7x10-9 K.s
CaddT0 ~ 30 mK
Csp
in+C
elel
ctro
n
Time (ms)
Pulse
Sig
nal siz
e (
U.A
.)
We suppose heat diffusion through conduction electrons very fast
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Matias RODRIGUES DRTBT09 11/05/2009
100
102
104
106
108
10-25
10-20
10-15
10-10
10-5
222121 rr
d
ffEfS
tt
t
electronspin
spin
CC
C
Spectr
ale
density (
eV
/Hz)
Frequency (Hz)
12
dt 12
espint
dt
Fourier spectrum of the signal
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Intrinsic sources of noise
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Matias RODRIGUES DRTBT09 11/05/2009
Thermodynamic fluctuations of the energy
2
2
21
4
d
dBE
fCTkS
t
t
A simple canonical ensemble with one system.
CTkT
UTkUUU BB
2222
D
1E-5
1E-4
1E-3
1E-2
1E-1
1E+0 1E+1 1E+2 1E+3 1E+4 1E+5 1E+6 1E+7
Frequence (Hz)
Po
we
r sp
ectr
um
(e
V/H
z1
/2) dB CTk t24
ms 1 pJ/K, 1 mK, 30 dCT t
C
dt
EParticle.(t)
T0 ~ 30 mK
12
dt
Low Temperature required!
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Matias RODRIGUES DRTBT09 11/05/2009
Thermodynamic fluctuations of the energy
22
2
electron
21
4
21
41
,10C1.0 ,
d
d
espin
espin
spinBspin
despinspin
electronspin
spin
ffTCkS
CCC
C
t
t
t
t
tt
Canonical ensemble with two sub systems
(Cadd ignored).
Fundamental limits of metallic magnetic calorimeter :
CspinZeeman+exchange
Celectron
ms 1μs, 25.0
mK, 30 pJ/K, 5.0
e-spin
d
spinelectron TCC
tt
espint
T0 ~ 30 mK
dt
EParticle.(t)
1E-5
1E-4
1E-3
1E-2
1E-1
1E+0 1E+1 1E+2 1E+3 1E+4 1E+5 1E+6 1E+7
Frequence (Hz)
Pow
er
sp
ectr
um
(e
V/H
z1
/2) dspinB TCk t 24
12
dt
espinspinB TCk t 241
12
espint
D
4/1
2
1
14
d
espin
eBspin CTkUt
t
Low Temperature required!
Minimized for Celectron = Cspin
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Matias RODRIGUES DRTBT09 11/05/2009
Other intrinsic sources of noise
Depends strongly on the way the sensor is coupled to the SQUID
1/f noise of Au:Er sensor
Independent of temperature and proportional to erbium concentration
tzfc
04
1TVkS B
mag 0
SQUID loop
xx
e-
Magnetic Johnson noise, random motion of conduction electrons in metalsfrom the sensor and the absorber
t
z
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Matias RODRIGUES DRTBT09 11/05/2009
100
101
102
103
104
105
10-15
10-14
10-13
10-12
10-11
10-10
10-9
Total flux noise
1/f from Au:Er
Thermodynamic fluctuations
Johnson noise
T = 30 mK
Cabsorber = 0.5 nJ/K
CAuEr = 0.4 nJ/K
tr = 1 ms
td = 5 ms
Signal size :
d0/dE = 1.7 m0/keV
Flu
x n
ois
e
02
/ H
z
Frequency (Hz)
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Matias RODRIGUES DRTBT09 11/05/2009
Signal to noise ratio
100
101
102
103
104
105
10-18
10-16
10-14
10-12
10-10
10-8
Signal (U.A)
Noise (U.A)
Signa/Noise
Frequency (Hz)
(U.A
.)
FWHM = 35 eV
(Fundamental limit from thermodynamic fluctuations FWHM = 24 eV)
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How to read the magnetization of the sensor
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Hzμ 15.0
mK 300 ... 100 pF, 1 pH, 100
32
0,
min
3
,
SQUID
squidsquid
SQUIDSQUIDBSQUID
S
TC L
CLTkS
Amplification and linearization
Hzμ 15.0 0 HzμΦ 7.1HznV 33.0 0,, elecelecv SSNoise limited by room
temperature electronics
Room temperature electronicsSQUID
SQUID Noise
SQUID
Rfb (150 W6xRfb
35xRfb
sensor
Shunt
resistor
Vs
30 mK 300 K
Limited bandwidth ~ 1MHz
Slew rate < 10/s, rise time ~ 1 s
Maximal signal size ~ 10
1 0
Ib
Vs
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Matias RODRIGUES DRTBT09 11/05/2009
100
101
102
103
104
105
10-15
10-14
10-13
10-12
10-11
10-10
10-9
Total flux noise
SQUID noise
1/f from Au:Er
Thermodynamic fluctuation
Johnson noise
FWHM = 69 eV, SQUID electronics white noise of 1.7 0 / Hz1/2
(FWHM = 35 eV with a noiseless electronics)
Flu
x n
ois
e
02
/ H
z
Frequency (Hz)
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Matias RODRIGUES DRTBT09 11/05/2009
Two stage SQUID set up
262628
26
106.0
22
2,
,
107.0 ... 08.0
2
2,
102
2
1,1015.0
1,,
4
GV
S
G
S
V
TRkSS
elecVgB
SQUID
VV
SQUID 2(single or array)
30 mK 30 mK – 4 K Room temperature
1,2
1
2
VRR
MG
VV
Sg
is
HzμΦ 1 to5.0 0, SQUIDS
3 ,μV/Φ 200
HzμV 33.0
50...1
HzμΦ 2 ... 15.0
HzμΦ 15.0
max,02,
,
02,
01,
W
GV
S
R
S
S
elecV
g
Lower power dissipation in the SQUID1 shunts Hzμ 8Hz 1 01, fSQUIDS
SQUID 1
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Matias RODRIGUES DRTBT09 11/05/2009
100
101
102
103
104
105
10-15
10-14
10-13
10-12
10-11
10-10
10-9
Total flux noise
SQUID noise
1/f from Au:Er
Thermodynamic fluctuations
Johnson noise
FWHM = 45 eV, SQUID electronics white noise of 0.5 0 / Hz1/2
(FWHM = 35 eV with a noiseless electronics)
Flu
x n
ois
e
02
/ H
z
Frequency (Hz)
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Matias RODRIGUES DRTBT09 11/05/2009
How to couple the magnetization of the sensor
to the SQUID
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Matias RODRIGUES DRTBT09 11/05/2009
Direct coupling
absorbersensor
sensor
loop CC
E
T
MV
r
G
0
Magnetic coupling factor between the sensor and the SQUID loop
T ≥ Tcryosat
SensorSQUID loop
xx
B
dSQUID ~ 50 m
Advantage• High coupling factor• Easy to realize
Disadvantage
• Josephson junctions are sensitive to BReduce the signal to noise ratio of the SQUID
• Thermal decoupling between bath and SQUID chip• Sensor size and SQUID noise limited by SQUIDloop radius
• Sensitive to magnetic Johnson noise
4343
, SQUIDSQUIDSQUID rLS
SQUID chip
Ibias
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Tcryostat (mK)
Tsen
so
r(m
K)
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Matias RODRIGUES DRTBT09 11/05/2009
Flux transformer
Input coilPick-up coil
SQUID
Tbath
winputuppick
SQin
turninLLL
MNG
uppick
uppick
SQUID
w
inputuppick
LS
L
LL
,
0
Advantage• Sensor thermally decouple from SQUID chip• Possibility to read large sensor, required for applications needing a large absorber
Disadvantage• Signal to SQUID noise ratio is smaller by a factor 2at least• Sensitive to magnetic Johnson noise
B
Optimised for
wL
abssens
s
uppick
inmag
CC
E
T
MV
r
GG
0SQUID chip
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Matias RODRIGUES DRTBT09 11/05/2009
p
AL
LL
MG
meandermeander
inputmeander
SQin
in
2
Meander pick-up coil :
I δI Input coil
sensor
absorber
V
Flux transformer with meander shaped pickup coil
I
I I
Interrupteur
SQUIDInput coil
Al bond wires
Normal at T > 1K
Pick-up coilsAu:Er
Advantage • Advantages of a flux transformer• Insensitive to external magnetic field, Johnson magnetic noise• No external field coil• Gradiometric • Microfabrication (reproducible, serial)Disadvantage
• Large current in the SQUID input coil• Microfabrication (expensive equipements)• Signal size reduced
?
?
B
Gmag
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Matias RODRIGUES DRTBT09 11/05/2009
Inhomogeneous magnetic field B
IBpGmag 0
Magnetic field B (mT)
Magnetic coupling Gmag (mT)
Pro
bab
ilit
y (
U.A
) magmagmag
magmag
dGGPT
MG
dGGPcVC
VG
pAuErAuErabsorber
AuErin
0
CAuEr Magnetization
sensor
absorber
pw
w = 2 … 5 m
p = 5…10 m
Field distribution
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Matias RODRIGUES DRTBT09 11/05/2009
Optimization, fabricationand
experimental set-up
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Matias RODRIGUES DRTBT09 11/05/2009
Optimization
• Tbath as low as possible but > 10 mK and fixed by the
cryostat
• Cabsorber as small as possible but fixed by the
application
• Signal size as large as possible but < 1 0 in the
SQUID loop
• td as long as possible but limited by the count rate
•
•
•
bathopt TB
bathopt Tx 31
Signal absorberC
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Matias RODRIGUES DRTBT09 11/05/2009
Meander shaped pick-up coil
Heater
1 : Heater
2 : Heater bond pads
3 : Field bond pad
7 : Meander pick-up coil made of Nb
8 : SQUID input coil bond pads
Current of 100 mA required in the meander
Good niobium film quality
1 mm1 mm
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Matias RODRIGUES DRTBT09 11/05/2009
AuEr sensor
Sputtering of the AuEr
Bad Au:Er Good Au:Er
Good Au:Er at low T
UHV required < 10-8 TorrFlu
x (
0)
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Matias RODRIGUES DRTBT09 11/05/2009
Wiring
Iheater
Ifield
Ibias
SQUID1
Ibias
Voutput
Ifb
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Matias RODRIGUES DRTBT09 11/05/2009
Detector stages.
Temperature regulation
with a PID at 15 to 20 mK ± few µK
In the cryostat
Dilution or ADR cryostat
SQUIDs of preamplification :
T reguled between 1.5 and 4.2 K
Thermalisation of the wires and filters
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ApplicationExternal sources
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Matias RODRIGUES DRTBT09 11/05/2009
X ray spectrometry
0
2
4
6
8
10
12
14
Dec-99 Nov-01 Oct-03 Sep-05 Aug-07 Jul-09
FW
HM
at
6 k
eV
(e
V)
measured
fundamental limit
T Cabsorber
(pJ/K)
Csensor
(pJ/K)
B
(mT)
/6 keV
(0)
SQUID noise
0/Hz1/2
FWHM
(eV)
30 mK 0.11 0.073 0.39 8 1.4 0.6 0.94
50 mK 0.19 0.067 0.26 12 0.65 0.6 2.2
Absorber: x150x150x3 μm3 95 % detection efficiency at 6 keV
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Matias RODRIGUES DRTBT09 11/05/2009
SensorsAbsorber
Josephson
junctions
Thermal link
Feedback
coil
200 m
X ray spectrometry
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Matias RODRIGUES DRTBT09 11/05/2009
Gamma spectrometry
T Cabsorber
(nJ/K)
Csensor
(nJ/K)
I
(mA)
/100
keV
(0)
SQUID noise
0/Hz1/2
FWHM
(eV)
30 mK 0.5 0.41 0.45 80 0.17 0.5 45
Sensor
SQUID
Thermal link
1 mm
MeandersAbsorbeur
= 1.1 mm, h = 340 m
Heat
switch
Absorber: x0.5x0.5x0.3 mm3 60 % intrinsic detection efficiency at 100 keV
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Matias RODRIGUES DRTBT09 11/05/2009
0
0,2
0,4
0,6
0,8
1
0 50 100 150 200 250 300 350 400
Energy (keV)
Intr
insic
dete
ction e
ffic
iency
Experimental data
Monte Calo simulation Monte Carlo simulation
Gamma spectrometry
Monte Carlo simulations
49
Matias RODRIGUES DRTBT09 11/05/2009Energy (eV)
Co
un
ts p
er
ch
an
ne
l
30300 30800 31300 31800 32300 32800 33300 33800 34300 34800 35300 35800 36300
10
60
100
K2K1
K3
K1
K2
K4
FWHM of
52 eV at 30 keV
and 58 eV at 81 keV
T = 13 mK
Energy spectrum of a 133Ba source
FWHM = 52 eV
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Matias RODRIGUES DRTBT09 11/05/2009
ApplicationEmbeded sources
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Matias RODRIGUES DRTBT09 11/05/2009
Absolute activity measurement of 55Fe
Source enclosed inside the absorber
4 p detection geometry
Gold absorber: high stopping power
thickness 12 µm: ≥ 99.9 % absorption
for electrons and photons up to 6.5 keV
high detection efficiency
Au foil
SQUID
loop
sensorabsorber
substrate
B
Au:ErFe source55
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Matias RODRIGUES DRTBT09 11/05/2009
log (E)
Em
issi
on
pro
ba
bili
tyK capture6539 eV88.53 %
L capture769 eV9.83 %M, N capture
84 eV 1.64 %
_<
X-rays
Augerelectrons
Magnetic
calorimeter
60 %
30 %
98 %
Semiconductor
detector
Liquid scintil-
lation counting
53
Matias RODRIGUES DRTBT09 11/05/2009
Beta spectrometry
Calibration source (57Co)
750 000 counts(3.2 cps)
DE = 750 eV à 122 keV
Using 1x1 mm² meander
pick-up coil
Absorber 800x800x500 m3
54
Matias RODRIGUES DRTBT09 11/05/2009
Advantage• Advantages of a flux transformer• No external field coil• Insensitive to external magnetic field, Johnson magnetic noise• Microfabrication of arrays
Disadvantage
• Large current in the SQUID input coil• Microfabrication
Flux transformer with meander shaped pickup coilI
Meander shapedpick-up coil
SQUID
Input coil
xxp
AL
LL
MG
meandermeander
inputmeander
SQin
in
?
?
B
Gmag
55
Matias RODRIGUES DRTBT09 11/05/2009
MARE project, neutrino massMARE Microcalorimeter Array for a rhenium Experiment
Superconducting absorbers
56
Matias RODRIGUES DRTBT09 11/05/2009
Thank you for attention
57
Matias RODRIGUES DRTBT09 11/05/2009
AgEr could be a better choice below 20 mK
even if the RKKY interaction is stronger than for
AuEr
AuEr
Cadd’ (hyperfine interactions between the
nuclear magnetic moments of Er168)
I = 7/2
Cadd (interaction between the quadrupole
moments of gold and the electric field gradient
due to the presence of Er3+)
58
Matias RODRIGUES DRTBT09 11/05/2009
59
Matias RODRIGUES DRTBT09 11/05/2009
133Ba source
85 kBq
Pb Collimator
Detector stage
Sn Collimator
6 cm
The activity of the source was measured
with a HPGe detector
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Matias RODRIGUES DRTBT09 11/05/2009
Z = 32 Z = 79
61
Matias RODRIGUES DRTBT09 11/05/2009