MKID MKID arraysarrays: : panoramicpanoramic

detectors for detectors for CMBCMB

experimentsexperiments

Dottoranda: Claudia GiordanoDottoranda: Claudia Giordano

Docente guida: Prof. Paolo de Docente guida: Prof. Paolo de BernardisBernardis

Università di Roma “Sapienza”

Dottorato di Ricerca in Fisica, XXII ciclo

Semnario finale, 23 ottobre 2009

MMicrowaveicrowave KKineticinetic IInductancenductance DDetectorsetectors

Superconductors below a critical temperature Tc have electrons divided in two

different populations:

-the Cooper Pairs, electrons bound together with an energy E=2 3.528*kbTc by the

electron-phonon interaction. They act as superconducting carriers.

- the Quasi-Particles, single electrons which act as carriers in a normal metal.

In this two fluids model the total conductivity

of the material is:

= 1(nQP) - j 2(nCP)

Quasi-Particles

Zs = Rs( 1, 2) + iXs ( 1, 2)

Cooper Pairs

and the complex surface impedance is:

Xs= Lint= (Lm,int+Lk)

Rs and Xs can be estimated using theMattis-Bardeen integrals for 1 and 2:

= (T) temperature (K)

Rs (

/sq

ua

re)

temperature (K)

Xs (

/sq

ua

re)

temperature (K)

dX

s/d

T (

/sq

ua

re K

-1)

nQ

P (μ

m-3

)

temperature (K)

The values of Rs and Xs depend on the

densities of QPs and CPs. By measuring

them, we can get information on nQP .

Which are the effects of incoming radiation

on a superconducting strip?

n CP< nCP

QP

CP

T<Tc

h >2 E

Zs changes because:

• nCP increases

• nQP decreases

• both Rs and Xs increase, in particular Lkin

How can we measure the small variation in Lk?film thickness (nm)

Lx (

pH

/sq

ua

re)

Cc

RQPLkin

Lmag

Cl

The superconductor can be inserted in a resonating circuit with extremely high Q.

Two different possibilities:

Feedline

Inductive Coupling

Inductive

section

Capacitive

section

1) Distributed l= bias/4 resonators

2) Lumped resonators l<< bias

response depends on

where the photon hits the

sensor

equivalent circuit: RLC series

needs some sort

of antenna

no current variation along its

length, acts as free absorberequivalent circuit: RLC series

Effect of a signal transmitted through the feed line past the resonator:

d

d

dNQP

= responsivity

x

x

xdNQP=(responsivity)-1 * d

Pabs =dNQP (0)

QP

(0), known

QP measurable

amplitude

dA

f01

LintC

phase

d

df0 d

x

C1

R1QPL1

kin

L1mag

C2

R2QP

L2kin

L2mag

CN

RNQPLN

kin

LNmag

RF carrier (f 1 + f 2 + f 3 + ... + f N)

Pixel 1, f 1 Pixel 2, f

2 Pixel N, f N

The fact that each resonator has no effect even few MHz away from its resonant

frequency makes these detectors ideal for frequency domain multiplexing:

Very resistant: materials are all suitable for satellite and space missions, like CMB mission.

Extremely simple cold electronics: one single

amplifier can be used for 103-104 pixels. The rest

of the readout is warm.

Very flexible: different materials and

geometries can be chosen to tune detectors

to specific needs.

order of 103-104 pixels read with a single coax

low thermal load!

CMB signals are very low

0,1μK B modes

missions 100 times more sensitive are

needed to get the polarization data

such a gain has to arise from larger focal planes,

with arrays of thousands of independent detectors

Low temperature detectors like spider web bolometers

at 0.1K work in BLIP conditions, so

1μK E modes

higher S/N, faster mapping speed

Lumped resonators for millimetric wavelengths: design process

1) pixel size: needs to be of order of at least one wavelength

2) meander section: optimization of the matching with the free space impedance

If >>s Zeff = Z(w + s)

w

=(Zeff Z0)

(Zeff + Z0)

3) Capacitive section: choice of the resonance frequency

2mm

2m

m

4μm

280μm

Sonnet simulation

CPWMS

• 9 frequencies

• 3 distances

from the

feedline

Our mask: 34 chips 1cmx1cm

+ 2 large arrays 3cmx3cm

• CPW, MS• line width 2μm, 4μm

• optical wavelength: 2mm, 1,25mm

• different numbers of resonators

Superconducting metal: Aluminum

• ok for mm waves: gap= 90 GHz

• Tc = 1.2 K

d

dNQP

QdT

dNQP

Q

V=LintL

1

t

Aluminum thickness t:

Lumped resonators for millimetric

wavelengths: materials and their thicknesses

lower t higher responsivity

lower t higher resistivity = better free space matching

Substrate material: Silicon and Sapphire

t=20nm, 40nm

Si 400μm, Si 170μm, Sa 300μm

Si 389μmSi 400μm

free space substrate resonator back short

The mask has been fabricated at FBK (“Fondazione Bruno Kessler”)

measured during my phd

better results on wafer 11

WAFER

SCN-CN coax

2xDC block

30dB cold amplifier

2xDC block

2x10dB atten

1xDC block1xDC block

1x10dB atten

KID

300K

30K

2K

300mK

CN-CN coax

Nb-Nb coax

amplifier

KIDs testbench: cryogenic system and RF circuit

3x10dB atten

bias generator and

acquisition data system

VNA : slower, easier, can give information on

the sanity of the whole circuit. Ideal for the

first runs.

IQ mixers: faster, essential to measure

noise, QP lifetime.36mm

Mechanical

supports for

the devices

Using IQ mixers it is possible to plot

S21 in the complex plane

0.3K 4K

Re(S21)

Im(S21)

information on both the

amplitude and the phase

of the signal.

frequency

fmax=4.0001GHz

fmin=3.9999GHz

fresonance=4.0000GHzS21

min

xiQ

xiQSS

min

+

+=

21

221

21

0

0=x

In microwave theory circuits are

described by the S parameters. S21

gives the ratio of the transmitted

wave to the incident wave

For an ideal RLC circuit:

Measurements: transition temperature

Tc =1.36K

n (1.4K)

n (300K)=R(300K)

R(1.4K)= 3.6

n (1.4K) = 3.61

2.67 10 8( m)=1.35 108( m)

RRR (Residual Resistance Ratio)=

Measurements: resonances

280±7288±710292±943423.354±0.01277

729±31763±2016161±5633375.301±0.01266

1923±772089±8124190±2543318.800±0.01555

4337±975913±10016271±2403254.320±0.02144

5878±3710902±2812754±743195.848±0.23333

7959±5319343±7613523±733144.330±0.1222

10799±9915032±10313523±2343091.392±0.06611

Q±Q± QQQQee±± QeQeQQii±± QiQiff00±± f0 f0 ((MHzMHz))# # lekidlekid

Power sweep

Effect of temperature sweep on:

phaseamplitude

Higher T Higher nqp Higher losses

Higher T Lower ncp Lower f0

=LintLTOT

f0(T)

f0(0)=

1

2

Lint (T)

Lint (0)= 0.062 ± 0.001

Distributed MKIDs with t=200nm have = 0.018

Effect of temperture variation on

the quality factors Qi, Qe and Q:

Qi = 0

L

R

Qi =LZ0

0M2

increases with decreasing

temperature

constant

weakly coupled lekid

strongly coupled lekid Q Qe

d

dnQP= 0.035 ± 0.003 (deg/μm-3)

the red crosses correspond to

the base temperature resonant

frequency

Volume 780μm3d

dNQP

= 4.5 10 5 deg/QP

All responsivity are in the interval:

2.3 10 6÷ 9.9 10 5 deg/QP

maximum power before saturation:

6.2 10 12÷1.4 10 13Watt

System modified for optical measurements:

300K 30K 2K

300mK

Po

lye

thile

ne

win

do

w

Flu

oro

go

ld

(40

0G

Hz lo

wp

ass)

Flu

oro

go

ld +

14

5G

Hz b

an

dp

ass filte

r

BB(77K)

chopper

KID

d

Ain

2dA

in=

Pin ( ,T) = ( ) BB( ,T) AKID

300mK

Signal 11deg

d =11deg

dNQP 2 105

d

dNQP

= 5.7 10 5 deg/QP

(0) 1.764kBTc0.57

Pabs =dNQP (0)

QP

The quasi-particles lifetime:

QP=33.56±0.14μs

Pabs =dNQP (0)

QP

= 0.34 pW Absorption efficiency abs =PabsPin

=0.34 pW

2.2pW=16%

Si 400μm

distributed MKID’s have abs 2%

Signal 8deg

Signal 13deg

abs=23%

abs=38%

Lekid 3 3196MHz: front illumination

Lekid 3 3196MHz: back illumination

Noise level 1.6 10 3 deg

Hz

S

N= 6.9 103 Hz

NEP =2.2 10 12W

6.9 103 Hz= 3.2 10 16 W

Hz

The Noise Equivalent Power:

S =11deg

Conclusions The Microwave Kinetic Inductance Detectors have many characteristics that

make them ideal for CMB experiments which require large arrays of detectors.

The first measurements already done on distributed Al and NbN chips were

very promising and confirmed the potential of these detectors.

We have developed a detector with a lumped geometry in order to optimize its

coupling to the millimetric radiation.

We have fabricated a mask and tested the first chips, determining theircharacteristic parameters (Q, responsivity) and the material properties (Tc, n , QP).

We have observed a light signal finding absorption efficiencies up to 38%, in

good agreement with the theoretical predictions and much higher than what we

obtained with the distributed MKIDs.

The measured NEP is

Some open issues:

the simultaneous measurement of more pixels

The development of a system to reach lower

temperatures

Work in progress!

3.2 10 16 W

Hz

Examples of typical lithographic

problems on wafer 12