Complete analysis of STJ detector performance via absorption of phonon pulses

M. Stokes, K. Wigmore, A. Kozorezov, Physics Department, Lancaster University, Lancaster, UK.P Verhoeve Science Payloads and Advanced Concepts Office, European Space Agency,

ESTEC, Noordwijk, The Netherlands

The absorption of phonon pulses was used to simulate the effect of photo-absorption in an STJ. For the first time we have beenable to determine device characteristics directly and completely from the phonon measurements.

Heater

STJ

Al2O3

SiO2

tε -

112

2,t121,ttε-

212

2,t221,t1

0

B 12 eε)ε-ε(

)Γ+ε-A(Γ - e

ε)ε-ε(

)Γ+ε-A(Γ+ξ=

eN

)t(Q

2112,t21,t

22,t1,t1 ΓΓ+ΓΓ+ΓΓ

)Γ+Γ2(Γ=ξ

ii,ti Γ+Γ=A

( ){ }2,t1,t2

212121

1 ΓΓ4+A- A-A+A=ε

( ){ }2,t1,t2

212121

2 ΓΓ4+A-A+A+A=ε

{ }tε-22,t2

tε-12,t2

12

1,t0B

21 e)ε-Γ+A(-e)ε-Γ+A(ε-ε

ΓeN=)t(Q

where:QB(t) is the integrated charge developed in the base electrode after time t

Solution of Rothwarf-Taylor Equations

The measured quantities, are respectively, the pulse decay constants, number of excited qps, peak current, and total integrated charge. The four fundamental parameters of each STJ, the tunnel rate and loss rate for each electrode can then be determined via the following simultaneous equations:

Determination of Device Parameters

2122,t11,t ε+ε=Γ+Γ+Γ+Γ

212112,t21,t εε=ΓΓ+ΓΓ+ΓΓ

)(1

2 211,0

22,

Bt

t QeN

1,t00 ΓeN=i

)(,,, ,0021 BQiN

STJ Characterisation using Phonons

+ Simulates key stage of qp excitation by heat pulses + Pulse profile can be observed directly to determine decay times+ Measure initial current directly to obtain number of qps + Energy input variable continuously over wide range+ Uniform response across whole STJ area

- High energy range only (lowest 50 keV at 1.3K, 1keV at 20mK)- Absorption only in the base film- Phonon system must be thoroughly understood

separation of longitudinal and transverse modes energy spectrum scattering

focussing Wolfe J.P. “Imaging Phonons” Cambridge Univ. Press

• Experiment: Ballistic phonon image for sapphire by Every et al. at 1.6 K. Detector and excitation faces are highly polished and cut in the R-plane direction, the plane of ESTEC wafers. The image is a ±32º horizontal scan with the R-plane direction at the centre of the pattern. Bright regions indicate regions of high energy flux due to phonon focussing.

• Theory Modelled map of fast (FT), and slow (ST) transverse focussing singularities. The thick line represents the slow transverse critical-cone channelling contour and the dashed lines are ‘precursors’.

Phonon Focussing

Phonon Focussing observations

• Data shown below for two different STJs on the same chip but in different directions relative to the heater. The L mode is barely focussed in sapphire so the magnitude of the L flux is the same in all directions. Thus the L flux is isotropic and can be calculated from input heater power via the average focussing ratio 0.11 However the focussing ratio (L/T) is very different in the two directions shown and the magnitude of the T flux is obtained via the observed the focussing ratio for the specific STJ.

KJL #7

highly de-focussed T peak

0 500 1000 1500 2000 2500 3000

-5

0

5

10

15

20

25

30

35

pu

lse

amp

litu

de

(V

)

t (ns)

L

T

KJL #8

slightly focussed T peak

Phonon Energy Distribution: theory

• The simplest model of the heater assumes that thermal equilibrium exists between the electronsand phonons so that the spectrum of emitted phonons

is a Planck distribution at a single temperature determined by the Stefan-Boltzmann law:

(P heater power, A area, T heater temperature)• However, this cannot be correct because the mean

free paths of most electrons and phonons arepredominantly larger than the thickness of the film.

• Perrin and Budd (Phys. Rev. Lett. 28 p1701 1972) modelled the form of the spectrum emitted from athin film heater in this scenario, but material detailsare not well known, such as film structure, and mean freepaths for phonon and electron scattering.

• The form of the spectrum displays two peaks, the lower energy corresponding to complete thermalisationof the phonons, and the higher energy to incompletethermalisation.

4Tχ =AP

Phonon Energy Distribution: experiment• By differentiating the phonon response with respect to heater power we can use the

2Δ cut-off to determine the phonon energies and hence the effective temperature of the energetic phonons. A peak in the derivative will occur when a maximum in the spectrum, equal to 2.8kT, coincides with 2Δ.

CVT #5

complete thermalisation

incomplete thermalisation

• The 1st peak corresponds to the high energy phonons (incomplete thermalisation). We modelled this as Stefan Boltzmann with a lower pre-factor, χ, in the SB relation is reduced from 121, calculated for Al-sapphire

KJL #8 KJL1 #7 CVT#5

χ 58.7 ±9.4 44.6 ±4.7 28.2 ±4.5

• By reinserting χ into the SB relation an effective phonon “temperature”, can be defined in order to determine N0.

Phonon Scattering

• Phonons can be scattered in the bulk of the substrate, at interfaces and within passivation layers.

• Elastic and inelastic scattering m.f.p in sapphire >> sapphire thickness.

• In amorphous passivation layers phonons can scatter back into substrate, reflect off bottom interface and be absorbed in STJ delayed phonon signal.

scattered phonons

KJL #7

• Scattered phonons result in a deviation of the decay of the pulse, adding uncertainty to ε1 and ε2.

• By keeping the heater power low, diffusive scattering can be minimised.

0 200 400 600 800 1000

-5

0

5

10

15

20

25

30

35

pu

lse

am

pli

tud

e (V

)

t (ns)

L

T

Summary of Experimental Data

• Pulses are those used to determine device parameters.

0 500 1000 1500 2000 2500 3000

-5

0

5

10

15

20

25

30

35

pu

lse

am

pli

tud

e (V

)

t (ns)

L

T

KJL #8 KJL #7

CVT #5KJL #8 KJL #7 CVT#5

E (keV) 131 ±17 78 ±5 98 ±6

N0,L 0.69 ±0.10 ·107 1.69 ±0.07 ·107 0.78 ±0.18 ·106

1/ε2 (ns) 475 ±5 664 ±5 466 ±5

QB(∞) (C) 1.19 ±0.05·10-11 4.29 ±0.16·10-12 6.74 ±0.27·10-12

i0,L (μA) 3.38 ±0.25 8.3 ±1.2 0.4 ±0.1

i0,T (μA) 31.90 ±0.75 12.2 ±1.8 27.0 ±1.2

STJ tunnelling and loss times

• τt,2 is calculated assuming tunnel times scale with electrode thickness, due to uncertainties in ε1.

• Vb = 400 μV• Tunnel times compared to theory

KJL #8 KJL #7 CVT #5

LAN CALC LAN CALC LAN CALC

τt,1 (μs) 0.33 ±0.04 0.33 0.32 ±0.09 0.33 0.31 ±0.12 0.31

τt,2 (μs) 0.64 ±0.07 0.64 0.63 ±0.17 0.64 0.59 ±0.23 0.59

τ1 (μs) 0.53 ±0.13 - 0.74 ±0.28 - 0.21 ±0.04 -

τ2 (μs) 0.45 ±0.05 - 0.63 ±0.17 - 0.72 ±0.10 -

TBkbeV

eeV

eVweN

b

bniijt

1

1)()0(4

221

,

Trap-enhanced recombination – origin of the initial decay?

• a mobile qp recombines with a trapped qp emitting a sub-gap phonon (<2Δ)• the phonon is immediately lost from the STJ• the trap is immediately occupied by a further mobile qp• thus the process is super-linear in qp density

Conclusions

The phonon technique complements photo-absorption to give interesting and valuable information on the properties of STJs. It can provide a complete quantitative analysis of device parameters.

In addition its versatility provides a alternative approach to broader physical problems, such as trapping and recombination.