# Presentation: 575130

## CPEM 2000 - Sydney, Australia

- WE3B-1
- A High Temperature
- Superconducting Transmission Line
- for Cryogenic Electrical Metrology Applications
- _Carl D. Reintsema_NIST, Boulder, Colorado USA
- Joseph R. Kinard, Thomas E. LipeNIST, Gaithersburg, Maryland USA

- NIST Boulder

## Introduction

- cryogenic metrology
- problem: getting calibrated electrical signals between low and high temperature test apparatus & instrumentation
- motivation
- ac-dc transfer errors in a prototype cryogenic thermal transfer standard (CTTS)
- MO2C-2 _Improvements in the NIST cryogenic thermal transfer standard_, Kinard *et al*
- applications
- CTTS
- ac & dc Josephson voltage standards
- ?, ideas welcomed

- NIST Boulder

## Desired Electrical Signal Path Attributes

- low dc resistance
- voltage drop
- power dissipation
- low thermal conductance
- power loading at cold stage(s)
- low parasitic reactance
- attenuation
- experimental error
- well defined characteristic impedance
- for high frequency applications

- NIST Boulder

## Fundamental Design Constraints

- low dc resistance
- metals
- superconductor R=0 (for T<Tc)
- low thermal conductance
- for metals
- KCu(77K) = 5.0 W/cm•K (peaks at 50 W/cm•K near 20 K)
- for HTS superconductors
- K(T<Tc) low
- KYBCO(77K) = 0.040 W/cm•K (drops T lowered further)

- Wiedemann-Franz Law

-  large K for metals

- NIST Boulder

## Technical Approach

- bridge 4 K - 77 K with high temperature superconducting transmission line
- YBa2Cu3Ox on single crystal LaAlO3 substrate
- Tline≤77 K < Tc (≈88 K)
- R=0, contributes no dc resistance to signal path
- use conventional coplanar line on circuit board between 77 K and 300 K stages
- plenty of cooling power at 77 K
- minimal dc resistance, well defined ac impedance
- adequate thermal conductance

- NIST Boulder

## minimize G
Gline<<Gcryostat 
Gcryostat defined by G10/stainless standoffs in commercial cryostat
KG10, Kss well known and characterized
KG10(77 K) = .001 W/(cm•K)
Gline defined by material thermal conductivity
Ksubstrate insufficient data for common HTS substrates
KLaAlO3(77 K) = 0.186 W/(cm•K) 
compensate with geometric aspect ratio
G   area/length
(A/l)LAO<<(A/l)G10 standoff

- Gline<<Gcryostat
- Gcryostat defined by G10/stainless standoffs in commercial cryostat
- KG10, Kss well known and characterized
- KG10(77 K) = .001 W/(cm•K)
- Gline defined by material thermal conductivity
- Ksubstrate insufficient data for common HTS substrates
- KLaAlO3(77 K) = 0.186 W/(cm•K)
- compensate with geometric aspect ratio
- G   area/length
- (A/l)LAO<<(A/l)G10 standoff

- Thermal Design Considerations

- K(T)

- T1

- T2

- A

- l

- P=GT1-T2)

- NIST Boulder

## solid thermal grounding on cryostat stages
OFHC thermal clamps at 4 K & 77 K
heat load dumped to 4 K & 77 K stages, not experiment

thermal coefficient of expansion mismatch(s)
design compensates for expansion at dissimilar material interfaces
electrical interfaces
Cu-Be circuit board spring fingers mate to Au pads on HTS transmission line

- solid thermal grounding on cryostat stages
- OFHC thermal clamps at 4 K & 77 K
- heat load dumped to 4 K & 77 K stages, not experiment
- thermal coefficient of expansion mismatch(s)
- design compensates for expansion at dissimilar material interfaces
- electrical interfaces
- Cu-Be circuit board spring fingers mate to Au pads on HTS transmission line

- Mechanical Design Considerations

- NIST Boulder

## Electrical Design Considerations

- for YBCO line
- conductor dimensions
- GYBCO not an issue  [(A/l)•Keff]YBCO << [(A/l)•Keff]LAO
- Jc (77 K) thin film YBCO typically >1• 106 A/cm2
- Imax = 0.8 A  for 200 μm center conductor
- process tolerance
- minimize contact resistance, c
- localized Joule heating
- design dominated by structural considerations
- for conventional line
-  K tradeoff
- terminations
- impedance discontinuities

- NIST Boulder

## YBCO transmission line design

- double sided 2” wafer
- 400 nm YBa2Cu3Ox on0.020” LaAlO3 substrate
- patterned by wet etchon one side (nitric acid)
- superconducting groundplane on backside
- coplanar stripline design
-  Zc=50 
- quasi-exponential tapersto contacts
- Au contacts by liftoffwith pre-dep sputter clean

- center conductor

- gap

- w=200 μm

- w=200 μm

- YBCO

- Au

- w = 3.2 mm

- L = 49 mm

- taper

- NIST Boulder

## transmission line structure

- BNC vacuum
- feedthrough

- 50  transmission lineon conventional G10
- circuit board inside
- cryostat extension

- SMA at 4 K

- YBCO transmission lineon LAO substrate

- 4 K shield

- 77 K shield

- 300 K cryostat wall

- vacuum

- atmosphere

- NIST Boulder

## Bare Transmission Line Support Sub-assembly

- NIST Boulder

## Partial Assembly

- NIST Boulder

## CTTS & transmission line

- YBCO microstripline
- on LAO substrate

- semi-rigid coax link
- to CTTS

- CTTS
- assembly

- 4 K OFHC
- supports

- 4 K transmission
- line terminus

- 4 K shield

- 77 K shield

- room temperature
- cryostat wall

- 77 K transmission
- line terminus

- 4 K baseplate

- NIST Boulder

## CTTS performance enhancement

- ac-dc differencevs frequency, (f)
- modified coaxvs YBCO line
- flatter response
- better at higherfrequencies
- residual errorin  due to fieldeffects at TESsensor
-  (Vsignal) dependence

- 
- leadreactance
- effects

- NIST Boulder

## High frequency performance

- lumped element for f ≤ 200 MHz
- expected performance: 200 MHz < f < 40 GHz
- loss mechanisms
- surface impedance
- for YBCO, rs  2
- insertion loss typically <<1 dB
- dielectric loss
- exotic substrates  high r
- relatively high tan 
- power handling
- high I  high B  flux penetration  excess dissipation
- typical onset mW-W range for CPW at f<40 GHz

- NIST Boulder

## Conclusions

- thermal performance
- cryogen hold time increased from 8 to 24 hours
- thermal power load reduced at 4 K
- mechanical performance
- robust  has endured multiple thermal cycles
- electrical performance
- CTTS input resistance reduced to Rinput=7.84 
- parasitic signal path resistance Rpath<1 
- CTTS application
- flatter frequency response
- higher ‘knee’ frequency

- NIST Boulder

## Thermal Conductivity of YBCO

- NIST Boulder