Small Sensors at Low TemperatureRevealing Cryogenic Turbulence

University of Florida PhysicsGary Ihas-

Yihui Zhou Ridvan Adjimambetov Shu-chen LiuIsaac LuriaMario Padron

Miramare June 10, 2005

Andrew RinzlerJennifer Sippel-Oakley

Mark Sheplak-University of Florida EngineeringT. ChenVadim Mitin-V. Lashkarev Institute of Semiconductor Physics, NASU, Kiev, Ukraine Funding: Research Corporation

Thank you Mr. Organizer

In his lab circa 2004 (with research trainee)

Thank you Mr. Director

In his lab circa 2005

Thank you Mr. Helium Vorticity

50th Anniversary of First Direct Detection of Quantized Vorticity

Outline Low Temperature Motivation-Small apparatus

size & Quantum turbulence decay studies Measurement Techniques

Thermal-Electrical Resistance Semiconductor technology Results

Mechanical Piezo-resistive Piezo-electric Capacitive Optical Results

Nanotube films Thermal Mechanical Results

Characteristics of turbulent flow

[H. Tennekes, 1983]

1. Irregularity — randomness

2. Diffusivity — rapid mixing and increased rates of momentum, heat and mass transfer

3. Large Reynolds numbers

4. Three-dimensional vorticity fluctuations

5. Dissipation — due to viscous loss; decaying rapidly without energy supply

6. Continuum — even smallest scales >>molecular length scale

e forceviscous forceinertial

ULR

Large Scale Turbulence

JPL

Intrepid Experimentalist

A Matter of Scale

Water Facility of Nikuradse

R=107

Oregon Cryogenic Facility

[H. Tennekes, 1983]

Grid TurbulenceGrid turbulence in a classical fluid [Frisch, 1995]

Eddy motion Larger length scaleSmaller length scale

(wavenumber, k > inverse of vortex line spacing, )1

(the mesh of grid the size of the channel)

Energy dissipation by viscosity (Re ~ 1)

Energy flow rate

Energy input

Dissipa-tion

1~ k

k

dt

dE

inertial regimeRe >> 1

Kolmogorov Spectrum

3/53/2)( kCkE

Two Fluid Model– Landau -1941

[J. Wilks, 1987]

Viscosity (P)

4He

(oscillating disc viscometer)

56 %

Fluid density

0 2.0 T

T (K)

n

s

=n +s

0.14g/cm3

Sn=SHe = n nnormal fluid

Ss =0s =0

irrotational

sSuper-fluid

Two fluids

entropyviscositydensityTwo Fluid model

0 s

Quantization of superfluid circulation:

scmnm

nhds / 1097.9 24

(postulated separately in 1955 by Onsager and Feynman)

The angular velocity is

(a) 0.30 /s, (b) 0.30 /s,

(c) 0.40 /s, (d) 0.37 /s,

(e) 0.45 /s, (f) 0.47 /s,

(g) 0.47 /s, (h) 0.45 /s,

(i) 0.86 /s, (j) 0.55 /s,

(k) 0.58 /s, (l) 0.59 /s.

[Yarmchuk, 1979]

1. Circulation round any circular path of radius r concentric with the axis of rotation=2r2

2. Total circulation=r2n0h/m (n0: # of lines per unit area)

3. n0=2 m/h=2 /

All superfluid vortex lines align along the rotation axis with ordered array of areal density= length of quantized vortex line per unit volume=

2000 lines/cm2

s

2

Quantization of Superfluid Circulation

Cryogenic Towed Grid Apparatus

Dimensions in inches

Superconductingsolenoid

Niobiumcylinder

Grid Liquid Helium

Drive Simulation

Techniques To Study Quantum Turbulence

Observation of rise in temperature of helium as turbulence decays

Localized correlated pressure measurements to detect vortex motion and density

Flow

Requirements for the thermometers

Two excellent candidates1. Neutron transmutation doped Germanium Bolometer-- [N. Wang, 1988]

sensitivity (rms energy fluctuation 6 eV at 25mK); T/T ~ 4.810-6

response time < 20 ms size: 1mm1mm0.25mm

2. Miniature Ge Film Resistance Thermistors-- [V.F. Mitin, et al.]

sensitivity =50/K- 100/K in the temperature range 50mK- 10mK

response time< 0.1s size: 650 m

1. Operating temperature: 10 - 100mK.

2. Sensitivity: T ~ 10-7K, or T/T ~ 10-5.

3. Short response time: t ~ 10-3 s.

4. Small mass & good thermal contact.

Conduction in a doped semiconductor

1 10 10010

100

1000

10000

100000

1000000

Electron Collisions

(R~T-1)

Phonon Collisions

(R~T-1/2}

Variable Range Hopping

(R~exp{T-1/4})

Coulomb Interaction

(R~exp{T-1/2})

Re

sist

an

ce ()

Temperature (K)

Mass Production/Consistency•Each wafer will generate sensors with very similar properties•Resistance measurements made on a single batch over the range 10K – 150K•A single fixed point measurement at 4.2K will approximate the sensors properties if the entire curve for any one sensor from the batch is known

1 10 10010

1

102

103

104

Re

sis

tan

ce,

Oh

ms

Tem p erature, K

Advantages of Thin Film Technology

Semiconductor Chip Technology

 

Ge/GaAs thermistors 300 m square by 150 m thick. Mass of the thermistor = 7.2 10-5 gram. 

Active layerInsulator

Thermistor R vs. T Development Work

10 100 10001

10

100

1000

#3

#2

#1

Th

erm

isto

r re

sist

ance

(K

oh

m)

Temperature (mK)

http://microsensor.com.ua/products.html

Pressure Transducer Requirementssampling on micron scale sensitivity: 0.1 Pascal fast: 1 msecfunction at low temperatures (20 – 100 mK) transduction: as simple as possible

MEMS Technology Pressure Sensors Piezo-resistive Capacitive Optical

Design Of Piezo-resistive Pressure Sensors Typical design: 4 piezo-resistors in Wheatstone bridge on a diaphragm diaphragm deflects from applied pressure causing the deformation of the piezo-resistors mounted on the surface

Wheatstone bridge

Piezo-resistive Pressure Sensor SM5108

Manufactured by Silicon Microstructures, Inc.

Semiconductor resistors joined by aluminum conductors in bridge configuration

Resistors placed on diaphragmTwo strained parallel to ITwo strained perpendicular to I

Piezo-resistive Pressure Sensor SM5108

Drawbacks of Piezo-resistive Pressure Sensors-Results Relatively low sensitivity Large temperature dependence temperature

compensation necessary

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.40

5

10

15

20

25

30

35

40

45

50

55 300 K 91.2 K - 94.6 K 64.4 K - 66.0 K 49.8 K - 51.0 K 40.4 K - 43.5 K 29.9 K - 30.4 K 22.9 K - 26.0 K 26.2 K

Voltage vs Pressure for Piezoresistive Transducer at varying temperatures

Vo

ltag

e (

mV

)

Pressure (Bar)

Capacitive Pressure Sensors Inherently nonlinear output of the sensor Distributed capacitance of read-out circuit

requires low T amplifierTypical design: parallel-plate capacitor integrated electronics for signal processing reference capacitors for temperature compensation

Advantages And Disadvantages Of Capacitive Pressure Sensors Over Piezo-resistive Sensors Advantages:

Higher sensitivity Long-term stability Smaller temperature dependence

Disadvantages: Non-linear output More complicated manufacturing due to the

integration of the compensation circuit and signal processing electronics to the sensor chip

Relatively high price

Optical Pressure Sensors

Optical techniques typically employ a microsensor structure that deforms under pressure resulting in change in optical signal.

Diaphragm-based sensors, for example, incorporate optical waveguides on the top surface.

Example Of An Optical Pressure Sensor

Simple Interferometer Sensor

Difficulty is readout

Production Process

Attach optical fiber

Nanotube/Film Technology•Small•Strong•Conducting•But not too conducting•Elastic•Stick to some surfaces

Can be used forThermometersHeatersStrain gaugesCapacitor platesFlow metersTurbulence detectors

Nanotube film AFM Image

1 micron

Helium liquid or gas flow

TinnedCopper

G10 (fiberglas)

4-terminal ResistanceMeasurement

Nanotube Film Flow Sensor Test

Nanotube film “rope” test jig

Nanotube film “rope” R vs. T

0.01 0.1 1 10 1001000

10000

100000R

(oh

ms)

T(Kelvin)

Flow past a Nanotube film

0.0 0.1 0.2 0.3 0.4870

872

874

876

878

880

882

884R

film ()

Flow (cubic feet/hour)V (mm/sec)

Nanofilm CapacitiveFlow/Pressure Fluctuation Sensor

AFM of Nanofilm

Flow

The Group minus Shu-chen Liu

Mario Yihui

GregRidvan