Handbook of High Temperature Superconductor Electronics Part 12 docx

ap-For the resistive TE detector with dc current biasing, the voltage response to steady input power W in watts is of the form where+ is the absorption efficiency %, G is the thermal con

It is already over 10 years since the discovery of high-temperature

superconduc-tor (HTS) materials with transition temperatures T cin excess of the liquid gen (LN2) temperature (77 K at 1 atm) In addition to the continuing mystery of

nitro-what exactly accounts for their high-T c, the relative ease of LN2cooling versusliquid helium (LHe) cooling promises to make a number of engineering applica-tions practical, ranging from magnetically levitated trains to microelectronicssuch as SQUID (superconducting quantum interference devices) -based medicalimaging devices In this chapter, we will present an overview of employing HTSmaterials in thin-film ( 1 m) form for the direct detection of infrared (IR) radi-ation, spanning the approximate wavelength range of 0.8 m to 1 mm Some ofthe examples, particularly for fast (picosecond) response, will be for HeNe lasersources (0.63 m) Excluded are heterodyne applications where the HTS materialserves the role of mixer (for instance, as a so-called hot electron bolometer) (1)producing a difference frequency between a radio-frequency input and a local os-cillator Also excluded are SQUID approaches in general, as the SQUID is cov-ered in a companion chapter An excellent review of the detector situation as of

1994 may be found in Ref 2

A typical resistance curve for an HTS material is shown in Figure 11.1:

Typ-ical T cs include
90 K for YBCO (yttrium barium copper oxide), 110 Kfor BSCCO (bismuth Strontium calcium copper oxide), and 125 K for TBCCO(thallium barium calcium copper oxide) Direct detection falls into two main cat-egories: thermal and nonthermal or quantum In the thermal approach, incoming

radiant power W causes a temperature rise in the HTS lattice (phonons are the

dominant heat-capacity medium at these temperatures, unlike the electron

com-ponent for low-T cmaterials); this temperature rise then modulate some HTS erty such as resistance, which is then detected The thermal detector is potentiallybroadband, limited by the spectral properties of the absorber However it is po-tentially slow (with a time constant %), especially due to the thermal inertia of the

prop-substrate An alternate approach is the quantum detector; here, the power W

di-rectly interacts with the HTS material with a quantum efficiency + However, theidea is not to excite the phonons, but rather to directly influence the Cooper pairs.Thus, for example, an incoming signal pulse directly leads to a reduction in theCooper-pair density, without needing to influence the phonons The quantum de-tector is potentially very fast, but at the expense of not being quite as broadband

as the thermal (the photons must be energetic enough to break the Cooper pairs)

Requiring Cooper pairs, quantum detectors operate at or below T c; thermal

detec-tors can operate below, at, or above T c

Infrared detection in the fully superconducting regime includes quantum tectors operating by pair-breaking, modifying an HTS property such as the kineticinductance or critical current The kinetic inductance and critical current can also

de-be changed thermally Another detector in the superconducting regime is thephotofluxonic detector (3), a photon-assisted generation of vortex–antivortexpairs In the normal region, only thermal detectors are possible A bolometer ispossible based on the metallic property of high-quality HTS materials Pyroelec-tric detectors are also possible In the transition region, both thermal and nonther-mal approaches are possible A very common detection method is thermal

F IGURE 11.1 High-temperature superconductor resistive transition.

modulation of the resistance Also possible is thermal modulation of the tion depth, leading to a thermal detector based either on magnetic inductance orkinetic inductance Detectors have also been made based on thermal modulation

penetra-of the microwave surface impedance The penetration depth and surfaceimpedance can also be modified by direct interaction between incoming photonsand the Cooper pairs

link The HTS material is the thermometer and is held near T c; incoming radiationcauses a rise in temperature that leads to a resistance rise, which is sensed by suit-

able electronics The incoming power W can either be directly absorbed into the

HTS material (Fig 11.2a), can be absorbed into a separate but closely coupled sorber (Fig 11.2b), or it can be coupled by an antenna before being coupled intothe HTS material Although Figure 11.2a may appear the most straightforward,ancillary concerns may make an alternative approach preferable Figure 11.2a isnot suitable, for instance, at long IR wavelengths when the HTS material is fullysuperconducting; at long enough wavelengths, the Cooper electron pairs are notbroken and the HTS absorption goes to zero For fully superconducting YBCO,the reflectivity can exceed 99% beyond a 25-m wavelength (4) Also, as one ap-proaches a 1-mm wavelength, the absorber sideway dimension also needs to ap-proach 1 mm for absorption efficiency When one considers the limited range ofsubstrate materials suited for HTS thin-film growth and the often high specificheats of these candidate substrates, the HTS-absorber detector can be quite slowdue to the thermal inertia of the substrate One can instead use a separate absorberand make the HTS thermometer rather small (Fig 11.2b), or one can use an an-

ab-tenna to couple W onto a much smaller detector (Fig 11.2c) The anab-tenna,

how-ever, will limit the detector to single-mode operation, whereas the nonantenna proach is multimode (5)

ap-For the resistive TE detector with dc current biasing, the voltage response to

steady input power W (in watts) is of the form

where+ is the absorption efficiency (%), G is the thermal conductance (W/K), I b

is the bias current (A), and dR/dT is the temperature derivative of the resistance

W+G

( out/W (V/W), the responsivitycan be factored into volts/watt  (volts/K) (K/watt) as follows:

ℜ ≡ ℜV/W ℜV/KℜK/WI b d d R TG+ (2)Consider, now, a body representable as a point with heat capacity or thermal

capacity C, connected to a bath with thermal conductance G (6) For

non-F IGURE 11.2 (a) High-temperature superconductor as absorber and mometer; (b) HTS as thermometer only; (c) antenna-coupled HTS as absorber and thermometer.

ther-(a)

(b)

(c)

steady operation, a quantity of heat Q causes a temperature rise T in the

where k is Boltzmann’s constant (1.38  10
23J/K)

Considering again the case of a detector with lumped-elements C and G, the

spectral decomposition of the mean square temperature fluctuations (mean squarefluctuations per hertz) is of the form

T2C

1

1 j)%

+G

 T 2 (12)Dividing Eq (12) by the square of the magnitude of ℜK/Wfrom Eq (8) (and as-suming unity +), temperature fluctuations of the detector thereby correspond to anapparent fluctuation of incoming radiation (units of W2/Hz) of

 W  4kT2 2

where NEP is the noise equivalent power (W/Hz1/2)

Clearly, it is desirable to make the NEP as small as possible The minimum

possible G, Grad, corresponds to radiative coupling alone For a detector and ground in thermal equilibrium at temperature T (8).

where is Stefan’s constant (5.67  10
12W/cm2/K4) and A is the detector area.

Thus, the minimum NEPradsatisfies the equation

prop-is 1.8  1010cm/Hz1/2/W at 300 K (NEP is 5.5  10
12W/Hz1/2for a 1  1-mmdetector) and 3.7  1011at 90 K, 20 times higher This is one of the major drivers

to develop an IR detector based on HTS materials, because although numerous,near-optimal thermal detectors have been built for operation at 300 K, there are

no more sensitive detectors until one cools to approximately 4 K Near 90 K,detectors could provide intermediate performance with intermediate coolingdemands

The state of the art for 300 K thermal detectors is 3.6  109for a Golay cell

at 6.5 Hz, 3.7  109for a pyroelectric detector at 6.5 Hz, 4  109for a couple detector at a few hertz, and 6.7  109for a thermal-expansion-based de-tector, at 2–3 Hz (9) None of these detectors is widely available The best com-mercially available 300-K detectors are (1–2)  109D* for pyroelectric or

thermo-thermopile detectors

1

11.3 RESISTIVE TRANSITION-EDGE DETECTORS IN DEPTH

11.3.1 Effect of Diffusion and Boundary Resistance on

Thermal Isolation; First Look at ␶Consider a transition-edge detector consisting of a HTS thin film on a plate ofbulk-type substrate material Let the plate be mechanically supported and ther-mally isolated by some insulating fibers, such as Kevlar (Fig 11.3a) The HTSmaterial is metallized with silver and gold, to which we bond fine gold wires, such

as are used in the microelectronics industry for contacting a die within a chip Apractical lower limit for the gold wire diameter is 18 m (0.8 mil) The thermalisolation is typically adjusted by changing the lengths of the electrical leads, usu-ally four, as in a four-wire connection However, for moderately cold tempera-tures such as 90 K and above, attention must be paid to the so-called thermal dif-

fusion length l0, which satisfies the equation (10)

where K is the thermal conductivity (W/cm K), ƒ is the frequency (Hz), s is the

spe-cific heat (J/g K),  is the density (g/cm3), and a

T ABLE 11.1 Thermal Properties of IR Detector Materials at 90 K

ity Typical values at 90 K for K, s , a, l0, and the Debye temperature Dare given

in Table 11.1 for YBCO and candidate substrate and wire materials Note that thediffusion length of gold at 10 Hz and 90 K is fairly short (2.2 mm) Basically, whatthis means is that the usual formula relating thermal conductance to thermal con-

ductivity for a wire of length l and cross-section area A wis modified to

G , 0 l l0

Also, for l l0, the heat-capacity contribution is one-third of the total heat

ca-pacity of the wires; for l 0, the contribution is 1.5 times one-third of the

con-tribution of length l0 For 18-m-diameter gold wire at 90 K and 10 Hz, four leads,the implied best thermal isolation due to conduction is about 10
4W/K From Eq.(13), the implied best NEP at 90 K is about 7  10
12and the D* is 1.5  1010for a 1  1-mm detector By way of comparison, the unity-absorption radiativecoupling [Eq (14)] is 6  10
6at 300 K and 1.6  10
7at 90 K

In addition to the thermal isolation between the detector and the bath, there

is also some amount of thermal isolation between the HTS film and the substrate

A typical value of the boundary resistance (11) between the HTS film and the strate is 10
3cm2K/W, 80 times larger than the acoustic mismatch model wouldpredict For a 1  1-mm detector, this implies a G of 10 W/K A detector based

sub-on this thermal isolatisub-on has an NEP about 300 times worse than the gold-wire

de-KA w

l0

KA w

l

tector, but it is potentially very fast For a 0.5-m film of YBCO, the heat ity is 5.6  10
7J/K and the implied time constant is 57 ns Because both the heatcapacity and thermal conductance scale with area, this time constant should beroughly independent of area.

capac-For the detector configuration of Figure 11.3a, assuming a lumped-elementscondition, it is straightforward to calculate the time constant For quick response,

a high Debye temperature is desirable For temperatures much less than D, the

phonon modes freeze out, leading to a T3dependence of the heat capacity FromTable 11.1, diamond is the premier candidate, but as will be discussed later, dia-mond is not well suited as an HTS substrate material Perhaps the second-bestchoice is sapphire, which is commercially available in 1-mil (25-m) thicknesses

A 1  1-mm, 1-mil plate of sapphire has a heat capacity of 10
5J/K; the bution of the gold wires is about 1.4  10
6J/K, plus a contribution from the goldball-bond Together with a thermal isolation of 10
4W/K due to gold wires, theimplied time constant is on the order of 100 ms This is toward the high end ofwhat is desirable for a time constant; the obvious solution is to further thin the sap-phire or decrease the area Decreasing the area, however, will reduce the absorp-tion efficiency toward a 1-mm wavelength, so the wisdom of doing this will de-pend on the application

contri-To approach the radiation-limited NEP and D*, it is necessary to obtain

bet-ter thermal isolation than is possible with gold-wire bonding; that is, the electricalleads themselves need to be thin films Consider the detector configuration of Fig-ure 11.3b, a so-called “monolithic” approach The idea is to start with a fairly thinsubstrate material, say 1 mil of silicon Then, most of the material is etched away,leaving a fairly thin frame and much thinner legs and a central portion (membrane)that serves as the substrate for the HTS thin film The thin-film wire connection andthe legs themselves must be thin enough to provide better thermal isolation thangold-wire bonding The heat capacity must improve even more than the thermalisolation to improve upon the 100-ms time constant, indicating that the membraneneeds to approach 1 m thickness Some HTS films have even been grown with-out a substrate (12) As we increase the thermal impedance of the metallic links, bythe Wiedemann–Franz law we also increase the electrical impedance As we willsee later, electrical impedance brings with it an extraneous noise term Berkowitz

et al (13) have presented a superconducting link to ameliorate this noise term

11.3.2 Bias: Effect of Electrothermal Feedback on Thermal

Isolation

As the resistive TE detector is run with an electrical bias, Eq (7) is modified to

C d T dt  GT  +W  dW dT h T (20)

where W his the heating due to the electrical bias This may be re-expressed as

where the effective thermal conductance satisfies the equation

Two common biasing conditions are fixed current through the detector and

fixed voltage across the detector For fixed current, W h  I2

R and dW h /dT  I2

dR/dT Thus, the effective thermal conductance for fixed current is

G e,i  G
I2

(23)

As dR/dT is a positive quantity, the effect of constant current bias is to reduce G e,

until the G ebecomes zero (at the destabilization current) and the detector becomesunstable (thermal runaway) Clearly, thermal runaway is most likely at the mid-

point of the transition The reduced G eis used for the responsivity [Eqs (8)–(10)],lengthening the effective time constant %e e The effect of G eon the phonon-noise-limited NEP is less clear The conservative approach (14), which we will

use, is to continue to use the low-bias G in Eq (13) This is not strictly true, as

the system is no longer in thermal equilibrium Indeed, there is evidence that thelimiting NEP can be reduced due to electrothermal feedback (15) For constant-

voltage biasing, W h  V2/R, dW h /dT 
(V2/R2) dR/dT, and the effective thermal

Also, V bdoes not appear to be limited (there is no thermal runaway condition), but

an arbitrarily high bias can overheat the detector and cause a fuselike destructionmechanism either in the connecting wires/traces or in the HTS film itself

11.3.3 Effect of Phonon Wave Interference and Mean Free

Path on Thermal Isolation

Equation (19) accurately predicts the “bulk” thermal conductance when the mensions, length and area, are large compared with the mean free path When adimension approaches the phonon mean free path, the thermal resistance can be

boosted A possible example is a thin film of HTS material on a substrate: If thefilm thickness approaches the mean free path, the sideways (parallel to thefilm–substrate interface) thermal resistance is boosted For YBCO, the mean freepath is 3 nm at 50 K (16) Most IR detectors employ films at least 100 nm thick,

so this is not an issue Films are generally thinner on silicon substrates to avoidmicrocracking, but the mean free path is probably still not an issue

We previously discussed the issue of thermal resistance between HTS filmand substrate The thermal isolation is not high, leading to an insensitive but fastdetector Consider the case of Figure 11.2a, where incoming photons are absorbed

by the HTS film, launching phonon waves into the HTS material Due to the erty mismatch at the film–substrate interface, the waves will be partly reflectedback to the absorber and those waves will be reflected yet again toward the inter-face The multiply-reflected waves can lead to destructive and constructive inter-ference, as is the case for optical elements such as Fabry–Perot interferometers.Under the right conditions, the thermal isolation of the film from the substrate can

prop-be increased (17) The frequency range of enhanced temperature rise is 2

to 9 2, where d is the film thickness and D is the diffusion coefficient (adiff

in Table 11.1) For YBCO, the frequency range of increased isolation and thermal

response is 6–57 MHz for 200-nm-thick c-axis YBCO.

11.3.4 Effect of Bias Current on dR/dT

It is common, given measurements of G and dR/dT, to predict the responsivity of

an IR detector using a relation such as Eq (1) However, care must be taken when

the dR/dT is measured with a bias other than the one in use for the detector cation, as there are a couple of reasons why dR/dT may depend on the magnitude

appli-of the bias current The first is thermal R versus T is logically interpreted in terms

of Tfilm, the temperature of the HTS film Yet, if T is measured by a thermometer separate from the detector, the measured T may be more typically Tstage, the tem-

perature of a thermally isolated stage that is varied to set the operating ture of the detector Consider the case of current biasing The low-frequency rela-

tempera-tionship between Tfilm and Tstageis

In the fully superconducting regime, R 0 and there is no offset; in the normal

regime, there is a positive offset The transition appears broader versus Tfilmthan

versus Tstage Equivalently, the transition appears narrower versus Tstage than Tfilm.

Thus, the film heating effect can make the transition appear narrower by anamount that depends on the bias current Heating at the contacts will be nearly

constant throughout the transition, so contact heating will not change dR/dT but may change the apparent T c

I2R

G

The other consideration is that increasing the bias current can broaden theintrinsic width of the transition This is fairly straightforward to show for a one-dimensional (wire) superconductor (18) Thus, in the general case, there is thepossibility for the appearance of both narrowing and broadening, and to determinewhich, if either, will dominate will depend on the details of a given detector (19).

11.3.5 Considerations on the Absorber Efficiency ␩

There are numerous possibilities for good absorption efficiency in the infraredregime Dielectric materials such as paints are hampered, however, by the need tomake the absorber about as thick as a wavelength, leading to high heat capacityand long time constants as the operating wavelength approaches 1 mm Metals are

a possibility, in two forms In one, the so-called “gold black” or “gold soot” (20),the gold is deposited in a poor nitrogen vacuum, forming a frothy layer mostlyvoid filled (about 0.5% of the density of bulk gold) The absorption is near unity

in the visible, declining to perhaps 20–40% near 1 mm, depending on the ness used Another possibility is the so-called “space-matched” coating (21).Here, an extremely thin metal film is deposited onto a substrate—the film is thinenough so that the resistivity is not the bulk resistivity but, rather, is determined

thick-by the film thickness For the appropriate thickness, giving an impedance of proximately half of free space (377 /square for a substrate index of refraction of2) radiation incident through the substrate is approximately half absorbed (44%for an index of refraction of 2) at the substrate–film interface, pretty much inde-pendent of wavelength; the rest is transmitted and none is reflected The advan-tage of the space-matched coating is that it is very broadband and very thin,thereby not increasing the time constant

ap-Finally, the HTS film itself can be used as the absorber Fully ducting, it is mirrorlike at long enough wavelengths, thereby providing low ab-sorption efficiency Within the transition region, it is metallike; however, relying

supercon-on it for absorptisupercon-on may impose csupercon-onstraints supercon-on the necessary thickness, which maynot be compatible with a thickness consistent with good film quality, depending

on the substrate On the other hand, there may be great benefit to depositing theheat directly into the HTS thermometer We have also mentioned earlier the pos-sibility of antenna coupling the incoming radiation to a smaller-than-usual HTSthermometer, with a limitation to single-mode operation

Thermal Structure

The simplest thermal model consists of a single, lumped heat capacity C and a gle, lumped thermal conductance G, a so-called single-node thermal model The

sin-single-node model has the Lorentzian frequency response of Eq (9), consisting of

a flat frequency response and 0° phase shift at low frequencies ()% 1), a

high-frequency phase lag of 90°, and a high-high-frequency amplitude response
1/).When the diffusion length becomes comparable to detector dimensions, either amultimode or distributed model is more appropriate We will now consider a fewsimple examples of these more involved thermal models.

We have already considered the case of diffusion in the thermal link At lowfrequencies, the diffusion length is very long and the thermal conductance is the

usual value (call it Gdc) For frequencies higher than the value where the diffusion

length equals the length of the thermal link (call this )D), the thermal conductance

depends on frequency as Gdc()/)D)1/2 Consider the simple case where the heatcapacity of the link may be neglected, relative to the detector absorber–ther-mometer unit Define the characteristic frequencies )0%0 1, where %0 dc.There are the two possibilities for the frequency behavior of the responsivity as

described by Eq (9), allowing for G to be a function of frequency through the

dif-fusion length dependence

Case 1:)D 0 In this case, G is not modified by diffusion until the heatcapacity becomes the dominant factor in the denominator of Eq (9), sothe frequency response is the typical Lorentzian

Case 2:)D )0 In this case, the responsivity begins falling as 1/)1/2at)D, until

for frequencies where the response is non-Lorentzian, the rolloff is slower than

Lorentzian Additional considerations concerning the thermal link may be found

in Ref 22

A further case is an absorber–thermometer–thermal bath (cold-stage) tem (23) Let G1be the thermal conductance between the bath and the thermome-

sys-ter and G2 be the conductance between the thermometer and the absorber Let C1

be the heat capacity of the thermometer and C2 be the heat capacity of the sorber Define   C2/C1,%1 C1/G1, and %2 C2/G2 The unity-emissivity re-

ab-sponsivity is terms of Kelvins per watt is of the form

where%1%2 %1%2and%1 %2 %1(1 )  %2 In this case, the response is

a double Lorenztian, faster than Lorentzian The high-frequency phase shift is

1

G1(1 j)%1)(1 j)%2)

)2)

D

))

D