Buschow K.H.J. (Ed.) Concise Encyclopedia of Magnetic and Superconducting Materials

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superconductivity, are governed by the exchange in-

teraction of the conduction electrons with the R 4f-

electrons. According to Fig. 2 YbNi

C should be a

superconductor becoming antiferromagnetically or-

dered at sufﬁciently low temperatures. In this com-

pound, however, hybridization of 4f-electrons with

the conduction electrons connected with correlation

effects results in heavy fermion behavior and sup-

pression of superconductivity.

The RTBC superconductors have been classiﬁed as

phonon-mediated type II superconductors (see Su-

perconducting Materials, Types of) in the clean limit

(i.e., the mean free path of the unpaired electrons is

large compared to the coherence length of the Cooper

pairs). They are s-wave superconductors with a

strongly anisotropic energy gap. Their superconduct-

ing and magnetic properties can only be understood

by taking into account details of the electronic struc-

ture and of the electron–phonon interaction. Thus,

the positive curvature of the upper critical ﬁeld H

a function of temperature T of LuNi

C (see Fig. 3)

is due to a strong dispersion of the Fermi velocity and

can be well described in a two-band model. The crit-

ical temperature T

is governed by nested regions of

the Fermi surface. In the case of antiferromagneti-

cally ordered RTBC, these nesting features induce

peculiarities in the magnetic long-range order which

is also strongly inﬂuenced by crystalline electric ﬁelds

(CEFs). The interplay of itinerant-electron-mediated

exchange and CEF results in a large variety of types

of antiferromagnetic structures with temperature-de-

pendent spin reorientation transitions as well as

(ﬁeld-dependent) metamagnetic transitions.

As expected these clean-limit superconductors

show an anisotropy of H

(T) due to the anisotropy

of the Fermi surface. In RTBC superconductors with

magnetic R-elements antiferromagnetic order causes

further contributions to the anisotropy of H

(T)as

can be seen in Fig. 4. ErNi

C and TmNi

C even

show a different sign in the anisotropy of their H

which obviously is connected with the different di-

rections of the R magnetic moments in these two

compounds.

In most known type II superconductors the ﬂux

line lattice does not depend on the symmetry of the

crystal lattice and is hexagonal as described by the

standard London or Ginzburg–Landau model. In

RTBC superconductors, however, hexagonal-to-

square vortex–lattice transitions have been observed,

depending on strength and direction of the applied

magnetic ﬁeld as well as on temperature.

See also: Electrodynamics of Superconductors: Flux

Properties; Films and Multilayers: Conventional

Superconducting; High-temperature Superconduc-

tors: Thin Films and Multilayers; High-temperature

Superconductors: Transport Phenomena; High-T

Superconductors: Electronic Structure; Supercon-

ducting Materials, Types of

Bibliography

Canﬁeld P C, Bud’ko S L 2001 Effects of local moment mag-

netism on the superconducting properties of RNi

C com-

pounds. In: Mu

ller K-H, Narozhnyi V N (eds.) Rare Earth

Transition Metal Borocarbides (Nitrides): Superconducting,

Magnetic and Normal State Properties. Kluwer Academic,

Dordrecht, pp. 33–44

Figure 4

Temperature dependence of the upper critical ﬁeld H

for TmNi

C and ErNi

C single crystals. Circles:

H8a; triangles: H8c (after Canﬁeld and Bud’ko 2001).

Figure 3

(T) of an LuNi

C single crystal measured parallel

to the tetragonal c-axis (J). The solid curve was

calculated using a two-band model. Dashed line:

isotropic single-band model (Shulga et al. 1998).

1210

Superconductors: Borocarbides

Cava R J, Takagi H, Batlogg B, Zandbergen H W, Krajewski J

J, Peck W F, Jr., van Dover R B, Felder R J, Siegrist T,

Mizuhashi K, Lee J O, Eisaki H, Carter S A, Uchida S 1994

Superconductivity at 23 K in yttrium palladium boride car-

bide. Nature 367, 146–8

Hilscher G, Michor H 1999 Superconductivity and magnetism

in quaternary borocarbides and boronitrides. In: Narlikar A

V (ed.) Studies on High Temperature Superconductors. Nova

Science, New York, Vol. 28, pp. 241–86

Lynn J W, Skanthakumar S, Huang Q, Sinha S K, Hossain Z,

Gupta L C, Nagarajan R, Godart C 1997 Magnetic order

and crystal structure in the superconducting RNi

C mate-

rials. Phys. Rev. B 55, 6584–98

ller K -H, Fuchs G, Drechsler S-L, Narozhnyi V N 2002

Magnetic and superconducting properties of rare earth boro-

carbides of the type RNi

C. In: Buschow K H J (ed.)

Handbook of Magnetic Materials. Elsevier, Amsterdam, Vol.

14, pp. 199–305

Nagarajan R, Mazumdar Ch, Hossain Z, Dhar S K, Go-

palakrishnan K V, Gupta L C, Godart C, Padalia B D,

Vijayaraghavan R 1994 Bulk superconductivity at an elevat-

ed temperature (T

E12 K) in a nickel containing alloy system

Y–Ni–B–C. Phys. Rev. Lett. 72, 274–7

Shulga S V, Drechsler S -L, Fuchs G, Mu

ller K-H, Winzer K,

Heinecke M, Krug K 1998 Upper critical ﬁeld peculiarities of

superconducting YNi

C and LuNi

C. Phys. Rev. Lett.

80, 1730–3

K.-H. Mu

ller and V. N. Narozhnyi

IFW, Dresden, Germany

Superconductors: Rapid Single Flux

Quantum (RSFQ) Logic

RSFQ superconductor digital devices were ﬁrst sug-

gested in 1985 and developed experimentally mostly

in the 1990s; for detailed reviews see Likharev and

Semenov (1991) and Bunyk et al. (2003). In compar-

ison with the previous generation of superconductor

logic, RSFQ logic offers a considerably higher speed

(up to 800 GHz for simple niobium-based digital cir-

cuits) and much lower power dissipation (of the order

of 10

18

Jbit

1

at liquid helium temperatures) at

comparable parameter margins (of the order of

730%). Because of these advantages, RSFQ logic

is a focus of research and development work, despite

the fact that its successful implementation requires

higher circuit design standards.

1. Physical Bas is

RSFQ circuit operation is based on the natural prop-

erty of superconductors to quantize magnetic ﬂux

F ¼

dA through any closed superconducting loop

in multiples of the ﬂux quantum F

F ¼ nF

; F

 h=2eE2  10

15

Wb;

n ¼ 0; 71; 72; y ð1Þ

Evidently, digital bits can be coded by certain values

of the integer n; e.g., the ﬂux states with n ¼0 and

n ¼1 may be used to present binary zero and unity,

respectively. If the superconducting loop is made of a

bulk superconductor, switching between the different

ﬂux states would require the suppression and resto-

ration of superconductivity in at least some cross-

section of the loop; the latter process would take too

much time (B100 ps for the most popular supercon-

ducting material, niobium). However, if the loop is

interrupted with one or more Josephson junctions

(see Josephson Junctions: Low-T

, Josephson Junc-

tions: High-T

), switching may be performed much

faster (in a fraction of a picosecond for niobium).

Figure 1(a) shows the simplest single ﬂux quantum

(SFQ) circuit with just one Josephson junction. Sta-

tionary states of this system can be analyzed by com-

bining the equation for Josephson supercurrent,

I ¼I

sinj, where j is the Josephson phase drop

across the junction, with the usual equation for the

total magnetic ﬂux through the loop, F ¼F

LI,

where L is the loop inductance, and F

is the external

magnetic ﬂux. (In electronic circuits it is frequently

convenient to create this ﬂux by passing an external

current through a part of the loop: F

¼MI

, where

M is the inductance of this common part.) Taking

into account the fundamental relationship j ¼2pF/

, these equations may be readily solved together to

give the stationary relationship between F and F

This relationship shows that if the LI

product is

Figure 1

(a) Simplest SFQ circuit (‘‘RF SQUID’’ or ‘‘DC/SFQ

converter’’) serving as an SFQ pulse generator. (b) Total

magnetic ﬂux F in the circuit as a function of applied

ﬂux F

for a value of LI

¼F

, typical for RSFQ

circuits. Arrows indicate ﬂux-state switching at critical

values of the external ﬁeld. The middle branch (with

negative slope) corresponds to unstable states. Filled

points show two stable states at the equilibrating value

¼F

/2.

1211

Superconductors: Rapid Single Flux Quantum (RSFQ) Logic

large enough (4F

/2p), the Josephson phase differ-

ence j (and hence the total magnetic ﬂux F and per-

sistent current I) may have several stable stationary

states for the same external ﬁeld F

, with the differ-

ence close to F

(see Fig. 1(b)). By ﬁxing a d.c. ﬂux

bias at F

/2, one can work with just two states (n ¼0

and n ¼1) with equal energy and stability.

Switching between the states may be achieved by

changing F

beyond a critical value at which one of

the stationary states disappears (see arrows in Fig.

1(b)). In order to avoid irreproducible multiﬂux

switching events, the Josephson junction has to be

overdamped (i.e., the McCumber–Stewart parameter

to be less than 1), for example by using external

shunting by normal thin ﬁlm. In practice, b

is made

close to 1; in this case the switching time is minimal

and is close to 3 units of

¼ F

=2pI

ð2Þ

where I

is the junction critical current and R

the

normal resistance. For typical Josephson junctions

the switching duration is a few picoseconds. Accord-

ing to Faraday’s law V ¼dF/dt, during the switching,

a short voltage pulse with the quantized area

VðtÞdt ¼ DFEF

E2mV ps ð 3Þ

is formed across the junction (Fig. 1(a)). In RSFQ

circuits these ‘‘SFQ pulses,’’ with amplitudes of the

order of 1 mV, are passed to other devices causing

their switching.

Figure 2 shows the basic RSFQ circuit, the set–reset

(‘‘RS’’ or ‘‘D’’) ﬂip-ﬂop. Its quantizing loop with in-

ductance LEF

includes two (rather than one)

Josephson junctions, but its characteristics are never-

theless almost identical to those shown in Fig. 1. The

supply current (DC IN) is close to, but smaller than,

the total critical current 2I

of Josephson junctions 1

and 2, so that it creates Josephson phase drops

1,2

op/2 across these junctions. Owing to its asym-

metric injection, the same d.c. current also creates a

magnetic bias F

close to F

/2 in the loop. Because of

this bias, the loop has two equilibrated ﬂux states:

n ¼0 (with the additional persistent current I

circulating counterclockwise) and n ¼1(I

of the

same magnitude, but circulating clockwise).

Let the device be initially in state n ¼0, so that the

d.c. supply current I

and the persistent current add

in junction 1, and bias it subcritically (j

Bp/3).

When an SFQ pulse SET IN arrives from the left

input terminal, it pushes the applied ﬂux beyond the

critical value (cf. Fig. 1(b)). As a result, the phase j

leaps by B2p, and the ﬂux changes by BF

, i.e., the

system switches from its ﬂux state 0 to state 1 (with

persistent current clockwise). Similarly, an SFQ pulse

arriving from the right input (RESET IN) provides

the reset of the device (i.e., switching from 1 to 0).

Simultaneously the latter process develops an output

pulse SFQ OUT, because the Josephson phase across

junction 2 leaps by 2p. This pulse may now go to

other RSFQ devices.

Other logic gates (‘‘elementary cells’’) of the RSFQ

family also have one or several coupled quantizing

loops, each interrupted with 2–4 Josephson junctions.

A detailed description of the available cells is avail-

able on the Internet (Bunyk et al. 1999). The follow-

ing important features are common for all cells:

the ﬂux state is stored in the cell until it is reset

by another pulse; hence each elementary cell can be

considered as a combination of a logic gate and a

latch in one device (‘‘clocked gate’’);

the reset pulse not only triggers the output

pulse, but also restores the device to its initial state,

so that the shortest distance between the set and reset

pulses may be just slightly longer than the width of

the pulse—just a few picoseconds for niobium-based

devices; and

the d.c. bias current provides the necessary en-

ergy ampliﬁcation of the SFQ pulses, thus compen-

sating for the inevitable energy loss in the passive

transmission lines and shunting conductances of the

Josephson junctions.

When ultrafast processing of digital information in

an RSFQ circuit is completed, the results may be

transferred to the usual (voltage-level) form using a

‘‘SFQ/DC converter’’ circuit which uses a d.c.

SQUID (see SQUIDS: The Instrument) to sense the

ﬂux state of the output RSFQ cell—in practice, gal-

vanically coupled versions of such an SFQ/DC con-

verter are used. The resulting d.c. voltage signal, with

a swing of several hundred microvolts, can be am-

pliﬁed by a latching superconductor circuit to a few

millivolts, extracted from the cryo-region using a

copper cable, and ampliﬁed to the standard semicon-

ductor transistor level of a few volts by inexpensive

room-temperature semiconductor ampliﬁers.

Figure 2

Simplest RSFQ logic cell, RS ﬂip ﬂop (crosses denote

Josephson junctions). Its basic mode of operation is

described in the text. Additional junctions 1

and 2

are

necessary to avoid possible detrimental back action of

the device on the input circuits. For example, if the pulse

SET IN arrives when the ﬂip-ﬂop is in state 1 and

junction 1 carries low current (d.c. supply current and

persistent current subtract in the left branch of the loop),

then junction 1

performs the 2p leap of the Josephson

phase, and the pulse is not reﬂected back to the source.

1212

Superconductors: Rapid Single Flux Quantum (RSFQ) Logic

Input interfaces for RSFQ circuits are even sim-

pler, because the energy of RSFQ signals is much less

than that of standard room-temperature electronics

signals. For example, even the single-junction circuit

shown in Fig. 1(a) may serve as the input stage (‘‘DC/

SFQ converter’’), although its parameter margins

may be improved by using two additional Josephson

junctions.

2. Status

After a slow start in Russia, in the early 1990s inten-

sive RSFQ technology development was begun at

several US universities and corporate research and

development groups, using both low-temperature su-

perconducting (LTS) and high-temperature super-

conducting (HTS) materials. A few years later,

several European groups started work on RSFQ cir-

cuits, mostly using HTS materials. In the late 1990s

several Japanese groups started a ﬁve-year program

focused on LTS RSFQ technology.

This progress has allowed the implementation of

several relatively complex LTS RSFQ circuits with

1000–2000 Josephson junctions each, mostly using

the 3.5 mm niobium trilayer fabrication technology of

HYPRES Inc. (e.g., see Fig. 3). The maximum clock

speed for this technology ranges from 20 GHz for

VLSI circuits to 70 GHz for simple digital devices.

The speed is inversely proportional to the linear

junction size, so that for deep-submicrometer nio-

bium trilayer technology the corresponding clock

frequencies may reach approximately 150 GHz and

800 GHz, respectively (for details see Likharev 1999,

Bunyk et al. 2003). Figure 4 shows an example of

such an ultrafast device, a digital frequency divider

(T ﬂip-ﬂop) tested to operate up to 770 GHz (Chen

et al. 1999).

During the 1990s several simple HTS RSFQ cir-

cuits (with up to 30 Josephson junctions) designed

for demonstration purposes were implemented and

tested at temperatures from 4.2 K to 77 K (e.g., see

Fig. 5). Unfortunately, both experiments (Ruck et al.

1999) and calculations (Likharev 1999, Bunyk et al.

2003) indicate that thermal ﬂuctuations impose an

upper bound for VLSI RSFQ circuits using HTS

materials (copper oxides) at about 10 K if a low bit

error rate (o10

10

) is a requirement. The potential

advantage of HTS Josephson junctions is that they

may have a higher I

product and hence provide a

higher operation speed than LTS junctions (see Eqn.

(2)). However, the HTS thin-ﬁlm junction fabrication

methods developed so far do not deliver on this

promise. Moreover, these methods still do not pro-

vide sufﬁciently low critical current spreads. As a re-

sult, by the end of the 1990s the development of HTS

RSFQ technology was not continued by most re-

search groups.

Figure 4

Scanning electron microscope image of an RSFQ test

circuit including a digital frequency divider (DFD) with

0.5 mm, externally shunted niobium trilayer junctions.

This device could operate up to 750 GHz, while 770 GHz

has been reached using its version with 0.3 mm self-

shunted junctions (after Chen et al. 1999). The power

dissipated by the divider is just 1.5 mW, some 5 10

times lower than for the fastest reported semiconductor

DFD operating below 70 GHz.

Figure 3

RSFQ analog-to-digital converter designed and tested

by a HYPRES/SUNY collaboration (Rylov et al. 1998).

The circuit has close to 3000 Josephson junctions, the

total power consumption being below 1 mW, with an

active area of 7 mm 2 mm. By 2001 the spur-free

dynamic range of the device had been improved to reach

12:3 effective bits for a 175 Mbps effective sampling rate,

better than for any reported semiconductor transistor

ADC.

1213

Superconductors: Rapid Single Flux Quantum (RSFQ) Logic

3. Application Prospects

RSFQ circuits using submicrometer junctions are

some 100 times faster than similar modern CMOS

circuits. Even more importantly, RSFQ devices dissi-

pate much less power energy per bit (about 10

times

less without taking into account refrigeration, and 30–

300 times less including the refrigeration needs). One

more important advantage of LTS RSFQ circuits is

that their fabrication technology is much simpler that

that of CMOS or digital circuits based on other mod-

ern materials (SiGe, GaAs, InP, etc.).

However, the necessity of deep refrigeration of

RSFQ circuits limits their possible applications to a

few narrow, though important, niches of the digital

electronics market. These applications (Tables 1

and 2) can be divided into two major categories:

circuits that may be competitive at the existing

(or slightly upgraded) level of LTS fabrication tech-

nology; and

applications that would require the transfer to

submicrometer, VLSI technology.

Despite the relative simplicity of LTS fabrication,

the cost of a pilot line for RSFQ VLSI circuits has been

crudely estimated at 30 million. Towards the end of

1999 the most important prospective driver of RSFQ

technology was the so-called Hybrid Technologies

Multi-Threaded (HTMT) computing project started in

the USA (Fig. 6). In this project, an RSFQ subsystem

will be responsible for all ‘‘number-crunching,’’ as

well as for interprocessor communication networks

(Dorojevets et al. 1999).

4. Material Issues

For the reasons outlined in Sect. 2, only LTS-based

RSFQ circuits are being seriously developed. The

leading role here belongs to the niobium trilayer

technology that was developed during the 1980s (e.g.,

Hasuo et al. 1988). In this technology, the tunnel

barrier of a Josephson junction is formed by thermal

oxidation of a thin (o10 nm) aluminum layer depos-

ited on the base niobium ﬁlm. After a few minutes of

oxidation in dry oxygen at a pressure of a few milli-

torr (Miller et al. 1993), a niobium counter electrode

ﬁlm is deposited without vacuum breaking, thus pre-

venting any contact between aluminum and water

vapor. The junctions fabricated using this technique

may exhibit very high reproducibility (random

spreads of the order of 1%) even for subnanometer

Figure 5

Scanning electron microscope image of a simple 14-

junction HTS RSFQ circuit (two DC/SFQ converters,

two Josephson transmission lines, an RS ﬂip-ﬂop, and

an SFQ/DC converter) fabricated using two YBCO

layers, which could operate up to 77 K (after Ruck et al.

1999).

Table 2

Possible applications of LTS RSFQ logic devices: 0.4 mm

technology with B10

junctions per chip.

System

Expected performance

examples

Communication digital

switching cores

100 Gbps at 128

channels; 1 chip,

0.1 W at 4 K

Digital signal processors 100 gigaﬂops; 1 chip,

0.1 W at 4 K

High-end workstations and

servers

1 teraﬂops; 4

processors, 0.5 W at

Petaﬂops-scale computing

systems

1 petaﬂops; 4000

processors, 250 W at

Table 1

Possible applications of LTS RSFQ logic devices: 3.5 mm

technology with o10

junctions per chip.

Circuit

Expected performance

examples

A/D converters 14 bits at 60 MHz;

noise: 3 db

Digital SQUIDs Noise: 1 f THz

1/2

1

D/A converters 10 bits at 18 GHz,

100 mV

D.c. and a.c. calibrators 10 V at 30 MHz, 10 ppb

Digital signal correlators 1 bit at 1 024 channels,

16 Gbps; 8 bits at 8

channels, 128 Gbps

1214

Superconductors: Rapid Single Flux Quantum (RSFQ) Logic

aluminum oxide barriers providing very high critical

current density j

(well beyond 1 kAcm

2

The important issues in the development of this

technology include its extension to higher j

(up to

100 kAcm

2

), which is necessary for self-shunted op-

eration of Josephson junctions with maximum speed,

while retaining the low critical current spreads. A re-

lated issue is the chemical–mechanical polishing of

the junction counter electrode, necessary for submi-

crometer junction definition, without disturbing the

ultrathin aluminum oxide layer. Despite considerable

progress in these directions (Miller et al. 1993, Chen

et al. 1999, Patel and Lukens 1999), high j

RSFQ

circuits of sufﬁciently high integration scale have yet

to be developed.

For some (especially space-platform) applications

the increase of operation temperature to B10 K is

important, because of higher refrigeration efﬁciency.

Niobium nitride-based Josephson junctions with

MgO tunnel barriers capable of operating at such

temperatures have been demonstrated (e.g., Kerber

et al. 1997, and references therein), but their fabri-

cation technology has to be further advanced to

enable VLSI circuit integration.

See also: Josephson Junctions: High-T

; Supercon-

ducting Materials: Types of; Superconducting Thin

Films: Materials, Preparation and Properties

Bibliography

Bunyk P, Likharev K, Litskevitch P, Rylyakov A, Zinoviev D

1999 RSFQ cell library; available at: gamayun.physics.

sunysb.edu/RSFQ/Lib/

Bunyk P, Leung M, Spargo J, Dorojevets M 2003 Flux-1 RSFQ

Microprocessor: Physical design and test results. IEEE Trans.

Appl. Supercond. 13, 433–6

Chen W, Rylyakov A, Patel V, Lukens J, Likharev K 1999

Rapid single ﬂux quantum T-ﬂip ﬂop operating up to

770 GHz. IEEE Trans. Appl. Supercond. 9, 3212–5

Dorojevets M, Bunyk P, Zinoviev D, Likharev K 1999 COOL-0:

design for RSFQ subsystem for petaﬂops computing. IEEE

Trans. Appl. Supercond. 9, 3606–14

Hasuo S, Imamura T, Fujimaki N 1988 Recent advances in

Josephson junction devices. Fujitsu Techn. J. 24, 284–92

Kerber G, Abelson L, Elmadjian R, Hanaya, Ladizinsky E

1997 An improved NbN integrated circuit process featuring

thick NbN ground plane and lower parasitic circuit induct-

ances. IEEE Trans. Appl. Supercond. 7, 2638–43

Likharev K 1999 Superconductor devices for ultrafast comput-

ing. In: Weinstock H (ed.) Applications of Superconductors.

Kluwer, Dordrecht, The Netherlands, pp. 247–93

Likharev K, Semenov V 1991 RSFQ logic/memory family: a

new Josephson junction technology for sub-terahertz-clock-

frequency digital systems. IEEE Trans. Appl. Supercond. 1,

3–26

Miller R, Mallison W, Kleinsasser A, Delin K, Macedo E 1993

Niobium trilayer Josephson tunnel junctions with ultra-high

critical current densities. Appl. Phys. Lett. 63 , 1423–5

Patel V, Lukens J 1999 Self-shunted Nb/AlO

/Nb Josephson

junctions. IEEE Trans. Appl. Supercond. 9, 3247–50

Ruck B, Chong Y, Dittman R, Engenhart A, Oelze B, Sodtke

E, Siegel M 1999 Measurement of the error rate of single ﬂux

quantum circuits with high-temperature superconductors.

IEEE Trans. Appl. Supercond. 9, 3850–3

Rylov S, Brock D, Gaidarenko D, Kirichenko A, Vogt J, Se-

menov V 1998 High resolution ADC using phase modulation–

demodulation architecture. IEEE Trans. Appl. Supercond.

9, 3016–9

K. K. Libharev

State University of New York, Stony Brook

New York, USA

Super-resolution: Optical and Magnetic

Techniques

In optical recording, an optical head focuses the beam

from a semiconductor laser to produce a probe spot

on the recording medium. The focused spot has a

Gaussian intensity proﬁle and a width determined ul-

timately by the laws of diffraction. When limited only

by diffraction, the diameter of the spot is directly

proportional to the wavelength of the laser radiation,

and inversely proportional to the numerical aperture

(NA) of the objective lens. If the width of the spot (d)

is taken as the distance between the half power points,

then in the diffraction limit dD0.56l/NA. In magne-

to-optics, as with most optical recording technologies,

it is, however, possible to write ‘‘marks’’ much smaller

than the total width of the diffraction-limited spot

Figure 6

Preliminary design of the HTMT petaﬂops-scale

computer room. Note that despite the RSFQ ‘‘COOL’’

subsystem being responsible for all the ‘‘number

crunching,’’ it occupies o1m

, just a tiny fraction of the

whole machine size. This compactness is possible owing

to the extremely low power dissipation of RSFQ

circuits, and is very important for providing very low

(20 ns) interprocessor communication latency (courtesy

of J. Morookian and L. Bergman, Jet Propulsion

Laboratory).

1215

Super-resolution: Optical and Magnetic Techniques

(see Magneto-optical Effects, Enhancement of ). As

shown in Fig. 1, this may be achieved by exploiting

the thermal nature of the write mechanism used by all

current recording systems, and involves making the

correct choice of the critical write temperature in

conjunction with optimization of the thermal re-

sponse or write sensitivity of the medium.

The resolution on readout, however, remains con-

strained by the total width of the beam, so that the

density at which information can be stored is deter-

mined by the rate at which the depth of modulation

(signal) falls as recorded marks are packed closer.

When the minimum separation between recorded

marks is reduced to half the diameter of the focused

spot, the signal falls to zero. Therefore it is the read-

out process that limits the density at which informa-

tion can be stored. At least three separate

technologies are under active development with a

view to overcoming this limitation, and they all rely

heavily on the material and material processing for

their successful operation.

The optical recording industry foresees (News

Letter no. 4 OITDA 1998) the need for a technology

in which the areal densities approach 1 Tbyte in

2

2010. Since the launch of optical storage products,

an intensive global research effort has driven down the

wavelength of semiconductor laser diodes from

around 800 nm to the 400 nm devices announced

(Nichia Corporation Japan 1999) early in 1999.

However, these developments alone only improve

the resolution by a factor of four. Moreover, they

have impacted primarily on the CD-ROM or other

read-only formats, since the shorter wavelength

(E650 nm) laser devices installed have been slow to

realize the power required for high-speed writing.

The other parameter governing the resolution of

an optical head is its numerical aperture. Unfortu-

nately, the improvements of a similar order that

might be achieved by increasing the numerical aper-

ture become increasingly difﬁcult to implement as the

NA approaches its limiting value (1 in. air), while

constrained to conventional optics by other system

requirements. The NA of current systems remains

limited to a value of around 0.55–0.65. It is clear that

to realize the density ﬁgures quoted above will in-

volve development of techniques that can bypass the

diffraction limit. The optical and magnetic super-res-

olution techniques discussed here offer that very pos-

sibility, but implemented by very different means.

The simplest way of achieving optical resolution

beyond the diffraction limit is to operate in what is

known as the near-ﬁeld regime, placing an aperture

deﬁning the required resolution between the laser

source and the sample. Providing the aperture-to-

sample separation is maintained at only a small frac-

tion of the laser wavelength, then the resolution is

determined by the diameter of the aperture and not

by diffraction. Perhaps the best early demonstration

of this technique is the work of Betzig et al. (1987)

using metallized optical ﬁbers tapered to an aperture

of only 40 nm using access technology borrowed from

scanning probe microscopy. Such techniques are of

course very inefﬁcient in their utilization of optical

energy, and although more recent demonstrations

(Hosaka et al. 1996) have achieved readout data rates

of 10 MHz for phase-change recording using this

principle, because of the current speed of their access

they will not be considered further.

1. Magnetic Super-resolution

‘‘Magnetically induced super-resolution’’ (MSR) as

originally conceived is the term applied to various

techniques developed to overcome the diffraction lim-

it by creating, in the surface of the moving medium,

an ‘‘effective dynamic aperture’’ much smaller than

the width of the readout beam. This technique, ﬁrst

proposed by Sony (Ohta et al. 1991), is realized in a

similar fashion to the direct overwrite (DOW) by light

intensity modulation (LIM) technology conceived

earlier by Nikon (Saito et al. 1987). The deposition

process is controlled to produce a medium having a

complex multilayer structure of magnetic ﬁlms that

are coupled to each other magnetostatically or, more

commonly, through the exchange interaction. At the

same time, the unique compositional dependence of

the properties of various amorphous rare-earth–tran-

sition metal (RE-TM) alloys such as TbFeCo, GdFe,

GdFeCo, etc., is exploited to control their Curie tem-

perature, coercivity, and switching ﬁeld (see Magneto-

optic Recording Materials: Chemical Stability and Life

Figure 1

Writing below the diffraction limit.

1216

Super-resolution: Optical and Magnetic Techniques

Time). The composition of each of the different cou-

pled layers that comprise the medium is varied, so that

its magnetic and thermomagnetic behavior is precisely

tailored to a specific task within the MSR readout

process. Activation of these different characteristics is

achieved by using a somewhat higher laser power than

employed for conventional readout, in conjunction

with an applied magnetic readout ﬁeld.

To appreciate the working principle of MSR sys-

tems, consider a basic three-layer medium such as

shown in Fig. 2 consisting of a conventional storage

layer, an intermediate or transfer layer, and a readout

layer. Domains representing the stored data pattern

are written conventionally into the storage layer,

which has a high Curie temperature and a very large

coercivity. An identical pattern becomes imprinted on

to the readout layer by exchange coupling through

the intermediate or transfer layer. The readout layer

also has a high Curie temperature, but its coercivity is

small, less than that of the applied readout ﬁeld (H

It is also made thick enough so that the readout

beam only interrogates this layer—no energy is al-

lowed to reﬂect back from the storage layer to the

detection system. As the beam tracks across recorded

data, it produces in the medium a temperature proﬁle

that has the basic Gaussian proﬁle of a laser beam,

distorted in the direction of the medium’s motion

(Fig. 3). The Curie temperature of the intermediate

layer is less than the temperature reached by the me-

dium in the hottest part of the beam proﬁle. In this

region the data pattern in the readout layer is thus

temporarily decoupled from the storage layer, and

aligns instead with the readout ﬁeld H

The data pattern under this part of the beam is

effectively erased, creating a region that behaves as

an active optical mask inserted into the beam in the

plane of the surface. Magneto-optic information is

therefore read out only with that portion of the fo-

cused laser spot that is reﬂected from the cooler part

of the irradiated surface. This is crescent-shaped, as

can be seen in Fig. 3. It is the width of the crescent,

typically only one-third the width of the focused spot,

along the track that now determines the resolution.

After the beam has passed a given portion of data,

the medium cools and the erased pattern is re-estab-

lished as the coupling between the surface readout

layer and the lower undisturbed storage layer is re-

stored. Throughout this process, the integrity of the

data in the storage layer is ensured by the high Curie

temperature and coercivity of this layer. In a similar

fashion, the high Curie temperature of the readout

layer maintains the signal quality of the data being

read out in the cooler aperture in the medium.

Although Figs. 2 and 3 show the operation of the

system with pulse position recording, it is also com-

patible with pulse length recording and magnetic ﬁeld

modulation, when the written domains themselves

become crescent-shaped.

The basic system described above is characterized

by the high-temperature mask trailing the detection

aperture, and is therefore known as front aperture

detection (FAD). Since it was ﬁrst conceived it has

been extensively developed and reﬁned. For example,

it is immediately obvious that if the relative positions

of the mask and aperture could be reversed, then not

only would the improved resolution be retained, but

the mask would now cover adjacent tracks, preclud-

ing crosstalk and permitting higher track densities

and/or land-and-groove recording. This is achieved in

rear aperture detection (RAD), though usually at the

expense of introducing an additional initializing ﬁeld.

In its most sophisticated embodiment, RAD can be

Figure 3

Reduced aperture and thermal mask in front aperture

detection (FAD).

Figure 2

Trilayer exchange-couple MSR medium.

1217

Super-resolution: Optical and Magnetic Techniques

implemented as a double-mask system that further

reduces the aperture and improves the resolution.

Finally, there is center aperture detection (CAD),

in which the temperature dependence of the aniso-

tropy of certain of the RE-TM alloys is exploited.

The composition of the readout layer is made such

that the magnetization lies in plane at ambient tem-

perature, but rotates out of plane at much higher

temperatures. A polar Kerr readout signal is there-

fore only detected from the very center of the tem-

perature proﬁle formed by the beam in the medium.

The cooler areas are effectively masked since, as the

magnetization still lies in plane, they display no polar

rotation. A major beneﬁt of this system is that it re-

quires no additional ﬁelds applied during readout.

For a more extensive description of MSR technol-

ogy, the reader is directed to the review by Kaneko

and Nakaoki (1996). Recent achievements of the

double-mask or CAD-MSR technology include the

2 Gbyte capacity, 90 mm disk reported by Fujitsu

(Shono 1999) and the 9 Gbyte, 120 mm disk reported

by Sharp (Murakami et al. 1996). Despite these suc-

cesses, a major drawback of the MSR principle is that

the signal level decreases with reducing aperture size,

since an ever-reducing portion of the focused spot is

actually used to detect the tiny domains. By 1996, it

had become apparent that a more sophisticated sys-

tem would be required to read out domains below

about 0.2 mm in diameter.

2. Magnetically Amplifying M agneto-optic

System

The magnetic amplifying magneto-optic system (MA-

MMOS) was proposed by researchers at Hitachi and

Sanyo (Awano et al. 1996) to address the problems of

reducing signal level in MSR systems. Again this is a

multilayer system, with the functions of storage and

readout separated into mutually coupled layers whose

properties are tailored to their specific task through

the correct combination of rare-earth and transition

metal elements. In MAMMOS media, the coupling

between layers is almost exclusively magnetostatic and

the working principle is relatively straightforward.

The stable diameter (d

) of a cylindrical reverse

domain written into a perpendicular recording medi-

um is determined by the balance of forces acting on

it. Energy stored in the domain walls acts to collapse

the domain, but is opposed by the resistance to wall

motion provided by the coercivity. In the case of do-

mains so small that MAMMOS is required for read-

out, the ratio of the thickness of the medium to the

stable domain diameter in general becomes such that

it is also necessary to take account of the contribution

of the magnetostatic energy to the stability of the

system. The demagnetizing ﬁeld associated with a re-

versed domain acts with the coercive ﬁeld to oppose

the collapsing ﬁeld and stabilize the bit at a smaller

diameter. Previous studies (Callan and Josephs 1977,

Honda et al. 1981) have treated these two opposing

forces by combining them into an effective ﬁeld

eff

), with stable domains being obtained when this

effective ﬁeld is less than the coercive ﬁeld (H

eff

In these circumstances, application of an alternating

external applied ﬁeld (H

appl

) synchronized with the

system data clock, and aligned to alternately either

assist or cancel the coercive ﬁeld, will expand or

collapse any domain.

Data domains written in the storage layer with di-

ameters as little as one-tenth of the full width of the

readout beam are resolved on readout by ﬁrst cop-

ying each in turn to the readout layer. There they are

then temporarily expanded, so that each one ﬁlls or

overﬁlls the beam to produce signal levels approach-

ing 100% saturation. The readout sequence may be

understood by reference to Fig. 4. In Fig. 4(a), the

instantaneous applied ﬁeld is in a direction and of a

magnitude such that it opposes coupling between the

storage layer and the readout layer, so that there are

no data domains in the readout layer. As H

appl

passes

through zero, as shown in Fig. 4(b), coupling is es-

tablished and a domain is copied to the readout layer.

appl

now increases to a maximum in the direction

that assists the coercive ﬁeld and opposes the col-

lapsing ﬁeld. The copied domain is therefore caused

to expand to a size that is readily detectable (Fig.

4(c)). During the opposite half of the applied ﬁeld

cycle, H

appl

again passes through zero when the do-

main is shrunk to its original size, before ﬁnally being

fully collapsed and expelled from the readout layer as

the cycle completes (Fig. 4).

Recent demonstrations of the potential of MA-

MMOS technology have included a carrier-to-noise

ratio (CNR) of more than 50 db from 0.2 mm domains

(Takagi et al. 1999), the observation of a MAMMOS

signal from 0.04 mm domains (Takagi et al. 1999), and

the combining of light intensity modulation direct

overwrite with MAMMOS readout (Tokunaga et al.

1999).

Figure 4

Basic MAMMOS mechanism using a.c. applied ﬁeld

synchronized to system clock.

1218

Super-resolution: Optical and Magnetic Techniques

3. Optical Super-resolution

Optical super-resolution refers to a suite of tech-

niques that seek to increase the resolving power of an

optical head by circumventing the limiting value of

1 for the NA in air of conventional objective lenses.

The principle employed is analogous to the use of oil

immersion objectives in microscopy. A solid immer-

sion lens (SIL) with a high refractive index in the

form of a hemisphere or truncated super-sphere in

used in conjunction with a conventional objective

having NA of around 0.5. Figure 5 shows the simple

case in which a conventional low NA objective is used

to focus the beam at the center of the ﬂat face of a

SIL having hemispherical form. In this arrangement

all rays enter the SIL along its radii and are unde-

viated or diffracted. Thus, although the angle sub-

tended by the cone of incident rays is unchanged, the

NA ( ¼n sin y) of the composite system is increased

by a factor n, since ﬁnal incidence to focus is now

through a medium having a refractive index greater

than air. The focused spot size is consequently re-

duced by a factor n , where n is typically in the range

1.9–2.3. Adoption of the super-sphere offers yet fur-

ther potential improvement.

It is well known (Nussbaum and Phillips 1976) that

a beam directed through a sphere of radius r is fo-

cused to a point free of both spherical aberration and

coma at a distance r/n below the center of the sphere.

If the material below the point of focus is removed, as

shown in Fig. 6, we have a situation similar to the

simple hemisphere. However, the peripheral rays de-

ﬁning the NA that were originally converging at f

now converge at a larger angle f

, given by

n sin

1

, to a new focus at the center of the plane

of truncation. The effective NA is in this case there-

fore increased by a factor of n

, since the beam is

again also incident through a media of refractive in-

dex n. Used in conjunction with blue lasers, this

technology offers the potential to resolve domains as

small as 100 nm. It is not, however, without its prob-

lems. Total internal reﬂection means that only a small

part of the cone of radiation forming the focused spot

can exit into air for coupling into the disk media.

In order that adequate ﬁeld propagates in the air gap

between the lens and media, it is necessary to rely

heavily on the evanescent wave whose intensity drops

rapidly away from the lens surface. Implementation

of the full potential of this technique therefore re-

quires operating in the near-ﬁeld regime, with the

air gap ideally much less than the wavelength of the

radiation.

Outside the near-ﬁeld limit, i.e., at lens-to-media

separations of around two to three wavelengths, the

technology does make attainment of NA equal to 1

Figure 5

Hemispherical solid immersion lens (SIL).

Figure 6

Supersphere SIL.

1219

Super-resolution: Optical and Magnetic Techniques