Characteristics of film cryotrons

Solid..State Electronics Pergamon Press 1960. Vol. 1, pp. 351-356. Printed in Great Britain

CHARACTERISTICS

OF FILM C R Y O T R O N S

M. L. C O H E N a n d J. L. MILES

Arthur D. Little, Inc., Cambridge, Mass. A CRYOTRON is a switching device, much like a relay, in which one current controls another. T h e characteristics of importance therefore are what current is necessary to switch the cryotron, how much current can be switched, and how fast the device is or how much resistance is available for switching. One would also like to know how these parameters vary, what determines their values and how they are interrelated. CRYOTRON MEASUREMENTS I n order to obtain the characteristics of film cryotrons and design parameters for cryotron circuits, single cryotrons are made and subjected to certain simple tests. For example, for each eryotron the normal gate resistance Rg and the critical gate current Ige, as a function of temperature T, are measured. T h e critical controlling current Ice is measured by the following technique. With an X - Y recorder, a graph of gate voltage

characteristics". T h e break in these curves, where the gate resistance increases rapidly, is considered to be the switching point, and an Ig vs. Ie plot of the switching points yields the "control characteristic" of the cryotron. This test is repeated at various temperatures, and the control characteristics are extrapolated to zero gate current in order to obtain the critical controlling currents at these temperatures, as shown in Fig. 2.

g o

8

o aJ

Control Control current F I G . 1. Q u e n c h i n g

Current

FIG. 2. Control characteristics.

characteristics.

vs. control current le is obtained for various values of gate current lg. Fig. 1 shows a typical set of these curves, which we call the "quenching

All these measurements are made on cryotrons of different gate thicknesses t, so that as the direct result of measurements on film cryotrons we have Igc(T,t), Icc(T,t) and Rg(t). 351

352

M. L. C O H E N and J. L. M I L E S COMPUTED

CHARACTERISTICS

' ' t ), G/X(T,t) and p/t(t). The beJge(T,t), Jee(T,

The measured characteristics apply to cryotrons of specific dimensions. For cryotron-circuit design more general parameters are desirable. Since, to a good first approximation, Ige and lee are proportional to the gate and control widths, wg and we, respectively (1) Igc J'gc = - andJ'cc wg 70i

L~ = --

(1)

Wc

i

. E

4.t T H E F I G U R E S O F M E R I T , Me, 21/11,Ms Now consider the problem of designing a cryotron circuit. The above parameters are functions of temperature and gate thickness. The first questions to be answered are naturally: What temperature and what gate thickness should

1

5C c o~ -~

havior of these functions is shown in Figs. 3 and

T l = 3 0 0 0 A°

40

3(3

2O

.

O ' L _ _ 34

.

.

.

.

.

.

.

.

.

35

3"6 Temperature,

3"?

3'8

°K

FIG, 3. Basic parameters vs. temperature.

are the desired parameters. The area resistivity

pit may also be computed: p/t = XRg

(2)

where X = wg/we is the crossing ratio of the cryotron. Finally, just as the current gain G of a cryotron is computed by dividing Ige by Ice, a general current gain, G/X may be computed by dividing J'ge by Joe. This last parameter may also be called "Silsbee efficiency"* or just "efficiency" because it also represents the ratio between internal critical field (that due to conducted current) and external critical field. Thus, the basic cryotron parameters are:

be used? The efficiency G/X increases as the temperature is reduced; therefore, it is desirable to operate at as low a temperature as possible. The choice of thickness presents more of a problem. The area resistivity increases rapidly with decreasing thickness, but the Silsbee efficiency drops. T h e relative weight of these two opposing factors depends on the circuit in question. Consider first a circuit in which a cryotron is driving only an identical cryotron. If all the interconnecting-lead inductance can be neglected, the time constant of this circuit is Lc/Rg. The inductance of the control is given by(1)

Le = 4~r× 10-9

= klX

(henrys)

(3)

We

* From Silsbee's hypothesis which attributes quenching due to conducted current to the magnetic field associated with the current.

"~These curves represent measured values and are typical of our "best" cryotrons.

353

C H A R A C T E R I S T I C S OF F i L M CRYOTRONS

I

"O

10{2)

:oo

Iooo

90

30

900

80

50

BOO

7O

q.O

700

60

20

600

50

O0

%

E

E 5OO

% "<~

40

30

400

50

50

300

20

~0

200

)-0

IOO

0

2

I

3

4

Gate lhickness,

FIG. 4. Basic

parameters

5

6

o

LclRg =

pit

(4)

For a given required current gain the crossing ratio is inversely proportional to the Silsbee efficiency; therefore

Le

5

Now consider a circuit in which the inductance of the cryotron controls is negligible compared to the inductance of the interconnecting leads; i.e. a circuit in which inductance is not proportional to the gate width. For a given current gain

X kiX ~

4

FIG. 5. Mo vs. thickness.

vs. thickness.

p/t so that

3 txlO 5 cm

and the gate resistance is Rg =

2

I

txl05cm

L

1

-R

o c Rg

1 oz ~

(7) G

p/t-S For this circuit the figure of merit

(s)

O C - -

Rg

The figure of merit M'2 is therefore defined by the equation

M2 = pit --~

G

Mt=o/t--~

(ohms)

(6)

High values of 3/2 mean small Le/R a time constants and high speed in those circuits where the cryotron control inductance predominates.

(ohms)

(8)

determines the optimum thickness. Lastly, there are those circuits in which the output voltage available is the primary concern and there is no current-gain requirement. For these circuits we define a third figure of merit

Mo = p/tJ'ge (volts/cm gate length)

(9)

These parameters, M0, M1 and M2, are also

354

M. L. COHEN and J. L. MILES

functions of temperature and gate thickness. Typical values are shown in Figs. 5, 6 and 7. Suitable gate thickness can be determined by

of

......

J--t \ \ !

E

] i

i

!',

2i

i

°

tx I0 s cm

2

I 4

Fro. 7. M2 vs. thickness. 6

7

lxlOScm

FIG. 6. Mz vs. thickness. noting the behaviour of the M-curve applicable to the particular circuit and temperature. THE LOW-TEMPERATURE LIMIT FOR CRYOT R O N CIRCUITS

As mentioned above it is usually desirable to operate cryotron circuits at as low a temperature as possible because of the increase in efficiency at low temperatures. However, at some temperature the external critical field for tin becomes greater than the internal critical field for lead. Cryotrons may not be operated below this temperature without the lead controls self-quenching before the tin gates are quenched by the controls. Furthermore, if the cryotron current gain is more than unity and the controls are required to carry as much current as the gates without quenching, the low-temperature limit will be higher, increasing with current gain, as shown in Fig. 8. At present our measurements of this limit are not exact, but it is clear that the fundamental limit is well below 3.0°K and that, for moderate values of current

gain (three to five), lead-tin cryotrons may be safely operated down to 3"4°K. COMPARISON OF GATE MATERIALS

So far only the characteristics of lead-tin cryotrons have been discussed, and the various parameters have been considered to be functions of temperature and gate thickness alone. These parameters, of course, are also functions of gate material. One should therefore consider what might be gained through the use of gate materials other than tin. For example, gate resistivity can be increased by alloying. Will an alloy cryotron be better than a pure-tin cryotron? In general, those factors which increase resistivity, decrease efficiency. Gate thickness is a typical factor of this kind. Obviously, the M-parameters provide a basis for comparison of different materials just as they provide a basis for the comparison of gate thicknesses. Some preliminary experiments have been performed with indium-tin alloys. The results are shown in Fig. 9. There is a notable increase in resistivity, but, as expected, the efficiency falls so that the net improvement shown by 3/1 and 3//2

CHARACTERISTICS

355

OF F I L M C R Y O T R O N S

/

1=36 °K t:25oo

i

"

200

g

ll

G 1"

I0(

-

.\

-

5 CE

2

5

4

Temperature,

5

7

[

°K

I

FIG. 8. Low-temperature limit.

!

are factors of 4 and 2, respectively. These results are for a 2500 h gate thickness, which is not the optimum thickness for either parameter, and therefore they do not represent the maximum improvement obtainable with these alloys. D E S I G N O F C R Y O T R O N CIRCUITS T o illustrate another use of these parameters, consider the design of a three-stage cryotron ring oscillator. Since the minimum gain required is 2,(2) let us specify a current gain of 3 and an operating temperature at 3.4°K. An oscillator is nearly an 3//2 type of circuit; therefore, a gate thickness of 3000 A is close to optimum.* At this thickness and temperature the efficiency from Fig. 4 is 30 per cent, and the crossing ratio, therefore, must be 10. T h e time constant of each stage may now be computed from the value of M2 (Fig. 7, 0.9 m ~ ) using the formula

klG 2 L/R =

3/2

10 -12 x 32

--

9 × 10-4

= 10 -8 (sec)

--

G/xl

(10)

Actually, the time constant will be longer because of circuit inductance other than the cryotron * The M2 peak lies between 4000 and 5000 A. The selection of a 3000 A gate thickness is conservative in that it provides a margin, 4, of safety against poor cryotrons at only a small cost in speed.

2 % Indium

FIG. 9. Effect of indium. control. I f the time constant is assumed to be 2 x 10 -8 sec, the maximum frequency of oscillation will be about 10-12 Mc/s.{ 2) Finally, the control and gate widths may be determined by dividing the desired critical current by the appropriate critical-current density. For example, let Ice be 1 A, fee (from Fig. 4) is 65 A/cm, and we is therefore 0.015 cm or 0.006 in. And, since the crossing ratio is 10:1, the gate width is 0.06 in. T h e oscillator described above has been built, and is shown in Fig. 10. When operated at temperatures of 3.4--3"45°K and supply currents of 1.752"0 A, it oscillated at frequencies of from 1 to 6 Mc/s. Table 1 compares the design and measured values for this oscillator. CONCLUSION From certain measurements on cryotrons, basic general parameters may be computed. Three figures of merit, the M parameters, are defined as certain ratios and c~-nbinations of the basic parameters. Although the M parameters, being derived, contain no new information, they are useful in cir-

356

M. L. COHEN" and J'. L. M I L E S Table 1

Design Measured

Rg

/ce

L/R

(M~2)

(A)

0,sec)

f (Mc/s)

1.0 0"85

1.0 ~1 '0

20 40-45"

10-12 6

* Computed from frequency.

cuit design and provide a basis for comparison and selection of cryotron gate materials and thicknesses to suit particular circuit applications.

REFERENCES

1. A. E. SLADE, Proc. I.R.E. 48, 1569 (1960). 2. M. L. COHEN, Proc. I.R.E. 48, 1576 (1960).