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Submitted on 1 Jan 1978
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A SIMPLE ULTRA HIGH RESOLUTION SQUID
RESISTANCE BRIDGE
B. Barnard, A. Caplin
To cite this version:
A SIMPLE ULTRA HIGH RESOLUTION SQUID RESISTANCE BRIDGE
B.R. Barnard and A.D. CaplinPhysics Department, Imperial College, London SW7 2BZ
Abstract.- A simple and inexpensive resistance bridge is described which can monitor small changes in resistance with a resolution of up to 1 in 107 . Its performance improves on that of the conventional SQUID potentiometric circuit by up to two orders of magnitude; its resolution equals that obtained with (expensive) current comparators, with the added advantage that, unlike the latter, it can be used with very small sample resistances.
The usual potentiometric circuit for the measurement of small resistances with a SQUID is shown in figure la : the SQUID electronics feeds back a current I2 so as to maintain a null across
the signal coil, and the sample resistance r^ is obtained in terms of a comparison resistor r2 and the ratio of the currents Ij/Ii- The limitations of this circuit are set by the stability of the sample current supply, and the measurement of the currents which is usually done by measuring the voltage drop across high quality room temperature resistors Rj and R2. With care a resolution of 1 in 105 can be achieved, but more commonly the performance is a factor of ten worse than this.
Recently two groups /I,2/ have overcome these
pro-blems by measuring the current ratio directly with a room temperature current comparator (figure lb); these devices have very high accuracy and resolu-tion (^ 1 in 107) and, because the SQUID feed-back loop itself maintains I2/I1 steady, drifts in the sample current supply are unimportant. However not only are current comparators extremely expen-sive, but in addition, if the sample resistance is small, the AC modulated flux gate magnetometer that is used for sensing current balance affects the SQUID operation; this interference limits the circuit of figure lb to sample resistances greater than about 10_5ohm. Our interest /3,4/ is in the low temperature behaviour of the resistivity of pure metals and dilute alloys; it appears that sur-face scattering and crystal defects have a confu-sing influence on the resistivity, so that ideally the sample should have as large a cross-section as possible, compared with electronic mean free paths that can approach 1 mm in these circumstances. So, for example, for a material of residual resistivity
10-9to IO-10ohm cm formed into a sample a few mm in diameter, the sample length would need to be
10 m or more for the circuit of figure lb to be usable.
Our circuit (figure lc) is essentially a resistance bridge. Because the SQUID feedback loop ensures that Ijri= I2r2, V , can be made zero by choosing Ri/rj = R2/r2i irrespective of any drift in Ij. In general (with Rj » r i , R2 > > r2)
Vab " X1R1 - X2R2= IlRlL! " 7^-tf > IlRl« (1) Fig. 1 : SQUID resistance measuring circuits. Heavy
lines represent superconducting wires, (a) the usual potentiometric circuit (b) potentiometric circuit with a room temperature current comparator (c) the new bridge circuit.
JOURNAL DE PHYSIQUE
Colloque
C6,
supplément au n"
8,
Tome
39,
août
1978,
page
C6-1219
Résumé.- On décrit un pont de résistance simple et bon marché, capable de détecter des changements faibles de résistance avec une résolution allant jusqu'à 1/107. Cette méthode représente une amélioration de deux ordres de grandeur par rapport à un circuit potentio-métrique SQUID conventionnel. Elle égale la résolution obtenue par comparateurs de cou-rants (une méthode coûteuse) et a l'avantage supplémentaire sur ces derniers de pouvoir être utilisée avec des échantillons de très faibles résistances.
where
a
(= 1-
rlR2/r2R1) i s a measure of t h e degree t o which the b r i d g e h a s been balanced.The b r i d g e i s s e n s i t i v e t o changes i n sample r e s i s t a n c e r l : R AVab =
-
-2 A r l I 1 r 2 b u t t h e e f f e c t of any d r i f t i n I1 i s reduced by t h e f a c t o r a. The b r i d g e i s , t h e r e f o r e , s u i t a b l e o n l y f o r looking a t small changes i n r e s i s t a n c e .C l e a r l y t h e b r i d g e depends f o r i t s p e r f o r - mance on t h e s t a b i l i t y of t h e r a t i o arm r e s i s t o r s R1 and R2, and of t h e comparison r e s i s t o r r 2 . We have achieved t h i s by winding R1 and R2 from phos- phor-bronze w i r e and innnersing them i n l i q u i d helium a t 4.2 K Because of t h e symmetry of t h e c i r c u i t t h e e f f e c t s of t h e temperature and power c o e f f i - c i e n t s of t h e two r e s i s t o r s a r e g r e a t l y reduced. The comparison r e s i s t o r r g , which d i s s i p a t e s l i t t l e power, i s a l s o h e l d a t 4.2 K, b u t w i t h i n a vacuum can. I n o r d e r t o m a i n t a i n thermal i s o l a t i o n of r l t h e superconducting i n t e r c o n n e c t i n g l e a d s a r e made from Niomax CN ; because t h e Cu-Ni c o a t i n g o f t h i s w i r e h a s a l a r g e thermopower we have been extremely c a r e f u l t o m a i n t a i n thermal symmetry of t h e SQUID i n p u t c i r c u i t .
Typical d a t a o b t a i n e d w i t h a sample of mo- d e r a t e l y high r e s i s t i v i t y a r e shown i n f i g u r e 2 :
t h e r e s o l u t i o n is of o r d e r 1 i n lo7. The s m a l l e s t r e s i s t a n c e sample we have looked af s o f a r r e s i s - t a n c e 5 x 1 0 - ~ ohm. On a sample of r e s i s t a n c e 4 x 1 0 - ~ ohm we have made a c a r e f u l a n a l y s i s of t h e n o i s e :
I n a 0. 1 Hz bandwidth t h e measured n o i s e , r e f e r r e d t o t h e i n p u t , was 6x10-l5 V. r.m. s. Johnson n o i s e i n t h e same bandwidth f o r a t o t a l i n p u t c i r c u i t r e s i s t a n c e of 1. 0x10-6 ohm ( i n c l u d i n g 2x10-7 ohm c o n t a c t r e s i s t a n c e ) i s 4. 5 x 1 0 - ~ ~ V. r. m. s. A t t h i s l e v e l we have not had any d i f f i c u l t y from thermal ms. We have used b o t h a d i g i t a l v o l t m e t e r of 0.1 pV r e s o l u t i o n and a n a n o v o l t a m p l i f i e r t o moni- t o r t h e b r i d g e output. N e i t h e r appears t o i n t e r f e r e w i t h t h e SQUID o p e r a t i o n . A$ f a r a s t h e SQUID itself i s concerned, no more t h a n t h e usual s c r e e n i n g pre- c a u t i o n s were taken. The sample c u r r e n t supply de- l i v e r s a maximum of 120 mA, and i s s t a b l e t o 1 i n 10
.
The maximum temperature a t which t h e b r i d g eFig. 2 : Typical d a t a on t h e temperature v a r i a t i o n of t h e r e s i s t a n c e of a s i l v e r 0.2 % gold a l l o y below 2 K; a t h i g h e r temperatures thermometric un- c e r t a i n t i e s c o n t r i b u t e a l a r g e r experimental s c a t - t e r . r l = 3.48x 1 V 6 ohm, r 2 = 3. 49 x ohm, R1 : 9. 74 ohm, R2 = 9. 76 ohm, a = 5 x10-~. 11 = 100.0 mA E f f e c t i v e bandwidth about 0. 1 Hz. C a l c u l a t e d Johnson n o i s e , r e f e r r e d t o t h e b r i d g e o u t p u t , i s 1. 5 X V r . m s . The two s e t s of d a t a p o i n t s r e p r e s e n t two r u n s w i t h an i n t e r v e n i n g p e r i o d of f o u r weeks a t room temperature, d u r i n g which t h e b r i d g e b a l a n c e s h i f t e d by about 60 ppm
References
/ I
1
Van Kempen,H.
,
Lass. J. S., Ribot, J.H
J. M, and Wyder, P. Phys. Rev. L e t t .37
(1976) 1574 121 Duwury, C . , Rowlands, J.A. and Woods, S.B. t obe p u b l i s h e d .
/ 3 / Barnard, B.R. and C a p l i n , A.D. Comm. on Phys.2 (1977).
141 Barnard, B.R. and C a p l i n , A . D . This conference.
