313

INDUSTRIAL EXPERIENCE WITH A QUANTIZED HALL EFFECT SYSTEM

K B. J a e g e r , P. D Levine. and C. A. Zack . .

Lockheed Missiles h Space Company, Inc. Sunnyvale, CA 94089-3504 Abstract s u p p l y f r o n t p a n e l and r a n g e from 0.01 t o 99. amperes/min. S c a l i n g of t h e magnetic f i e l d v e r s u s s u p p l y c u r r e n t is e s t a b l i s h e d through t h e use of c o n v e n t i o n a l c r y o g e n i c Hall g e n e r a t o r s ( 2 ) . b ) He3 R e f r i g e r a t o r . S t a b l e t e m p e r a t u r e s between 0.3 and 1 0 K c a n be r e a d i l y maintained in t h e s o r p t i o n pumped He3 i n s e r t mounted in t h e He4 main dewar. c) Mapping E l e c t r o n i c s Mapping of t h e sample behavior i n v o l v e s measuring and t h e l o n g i t u d i n a l b o t h t h e Hall r e s i s t a n c e

In a n e f f o r t t o create t h e c a p a b i l i t y f o r primary
c a l i b r a t i o n of s t a n d a r d r e s i s t o r s t r a c e a b l e t o p h y s i c a l c o n s t a n t s , a measuring s y s t e m based on t h e Quantized Hall E f f e c t (QHE) was assembled a t Lockheed Missiles 6 Space Co. ( M C ) d u r i n g t h e f a l l of 1989. P r e l i m i n a r y s t u d i e s have been performed u s i n g t h r e e d i f f e r e n t samp l e s of modulation-doped GaAs-(AlGa)As h e t e r o j u n c t i o n p r e p a r e d v i a beam e p i t a x y t e c h n i q u e s . T h i s paper r e p o r t s t h e r e s u l t s of s t u d i e s performed w i t h one of t h e s e samples a t t h e n-4 p l a t e a u . These measurements were compared t o a 1O.k ohm primary r e s i s t o r whose v a l u e is d i r e c t l y t r a c e a b l e t o t h e N a t i o n a l I n s t i t u t e of S t a n d a r d s and Technology (NIST). Introduction
The d i s c o v e r y of t h e QHE by von K l i t z i n g e t a1 ( 1 ) in 1980, h a s provided t h e i n t e r n a t i o n a l metrology commun i t y w i t h an i d e a l s t a n d a r d f o r e l e c t r i c a l r e s i s t a n c e . S i n c e January 1990, t h e Q E h a s been recognized as t h e H o f f i c i a l r e s i s t a n c e standard using t h e latest "best" 2 value f o r the r a t i o h / e Advances in r e a d i l y a v a i l a b l e c r y o g e n i c technology and e s p e c i a l l y w i t h small b o r e s u p e r c o n d u c t i n g magnets has allowed e a s y access t o c r y o s t a t volumes w i t h t e m p e r a t u r e s as low as 0.3 K and magnetic f i e l d s in e x c e s s of 9 Tesla. All hardware i t e m s , e x c e p t f o r t h e QHE samples, a r e r e a d i l y a v a i l a b l e as o f f - t h e - s h e l f equipment. It is t h e r e f o r e p o s s i b l e f o r any primary s t a n d a r d s l a b o r a t o r y t o assemble t h i s t y p e of hardware and perform r e s i s t a n c e comparison measurements on a routine basis.

v o l t a g e drop Vxx a t c o n s t a n t c u r r e n t a s a f u n c t i o n of magnetic f i e l d B. This is accomplished u s i n g two 8 112 d i g i t d i g i t a l uultimeters (DMM) ( F i g . 1). A p l a t e a u a p p e a r s as a c o n s t a n t w i t h Vxx a t a minimum in t h e

hundreds of n a n o v o l t s ( 3 ) . (The l e a d r e s i s t a n c e s g i v e rise t o a few hundred n a n o v o l t s , o t h e r w i s e t h e Vxx s i g n a l would be a t t h e l e v e l of a few n a n o v o l t s , e s s e n t i a l l y t h e n o i s e f l o o r of t h e DMM.) Fig. 1 i l l u s t r a t e s t h i s measurement arrangement. Measurement Techniques

The Hall r e s i s t a n c e , q u a n t i z e d w i t h t h e s e samples, follows t h e r e l a t i o n s h i p ( 1)

%(ohm) h e 2n w i t h h b e i n g P l a n c k ' s c o n s t a n t , e being t h e e l e c t r o n i c c h a r g e , and n t h e quantum s t e p number ( 1 , 2 , 3 , 4 , ). 2 The v a l u e of h / e h a s been f i x e d i n t e r n a t i o n a l l y s u c h that (1)

...

System D e s c r i p t i o n and O p e r a t i o n
A s c h e m a t i c of t h e o p e r a t i o n a l s e t - u p is shown in Fig. 1. The e s s e n t i a l hardware c o n s i s t s of a vapor c o o l e d He4 dewar, superconducting s o l e n o i d w i t h power s u p p l y , He3 r e f r i g e r a t o r i n s e r t . t h e sample probe assembly, measurement e l e c t r o n i c s , and d a t a a c q u i s i t i o n system.

%(ohms)

= 25,812.807

I n.

I n i t i a l e v a l u a t i o n of each sample involved t h e mapping of I$ and Vxx ( t h e v o l t a g e in t h e d i r e c t i o n of t h e a p p l i e d e l e c t r i c f i e l d ) as a f u n c t i o n of B ( a p p l i e d magnetic f i e l d ) . Fig. 2 shows t h e t y p i c a l measuring c o n f i g u r a t i o n f o r c o l l e c t i n g t h e ' d a t a in t h e comparison mode. Care was t a k e n t o e n s u r e t h a t t h e B f i e l d was o r t h o g o n a l t o t h e p l a n e of t h e sample and t h a t t h e e l e c t r i c f i e l d ( r e s p o n s i b l e f o r t h e Hall c u r r e n t ) was applied orthogonally t o t h e B f i e l d along the longit u d i n a l dimension of t h e sample. On a p a r t i c u l a r Hall p l a t e a u , t h e c u r r e n t flows o r t h o g o n a l l y t o t h e a p p l i e d e l e c t r i c f i e l d , i.e., t r a n s v e r s e l y i n t h e sample. Hence t h e l o n g i t u d i n a l v o l t a g e d r o p , Vxx, in t h e d i r e c t i o n of t h e a p p l i e d e l e c t r i c f i e l d is z e r o o r a t l e a s t a t a minimum. The t r a n s v e r s e e l e c t r i c f i e l d i s z e r o even though t h i s is t h e d i r e c t i o n of t h e c u r r e n t flow.

pizq
CONTROLLER

r
I

I____________________

Fig. 1

C R Y O S l A l ~

-'
VARlABCE R E S T O R IN M L (R LIMIT)

a ) Superconducting Solenoid The s u p e r c o n d u c t i n g s o l e n o i d is of Nb-Ti cons t r u c t i o n w i t h a 5 2 mm bore and i n t e g r a l supercond u c t i n g s w i t c h . I t is c a p a b l e of producing a 9 T e s l a f i e l d a t 4.2 K which is homogeneous t o 1 p a r t in lo3 in a 10 mm d i a m e t e r s p h e r i c a l volume a t t h e s o l e n o i d c e n t e r . Ramp r a t e s are a d j u s t a b l e from t h e power

Fig. 2

CH2822-5/90/0000-0313 $01.00

1990 IEEE

3 14
Fig. 3 c l e a r l y shows t h e Hall p l a t e a u s f o r one of t h e samples a t n-4,6,8,10, e t c . w i t h Vxx v a l u e s a t a minimum. The n=4 p l a t e a u h a s been e x p l o r e d i n d e t a i l v i a a very slow B-field ramp rate and is p r e s e n t e d i n Fig. 4. It should be noted t h a t Vxx is a t a minimum of .2 t o .6 u v o l t s while is s t a b l e and f l a t . The
a s s i g n e d v a l u e , Rs, was s u b t r a c t e d from R r t o y i e l d A R = Rr Rs. These v a l u e s a r e shown i n Fig. 5 w i t h t h e i r e r r o r s based on t h e s t a t i s t i c a l d a t a i n each case. The o v e r a l l mean v a l u e +/- 1 sigma is shown as t h e solid and two broken l i n e s w i t h a v a l u e of (- 0.35 +/- 0.06) ppm.

b e h a v i o r of

a t t h e b e g i n n i n g of t h e p l a t e a u ( r i s e ) and a t t h e end ( d i p ) w i l l not be e x p l a i n e d a t t h i s

RH

time D e t a i l e d comparisons, d e s c r i b e d below, were o n l y performed on t h e p o r t i o n of t h e p l a t e a u where V x x was a t an a b s o l u t e minimum, i.e., a t a magnetic f i e l d between 8.0 and 8.5 T e s l a .
6500.0..
5000.0--

IL
+.2.
0.

20pA
x 25pA
+ 30pA
0

5500.05000 0 .

4500 04000.0-

3500.0..

2 3000.0-
2500 0
2000 0
0 0

-.6

t
B C

40pA

1500 0
1000 0

0 0
0 0 1 0

+
Mi
Fig. 5

+
E,

500 0

2 0

3 0

4 0

5.0

6 0

7 0

a 0

PLATEAU LOCATION

Uncertainties

5459t

Using t h e s t a t i s t i c a l u n c e r t a i n t y combined w i t h s y s t e m a t i c e f f e c t s , a v a l u e of +/- 0.08 ppm w a s estimated. This v a l u e was m u l t i p l i e d by a f a c t o r of t h r e e t o y i e l d an o v e r a l l v a l u e of A R (0.35 +/- 0.24) ppm.

--

6451

6447

7 2

7 4

7 6

7 a

a 0

e 2
(TESLAI

8.4

8.6

a a

! 0 001 9 0

e.-FImo

Future Plans
vi11 a l l o w mapping of samples up t o 11 T e s l a .

,002

. 00 1

The n e a r term u t i l i z a t i o n of t h e lambda r e f r i g e r a t o r Detailed s t u d i e s w i l l be performed t o a s c e r t a i n p l a t e a u characteristics. Acknowledgement S p e c i a l t h a n k s are extended t o Dr. D. C. T s u i from P r i n c e t o n U n i v e r s i t y f o r p r o v i d i n g u s w i t h t h e QHE samples and f o r h i s c o n t i n u o u s encouragement and s u p p o r t . W are f o r e v e r t h a n k f u l f o r t h e a d v i c e and e c a l i b r a t i o n of t h e Hall g e n e r a t o r s which was g r a c i o u s l y provided t o u s by Mr. L. Rubin from t h e N a t i o n a l Magnet Laboratory. References

,000

Fig. 4
Comparison Data Comparison measurements were made using a 10 k ohm r e s i s t o r ( R r ) , a Zener v o l t a g e s t a n d a r d i n series w i t h a v a r i a b l e r e s i s t o r , and two 8 1/2 d i g i t DMMs. Hall 7 c u r r e n t s were t h u s r e a l i z e d , s t a b l e t o 1 p a r t i n 10 By i n c o r p o r a t i n g c u r r e n t r e v e r s a l s , and accumulating sets of d a t a f o r each c u r r e n t , s e v e r a l comparison v a l u e s were o b t a i n e d a t t h e b e g i n n i n g (Be) around 8.0 T e s l a ; a t t h e middle (Mi) around 8.25 T e s l a ; and a t t h e end (En) around 8.5 T e s l a . The Hall c u r r e n t was determined from IH = VH/6453.202 and t h e r e f e r e n c e

K. von K l i t z i n g , G. Corda, M. Pepper

Phys. Rev. Lett. 45, 494 (1980) Three r e g u l a r Hall g e n e r a t o r s were procured for o p e r a t i o n up t o 15. Tesla. W are g r a t e f u l t o L. e Rubin from t h e N a t i o n a l Magnet L a b o r a t o r y who provided u s w i t h f i e l d v e r s u s c u r r e n t c a l i b r a t i o n of t h e s e g e n e r a t o r s . The Quantized Hall E f f e c t H. L. Stormer and D. C. Tsui, S c i e n c e , 220, 1241-1246, 1983.

r e s i s t a n c e value from R r = Vr/IH.

F i n a l l y , the