measurement of extrinsic series mesfets

8/8/2019 Measurement of Extrinsic Series Mesfets

1/6

MEASUREMENT O F THE EXTRINSIC S ER IE S E LE ME NT S O F A M IC RO WA VE M ES FE T UNDERZERO CURRENT C O N D I T I O N SF . D i a m a n d , M . L a v i r o n

ABSTRACTA n e w m e a s u r e m e n t m e t h o d o f t h e p a r a s i t i c s e r i e s i m p e d a n c e s o fa microwave MESFET i s p r e s e n t e d . T h e b a s i c p o i n t o f t h e m e t h o d i s t h a tt h e MESFET i s p o l a r i z e d u n d e r zero d r a i n v o l t a g e , r e s u l t i n g i n a s i m p l ea n a l y t i c a l m o d e l . C o m p a r i s o n w i t h experiment i s d i s c u s s e d .

I N T R O D U C T I O NA MESFET w i t h a n u n b i a s e d d r a i n i s a f a i r l y s i m p l e s y s t e m i ncontrast t o t h e case o f n o r m a l operating c o n d i t i o n s . F o r z ero drainv o l t a g e , t h e r e g i o n under t h e gate c a n b e described b y a d i s t r i b u t e d ,u n i f o r m , R - C transmission l ' i n e [ 1 ] , l e a d i n g t o a s i m p l e analytical m o d e lw h i c h c a n b e e x p e c t e d t o b e o f g o o d accuracy. I t w i l l b e s h o w n t h a t t h i sm o d e l , c o m b i n e d w i t h t h e l u m p e d c ' i r c u i t m o d e l o f t h e extrinsic p a r t o ft h e M E S F E T , i s very s u ' i t a b l e f o r c o m p a r i s o n w i t h e x p e r i m e n t a n d l e a dt o a s t r a i g h t f o r w a r d m e a s u r e m e n t m e t h o d o f s e v e r a l d e v i c e p a r a m e t e r s ,i n p a r t i c u l a r t h e p a r a s i t i c s o u r c e , g a t e , a n d d r a i n r e s i s t a n c e sa n d r e a c t a n c e s .

T h e a n a l y t i c a l f o r m o f t h e m o d e l w i l l b e d e r i v e d a n d t h e r e l a t e dmeasurement method o u t l i n e d . T h e n i t w i l l b e c o m p a r e d w i t h e x p e r i m e n ta n d i t s v a l i d i t y d i s c u s s e d .D ES CR IP TI ON O F T H E M O D E L

F i g . 1 s h o w s t h e e q u i v a l e n t c i r c u i t f o r t h e z e r o d r a i n v o l t a g ec o n d i t i o n . T h e r e g i o n u n d e r t h e g a t e i s m o d e l l i z e d w i t h d i s t r i b u t e de l e m e n t s , t h e e x t r i n s i c r e g i o n w i t h l u m p e d e l e m e n t s . P a r a l l e l l e a dp a r a s i t i c c a p a c i t a n c e s a r e n e g l e c t e d .T h e ( Z ) m a t r i x o f t h i s 2 - p o r t i n t h e common s o u r c e c o n f i g u r a t i o ni s d e r i v e d . W i t h a concern o f c l a r i t y , t h e i n t e r - e l e c t r o d e c a p a c i t a n c e sC , C d Cd a r e f i r s t n e g l e c t e d . T h e n t h e ( Z ) m a t r i x i s f u r t h e rsmpl i i e d j , u s i n g t h e l o w f r e q u e n c y - a n d - o p e n c h a n n e l c o n d i t i o n ,a n a p p r o x i m a t i o n w h i c h i s c o n s i s t e n t w i t h our m e a s u r e m e n t c o n d i t i o n s .F i n a l l y t h e i n t e r - e l e c t r o d e c a p a c i t a n c e s a r e t a k e n i n a c c o u n t .1)C C C nelcdg s ' g d s d n e g l e c t e d

t h e ( Z ) m a t r i x i s t h e n g i v e n b y

T h o m s o n - C S F , L a b o r a t o i r e C e n t r a l d e R e c h e r c h e s , O R S A Y , F R A N C E .

4 5 1

Authorized licensed use limited to: BHABHA ATOMIC RESEARCH CENTRE. Downloaded on June 01,2010 at 05:30:21 UTC from IEEE Xplore. Restrictions apply.


2/6

r l1 2 9 s + jC t h F l( c( Z ) = r I ( c h r l - l )Z + C . W s c ,.\ s i @ C ~ ~ ~ ~ ~ i c Sr l ( c h r l - 1 )Z s + j w C s h f lc J2 r l ( c h r l - 1 )

Z S Z d J j w C s h l/Icwhere Z = + j L g w , Z = + jL w Z = + j L c r 1

= ( j w R C )s s

9 d d cF'ccr i s t h e p r o p a g a t i o n c o n s t a n t o f t h e R - C t r a n s m i s s i o n l i n e , t h e g a t el e n g t h , R t h e c h a n n e l r e s i s t a n c e , C t h e g e o m e t r i c d e p l e t i o n l a y e rcc ccapacitance.2 ) L o w f r e q u e n c y - a n d - o p e n c h a n n e l l i m i t

S t i I I n e g l e c t i n g C g s 9 C g d c C d s , w e a s s u m e t h a t1 1 2 1 2 1 = o R C C c


3/6

w h e r e C x = C , C o r C d s ' b u t t h e s e c a p a c i t i e s a r e i n g e n e r a l s m a l l e rt h a n C c , s o F h a t S o n d i t i o n ( 5 ) i s w e a k e r t h a n c o n d i t i o n ( 2 ) . T h e n t h ei m p e d a n c e m a t r i x i s g i v e n b y ( Z ) = ( R ) + j ( X ) , w i t hC C + 3 C d s + 3 C d C C + 2 C g dP R +1 C d s dR R Rs9 c ~ ~ g s g d c gs + g d( R ) - (R+~~ ~ P + R + Rs +2 C gs C g d c s d c

L s + L 9 w w ( c c + C 9 + C g d L s w @ 6) dc+gs + g d ~( X ) =

X ) L s + L9 L s w 1 g d ( L s +L d ) ( 6 )C O M P A R I S O N W IT H E X P E R I M E N T

T h e ( Z ) m a t r i x ( 6 ) i n v o l v e s o m e i n t e r e s t i n g f e a t u r e s w h i c h p r o v i d ea s t r a i g h t f o r w a r d m e a n o f c h e c k i n g t h e v a l i d i t y o f t h e m o d e l a n d o fd e t e r m i n i n g t h e p a r a s i t i c e l e m e n t s :- e a c h m a t r i x e l e m e n t Z . . i s a l i n e a r f u n c t i o n o f Z , Zs Z d R c .- t h e r e a l p a r t o f t h e m a t r i x i s i n d e p e n d e n t o f f r e q u e n c y ; X 1 2 X X 2 1 X 2 2a r e i n d e p e n d e n t o f V a n d a r e s i m p l y r e l a t e d t o L s a n d L d 1- f o r a f l a t d o p i n g p r o f i l e , R P = R c o ( l - c t l / 2 )- 1 s o t h a t G r e b e n e ' sm e t h o d [ 2 ] c a n b e e x t e n d e d t o R . . e l e m e n t s i n o r d e r t o measure

t h e p a r a s i t i c r e s i s t a n c e s . I n p 5 4 t i c u l a r t h e p l o t o f R v e r s u s( l - a / 2 ) c ' m u s t g i v e t h e s a m e s t r a i g h t l i n e , w h a t e v e r 4e f r e q u e n c y ,a n d i t s i n t e r c e p t w i t h t h e o r d i n a t e a x is g i v e s R + R d T h e s a m ep r o c e d u r e , a p p l i e d t o R P 1 a n d R 1 2 , g i v e s r e s p e c t i v e l y R + Ra n d R . I n t h e s e l a t t e r c a s e s , t h e s l o p e o f t h e l i n e d e v i a t e s s l i g h t l yf r o m a c o n s t a n t ( b e c a u s e C d e p e n d s o n a ) , b u t t h i s d o e s n o t a f f e c tn o t a b l y t h e e x t r a p o l a t e d v a l u e s o f t h e p a r a s i t i c r e s i s t a n c e s .

- i d e n t i f y i n g X 1 1 w i t h a r e s o n a n t c i r c u i t f o r a g i v e n value o f V a l l o w st o d e t e r m i n e l + L a n d C = C + C + C L + L m u s t b e i & d e p e n -d a n t o f V . F o r a f l a t d o p i n g p r o f i e , p l 8 # t i n s C v g r s u s a - 4 g i v e sC ( V ) w 9 i c h m u s t b e c o n s i s t e n t w i t h N d .c g dT h e m e t h o d was t e s t e d o n a M E S F E T r e a l i z e d i n t h e l a b o r a t o r y , g i v i n gl 1 d B g a i n a t 1 0 G H z , a n o i s e f i g u r e N F = 2 . 4 d B w i t h G = 8 . 5 d B .D e v i c e p a r a m e t e r s are : N D = 1 . 6 1 0 1 7 cm3, l a y e r t h i c n e s = 0 . 3 p ,c h a n n e l t h i c k n e s s u n d e r reces s = 0 . 1 5 } p , g a t e l e n g t h = 0 . , 8 p g a t ew i d t h = 3 0 0 p , s o u r c e - d r a i n s p a c e = 4 p .T h e S - p a r a m e t e r s o f t h e M E S F E T were m e a s u r e d w i t h a n a u t o m a t i cn e t w o r k a n a l y z e r i n t h e 2 G H z - I O G H z r a n g e , t h e t e r m i n a l p l a n e s o ft h e 2 - p o r t b e i n g v e r y c l o s e t o t h e c h i p , b u t t h e g a t e a n d d r a i n l e a dc o n n e c t i o n s are i n c l u d e d i n t h e 2 - p o r t . T h e n t h e Z - p a r a m e t e r s arec o m p u t e d .

4 5 3



4/6

F i g u r e s 2 , 3 , 4 represent respectively t h e p l o t o f R 2 2 , 1 ( R 1 2 + R 2 1 )a n d R P versus ( 1 - a l / 2 ) , f o r s e v e r a l f r e q u e n c i e s . G o o d l i n e a r i t yi s o b i 4 i n e d i n a l l c a s e s . F o r f i g u r e s 2 a n d 3 , t h e d e p e n d e n c y o n frequen-c y i s v e r y w e a k , a l l o w i n g t o measure R = 2 Q , a n d R d = 3 , 2 Q , w i t h a g o o da c c u r a c y . Poorer agreement i s o b t a i n e d f o r t h e R P p l o t s w h i c h s h o wa more p r o n o u n c e d d e p e n d e n c e w i t h f r e q u e n c y , r e s u l t i n g i n a s p r e a d o f1 0 % f o r R + R w h e n F v a r i e s f r o m 7 G H z t o 1 0 G H z R = 3 , 2 Q i so b t a i n e d f o r F 9 1 0 G H z . R P d e c r e a s e s w i t h f r e q u e n c y 4 T h e question a r i s e si f there i s s o m e error I n t h e 1 - h e o r e t i c a l m o d e l o r t h e e x p e r i m e n t a lp r o c e d u r e , o r i f R i s r e a l l y f r e q u e n c y d e p e n d e n t . I t s h o u l d b e n o t e da l s o t h a t t h e v a l u g o f R d e , u c e d f r o m W o l f ' s f o r m u l a [ 3 ] i s n e a r l yt w o t i m e s s m a l l e r : R / 3 9 n 2 - 1 , 5 Q . F i g . 5 s h o w s t h e p l o t o f L 5 , L d ,a n d L versus V . F o r e a c h V value L w a s determined b y :9 9 9 5L - z ( X 1 + X 2 1 ) / w , f o r s e v e r a l f r e q u e n c i e s ( F - 3 , 4 , 5 , 6 , 7 , 8 G H z )a n d t d k i n g t h e m e a n . S i m i l a r l y , u s i n g X 2 2 , L s + L d a n d t h e r e f o r e L dw a s c o m p u t e d . The s t a n d a r t d e v i a t i o n i s t y p i c a l l y . 0 1 n H . T h ei n d u c t a n c e v a l u e s are w e a k l y d e p e n d e n t o n V g f o r I V 1 < 0 , 6 v , t h e n t h e yd ec re as e m or e a n d more s t r o n g l y w h e n p i n c h - o f f i s a p p r o a c h e d . L + Lw a s d e t e r m i n e d t o g e t h e r w i t h C = C + C + C d ` f o r e a c h V v a t u e ,b y i d e n t i f y i n g X 1 w i t h a r e s o n a n t c i r c a s t f o F d i f f e r e n t f r g q u e n c i e s( F = 3 , 4 , 5 , 6 , 7 , 8 H z ) , t h e n u s i n g t h e l e a s t s q u a r e m e t h o d , t o computeL a n d C . F i g . 6 s h o w s t h e p l o t o f C versus O f z , f r o m w h i c h C h a s b e e nd e d u c e d . F r o m C ( V ) w e f o u n d N d = 1 , 6 8 1 0 1 7 c m - 3 w h i c h a g r e S s w e l Iw i t h t h e nom n a 4 s u o p l i e r v a l u e .C O N C L U S O N

I n s p i t e o f some s l i g h t d i s c r e p a n c i e s w h i c h we are t r y i n gp r e s e n t l y t o s o l v e , t h e e x p e r i m e n ta l p r o c e d u r e d e s c r i b e d h e r e o f f e r sa c o n v e n i e n t mean o f c h a r a c t e r i z i n g t h e e x t r i n s i c m o d e l w h i c h i s u s u a l l yc h a r a c t e r i z e d t o g e t h e r w i t h t h e i n t r i n s i c m o d e l b y s o p h i s t i c a t e dcomputer o p t i m i z a t i o n m e t h o d s . W e b el i e v e t h a t t h e i n d e p e n d e n t measureo f t h e e x t r i n s i c m o d e l w i l l r e s u l t i n i n c r e a s e d accuracy f o r t h e s ep a r a m e t e r s . O n t h e o t h e r h a n d , b y r e d u c i n g t h e n u m b e r o f unknownp a r a m e t e r s , i t c o n t r i b u t e s t o s i m p l i f y t h e c o m p u t e r o p t i m i z a t i o n m e t h o d .R E F E R E N C E S1 . K . L e h o v e c . A p p l . P h y s . L e t t . 2 5 , N 0 5 , 2 7 9 ( 1 9 7 4 )2 . A . B . G r e b e n e . P I E E E L e t t . 2 0 3 1 , ( n o v . 1 9 6 7 )3 . P . W o l f . I B M J o u r n . O f R e s . a n d D e r . 1 4 N 0 2 ( 1 9 7 0 )

4 5 4



5/6

R11 1 6

F i g u r e 1 . E q u i v a l e - n t c i r c u i t model f o r V d s 0

d s ~ ~

// ,;

i

, i

. E GHz

+ 9 0A 4 0

a~

I

/ 1a A S--

F i g u r e 3 . Determination o f RF i g u r e 2 . Determination of R s + Rd

4 5 5

C 3 6

4R A2 5

4 5

A D I

S

-I-+

4

+ 94 . 4 0

( I -.4) 4,.-b4a 4 i9 ( 4 - ) K - ~Authorized licensed use limited to: BHABHA ATOMIC RESEARCH CENTRE. Downloaded on June 01,2010 at 05:30:21 UTC from IEEE Xplore. Restrictions apply.


6/6

e..

* AAOS F i g u r e 4 . D e t e r m i n a t i o n o fR + Rs g

4 r - 4-f

I I

F i g u r e 5 . Gate v o l t a g es e n s i t i v i t y o f L , L , L d

C~~~~~~* C = C r s t C e + C c

d r4 8 3 - 2 j 3 3 v

F i g u r e 6 . D e t e r m i n a t i o n o f t h e/ g e o m e t r i c a l d e p l e t i o n c a p a c i t a n c e

* 1 1 i "

4 5 6

A l lR ( I t, 4

* ; a. - : :-

- : - . a

L F * 0 3

0 , 4

0

L 0 .

L AW-

IltA

5 - . ( . 1 - , i s i o

measurement of extrinsic series mesfets

Documents