Review of Hall Effect and Magnetoresistance Measurements in GaAs Materials and Devices

The use of m a g n e t i c fields in t he e lect r ica l cha rac t e r i za t ion of s e m i c o n d u c t o r ma te r i a l s is fami l ia r to e v e r y o n e in t he fo rm of Hal l -effect m e a s u r e m e n t s . However , t h e r e is a n o t h e r magne t i c f i e ld -based p h e n o m e n o n , m a g n e t o r e s i s t a n c e (MR), w h i c h is h igh ly use fu l b u t no t nea r ly so fami l ia r to t he ma jo r i t y of workers . One of t he u n i q u e fea tu res of MR measu re m e n t s is t he i r app l icab i l i ty to c o m m o n dev ice s t ruc tu res , in par t icu lar , f ield-effect t r ans i s to r s (FETs) and contac t r e s i s t a n c e pa t t e rns . We will s h o w h o w c h a n n e l mob i l i t y i n f o r m a t i o n can be e x t r a c t e d f rom the MR da ta in me ta l s emicon d u c t o r FETs (MESFETs) a n d m o d u l a t i o n d o p e d h e t e r o s t r u c t u r e F E T s (MODFETs) , a n d also h o w the ma te r i a l u n d e r o h m i c con tac t s c an be c o m p a r e d w i th t he u n p r o c e s s e d ma te r i a l to see i f a p p r e c i a b l e c o n t a c t e l e m e n t d i f fus ion has occurred . Final ly , we will cons ide r some c o m m o n p r o b l e m s w h i c h are o f ten ove r looked in p e r f o r m i n g s imp le Hall-effect m e a s u r e m e n t s on t h i n s t ruc tures . S o m e use fu l fo rmulas a n d p lo ts are p r e sen t ed . Magne t i c fields h a v e b e e n a pa r t of me ta l a n d semicond u c t o r cha rac t e r i za t i on for m a n y years , at leas t s ince 1879 w h e n E. H. Hal l m a d e his f a m o u s d i scove ry of w h a t we n o w k n o w as t he "Hall ef fect" (1). In w h a t m u s t b e reg a r d e d as a c lassic u n d e r s t a t e m e n t , Hal l s u g g e s t e d t h a t "a m o r e c o m p l e t e a n d accu ra t e s tudy of t he p h e n o m e n o n wil l p r o b a b l y o c c u p y m e for some m o n t h s to come ." Indeed , i t h a s o c c u p i e d t he t i m e of a grea t n u m b e r of r e sea rche r s s ince t h e n a n d t h u s wou ld s e e m i n g l y be too f ami l i a r . and m u n d a n e a top ic to be w o r t h w h i l e for th i s s y m p o s i u m . However , t h e r e are m a n y aspec t s of t he Hal l effect w h i c h are no t as fami l ia r to t he genera l worker , a n d yet can b e ve ry i m p o r t a n t for cha rac te r i za t ion pu rposes . We wil l br ief ly d i scuss severa l of t he se a n d will also p r e s e n t s o m e usefu l f igures a n d f u r t h e r re ferences . B e c a u s e so m u c h e m p h a s i s is b e i n g p laced on th in layer s t r u c t u r e s t h e s e days, we will c o n c e n t r a t e on t h e pa r t i cu la r m e a s u r e m e n t p r o b l e m s assoc ia ted w i th t h i n layers. Bes ides t h e Hal l effect, however , severa l m o r e r e c e n t dev e l o p m e n t s i nvo lv ing m a g n e t o r e s i s t a n c e in dev ice s t ructu res h a v e p r o v e n to be of use in s e m i c o n d u c t o r character izat ion . T h e m a j o r v i r t ue of t h e s e n e w t e c h n i q u e s is t h a t t h e y ' c a n give ma te r i a l s p a r a m e t e r s in ac tua l dev ice s t ructures . In par t icu lar , we will d i scuss m a g n e t o r e s i s t a n c e in M E S F E T s , MODFETs , a n d con tac t r e s i s t ance t r a n s m i s s ionl ine -mode l (TLM) pa t t e rns . Our p r i m e e x a m p l e s will b e GaAs a n d A1GaAs/GaAs, s ince m u c h of t he r e c e n t magn e t o r e s i s t a n c e work has i nvo lved the se mater ia l s , and also s ince t he p r e s e n t a u t h o r is m o s t fami l ia r w i th t h e s e par t icu l a r mater ia l s . The Hall Effect: Experiments in Bulk Materials W h e n a s y s t e m of e l ec t rons in e q u i l i b r i u m is p e r t u r b e d by t he app l i ca t i on of electr ic a n d m a g n e t i c fields, collis iona l forces will a t t e m p t to res to re t he s y s t e m to equi l ibr ium. Fo r m a n y types of s u c h coll is ions, th i s r e s to ra t i on wil l be e x p o n e n t i a l in n a t u r e w i t h a cha rac t e r i s t i c t i m e c o n s t a n t ~, t he " r e l axa t ion t ime ." Then , in s imp le i so t rop ic sys tems , t he c u r r e n t dens i t i e s se t u p b y t he fields wil l be g iven b y Jx = ~xxEx + ~x~E~ [1] j~ = ~yxE= + ~ E y [2] w h e r e Ex a n d E, are t he e lectr ic field c o m p o n e n t s , and, for an n type s a m p l e ne2< ~ ) ~xx = ~,, = ~ ~ + ~ [3]