why does conductivity of semiconductors increases while that of metal decreases

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$T h e c o n d u c t i v i t y o f a p u r e f r e e m e t a l d e c r e a s e s w i t h i n c r e a s e i n t e m p e r a t u r e . T h i s i s b e c a u s e t h e r m a l e n e r g y c a u s e s a t o m s t o v i b r a t e a n d m a k e t h e m t o g o t o e x c i t e d s t a t e . I n t h e e x c i t e d s t a t e t h e s e a t o m s i n t e r a c t a n d s c a t t e r e l e c t r o n s . T h i s r e d u c e s t h e m e a n f r e e p a t h a n d t h e m o b i l i t y o f e l e c t r o n s d e c r e a s e s, t h u s r e s i s t i v i t y i n c r e a s e s . S o m o r e t h e r e s i s t i v i t y l e s s w i l l b e t h e c o n d u c t i v i t y . T h e c o n d u c t i v i t y o f s e m i c o n d u c t o r i n c r e a s e s w i t h i n c r e a s e i n t e m p e r a t u r e . T h i s i s d u e t o t h e r e a s o n t h a t t h e e l e c t r r o n s i n t h e v a l e n c e b a n d g a i n e n e r g y a n d m o v e t o h i g h e r e n e r g y c o n d u c t i o n b a n d a n d t h e y b e c o m e c h a r g e c a r r i e r s .$

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