Energy Band

BAND THEORY OF SOLIDS AMIT SHARMA

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ENERGY BANDS IN SOLIDS There are discrete energy levels in the case o an isolated ato!"

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Arrange!ent o electrons in an isolated Silicon ato!

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Electron arrange!ent in a silicon ato!

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In solids # the ato!s are arranged in a syste!atic s$ace lattice and each ato! is in%&enced 'y neigh'o&ring ato!s" The closeness o ato!s res<s in the inter!i(ing o electrons o neigh'o&rring ato!s"

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D&e to inter !i(ing o electrons# the n&!'er o $er!issi'le energy levels increases"  Instead o a single energy level # there )ill 'e 'ands o energy levels" A set o s&ch closely $ac*ed energy levels is called an energy 'and"

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,ENER GY 

Gra! o silicon contains ."/,0 ( 1/,0 ato!s

ATO +S

ATO +S 9/2/15

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A 'and )hich is occ&$ied 'y the valence electrons or a 'and having highest energy is de2ned as valence 'and" The valence 'and !ay 'e $artially or co!$letely 2lled"  This 'and can never 'e e!$ty" 9/2/15

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In so!e !aterials valence electrons are loosely attached to the n&cle&s" Even at roo! te!$erat&re # so!e o the valence electrons leave the valence 'and" They are called ree electrons" 9/2/15

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They are res$onsi'le or cond&ction and so they are called 3ond&ction electrons" The 'and occ&$ied 'y this electrons are called cond&ction Band" This 'and !ay 'e e!$ty or $artially 2lled"

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Energy 'ands in Silicon crystal 6s#6$#6d#6   3o!$letely 5acant

3ond&ction Levels

0 d 3o!$letely 5acant 0$ 4artially Filled 0s 3o!$letely Filled

,$ 3o!$letely Filled ,s 3o!$letely Filled

5alence  Levels

3ore  Levels

1s 3o!$letely Filled 9/2/15

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Energy 'ands in Silicon crystal

3ond&ction Band 7 E!$ty or 4artially 2lled Band8 5alence Band F&lly or 4artially 2lled Band8

3o!$letely 2lled Band

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Energy 'ands in Silicon crystal

5alence Band

For'idden Energy Ga$ 1"11 e5

3ond&ction Band 9/2/15

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The se$aration 'et)een valence 'and and cond&ction 'and is *no)n as or'idden energy ga$" I an electron is to 'e transerred ro! valence 'and to cond&ction 'and# e(ternal energy is re9&ired# )hich is e9&al to the or'idden energy ga$" 9/2/15

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Ins&lators 3ond&ction Band

FORBIDDEN GA4

     g      r      e      n       E     y

5alence Band

Filled Band

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In an ins&lator# the or'idden ga$ is very large and in general is !ore than 0e5" No electron is availa'le or cond&ction" Large a!o&nt o energy is needed to !ove electron ro! valance 'and to weyes57 16

Ins&lators 3ond&ction Band

FORBIDDEN GA4 Aro&nd 1/e5 7Glass8

     g      r      e      n       E     y

5alence Band

In the case o !aterials li*e Glass at / :# valance 'and is co!$letely 2lled and the or'idden ga$ energy is o the order o 1/ e5" High electric 2eld can not !ove electron ro! valance 'and to cond&ction 'and"

Filled Band

;hen the electron is s&$$lied )ith very high 9/2/15

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Ins&lators 3ond&ction Band

FORBIDDEN GA4

     g      r      e      n       E     y

5alence Band

;hen the te!$erat&re is increased# then# so!e electrons )ill !ove to go to cond&ction 'and" This is the reason )hy certain !aterials )hich are ins&lators at roo! te!$erat&re 'eco!e cond&ctors at high te!$erat&re" The resistivity o an ins&lator lies

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Se!icond&c tors 3ond&ction Band FORBIDDEN GA4 Aro&nd /">e5 7Ge8 and  1"1 e5 7Si8      g      r      e      n       E     y

5alence Band

Filled Band 9/2/15

In the case o se!icond&ctors the or'idden ga$ is very s!all" At /: the cond&ction 'and is e!$ty and the valence 'and is co!$letely 2lled" ;hen a s!all a!o&nt o energy is s&$$lied# the electrons can easily