Two arbitrary semiconductors generally have different electron affinities, bandgaps, and effective DOSs. An arbitrary example is shown below.

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1 9. Heterojuctios Semicoductor heterojuctios A heterojuctio cosists of two differet materials i electrical equilibrium separated by a iterface. There are various reasos these are eeded for solar cells: ) difficulty dopig a desired material p- or - type, ) to form widow layers or back-surface fields (BSF) layers that passivate carriers ad passivate surfaces. Promiet examples of heterojuctios are CuISe /CdS, CdTe/CdS, ad Al w Ga -w As/GaAs. But the iterface betwee differet materials may ofte cotai surface states that comprise carrier traps or recombiatio ceters. Two arbitrary semicoductors geerally have differet electro affiities, badgaps, ad effective DOSs. A arbitrary example is show below. C C The bad offsets are related to other, fixed parameters by E C, E E E E E V g g C g V V where Eg Eg E g. The itrisic carrier cocetratios are E e g kt E i C V ad e g kt i C V Whe the metallurgical juctio is formed betwee the materials, the bads must bed to satisfy the offsets at the iterface.

2 The built-i potetial is qvbi p where p EC EF p ad E E I equilibrium we have EF p EF The build-i potetial becomes qvbi p EC E p C otice p EC. ow C F a ip d So that i e e Ei EF kt p E E kt if i a d Ei E l p i kt i p i The itrisic level is

3 3 EC EV kt C Eg kt C Ei l EC l V V Recall that So E C Eg kt C Ei l V or kt C p Vp EC E l p C E i E p i E g E p g C V a d kt p p C V EC E l l p C E V EC kt i p i C V ow we have a d kt p p C V qvbi EV EC kt l l i p i C V Recall that C mc V mv So we ca write 3 a d l 3 kt mc m p Vp qvbi EV EC kt l i 4 p i m C m V Let's take the average bad gap Eg Eg E p g ad average bad offsets: E EC EV Defie a "average" itriisic carrier cocetratio i C Vp e E E kt g These defiitios allow us to write the built-i voltage i a more familiar form kt a d Vbi l q i otice that where C m m C ad Vp m m Vp 0 3 0

4 3 mkt cm I priciple, two dissimilar materials could for a juctio with bi 0 V, as show below 4 Cotributios to electro curret The electro curret desity is def J where EC EF kt C e The quasi-fermi level is the E E kt F C l Its derivative is def dec dc d kt C The slope of the coductio bad is C So dec devac d d q

5 5 def d kt d C kt d q C We fid that there are four cotributios to the electro curret d d d J q kt kt kt C Cotributios to hole curret Similarly, for holes J where p de p p F p EF EV kt p V e The quasi-fermi level is V F V l p E E kt Its gradiet is p defp dev dv dp kt V p The slope of the valece bad is de de d d q E E E, we have V vac deg deg Usig V vac g C defp d deg kt dv kt dp q V p With kt p q Dp, we fid dp d deg p d J p qp pqdp p p qdp V Juctio curret, case I drift Cosider a homojuctio with o gradiets i carrier cocetratio: d dp d de g d 0, 0, C dv 0 The curret desities are J q q J q pq p p p p V

6 6 I this case, a real electric field is preset at the juctio, producig forces F q o carriers, which will have drift velocities v ad vp p. I other words, electros ad holes will flow i opposite directios across the juctio. Juctio curret, case II: diffusio ow assume istead that there is o electric field across a homojuctio So: d de g d 0, 0, C dv 0 J qd d q v J qd dp qp v The p p p d v D dp vp Dp p

7 7 I this case, the electro ad hole flows are idepedet. Juctio curret, case III: electro affiity ad bad offsets Cosider a heterojuctio with o electric field or cocetratio gradiets. d dp dc dv 0, 0, 0 The curret desities i this case are d J q v d deg Jp p p qp vp The carriers will move to equilibrate with the local eergy levels of the bads v D d Dp d deg, vp kt kt

8 8 Juctio curret, case IV: bad-edge effective desities of states Cosider a juctio betwee two materials with o electric field of cocetratio gradiets, ad o bad offsets. d dp d de g 0, 0, 0 The curret desities must arise from differeces i effective DOS (i.e., effective masses) So d J qd q v C C p d J qd q p v V p p p V dc v D C dv vp Dp V

9 9 Metal-semicoductor juctios: Schottky barrier (I) The behavior of a metal-semicoductor juctio depeds primarily o the relative positio of the work fuctio of the metal to the CB of the semicoductor. For a -type semicoductor cotactig a metal, Schottky barrier is formed if. m I this case, whe cotact is made betwee the materials, electros will flow from the semicoductor to the metal to establish equilibrium, resultig i a built-i potetial of Vbi m s To travel from the metal ito the semicoductor, electros must over commo a barrier at the iterface of height is give by E E b C F juctio m

10 0 Metal-semicoductor juctios: Schottky barrier (II) The Schottky barrier depletes the semicoductor side of the juctio of majority carriers. Assume the height of the barrier is greater tha a few kt. If we cosider the metal as the aode (+) ad the semicoductor as the cathode (-), we see that the barrier prevets curret from flowig i reverse bias (Va<0). However, the curret icreases o-liearly i forward bias (Va>0), as the applied voltage raises the semicoductor CB ad icreases the electro cocetratio at the iterface. Metal-semicoductor juctios: Ohmic cotact (I) If m, there is o barrier for electro flow i either directio. Metal-semicoductor juctios: Ohmic cotact (I) For a ohmic cotact, the semicoductor-side of the juctio has a abudace of majority carriers.

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