FYS Vår 2016 (Kondenserte fasers fysikk)

Transcription

1 FYS Vår 2016 (Kodeserte fasers fysikk) Pesum: Itroductio to Solid State Physics by Charles Kittel (Chapters 1-9 ad 17, 18, 20) Adrej Kuzetsov delivery address: Departmet of Physics, PB 1048 Blider, 0316 OSLO Tel: , e-post: adrej.kuzetsov@fys.uio.o visitig address: MiNaLab, Gaustadalee 23a

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3 Lecture: P-N juctio Repetitio: itrisic ad extrisic semicoductors Charge carrier trasport mechaisms diffusio ad drift Bad bedig as a fuctio of carrier cocetratio P-N juctio i equilibrium Gauss ad Poisso equatios for the depletio regio P-N juctio with applied exteral bias

4 Lecture: P-N juctio Repetitio: itrisic ad extrisic semicoductors Charge carrier trasport mechaisms diffusio ad drift Bad bedig as a fuctio of carrier cocetratio P-N juctio i equilibrium Gauss ad Poisso equatios for the depletio regio P-N juctio with applied exteral bias

5 Itrisic ad extrisic semicoductors

6 Summary of Charge Carriers Itrisic ad extrisic semicoductors CH2 Basic Physics of Semicoductors 6

7 Lecture: P-N juctio Repetitio: itrisic ad extrisic semicoductors Charge carrier trasport mechaisms diffusio ad drift Bad bedig as a fuctio of carrier cocetratio P-N juctio i equilibrium Gauss ad Poisso equatios for the depletio regio P-N juctio with applied exteral bias

8 Diffusio of charge carriers Particles diffuse from regios of higher cocetratio to regios of lower cocetratio regio, due to radom thermal motio.

9 Diffusio of charge carriers J,diff qd d dx J p,diff qd p dp dx D is the diffusio costat, or diffusivity.

10 Drift of charge carriers v h p v e The process i which charge particles move because of a electric field is called drift. Charge particles will move at a velocity that is proportioal to the electric field.

11 Diffusio drift of charge carriers J J J p J J, drift J, diff q ε qd d dx J p J p, drift J p, diff qp ε p qd p dp dx

12 Lecture: P-N juctio Repetitio: itrisic ad extrisic semicoductors Charge carrier trasport mechaisms diffusio ad drift Bad bedig as a fuctio of carrier cocetratio P-N juctio i equilibrium Gauss ad Poisso equatios for the depletio regio P-N juctio with applied exteral bias

13 Bad bedig as a fuctio of carrier cocetratio The positio of F relative to the bad edges is determied by the carrier cocetratios, which is determied by the et dopat cocetratio. I equilibrium F is costat; therefore, the bad-edge eergies vary with positio i a o-uiformly doped semicoductor: c (x) F v (x)

14 The ratio of carrier desities at two poits depeds expoetially o the potetial differece betwee these poits: 1 2 i2 i i 1 i 2 i2 i1 i 2 F i2 i 1 F i1 i 1 i1 F l 1 l l l Therefore l Similarly, l l q kt q V V kt kt kt kt kt Bad bedig as a fuctio of carrier cocetratio

15 Bad bedig as a fuctio of carrier cocetratio N e c ( c F )/ kt c (x) d dx Nc kt e ( c F ) / kt dc dx F v (x) kt d dx c kt qε

16 Lecture: P-N juctio Repetitio: itrisic ad extrisic semicoductors Charge carrier trasport mechaisms diffusio ad drift Bad bedig as a fuctio of carrier cocetratio P-N juctio i equilibrium Gauss ad Poisso equatios for the depletio regio P-N juctio with applied exteral bias

17 P-N juctios i equilibrium <= N-type, high F <= P-type, low F - = fixed ioized acceptors = fixed ioized doors = mobile holes, p - = mobile electros, What happes whe these badstructures come ito cotact? Fermi eergy must be costat at equilibrium, so bads must bed ear the iterface Far from the iterface, badstructures are coserved

18 P-N juctios Time < 0i equilibrium P-type piece N-type piece Time < 0, i.e. before the cotact is established

19 P-N juctios i equilibrium At time = 0, slam the two pieces together Time =0, the cotact is just established

20 P-N juctios i equilibrium Hole gradiet Questio: How l J p, diffusio = -qd p dp/dx = curret right, holes right lectro gradiet J,diffusio = -qd d/dx = curret right, electros right left

21 P-N juctios i equilibrium Hole gradiet Questio: How log the diffusio J p, diffusio = -qd p dp/dx = curret right, holes right will og o!? lectro gradiet J,diffusio = -qd d/dx = curret right, electros right left

22 P-N juctios i equilibrium Whe the juctio is first formed, mobile carriers diffuse across the juctio (due to the cocetratio gradiets) Holes diffuse from the p side to the side, leavig behid egatively charged immobile acceptor ios lectros diffuse from the side to the p side, leavig behid positively charged immobile door ios acceptor ios p A regio depleted of mobile carriers is formed at the juctio. The space charge due to immobile ios i the depletio regio establishes a electric field that opposes carrier diffusio. door ios

23 P-N juctios i equilibrium

24 P-N juctios i equilibrium

25 P-N juctios i equilibrium

26 P-N juctios i equilibrium Depletio Regio

27 How big is the built-i voltage? Right i F Left F i bi qv ) ( ) ( P side N side i a Left F i kt i a a N kt e N N p F i l ) ( ) ( i d Right i F kt i d d N kt e N N i F l ) ( ) ( P-N juctios i equilibrium

28 P-N juctios i equilibrium How big is the built-i voltage? V bi kt q N l a i kt q N l d i V bi kt q NaN l 2 i d N a acceptor level o the p side N d door level o the side

29 Oe side of the juctio is heavily doped, so that the Fermi level is close to the bad edge. e.g. p - juctio (heavy B implat ito lightly doped Si substrate) i d G bi i D Right i F G V i Left F i N q kt q V N kt l 2 l ) ( 2 / ) ( P-N juctios i equilibrium

30 P-N juctios i equilibrium "P - N" => N a >> N d "P - N " => N a << N d

31 P-N juctios i equilibrium Thermal geeratio p-type ND J p, drift J, drift J, diff J p, diff -type N A Thermal geeratio q bi

32 Lecture: P-N juctio Repetitio: itrisic ad extrisic semicoductors Charge carrier trasport mechaisms diffusio ad drift Bad bedig as a fuctio of carrier cocetratio P-N juctio i equilibrium Gauss ad Poisso equatios for the depletio regio P-N juctio with applied exteral bias

33 Gauss ad Poisso equatios for the depletio regio Charge is stored i the depletio regio. acceptor ios door ios p eutral p regio depletio regio eutral regio charge desity (C/cm 3 ) distace

34 Gauss ad Poisso equatios for the depletio regio Gauss s law describes the relatioship betwee the charge desity ad the electric field. S 1 ecl da dv V Q d dx 1 x ( x) ( x0 ) ( x) dx x0 Poisso s equatio describes the relatioship betwee the electric field distributio ad the electric potetial x 0 x ( x) ( x ) ( x) dx Gauss ad Poisso equatios i oe dimesio 2 d x d x x ( ) ( ) ( ) 2 dx dx 0

35 Gauss ad Poisso equatios for the depletio regio 0 x qn qn a d x p0 0 x x 0 x 0 ad 0 x 0 x x, x x p 0 0 ρ o (x) p qn d ( ) qna ( ) ( 0) 0 x x xpo xpo x s x o ( x) qnd ( x) dx ( xo) ( xo x) x 0 s qnd 0 ( x) ( x xo) (0 x x ) o s s p -x po -x po -qn a 0 (x) x o x o x Gauss s Law x (0) 0 qn a s x po qnd x s o

36 Gauss ad Poisso equatios for the depletio regio p 0 (x) -x po x o x Poisso s quatio 0 ( 0 ) qn a x s po qn d s x o qn 2 d s x 2 o qn a x 2 s 2 po 0 (x) -x po x o x

37 Lecture: P-N juctio Repetitio: itrisic ad extrisic semicoductors Charge carrier trasport mechaisms diffusio ad drift Bad bedig as a fuctio of carrier cocetratio P-N juctio i equilibrium Gauss ad Poisso equatios for the depletio regio P-N juctio with applied exteral bias

38 P-N juctio with applied exteral bias V D p The quasi-eutral p ad regios have low resistivity, whereas the depletio regio has high resistivity. Thus, whe a exteral voltage V D is applied across the diode, almost all of this voltage is dropped across the depletio regio. If V D > 0 (forward bias), the potetial barrier to carrier diffusio is reduced by the applied voltage. If V D < 0 (reverse bias), the potetial barrier to carrier diffusio is icreased by the applied voltage.

39 P-N juctio with applied exteral bias p 0 (x) -x po x o -x p x x Built-i potetial bi = qn d x 2 s 2 o qn a x 2 s 2 po 0 (x) 0 ( 0 ) qn a x Higher barrier leads to less curret! s po bi -qv D qn d x s o bi -x p -x po x o x x

40 P-N juctio with applied exteral bias p 0 (x) -x po -x p x x o x Built-i potetial bi = qn d x 2 s 2 o qn a x 2 s 2 po 0 ( 0 ) qn a x Lower barrier lead to more curret! 0 (x) s po qn d x s o bi -qv D bi -x po -x p x x o x

41 P-N juctio with applied exteral bias As V D icreases, the potetial barrier to carrier diffusio across the juctio decreases*, ad curret icreases expoetially. V D > 0 p The carriers that diffuse across the juctio become miority carriers i the quasi-eutral regios; they the recombie with majority carriers, dyig out with distace. I D (Amperes) I I e D S qvd kt ( 1) V D (Volts) * Hece, the width of the depletio regio decreases.

42 P-N juctio with applied exteral bias As V D icreases, the potetial barrier to carrier diffusio across the juctio icreases*; thus, o carriers diffuse across the juctio. V D < 0 p A very small amout of reverse curret (I D < 0) does flow, due to miority carriers diffusig from the quasi-eutral regios ito the depletio regio ad driftig across the juctio. I D (Amperes) V D (Volts) * Hece, the width of the depletio regio icreases.

43 P-N juctio with applied exteral bias Diode I-V Curve I I d s I ( V ) I d d S Id IS e qv d kt 1 1 qv d kt Diode IV relatio is a expoetial fuctio This expoetial is due to the Boltzma distributio of carriers versus eergy For reverse bias the curret saturatios to the drift curret due to miority carriers

44 P-N juctio with applied exteral bias Whe a large reverse bias voltage is applied, breakdow occurs ad curret flows through the diode icreases dramatically.

45 P-N juctio with applied exteral bias Whe a large reverse bias voltage is applied, breakdow occurs ad curret flows through the diode icreases dramatically. Zeer breakdow or tuelig mechaism, occurs i a highly doped p- juctio, while the coductio ad valace bads o opposite sides of the juctio become so close durig the reverse-bias that the electros o the p-side ca tuel from directly VB ito the CB o the -side. Avalache breakdow mechaism occurs whe electros ad holes movig through the depletio regio ad acquire sufficiet eergy from the electric field to break a bod i.e. create electro-hole pairs by collidig with atomic electros withi the depletio regio. These ewly created electros ad holes move i opposite directios due to the electric field ad thereby add to the existig reverse bias curret.