Lecture 3. OUTLINE PN Junction Diodes (cont d) Electrostatics (cont d) I-V characteristics Reverse breakdown Small-signal model

Transcription

1 Lecture 3 AOUCEMETS HW2 is osted, due Tu 9/11 TAs will hold their office hours i 197 Cory Prof. Liu s office hours are chaged to TuTh 12-1PM i 212/567 Cory EE15 accouts ca access EECS Widows Remote eskto servers OUTLE P uctio iodes (cot d) Electrostatics (cot d) - characteristics Reverse breakdow Small-sigal model Readig: Chater , 3.4 EE15 Fall 27 Lecture 3, Slide 1 Prof. Liu, UC Berkeley

2 The eletio Aroximatio the deletio regio o the side: de dx E ρ ε q ε si si q ε si ( x + b) ρ(x) q a -b -q A x the deletio regio o the P side: de dx E ρ ε q ε si si A q ε si ( a x) a A b A EE15 Fall 27 Lecture 3, Slide 2 Prof. Liu, UC Berkeley

3 More o the Built- Potetial ( ) Q: Why ca t we haress ad use the P juctio as a battery? A: A built-i otetial also exists at a juctio betwee a metal ad a semicoductor (e.g. at a cotact). f we coect the P ad regios together, there is o et voltage dro across the device: b + + b b b? EE15 Fall 27 Lecture 3, Slide 3 Prof. Liu, UC Berkeley -b (x) + a o et curret flows across the juctio whe the exterally alied voltage is! x

4 Effect of Alied oltage The quasi-eutral -tye ad P-tye regios have low resistivity, whereas the deletio regio has high resistivity. Thus, whe a exteral voltage is alied across the diode, almost all of this voltage is droed across the deletio regio. (Thik of a voltage divider circuit.) f < (reverse bias), the otetial barrier to carrier diffusio is icreased by the alied voltage. f > (forward bias), the otetial barrier to carrier diffusio is reduced by the alied voltage. + EE15 Fall 27 Lecture 3, Slide 4 Prof. Liu, UC Berkeley

5 P uctio uder Forward Bias A forward bias decreases the otetial dro across the juctio. As a result, the magitude of the electric field decreases ad the width of the deletio regio arrows. ρ(x) -b -q A q a x (x) -b a x EE15 Fall 27 Lecture 3, Slide 5 Prof. Liu, UC Berkeley

6 Miority Carrier jectio uder Forward Bias The otetial barrier to carrier diffusio is decreased by a forward bias; thus, carriers diffuse across the juctio. The carriers which diffuse across the juctio become miority carriers i the quasi-eutral regios; they recombie with majority carriers, dyig out with distace. (x) x' edge of deletio regio Equilbrium cocetratio of electros o the P side: 2 i A x' EE15 Fall 27 Lecture 3, Slide 6 Prof. Liu, UC Berkeley

7 Miority Carrier Cocetratios at the Edges of the eletio Regio The miority-carrier cocetratios at the edges of q / the deletio regio are chaged by the factor e There is a excess cocetratio (, ) of miority carriers i the quasi-eutral regios, uder forward bias. Withi the quasi-eutral regios, the excess miority- carrier cocetratios decay exoetially with distace from the deletio regio, to zero: ( x ) ( x ) 2 i + / T ( e 1) x / L A ( x ) e EE15 Fall 27 Lecture 3, Slide 7 Prof. Liu, UC Berkeley x' kt e otatio: L electro diffusio legth (cm) d q q / T x / L ( e ) e 2, diff i q dx AL 1 / T

8 iode Curret uder Forward Bias The curret flowig across the juctio is comrised of hole diffusio ad electro diffusio comoets: tot, drift x +, drift, diff, diff Assumig that the diffusio curret comoets are costat withi the deletio regio (i.e. o recombiatio occurs i the deletio regio): 2 i, diff x AL tot S q ( / e 1) T ( / 1) T e where EE15 Fall 27 Lecture 3, Slide 8 Prof. Liu, UC Berkeley x S + q 2 i x L A + q + L x 2 i, diff x L ( / e T 1)

9 Curret Comoets uder Forward Bias For a fixed bias voltage, tot is costat throughout the diode, but (x) ad (x) vary with ositio. tot -b a x EE15 Fall 27 Lecture 3, Slide 9 Prof. Liu, UC Berkeley

10 -Characteristic of a P uctio Curret icreases exoetially with alied forward bias voltage, ad saturates at a relatively small egative curret level for reverse bias voltages. deal diode equatio: EE15 Fall 27 Lecture 3, Slide 1 Prof. Liu, UC Berkeley ( ) + A i S S S L L Aq A e T 2 / 1 deal diode equatio:

11 Parallel P uctios Sice the curret flowig across a P juctio is roortioal to its cross-sectioal area, two idetical P juctios coected i arallel act effectively as a sigle P juctio with twice the cross-sectioal area, hece twice the curret. EE15 Fall 27 Lecture 3, Slide 11 Prof. Liu, UC Berkeley

12 iode Saturatio Curret S S ca vary by orders of magitude, deedig o the diode area, semicoductor material, ad et doat cocetratios. tyical rage of values for Si P diodes: 1-14 to 1-17 A/µm 2 + A i S L L Aq 2 EE15 Fall 27 Lecture 3, Slide 12 Prof. Liu, UC Berkeley tyical rage of values for Si P diodes: 1 to 1 A/µm a asymmetrically doed P juctio, the term associated with the more heavily doed side is egligible: f the P side is much more heavily doed, f the side is much more heavily doed, i S L Aq 2 A i S L Aq 2

13 Reverse Breakdow As the reverse bias voltage icreases, the electric field i the deletio regio icreases. Evetually, it ca become large eough to cause the juctio to break dow so that a large reverse curret flows: breakdow voltage EE15 Fall 27 Lecture 3, Slide 13 Prof. Liu, UC Berkeley

14 Reverse Breakdow Mechaisms a) Zeer breakdow occurs whe the electric field is sufficietly high to ull a electro out of a covalet bod (to geerate a electro-hole air). b) Avalache breakdow occurs whe electros ad holes gai sufficiet kietic eergy (due to acceleratio by the E-field) i-betwee scatterig evets to cause electrohole air geeratio uo collidig with the lattice. EE15 Fall 27 Lecture 3, Slide 14 Prof. Liu, UC Berkeley

15 Costat-oltage iode Model f <,o : The diode oerates as a oe circuit. f,o : The diode oerates as a costat voltage source with value,o. EE15 Fall 27 Lecture 3, Slide 15 Prof. Liu, UC Berkeley

16 Examle: iode C Bias Calculatios X X R 1 + X R1 + T l X S X X 2.2mA.2mA for for X X 3 1 This examle shows the simlicity rovided by a costat-voltage model over a exoetial model. Usig a exoetial model, iteratio is eeded to solve for curret. Usig a costat-voltage model, oly liear equatios eed to be solved. EE15 Fall 27 Lecture 3, Slide 16 Prof. Liu, UC Berkeley

17 Small-Sigal Aalysis Small-sigal aalysis is erformed at a C bias oit by erturbig the voltage by a small amout ad observig the resultig liear curret erturbatio. f two oits o the -curve are very close, the curve ibetwee these oits is well aroximated by a straight lie: e x 2 3 x x 1 + x ! 3! EE15 Fall 27 Lecture 3, Slide 17 Prof. Liu, UC Berkeley d d s T e 1 / T 1 1 T

18 iode Small-Sigal Model Sice there is a liear relatioshi betwee the small-sigal curret ad small-sigal voltage of a diode, the diode ca be viewed as a liear resistor whe oly small chages i voltage are of iterest. Small-Sigal Resistace (or yamic Resistace) r d T EE15 Fall 27 Lecture 3, Slide 18 Prof. Liu, UC Berkeley

19 Small Siusoidal Aalysis f a siusoidal voltage with small amlitude is alied i additio to a C bias voltage, the curret is also a siusoid that varies about the C bias curret value. ( t ) + cos ω t ( t) + cos ω t s ex + T cos ωt ( / ) T EE15 Fall 27 Lecture 3, Slide 19 Prof. Liu, UC Berkeley

20 Cause ad Effect (a), voltage is the cause ad curret is the effect. (b), curret is the cause ad voltage is the effect. EE15 Fall 27 Lecture 3, Slide 2 Prof. Liu, UC Berkeley

21 Summary: P-uctio iode - Uder forward bias, the otetial barrier is reduced, so that carriers flow (by diffusio) across the juctio Curret icreases exoetially with icreasig forward bias The carriers become miority carriers oce they cross the juctio; as they diffuse i the quasi-eutral regios, they recombie with majority carriers (sulied by the metal cotacts) ijectio of miority carriers Uder reverse bias, the otetial barrier is icreased, so that egligible carriers flow across the juctio f a miority carrier eters the deletio regio (by thermal geeratio or diffusio from the quasi-eutral regios), it will be swet across the juctio by the built-i electric field collectio of miority carriers ( / e 1) T S EE15 Fall 27 Lecture 3, Slide 21 Prof. Liu, UC Berkeley