Real p-n junction diode I-V characteristics Consider a diode rectifier rated for 1000 V reverse bias.

Transcription

1 Real - juctio diode I-V characteristics Cosider a diode rectifier rated for 1000 V reverse bias. To metal cotact + -layer (heavily doed) d diode base: -layer, thick ad low-doed to absorb high voltage d Bottom metal cotact 1

2 Desig the required thickess of the diode base (-layer) Plot the deedece F m (N D ) at V r = V Em 1.60E E E+06 V=1000 V Em, V/cm 1.00E E E E E+05 F m = ( ) 2qN' Vbi Vr εε E E E 2.00E 3.00E 4.00E 5.00E 6.00E 7.00E 8.00E Doig, cm-3 2

3 Desig the required thickess of the diode base (-layer) Plot the deedece F m (N D ) at V r = V Em 1.60E E E+06 V=1000 V Em, V/cm 1.00E E E E E+05 F m = ( ) 2qN' Vbi Vr εε E E E 2.00E 3.00E 4.00E 5.00E 6.00E 7.00E 8.00E Doig, cm-3 The doig i the -tye material must ot exceed ~ 5*10 14 cm -3 3

4 Fid the deletio regio width at N D = cm -3 ad V r = V 5.00E E E+01 V=1000 V 3.50E+01 W, um 3.00E E E E E E E E E E E E E E E E+ 15 N, cm-3 The thickess of -tye material must ot be less tha ~ 50 μm 4

5 Now cosider the diode at zero or ositive bias: The deletio regio width W(V=0) 0. Therefore, the equivalet circuit of the diode at V 0 is: To metal cotact + -tye material (heavily doed) R s d -tye material R s d = 50 μm Bottom metal cotact If the -layer is highly doed, it ca be made very thi => R s 0 5

6 Let us fid the resistace R s Assume the device area is 1mm x 1 mm (ower device) metal cotact N D = cm -3 μ = 1000 cm 2 /(V*s) doed) R s d d = 50 μm A = 1 mm 2 R s d = μm σ = q**μ = 0.08 S/cm R s = (1/ σ)*d /A = 6.25 Ohm m metal cotact 6

7 Diode I-V characteristics Ideal diode Real diode w 50 um base This lie does NOT rereset real -diode I-V because it does ot accout for carrier ijectio at forward bias 7

8 - juctio uder forward bias q (V bi - V R ) q V R =qv o q V bi qv q V F qv o - qv q(v bi -V F ) V>0: the bias is called POSITIVE or Forward, if the olarity is oosite to the built-i barrier. Tyical otatio: V F. Forward bias REDUCES the otetial barrier V<0: the bias is called NEGATIVE or Reverse if the olarity is the same as the built-i barrier. Tyical otatio: V R. Reverse bias INCREASES the otetial barrier 8

9 Electro ijectio q (V bi - V R ) q V R =qv o q V bi qv q V F qv o - qv q(v bi -V F ) V =0; The electro cocetratio o the -side: Also, = 0 V >0; New barrier height = qv - qv. = e (equilibrium electro cocetratio o the -side) because the juctio is i equilibrium bi qvbi qv qv kt kt = e = 0 e The cocetratio of ijected electros exoetially icreases with the forward voltage qv bi kt 9

10 Hole ijectio I the equilibrium 0 0 = e qv bi / kt (1) Uder forward bias V F, the barrier decreases by qv F : 0 = e qv ( V)/ kt bi (2) Dividig (2) by (1): 0 = e (3) = e 0 The cocetratio of ijected holes exoetially icreases with the forward voltage 10

11 Summary of ijected electro ad hole cocetratios Ijected electro ad hole cocetratios: =qv o qv = e 0 qv / kt qv o - qv -x 0 x 0 = e 0 qv / kt The chage i the electro cocetratio i the -regio: Δ = = ( e ) The chage i the hole cocetratio i the -regio: Δ = = ( e ) 11

12 Carrier ijectio ad forward curret mechaism i - juctio Electros + - -tye -tye Holes Forward bias lowers the otetial barrier betwee - ad -sides. Electros ad holes diffuse through the lowered barrier ito - ad -sides. Sigificat amout of extra electros ad holes gets ijected ito - ad -sides corresodigly. Ijected electros recombie with holes i -tye material; ijected holes recombie with electros i -tye material. To comesate the loss of carriers due to recombiatio, additioal electros ad holes are sulied by the voltage source through the cotacts the forward curret flows through the - juctio. 12

13 Ijected carrier satial distributio (1) =qv o qv Note that the carrier ijectio takes lace OUTSIDE the sacecharge regio of the - juctio. We assume that the sace charge regio is thi so that hot carriers quickly drift through the deletio regio due to high iitial velocity. Outside the deletio regio the field is low. Therefore the electro ad hole trasort ca oly be due to diffusio. qv o - qv -x 0 x 0 13

14 Ijected carrier satial distributio (2) Electros + - -tye -tye The ijected carriers diffuse ito - ad -ortios of the juctios ad RECOMBINE alog with DIFFUSION; Holes Sace- Charge regio 14

15 The steady-state distributio of the ijected holes ca be obtaied from the followig balace equatio: We defie Ijected carrier satial distributio (3) t = { Icome} { Outcome} = D τ 2 x + = 0, or δ = 0 which is the excessive hole cocetratio The solutio is: δ ( x) = δ ( ) e L where = τ is the diffusio legth of the holes. x / L 0 D Similarly, for ijected electros: δ ( x) = δ ( ) e x / L 0 where x is the absolute distace L = is the diffusio legth of the electros. τ D 15

16 Ijected carrier satial distributio (4) This solutio describes o-uiform satial distributio of the ijected carriers: δ ( x) = δ ( ) e x/ L 0 The solutio alies to the regios that begi at the sacecharge regio edges. -x x Thus, (0) is measured at x = x Tyically, for Si: L 500 μm; L = 200 μm 16

17 Ijected carrier voltage ad distace deedeces As a fuctio of distace from the deletio regio edges, the ijected carrier cocetratio ca be foud as x x / L ( x) = 0+ 0 e 1 e ( ) = ( ) ( ) ( ) ( ) 0 1 ( ) x x / L 0 1 Δ ( x) = ( e ) e x x L x e e / Ijected (excessive) electro ad hole cocetratios: ( ) Δ ( x) = ( e ) e / x x L x x -x x (x-x ) ad ( x -x ) are the absolute distaces couted from the edges of the sace charge regios o the - ad - sides corresodigly. 17

18 Forward curret of the - juctio Ijected (excessive) electro ad hole cocetratios i the - juctio: 0 1 ( ) x x / L 0 1 Δ ( x) = ( e ) e ( ) x x L Δ ( x) = ( e ) e / Total excessive ijected charges (A=juctio area): ( 1) 0 ( ) 0 Δ Q = q A Δ x dx = q A e L ( 1) 0 ( ) 0 Δ Q = q A Δ x dx = q A e L The charge ΔQ recombies at the rate of ΔQ /τ The charge ΔQ recombies at the rate of ΔQ /τ The curret sulied from the cotacts to comesate the recombiatio: I =ΔQ /τ + ΔQ /τ Total ijected electros er uit area Total ijected holes er uit area 18

19 I Forward curret of the - juctio (2) ( Δ Q ) = q A 0 e 1 L ( ) Δ = 0 1 The comesatig curret: I =ΔQ /τ + ΔQ /τ Q q A e L ( 1) ( qv kt τ / 1) I= q A e L / + q A e L / τ 0 0 Electro curret Hole curret ( ) L L I= q A e τ τ L = D τ,,, 2, L, / D, τ = ( ) D D I= q A e L L 19

20 20 1 S qv I I kt ex = + = S L D L D q A I 0 0 This curret ca be re-writte as: where Total (e- ad h-) - juctio forward curret ( ) qv kt D D I q A e L L / = +

21 P- juctio curret voltage characteristic (I-V) I qv = IS ex 1 kt Forward curret 21

22 Reverse curret of the - juctio is give by the same exressio as for the forward curret ote that ex qv kt qv I= IS ex 1 kt 0 whe V<0 ad V >> kt/q V Uder tyical reverse bias, V R >> kt/q: I I S I S D = q A L 0 D + L 0 22

23 Reverse curret of the - juctio I qv = IS ex 1 kt I I S at egative V Reverse curret 23

24 The above I-Vs did NOT accout for the ijected carrier rofile. Ijected holes sigificatly icrease the electro-hole air cocetratio i the base: 6.00E E+16 Ijected hole cocetratio (also the electro cocetratio) 4.00E E E+16 ( ) ( ) x x / L ( ) = x e e 1.00E E+00 Equilibrium electro cocetratio (N D = cm -3 ) x Parameters used: V = 0.7 V; L = 200 μm 24

25 Ideal diode Diode I-V characteristics Real diode w 50 um base (icludig ijected carriers) Real diode w 50 um base (igorig ijected carriers)