ECE 340 Lecture 19 : Steady State Carrier Injection Class Outline:

Transcription

1 ECE 340 ecure 19 : Seady Sae Carrier Ijecio Class Oulie: iffusio ad Recombiaio Seady Sae Carrier Ijecio

2 Thigs you should kow whe you leave Key Quesios Wha are he major mechaisms of recombiaio? How do we accou for recombiaio i our aalysis? How does he usio curre chage whe we kee he sysem erurbaio? How far ca a mioriy carrier use? M.. Gilber ECE 340 ecure 19 10/10/1

3 iffusio ad Recombiaio M.. Gilber ECE 340 ecure 19 10/10/1 For he las lecures we ve bee discussig usio efie he carrier flu for elecros ad holes: φ φ ( ) ( ) d d d ( ) ( ) d Ad he corresodig curre desiies associaed wih usio d( ) d d( ) d Carriers move ogeher, curres oosie direcios.

4 iffusio ad rif of Carriers M.. Gilber ECE 340 ecure 19 10/10/1 Ad wha haes whe drif ad usio are occurrig simulaeously e- h+ E () () The oal curre mus be he sum of he elecro ad hole curres resulig from he drif ad usio rocesses ( ) µ ( ) E( ) ( ) µ ( ) E( ) rif Where are he aricles ad curres flowig? φ () φ (drif) + ( ) d d d d ( ) iffusio φ () ( ) + Elecros Holes φ (drif) () (drif) () (drif) ashed Arrows aricle Flow!!Solid Arrows Resulig Curres!!!

5 iffusio ad Recombiaio M.. Gilber ECE 340 ecure 19 10/10/1 Bu from revious lecures, we kow more i haeig We have comleely igored recombiaio!! Tye 1: irec recombiaio Elecro ad hole drif io he same viciiy ad recombie. They ca give off ligh if he semicoducor has a direc badga. Tye : R-G Ceer recombiaio R-G ceers may be imuriy aoms or laice defecs. Creae saes i he bad ga. Elecros see a oeial well ad ge raed losig eergy. Holes are araced o he elecro ad aihilaes i givig off hea o he laice. Tye 3: Auger recombiaio Collisio bewee wo like carriers. Eergy released by recombiaio is give o he survivig carrier. Survivig elecro he loses ecess eergy hrough laice collisios.

6 iffusio ad Recombiaio M.. Gilber ECE 340 ecure 19 10/10/1 So wha does his mea? Cosider his semicoducor: The hole curre desiy leavig he ereial area may be larger or smaller ha he curre desiy ha eers he area. This is a resul of recombiaio ad geeraio. e icrease i hole coceraio er ui ime, d/d, is erece bewee hole flu er ui volume eerig ad leavig, mius he recombiaio rae.

7 iffusio ad Recombiaio M.. Gilber ECE 340 ecure 19 10/10/1 How ca we elai his? The e icrease i hole coceraio er ui ime is he erece bewee he hole flu eerig ad leavig mius he recombiaio rae + 1 ( ) ( + ) Rae of hole buildu. Icrease i hole coceraio i A er ui ime. Recombiaio rae As goes o zero, we ca wrie he chage i hole coceraio as a derivaive, jus like i usio (, ) 1 Holes These relaios form he (, ) 1 coiuiy euaios. Elecros

8 M.. Gilber ECE 340 ecure 19 10/10/1 iffusio ad Recombiaio Are here ay simlificaios? If he curre is carried maily by usio (small drif) we ca relace he curres i he coiuiy euaio We u his back io he coiuiy euaios iffusio euaio for elecros ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) d d E d d E + µ µ ( ) ( ) 1, 1, iffusio euaio for holes Useful mahemaical euaio for may ere hysical siuaios

9 M.. Gilber ECE 340 ecure 19 10/10/1 Seady Sae Carrier Ijecio To his oi, we bee assumig ha he erurbaio was removed Wha haes if we kee he erurbaio? The ime derivaives disaear d d d d Elecros Holes Where iffusio egh

10 Seady Sae Carrier Ijecio M.. Gilber ECE 340 ecure 19 10/10/1 e s cosider he followig siuaio e s assume ha we are ijecig ecess holes io a samle of silico. We do o remove he erurbaio, so we maiai a cosa ecess hole coceraio a he ijecio oi, δ ( 0). The ijeced holes he begi o use alog he bar recombiig wih a characerisic lifeime,.

11 Seady Sae Carrier Ijecio M.. Gilber ECE 340 ecure 19 10/10/1 Wha should we eec? We eec he ecess hole coceraio o decay o zero a large disaces from he erurbaio. This is due o recombiaio. Solvig he arial ereial euaio for holes, he soluio has he form δ 1 ( ) C e + C e The boudary codiios are: δ 0 for large δ for 0 C1 0 Ge cosas from boudary codiios. Which are wha? Average disace a hole ravels before i recombies. δ e C ( )

12 Seady Sae Carrier Ijecio Bu we really wa he average usio legh Wha is he robabiliy ha a ijeced hole recombies i a aricular ierval? We kow ha he robabiliy ha a hole ijeced a 0 survives o is: ( ) δ e Raio of seady sae coceraios We kow ha he robabiliy ha a hole a recombies i d is: ( ) ( + ) ( ) Mulily he wo robabiliies d e 1 e / d ( d( ) d) d ( ) Comue eecaio value 0 e d M.. Gilber ECE 340 ecure 19 10/10/1 d isace mioriy carriers use io a sea of majoriy carriers

13 Seady Sae Carrier Ijecio M.. Gilber ECE 340 ecure 19 10/10/1 The disribuio of ecess holes causes a curre We have a usio curre of holes movig from high coceraio o low: lug i wha we kow abou he rae of chage of he hole coceraio wih osiio: δ Begi o reduce he euaio e δ ( ) The usio curre deeds o he ecess carriers a a oi ad o o he iiial coceraio.