The pn junction: 2 Current vs Voltage (IV) characteristics

Transcription

1 Th pn junction: Currnt vs Voltag (V) charactristics Considr a pn junction in quilibrium with no applid xtrnal voltag: o th V E F E F V p-typ Dpltion rgion n-typ Elctron movmnt across th junction: 1. n p th Elctrons outsid th dpltion rgion with nough thrmal nrgy (>V ) can ovrcom th junction barrir. p n o Elctrons gnratd in th p-typ matrial nar th junction by thrmal xcitation can fall down th potntial barrir.

2 Th magnitud of th dpnds on th hight of th potntial barrir. th is givn by a modifid form of th Boltzmann quation: th V whr cons tan t o is indpndnt of th barrir hight it dosn t mattr how larg th barrir is, lctrons will still fall down it. For no applid xtrnal voltag th systm is in quilibrium. n othr words thr can b no nt flow of lctrons across th junction. This givs: th o Thrfor V V + (1) 0 0 Th sam argumnts also apply to hol movmnt across th junction

3 Forward Bias p-typ positiv w.r.t n-typ p-typ o th n-typ (V -V) Vxtrnally applid voltag o is th sam as for zro xtrnal voltag th is incrasd as th potntial barrir has bn rducd from V to (V -V) th (V k B V) T V. V + From (1) 0 V + Thrfor V V V + + th V + Now, th nt lctron flow across th junction is givn by: th 0 0 V V + 1

4 Rvrs Bias n-typ positiv w.r.t p-typ p-typ o th (V +V) n-typ o is th sam as for zro xtrnal voltag th is dcrasd as th potntial barrir is now much largr th gain, substitut in for : (V + V) 0 th V V. V Nt lctron flow across th junction is: th 0 0 V 0 0 V 1

5 Ths rsults can b comnd to form a singl quation: 1 0 T k V B whr V is positiv for forward as and ngativ for rvrs as Similarly, an quation can b drivd for hols (although th pr-factor is diffrnt) 1 0 T k V h h B So, th total currnt flow across th junction is givn by th sum of th lctron and hol componnts T k V h B Whr o o + oh

6 vs V charactristics (V) Zoom in: V o pn junction allows a larg currnt to flow in on dirction, but only a vry small on to flow in th othr dirction For xampl: o (xp(v/kt)-1) 0.5V forward as at 300K, o xp(0.5/kt) 5x10 8 o 0.5V rvrs as, ~ - o Hnc a pn junction bhavs lik an lctronic valv

7 Carrir transport in a pn junction p-typ Elctron injction Hol currnt rplnishs hols which rcomn with lctrons or ar injctd into th n-typ matrial Hol injction n-typ Hol dnsity in n-typ matrial Edg of dpltion rgion ρ Equilibrium minority carrir dnsity n n-typ matrial distanc

8 What is th valu of 0? Simpl analysis, th sam rsult is obtaind from mor involvd calculations 0 is qual to th numbr of gnratd carrirs (lt s tak lctrons) making it to th dg of th dpltion rgion. Now, G R nmin ni (rmmbr nppp ni and pp τ τ.n N ) Of cours, lctrons gnratd far away from th dpltion rgion can t contribut (thy ll rcomn bfor gtting thr) so lt s only considr lctrons with th diffusion lngth, L. Thus, 0.L.G Whr is includd as w ar considring charg carrirs, so w now hav, for lctrons and hols: Lni τn. V k T B i.l.n τ.n Lni 1 + τnd. V k T B 1

9 Mor advancd tratmnt Us statistical mchanics and lctron and hol diffusion quations to calculat a valu of o. Th quation drivd in this lctur adquatly dscribs th V charactristics of som pn diods (g G). Howvr, only qualitativ agrmnt is found for Si and Gas matrials. Svral factors contribut to this, including: Surfac ffcts which giv ris to surfac lakag currnts Gnration and rcomnation of carrirs in th dpltion rgion High injction conditions i.. injctd minority carrir dnsity ~ majority carrir dnsity Sris rsistanc ffcts in th bulk smiconductor away from th junction Brakdown ffcts valanch and Znr procsss

10 From Principls of Smiconductor dvics

11 Rvrs brakdown t a crtain rvrs as th currnt flowing through a pn junction is found to incras rapidly. This is known as rvrs brakdown: V r Rvrs as V Th siz of th brakdown voltag Vr dpnds on paramtrs of th pn junction, in particular th doping lvls 1000 V r (volts) valanch brakdown Znr brakdown N (cm-3 )

12 valanch brakdown Occurs for rasonably low doping dnsitis and for voltags in th rang V nitial thrmal xcitation of on lctron and hol Elctron acclratd by E-fild in dpltion rgion gains nough kintic nrgy to crat a nw lctron-hol pair Th two lctrons may crat furthr -h pairs Th initial small rvrs as currnt flow is gratly amplifid by th avalanch procss. incrass rapidly with furthr incras of V.

13 For avalanch brakdown to occur, th lctric fild in th dpltion rgion must rach a crtain critical valu E br, which is a proprty of th smiconductor From lctur, th maximum E-fild occurs at x0 E max x d N ε D x d ε N ( V V) N ( N + N ) D D E max ( V V) N ε( N + N ) D N D nd if N N D N E max ( V ) V N ε For avalanch brakdown to occur, E max > E br ( V V) N ( V V ) ε E br εe N br εe So, br Vr V i.. V r proportional to 1/N N

14 Znr (or tunnlling) brakdown Occurs in highly dopd pn junctions and for low voltags: p-typ n-typ Elctrons in th valnc band tunnl through th potntial barrir into mpty stats in th conduction band E G Quantum mchanical tunnlling Potntial sn by an lctron in th valnc band of th p-typ matrial

15 For significant tunnlling to occur th dpltion rgion width must b small: W ε ( V V)( N + N ) N N D D f N N D N: W 4ε ( V V) N Which shows that for a small W (and hnc high probality of Znr tunnlling) a larg N (high doping) is rquird.

16 Conclusions: V charactristics of a pn junction Forward and rvrs as Drivation of 0 V 1 Simpl analysis of 0 Limitations of this quation Rvrs brakdown