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Unformatted text preview: Forward biased p — n junction A voltage source VI . atteh p . I]
as a battery 15. eenneeted with the punitive tenninal
to the p  side and the negative
terminal to the n — side. Forward biased p — n junction I] A voltage source VI . aneh p
as a battery is. eennected with the punitive tenninal to the p  side and the negative terminal tn the n — side. As per our earlier discussion, the Fermi
{eve} in the neutral n — region is shifted
upward by an amount equal to qVF with respeot to the Fermi level in the neutral p e region neutral n — region Ilﬁlltl'ﬂl p — region Ea. under ﬁjrward bias. is shifted upwards by an 31113th
q‘VF in that neutral :1 — ruginn uncler fnnwsrd hiss with
FESpuct tn where, it was in the p — rsginm Under
anvsrd Elias? harrisr hsight is q{vhi _ VF}
The space shsrgs rsginn ssrrsspsnds is s rcducsd barrier
hsight q[‘w’hi — VF],
The width of" this spacs Chargi: rcginn can be determined by solving Phisssn squalisn 01‘ [mm Gauss Thssrsm ss hcthrs
Barrier height in thermal Equilibrium is qvhi : [min + Li 95.1 The expression fer the widths cf the space
charge regicn will essentially be cf the same
form except VH1 will be replaced by Vb. —VF The physical reason why the barrier height
is less is because less amount of charge is
needed in the space Charge region to support
a reduced barrier height. Thermal Equilibrium Forward Bias Electrons in the 11 side 1arith energy above the barrier
height will diffuse to the 13 side. Under forward bias
more electrons have higher energy and will be able to
dif'Fuse to the p — side resulting in an increase in the di fusion current. Similarly mere hules will diffuse frem the neutral p — regien tn the neutral n — reginn. Due tn the dif‘Fusien ef eleetrnns tn the p — side, the minnrity earrier {:lensitj.r in the [3 —side inereases.
Siimilarl}r due tn the diﬂ‘usien ef hnles, the minerit},r
earrier density in the n — side inereases frem its thermal equilibrium value. This prneess is ealled minnrity carrier injection. In thermal equilibrium, there was a diffusien eurrent and a drift eurrent ﬂewing in eppesite elireetiens and the twn eempenents were equal
resulting in aere net eurrent. But these twe
eenlpnnents are very large in eeniparisﬂn with the diffusiun eurrent under Femat‘d bias.
This a]lews us te use Beltaman relatien even
under femard bias whereas Beltanian relatien
is valid nnl}r under eenditiens ef aere eurrent flew. As befnre 1w: “will Chﬂﬂﬂﬂ the ﬂrigin K = D at lhﬁ metallurgical junctiﬂn. I _ l ,
I“:.—1"""—:7"I :f—‘HH—L‘FI ﬂﬂllll‘ill Ilttutl‘ﬂl [ 3.1“ + 11'“ ] np(E:—EP)=HH(K:KII)e—q RT
Jul—v.)
pints; Eﬂ)=pn(x=—xp)ﬁq kT
£p(x:xn):pn(x=ﬂn —pn{}
an(E:—xp)=ﬂp(x:_xp)_ﬂnﬂ
pp(K=—J{p app” [Judalbum I'I'Iﬂdﬂt‘ﬂtﬂ inj Edin: _q I
_ _ _ _ ILT
nn{x— xrj—nn{x —H”]ﬁ
15 'u
=I] E—q ﬂ+ﬂqﬁ
L'al'll
1."
El
_... k'l'
qr:
— —_ _ _... Ic'l' _
ﬁn—nn{1— xp ﬂm—I'In” I: ] Similarly pn{x=xn]=pp[x=_xp}ﬂq kT _qxu HIE
= pailE: ET: kT
qﬂ
= E it'l' PH” , I“?
q ﬁpix = x“): I:'I'I [x : En}_pnﬂl = pm] E kt _1 Example :
Calculate the width at" the space eherge regien. uf an abrupt
p—n junctien 1with a net impurity density elf' "MA = lﬂ'ﬁem 3 and NU z lﬂ'iem 3311 the n —side. a] in thermal equilibrium and h} under a ibrward him: (if [1.4 VieIt. I' IS
em. =.U259[II1[%H = ﬂeeev 3] Thermal eqmlibrium —11 lﬁ i
xp: wxﬁm =.ﬂ336xm‘cm
1.5mm xﬂﬁx(1n”+mm)
Similarly x“ =.336x MEI—‘1 cm xd = Kn + Er. =[.ﬂ335+.336]x1ﬂ"cm =.9T5Hlﬂ'”cm b} Forward Bias; {1f (1.41.?
The bﬂTTiEI‘ height is Vhi — VF
= 0.65 — 0+4 = 0256%? “HF and 3;“ calculated in part a) has 0.256 0.6513 tr: he multipliad by .05533x104cm +553H1EF4£=m K n 3': l1. ...
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This note was uploaded on 01/24/2012 for the course EE 3 taught by Professor Staff during the Spring '08 term at UCLA.
 Spring '08
 staff

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