Final Notes_EE2003 Lect 21 SEPT 15

7/23/2019 Final Notes_EE2003 Lect 21 SEPT 15

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21 September 2015

Summary of last lecture

PN JUNCTION

• At thermal equlbrum !e ha"e co#ce#trato# $ra%e#t e&sts for

electro#s a#% holes across the 'u#cto#• (lectro#s a#% holes %)use* meet #ear metallur$cal 'u#cto# a#%

$et recomb#e%* %epleto# re$o# starts to form

• Pote#tal %)ere#ce P+ formato# %ue to ,&e% %o#ors a#%

acceptors a#% acceptors

• P+ creates electrc ,el%* !hch !ll try to %rft the carrers # the

opposte %recto#

• As lo#$ as %)uso# compo#e#t-the %rft compo#e#t* carrer

%)uso# !ll co#t#ue a#% the %epleto# re$o# !ll $ro!• Stea%y state* %)uso# compo#e#t s fully bala#ce% by the %rft

compo#e#t. At ths po#t* /o pote#tal barrer* o%epleto# !%th*

a#% ξ electrc ,el% are %e,#e%

To be remembere%3 co#ce#trato# $ra%e#t causes %)uso#* electrc ,el% causes

%rft compo#e#t

At equlbrum* the hole Jp a#% electro# J# curre#ts are 4eromea##$* #o #et curre#t o! across the 'u#cto#3

The total curre#t %e#sty J sum of both the hole a#% electro# curre#ts

s thus also 4ero at equlbrum3 J 6 Jp 7 J# 6 08J s the curre#t %e#sty Ampere9meters

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21 September 2015

To%ay:s ;ecture

Sl%e 5<

Ths s the pcture of the process of PN 'u#cto# s create% #ot ,#she%

yet

There are Co#%ucto# =a#% (c o# the left a#% r$ht s%e

At the co#%ucto# ba#%* ca# be see# less #umber of electro# as the

e#er$y le"el s #creas#$. Smlarly for the holes.

There !ll be a J J is the current density, units=m!ere"meter %)uso# o#

the %)uso# re$o#* but the J %rft !ll al!ays try to a$a#st t. U#tl

both of them meet at equlbrum !here the J %)uso# a#% the J %rftare equal.

Al!ays %)ere#tate bet!ee#

(c a#% (" at P s%e* (c a#% (" at N s%e.

The pote#tal barrer #otential Energy $arrier for electro# %)us#$ from #

to p s%e s the %)ere#ce bet!ee# these 2




21 September 2015

Sl%e 5>

?@p0 s %e,#e% o# P s%e %-& !0 is the length o' de!letion o' the ! side(

@#0 s %e,#e% o# # s%e

e %e,#e% 7& to be from p to # %recto#

The curre#t %e#sty equato# for %epleto# re$o#3

+rft %ue to the electrc ,el%* %)uso# %ue to co#ce#trato# $ra%e#t.

hy there s a m#us o# the %)uso# term =ecause t mo"es fromh$her co#ce#trato# to lo!er co#ce#trato#.

The# !e $et

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21 September 2015

=y substtut#$ these 2 equato#s to eq. * !e $et

+epleto# re$o#6,&e% post"e char$e a#% #e$at"e char$e

hy the /p a#% /# s u#form S#ce both pote#tal are outs%e the

%)uso# re$o#* they are compe#sate% by ther o#4e% %opa#ts %do!ants

is a trace im!urity element that is inserted into a su$stance()

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21 September 2015

P s%e 3 ma'orty s hole

Ppo s the hole co#ce#trato# o# P s%e at thermal equlbrum

I# PN 'u#cto# !e assume all %opa#ts are o#4e%

So* Ppo equals Na

##o s the electro# co#ce#trato# o# N s%e

p#o s the hole co#ce#trato# o# N s%e

*+oo at the !otential diagram

/p a#% /# s u#form* the cha#$e s o#ly o# re$o# %ue to

co#ce#trato# $ra%e#t




21 September 2015

Sl%e D23

e !a#t to ,#% the e&presso# of /o the co#tact pote#tal

Pote#tal cha#$es from /p to /# E hle carrer from ppo to p#o

Apply the #te$rato# !th the lmt

e $et

As ca# be see# # the formula* t %epe#%s o# the #tr#sc co#ce#trato#

ma'orty hole co#ce#trato# at p?s%e a#% m#orty hole co#ce#trato#

at # s%e

Co#cluso#3 co#tact pote#tal %epe#%s o# %opa#ts co#ce#trato# a#%

#tr#sc carrer co#ce#trato#.

/o !ll cha#$e for each %)ere#t semco#%uctors. /FaAs-/S

hy /FaAs-/S

=ecause ($ FaAs s $reater tha# ($ S* !hch mea#s # FaAs G # S

because # ∝e

− E g

kT * !hch mea#s the lo$arthmc terms # /0 s b$$er*

!hch result#$ a b$$er /0.

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21 September 2015

Sl%e DB

e ca# use mass acto# la! because t:s happe#e% o# thermal

equlbrum

(quato# > tells that the carrer co#ce#trato# of the same type from

o#e s%e s relate% to the other s%e of PN 'u#cto# by the co#tact

pote#tal.

Fo to e&ample o# sl%e D

Herm le"el The energy o' the highest occu!ied state at 0 is re'erred to as the Fermi

energy EF . re'er to the lecture note /ee 2 %epe#%s o# the co#ce#trato# of the

%opa#t

The (p s the I#tr#sc Herm ;e"el

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21 September 2015

Part b* use the formula $"e# before to calculate the Pote#tal barrer

The Herm le"el of PN 'u#cto# rema#s co#sta#t. O# %a$ram abo"e* !e

are try#$ to al$# the ferm e#er$y le"el for PN 'u#cto#.

hy are they %e#ctcal

;oo at equato# <

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21 September 2015

SPACE CHARGE

Assumpto#

• No free carrers !th# %epleto# re$o# * or !e may say re$o#

co#ssts of o#ly char$es %ue to u#compe#sate% %o#or a#%

acceptor o#s.

• Char$e #eutralty s ma#ta# outs%e

The char$e %e#sty o# p s%e s the %opa#t co#ce#trato# tmes the

char$e

The area of ths $raph s the Char$e %e#sty. A %e#otes the area

co#tact of p# 'u#cto#* A tmes &#0 results the "olume* N% a#% Na s the

%opa#t co#ce#trato#

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21 September 2015

Sl%e D> s the %er"ato# for the char$e #eutralty arou#% p# 'u#cto#

The rato s commo# for both formulas 11K12 $ree# bor%er bo&es

&po %epe#%s o# N% E a#% &#o %epe#%s o# Na

Sl%e <0 O#e s%e% abrupt p# 'uc#to#s

+epleto# #to the l$htly %ope% s%e

hy See equato# 11 a#% 12* the le#$th of the %)uso# re$o# s

%epe#%e% o# N% a#% Na.

Sl%e <1 for further llustrato#.




21 September 2015

(lectrc ,el% "arato# !th#

e are %eal#$ !th ho! the electrc ,el% cha#$es !th# re$o#

It:s a l#ear equato#* !e ca# %o the #te$rato# as !rtte# o# sl%e <B

S#ce the electrc ,el% s "are% across the p# 'u#cto#* t:s esse#tal to

,#% the pea electrc ,el%.




21 September 2015

The ma&mum electrc ,el% s at &60 at state% o# sl%e <

Sl%e <5

/o s the co#tact pote#tal. The area of the tra#$le o# the pcture belo!

s the co#tact pote#tal.

s the %)uso#9%epleto# !%th




21 September 2015

(&ample 2 o# sl%e <D

F"e#

Nd % donor concentration (

Na % acce!tor concentration (

% area (

ni % intrinsic carrier concentration (

Plu$ # all the $"e# "arables to the formulas.

There s a brea o# the %a$ram o#

sl%e < pcture o# the left

t:s #ot easy to %ra! a lo#$ l#e

l#early* the brea smplfy the

%a$ram.

Fe/ sources+N2-#N Junction in E1uili$irium !d' lecture notes

2+4 to +5Energy 6and o' SemiconductorsN78 %ug 209:( !d' lecture notes

This is a lin o' an e-$oo 'rom NTU li$rary %not mention in the lecture, ;ust my recommendation(, you can <nd 'urther e!lanations a$out !n ;unction 'rom !age >> on/ards)

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B3dHN=ntu)aA30@A5Cd$=cat00903a

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Final Notes_EE2003 Lect 21 SEPT 15