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Жигальский_Твердотельная электроника

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jKUl'aJlbCKUH A.A.

 

 

 

 

 

TBep.n;orem.HaJI

3JleKIpOHHKa:

MeTO.n;HQecKHe YKaJaHHSI

no

BbInOJIHeHHlO JIa60paTopHbIx

pa6OT.

TOMCK: TOMCKHU

rocy.n;apcTBeHHblu

YHHBepCHTeT

CHCTeM

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H

pa.n;Ho:.:meKTPoHHKH, 2011 ­ 59 c.

 

 

 

 

llpHBe.n;eHhI onHcaHHe H YKa3aHHg no BbInOJIHeHHIO KOMllJIeKCa JIa60paTopHblX pa60T no KYpcy «TBep.n;oTeJIbHaJJ 3JIeKTPOHHKa».

MeTO.n;uqecKHe yKa3aHHSI rrpe,ll;HaJHaqeHbl ,ll;JISI cry.n;eHTOB CneU;HaJIbHOCTH 210104.65 «MHKp03JIeKTPoHHKa H ttep.n;OTeJIhHaJJ 3JIeKTpoHHKa», HanpaBJIeHHU no.n;roTOBKH 210100.62 «3JIeKrpoHHKa H MHKp03JIeKTPoHHKa», 210100.62 «3JIeKTPOHHKa H HaH03JIeKTPOHHKa», 222900.62 «HaHoTeXHOJIOrHH H MHKPOCHCTeMHaJJ TeXHHKa».

© )l(HranbcKHH A.A.,

2011

© TOMCKHU rocy.n;apcTBeHHhIu

YHHBepCHTeT CHCTeM ynpaBJIeHHSI

H pa.n;H03JIeKTPoHHKH, 2011

CO~P)l(AHHE

 

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2 MCCnE.D:OBAHI1E BOnbTAMITEPHOH

 

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3 M3Y4EHl1E I1EPEX0JJ:HbIX IIPOQECCOB B

 

IIOnYflPOBO.n;HMKOBbIX .D:YlO.n;AX .............................

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4 113Y4EHI1E BOnbT-AMIIEPHOM XAPAKTEPI1CTMKM

 

TYHHEnbHOrO .D:HO,l(A ..... ....

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5 MCCnE.D:OBAHME CTATM4.ECKYIX XAPAKTEPYlCTMK

 

6lli10mIPHOrO TPAH3MCTOPA ..................................

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6 OIIPE.D:EnEHME I1APAMETPOB 6l1IIOmIPHOrO

 

TPAH3l1CTOPA ..................................................... ....

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1.2 TeOpeTHqeCKaB qaCTl.

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5

 

E

 

 

 

 

 

++

 

 

a

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+ +

 

 

 

 

 

 

 

 

 

Ec

 

o

 

k

6

JlF

Ev

Ln x

1.106paJoBIDme nOTeHUHaJlbHOrO 6apbepa p-n rrepexolla:

a crpYKTYpHaJI cxeMa; 6 30HHaJllIHarpaMMa

4epe3 p-n nepexo)1, npeKpaTHTC,SI. HacrynaeT paBHoBeCHoe COCTOH­ HHe, npH KOTOPOM ypOBeHb (J)epMH 111' BO BceM nonynpOBO)1,HHKe )1,OJ1:JKeH 6hJTh O)1,HHaKOB. 3T0 3Ha'lHT, 'ITO Me)K)1,)' p- H n -06J1aCT,SIMH

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J1aCTb nOJ1ynpOBO)1,HHKa, r)1,e OHH HBJ1HIOTC,SI HeOCHOBHblMH (pHc.1.2,6). ITepeXO)1,HYIO 06JIaCTb nOJ1ynpoBO)1,HHKa (-Lp~n), B KOTOPOH CYllJ,eCTByeT nOJIe, 6Y)1,eM Ha3hlBaTb 06J1aCTbIO npOCYpaHCT­ BeHHoro 3apH)1,a p-n nepeXO)1,a. B 3TOH 06JIaCTH KOHueHTpaUHH HO­ CHTeJ1eH 3apH)1,a MHoro MeHblUe, 4eM B p- H n-06J1aCTHX. TaKHM 06­ Pa30M, p-n nepexo)1, MO:JKHO paccMaYpHBaTb KaK KOH)1,eHCaTOp, B KO­ TOPOM pOJ1b 06KJIa)1,OK BhmOJIH,SIIOT HH3KOOMHhIX p- H n -o6J1aCTH, a pOJIb H30JIBTOpa Me)K)1,y 06KJIa)1,KaMH - BbICOKOOMHbIH CJIOH npo­ cTpaHcTBeHHoro 3ap,Sl)1,a. BeJIH'illH)' 3TOH eMKOCTH MOIKHO HaHTH no cpopMyJIe nJ10CKOrO KOH)1,eHCaTOpa

Ln H X

 

 

6

 

 

C

S&&o

(1.1 )

 

6

L'

 

 

r)J,e S -

nJIOIll3)J.h p - n nepexo)J,a;

 

E -

OTHOCHTeJIhHIDI )J,H3JIeKTPHLJeCKIDI npOHHlJ,aeMOCTb nOJIynpo-

BO)J,HUKa;

 

 

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L

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d2cpk(X) _p(x)

 

 

 

 

 

 

dx2

 

(1.2)

 

 

 

 

 

 

liliO

 

r)J,e CPK(X) -

3aBUCUMOCTh 3HeprHu 3JIeKTpOHa OT Koop)J,HHaTbl B 06­

JIaCTH rrpoCTPaHcTBeHHoro 3ap}l)J,a;

 

 

p(x) -

06beMHIDI rrJIOTHOCTb 3apH)J,oB OII3.

 

 

PaCCMOTPHM )J.Ba cnyttIDI pacnpe)J,eJIeHHH 3apH)J,oB:

 

 

1) pe3KHH p-n nepexo)J,

 

 

 

Pe3KHM

Ha3bIBaeTCSI

p-n

nepexo)J" B KOTOPOM

pa3Mep OlI3

MeHbll1e )J.JlHHbI )J,H<P<PY3HH HOCHTeJIeH 3apH)J,a.

 

 

 

Pacnpe)J,eJIeHHe KOHlJ,eHTpaquH )J,OHOPOB Nd , aKqenTopoB Na

 

 

Na

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

No

 

 

 

 

 

 

 

 

 

 

 

 

 

x

PMC. 1.2 - CXeManlQHOe

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

o

 

pacnpe)],eJJeHHe npHMeceFi 1'1 nJJOTHOCTH

 

 

 

 

 

 

 

 

 

 

ooo,.eMHoro 3apl1,lJ.a Bp

n nepexo)],e

 

 

I

 

 

 

 

 

 

 

 

 

 

-LfJ:

 

+++

 

 

 

 

 

 

 

 

 

 

+++

 

 

 

 

 

 

 

 

 

 

 

o

 

x

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

H TlJlOTHOCTb 06beMHoro 3apMa p(x) B p-n rrepexo)J,e )J.Jl.sI )J,aHHoro

cnyqIDI nOKa3aHhI Ha pHcYHKe 1.2. EY)J,eM CttHTaTb, 'ITO rrpH pac­

7

CMaTpHBaeMblX YCJIOBHHX BCe npHMeCH B nonynpOBO)J,HHKe nOJIHO­

CTbfO HOHH3HpOBaHbI. OTCfO)J,a, C YLJeTOM pHcYHKa 1.2, cJIe)J.yeT, CTO

npH x<O Nct« Nc" a rrpH x>O NJ» No.

II03ToMY MO>KeM CttHTaTb, ttTO

p= -qNa npH-L S x S 0,

P = qNo rrpu 0 s x S Ln,

r)J,e q - 3apH)J, 3JIeKTPOHa.

PeillaH ypaBHeHue IIyaccoHa, uCnOJIb3YH COOTBeTCTBYfOllJ,He

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illYfOCH BeJIHLJUHY L B <P0PMYny (1.1) MO)KHO orrpe)J,eJIUTh 6apbep­ HYIO eMKOCTb p-n rrepexo)J,a.

C = S q 2&&0.

NaNd

)1/2

6 [ 2~

(No +Nd)

(1.3)

 

IIpH rro)J,a'-le Ha p-n nepexo)J, BHell1HerO Hanp.sI>KeHH.sI V OCHOBHaSl

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HanpaBJIeHO npoTHBOnOJIO>KHO nOJIfO KOHTaKTHOH Pa3HOCTH rrOTeH­ IJ,HaJIOB (rrpHMoe HarrpasJIeHHe), TO nOTeHIJ,HaJIbHblH 6apbep YMeHb­

lI1aeTC.sI

rpk

rp2 - q V (Vk - V).

IIpH nOM conpOTHBJ1eHHe

p-n rrepeXO}1;a YMeHbll1aeTC.sI H Ha'-lHHaeT

lI1YHTHpOBaTb eMKOCTb CGB pe3YJIbTaTe YMeHbll1eHH}I )J,06POTHOCTU p-n rrepexo)J,a U3MepHTb eMKOCTb C6 OKa3blBaeTC}I OtteHb TPY}1;HO. ECJIH K p-n rrepexo)J,Y rrpHI(Jla)J,bIBaeTC.sI BHell1Hee Harrp.sI>KeHHe B 06­ paTHoM HanpaBJIeHHU, TO V, CYMMHPY.sICb C Vii;, YBeJIH'-IHBaeT rrOTeH­

.

~j!

8

QHaJIbHbIH 6apbep H, CJIe)J,OBaTeJIbHO, COrrpOTHBJIeHHe p-n rrepexo)J,a. B 3TOM cJI)''Iae eMKOCTb

C6 =s[ q&&O

. NaNd J2

(1.4)

 

Yz

 

2(Vk + V)

Na + Nd

 

31'0 BbIpIDKeHHe MO)l(}fO 3arrHcaTb B HeCKOJIbKO HHOM BH,lJ,e

1

_ 2(Vk + V)

Na + Nd

(1.5)

cg

q&&OS2'

NaNd

 

OrclO)J,a BH,lJ,HO, 'ITO 3aBHCHMOCTb 1/C6 OT BeJIH'IHHbI rrpMO)l(eHHOrO HarrpH)I(eHHH HBJIHIOTCH rrpHMOH C TaHreHCOM YrJIa HaKJIOHa

d(Yci)

2

Na+Nd

1

(1.6)

dV

q&&o

NaNd

'-2'

S

 

Ha rrpaKTHKe p-n rrepexo)J, C03)J,aeTCH BBe)J,eHHeM B HCXO)J,HbIH MaTepHaJI rrpHMeCH, KOTopaH 06eCrre'IHBaeT rrpOTHBOrrOJIO)l(HbIH THrr rrpOBO)J,HMOCTH. HarrpHMep, aKQerrTOpOB B rrOJI)'rrpOBO)J,HHK n-THrra

MH )J,OHOPOB B rrOJIyrrpOBO)J,HHK p-THrra. ,lVIH TOro,

'IT06bI 06pa30­

BaJICH p-n rrepexo)J"

He06xo)J,HMO Y)J,OBJIeTBOPHTb

HepaBeHCTBa:

Na»Nd B rrepBOM CJIY4ae H Na«Nd -

 

BO BTOpOM. TaKHe p-n rrepe­

XO)J,bI Ha3bIBaIOT HeCHMMeTpH'IHbIM. B

3aBHCHMOCTH OT BH)J,a Hepa-

BeHCTBa, rrpH 06paTHOM CMern;eHHH, rrOJI)'4aeM

 

1

2(V. + V)

 

 

»N

(1.7)

- =

k

rrpHN

 

C2

q&&0 Nd

 

a

 

d

 

6

 

 

 

 

 

 

MH

 

 

 

 

 

 

_1 _ 2(Vk + V)

N

N

(1.8)

2 -

q&&ONa

rrpH

a

C6

 

 

 

 

 

TO eCTb eMKOCTb orrpe)J,eJIHeTCH TOH KOHQeHTpaQHeH rrpHMeCH, KOTO­ POH MeHbllIe. 3HaH BeJIH'IHHY eMKOCTH H3 <P0PMYJI (1.7) H (1.8) rrpH YCJIOBHH V» Vk , KOTopoe JIerKO peaJIH3yeTcH Ha rrpaKTHKe, MO)l(}fO orrpe)J,eJIHTb Nd MH Na.

9

2)nJlaOHbIii p-n nepexo)J,

IlrIaBHbIM Ha3bIBaeTCH p-n rrepexo)J" B KOTOPOM pa3Mep alB

60JIbllIe )J,JIHHbI )J,H<P<PY3HH HOCHTeJIeH 3apH)J,a.

IIpocTeHllIHM rrpHMepoM rrJIaBHoro p-n rrepexo)J,a HBJIHeTCH rre­ pexo)J, C JIHHeHHbIM pacrrpe)J,eJIeHHeM rrpHMecH, KaK rrOKa3aHO Ha pHcYHKe 1.3. BH,lJ,HO, 'ITO rrpOCTpaHCTBeHHbIH 3apH)J, JIHHeHHO 3aBH­

NaNa

-Lp PHC.l.3 - PaCIIpe~eJIeHHe

IIpHMecH H Ofi'beMHOH IIJIOTHOCTH 3apNlOB B IIJIaBHOM

p-n - IIepexo~e

x

CHT OT Koop)J,HHaTbI

 

p(x) = qax,

(1.9)

r)J,e a=grad N - rpa)J,HeHT KOHQeHTPaQHH rrpHMecH.

 

EY)J,eM C4HTaTb, 'ITO Ln=JLp J=Ll2. ,lVIH orrpe)J,eJIeHHH

eMKOCTH

nJIaBHoro p-n rrepexo)J,a HY)I(HO, KaK H npe)l()J,e, pellIHTb ypaBHeHHe IIyaccoHa, KOTopoe Terrepb 6y)J,eT BbIrJIH)J,eTb HHa4e

d 2 rp

qax

(1.10)

d:x;2

&&0

 

PellIaH ypaBHeHHe (1.10) C cooTBeTcTBYIOrn;HMH rpaHH'IHbIMH YCJIOBHHMH rroJI)''IHM orrpe)J,eJIHM 6apbepHYIO eMKOCTb MaBHOro p-n

- rrepexo)J,a

c =S &&0 = s[q2a(&&0)2]113

(1.11)

6

L

12rp~

 

 

 

p-n -

T

10

ECJIH K p-n nepexo~ npHKJIa,JJ:bIBaeTCH HanpIDKeHHe V B 06paTHOM

HanpaBJIeHHH, TO, npHHHMaH BO BHHMaHHe, l.fTO rp~ = q Vk ,

nOJIYl.fHM

C =s[ qa(880 f ]113

(1.12)

6

12(Vk + V)

 

 

 

IDIH

 

 

 

 

1

12(Vk + V)

(1.13)

 

C~

S3 qa(88o)2

 

 

OrclO,na BHAHO, l.fTO 3aBHCHMOCTb 1/C6 OT V RBmleTCH npHMoH

JIHHHeH C TaHreHCOM yma HaKJIOHa

 

d(lI C~)

12

(1.14)

 

dV

S3qa(88o )2 .

 

 

113 <P0PMYJIbI (1.12) MO)I(HO onpe,lJ.eJIHTb rpa,JJ:HeHT KOHlI,eHTPa-

lI,HH npHMecH a.

~;~

6 6

,,,

,,

o Vk v

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TaKHM 06Pa30M, H3 npOBe,neHHblx paCCY)l(.lJ.eHHH CJIe~eT, l.fTO eMKOCTh p-n nepeXO,lJ,a 51BJI5IeTC5I <pYHKLJ,HeH npIDIO)l(eHHOro HanpH­ )l(eHHR. HcnoJIb3Y51 <pOPMYJIbI (1.5) H (1.13), MO)I(HO nOCTpOHTb 3KC­ nepHMeHTaJIbHble rpa<pHKH, KOTopbIe HMeIOT BH,lJ., nOKa3aBHblH Ha

11

pHCYHKe lA, npH yCJIOBHH V»Vk 3KCTpanOJIHpYH npHMYID .n:o ne­ peCel.feHHH C OCbID Op.n:HHaT, MO)l(HO onpe.n:emfTb eMKOCTh p-n nepe­ xo,na npH OTCYTCTBHH BHeUIHero HanpH)I(eHHH. ECJIH npo.n:OJI)I(aTb

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1.3 3KcnepHMeHTWlbH8H YCT8HOBK8

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BOJIbTMeTpa. oapbepHaH eMKOCTb nepexo,lJ.a ,lJ.HO,lJ.a npH

Pa3JIH'IHbIX 3Ha'leHHHX 06paTHoro HanpH)I(eHHH H3MepHeTCH

MeTPOM.

Co

Q-MeTp

HIl

PRe. 1.5 DJIOK-CXeMa 3KcnepHMeHTaJlhHOA YCTaHOBKH

1.43a.n:aHHe Ha pa60TY

104.1r!3Yl.fHTb H3MepHTeJIHYlO cxeMY H nopAAoK 3KCllJIyaTall,HH

Q-M~aE4-4.

104.2CHHTb 3KcnepHMeHTaJIbHYlO 3aBHCHMOCTb eMKOCTH p-n­

nepexo,lJ.a ,lJ.Ho.n:a OT BeJIHl.fHHbI o6pnaTHoro HanpH)I(eHHH.

= f(V) U

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--------------~----------

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20

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,IleTeKTOpHbIH ,lJ,HO,lJ, (MapKa)

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21

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11

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