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r::;-:~STIGA TIO~- OF TPE CP.t\.RACTEniSTICS

rJ.'F .. :.i~SISTOR

by

rhillip B. }'riodrichs )/

Captnin, lJni ted Sw teo 1£-rinc Corps

Suhr:~ittcd in ·crtiol :f'l,J.filJnont of tbo r cc:_n:trc:-:lCDts for tho C~G[;l:'C:I0 of

1 ~·.sm~. OF SCIEJ:TCE I II

E~:Gr;rr~:rn.IFG ED::CTROriCS

United Stntec Ynvnl T-osterndt'Dte School ~ ·onterey, Cnlifornio.

1 9 6 2

tJ S. NJ'I \'

"

TR.A-.SIS'i'OR

by

'~HOOt

I1.'lil1ip n 1 :2-.cicdr 1.chs

This ' ·or l: is occc--;ted c.s fulfillir'G

t h e thesis r eqyirenents for the c_et;;ree of

l :t~STER OF SCI Er CE

I l7 ~.

fror:l t he

Unitec States rnval r ostcro.dua te School

1~ stu~fc cc 'oter:tie.l cor: .. rolled t.rc Lsistor tias recently dcvelopeu 7

t l-:e cl:ar::-,cteristics of ',;ldch c"er'cnd tP)On t.uo scniconductor nhcnomcrn.

u suo.lly thot:c;ht of c.s (ieleterious tc tr2.r cistor opera tior.~ These o.re

corricr recm;tbir..:l tion and channel effects. The dev"ice is characterized

by a hich i:".1rcc:ance v-id l!hich allo1:s efficier:t opero tion from. a loH

l:·1pedance solu~ce . It offers pronise cf reJ!l2 cine V[lCUl.1J:l tubes in mary

appliro.tions not previously possible .

The rhysics of or;era tion are cx1;laim:d nnd the description of the

device i n t crr:ls of hybrid :r:ar arJ1eters is given. The variation of these

:rnraneters Hi th bi a s conditions i s investigated and expl ained in terms

of the underl yi ng physics . The cl-:aracterization of the d.cvice as a trans­

ducer i s derived i n terms of e;ain and impedance levels.

The ur i t er 1-ii shes t o expr ess his appreciation to He. James rartin

and l'r . Ben Ani x:ter of Fairchild Semiconductor EroO.ucts; to 1J-. Fred

l:crrison and 1-a- . Bnndolph l:oore of I<oto1~o1a, Inc . , Lilitary Electronics

Divis ion f or tJwir a s si s ta nce in oataininc the devices for ex:rerimentation;

a nd t o Dr . H. E. Ibuer of the U. S. lbvul Postgradl1ate School for his

a ssistance a net encoura gement i n this investit:a tion.

ii

~BLE CY cc::'J.'ErTS

Section Title

l. Introduction

2. Description of lbnufacture

3 . The Ibcno:r:1enon of Cho.m}el in Seniconductors

~- · The Fhenorc.enon of Recombiro. tion in Seniconduc·t.ors

5. Effect of Ch:;lnnel o nd Recombim tion on Transistor Action

6 . Hybrid F_,qtlB. t i ons and F . .qt1i valent Circuit

7 . E::plan1 tion of Fa rame ter s nne~ Their Variations in Terms of tho Underl yinc Physics

8 . Gain a nd Impeda nee Eqt1B. tions

9 . !\11 scelln neous Notes a nd Observa t ions

10 • S'urrlrlary

11 . Bi.bliog:raphy

iii

Fage

.))

61

•'...L

FiQJre

1.

2.

3.

!.; .•

6.

7.

8 .

9.

10 .

11.

12.

13.

l L; .•

15.

16.

17 .

lS .

19.

LIST OF ILLUSTP..ATI01~S

1-:e thod. of l£nm_fa cturinc Sllrface-rotcntial Controlled ':L'rD nsis tor

Pro ''Tessi vc Stens in the Forme. tion of Cr..annel (re~rristic liodei)

l:::ffect of Chc::.nnel Ctu>rent on Cha1:mel Depth

Im:ptrri ty Distribution Formed Durinc Diffusion

Energy Level Diagrams for Progressive Stages of Channel Forma tion

'i'etrode Symbol ancl Current-Voltage Conventions

Tetrode Linear Equi wlent circuit

Comnon Emi tter Current 'r.ransfer P.atio as a Function of Grid Voltage

Cormnon Eni tter Current Transfer fiLl tio as a Function of Collector Ctrrrent

lise Current c.nd Connon ErJi tter Current 11>ansfer Ratio at Lou Ccllector Currents a s a Function of Gri d Voltage

Grid Transconductnnce as a Function of Grid Voltage

Grid Transconc1uct:::.nce a s a Function of Collector Current

Bose Resistance as a FUnction of Collector Ctrrrent

Ba se Resistance as a l~tnction of Grid Voltage

Colle ctor to Ease Feeclro ck Ha tio a s a Function of Collector Current

Collector to Ea se Feedback Ratio e.s a Function of Grid Voltage

Grid t o B:r se FeedOO. ck RD. tio a s a Function of Grid Vol tn.ee

Tetro de Con1':1on }}.1i tter Sr1all Signal Linear ~ui valent Circuit

Common fui tter Tee F..quiwlent :'o.se Circuit He electing Feedba cl: Terms

iv

rage

11

13

15

39

44

53

56

1:''7 .).

60

62

1. Introduction.

Ir. 1961, Dr . c. T. S:J.h described o. ncu se;:;icorx:luctor device 1.:hich he

called a 11 surf2 ce-poter.tinl cor.trollod trc.r sistor~/J/ In addition to t he

usual cni ttcr, base anc collector ter1 .1in.."..ls this dcv.l.ce fen tuTes a fourth

termiro l knm-m a s a crid. It is the effect on collector current of a

potentia l arplied to the gri d anc1 the hir;h impedance of this termiml

vrhich sots this device o.p1rt. frou the remainc1cr of the trc..nsistor fan ily.

Because of the fourth torT.1ina1 o.nd the similari tics -'co vacuur:1 tube opera­

tion, t his device i s appropriately ,described by the term 11 t etrode 11 and

such it shr.ll be cc.llod a.uring the rema inuer of this discussion.

The tetrode depcr.ds upon tuo scrlliccncluctor phenomer.a for its opera­

tion. These phenomem are chaT'I..nel a ne. recoMbim tion of holes and elec­

t rons. Until the ad.vent of the tetrode these tHo effects uere deleteri­

ous to transistor a ction and_ strong efforts i·lOre made to ctu-•b them.

Since they 1.-1ere reQlrded as second· order effects , most engineers are

unfaniliar ui th the me chani sms involved. They uill be described in

Sections 3 and 4 of this paper .

The tetrode may be described by a set of throe hybrid equations

defined by the current-vel tage reJn ticnships at each of the three inde­

pendent terr.liro.ls . These chnracteristics ar.d their variations ui th bias

condi t i.ons uill be preaented in Section 7 a1ong ui th the as so cia ted linear

equivalent circuit . An expla t'.ation of the re-rameters in ten's of the

physics of the tetrode 1.1ill also be given. Fim.lly, the expressions for

voltaee eain, input impedance and outpt.r'c i mpecln.nce Hill be derived and

discussed together Hi th some cautions resnrding use of this device in

circuits.

1

2. :!Jcsc.ript:ton of : :[' pufa cturc .

A kr,c•,rlcci~e of t)'c construction of the tetroCe uill be an aid in

tnK;erst.?..l<d.nc the c. ction of t!::.c tr[.11s:! stor in J.ater C::isct~ssions . Con-

s t r u ction J;ellous the sequence for the surf<:' ce y:assivatod plo..rcr.. j-im!·­

evcr, the last pha so involves der osi tine a r.1o u '. J. cont.o.ct on t he rrotee­

ti ve oxioo layer of t.bo et1 i tter-bnse junction. Fi [.;1.:.ro 1 illustra tos the

steps in manufactm"'e.

An n-type silicon substrate forn s the collector. This is e tched

to clean t he surf<:"'l ce and then exposed to u. steam and oxygen a t r:1osphore

1-rhich rouses a stable silicon dioxide to gi'ou into tho surface. It is

this protective oxide ul1ich p:J.ssivates the surfs co and provides the

extremely lm.; leakage current3 in plan.'1r transistors (of tho order of

tenths of nanoamps). This is shmm in figure 1 (a).

A uindm-r is etched in the oxide layer exposing the n-type silicon

for the rose diffusion (figure l(b)). The base is diffused into the

collector fror:1 a boric a cid '\lttpor a tinosr.lhere . The metallic boron dif­

fuses into the exposed silicon and forms a p-typo layer. It is i nportant

to note in fi~ure l(c) tbnt tho ,iunction is formed underneath the oxide

layer coYer ine; ti1o collector. This 1neo.ns t bD. t t he junction surface has

not been expo sed to a contaminating atnosphore as is the case in conven­

tional transis-tor manufacture . Durine the base diffusion, another oxide

layer grovTS into the previously exrosed silicon. In the case uhere boron

is used as the ba se diffusant, tl1is l":lC.Y tal:e tho form of a borosilic-a te

glass.

As before, a uincou is etched. in the o:dcle over tho base to oxrose

the p-type s:tlicon to the eni ttor diffusant (figure 1 (d)). Phosphorous

is used a s tLo donor i t1purity for tho e:·}itter ~-typo lo.yor . It i s dif­

fused i nto the 1x.se from a phosphorous pcnto::ide atmosphere. The

2

H~typo si.licon

c

· 1-~----;.--s_:i_c_2_ ;.~ 4

,_-

P-type base c

B - ----------·c-

,..., lJ

- . ·- -- ----·- ________ .9__ -·

c E

~-~~-,.l.<Cor c 'f ..... "-~- r-• .-ro_.;:!f! - ~~-{/-r·~l

D .... v

)

j

i ·---:

(a ) O·dcs gr01m lnto cntiro SllrE l·I'U Jc~:;

(b) H:Lncoli ctc:ccd for h:J.s8 diffusior:

(c) Oxide [To us deeper dur­ing boron C.ii'fusion of base

(d) Hind ou etched for &"'tj_ t­tcr diffusion

(e) Oxide crovs dGe})er (Ltr­

inc; phospborons difi\··~;-­~ or. of erd.tter

(f) :JiPdous for obr ic cor.­tacts etched . :lnittcr, l)C} so and r:rid o::::ide sre :,10tallized

Fig . 1 : r>thod of mm..l.fo.ct,Jre of surfacc-potentie.l con~rollcd. trar.s::i stor .

(fic;uro l(e))

1-rov~sion fo::: ohoic contacta is :1o.c e b~· etcbir s 1r:Lnc.oHs O"',rer the

o:1itter and bcse rngJ.o!'ls o.nc1 '!E'to.lli::;;in · 1rit·:1 nl,:-Jninum. 'l'i1e etchinrs; of

the ohnic coPtac t Hinc~ous leaves ~n oxide loyer protectint:; the eni tter­

base junct ion surf&ce. It is this ozidc '·.!hich provi des the possibil:l ty

of a fou rth tern i nal. Tl:is oxide i s netz.lli~ed and a lez..d i s bonded t"-'

i t, thu.s fornin~ t he cricl $ ':::'he ef fe c t of a potential applied to this

grid i s the subject of t.ho renuinder of this p1per.

3., '::'he 1 hc~cnc r:oi1 of Chc. m1el iP Seuicol'Ccuctors •

• • 1. ,..::nc'erstr!.nc:ir' ·· of t.:.lc ',r.J:,r i1~ , .. rhich col lector cu:rr cnt is coL trol led

by r.ric: vol t .::tr•o i r~ t;l;.e tctroc'e rec:uircs < n unO.erstrnd.ir~.: of a n efft)Ct

~·:n01·m r s chr1nnel conductivity it:t se?riconductors. Thi s effect h:-· s ~)ec'n

ob scrvec\ for nany ye['. rs in transis tors and lms been used t o explain cx·­

ccssi ve l cs.l:nge ctrrrent in p- n j unctions /2/ as Hell as the drift in

pot e nt i al of an open-cir cnited mn tter uhen t he colle ctor--base j unct ion

is r everse bia sed ./3/ This latt er ef fe ct is kno\m u. s "floating pot enti.J l"''

Chnnnel conductivity may be G.escribed as a reeion near a p-n j unc­

tion into uhich either electrons or holes from the other side of the

junction nay floH Hi thout encounterinG a. potential barrier ./1/ TI1is is

often mistaken for an inversion lnyer i·!hich is a layer of n-typc se!ni=

conductor nco.r the surface of a na tcrio.l uhich bas been doped to be ~

t:lpe or vice vcrs~· . Several investicntors have concerned themselves irith

ncthods of creating and controlli ng channels ar-Gj.ficially in the la"vora­

tory . J. 'l' . IDu a. t t ributed t his ar.oY'i.nlous conCi.uctivi ty to ~n ionic C'..IT:rer1t

in a l a yer of 1nter adsorbed on tl:e SlU'fO. CE: uhen c. reverse bias i·JaS

a pplied to a IJ-n junction./4/ At a pproxjJuately the so.ne tine , H .. Chris­

te nson isolated the chz::. nncl conductivity from Ia;.r's ionic c1u-re nt theory

by freezing the adsorbed vr:. tor 1c.yer at ci .. r~· ice tCI'1?Cra ture . He lrr:lS t.tu s

able to shoH t hat t he chanr:el \13.S, c.t least in plrt, due to crerge ~ !Tiers

i·:i thin tlle bulk . /5/ Ee a ttributed the chc nnel t o an electric fiel d at tho

surfa ce . This electric ficlc.'l c:istm:bed the equilibriun charge distribu ­

tion near the surfc.co thus rous ing t he cho.1;nel . U.L. r ro·..rn /3/, foll01Jing

J . :ltrdeen' s t heory of snr f c co sta tos /6/ developed o. r:1a thena t i cal t r oo. t -·

ment f or dcscrih1ne tho e l e ct r i c field i n the interior and at the surft\ ce

of a GeLiccnc~uctor 1ri t.h suc1: an <..:cJ.sor~)ed layer of stu·f [ .. ce cb.arr;e. Hi s

~1odel ,.ns exte nC::.cC:. ~'Y .\ s l . r.:c~ !horter c nd .:1 8H8 1\ir:.gston uho a ssumed a

5

is vr:lic.~ only ior cer·-:c nh1J.l s&ITJ.~- les ~ince rcc01:1birn tion current i iU s nee-·

lcc~~,ec " St,_ch r c conbirJc.tion is of the utnost inport:1nce in describinc the

tetrode n nd Hill be discusse ci. in detr. il J..e, ter.. In 1957, 11. Cutler and

H .. ~· . D< th nodified the 1rork of !ld.fl1orter and Kinc;ston to explo.in the non~

&'l tv . .ra t ine; reverse C1J.l'rcnt and loH fort."'c.\rd. current characteristics i:c

silicon c~iodos ./7/ R. E. ringston and s.::::·. Feustadter folloued o. develop-

nent rcrallel to Brmrn 1 s in calcnla tine the srnce charge and free carrier

concentration o.s ~.Jell as the electric field at the surface of a sonicon=

ductor ./C/ J.11ese uorks provide o. useful C.erart1.u-·e point for the troa t~

uent of the clnnnel effects in the So.h tetrocle. Unfortun'1 tely, all of

these ·treatments nre directed tor..;ard the inc:i vidual vho is uell versed j n

the concepts of the p~1ysics of the solid state and not the o.vern go elec·-

tronics enc;inecr. The dovolopnent 1.-1hich folloHs is ~ m.oc?.el for the

crer tion of a channel ' .. rhich uses concepts fo. r:.ilinr to the engineer. The

reacer should be cautioned ngo.inst pressint, the model beyord its applic-

ability . It is intended c.s a heuristic model.. A r1ore conprehonsive !'lodel

ui thin the pre cepts of solid sta -'co physics uill be presented la tor. 'l'he

reader 1..rho is i nterested in follm-rinc; the lc.. ter c.'evelornont or uho feels

need of a revieu of se:-:J.iconductor phJ'sics is referred to the nou clas sic:

boo:: on the su11ject by H. Shockl€y; J:OrticuJ.o.rly chapters 1, 5, 9, 10

and 1?. A f ounde tion in quentur:1 :10clw.nics oriented tm·Jard seraiconductors

is set out in furt III of the saTJC voltnne./9/

As stated earlier 1 thoro is a difference betueen the forna tion of a

cha r.nel and an i nversion lo.yor e A chc.nnel is associated only ui th tl-:.G

m~oble~.1 of 1.Jhother a ch<:rgo C[lrricr sees a rotontir'l burrier [~t a june-

tion, regCJ.rd}.ess of the actt·.o.l carrier concer:t.rations in the immedia te

vicinity. An inversion layer is defincd in terms of the relative co.rrier

concenb~a t.ions and frlr,y occtu' inc~e~;enoent of uhether the cr,rriers see a

potel"1ti[11 burrier . Inversion is present Hhenover the concentro.. tion of

the normolly n i nori t.y carriers exceeds the non:1r..lly noj ori ty co.rrior con-..

centrntion. This mo.y occur before, nt t he samo time, or nfter the onsot

of a channel. A channel occurs lrhenevcr the potential barr:i.er for rnnj or­

i ty c<:'.rr:1.ers in a p-n j1mction is reduced to zero. For emnplo, if clec-,

trons in an n-type material sec no potential bnrrier to restrain them

from diffusing to the p side of a p-n junction, the condition of channel

is said to exist . To s:i.mpljfy ma ttors, it '!.·rill co a~stlr.lOd t}"l.n t the onset

of channel and the fort1C. tion of an inversion layor occur sinul tancously.

Under this o.ssurnption tho uords 11 chonnol" nnd "inversion 1o.yor 11 nmy be

t~sed inter cho ngca bly .

Consider the p-n junction in thormol equilibrium shoun in fi t;tn'o 2(n).

Under 'l:.hcse conditions ·t.ho junction is oocl: bio.sod by n n amount Vd clotol·­

rnincd by the difi'union of mc.jori ty carriers acrons the junction. The

majority currier sracc distribution is unifor'Ill in the y direction. '1110

electron3 on tho n sir:lo nou cnnnot surmount the repolline; electric field

in tho transition region.

NoH lot a positi vc potential V0 be applied to· the ourfuce of the p­

typc materinl . The nssocio.tod electric field repels the holes nearest

the surface nnd ur..covers some of the necutive ions. Hinority electrons

are olno attracted from the bulk tot·!nrd tho surface. The migration of

tho cbnrr;o currier s nnd the uncovering of ions ends uhon the potential o.t

the surface hns been neutralized and tho syster.1 is once more in equili b-·

ritun, One effect hns been to reduce the concentrc.t:i.on of free holes neur

the surfo.ce nnd increase tho nu:nbcr of free electronn f1•om ·their normc.l

equil.ibrium volueG. Another effect hos boen to lo~-ror the potential

7

p-n

(A)

v

Zl ~ X J

JUNCTION BIAS AT SUnFACE

• • • I o o o

00GG GGGG • • • I o o o

G GG G I 0 G G G e·Ge ·e 1 eoe oooG

• • • I o o o

G GG G 1 G G G G • • • I o o o

8 GG G 1 G G 8 8 n TYPE 1 p TYPE

- ... x+ + +

(B) e e • 11 ~ o o Q

X

(C)

8GGG 8800 0 • G . 8 ·e 8 o G. 8 ° G

• • • 0 0 0

GG GG GG GG • • • 8 G GG 0 0 0

08 GG • • e 0 0 0

GG GG GG GG n TYPE II p TYPE

--tt-X++ + + + + + ++

8888 0080 n TYPE 11 p TYPE

.., , c ioJ '":., < _ .... ct-r o. -f_. ic.

'l'he re~·ion ilcc..r -ch0. Sl'.l'.fc;.ce is :;: o· r les.:: p-typo tha;.l. before.

Le-~ the Sl.Trf<'.ce potential be ilwrce sec~., 1'1-J.e ntlTJber of electrons

r-.v<.:'.ilr-ble fro:1 the p-type ~)ull-. is l~,i tee IJy tl:E: depth cf pcr ... etra tion of

thE: electric fiolc. into the bulk . Eo1-:ever, increasing the surfo ce peter.-

tial tenc~s to fo:n~rd bias the junction near the sttrface e:~ nd thus r.lal-::Gs a

large supply of electrons e..vailable in tl::.is area . Therefore, afte:.r an

initial supr1y from the p-type m.a. terinl , nearly all of the electrons

needet to neut.rc.lize the s1.1.rface potential come from the n sicio e.nC: the

chane:e in surfo.ce potential is nanifested in a ch..ar~ge in bias across the

junctior: nea.r th0 surf2 ce necessary to provide these electrons. It sh01t1cl

be clear thu.t for so;::e v<::.lue of surface potential , the number of e1ectrons

Hill exceed the nv.mber of boles in the loc.."il regio~ at the S1..i.rfn ce . This

describes an n type ma ter ia1 by defi.ni tion . The ftn•ther the potential

increases , t.hG no:-te stron[;l;:l n-t.ype the layer be comes . Since the electric

field co.usecl by the s1.u·f['.ce yJOtentiul decrec.ses as o. fu .. nction of derd:.h

from the s1.1.rfaco into the bulk, the r .. -ty~;e lEyer is less strongly n-typ0

as ue go from the Sl.:trface into the bulk . I:ver~tu8.lly, at some depth, the

concentrat:i .. or:. of free holes again exl.!eeds the free electron concentration

D.nc~ the r::.ate1'ial is again p-t.ype . This indiC'.-atcs tr.u:"lt tho n-type layer

6oes not extend very far into the bulk since the elk-: nee in surface poten-

tic.l ser-ves nore to forun.rd bic s the junction t.r..an to rerel holes from the

surface. The fn ct the t the deptb of tho st~'"'face ~-·::ype layer sa tur·a tcs

very ~ni~!cJ.y 1.rill be denonstrated by the results of a later caJ.culntion.

It shouJ..d be r..ot-ed that 1-m rJf." .. ,.e sa tisfieG. otu· c~ofi:ni tion of 2 chc.nnel:

0

sbo''l- 2 J_ so 1;e 1 ·o~EC'_ tL t -::, 1is junction is reverse bi<:.sec' since the n

regior: i.s 2-G a ~JOsitivc :'OterrtiDl 1:ith 1·cs:)· ct to the p recior:. . ::='o pre-

current flo1rinG ir tl:o ch.c.1mel to1rvrd the jur.ction. The channel is

quite resistive and a vol t::.cc ciro~~ occurs in tho c1:annel uhich reduces

the reverse bi<:;.s ccross the c}'1c.nncl jtmc~ion. Thus the chf'.nnel lJecorr:cs

':"iC:er c. s 1.re 2.ll)::Jl'Of' ch tb.e no::":cl junction lror1 the nomimlly p side . . ~s

1:e shc.ll see l2. ter , such c: currer.~.t is cc.uscd by reconbir:c tion of electrons

o.nc holes in tl1e cl:c.nnel. Fic1n·e ;. TCfTesents this si tm tion for a con-

sU.nt current flo·.Jinc in 2. channel of m!.iforr.1 resistivi ·~.y . The potentia}

crop is then 8. linear funct:.on of c~istancc .

The case ul~ich is of in·ccrest to us :i.s the tetrode . The source of

tl1e positive potential 1roulo , of course, be a source c,p~'licd to the t:rricl

of the tetror~o . Since the oxide l::1yer over tho emi tter-baso ,iunctiot: is

an e:z:cellcnt in::mlc t or 1-rith a resistivity of 2pproxir.1ately 5:;J_o9 oh.m-cn

at 250°C the llrc vious ass1.mption of no ctu-·rent leavirr:; the surfecc is

valic . The C.oscription of ch2nncl fo:..~r:le.ticn used oruy 2 potential a:-Jplicd

to the p--typc r0.a i..erial . Tl~e oxiC.e lu.ycr -..~~~ich forms the rrrid c:::tencL::;

over the n-type mc:.terial as uel1 . Such u.s applied potentiel on the n-

sic1o uou.lc null ify the bi:::: sin[ ef:::'ects of the ch2 nee in potential on the

p- si6.ea I'l'.US it rust be c:.sst'!m.<?d that the ro.turc of the intcrfc.ce bet;wen

the silicon nne, the oxiuc is 0iffcrer:t for tho t1.·o typos of silicon and

fc.ce of n-ty:;'•· si~ ::.con. S:::.h h:::: s [t ttrilmted t~Jj_s nffcct to the

+ I

+ I + I

I + I

I A +) I

+

p.. 0) "0

.... I

Q) s:: ]

+

j I (.)

I d

+

I 0

~ I s:: Q)

~ (.)

I I

+

...... Cl>

j ()

\1 0

+) (.) Q)

Ct-1 ~ ~

('C'\

• tiD ..... ~

ll

:l.ffl!.SD.r t) is reiected hv t he . ~ ~

forms c. c~C'c;cr8ro -t.e lo ycr (1nc tal J ic lnyer) ullich s creens the surf~ cc of

the si lj_ce n f ror.1 the opplie0. c,-.cic1 potentie l . ::cnce an nrplied r;ri d vol t-

o.ce •.dll l:.o-'.:. a ffec t the cist.ributio n of c1'"'.D.rge C<:'.rriers in the r-t~<-:--e

affinity for t he ba se di ffusant (boron) c:.urir.t£; diffusion so trJD.t the

regior. a t t he sm"fa ce, under the oxici e i s l ess heavily coped thc.n the

bulk mater ial i n t he inter i ol". As a res1:J_t , the surf a ce ha s a lmrer

equilibrimn hole concent ra tien o.nd the charge distribution 1Till be r;:ore.

r e sponsi v e t o gr id voltage chant:e s . Figttre 4. illus trates t he se point s .•

For nation of a cr..c nnel on t he p- s i do of a n r..-p junction has been

de s cribed . Thi f: cor ;:·osponds to u cha m'lel under the gric in the base of

a n n- p-n tetro~c. I n order t o r:1ore ful ly c~e scribe the for171a tion of the

ba s e cho nne1, ue mus t t ur n to o.n ana l ysi s of pot en-t.ial ui thin t he base .,

The qua l i ·t.a t ive descr i ption of chs.nnel f ornation given above can be

m['. de nore c.~.ua nti t.c'J. ti vely ricorous by deterr;J.i ninc the electric field in

the blll k of the ba se . Yore i mportantl y , soJ.ut j_on of -'.:.he probl e!rr for the

electros ta tic potential 1li t hi n the volme uill yield i nformo tion as to t he

depth of penetr ation of the chr:.nnel i nto the bul]~ . IE.t er i t uilJ be

possible to co::rr ela te potenti a l 1:i th channel cur.rent by considering r e-

combimtion current in the cho.nneJ. ar:.d its effe ct upon -t.he C:epth of t he

channel. I n orcer t o f'orrnul::; te the problem. , it 'i·rill be ne cessary to

descr i be ctam1el fo rme t ion in terrr_s of the ener gy of cJ.'l..c.r ge carr iers .

The de s cription uill be sommilm t }Xlrallel to th<=• t e i ven by Prm-m /3/ s.nd

E:Lngston anC. reustadtcr /8/ .

Fi~rre 5 is e t hree dinensionc.l repre~:;ellt.n t ion of tho ener;;:y of an

12

G 8

0 0

e 0

0 G

OHMIC CONTACT

.··=~~~=~:~:~:~:~:~:~:::::::;:::=::;:::~:::::::;:::;~:-=:««=:~:::::::::;:::=:::::::::::::::::::::::;::::::::::::::::::::::::;:;:~::-;:;:::::;:::;::::::::::::::::::t~:~:::;:::~:::::::::::::::::::::::::::~;:;:?

·.·~ OXIDE ACCEPTS BORON DURING DURING DIFFUSION DEGENERATE LAYER OF NEAR SURFACE

PHOSPHOROUS CREATED0 _ 0. t::\ 0 0 1':\ f.:Vr::\ D DURING DIFFUSION V \J \::./ \J c.J

G GGGOGOGG

0 0 G 8 811° G GGGG)008000801 0888GG8G.00G0: 8 0 0 0 0 0 0 ,{:------------~:

G 0 I I

0 0 G G G 0 II N REGION I

I 0 G 0 G G 0 II

I

88000888 P REGION

80008888

8 8

G 0

0 0GGGGG0 000G000G GG

0 0000000

88 8 GG GG ---- - --- ------------

0008008 000

Fi e . 4 Impurity distrirPti 0 n f"ormed during diffusion.

l c ~c L ~

dcfon:1c~ tion of the onere;:' level::; ir. the "'ticiri t~; of the surfa ce. ~ Ccnd

¥{ are the notcrt..ic.ls at 1.rhicll the ::>cr"li cr>cr:~y v:ould lie for ec:_ual con-

centro.tions of electrons ancl holes . At the inte-rsection of t{lis surface

c. nt: the :?erni sr:rfa cc , <p , n = p . For the c~1..~.ilib:ci11l"2 concii tior. this

occurs at the center of the junction . ::.s before , it uill be nsm:r~md thn t

a rotontk.1 n~!}"licd to tho ~;rid (the pl0ne y = 0) ;rill not chnnr;e the

potcntic.l n t tl-:.c surface in the n J:>ecion* V0 is the reverse bias r.;cner-

ated to cour.:'.:.orc:.ct the diffusion of carriers acr oss tho junction . l'J:1e

subscri})t 0 refer::; to tho therr1al cquilibritt:l vc,lue of the que~ n-ti ty col:J"'·

corr:.ed . ·.~.110 subscript n or p refers to the vnluc of the C{UD.ntity on thE-

n or p si~o rcspcctivoly a

The potcntic l ~ or ~ is clei'iEcd by the rcla tior~.ship

;j/ == t [w + tf/v .,. ~r;:tfn .. {lv v/N~ )] 1:herc q is the electronic ch<:,r~e , tj{_ &nd 1//,.r <:.re the potentic ls at the

botton of the conc~uction bo.nd c.l'Ct top of the V<::'.lcncc b.1nd resroct.iYcly,

k is :Joltzna nn' s constant, T is tho ambient temper8. t-u...~"':"e in °K and Pv ~lrld

lJc nrc tho cffccti vc L~cnsitics of stc. tes in the conduction n nc· v-•. : le1:0o

ban<ls rcs:,cctively as defined by Shockley on 1n:;c .303 of his book./9,'

In a perfectly intrinsic l'llC. terinl Ev ::: 1:c and tj/ ::: f ( ¥/c +'j/1..1" ) or or.e

hclf of the Cl1E'rgy c;ap ,

In fi~:m~e 5(b) o. for~.:::~rd bic::s Va h8.s been o.rplicc to \:.he junctior'

in thE: con\:c:!tlor;;,: 1 nonncr . ':L'::is is uanifcstocl ir.. o. loucrirc of the

1/l-

- t/1 OR + e_ FOR ELECTRONS

tflc

¢p ~ t{!p

_ _1 / ___/

- cJ>p

1/Jv

/

/ /

/

/

1/Jb

/

/ /

/

INTO BULK

y

Fig. 5a Junction at equi.Jibrium with no a rplicd bie.G or surface pot ent]al •

._----------------~~--------------------------------------------~•x N REGION JUNCTION P REGION

t/1

- 1/1 OR + ~FOR ELECTRONS

"'b

n

t/J c

/ /

/ I /

lflp /

cpp-.Pp / _______ i __ _/

¢p

rf1v INTO BULK

y

Fig . 5b Junction with forward bias Va but no a pplied surfa.c e potential.

~-------------~-------------------------------------------.. x N REGION JUNCTION P REGION

/

/ /

/

/

o1~ the n sic."e -~o c:rc:-:s to tL0 p sic'e. '..:'Li::~ i~ cc<1Vc1·tioG·:. C.:.:~_oCe o:-cca.-

tion. It is v.st1ally stc. toe: "~ s the cLcl-:[}"l ir. thE.' c rc-, si ~··crr.1i levels .

This is a :Lso s ;:o~m in fir;..u·e 5 (b). ':!.'Lc conccntra tion o:' holes in gcncr2 oL

c.uc ntity

\.rhere ~ is the intrinsic chnrr;e carricr co:1centro.tion. It is o. fnr:ctir·n

of temre rr.. t1JJ."'e orJ_~, for o. c;i ven t.j/ . '1'he corresiJoncine e::~:9ression for

elGctron concentration is :

( l )

I t is seer: thElt the c:t'l[,ntity tp-f// is positive or.. the :J side C.l'~.G hence

.Pr )>)1p as expected (the orc!irn te of ;figtu·e 5 is -(// ) ·..rhil e ((J -f// is

ne2;a tive on then s i cle o.nd )'\-. >>f'~"· • It o>oulc:. be rointed out that

a::0:0l~·ing the bins , Va , 0.i~ not mo.tericlly ch::·,nzc the quantity r'j)-fj/ und

so the carrier concentrationG he.ve 1'1ot been nodified . This is only true

\>!here the injected car rier density is Sfiiall coBp;..red ui th the equilibril!.l'1

ma jori t:;· co r..centro. tion on t he other sic~e of the barri er. Therefore ~re

r:ay avo i d explicit mm"tion of bias conc~i t.:tons and cis cuss the effects of

The effect of o ppl yi:1,s a ~os~ tive IJoter:tial to ·C.hc [Ti( is ~l'om. in

f igure 5(c). As prevl.ou::;ly assu.r:J.f'd, it r,.r' s no effect upon then side~

The effect upon the p si~e is to lm·rer tho energy of all of the allm:ecl

stn tes in -Gr,o region to \·Thich the suJ.~fc ce-.:'1 }""'plied electric field :~)ere-

t r a tes . There c.re TIOi·i more electrons ui th er:er r;ics :;;rc.s t.Eir thnn or E:'CJ.U..-1

to the neu ener gy of these previously enpty stntcs . These electron:: ·uill

nal::e trnnsitions to these er:pt;y states 1.rhich rz ises the Ferr1i level to·:etrd

17

1/Jn

- o# OR ~ FOR ELECTRONS/

1/Jc ///

t // =-==__.!_ __ - 1/Jp I / T ___ =:Y

INTRINSIC ....--- INTERSECTION

v

INTO BULK y

cf>p -"'p

PROJECTION OF INTRINSIC f~ INTERSECTION ON X- Y PLANE

¢p

/ /

/

~ s

~------------------~--~--------------------~------------------~•X N REGION JUNCTION P REGION

Fig . 5c Junction with forward bias Va anci posit:i.vP rot cntial V s appli Nl to the surfClce.

1/!b

/

// /

( .'''€' er J.

con('ucticn be YlC • =n ii:~;.n~c 5 (c) , Yf is the reference level SO t1~.G - u 1 J ,.I·

of tLc :;}'er:'i level is !'l&l:ifostod b=' the i'Jel•c~inr of ttc eEcrgy lc.vels l ;,'11

t oiJ2.rC'c tLe :.::'crr1i lErvc l .) In te1~·1s of ·tho belJ.& vior of tho se:-:i.conc't:2"'.o:e

riluch s=-1fl.llo::c tt .. a n its pi~ev:Lous vc. lt~e o1: the ~) sic:.o . ~i. s :::, r osul t, t1t-

m:::;::-onent of the ox:rression for tho cor~ccl'tro t.ion of holes is snLller <..'.r:<~ ..

therefore p :.t..s swaller . Conversely the exr onent in the c~:Pl~os sion for n

increases and n is larger . The tuo 2.rc 1~1ore no£:Tly equal o.nd. thG materiru ..

more nearly intrinsic.

An interestin~ point to r,ote in rassing is that the conductivity of

the surface la .. yer increases as tho concentr ation of electrons increases .

This i s duo to tho higher mobility of el ectrons over th..n t of holes~

cr = 'i ~" t\ + Ji P-1' >

=~~)\ ( )\ + fo;..p l '\-There jA,./j'lt <I. t1 is the semiconductor cor:ductivity, )'n o.nd }AP ar e

the respective mobilities for electrons ~nd holes . Tne conductivity i;l

seen to incrense i·rith 'f\ • Since 'f/ decrec.ses as a fu::1ction of d.opt.h

into tho material , so docs n n:nd consequently rr • Therefor e the voJ t;.:t~}

drop due to a longi tudiml channel current i s loss nonr the surface oi'

the cham".e l t:b.an clee:;~er i nto the chD.nnel . This is ::mother fa c t or uhiuh

tends to confine cl12nnel currept to the ir~edi<J. te strrf£1 ce l a yer .

:ncrea sing the grid voltage further r esul ts in the situation sh-wn.

i n ficure 5 (d). The energy bn nds h8ve been lm,:ored so f t,. r t h.c .. t t.he Fcrn1..

level i s no·:r be tueen (// c nd t he conduct~_on band. The sign of cp- f// has

cha11f;ed c.nd n i s nm: [:;rca t.er t han p. 'J.."~he surface l Gycr i s no1 .r n-t;; 'x;

J.C)

w n

- </1 OR + ~ FOR ELECTRONS/

INTRINSIC INTERSECTION

INTO BULK

y

CHANNEL DEPTH

1/Jc l I

1/Jp

t/Ju

'-- ------ -- ---- -- - ----

~

/

/ /

/

/ /

/ /

/

/ /

/

v r

~------------------~----------------------------------------------• x N REGION JU-NCTION P REGION

Fie . 5d Junction with for·.·a rd bias V a and Ufl! li(:d surf<'ce pott.ntie.J. V s • Notice t bat the intrinsic intcr~ection no lon~c· t ouches Stl""!'acc- . An n- t yv lr;.y~ !' hue; br.·, n forrr:ed on t!.c surfr.cE: .

"' b

/ /

/

r::.-·ccrJ.a J.. ·:rhi s sc.t.isfic s t1 1c crcvio1.1.s c~inition of cb.~ nnel ..... s co ,- K

seen f r oB fic,"l:rc 5 ( c~ ), tho Ll~' ycr c::tcr.<s i1:to tho ::'-ty~ .... c r:1e teri:-l tor'

C.e pt h Ceter, ~ inec~. by t :1c intersection of (// e.ncl C(J •

i ... c~etcrmin.'1 tion of t he c~ e::rth of the c:1c.rmcl m:: y be mc:c~e by solving

Poiss on 1 s cqtlf\ t ie r. for tho :oten-ti~~ J i n t lw interior of the p r egion ~s

n function of tho e;rid- inducec1 su.rfn ce potenti a l :

lihere ~(r) is the chcrge density as 2 fv.nction of position nnd E is the

per:nittivity of t he ser!i iconc:uctor.. ':2he ap;_")rooch 1:ill rzrallol the [: n?ly-

sis proser:ecd by l:inr:;ston and i~oust<::cl. tcr /8/. It Hill bo assuned t r..r.t t he

variation of potc ntiol is nnic1irectior:nl o nd not n function of ti"l1e . The

surfa ce i s the oricin of the y coordi n'l te of fir;t..u"'e 5. ::.'he energ:,· origin

is tc!cen u s the :i?<?nni level in the p- typc r.10. terinl . 'l'he variation of po-

tential i:r: the t.rc. nsi tion region is necle ctecl so tha t our discussion is

li.-r::i ted to t he rce;:i.on in uhich the L'l"id ha s tho v.~ea test effect .

The cr.llrgc acn~si ty is c i ·ven by :

Dee:; in the bulk •.j.. lu is ~~nmm -Ghat clw.rge neutrolit..y exists c.1x~ tho elec-

tric field J.. s ~ero . The potenti:J.l has smn.e ec:uilibrim: value f//8 shmn1

in fignre 5. Usin6 the chnrc;e neutrality condition ue b£ve:

p a N~ - N e. + -t- "'A 0

'If\ -1":: NJ - N~

n and p a re given by (1) und (2)

( ) { ttlr-rNJr -?J(t?- !fJJ!Je-r} Y\- .f = Y\ ~ e - e

= 2'1'\~ sill ~t ~r/JcT

?1

Dce:;:J in tte ~n,J L lj/= ~ D 1-x~ n-~ = l c.~-rc , hence:

N&~ "'a. = 2 Y\t s t n h 't tfl'e./}T Sinilo.rly y-.: = -z·~t S(Y<l~ ~~atr i.1:. cencrc l.

Poisson ' s ccuation for the one C.ir.'lcnsior~'"'1 c:::sc becomes

Using the icontity

(3)

This integration is fron tho bull: t.o".:C.rd the stu-•faco [ no. yields an G:A~es-

sion for the oloctric field rs a function of the potentinl at any point:

Equa tio n (4) must noH be integ-.ca ted to find tho r otcntial rf as a function

of x :

The solution of this integral i·rilJ. yield the potential at any Ciepth@

Eore irr(~ort.D.ntly, if ~'• 0 is t he up:;_x;r lin.i t of the right r...a nd. int.er':l'al~

the corrospc~C: i rlc?; vnlue of x 1-:ill be D mec. sure of the de!Jth of penotrc.~-

tion of the channel into the ::n.-L!_k ns a fm:ction of ~ • A solutioP ir

closed fern is not ~--ossiblc hoFcver a p11'usibility r.r Q.l.I""J.ent uill shm-r

22

The initi<- 1 "',Tc luc oi' Its is ros5_ti ve 0. no ~ is r..oce- ti VG. 'lne int0-

gT<:tnd is the s lope of the intoual . For lareo positive values of <./'; the

c onor:1ir.11 tor al_)proc~ che s illi'iP.ity uith the cosh ~ hence tho intoc.;rc nd.

o.pproachos zero . For smG.ller -vo.lues of C//s tho slope 1-:ill h..z. ve a noasur­

able magnituC.e . For fairly largo ~ (> S~) the :into.=rrm uill ~c es­

sentio.lly exp (- r%) Hhich l'Cl.llidly DpprOC'.ChGS ZOrO C.S C.D C s:;rmptotc .

Thus i t can bo seen that incre<3.s i nz tfS Fill not rnz.terially affoct tho

intoe;r a l 2-nd hence the c? opth of tho channel .

!..;.. The fheEo;;.cnon of l.cco""lbirr tion ir Seniconcuct ors

The phc norncnc'l' of rccombir£.t.icn of electror:s anc1 holes in som.i­

conL1nctors h[' s been observec_ lnrcely in conPection ui th rhotocor: .. >:.ction

processes. In such a process, holc-cloctl.~on rairs o.ro r;enoro ted by a b-

sorption of or:ergy from light incident U }-on a semj_conductor. Hi th an

cxterrnl electric field applied thGfJe ce.rriers constitute a drift ct.uTent

lihich is observed to decay c:-:por.entiolly '\.'i th Ciistnncc from the incident

light som~co. Such c~oe<?.y cz.n only be explr i ned by r rocuction in the

nw.ber of cho.rge carriers and b..o. s been Cescrib0d as a recombim tion of the

light generated hole-electron ~drs. This is c rnndor:1 pro cess uhich is

best described srn tistically . Tho most 1:ridoly o.cceptccl I:oJ.el for recom~

birotion rrocosses lro.s described by H. Shockley and IJ .T. Reac', Jr./10/

Their model \Jas concerned. uith t he recombir..ntion rate in a bulk material

uith 1:0 p- n junctions. This ~r;.odcl 1:ras usee by C.T. So.h, R. H. l~oyce and

~·1. Shockley to describe the same r:on- satm·able le~.:Jxge ctn·rent and loF

for \-ro.rd current charncteristics in silicon p-n junctions as Here explained

uith channel considerations by Cutler and :Bath.

Recombil';s.tion 1:~y be c:escribed. as e ither one or b.Jo step processes.

The one step ].:roccss is n direct cncolmter of an electron by a l1ole uhich

results i n the remove 1 of both from tho conduction process. Essenticlly

the electron has maclc a trar:si tion from the corJ.ouction band to fill a

vaca ncy in t he valance bond structure. This process is unlikely ~ince

the electron r.mst make an energy-losing collision lli th sor1e other r-arti­

cle ~- t the precise point in time end srn ce i:hore the hole is loca tecl.

Since the hole is a.Jso T"l.ovine through the cryst:J.l this is tantm:1ount to

a ron thr01 .. .ring one bosebnll r c-,ndonly into the a ir and c.r:other to n batter.

If the second baseball rac.kes a collision l:ith tho bat c.nc1 subsequently

hits the first 1.).']11 you he ve d.e scribec't c. c~irect cclJ.ision of an electron

the electron or tl:e to1e in c loc['.lizod volu.me in SJ:Xl ce. Since its

probo.bllity of l'ciq~ 2t o C';ivcn point i n s:;a ce is r.ou c-.ceater , tho prob­

e.bili ty of ')einr: encountered or hit b~· 3.nother }.Xrticle is £::1"ea ter. 'l"'he

effect of trc.:rs is to increase the rate of recoli1birn.tion over the co se

uhere r.:.o tr::::rs c.re present .

Avy locr.lized i.mperfectio:~ .. in the crystal mety a ct as a trar'. An

i.rn:rerfection i n the crysif:ll mc.y to.ke the forT.l of a V['Ca ncy i n the la t tice ,

an :i.J.1::;m""'ity &ton, a c:eyswl dislocation, en interstitial ato~ .1 , or e. grain

bm.mclary . Since the swfr: ce of a seiJiconductor ali;ays define s a crystal

grain boundary , there Hill ahro.ys be a cer"t:1.in concentration of traps at

the surface. This is reflected in the relc.tive ~::1portance of surface re~

combi nation as or-:rosed to rccor.bir.ation ill the bulk materia l . The pres­

ence of a crystc.l irr!perfection i s nanifcsted by an allm·red sm te Hi thin

the for')idden band betueen the valence and conductior .. bands . The :roten­

t i a l lcve1 of tl1is e.J.lo;ved sta. to is dependent upon the tyre and Joca tion

of the i:T;~erfection . Ano t:.i·(:~r 1·1<''!~' of ( ascr ibing a t rap i s in terms of a

l oCBJ.izecl electric field 1-:llich attrncts an elec tron or hole and holds it

in a loca1 nrea 1.-:l:ose radius is dependent upon the strength of the local

ficlC: . If the field attr2.cts o. n electron very strongly , i t corresponds

to nearl~.r immobilizing the electron uhich makes it. ver y easy for a ho1e

to su!)sequcnt1y cn pt ure it. The corrE:sponcli ng ener (;IJ level of the trap

'l-ro·alc, be ncar the va1ence lx'.nd.

The rate at uhich rE:' combir:a. tion take s place describes a l oss of

current. The fact thn t. rccombir£ tion also takes pl a ce in channels es-

tabli shos an inter-relation behrecn the tuo phenomer.a I.Jhich is ir1rort--~ nt

to t he description of tra1"lsistor action in the tetrode . The follouine;

25

;J}~oc\lcy [; nc ' .~ " /10/ "' -,_c._. c. u. nc.

lToycc nnd ShocJ.cley /11/, o.rrivine; at on cx~('ression [;iven b;.r &h for the

recombim tier: rate as o. function of the elsctrosi:D. tic potential at the

surfrtce anc.! iE the bulk . Usinc this eXJTession ue may then correlate

the reconbirotion crJ>rent in tho chc~nnel uith the depth of the chf:nnel

an6 sm~fc ce poter-tial * T:'lis sl:ould &llou us to ser:cra te the effects of

m:trf2.ce potont:i.al upon cl::....<J.r:.~.-~el c"epth ar~d recombirn.. tion rate.

Let us suppose U1c t in 01.1r r~JB. terial there is a density of traps ITt .

I t 1-Til l be assumed tlm t these traps oll have the sume energy level. This

asstunpti on is rela ti ~,,ely -:l21id for a uell p1n1 ified sem.icor:ductor \·.rhich

ha s been do:Jed 1.rl-ile carefully o..voidin;:; umranted :inpuri ties and carefu~

crystal grmdng to el:i.m.i r~. te lB. ttice vacancies and clisl oca t ions .

A trap may have one of tuo conditione : it may be occupi ed by an

elect ron or not occupied by an electron. It is to be remember ed thz.t a

trap is s i:'lpl y a qunntum eners-J s·'t:a te or 11alloued ener gy" f or an electron.

As such its probability of beine occupied by an el ec t r on i s descr ibed by

th~ Fermi~Dirac st.a tistics in e:mctly the same n.anner us electr ons and

holes . I f a trap is occupict:.l by nn electron, it I!1..ay either eni t that

ele c t ro n to the conduction banC. or cc.ptlD:-e a hole fron the valence bend~

(The ele ctron nctu.£.11y nal:c.?s a second transition to the valence band to

f ill a vacant bond .) In either case the encl result is that the trap is

enpty . If a tra:;; is initiolly empty, it nay capture an eJ.ectron fron

the conluction band or enit a hole to the vaJence bond . (In tho latter

case a valence bond is broken and the releo sed electron is trapped rn ther

than Going to the cor.c~uction band $) The end result in either c<:~ se is

thc.t the empty stn te is filled by e.n electron. Obviously the density of

fiJled tro ps r lus the density of empty traps is 0(:..1.Wl to the total density

of trapsa Thus the prooobility thD.t a trap is full plus the proxbi1ity

.... J.

L.l ~-C'\·.'C

(r:-s1 I )~-r e

Since ~~ = -~<f' nl:ero if/ is potentio 1 (or vol tc.ge) :

.f ( E ) .:. e'\ ( 'P -SV) /~ ;:: e 'b ( !//-If' ) I k-r

t (£) ~ r

This ron also be 1-Ti t ten o.s:

ll

+r (E) (' (:_-F)jjT -r (e) e -

The proba.b:i.li t:·· th:.., t. n trDp lS i 'u.1l nust then be given b;y:

and er.1pty by

uhere Et is the energy l evel of the trnr e.nd Ft is the Fermi l evel for

the tr~.ps ~ ':o w.J.so c:cf:t.~~e 711 o.ncl F:9 c.s being the Fer?li levels for clec-

trcns n '-"ld holes respectJ.ve1;y. Under conditions of therr:al oc~uilibril.un

(Eo 2.~plicd binses) all of these Forrri levels coi r:cide. :·oFever , uhcn

the conccnt.rc.tions oi.' (.!<--:'rrj_crs ['TO rot C1t their ec~"Ldlibriun ·vD-luC's, the

tro ns 0. rd tole s e In oru:r to sl1::ll ro.te

uhicl: clect:rons arc be~.ne trC'pJX·c by the empty tro.ps and tho rate at

Hhich f"-111 tr.;:p:::; c:.re eni tti::-1_:; thr::Lr elec-=:rcns to the condu.ction ·oa:r:.6 .

The cii ff'erence 1:iJ.J. oe t.!1c net clec·~ron co.pttu1 e rate. Sil'lilurly, the

r ate of hole capture amJ enission uill be f our..cl. i n order to detcTn:inP

the net hol e co.~ture rate . ;:. t steady-state (but not equilibr i't.m ) con~-

di t ions , the net hole cetpt.uTe rate anc' YJ.et c1cctron captlu:-e r ote m·st

be eqt1B1 . Th::. t i s , U'e r.sd~e of filJing er1pt y t raps nus-G equ::-. 1 the; rate

of eraptyin2~ filled trc.pr:~ . This , tben, is the rz~ -t.e at uhi ch ca r riers are

being rer::.ovec from t he condu.ction process a nd i s the rate of reccmbins.tion ~

For every hole-elect r on r~dr uhich r econbines, one elect ro n nust f1o;.r in

the external circui t us com:pen:;..-3. tion . 'l'hi s ccnsti tutes a reconbir..& tion

current . He ·uiil r..ave more t o say o..bout this later . The energy t;hich i.s

given up uhen D.n elect ro n and. a hol e recombi ne is converted to lattice

vibra tior.a1 ener gy . 'i"l1is raust be considered a. s rnrt of the tc tal :po·t.Jer

d.issira t.io n of the tetrode . l~ore l.rill be said about thi s i n Section 9

'\·Then beh2 1rior of the tetrocle uill be discu.ssecl .

The r a tE: at uhicb. elcctroi.1S are capt' Ted i s cle:;:-er..dent upon;

mr.1ber of eJ.c:ctrcns c>.vailrbJ.c in tl:e condnc cion band for ro. ptn:~c; (2) the

munber of trc.ps ;..ft1ich nre em1: ty an( her~ce capable of t r appi nG an cls·c tron;

D.l'l..cl (3) thE rro1::ebility per ur...i t time tbo. t an elect ro n Hith o. given energ-y

1dll be trapped by an cm!"tY trop at. a gii:en ener gy. The prodt,ct of the::.e

f actor s yields th0 ro ·te of elcc+.ron capture. l::..na J.ogousl y , the ro. te of

elect r on emission fr on f:.,~J trDps to the conduction band is Given '!!y the

proc~uct of (1) the m:onbcr of e:npty s"W tes in the conC:ncM_on bc~nd o. s a

function of ('nerr:y; (2) the nl"~:lber of full traps (hcnco CC.JTble of er:dt.tine;

28

an electron); c~nd (3) the ~)l~o~~obilit~' per •J.r<it t luc of a full trap

emi-::;ti1'C an e::'.cc·~-1"'0~:. to a c;iven c11orgy level in the conduction bD.nde

The l"c"LtcJ.bcr of clectrol:.s D."\i"D.il o.ble in tJ:e cor:.duction band , n , is

given b~r the i'2"o0_t'_c t, of "CllC nul.u.bcr of str.tes ~.ncl the probD.bility of that

state bein.~ occupied int eero.. ted over· the conduction band ., For a non~

degenerr.. te ~~ semiconductor, the effective dcnsi ty of states i n the con-

duction band a cts like a nLur>.ber of states, He, all concentrated a t the

bottom of the conduction ba;.1d. Hence the electron density integ-ral do~

generates to :

00

Y\ ;; I N (E)+ (E) dE Ec

= N r ( ) - .. ' (r.,.- Ec.)/e-r C. 1' E'c - I~C e

N (E.) = { o; E. :f Ec N,; E = Ee

<s)

'I'he ntmber of traps uhich nrc m:"lpty is ci vcn by tho product of the

density of t r aps and the probability of a trap being empty integra ted

over all energies. I t ha s been c. ssu.'!led that a density of traps, Nt, is

concentr ated at the single energy Et• The integral degenerates as in

(5) a bove:

l\pt = J 1'4 frt (E) = Ntf~ (Et) = l'h·ft e<Et-r..)/J.r 0

'Tho :probability per unit ti_rne t hat an electron uith a given energy

vri 11 be trapped is give:-1 by the product of t he thc!T.lnl velocity of the

electron and the CD.pttu"'o cross section. TDis is a cons tnt 'l.."i th rosrect

to energy for a non- clegcneru tc seniccnductor since a ll of the conduction

band electrons are effectively at Ec o This factor shall be collcd c.:.1 •

i*A non- 6egcner a te semiconductor is one 1:hich is s'Luficiently pure t:r.cat t he cloc".:..rons i n the conduction band nrc essentially at the 1m-rest end of the oond . This inplios t ha t the dcr:si ty is still a function of tenpcratm:·e . If the density of electrons becones too hit:;h the ccncen­t r a tion loses its tenpcra ture cependence :?.nd t he SCr:J.iconductor takes on t he properties of a metnl . '.O"io l[' ttcr condi tion is }:rmrn as c. dezeneracy.

29

Usin; th( st: rcs'LL. t,s~ the !'i:?.te Gf electron C2 :;ttu""e is:

ConsicJ.crin[~ the :r'<"'- te of eni::;sio~1 in an D_ no.loeous 1-:1.anner, the j_"lu~aher

of enpty stc. tes ir: the conduction be.nd is Fe-n ·dhich is:

The mnnber of ftill t:r·a ps ~s :

and t ho co:-responding prorobility of enissi.on per ll..ni t tine is e., .,

1"1~esc factors give the ru te of electron e1:1ission to the conduction. be.nd

a s:

( 1)

'lbe net ra te of electron capttu~e is found by differencing (6) ond ('7).

Uen = Nc:+ (Ec.) Nt.fpt (Et)C-tl- Nc tp (fc.) Nt.f-t. (Et)e-Y'.

= tJ, N-t c ... [.f(c.}f.\ .. Hr-~;J - .fP cr.>-& (Etl ~:] If the thermal equilibritm nrg"Uffient is invoked, the r ate of cr::.ission nnd

t he rate of capture rmst be eqt'l£.1 o.nd Ft = F11 • Under this condition

Ucn = 0 Hhich means :

t(e~)tp:t (Et:) : tp (Ec. l ft(E't.l ~ + (r~) fdEt>e(fT-Ft JAr ~ f {f. ) e~-r...JJ:r f. (rJ ;;.

f f.r- [ _\ IJ:T ~ "' e _ ~'fA =: ~: (g)

Since Et is al110ys less than Ec , the rate at uhich e1ectrons are em:i. t ted

from the traps to the conduction band tmder equilibrilun cond.i tio:ns is

al1-.rays les s than t he rate at 1-1hich electrons D.l"'e fallinr; into the traps

front the conduction bansJ:o This should not be construed. to r1ean that tho

tr~:ps co.n never be em:pt yine as fast as they are fillifl_.e since >m have f

not yet considered the other !JW11S of emptying traps : hole cc.pture~

30

:E::p-J. nding tl:2.s exp:res sicn a r:ci isolating the e::~>onential rart:

It ;..rill be fou.nd convenient to express the electron emission tern in

tcr.:..iS of a fict.i cious electron der:si ty 1rhich r.LD.s all of the cho.rac-Ler-

istics of an el ectr on distribution ui th the Ferni level u t Et . Designn te

thi s by

... 1 (Et-Ec.)kr Y\ R = 1'1 c e th e )1

Ucn = Yl tpt (Et)C.,. - n, tt (Et )Cn ( EO )

Tho term Cn = ITt en exp:-cesses the rnrmber of electrons per unit time 11hich

110tu d be capt wed if all of the t iaps uere empty. The r ee-der should not

t ry t o attz.ch meat:ing to the individual ter:ns in the emi ssion r ate terr:-1

of (10). ~lbe physical ne.:l'1.ings have been distorted by the me:: thematical

nanipulation. ~'he only sign1.fie::;.nt thing to remember :i.s that n1 desc:rib€s

na t hcma tic."llly o.n electron concentrn tion a mlogous to n but ui th the F0rrd

l evel c. t Et e This 1-rill be found useful.

Turning noiJ' to the net ~~pture ro. te for holes , the same procedu.rt;

~-Y be f olloHed i n obtainirtg Ucp .. The r~ te of hole capture is the pro-

duct of hole density, filled trQps uncl a capture ra te t erm, cp . The rate

of hole enission is the prodlJ.ct of the nur11ber of .fiJ~ed hol e s in the

val ence bnnc1., Fv-·.P, empty traps and nn emission ra to t enn . The ne t hole

captu.1·e rn te i s :

(tJ~=.p ).fpt (Et) ep 31

defined a s - N (f.--v- f:t )/!rlr ft = . 'lr e then

Ucp ~ ·f ~ (Et) Cr = .P ~ .lpt (ft. ) cp

I f s teady s tD. t e condi tioi.1s are assumed, the ne t r a t e s of hole a11.d

electron ca pttu"'e a r e equ..'11 u.n~ this rate becomes t he rccombire tion ra t.a .

~ua ting Ucp c.nd Ucn e.nd solving the equation f irst f or fpt and then fc·r

ft : ~+t (£.,) Cp- f t fpt (f-t) c,.::::. "l f p+ (E:t> C-vt - n I ft (ee) ell ~ { 1- tptCEt)} Cp -..p, tpt (Et> Cr = "fft (ft)C,.. -11,{•-tpt (Et>_} C"lr\.

fpt: ~-~-P-t..J!.LC~-n;__ rbb (p., p,) +- cil (Yl+n,)

The substi tution of fpt = 1-ft yields:

fi = _-., CVl + .Pe CP {p Cf+ Pe)+ C~(-r.A··Yq )

vn1en the so expressions are substituted beck into (10) or (12) it is

found thn t :

U = 4'vt C-r-. Cp + 'fl l24- 1J...1P c:- .f:r 1l , CV\C.,_ C~(J?~.f> , ) + C-n(ut+"J\s}

:: ~n -jlJ!to _ __ _

(.P+.-rtl!r.r. + (n-t-~· c}/C~ (n~)

If Cp and Cn, Hhich hB.ve the dimensions of reciprocal seconds, are de-

fined a s the lifei:.imes of holes i n hi ghly n -,type material and electrons

i n hichly p--type ma t er ial re s:- cctively ,

then

U = .Pn = ~,'!!, l-t+t,) t;.~ + (~. {"'(~~ > 'ip(J

" . -·

is 'V'2t lid for ste~.dy st.2. te non-ccy .. :Llibri't::.:'l conui tionc ~ If the product

Pl n1 is Ervalmt ted u:3i:ng (9) and (11) it is found to be

I t is nct-r conver..ient to recall thc'1 t the ficticious ccrrier concen···

tra tions Here descl~ibcd in the &.V.le rr~m1er as the true carrier conccnt.r:,3.~~

tions . Also r ecall trill t the carrier concentrations c:1n be e::presseD. in

terns of an intr insic energy l evel , an int:::-insic concentrc. tion and the

Ferni level$ The reference fer energy has been established as thG Fermi

level so the usual raethod of expressine; ·vr.riution of carrier concentra·-

tions in terms of quasi Fermi levels for electrons ancl holes 1-.rill not be

used. I ns t ead these ·VPriations ui11 be expressed in terms of the variable

tf'• 'l11e Fermi level for tolcs in t he p-type bulk uill be established n s

These quanti ties substituted in (14) give an expression for recombin'.l t:ion

of the foni1 derived by fuh and Shockley:

33

( J s)

This GXJ.Jression DO\J gives the r2.te of reconbim tion of electrons a nd

holes in tho &lr.-.nncl and the ju!1ction transition region cs a function of

the intri nsic Fermi level . This expression may be u sed to determi ne the

current in the crJD.nne.l and the tru.nsi tion region., A correlation of t his

rcsu~ t 1d t h. the depth of ·tlw cr...a:nnel shou.ld :reveal the connect i on if o. ny

betueen cb.annel ctn-rent and dep-th of cha:r..nel.

34

5. Effect o:~ Cl~ nncl c. nC::. Rcco!Jb::;..n':l. tion on Trnnsistor Action

I n sections 3 e.nd 4 the mode1 n for· channel and recombination 1mre

developed ['.nd their dependence on the surface poteutic:.l lklS GiVene rot·l

it is necess&ry to describe Hr..D.t effec.t these tuo phenomero bnve on tho

device a s a transistor e

Consider a transistor biased iD. the usml mo.nner . The enitter-';J3se

junction is foruard biased and tb.e collector-base junction is reverse

bin sed. For an n-p- n transis-tor, electrons are the minority carriers

in the 1Xl.se and r:lD.ke up :2ost of the current uhich flous. IIoJ.es from the

base constitute a small fraction of the toml hot-rever. The ratio of

electron current to totnl cm~rei.1t in the emitter base junction is given

by the emitter efficiency. For a given ,itm.ction vol t.1.go, a total ctu·rent

ei ven by the usUD.l diode eqtm t1on uiJ.l fJ.oH.

l7ou apply a potential to the f,Tid of the tetrode sufficient to

crca te a channel such as described in section 3. Electrons uill flou

from the eni ttor into tho cho.nnol. Eouever this in itself -vrould not ·ho

any cause for concern for it docs not constitute a ct~rent in the steady

state sense. The electrons hcve not crossed a j1mction into the base

becunso the junction effr; cti vely Jicn betvmen the c:b.1.1nnel and tho b::t s e _

But recombiro tion of all electron :::.nc1 c. hole uill occur in tho channel at

a rate depending on t.he stu~face potential end given by ecp .. mtion (15) of

section ft.. This is n t the heart of t.he tetrode 1 s functi oning . For every

electron-hole recomb~1ntion, an electron r::ons t flovr into the channel f·rl"'>ffi

the or.d ttor and a hole mnst enter the channel fror:: the base t.o res tore

the channel to its former smto. 'llJ.':tis is again determined by the surfc.ee

r:otential a s l.O.s shmm in section 3 by eq1..10. tion (5). Th<.c1 electron wllich

cones from the e:·;.1ittm· does r~ot cross a junction and hence does not con-

sti tute current in the sense of tho diode oqu.a tion. I:ouever the hole

cordnrr fron the bo.se doe s cross tbc j,L~_nction D nd heDce does cGrry C"L'Xre!"lt.

The m1:-::her of recernbiw. tior.s H1~ich tz.tcs place depends upon the c'l-12 rr::.f'J

vo1t:J:'tG c nd tl:e rn tc per unit vo1une at t·.·h:i.ch tLcsc reco1·,~)iro tions are

tnkinc: ylc.ce. J~C 1.18 s shoun in section 3 ~ the size of the c:b..r nnel becomes

nearly a const.o.nt very qn:i.cY~y so the r:JD.jcr effec-t is thnt of tho ch7.np;ing

current vas the er~i tter efficiency$ Ttc tot£.1 current is fb:ed by the

junction volt~ge.. Thus for every hole 1.1hich crosses the junction int.::J

the channel , one less electron C:I:·osscs the cr:li tter junction ir:to the bD se

ul".cre it subsecj_ucntly c~iffusc::; to the collE~ ctor r nd becomes collector·

c1.trrent . It is fEdrly en::c.rent th[": t -the more holes ~.-rhic:1 flou into tbc

chc Th'1el, the feuer electrons ·Hill flm: i~1t.o tho bn se and f:ron thE:re tn

the collector . Inc~_ced it is rossible for the 0ntire current rE~c~l'lirod. by

the diodo eqc.lfl tion tc· be ;r;a .:.1o up of holes floHinc into the cho.l~"'lel 'tho.s

re:G.ucinc; ole ctron current (und thereby colle cto:c cm'Ter:c) to zero . This

cc. n r.lso be c.cscrihed in terms of the 8T'1itter efficiency beinc r ecuccd to

zero.

'1.11c current trE'..r:sfer ratio, o< , is the ratio of cru~rent crossinG tha

e:-:1ittcr-b2.se junction to the c1..u-·rent crossing the collector base junction ..

It iG u::n.mlly consic;_ered. to be r:adc up of three factors; (1) 'V, the

er;litter ef:2icioncy; (2) ~ , the b·ansport foetor; and (3)f, the colle(:tor

multiplication factor~ r is norm.e,lly unity for the usual · trnnsiGtor bias

conditions . f describes tbe number of minority carriers uhich cross the

eni ttcr-base jm1ction and the co11ector-b8.se jtu:.ction. It is a measure

of the 1::ir:.ori ty et"'lrricr rocoubinatlon in the b:~se bulk. !:oC:.ern techr~o1-

oz;y ms nade tl'.is fc ctor r.o~n·J~r ur:i t~r also. This lea vcs ()/. as being fe-r

the r:ost ~X'rt dependent on "( • In nocern trc.nsistors this is aJ.nost

36

urj_ty <:.lso ul~icl: c.ccou.r:.ts for the VCl'~r :.ir-:1 liT .lues ol' o< encour.tercd,. It

is true thc.t :

uhere ~ is nou the co1nnon enitter current t:r-C1Esfcr

ratio , not tl:c tr2 nsr_,ort f.::ctor . It can be see1:. trat ns reconbir..2 tion in

the crnnnel dec,-.cades the e:::t tter efficier;.cy, o< is reduced and conse-

quently ~ i s reduced c_ui t e rapidly .. Thj_s 1rill be seen to be ·t.he rosB

in section 7 uhere cx-.pcr iinon·tzl cu1·ves shou the effect of cri d vol Jm ce

en

37

7ho tetroc~o is r :.':' xrr terrl.iDal llcvice :1er.ce, relative to one of

t.he :-- e tcr:·,in:~::Ls, it n2.y be dcscr ibec in torfl'.s of t he current a nd volt~

ago at eo ch o: the rer~5ning trrr·~e terrd.l'1fl.ls~ i'-... s in:!Jle extension of'

the hybrid equations for a t r8.r:ci stor adeq_untely de s cribes the tetrode ~

I n tern.s of the notn t i on of figure 6, the hybrid equations are :

V1 = h11r1 + hJ ~V2 + h13v3

12 ~ h21I1 + h2?iJ2 + h:-'3V3

1:3 = h31Il + h32v2 + h33v.3

The defining ex~ressions for the h- p::tra:moters 2re the sane as for t he

conventiornl transistor p3.raraeters . rote that h11' h12' ha and h22 nrB

vi rtuall y the same p:-.rametcrs as in t he tr.::;. nsistor case, tho only differ-=

enco being t}:t.a t it is also necessary to specify the short circuited e:on-

di tion of the grid (ternil-nl 3). Tho equival ent circuit for t he tet::-ode

·Hill be deYolopod from a ~·hysical interpret.a tion of tho }.Xlraneters., TI!e

comm::m emi tter configuration Hill be used.

Tho vol mc;e at the base tcrmi r.al is made up of three terms reflect i ng

t he conditions of the base, grid and collector .

Ze=in= ~V. ~ is the far.1ilior expression f or the base inp1_,_t, ()I, ~=V3:0

:L.-·nrecla nee and is descr i bed 1-ii th the collec tor

c nd grid short ci rcuited .

is a -voltage feedback ratio reflecting th~

effect of collector voltage on base volta r;e ..

The base is oren and t he erid short-circuited. '.I'hio rurameter i::. mani-

fested in tho equivalent

~ _ o ,.- av. 1 I ""B-A'll.,--

c)V3 I ==V.rO

circuit by a voltage controlled volJwge source .

io also n vol t.age feedback ratio reflecting

t he effect of grid voltage on rose drives

Tho bs.so is open and the collector ohort-circui ted. This r.erruneter i s

38

c /

~· 8 / + .r ! I 1 \.

G l E I

v2.

l t ,··----· --- -____ L ____________ , ··-···--- '· · .. ··--·--------------0

Figs 6 Tetrode syr.:bol and Clu~rcnt->tol t..nee conventions

3

G

! --1

Figc 7 Tetrode linear equivalent circui.t

39

- -1 I z

--..!--~---·---0

c

--'

:1 eontrol .. r;.. ""!(~}\._ r-:e cource.

The co:' lector· c:T.:-01 t is to be node up of t.rJ..Y'ee terr:1s uhich uill c.dd .i.n

is t..he for1~.rcl base -collector short circuit

currert tr2nsfor ratio. It is defined 1:ith

is the collec·(.or o.c2ni tt.o nee since it has the

c1iJ:J.ensions of mhos. The bo. se is open and the

grid sr-ort-circuited for this measurement.

is perhD.ps the most significant rarameter of

ti:e tetrock. It describes tho effect upon

collector current CDuscd by e. potential iTip:t·essed upor2. the hich r1pcdance

grid . It hns the d:l.r;wnsions of a concJ.ucmnce o.nd c.e scribes the grid-·to-

collector trc n:~fer effect. Eence it. is tl:e grid-collector tra nsconc.uc-

i:nnce, entirely 2.T1<l10[0US to a V~"'CUUT.":. tube ~:;rid-~latc transconductance.

It is defined. Hith the base open and the collector shol't-circuitod. In

the ec .. uivalcnt circuit it i;:. sl"'o''7."' as .'J \'ol-tz:e contro1J.cd c"L:.zorc~;,t 13c-urce.

The third br~·nch of the hybrid ecyivalent circlLi.t is aJ.so descrip-

ti ve of a current P nd so ~Jill be mo. de up of equi lla.lcnt shunt. elements o

It describes tl:e comroner.ts of fa:'j_d cmTer.t.

is a bc'lse-gi·id current transfer ro.ti.o of t!:e

so.ne type as h21• Em·revcr, it do scribes a

feedrock factor r~. ther tha n a forl!ard trarsfer ratio. It tal:::cs the forn

of a current controlled ctu~r0nt cencra t or in tho equivalent circuit.

~cq ~132= d~~ is G.r•otLcr feccLbad: cor~C:.t:ct:mce givinr; the 0 dVz

· r~Va:::o effect of colloc·cor vol bge on crid current~

It tD.J:cs t}~c for o:': ~ c 1 cc!' c.rollcc: cuxrcu.t ~oncra tor in the

purposes since the co:ncll.,_c-!:ance is very nec.rly zero through the grid ox.ide

ln.yer .

This theYJ. describes the tetroC.c in tcrR.s of neaslu·able yxn~o.mote:rs

pi·ovidcd tho d.ri'\."'ir:p; sigrol is SI.'lO 11.. It rena ins to describe these p-;.ro.=

meters and their variutionc uith bins conditions . The beh .. a:vior of ·the

tctrodc as n trc.nsducer 1ril~ .. then be predictable f or circ1;.it applicntions_

,· i ..• 1rir

·. l".

~ .. <' ~)lC of ei c.l er D. Cll.lTent ::-;o(e

1 !1. ..~.. L 7 id t j " s 2 T [7- ti ~..,-e, the cu..::Tc n

~.cid ); - '"' ~ .... ncr:a -::,~_vr r '· t ""/~ ~;_e t;= n, or . ,eta ~ !? c ·"' •lc; ·' 1or. 0 , .• ~ C' 11-~ ..) .J..•"> ,. J

r":it~Gl13 l s "Ol.T• J_l"~ 1~~. '( (><"'! (' ('"\ l lG~ 2i .. .re r' c o; s e·w for '!7~:..11-..~ -· ~)

' (... .• 4 u. : ....... 8\

s f1.111c do 1 of ~Tic. ·nL s.

T".i1c cx~,l~rLtior is .2oU'K L'

fi gL"'-YC 5.

r:::.J..on layer.

'2

I = 0. 5 ma.

40

- 2S =as- -ao -s G,t<JQ VOL:t~t· e£ ~£ (~IOLT:J)

t:r-a.Lsf sr r·8. tio n s a function of \:_sc

9 u

~ 0

0 ~ ~

0 ~ u u

~ ., qa

u -0 ~

C«D 0 ~ 0 -.!}

~ 0 ~

e II.!)

c 2 ~ 0 ~

n ~ Q

I ~

L ~

0 ~ 6 "' ~ :1 0 ~ Qf

' ~ ~ ~ ~ ' ~

\ 1¥(, ~

- - - (f;~ .J,ttf;lf}~fl~ !J$~{i ~ \ ~ ~

-- (~) 01.1.~11 llfri~.,Q.L .A~£01~1'1, \ \ laa ...

D b 0 ~ 4 a ~

~ i ...a 0 ~

fit Q t -

~ lltl ~ ...

' ~ ~

~ !(£

:t: ~

~ ~ ""' ""' ~

0 ~ ~ - Q I

~~ .... ~

~ ~ ~

~ 0 II(J) llj

I -a ~ @ ~ ~

~ T ~} ~ ¥J1)

0 ~ <J)

~ ~ ~ 0 ~

0 0 f4.

8 - < Ill ~ 0 ! ~

a II!. ~

45

0

clectx·cn cm'-.:E.J. trc~ tJ..on .. Apr~lyin~ a still ::1m~c .1ec;a ti vc vo1tage u1.1:'t

r 2s·C.cre -~.he ccnC.i tio1 s of fif)L-1Te 5b r n.:::. cvont-v.cll~r bone:. tho levels up-

1;orc' 'tFlti.l t:b.c junction at, the surfo.ce is loss biE' sed than the bulle,

The point of n<:::irmJ..---:-1 ::..~econ,Jiration vill shift further out of the junc'tion

1..mtil fDJ.."t,llcr increc ses in grid vol ta::::e do not sienifice ntly clltlnge the

rate o:: reconbirr' ti.::)l;. i n the juncti::>ne 'l'his o. ccounts for the levelil:.:-;

off of bet.'1. •.rit.l1 eric voltq:5o uell neg::;tive~

1·fl1en the e;-rid voltar·e is :-1ade positive o.. chc.nnel is formed under

tho gri d r~ s sl1our. in fi guxo 5d a nd a region of high reccmbim tion is

formed . :.'D.e r e c01.1biro tion in this re t;io n reduces the number of T'lincr 2.ty

carriers -v:hich arrive at the collector . Since both the ra te of r c;combi.-·

nation in the channel and the carrier concentration in the cb.annel c.ra

f unctions of the emitter-base junction voltage, a tirw va rying junctl :Jn

vo l tc: 2:e rouses a t :Une varyine; recom.bination current 1·Ihich suings about

the recombir:ntion current deternincd by t:.he DC f,Tid bias . This is equiv­

alent to a loss of sigml in the f orm of sigDal cor.1:ponent of rccomhirB~­

t i on . Thus , as gJ."'id vol mge is mude positive , both the a-c and the c>-c

beta a r e reduced . The terr1irla.l value of beta for large positive crid

vel tage is, of course, zero since it is possible to cut. the colle •..::tcn ...

of f by means cf the gTid vol i:age.

'I'he anoma.l ous bunp in the curves of figu.re 8 in the vicinity cf

VGE = 0 a~pear to coincide ui th the onset of cho.nnel and the alnost. bi.­

media te sc. tu.ra tion of the c.epth of the cho. nnel.

FiGure 9 displcys the vs..ria tion of beta as a function of collector

current . It is typical of t r ansis tors to r..nve an increasing beta vs ~

collect or current characteristic, hC'Hever it is o. r:'wntonic f unction.,

The curves of figure 9 hnve an anor.1alous lm.; current behavior, the cause

of ~·:hich is not clear. I n figtrr'e 9 the collector current 't.'as r'leintaincd

1cc-'cor CPYl'Ci' ~ [' r:.c ~':£' sc C'L:.rren-t ·.rE're o.Jlo·. rcc_ to floo. t.. In this irst;J ~ce

nee . These characteristics are o~viousJ~r o.ssocic.tcd. uith the onset of

charn;.e l ana the cl-..nrc:ctex·istics of t~1e chc!;.nel. But it is not ox;Iain=

able in ter:-~s of the s5.r'1ple model bei11..g 11cod here . The polarity of bo ta

is such c.s to gr:c a 180° phcse sbift and so ~sc is positive uccording

to the convention cf figtiTG 7 ~

GRID-COLL!i:CTOn TRA:-scc-DUC'fA.l~CE: The charo.c:.eristic vrhich sets the tot·-

rode a}l'lrt fro:c1 the present frrrrdly of trc.nsistors is that, like w cuur:

tube sn:all si1:;nal amplifiers, it d.rnus no pouer from the signal souxc~.

This is 1Jrought about by the insulation of tho surface of the cnittcr­

bo se d.iode by the si1icor:. dioxide t,'"l"id and the effect on collector c1-tr~

rent of an electrostz tic field i mposed on this oxic.e layer . In tc.rns of

equiw.lent circuits tl:is is e voltage controlled current source in the

coJ.lector and describes a tr2,rtsfer chargcteristic or transconductance~

Figures 11 and 12 shm.r the "{.raria tion of the g-rid transconductance e

?iC' ... U"G 12 p1ots transconducts.r~ce as a function of collector current ~

Fron zero at collector cutoff, tho -t~ansconductDnce increases monotm-:;­

ic2,lly \ri th i~creasil:.g collector CtTront., Hhon collector cDrrent in­

crco.sos, it is the re m.J~t of en incree.sed bins on the emittcr-'xse

junctione An increased bias as 1.-re have seen chsnges the c:r..c.racter ·Jf

the channel and the :ra tc of reconbi rn. tion in the c"b.Rr~nel. Spocif'iea l ly ,

the position of the point of m.nxj_rmrn recombination shifts Hi thin the

chn.nnel . Since carrier concentration, conducti .. ,;i ty and recombiriD. tion

r[: tc cere 2ll functions the s·l'rfc.ce potential (ancl hence x sc bie.s) the

2~~~---

24

40 r c. = 4-o 'llt}a. ~ ...

t1

~ I,::: JO rn~ ~ 20 ~ c.,

C'\

~ t q Zc::: 2D rn~ ~ 16 ~ ~ It\

~ "

y 12 Ic=IOma.,

< )( .... 0 .., '-'

8

46---

5

Fig. 11 Gri6 trc.r.::;conductar~.ce us o. function of grid vol wr;o

Fig. 12 (~rid trnnsco~du.ctnnce as a fu:rction of coll0ctor c1.1rront

totnl rccomb~_r.c"tion currc:n~t chanc;cs, as ucll us the slope of the recom­

binl.tion curr m1t vo. -~otcntic::\1 ch.1ractcristic . Since the slorc of this

characteriotic c~etcri:lincs the chanGe in collector current for a chnnge

in r;ricl vol tD.r:e, in ef fe ct it de ternines the trans conducta nco of t he

[,Tid.

The chance in trnnsconducto.nce Hi th srid volto.. : e is given i n fizux·e

12. I:ero i t is noticEd that the antithe s is of the beta clmro. ctcristic

takes place. For a negc::.'. ti ve grid vol to.. c;e the chs n~cl i s olin irn ted en­

tirely D nd a tirnc vnrying small si5Y1..n l on t he p"id uill produce no change

in collector ctrrrcnt. 1be transconductance is zero. As sTid bi as is in­

creased from a l a rge no en ti ve value t01-:urd positive it'D. lues, a channel

forrt1s and the cr..e.r2 ctcristic r c combimti on current begins to flm-1. If

a time varying sigrJB l is supcrimroscd upon the e-..cid bias , the rcconbira­

tion current 1-rill be modulated ui th this S[a.:.c tine variation. If the

base is biased fron a d-e source, the modulation of the recombi11aticn

current Hill a pp0ar as a oigno.l in t he collector circuit. The transcon­

ductance incre ses rapidly and then levels off, indicn ting t ha t the

oper ating point is en t~1e broad , fairly straight side of the recoDbir.,o.­

tion rate curve. (It is t ho slope of the r cconbit1..n tion rote curve uhich

prcdm:1ilnntly deter n incs t he transconch:.cte.nce.) In tcr:-,1s of fi rruro 7 >

gGC is negative since there is no sigr.al phase shift fron g-..cid to collec·­

tor.

li.s in ihJ co.se of beta, an anomalous behavior around zero volts is

observed. Houcvcr t here are t-t-.ro anomalies instead of th~ one previouoJ.y

encountered. There are several plausible expla Da tior.s uhich involve the

levels of recombi1~tion centero (traps), recombination r ate vs. s~~face

potential and the onset of channel and its saturation in depth . The

real c:::plenr.tioJ::. is probably sone adJ.nixttu"c of all of t hose but in o.ry

50

event) any such conclusion 1.'01..lid r:ot be supported by experimental evi-

dence in this p:1per.

The transconductance appears to rea ch a maximum at approximately

five volts and t hen starts a slow declines An inflection point in the

recombina tion current cf1..a r acteristic has been reached and the slope de-

creases as the recombimtion current tenus to·uard a maximum.

It is interesting to com:r:are the magnitude of transconductance of

the tetrode with some typical vacuum tubes:

12DS7 • • 15,000 rmhos 12Dt\8 c • • • 15' 000 r mho s 12DL8 • • 15,000 tmhos TETRO DE ~ • • 20, 000 Jmho s

The semiconductor tetrode compares favorably as can be seen. Its obvious

limitation is its pov1er handling capabilities although the free air dissi-

pa.tion of 0.8 ·Hatts and a collector breakdovm voltage of the order of 100

volts speaks vrell for the tetrode.

GRID AilHTTANCE, yc: Coupled -vii th the ability to control collector cur-

rent by means of grid voltage, the impedance level of the grid is a not-

able characteristic putting the tetrode in a category of electron devices

vrhich includes vacuum tubes. As announced by Dr. Sah, the input admit-

tance was that of a very low loss capacitor of the order of 80 pf. There

\.Ja.S no change in admittance levels noticeable 1-Ii th the change of any d-e

bias condition. No change in the loss coefficient 1..ras noticeable from

d-e to 10 megacycles. This property is, of course, due to the very good

insulating properties of the silicon dioxide layer 1-1hich grovlS during

the m~ nufQcturing process. Such a hieh input impedance opens areas of

circuit applications here-to-fore held to be the sacred domain of vacuum

tubes. Included are such applications as operational amplifiers, PAN

. -.,

:i.n:'""'cc'J.c_pcE is 1i::;t·nlly tLouc~ht of ns beinc made up of t;.·o resistors in

. ,.,.,, ,.,. t . r I tl t.. • re~.; -~~~nee f tb , 1 ,, , . serJ.es . ..._1e 2..2:::-s · J..S bi> , 1c or!Y,1J..C ::.;_._:.; LM o .c rose )1:-LK na "Lc--·

r ial r.nc~ t.ho second is the res:ts-i:<?Pce o.ssocinted 1•ith trc cctivo jt1nction ..

I n the Toe cqtl.ivclcnt of the co:-17-~01: e2'1i tter co1l.fic:uru. t.ion the resist.£> nee

of the a c-'Gi 'V'C junc-z,io:r: ifl COI1y:'OSCG of th.'1 t }Jor t.ion tlu,ouc;h lThich orJly the

base ct1rrent flo1!s o.ncl that -'cLrou;:h -.,hich tho c:rJ.it-'-,er current flo·'s, U:n.t

res~ectively.

the vol tac;e c"i'op I~ rE 1-:hicl~ is co:1J11on to ~)oth the l)2.se and the e::i ttcr

circuits may be represented in the oose circuit as (p+l) IerE , e.n ec~t·iv­

alent re s i stD.nce (p+l ) time s as lc.rge . r o-vr rb' i s the r es i stance of t~le

fol .. vro.rd bic:.scd cri'li ttor- ba.se diode ::1.11c.t rJJ.Y be eJ~lJresscd. as :

reglocting the reactive component of the bc.se input i l"1pcdc.nce CC'used by

diff us i on cape citnnce, the ex~;ression for the res istance cc. n be ~r.ri ttcn

as :

This expression conta:i.ns ~ .ri thin itself the cxplc.mtion for the observed

vnria tion of r a ui th bi& s conC.i tions sho·.rr: in figtrrcs 13 c.nci 14. In

figure 13 i i:. i s observed that for lm; ct,~"rer.t the base i mpedance is sev~

eral thouso.nd oh:!ns but dr ops very ra:~:tdly to a sn tura t i on level for-- Ci.tr·-

rents noo·"e a n ill iam:o . Usinr.: collector cm,re l".t c.s an c.p:"ll'o:d.rilation to

cmi tter c1:2.,rert, it is see r: t:-£.t the se cord ter:-:1 of (1) i s very lc.rge ..

f or very lou current ~Jut drops to ?6 ohms at. one nilliamp . Thi~: is t.l~s

fc. c tor uhich C<.'1uses rc.pid cho.rc;es il1 recistance uith colle ctor cu.r:roT1t.

r otice that the curves for ncr-:ctivc r-rid volt[:_~e do r..ot c~rop as rcq:;idly

52

'

4.011"": --

3.C~ ....... -

2.S

'""" c: ~

~

1\1 2.0 tu v < ~

~ 't ~ 1.5' ... ~ ~

~ lu ..., ~ /. 0 'b

0 10 30 40

Fig. l _ n:::e rcsisi:c.P.ce as o. fr:1ctio::.--. of collector c1.1rrEmt 53

50

BASE INPliT RE$1$ r>4JJcE ee ( k ..ll.)

~

~ d (:j

"' ~ ~ ~ ID 0 ~ 0

H 0

~I II -.11

~ Ill ~

~~ \oi

51,

C)

N

'

~

'

----a tie

'

0 _, __ ,

-t -.1)

C) '!:lo '-~

~

"' \t)

oct .... ~ 0 ~

() -Qi \!}

c:ri( vol iT.:~c::; but

~:hoE collector

o.ch.19ll;:; occtTs is Sl.lr·r··cstcc~ h:, ·I}~c ncr- ging of thE: curves · ·hen ~Tid voJ.t-

The coJ.lc ctor-bo se fccC::ba ck ratio ir f-1-~ VJ.:.•.J

tetroc~e :L::: <"'~ro.loc;Ol~:J to the ::;;;.r:e ro.rnnetcr in ordi11~r;y· tro. nsistors . In

the CO'V1011 e:'"1itter coruir·1_'J."'<:'..tion this intcrn'JJ. feedback ic positive .

l'£1l cc.usos tJ~c collector jm:.ctioi.1 to s:Tcc.d into the !)use . This rouses

currcn:t. Sil:.cc tlw c1ittr1· cv.:;."':ccnt is c~ircct.:.y re1atcd to tho ix1sc

l.'cl·t:ace ~-~~r tl~e diode ec:l1D.tion, this cba1:.ge CC"'Usos nn increo.se ir. forr.-~rd

bic:..s or tlc€ 1?1 itc.er-1X-30 jul~ction. 'll1us it c2-n be seen to boa positive

vol t:;c .:'cE:db[. c': in tl:c cor1u-::on m.1i t-tcr co1lfio.:rra tion . ;_:'his is &lso t:ruc

of trc' tetroc1c . ::?i[;,_u·cs 15 un~ 16 shmJ the V'<e1l"'i8. t.ion of collcctor~ba se

fcec"Jx.cl: rc.t:_o c1.s functio11.s of collector current c.rC::. [f.Cid cm:'rcr..t. rcs~'cc~

tivcJ.y .

lou collcct.o::t· ct:rrent::; rc~-a ti ve gricl vol mccs' tr.c fccdbo.ck

55

56

~ <;It

~ .... ~ ~

~ ..... ~ '\($

~ ~

< 0.

t.JJIJt) ()IJ.l9 1n~llti~'U Jl$11(1 At fi&~S"f'V@) .. t I I f Dt 0 ,,

I UU i ,,

:f ~

,-... ...... ~ (f) ~ ... . ..,

-J ~

() ~

c~ lt.

~

l.U ~ ->? ~

"' a

"' {;:

~ "t

t4looll ~

t 0 ~ ~ ~

~ a c~ - ~ ~ ~

' \0 ~

"-·

' ~ ~l.!l

c:t ~ I ~ -

9~ s, 0~ 8~ ~ ,n 18

.:

t ~ ·~ ' h ~ ~ il 09 OQ ~ .; tu

D-0 we

e thl

Q! e

.I

~

~ ~ ~ e ~· lltUi ~J ~I

'~ u

\.!£} - """ Q ...

~ C;:,

\.A,..

57

ordirar;;· t.rc r_si;:;toro -::- Fl'icl· reinforces -'cL8 notion the. t tho totroco oc-

l1::->vos ir. the v.m .. ,.el trrrsistor :rtlc.:nrcr ubcn c;ri<.1 Yolto.cc is nor,ntivc.

O::.ce collect or current :·cts r.~)ovo c::':)out 10 me, tho feccrXtcl~ ra tio is

insCl~ sitive to ei thor grid vol i:.u,:;c or frrtLm.~ increase::; i n colle c t or

current.

\f(loll the g-rid voltaco bccones positive and the surfa.ce chrrnnel io

forr.1ed , thE: feedback ratio ch,ops rcgc;..rdleso of collector current. It

can be seen fror:1 fi g·urc 16 that for grid volta c;o geater than tuo volts,

tho feedback y:o.rancter is essentially constant. In t his respect, t he

stu-fo. ce cr..annol act s in a manner analogous to c. stlr(;C -b11..l,: in a fluid

system. As the chan&e of collector vol tn ge changes tho concentration

gradient in tho base, this char..ge is reflected in a cha nge in the rocon­

bina tion rate in the c:b..:.rmcl rreferontiaJ.ly to a chanGe in bias acro ss

the emitter-base diode i n the bulk. In essence then, tho change in col­

lector vol t.ago may be thought of as causinG tuo opposing foec~OO.ck effects:

(1) tho usuol interr)[t l feec~bn cl: (positive) and; (?) a r..ec;ative fcodbac.~.<:

Hhich is c. function of gTid vol taco (r.e[,-a ti vc).

GniD-IlA.SE li':EEDrACK Rli 1'10: This r[l. tio raoasuros the effect of a sigr.nl on

the grid in tho bo.sc circuit. Hith Grid voltage nega tive ::nd no ch2m-;.el

f ornerJ, the fceclba cl~ is thut uhich is associated 1:ith tho C<l]Xlcity of tho

mci::J.l-o:xidc-ser1ico nC.l~Ctor sand1-.rich. lJi th increasing grid Vol t.age the

SUl"fc ce cronnel forns . A si2ml applied to the grid moC:.ula tes the rc~

co111bi ra tion current in tho channel. Since this current reduces tlA.c cur·­

ront crossing tho emitter-base junction, it is reflected a s a reduced

junction voltage. Since a. rositivo chango in grid volta ge decrea ses

junction voltage, the feedback is nega. ti ve. In po.rt, this feedback nay

*See, for instance, GE Transistor 1-.:anual, Fourth Edition

58

t -"'""' '- ,

r ~_v '"!.. '· ~ \/ ._ J. '..A.

' " ~--1.0

-., ..... ,_,

( , .... "'~ ......... t .. \...""' ...

. . '

~·"lc· '

.~ .. ;.t.o-r

1 i. ~: 1--;)~

- ' L,.C.a(:. cet: ;:;c-.:~~

ll ~oci i!l tLu

\"' f ) . ; ;

v '"' , __

lJo.. 1 J.

/.

- .(..., t. •

I

i I I

..J ~

I~ I 0

~ 0

c.. .\...... ~... .. ~ • .. r.,J

_\ ____ , ,_., .

...., -,

:.~,~t_ -.!. ._. ~ 'I

~ vol +£..ge co.ill ,

po!'dcnt of th0 conditions Hhicl1 exist o.t the c.cid and cvllc(!tor . Ass,.l.J.c•

tba t tlnre is o. bOUrc-s 'Jf biaz ::n·,J. a sigu:l pouc i' :n tho '~-Jase <:1 rd g:riG.,

ca.ch 'l·ri t h an 2. ssocin ted inpcdance , und a lvo.d inpedo.nce in the collector

cu.rr']nt as sl1mrn in fj_r;ure lG . :<'roLJ. this ec.:.ui·vc'lent circnit i t is p ... •s·-

ternir•nls ir: the C-')b'!cn cr:dtter c.orui.cu:·ution. 11-c dm~ivation of tl:i::;

tl

~r '..., ~----

' 1 .. I_ ' " .J ..... .L

colloctor c1.rrrents . (:;o ::-on o:~.ittcr o..:.tptLl inpcdcmces~ 1/y:J ~ b.aye h0~.1r

the llt'.:.'10ro ·::,or of the ..Last p.1rt of the i'1~ in e:xp::resnion '.rould bo very ~.£.:J.

gGG is C..})pro~dn~ te1y zE:·ro ~or noga ti ve grid vol ta.go so tho donomin.:.\ t.or e:f

tho lc.st brc eke ted oxrression l~ unity . The product Yc-P'-.J is nearly :.r:I'.':'

since Yo ic os0ontially ::::oro and Rc is tho lnpcdalKO of a d -e bias sc'/t.n•e.;)ft

}Ga is essentially z0ro for this c.nso as is shOim by figtu•e 17 . ner.ce

r or th0 C8. so oi' lo.r eo ~10gc. ti ve grid voltage' : i ~" retluco s to a pprox1-

ma tcly :

In the volt.o:,c moC:.e tri th lnrge positive Q."'id vol taco, the bO..BG

i.fOtLld lx: oporntod c.t ~> c ground aud tho ~:u.se inpnt impodDnco is of no

inportar.ce .

ThD grid il~f;".l.t ad.mi't'U"lnt.:,e is de:r.ived in ~\ppenllix 2 and is given by:

This o:;~!·ression is uneful uhen tho tetrode is boinc used i•l the vul t£.1.~(;; 1

or grid input , node . For this covdit,;_on tbs [;rid biL.s is larce und

(J

... x. '

... ,

, . c.:. 'I ~-!.,.. :..~t.

forn :

ly cont rolled by Yc· There

.,... n,~, 'l:r "'·~ ..... .._"'-_· v G :1.: .

csser-t-ic:.ll y u::1ity; ~ec • fr.B is a.~~}_:':'.;::1.~12ts1y Oo2 for I c ~ l On:-, .J.rd

1

R '"> + l 8 :i.:: of the ordr:r of lO'+. Hi th ttc se a ppro:d.r1.a t :ions , Y O\'..t L.:: ::•'~· u; ~ ,_J

I n t he volta ~c ncC.e frsc &nd VB e r e appro;::ina't,c:ly zc:ro •

.. 4.. s before , YC is seen t-:) ;..;ct the ,--;r~::s -:w.l·Go of the out:mt ndni·ti:.:;.r ..

The vol tage mode gain expression is given by:

Av " C pec/'36 f,. - ~ \c (Rp~e) p':..l_ f- ~~0 R, ·:! \,.( l ( R. +t B) { R, ';!< + 1) -· fs• j" $ R· j l ( Re +r8) (R.. ~,+ 1 )-fee./'•'' '·\( ·v1

and is derived in Appendix 4. Large positive grid voltages drive

to almos t zero which immediately simplifies this expression to:

JGcRl.

R~.-. ~c:+ I

This is identical to the vacuum tube expression for gain. It must b~

remembered t hat there is no phase sijift through the tet rode so gGC is

a negative number according to the completely arbitrary polarities as=

signed in figure (18).

Current gain in the current operated mode i s g i ven by:

Figure 11 shows t hat gGC goes to zero for large nega tive gr i d voltages.

;. This defines t he current mode and current gain simplifie s t o:

.. (~

A; = t' B.:

The expressions given a bove describe the tetrode in its t wo usual

modes of ope r ation for low frequency~ small s ignal operating cond ition~.

They should provide the circuit designer with an insight into how the

tetrode will r espond for a g iven circu it a pplication.

65

9. Lisccllc.ncous J:otcs '~-Del Clx;crv~ ·0ions

7he tetroc:c c::_'".ibi tC'd 'cno cL.~r.::-.ct.C'ristics trl~ich, if r.ot kept i

n ir:d, mi ght deotroy the c-:cvice or r;rcvcrt o. circv.it fron o:rxrc, ti~c

properly. The first of · these is the effect of br'.se c1..1rrent on total

pouer C:issi!\-':. tion e.nd tbe seconc.1 is an observed bic.s ~;oint instability .

The tetrode co11ectoT c11rrent !:Iny be cut off by the o.pplico.tio~1 of

a sufficiently hic;h positive r;ric~ voltD.~e . This does t~ot ncan, 1-:.m··:;"'/"r..,

thnt base and er:.itter c;__u~rent is not f)_oHing . Indeed , quite c.. l arce

recombinr::cion ctu~rent no.y be flmring in the chcnnel. Thi s can be selr=·

erc.l hundred r:dllinmperes under so::-:12 conditions. The potential dif'fe:l."~

ence through uhi c~1 t his current flm.rs is the emitter base voltage e 'Th<:o

product of ·the tuo is the pouer being O.icsircted ns o. result of roccn·­

bi'fi..D. tion and this c.ppenrs as lc ttico vibration or kinetic enereY of thE:

crystal o.to;ns . If this po'.~er exceeds the clissir:o. tion cap bility of tht":

device, clestructj'_on uill result; and l .. ritl~out ever having draHn any polrCL

at c..ll fro1:1 the colle ctor source. Thus i t ~:Jeco:-aes o.~1parent that caro:S

nust be t.'11~en to r,1oni tor collector current, rose current, emi-~ter-oc ;;2

voltage and collector-base vol to. r;c. The tobl pouer being dicsira ted

is t hen :

ui th I:g no longer ncgJieiblc. Cor:trnst thi s Hi th the old rule of thr1nl: ;­

p = VcEic. It is obvious tl"fl t the circuit desip1er Hill have to be 8i-:<:T.?

of this r.itfo.ll uncl nindful of the actual physics of this device rather

t1nn relying u:p::m the 11 rr~e of thunb 11 methods of desi rn uhich sec:'\ to

hove gJ."'oun v.p Hith the trc.'l-:s i stor .

Bias :;;oint i:rct~J.bilit:r HD s first ooservcc,_ '.:hen the lou collector

current c.-c bc·::..C. 1:Lo beiP~: ir~:esti co.tec;_. It u..:o noticed tho.t foro. Sl'i'f'n

66

col1cctcr ctP ,,. J y •.~o1t , coll c ctor currc 1 t r nd co1lc ct.or i~ . 'C 'r neE:~

ini tiol co1x"i ·Lior'.s cor~C::. he rcstcrcC:: :]y ,·}'[' r~~.1:.c tho be ::;c cv.rrcnt.

~i1Jilc r.ot c n nr:cx":c cte<.J result oL the st'Tf<- cc, it ~~ro :::: Cl:.ted c n unc~cs.ir-

2bl o foc(lx c\ f uctor ur.l oss it could be elimir.cted . Fro:-1 c,n c -c swnd-·

point it uas found thn t the focdb<: ck could be eli:-1.im ted by t he ud C:J. tivn

of a by- ressod r es i s tor in tho enitter load.. This is tho sawe n.p::-;roach

as is 1.:· .. sod ir~ self bias rob;or!(s i n both tubes and. t r o nsistors . liO\·~cvc-c- ~

the philosophy of uhy it uorks is not the &'me .

Essentia lly,. chEtneing tho G,rid voltage chnn[;es tho C::. -c bot.~ cr-0.

hence Ic. Dut d u::TGine Ic rosul ts in a cho. nrc in tho cormon cn i ttt';x-

in~ut. rcsisW.nco us 1rr s c::~-Ja inoc: in r::oc t:~on 7

If c r o ::d.,si:D.ncc, RE, is pl Rccc:l in series ~. iith tho cnittor, this oxrrcs~

::;ion bc coJ11es :

Since ~ ! 8 = I c , it folloi·m tho t for initial conditions ~·I a,= I c.~ m:.J.

for finol conditions (after grid voltc'1ce cho.ngos), ~2 Iez.=Iu .. .. If tr.:.c

grid voltage cbnnge ::i.ncro2.ses p 1 and IB is from a hi gh inpodo. nce sour-ce)

JB uill r:ot clx· ngc significantly been usc ~ 8 is a small frac tion of tlw

toml i nped.cnco in tho base loop . Iroltcver, if IB is derived from a lm;

inpedc.ncc sotu~ce, I B co. n be no.d.o to 11 tru.cl{ 11 (3. This i s shoun to be tbs

caoe i n t he follm.ring ornlysi::; . 'l'ho de sired result is Icl = Ic2. Refer

to fi Q7TO 19 .

Ra, = Rs + r8 + (~,+1) (If +Re)

f?ez.= Rs + ra +(~+f) (re-rRe)

I _ Vs s,-­l?et

=

:::

Rs + r9 ... rs

l?s + r8 + re

Ia2 = Va Ra"Z.

67

+RE + ~.(re+R~} + Re + ~z (re + RE)

I I r~,b rb ~

Rs ~ (p+•)rE

I I

Ye -!

(~~I)RE

I I

i

:Fig . 19 ·~o_:~oE c :i·::,tcJ.."' Tee cc"u.i'\ulont base circuit :~cr: ~ cc-tinG fccc"roc]c tcr s

r ou l et Pz=~ 1 +A~ '.'l~ero-6~ is the chr~ nce caused by D. cha~1gc in Grid

vol tagc . Then :

Ie2 = ~ = Va Re~ Rs + re-+ rE + Re ... (~,4-t.p)(tE+RE)

and ~1 Ia1 = ~.J8z +AP fez if the desired Ice::: Ic2. i s to be achieved . In

order to do this, it is necessary to make t he r atio I B1/IB2 as nea rly

equal to ~~~~~ as possible. Therefore i t is ne cessary tha t:

~! Rez ... I?$+ Y8 + rE + Re .,_(~A~)(JE +l?r:) Iea - Re·, ·~ ~ - -R; + ra · :;·~-;·RE-1- ~· (r;-~·1?;)-.·

be as nearly equal to (p.+Af)/~, a ·s po-ssible. If the d-e beta is rea son~

ably large (NlO) and Rs is very small, it can be seen t hat roking RE

large vill reduce the above expression to:

as desired. Hhen tested, this technique 1-.ras observed to almost elimira te

the bias instability previously notede By-:r;assing Re ui th a ca:raci tor

alloHed an a-c signal on the grid to have the desired affect on betn

uithout changine the d-e bins conditions.

69

10. Su:r.u:r.ry

A ncu scniconut'ctor cJcvico kroi.·:r"'. ::: s the surfuce-r:otentiol corltrollcd

t r n DD i 0tor or semiconC.uctor tetrode has been described" The underlyi ng

physics have been laid out to aid in the understa11dinc of hou it obtains

trnnsistor action. Tho device is characterized by a hiGh i mpedance tcr­

mirol to uhich a potential may be applied to effect control of collector

current.

The description of the device in terms of a hybrid set of parameters

v~s aiven and the behavior of these parameters under varying bias con­

ditions liaS investiga. ted. Based upon these investigations, the descrip­

tion of the tetrode as a transducer was derived and discussed.

The tetrode is not a commercially available device hO'\-Jever, uhen it

in marketed it offers great promise of a pplications previously barred to

semiconductor devices.

70

I

.,

..L. C. T. ;,::._ ~1, H ·c · ;c--~iccrx!uc-t.or 'i'ctrcc·c--'l.'hc .::1-L:..cf: cc-~ot.c1 t~.c:'_ CortroJlcc '_:>rc. Ps:l.stor , :'J:oc" I:J.:S 7 ·rol. !/", ro , 11, -::-'9 · 1~~.?-::-'.'., }""ov . , ~ n(.:L.

A. I. : :c:Tt1orter 2~cl TI. r . Finr;stc.r, Ch~:::1E:'l:J one: :.::cess Hovcr:::;c Gm~roPt in (\'o\'1~ ncT>"'C.niu.~ r-:· :r..1 ct:Lon. :0ioC.c:::;, Iroc.. 1-:i.E, vol. 1:.2~.

no . 9, pp 4 1375-CO, Se~')t,, 1 C) 51: .•

3. 11. L. Dro~m, r-Ty;'e .swfoce Co nc:uct,j_vity on r-T;r~:o GcrLG1lil1J')J Thys. Rev., vo1. 0J., p . 5lt') 1 Ancq 1953.

4. J. T. L:: u, A : :echa.nim:1 f or 1...Ja. tor InducoCi ~~:cess Reverse Ihrk Current on Groun Gor:::c.niW:l r-r Junctions, rroc4 I::?.E, vo1. /.,.2, To . 6, pp . 907-13, Juno , 1954.

5. H. Cln--ister; scn, S1.1.1·fo.ce Conduction Chonnel Thenomem i n Gormaniun, P.rcc. mE, vol. 1:2, r:.o. 9, pp . 1371-·75, So:rt., 195/~ .

6. J. Bar doer , SurfEco States and J.cctif icc.tion at a :·owl So;Jiconduc­tor Contc.ct, Ihys, ~cv ., vo1. 71, p:r . 717-27 , l o.y , 19!.,.7.

7. H. Cutler nr.d H. l~. ::D.. tb., Sm~face LeoJ:ncc C'UI'rent in Silicon FuscC. Junction Diode s , Proc. IRE, vo1 . 1:5, no. 6 ~ pp . 39-43, Juno, 1957.

S. R. II . I~iq;stor. s nd. S. F. rcus"tr:dtcr, Ca J.cu1n tion of tho C~co Chnrge, Electric Field, 1:1 nd Free Corrier Co nccntr u tio n at the Surface of a SeTlliconductor, J. Appl. Phys., vo1. 26, no. 6, pp. 718-20, June, 1955.

9. H. Shocl:ley, Electrons and Holes in Semiconductors, D. Van rostrand Co., 1950.

10. H. Shocl:lcy and :1. T. Read, Statistics of Recor,11)iration of Foles and Electrons, Phys . Rev., vol. 87, pp. 835-/~2, Sc::;t., 1052.

11 . c. T. Ss.h, n. :·. ~·oyce, an6. Tl. s:1oC!i:loy, Cc.r ricr Generation and Recor:1bil~n tion in P-1' Junctions ard f-T Junction ChnTa ctel~:istics, rroc. mE, vol. /.,.5, r:o. 9, rp. 1222-1~3, Sept., 1957.

71

v2 = ilsci, + Cf,c Vl) RL RL ~c +I

APn~:-nrx I

CO:: ~or; TI ~ITffi1 COIJI'IGtRJ~ TIOU

Refer to fie;-t'J:'O 18

V3~ v ~ + l?.:r ~(" v2 t ~8£; ~r~ ~ RG ~G + I

3ubst:ttutins t he expression for v2 i nt o

Using this result to solve for V2 ~

Vz = RL ~Be 1, + ftGcRL.l [Vs ~(-~!~~)I, + ~8S R~ r~ RL ttc+ I ~ ~5+ '~ I + R..'#'- R&I?L ~c.<>1&t. J

Substituting these expressions for V2 and V3 into the original expres-

· sion for V1, it is found to be a function of I1 alone~ Since the ra tio

of V1 to I1 is the input inpcclance of the base, tho solution may be

found:

72

T3

r~ = p Be I, + 1a ( v 3

V2 = ( ~ s" r, + t ~ c ~~~ ) f(!. tc.... )

Refer to fi_r_:P.re lS

I~ == Va- fr.s ~ - t:G e V3 Re + ls

Substituting the e::pression for v2 into t he expression for I 1 :

Substituting those expresji ons for v2 and v3 into tho origirBl expres-

sion f or r3 , it is found to be a function of V3 nlone. Since the ratio

74

75

.,.

I~cfcr to f:Lc,UJ.'G 18

In~ J[a~ /~G@ ~ -1;~5/v~ ;

If?~+ fe

Substi tut.ing the expr·Jss.ion for I1 into the expression for v3

sion for I2, it is found t/.) be a functio:1 cf V2 alone. Since the ratio

76

77

v~ ~ (f£cJ t {!- ~~c ~} Rfr, Rr.. ~ ·t....,.'

l g' Vs = l~•C8 vt2. ~ (6B ~ Re: + t~

Ita , _ r ~at ( Vr~ = po~!t.. -r4elll) ) + ~li;~ ~~a] R'l.

[ ri'e + ~a : f?B.. ~~+ r

: = Psc. Vv Fh, ~ ]:roc~~ R~ ~ +__j!J~frueRA.V.~ _ 2o~Rt Vg (~at-l~~} (Rt.. ~c+l) (Ra+le) (P-9..6'-to)(t?e+le} (~&.~f:~·b){fi'tl<+&@ {l?t '2f~·H)[Re'f."i~·,}

[{Re + le ){/i'. ~,.,.. ) - p Be. tc tl ·!?;] vd, :::;_· ffetjl~ll /?. -1&<1i'L (~•le~ 113 - ..J!.!!.c I? .. Ve .

(R~+ta} (R'L~c+l) th (~G+es )(R&,~t+f) "j (R8tt.8}(itt.~~ .. ~)

/hr :. [l::=J'(e;e{(;: ~r£JC lRr... ( Re+-l's) J ~ f _ pe< Rt J V~ {~+co){f?J.~G ~')- P'ir.fce R.t. [fs+l'e)(Ra.~b+ i) - r(JCft!J t?,. v3

A·-t. -

79

thesF887

Investigation of the characteristics of

111~11~11111~111!/llll!ll~l~illllll~i~l~l~