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Unformatted text preview: CHAPTER 14 15...]. {a} MS. Schottky, and Hot Carrier are just alternative names for a rectifying metal—
senticonductor contact. Hot Carrier diodes are typically small area devices. {b} If (DM = x in an ideal M5 contact, the contact is borderline rectifyingfohmic independent
of the semiconductor doping. (claim; is computed differently.
...In pn junction analyses it is common practice to take V = t} on the p—side of the
junction. In MS work the semiconductor bulk is typically employed as the zerovoltage
reference point. (d) Thennionic emission current m majority carrier injection over the surface potential—
energy barrier. {e} Since IM.H+5[VA} = IM.—}S{ﬂ} = 45041.1{9}. the Mar—15 component is obtained by
evaluating the So—tlvi component at zero bias. (f) The diffusion capacitance and crmductance arise from the ﬂuctuation of the minctity
carriers stored n1 a quasincun'al region adjacent to the depletion region. The minority
carrier storage is large 1n n fonvard biased pn junction diode and leads to a signiﬁcant
diffusion admittance. In an MS diode there is minimal minority carrier storage for
operational forward biases. (3) There is a minimal number of stored minority carriers to be removed in going from the
forward—bias “on” condition to the reversevbias “off” condition. (It) It is a special circuit or fabricated—in arrangement where an MS (Schottlry) diode is
connected between the base and collector of a BJT. The arrangement leads to a signiﬁcant
reduction in the turnoff time when the BIT is used as a switch. {1} l[Cihrnic contacts are usually produced in practice by heavily doping the surface legion of
the semiconductor immediately beneath the contact The device structure is also routinely
anneaied (heated in an inert atmosphere) to minimize the contact resistance. {j} “Spitdng” is the nonuniform penetration of Al into Si beueath an Ai—Si contact. (See
Fig. 14.1 1a.} 141 14,2
(NUTE: In the ﬁrst printing, all of the semiconductors were erroneoust identiﬁed as
mume. Combinations E, D, and F should have been labeled as NA doped.) For a given combination, it is ﬁrst necessary to determine the nature of the contact. This
requires that we compute IDS using 1's = :1: + {EcEFJFB E x + 56” _ (EFEﬂFn Hominid} ntype
—tT1n{Ng.’ni} ptype
Doping n1 EF—Ei Eﬁfl
"m (cma} {m
”—m
Gt: 3 5
—ﬂ' [1915 (En—EiJFn = { ﬂ—nm
“—nm H.293 m—
unnmmm
nn—— um
I: n_ 41.535 Noting the semiconductor type and whether (I’M : tlts or IBM a: {115, the ideal nature of the
contact is deduced by referring to Table 14.1. Part {b} argument
similar to similar to that in
Fi.(bJ.Exer141 FL. a}, Enter. 14.]
Fi_. 14.2(b Section 141 ' 'n Fi. (a), Exer. 14.] Exercise 14.! Fi . 14.2(d Section 14.1 l4v2 M (a) ‘1‘]: = mm— 3; = 5.10— 4113 = Li]? «W (b) (E: — EF)FE E Eoﬂ — (EF" EtJFB = EGR  JET 111(Nofni}
= {155 — {noosajtnuolﬁnowj
= 0.215 EV m = é[oM_ (Eu—5mm = LﬂT—ﬂlﬁ = 0.31 v (o) VA = ﬂ ttotlor equilibrium conditions and
m 14 ”1
“FE—5'3“ vm] _ [2(11.E}[3.35x1ﬂ man 2 1.113 x 10.4 m rtNo (1.5x1o19}(1o'5) {d)5m— _ ar=o = ELI) w z W_ _ 1.53 X 1114 me K520 (113}(335x1o14) 14.4
The computations wort: performed omploying Eq. {14.12} with VA  [1, Eq. (14.3}, and {EC — Elﬁn; E Egﬂ — kT IItINDIm}
Tl‘tt: resultant plot and associatoti MAME m—ﬁlo art: displayed below. Lama program script...
$Equilibrium Depletion Width [ProblEm 14.4} %Initialization
clear; close iftrtiotitti'oants and Parameters
q=1. tie—19; oﬂB.85e14; kT=o.tI259; 143 EG=l.12: ni=1.ﬂe1ﬂ; K5=11.B: BH=[D. 5, D. E, D. '1'}; %Earrier Height
NDlogspace {14,1T1 : Enepletinn Width Calculation
ECF=EGI2*kT*1Dg {ND . Ini] ;
HDnl] :
for i=1:3,
VbiBHH} ECF:
W=3qrt I (2*K3*eﬂ. *VbiJ . 3‘ 1:131:13} J .
WU=Ewﬂ;W]:
End 1!:le result 10910? [Minn] I
axis{[l.ﬂe14,1.3e1T,5eE,564]I: grid
xlabelt'ND [CmF3l‘l: flabElI'Hﬂ {cmj‘l
text{2e15,2.33—5,‘BH=ﬂ.SeV‘] text {2915, 635, 'BH=U.'TF~.V'] ND [ma] 144 iii (amhﬂe) A sample MA'ILAB program that generates MS diede energy band diagrams
(equilibrium, 302} K} is included on the instructor‘s disk as m—ﬁle P_l4_ﬂ5.m. The
program can generate both n and p—type Si diagrams plus n— and ptype GaAs diagrams.
Sample plots are displayed below. ' simmered: Mlﬂm “Wm {IE i M I
Minn “Smiiﬂlll l4r5 liﬁ
3 Substituting Eq. (14.1?) into Eq. (14.16} gives I mm: (mm ““1“ Mm”;
SuiHr! = ¢IA h3 E “the dvx _qg(_mn_] {WT “mama; m where the second form of the above equaﬁon is obtained by interchanging the limits on the
integral and changing variables frmn v; to— 4.1; Next evaluating the integral yields I vie gIimnﬂkﬁvx dvx = _ E)e—(na§ﬂmv§” _{ﬂ g(m:f?iﬁvnun
“min mil ”min Thus, noting from Eq. (14.14) that 11min: = (Mfmn'l‘KVHVA}, we obtain 2
IS . 4M QA{M) efEFvEcHET E ﬂvbi—Vﬂfki' ’13 quifkT = ¢BfkT+ (EpEclfkT 2 ‘2 j' t ‘2
all?!“ T mu = A ﬂ [41mm )T2 = Aﬂ*T2
s3 ”‘0 I13 and leading to the conclusion I5._,M = Aﬂi‘TEE‘Wl“TE‘IVNM 146 1&1
{a} With positive current ﬂow as deﬁned in Fig. 14.3ta}, the shortcircuit photocurrent is negative. (Note that Em = EFS in the energy band diagram because the device is short
circuited. However, both F” and Ft: deviate from Epg near the M—S interface.) (b) A fotward bias must he developed under opencircuit conditions so that the negative
going photocurrent is precisely.r balanced by a positive—going thermionic emission current. {Domcircuit diagram} {c} Paralleling the approach presented in Subsection 9.11, the photocurrent UL} will be
equal to en times the electron—hole pairs photogenerated per second in the volume A(W+Lp). or
IfI. =  thW + LP}GL {d} The I—V sketch should be similar to one of the G0 at t] curves in Fig. 9.3; i.e.. a
constant value is subtracted from the dark l—V chatacteﬁstic to obtain the lighton
characteristic. Consistent with the part (t1}ttnd (b) answers, i’ s: [l ifthe device is short—
circoited (Va.L = ﬂ} and V :1 i] if the device is open circuited [I = ﬂ). 1' 14—7  13.3
i When tlte series resistanoe cannot be ignored, Eq. {14.24) assumes the modiﬁed form f = [5(gﬁ'vlfkT_ 1)
where
hﬁ = FEE—IRS or 1%; = hjFLRS 'Ihe I—V relationships here are totally analogous to the high—eutrentpn junetion
relationships presented in Subsection 6.2.4. in perfonning computations. it is convenient
to ﬁrst choose a value for V], compute I, and then compute VA. The requested I—V
eharaeteristies illustrating the effect of the series resistanoe ate reproduced below. 10 1'0 ._ i! . lllrlllFlgl: 0 D. 1 I12 0.4 {15 [LE
to. {volts} MATLAB program script...
thfeet of RS on MS diode 1? Characteristics %Initialization
clear; Close hConstants and Parameters
itT=D.t1259; 14—3 VJ=linspacetﬂ,ﬂ.ﬁ}: $Ca1cu1ate I versus VA
=Is.*{exp{VJfle1]; VH=; for i=1:4, VA=[VA:VJ+I.*RS{1] ] ; end %Plot result semilogyfVA,I,'w'J: axis{[ﬂ,D.E,1.ﬂe9,l.ﬂel]}; grid xlahe1{'VA {voltsl‘}: ylabelt'I [ampsl‘]
text{ﬂ.34,5.ﬂe2,‘RSED'J; taxtiﬂ.41,2.09#2,'RS=1 ohm'i
text{ﬂ.4l,4.De—3,'Eﬁ=1ﬂ ohms'} ' Is=1.0eE:
RS=[G,D.1,1.D,10]:
 .113
F01" apt” junction...
2
IDIFF = Inteqvﬂﬂ— 1): qgﬂli_i_(£qukr_ 1)
LP ND and mplaying Eqs. (14.24!14.25),  In; = Isteql’afﬂ— n = amrzﬂnrkrugeewrcr 1; Thus noting
D r (We?)
H2 H2
IDIFFz L: HQ 32p ND l (Lﬁx 10.]9{{—_U.{}259}(43T}‘1ﬂ(1ﬂg)
' (lﬂ4ﬁ ﬂlﬁ ‘ W= ‘ 149 515 X Ill“? H.111
(aims) The computational results for parts (a) and {b} and the associated MATLAB tn—ﬁle are
included after the pan (c) eonnnents. The primal11.r relationships employed in the
computatlons were: For part {a}... “(433:9 (ﬁlm; in eV} ND zqnp ”3
l8 I ‘5" W: (vb1m]
S stn Ksn: '— = glide — (Err EsiFa] (EuEFJFB= Eel? (EF— EilFB — EGJ'Z— lenWDin}
For part be" f__s(VA} _ M I gitbalﬂl‘I'aiVaJlfkT = gtaentvcﬁenwllfﬂ
James) genomic {c} The A¢B(e‘v') versus VA plot shows that the change in :1th tends to be quite small,
only M14? eV corresponding to a avg = 50V in the given calculation. However. because
I; depends exponentially on the barrier height, the effect of a small Mia change on I; is
very signiﬁcant.— f5 changes by more than a factor of s over the examined voltage range! 1' Muhmmﬂj
Immhhiﬂnl
L vlul I n—l—v hiaTLABiﬁegnunscﬁpL"
$5ehettky Barrier Lowering Computation EInitializatien
C1 ear ; close iCDnstants and Parameters
q=l.Ee1El: eﬂ=3.BSe14: kT=ﬁ.ﬂ259; KS=11.B; EG=1.12: ni=1.ﬂalﬂ: HD=1.DelE:
BH=ﬁ.?2: %Eﬁ=barrier height in B? 
%Cﬂmputatinn of ﬂBH
VAFlinapace{ED,UJ:
ECF=EGIEkT*log{NDInil:
Vbi=EHECF:
ESaqrt{[2*q*HD}f{KS*eD}.*{Vbiva1]:
ﬁBH=5tht{q.*ESJ.ftd*pi*HS*eDJ};
pletIVA,ﬁBH]: grid
xlabelt‘va {volta]‘]: ylabe1{'Decrease in barrie: height {eVI'I:
pause $Cnmputatian of IafIa{ﬂ} Ian=expitﬁEHaﬂﬂ{1ﬂﬂll.fkT]: p10t{VA,Isn}; grid xlabelf'va [volts}']; ylahelI'Ia normalized to Is at Vﬁeﬂ‘l: 1411 ij 12.11 i If not explicitlyr given in the problem stateroom1 the device area (A = 1.5 X Ill3 an?) Intor
: be obtained from Exercise 14.4. Effoetiog the fit employing the MATLAB program listed below, one ﬁnds:
Iiiﬂsaaha Iaaannaothi ND = 9.62 x ioiircmﬁ ND 5 9.? x inﬁrm? Vb; = {1613 ‘9' V5 E on V (115 = ﬂ.ElﬁeV [pH 5 [LE av
The ﬁt results obvious];r compare very favorably 1with the approximate results obtained in
Exercise 14.4.
Mam program script... % Determination of Uhi, ND, and BH of HE diode
% employing P14.11 CV data iInitialization
clear; close
format oonpact; format short e ilnput data...¥=1fCJ2 = [1.oa,2.oa.3.ov.4.os.s.os.s.o4,7.o3,a.o2,s.o1,1o1;
Y=1.De21*[ﬂ.953.1.494,2.ﬂ35,2.5?9,3.125,3.ET3,4.217, ... .
4.ass,s.szo.s.asoJ: 3 %Fit p=po1yfit war, 11
HD=2.I{1.Ee~19*11.3*ﬂ.35E14*{l.5&3]“2*(—p[1}}1
VbizplZJHPlll %Earrier Height Computation
EG=1.12; ni=1.Uo1D: kT=ﬂ.0259;
ECF=EGf2kT*loglNDfni}:
Bﬂnvbi+ECF ilfCJE vs. VA plot {not required} plot {n.3, '+'} axia[[—11,2,D,1.1*max{Y}ll; grid alabell'VA {volta}']: plaboll'IICJ‘E [lfFﬂzi'l 14 12 graded MS diode closely parallels the uniformly {lope1i analysis in Subsection 14.2.1. The
results obtained are analogous to the linearly graded pn junction relationships established in
Subsection 5.2.5. (a) With Nntx} = or for x .32 i]. invoking the depletion approximation yields
PL!) = Qttr ".0515“? Substituting into Poisson’s equation gives EEL=LE£1 ".05sz
it K580 K380 M12.
In general the development ofreiaﬁonships for the eiecnostatie variables in a lineaziy so) = ~61? {2W33W2x+x3} age it ' Finally, V ==—[V1.1 — VA} at: = ill, and therefore 14—13 {h)Pa1alleling the development for the lineari3r graded pn junction in Subsection 5 2 5 the
Eq. (14 3] expression for Vbi must be modiﬁed to read Vet = $le — (IE2:" EFllmwn] . where Wu' 1s the depletion width when VA = i}. Sinee approximate charge neutrality applies
" for): : Wot it follows that dx=Wo = aiEHEFrEiEWoF” s Nlex=Wﬂl = 0W9
Ul'
(Er—EFL a: = Eea trek—LTD) Thus, to determine Vbi. one tnn st simultaneoust solve the following two equations
employmg ntuneneal techniques Wu  em a ” m = l[eB EﬁfZ+len(a—i—WGJJ {o} =.jl'i— _____Sﬂﬂ__
[343$ {VetVal] ’5 1414 ...
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 Fall '07
 HAMBLEN

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