L08 07Feb021 EE 4345 - Semiconductor Electronics Design Project Spring 2002 - Lecture 08 Professor...
-
Upload
avice-brown -
Category
Documents
-
view
219 -
download
1
Transcript of L08 07Feb021 EE 4345 - Semiconductor Electronics Design Project Spring 2002 - Lecture 08 Professor...
L08 07Feb02 1
EE 4345 - Semiconductor Electronics Design Project Spring 2002 - Lecture 08
Professor Ronald L. [email protected]
http://www.uta.edu/ronc/
L08 07Feb02 2
Dates for Technology Project Reports
12 Feb - TP1.1 Eyad Fanous Group 12 Feb - TP1.2 Nam Nguyen Group 14 Feb - TP1.3 Viet Tran - The Pentagonal
Group 14 Feb - TP1.4 Fares Alnajjar Group 19 Feb - TP1.5 Carlos Garcia Group19 Feb - TP1.6 Robert Colville Group21 Feb - TP1.7 Jepsy Colon Group21 Feb - TP1.8 Preeti Yadav Group26 Feb - TP1.9 Peter Presby - Group 626 Feb - TP1.10 Derek Johnson Group
L08 07Feb02 3
npn BJT currents(F A region, ©RLC)
IC =
JCAC
IB=-(IE+IC )
JnE JnC
IE = -JEAE
JRB=JnE-JnC
JpE
JGC
JRE JpC
L08 07Feb02 4
Ebers-Moll(npn injection model)
C
E
B
1
expt
BC
R
S
R
EC
VVII
t
BC
t
BES
ECCCCT
VV
V
VI
III
exp
exp
1
expt
BE
F
S
F
CC
V
VII
(common-emitter)
L08 07Feb02 5
eff,o
taieffavgrec
o
taimaxfpfna
fnfii
fifni
x
xeffavgrec
2V2/Vexpn
qWxqUJ
2V2/Vexpn
U ,EEqV w/
,kT/EEexpnp
and ,kT/EEexpnn cesin
xqUqUdxJ curr, ecRn
p
Effect of carrierrec. in DR (cont.)
L08 07Feb02 6
High level injection effects• Law of the junction remains in the same
form, [pnnn]xn=ni
2exp(Va/Vt), etc.
• However, now pn = nn become >> nno = Nd, etc.
• Consequently, the l.o.t.j. reaches the limiting form pnnn = ni
2exp(Va/Vt)
• Giving, pn(xn) = niexp(Va/(2Vt)), or np(-xp) = niexp(Va/(2Vt)),
L08 07Feb02 7
High level injeffects (cont.)
KFKFKFsinj lh,s
i
at
i
dtKFa
appdnn
a
tainj lh,sinj lh
VJJ ,JJJ :Note
nN
lnV2 or ,n
NlnV2VV Thus
Nx-n or ,Nxp giving
V of range the for important is This
V2/VexpJJ
:is density current injection level-High
L08 07Feb02 8
Summary of Va > 0 current density eqns.• Ideal diode, Jsexpd(Va/(Vt))
– ideality factor,
• Recombination, Js,recexp(Va/(2Vt))– appears in parallel with ideal term
• High-level injection, (Js*JKF)
1/2exp(Va/(2Vt))
– SPICE model by modulating ideal Js term
• Va = Vext - J*A*Rs = Vext - Idiode*Rs
L08 07Feb02 9
Plot of typical Va > 0 current density eqns.
Vext
ln J
data
ln(JKF)
ln(Js)
ln[(Js*JKF) 1/2]
Effect
of Rs
t
aV
Vexp~
t
aV2
Vexp~
VKF
ln(Jsrec)
Effect of high level injection
low level injection
recomb. current
Vext-Vd=JARs
L08 07Feb02 10
Reverse bias (Va<0)=> carrier gen in DR• Va < 0 gives the net rec rate,
U = -ni/, = mean min carr g/r l.t.
NNN/NNN and
qN
VV2W where ,
2Wqn
J
(const.) U- G where ,qGdxJ
dadaeff
eff
abi
0
igen
x
xgen
n
p
L08 07Feb02 11
Reverse bias (Va< 0),carr gen in DR (cont.)
gens
gen
gengensrev
JJJ
JSPICE
JJJJJ
or of largest the set then ,0
V when 0 since :note model
VV where ,
current generation the plus bias negative
for current diode ideal the of value The
current the to components two are there
bias, reverse ,)0V(V for lyConsequent
a
abi
ra
L08 07Feb02 12
Reverse biasjunction breakdown• Avalanche breakdown
– Electric field accelerates electrons to sufficient energy to initiate multiplication of impact ionization of valence bonding electrons
– field dependence shown on next slide
• Heavily doped narrow junction will allow tunneling - see Neamen*, p. 274– Zener breakdown
L08 07Feb02 13
Ecrit for reverse breakdown (M&K**)
Taken from p. 198, M&K**
L08 07Feb02 14
Reverse biasjunction breakdown• Assume -Va = VR >> Vbi, so Vbi-Va-->VR
• Since Emax~ 2VR/W = (2qN-VR/())1/2, and
VR = BV when Emax = Ecrit (N- is doping of
lightly doped side ~ Neff)
BV = (Ecrit )2/(2qN-)
• Remember, this is a 1-dim calculation
L08 07Feb02 15
Junction curvatureeffect on breakdown• The field due to a sphere, R, with
charge, Q is Er = Q/(4r2) for (r > R)
• V(R) = Q/(4R), (V at the surface)• So, for constant potential, V, the field,
Er(R) = V/R (E field at surface increases for smaller spheres)
Note: corners of a jctn of depth xj are like 1/8 spheres of radius ~ xj
L08 07Feb02 16
BV for reverse breakdown (M&K**)
Taken from Figure 4.13, p. 198, M&K**
Breakdown voltage of a one-sided, plan, silicon step junction showing the effect of junction curvature.4,5
L08 07Feb02 17
D DiodeGeneral FormD<name> <(+) node> <(-) node> <model name> [area value]ExamplesDCLAMP 14 0 DMODD13 15 17 SWITCH 1.5Model Form.MODEL <model name> D [model parameters] .model D1N4148-X D(Is=2.682n N=1.836 Rs=.5664 Ikf=44.17m Xti=3 Eg=1.11 Cjo=4p M=.3333 Vj=.5 Fc=.5 Isr=1.565n Nr=2 Bv=100 Ibv=10 0uTt=11.54n)*$
L08 07Feb02 18
Diode Model Parameters (see .MODEL statement)Description UnitDefault
IS Saturation current amp 1E-14N Emission coefficient 1ISR Recombination current parameter amp 0NR Emission coefficient for ISR 1IKF High-injection “knee” current amp infiniteBV Reverse breakdown “knee” voltage volt infiniteIBV Reverse breakdown “knee” current amp 1E-10NBV Reverse breakdown ideality factor 1RS Parasitic resistance ohm 0TT Transit time sec 0CJO Zero-bias p-n capacitance farad 0VJ p-n potential volt 1M p-n grading coefficient 0.5FC Forward-bias depletion cap. coef, 0.5EG Bandgap voltage (barrier height) eV 1.11
L08 07Feb02 19
Diode Model Parameters (see .MODEL statement)Description UnitDefault
XTI IS temperature exponent 3TIKF IKF temperature coefficient (linear) °C-1 0TBV1 BV temperature coefficient (linear) °C-1 0TBV2 BV temperature coefficient (quadratic) °C-2 0TRS1 RS temperature coefficient (linear) °C-1 0TRS2 RS temperature coefficient (quadratic) °C-2 0
T_MEASURED Measured temperature °CT_ABS Absolute temperature °CT_REL_GLOBAL Rel. to curr. Temp. °CT_REL_LOCAL Relative to AKO model temperature
°C
For information on T_MEASURED, T_ABS, T_REL_GLOBAL, and T_REL_LOCAL, see the .MODEL statement.
L08 07Feb02 20
The diode is modeled as an ohmic resistance (RS/area) in series with an intrinsic diode. <(+) node> is the anode and <(-) node> is the cathode. Positive current is current flowing from the anode through the diode to the cathode. [area value] scales IS, ISR, IKF,RS, CJO, and IBV, and defaults to 1. IBV and BV are both specified as positive values.In the following equations:Vd = voltage across the intrinsic diode onlyVt = k·T/q (thermal voltage)
k = Boltzmann’s constantq = electron chargeT = analysis temperature (°K)Tnom = nom. temp. (set with TNOM option
L08 07Feb02 21
• Dinj– key par: IS, N(~1) – rd=N*Vt/iD– rd*Cd = TT =– Cdepl given by CJO, VJ
and M– HLI: IKF, VKF
• Drec– param: ISR, NR(~2)– rd~NR*Vt/iD– rd*Cd = ?– Cdepl =?
SPICE DiodeStatic Model
Vd
iD*RS
Vext = vD + iD*RS
L08 07Feb02 22
DC CurrentId = area(Ifwd - Irev) Ifwd = forward current = InrmKinj + IrecKgen Inrm = normal current = IS(exp ( Vd/(NVt))-1)
Kinj = high-injection factorFor: IKF > 0, Kinj = (IKF/(IKF+Inrm))1/2otherwise, Kinj = 1
Irec = rec. cur. = ISR(exp (Vd/(NR·Vt))- 1)
Kgen = generation factor = ((1-Vd/VJ)2+0.005)M/2
Irev = reverse current = Irevhigh + Irevlow
Irevhigh = IBVexp[-(Vd+BV)/(NBV·Vt)]Irevlow = IBVLexp[-(Vd+BV)/(NBVL·Vt)}
L08 07Feb02 23
vD=Vext
ln iD
Data
ln(IKF)
ln(IS)
ln[(IS*IKF) 1/2]
Effect
of Rs
t
a
VNFV
exp~
t
a
VNRV
exp~
VKF
ln(ISR)
Effect of high level injection
low level injection
recomb. current
Vext-
Va=iD*Rs
t
a
VNV
2exp~
L08 07Feb02 24
npn BJT currents(F A region, ©RLC)
IC =
JCAC
IB=-(IE+IC )
JnE JnC
IE = -JEAE
JRB=JnE-JnC
JpE
JGC
JRE JpC
L08 07Feb02 25
Charge componentsin the BJT
From Getreau, Modeling the Bipolar Transistor,Tektronix, Inc.
L08 07Feb02 26
Gummel-Poon Staticnpn Circuit Model
C
E
B
B’
ILC
ILEIBF
IBR
ICC - IEC =
IS(exp(vBE/NFVt
- exp(vBC/NRVt)/QB
RC
RE
RBB
L08 07Feb02 27
Gummel-PoonModelGeneral FormQXXXXXXX NC NB NE <NS> MNAME <AREA> <OFF> <IC=VBE, VCE> <TEMP=T>Netlist Examples
Q5 11 26 4 Q2N3904 IC=0.6, 5.0Q3 5 2 6 9 QNPN .67
NC, NB and NE are the collector, base and emitter nodes
NS is the optional substrate node; if unspecified, the ground is used. MNAME is the model name, AREA is the area factor, and TEMP is the temperature at which this device operates, and overrides the specification in the Analog Options dialog.
L08 07Feb02 28
Gummel-PoonStatic ModelGummel Poon Model Parameters (NPN/PNP)
Adaptation of the integral charge control model of Gummel and Poon.
Extends the original model to include effects at high bias levels.
Simplifies to Ebers-Moll model when certain parameters not specified.
Defined by parameters
IS, BF, NF, ISE, IKF, NE determine forward characteristics
IS, BR, NR, ISC, IKR, NC determine reverse characteristics
VAF and VAR determine output conductance for for and rev
RB(depends on iB), RC, and RE are also included
L08 07Feb02 29
Gummel-Poon StaticModel Parametersname parameter units default area
IS transport saturation current A 1.0e-16 *BF ideal maximum forward beta - 100NF forward current emission coefficient - 1.0VAF forward Early voltage V infiniteISE B-E leakage saturation current A 0 *NE B-E leakage emission coefficient - 1.5BR ideal maximum reverse beta - 1NR reverse current emission coefficient - 1VAR reverse Early voltage V infiniteISC B-C leakage saturation current A 0 *NC B-C leakage emission coefficient - 2EG energy gap for temperature eV 1.11
effect on ISXTI temperature exponent for effect on IS - 3
L08 07Feb02 30
Gummel-Poon StaticModel Parametersname parameter units default area
IKF corner for forward beta A infinite *high current roll-off
IKR corner for reverse beta A infinite *high current roll-off
RB zero bias base resistance W 0 *IRB current where base resistance A infinite *
falls halfway to its min valueRBM minimum base resistance W RB *
at high currentsRE emitter resistance W 0 *RC collector resistance W 0 *TNOM parameter - meas. temperature °C 27
L08 07Feb02 31
Gummel Poon npnModel Equations
IBF = ISexpf(vBE/NFVt)/BF
ILE = ISEexpf(vBE/NEVt)
IBR = ISexpf(vBC/NRVt)/BR
ILC = ISCexpf(vBC/NCVt)
QB = (1 + vBC/VAF + vBE/VAR )
{ + + (BFIBF/IKF + BRIBR/IKR)}
L08 07Feb02 32
Gummel PoonBase ResistanceIf IRB = 0, RBB = RBM+(RB-RBM)/QB
If IRB > 0RB = RBM + 3(RB-RBM)(tan(z)-z)/(ztan2(z))
[+iB/(IRB)]1/2- (/)(iB/IRB)1/2
z =
Regarding (i) RBB and (x) RTh on slide 22,
RBB = Rbmin + Rbmax/(1 + iB/IRB)RB
L08 07Feb02 33
References
Semiconductor Device Modeling with SPICE, 2nd ed., by Massobrio and Antognetti, McGraw Hill, NY, 1993.
MicroSim OnLine Manual, MicroSim Corporation, 1996.
* Semiconductor Physics & Devices, by Donald A. Neamen, Irwin, Chicago, 1997.