THE D.e. MODELING OF THE iL GATE WITH THE NON-LINEAR
CIRCUIT ANALYSIS PROGRAM TRANZ-TRAN
By
T. RANG*
Tallin Poly technical Institute. Estonia USSR Received February 17. 1981 Presented by Prof. Or. K. TARSAY
Since the presentation of integrated injection logic (/2 L) [1. 2J and later published review articles [3. 4J several investigations have been done in the field of modeling of the /2 L structures [5-10].
All previously mentioned models did not take into account a lot of physical effects (for example T". T p concentration dependence and so). Also the most part of the models need measured model parameters. and because of it is impossible to give physical explanation to turn over process or to explain which factors determine, for example, the transfer characteristic behaviour.
The model described here is based on ideas of Ebers-Moll transport model [11].
The strategy of building up the model is following:
For the /2 L structure the circuit diagram (physical-topological model.
Figure 1), corresponding to cross section AA was built up and is shown in Figure 2. In such "two-dimensional" model the model parameters (saturation currents. base resistance. current gains) have been determined from doping levels. technological and electrophysical parameters. The model is examined with the non-linear circuit analysis program TRANZ-TRAN [12].
Fig. /. Structure oriented model of the /2L gate
* Theses made at the Department of Electronic Devices. Technical University. Budapest.
2 Pcncxllca Po!~technlGI EL ::5 ::
104 T R.·ISG
Fig. :c. Comenti,'nai J 2 L structure
The dimensions model structure are in agreement with those in literature (see for example [13. 14]. The doping profile is determined by exponential function [15. 16].
mathematical model
model. described here. is constructed so, that the currents injunctions are represented different diodes. For the diode the following equation is valid:
[ (
C -. ] J J 0 exp .. -.-.-.-) - 1
IIIL T
(1)
vvhere saturation current density. \vhich depends on various physical and technological parameters and temperature:
ill bulk recombination factor (1 ~ m ~ 21-
first one must determine the different saturation currents. For the saturation currents the following equations have been developed.
Tilt' IWt'ml pnp part o/tht' {CL stnlClllre (Figure 3)
m=1. (2)
X)h
=q :
J
[:Y" (llfD,,)] dx:. 111= 1. (3)(l
JIODELlSG OF THE f'L GATE WITH PROGRA.\f TRASZ-TRAS
o
/=:=-=:.::.::==::(:==:.::.::.::..:::==~-*- Xje
I;::.l:::'-:::'::::':::'::::;::::::"""''::::-:='''''''"""",,~::='i~~~=t---c,r-X j sub
Fig. 3. Lateral pllp part of the [CL gate
XjB
Xjsub
The rertical Ilpll [Jar{
or
il/(, /2 L sTrllCiure ( Figure 4)Xli)
J"mu=q :
J
[S" (nfD,,)] dx; . i11=1.(l
m= 1.12.
m= 1.
XJC
m=1.15.
1i1=1.
m=2.
2*
105
(4)
(5 )
(61
(7 )
(8 )
(9)
106 T. RANG
In Equations (2-9) the following effects were neglected:
1. High level injection, which should be taken into consideration with so called "knee" voltage factor in formula (1) [9].
.2. The geometrical effects of the junctions (cylindrical or spherical), which should be taken into consideration with correction factor in formula (1), but which changes considerably by high injection levels [15].
The temperature dependence of the saturation current densities is shown in Figure 5.
The current gains have been modeled with the help of the current generators (Figure 1). For the current gain one can write
(10) where (j is the collector efficiency which is practically 1. For lateral pllp transistor the normal and inverse current gains have not been calculated. The data are taken from literature [17J, :X;llp=0.85 and :X~llp=0.75.
To calculate the current gains in vertical npn part, the emitter and collector junction areas equality is assumed, which is not typical for /2 L structures, but in case of one collector this assumption is satisfactory. In the case of many collectors the following formulae must be improved.
The current gaills
i fl - - - X - " ) l - ' - - - -
l
(N,dDIl)dx+
Xj'-c _ _ _ _ Xl'1
(Nd/Dp)dxi i - --X-'J'-' - - - -
J
(NjDIlI dx+~X),---C _ _ _ _ Xjc
J
(Nd/Dp) dxo
(11 )
(12)
(13 )
(14)
MODELlNG OF THE [oL GATE WITH PROGRAM TRANZ-TRAN 107
10_8~----i-
_ _----\-;4L#~---+---+---
I
Tj
50 o 50 100 150 ['cJ
Fig. 3. Saturation currents (J,,) dependence on temperature (T )
The breakdown voltage of the junctions have been determined by calculations given in literature [18], because in 12 L structures the breakdown and multiplication properties are not important. The temperature dependence of breakdown voltage described for example in [19J was left out of consideration_
The base resistance consisting of active and passive base resistances is determined and so is the collector contact resistance.
The resistClllces:
R=R"b+Rpb' (15 )
H" . 1
Rpb = -XJ-'b~~-- (16)
J
q~liY" dx o(17 )
I - (.
f
(18)
108 T. RA .\(i
To determine the model parameters (Equations (2) ... (18) the following equations are needed:
llio=AI T3 2 exp (-A2.CT ). (19)
+ 12J, (20)
(21 ) _ . 41".['1. \([ .. !~:i" 7
P".I'-f.1"().f10 ' 5 1 (22)
\'Ihere 'v f.' '"". ,[W' Ll .4I,;".!'.I,) , fOllnd \'n [)_OJ.
D
=
----~----",[1 1...L., (.I\i 4 )D
" 10°",!'
(23)
TOl1
(24)
T"
= ---
I+N A l l '
T I' = (A I 2 ' l'·i'! l ' ) I (25)
T"
=
--====---:===--2.,./ T poT"" ch [(Ll ~~;ikT) In,\: ;:-po T",J
(26)
where T po' T"o carrier lifetime in junctions.
(27)
b=p"pp' (28)
L".p
=
'v' r",[1 . (29)MODEL/SG OF THE r-L GATE ;1 iTH PROGR.HI TRASZ'TRA.\
Nb/!
rl=ln-,-.
]'v be
More detailed informations about the model can be found in [21].
The results of calculations
109
(30)
(31 )
At first the transfer characteristic dependence on the change of the base surface concentration (N"s) has been investigated. The results are shown in Figure 6. As one can see, to larger surface base concentration greater input voltage is needed for the turn over. The reason is, that the increase of the base surface concentration (N"s) causes the increase of the base integral. due to the active base current decrease. Due to it higher input current is needed to turn over the gate. Larger input current is reached by increasing the input voltage.
Conc1usionally it means, that the tLlrn over level of the transfer characteristic of the [2 L gate moves to right
In Figure 7 one can see transfer characteristic dependence on the change of the epitaxial layer concentration (NcD) Similarly to the previous case. the increase ofthe epitaxiallayer concentration (N"pd pushes the turn over level of the transfer characteristic to right. The change of epitaxiallayer concentration (N
epJ
influences the lateral and /l layer current in explicite \vay 'while the0.8 -i---~~
0.6
0.4
0.2
0
0 0.2 0.4 0.6 0.8
1. N~s =
1.0 m -3
I Z 3
1.2 r "
UinLVj Fig. 6. Transfer characteristic dependence on the change of the base surface concentration !.\'," I
110
cvJ I
Uout 0.8 I! I I
0.6,
0.4 ~
0.21
, 0.4
T. RANG
I 2 3
0.6
1. Nepi - 1021 m-3 2. Nepi - 1022 m-3 3. Nepi - 1023 m-3
,
0.8 1.0
Fig. 7, Transfer characteristic dependence on the change of the epitaxial layer concentration (/V cri J
active base. injector vertical and substrate current in implicite way. The increase of epitaxial layer concentration (N epi) causes the increase of base integral due to the active base current decreases, and the transfer characteristic turn over level shifts toward greater input voltages,
The calculations show, that the increase of base surface concentration (N as) and decrease of epitaxiallayer concentration (N epi) cause the decrease of normal current gain
(C(;:PII)
of 12 L gate. The decrease of normal current gain (C(;:pn) causes decrease of the curvature of the transfer characteristic. but the change is not so considerable that it should be followed on transfer characteristics.On Figure 8 the transfer characteristic dependence on the change of active base thickness (n'ab) is shown. The increase of active base thickness (wan) yields the increase of base integral due to the active base current decreases. Also small increase of injector lateral current was observed.
Consequently the transfer characteristic moves toward larger input voltages.
Increasing the active base thickness causes decrease in base transport factors
(K::;IIJ
due to the current gains C(~;II decrease. The increase ofC(;:PII
causes the increase of curvature of the transfer characteristic of the 12 L gate. From the calculations one can conclude that the transistor technological condition(Wan < LIIJ should remain.
The calculations also show that other geometrical parameters (passive base thickness H'pb' lateral base thickness wp , epitaxial layer thickness Wepi,
structure wideness 1. and some other parameters (for example Illl junction
[v]
IUOllt 0.80.6
0.4
0.2
o
MODEL/SG OF THE T-L GATE WITH PROGRA.I[ TRASZ-TRAS
0.2 0.4 0.6
1. Wob = 0.5 }lm 2.Wob= 1Jlm
3.Wob= 2 J-lm
0.8 1.0 1.2
rv., L
J
Fig. (\. Transfer characteristic dependence on the change of the active base thickness 1 '''"h I III
recombination speed CIl, , - . Si-Si02 surface recombination speed cox) practi- cally do not influence the transfer characteristics of the /2 L structure.
In the model, the model parameters depend on temperature. The.
temperature dependence of the carrier lifetime is described by, the following formula [22J
(32) where
7;,=25 C.
The influence of neutron irradiation is presented with the following formula [23J:
(33 ) where
10 neutron Ko = 3· 10 " s .
m-
In Figure 9 the transfer characteristic dependence on the change of the temperature (T) is shown. The change of temperature has strong influence on the transfer character. ,tic of the /2 L gate. The increase of the temperature causes the increase of the whole currents in the structure, due to it the /2 L gate comes nearer to turn over level. Because of it the turn over level of the transfer characteristic moves toward smaller input voJtages. The high temperature
112 T RA,YG
[V]
0.8
0.6 -
1.T:-50·C 2. T : 25'C 3. T : 100 'C 4.T = 175'C
3 2
0.2.,
Uin
0 0 02 0.4 0.6 08 1.0 1.2
fv
-1
~Fig. 'J. Transfer characteristic dependence on the change of the temperature (T I
, Uout
M~---~~
0.6-
1.:p
o 0 ... 1013 neut~onIT>
2.<j
101' neutr,on5
3. p
01015 rn- 1 24.p
1016 neutr,on m 3 4 5.p
1017 neutr,onIn
Fig. J(J. Transfer characteristic dependence on the change of the neutron irradiation (<p I
(T ~ 175 C) causes the loose of the high output level on the transfer characteristic of the 12 L gate.
In Figure 10 the transfer characteristic dependence on the change of the neutron irradiation (cP) is shown. The dependence is quite strong. The increase of neutron irradiation (cP) causes the decrease of :':::PIl and :':~IlP due to the
JIODELl.\G OF THE I:L GATE WITH PRO(iRA.\f TRASZ-TRA.\ 113
curvature of the transfer characteristic decreases. In the case of modeling the neutron irradiation the transistor technological condition (w"" < LH) should remam.
Conclusion
The structure oriented "t wo-dimensionar' model of J 2 L structure is presented. The transfer characteristic dependence on main technological parameters. temperature and neutron irradiation has been examined.
The calculations shO\v. that the change of the active base thickness (>I'ub)'
temperature (T) and neutron .irradiation (<P) have the strongest influence on the transfer characteristic. while the changes of base surface concentration (lV u,) and epitaxial layer concentration (lV "pi) ha \e \>.,eaker influence. Other geometrical and physical parameters do not affect the transfer characteristic of the J2 L gate.
Acknowledgement
The author would like to thank professor KiilmiHl Tarnay. the Head of the Department of Electronic Devices for the useful consultations in the course of doing this work.
Summary
A structure oriented phjsical-topl1logical model of the /' L gate is described. The mode! parameters (saturation currents. base resistance. current gains) ha \e been calculated from doping Ic\els. geometrical and electronic parameters.
The model is examined bJ the iwn-linear circuit analysis program TRA?\Z-TRA?\.
The transfer characteristic dependence on main technological parameters. temperature and neutron irradiation. has been investigated. It has been shown that active base thickness ('''.,i'l. temperature (T I and neutron irradiation (<p I ha ye strong ini1uence to transfer characteristic of the /' L gate. \Veaker affect is followed [rom base surface concentration ! S." I and epitaxial layer ct)ncenlration (.\ I to transfer characteristic of the /' L gate. Other techn,llllgical parameters (,,. . \\ \\, I" \\. I) practically not affect the transfer characteristic of the /' L gate.
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dr Toomas Tallin Poly technical nstitute. l:.SlOma. USSR Tallin 200026. Ehilajate tce 5. Chair of Electronics
