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Hot-carrier triodes with thin-film metal base
Solid-State
Electronics
Pergamon
Press 1963. Vol. 6, pp. 245-250.
HOT-CARRIER
Printed
TRIODES WITH METAL BASE*
M. M. ATALLA HP Associates, (Received
in Great Britain
THIN-FILM
and R. W. SOSHEA Palo Alto, California 4 February
1963)
Abstract-.4nalysis is presented of the frequency performance of various metal-base hot-carrier triode amplifiers that differ only in the type of hot-carrier emitter they utilize. The triodes considered are: (1) the SMS, or semiconductor-metal-semiconductor, triode utilizing a Schottky triode. barrier emitter; (2) the space-charge-limited emitter triode; and (3) the tunnel-emitter The results are compared with the performance of the bipolar germanium junction transistor. It is shown that for all three hot-carrier triodes, the maximum gain-band product increases with current density, and approaches an asymptotic limit of about 1.4 x lOs/S which is due to collector limitation, where S is the stripe width in centimeters. It is further shown, however, that this limit is closely approached at reasonable current density only by the SMS triode. This limit is to be compared with a value of 5-12 x lOs/S for the germanium transistor. At an emitter current density of 1000 A/ems and a stripe width of 10 p, the maximum gain-band products, or maximum oscillating frequencies, are 60 kMc/s for the SMS triode, 38 for the spacecharge-limited emitter triode, and 10 for the tunnel-emitter triode. RCsumB-On presente une analyse du rendement de la frequence de diverses triodes amplificatrices a base de metal et a porteurs chauds qui different seulement dans le type d’emetteur a porteurs chauds qu’elles utilisent. Les triodes considerees sont: (1) la triode SMS, semiconducteur-metal-semiconducteur, utilisant un Cmetteur de barriere Schottky (2) la triode a Cmetteur de charge d’espace limitee et (3) la triode a emetteur tunnel. Les resultats sont compares avec le rendement du transistor a jonction bipolaire. On demontre que pour toutes ces trois triodes a porteurs chauds le produit gain-largeur de bande maximum augmente avec la densite de courant et tend vers une limite asymptotique d’environ 1,4 x 106/S qui est due aux limites du collecteur, ou S est la largeur de bande en centimetres. On demontre aussi que toutefois cette limite est approchee de pres a une densite de courant raisonable par la triode SMS seulement. Cette limite est comparee avec une valeur de 5-12 x lOs/S pour le transistor au germanium. A une densite de courant emetteur de 1000 A/cm2 et une largeur de bande de 10 p, les produits gainlargeur de bande maxima ou les frequences d’oscillations maxima sont de 60 kMc/s pour la triode SMS, 38 pour la triode a Cmetteur de charge d’espace limitee et 10 pour la triode a Cmetteur tunnel. Zusammenfassung-Die Frequenzleistung verschiedener mit heissen Elektroden arbeitenden Trioden-VerstPrkern mit Metallbasis, die sich durch den Emitter der heissen Elektronen unterscheiden, wird besprochen. Zu diesen Trioden gehoren: (1) Die SMS oder Halbleiter-MetallHalbleiter-Triode mit einem Sperremitter nach Schottky: (2) Die Triode mit durch Raumladung begrenztem Emitter (3) Die Tunnel-Emitter-Triode. Die Ergebnisse werden mit der Leistung eines Es wird gezeigt, dass fiir die mit bipolaren Transistors mit Germaniumiibergang verglichen. heissen Elektroden arbeitende Triode das maximale Bandbreitengewinn-Produkt mit der Stromdichte zunimmt und asymptotisch einem Grezwert von 1,4x 106/S zustrebt, was auf der Begrenzung durch den Kollektor beruht, und wo S die Breite des Streifens in cm ist. Es ergibt sich ferner, dass bei annehmbarer Stromdichte nur die SMS-Triode diesem Grenzwert einigermassen nahe kommt. Fiir einen Germanium-Transistor ist der entsprechende Grenzwert 5-12 x 106/S. Fur eine Streifenbreite von 10 p und eine Emitterstromdichte von 1000 A/cm2 sind die maximalen Bandbreitengewinn-Produkte oder die maximalen Schwingungsfrequenzen 60 kMHz fur die SMS-Triode, 38 fiir die Triode mit durch Raumladung begrenztem Emitter und 10 fiir die TunnelEmitter Triode. * This work is supported by Contract No. AF19(628)-1637, Cambridge Research Laboratory, Office of Aerospace Research, 245
Electronic Research Directorate, USAF, Bedford, Massachusetts.
Air Force
246
M.
M.
ATALLX
and
R.
W.
SOSHEA Comparison
I. INTRODUCTION
of triodes
CONSIDERABLE interest has recently been generated
in solid-state triode amplifiers based on hot-carrier transport in thin metal films. Various structures have been proposed,(r+ and evidence of hotcarrier triode action has been demonstrated.(3,5*s) Furthermore, independent measurements of transport of hot carriers in various metal films have been carried out,(T) indicating ranges as high as several hundred angstroms in the l-eV energy range. Three principal hot-carrier triode structures have been proposed. These are listed in Table 1, together with other more conventional triode amplifiers. The basic operation of the three hotcarrier triodes indicated is essentially the same. They differ, however, in one all-important respect, namely the structure of the emitter and the mechanism of hot-carrier injection into the metal base. The consequences of utilizing the various emitters indicated, on the general amplifier characteristics, and particularly its high-frequency limitations, are developed and presented in this report. Comparisons are also made with the performance of the more conventional bipolar transistor. Table 1. Someproposed or existing triode amplifiers
.._A I Bipolar transistors II Unipolar transistors
III Hot-carrier
triodes
(1) n-p-n or p-n-p (2) Field-effect transistor (a) junction transistors (b) surface transistors (3) Analogue transistor -___
(1) n-p-n- Junction triode
I
StI --_ ‘“k .&
----
‘/
W
_-a-
(2) Tunnel-emitter
triode
w
---
(3) Space-charge-limited
1
emitter triode
I
(4) Tunnel-emitter triode (5) Space-charge-limited emitter triode (6) (SMS) Schottky emitter triode
II. COMPARISON
OF TRIODES
11.1 Mechanisms of operation Fig. 1 is a schematic presentation of the energyband diagram for each of the triodes compared. a conventional n-p-n Diagram 1 represents transistor. Diagram 2 represents a tunnelemitter hot-electron triode. Hot electrons are into the metal base by quantuminjected mechanical tunneling through a thin insulating
(4) Semiconductor-metal
emitter triode (SMS)
FIG. 1. Schematic energy-band diagrams for a bipolar transistor and three hot-electron metal-base triode amplifiers.
layer W. Hot electrons transported across the metal base are collected by passing over a lowerenergy base-collector barrier into the space
HOT-CARRIER
TRIODES
WITH
charge of the reverse-biased collector. Diagram 3 represents a hot-electron triode with space-chargelimited emitter. Hot electrons are injected into the metal base by flowing from a metal (extreme left) into the conduction band of an insulating film W (or high-resistivity semiconductor) and finally into the metal base. The electron flow in the emitter region Win this case is determined by the space charge of the flowing electrons. Diagram 3 represents the SMS or semiconductor-metalsemiconductor hot-electron triode. The emitter is essentially a Schottky-type barrier, which is so chosen that, in forward bias, current flow is primarily due to majority carriers in the semiconductor (in this case electrons). This current will flow into the metal base as hot electrons. II.2
Basic emitter characteristics
The emitter characteristics pertinent to our discussion are the capacitance-voltage and currentdensity-voltage characteristics under forward bias. These are summarized in Table 2. The assumptions and notations used are as follows : (1) For the n-p-n-transistor emitter, the
THIN-FILM
METAL
247
BASE
emitter junction is a step n+-p junction of unity injection efficiency. The base region has width wb and concentration Nb. A unity base-transport factor is assumed. q is the electron charge, vb is the barrier height, U is the applied forward bias, K is the semiconductor dielectric constant, rzt is its intrinsic carrier density and D, is the diffusion coefficient of electrons in the base region. (2) For the tunnel-emitter triode, it is assumed that current flow obeys a Fowler-Nordhiem relation of field emission or tunneling through a triangular potential barrier.(s) W, is the thickness of the insulating emitter film through which tunneling occurs, 4 is the metal-insulator barrier height, and K is the insulator dielectric constant. The numerical constants given correspond to T = 300°K. (3) For the space-charge-limited emitter, it is assumed that the emitter region W, is free of fixed charges or traps, and only a single carrier is present. It is also assumed that throughout the region the carrier velocity equals @, where p and 15 are the carrier mobility and electric field, respectively. (4) For the SMS triode, the emitter-barrier efficiency is unity (i.e. no minority carriers are
Table 2. Comparison of basic emitter characteristics* Capacitance
Triode
(1) n-p-n Transistor
Current density (je)
(Ce)
Voltage (U)
Voltage (U) c, =
(sn/‘C)(vb-
nf
l/2
qNb
Dn
j, = q ,*-&exp(qU/kT)-11 u>
1
b
(2) Tunnel-emitter
b
1 c
je = 1.54 x 10-s
triode x exp
-
6.82
u w,
a
O( 1 1 X
lO’$s’s
( Ul We) (3) Space-chargelimiter emitter triode (4) SMS
triode
c, =
qNe gr/K[vb - W/q) - u]
* All equations are in e.s.u. except where noted. ? Units are amperes, volts and centimeters.
l/2
1
j, = qnoN, exP[-qVb/kT] kxP W/W
-
11
248
M.
M.
ATALLA
and
R.
W.
SOSHEA
injected into the semiconductor), the emitter is uniformly doped to a concentration Ne, the barrier height is vb, and 00 is the electron thermal velocity (kT/Znm)l~s in the semiconductor. II.3
Emitter
conductance
Based on the relations given in Table 2, the emitter conductanceg, = (dje/dUe) was calculated for each triode at different current densities. The results are shown in Fig. 2 as gm versus emitter current density. It is seen that the transistor and the SMS triode have the highest emitter conductantes due to their strong exponential dependence of emitter current on voltage. The tunnel-emitter triode follows with intermediate values of gm and finally the space-charge-limited emitter triode with the lowest emitter conductance due to its weak current-voltage dependence( j, oc Us). At 1000 A/cm2 emitter current density, the respective values of gm at 300°K are : mho/cms SMS 40,000 Transistor
Space-charge-limited =
10,
p
=
emitter 200
10’
FIG. 2. Comparison of emitter conductance vs. emitter current density for various triodes.
Emitter$gure
12,000 triode
cm2/v-set,
W, = 1CF4 cm) II.4
10
40,000
Tunnel-emitter triode (fee = 4, IV, = 20 A) (Ke
_.
900
of merit, g,,/C,
For the four triode structures under consideration, comparisons were made of their emitter figure of merit, g,/Ce, which is the reciprocal of the emitter charging time TV. The results are given in Fig. 3 as gm/C, versus emitter current density. The calculations were carried out at the specific conditions indicated at the top of Fig. 3. It is to be noted that here again both the SMS triode and the transistor have essentially the same emitter performance, as expected, both having the highest figures of merit. They are followed by the space-charge-limited emitter triode, and finally by the tunnel-emitter triode, which exhibits the most serious emitter limitation. It should be further pointed out for the case of the tunnel emitter that, for given emitter current density, an increase in emitter width IV, will not change its g,/Ce, since the resulting decrease in emitter canacitance decrease --or - is offset bv_I a nronortionate I I
10
10’
10’
i e : amp/cm* Emitter figure of merit (g,/Ce) (1) Semiconductor-metal: Si-Au, N, = 101s/cm3 (2)‘n-p-n: Nb = 1017/cm3, 7.06= lo-” cm (3) Space-charge-limited: we = 10e4 cm (4) Tunnel emitter: 4 = 1 eV, ZL’~= 20 A FIG. 3. Comparison of emitter figures of merit vs. emitter current density for various triodes (g,/C’c is the reciprocal of the emitter charging time).
HOT-CARRIER
TRIODES
WITH
in g, (as can be readily verified from the relations in Table 2). At 1000 A/cm2 emitter current density, the figures of merit g,/Ce for the various emitters are as follows: SMS Transistor Space-charge-limited emitter triode Tunnel-emitter triode II.5 Triode of merit
ampliJier gain-band
c/s 2.2 x 1011 1.7 x 1011
Jigure
We shall now compare the frequency performance of the triodes under consideration. A convenient form of gain-band product expression(s) is K = (power gain)l/s(bandwidth) = fmax.osc.
= 3&cLhl”’
(l)
where a is the triode current-transport ratio, ?‘b is the base resistance, CJ, is the collector capacitance, and Q-~~is the emitter-to-collector signal delay time. 76(3 is the sum of three terms: (1) the emitter charging time 7ec = Ce/gnz, where g, and C, are the emitter conductance and capacitance per unit area, respectively; (2) the base transit time 7b = Wb/‘Uth.m., where Wb is the metal base width, and vth.m. is the velocity of hot electrons in the metal; and (3) the collector transit time 7c = Xm/2z’sc~rrm., where X, is the width of the collector depletion region, and vge.rrm is the scatter limiting drift velocity of the carrier’ in the collector. For all three hot-electron triodes considered, the base transit time is small and can be generally neglected (for Wb = 10-a cm, and vth.rn. 1: 108 cm/set, 71, = lo-14 set). Hence
Tee =
(
Cc?/gm+~
&I
2Vsc. lim.
METAL
1
The dependence of gain-band product K on base width wb is, therefore, only through the dependence of a and r’b on wb. Following EARLY'S treatment of the bipolar junction triode,(le) consider a simple linear stripe geometry of unit length with an emitter stripe
BASE
249
width s, spaced s/2 from the base stripes. The collector capacitance is then sCc, and the base resistance r’b = &+,&/Wb, where Ce is the collector capacitance per unit area [= (K/h)(l/xm)], and pnais the resistivity of the metal base. For a hot-electron triode with unity emitter efficiency, its gain is given by M = (1 -R)
6 x 101” 4x 109 product
THIN-FILM
exp( - wb/L)
(3)
where L is the hot-electron range in the metal base, and R is its reflection coefficient at the collector. Substituting for r’b, Cc&, and a in equation (l), gives
K, obviously, has a maximum, which is reached when Wb = L/2, i.e. when the base width is just one-half the hot-electron range
(5) Substituting K max=-
for T~(: from equation (2) gives 1-R S
(3/8re)L/qh [ l/%c.lim. +2/x&m/Ce)
1
I.12 (6)
This relation is applicable to all three hot-electron triodes under consideration. It indicates the dependence of Kmax on the figure of merit (gm/Ce) of the specific type of emitter that the triode utilizes. From the dependence of (gnz/Ce) on emitter current density je, as discussed in Section II.4 and presented in Fig. 3, and from equation (6)) one obtains the dependence of Kmax on emitter current density. This calculation was carried out, and the results are given in Fig. 4 as Kmax versus emitter current density for the three hot-electron triodes under consideration. For comparison, EARLY'S value of gain-band product of 5-12 x lOa/S for the bipolar germanium transistor is also indicated on the figure. From the results, the following conclusions may be made: (1) The highest-frequency performance should be obtainable by the SMS triode, followed by the space-charge-limited emitter triode and finally by the tunnel-emitter triode. (2) While
250
M.
M.
ATALLA
and
R.
W.
35Oi GOLD
SOSHEA
BASE-
Si Collector
e Width
10 Microns
FIG. 4. Comparison of gain-band product vs. emitter current density for three hot-electron triodes. The corresponding performance of the germanium transistor is also indicated.
both the SMS triode and the space-chargelimited emitter triode have high-frequency performance superior to that of the bipolar transistor, the tunnel-emitter triode performance will not exceed that of the bipolar transistor except at rather excessive emitter current densities. (3) For all three hot-electron triodes, K,,, approaches an asymptotic limit with current density that is due to collector limitations. As shown in Fig. 4, however, only the SMS triode closely approaches this limit at a reasonable current density. This limit is readily obtainable from equation (6) by setting g,/Ce = co. Under the conditions of Fig. 4, one obtains 1.4 x 10s (Kmsx)rss,.So c/Is (7) which is one to two orders of magnitude higher than calculated for the bipolar transistor.(rs) Finally, at an emitter current density of 1000 A/ems, the maximum oscillating frequencies for the triodes under consideration are as follows:
SMS triode Space-charge-limited emitter triode Tunnel-emitter triode (Bipolar transistor
kMc/s 60 38 10 5-12)
REFERENCES 1. C. A. MEAD, Proc. I.R.E. 48, 1359 (1960). 2. J. P. SPRATT, R. F. SCHRARZ and W. M. KANE, Phys. Rev. Letters 6, 341 (1961). 3. M. M. ATALLAand D. KAHNG, IRE-AIEEDevice Research Conference, University of New Hampshire (1962). 4. D. V. GEPPERT, Proc. I.R.E. 50, 1527 (1962). 5. D. KAHNG, Proc. I.R.E. 50, 1534 (1962). 6. M. M. ATALLA, NEREM Rec. p. 162 (1962). 7. W.G. SPITZER,C.R.CROWELL~~~M.M.ATALLA, Phys. Rev. Letters 8, 57 (1962). 8. A. G. CHYNOWETH, Progr. Semicond. 4, 97 (1959). 9. R. L. PRITCHARD, Frequency Response of Grounded Base and Grounded Emitter Transistors, AIEE Winter Meeting, New York January (1954). 10. J. M. EARLY, Proc. I.R.E. 46. 1924 (1958).
Electronics
Pergamon
Press 1963. Vol. 6, pp. 245-250.
HOT-CARRIER
Printed
TRIODES WITH METAL BASE*
M. M. ATALLA HP Associates, (Received
in Great Britain
THIN-FILM
and R. W. SOSHEA Palo Alto, California 4 February
1963)
Abstract-.4nalysis is presented of the frequency performance of various metal-base hot-carrier triode amplifiers that differ only in the type of hot-carrier emitter they utilize. The triodes considered are: (1) the SMS, or semiconductor-metal-semiconductor, triode utilizing a Schottky triode. barrier emitter; (2) the space-charge-limited emitter triode; and (3) the tunnel-emitter The results are compared with the performance of the bipolar germanium junction transistor. It is shown that for all three hot-carrier triodes, the maximum gain-band product increases with current density, and approaches an asymptotic limit of about 1.4 x lOs/S which is due to collector limitation, where S is the stripe width in centimeters. It is further shown, however, that this limit is closely approached at reasonable current density only by the SMS triode. This limit is to be compared with a value of 5-12 x lOs/S for the germanium transistor. At an emitter current density of 1000 A/ems and a stripe width of 10 p, the maximum gain-band products, or maximum oscillating frequencies, are 60 kMc/s for the SMS triode, 38 for the spacecharge-limited emitter triode, and 10 for the tunnel-emitter triode. RCsumB-On presente une analyse du rendement de la frequence de diverses triodes amplificatrices a base de metal et a porteurs chauds qui different seulement dans le type d’emetteur a porteurs chauds qu’elles utilisent. Les triodes considerees sont: (1) la triode SMS, semiconducteur-metal-semiconducteur, utilisant un Cmetteur de barriere Schottky (2) la triode a Cmetteur de charge d’espace limitee et (3) la triode a emetteur tunnel. Les resultats sont compares avec le rendement du transistor a jonction bipolaire. On demontre que pour toutes ces trois triodes a porteurs chauds le produit gain-largeur de bande maximum augmente avec la densite de courant et tend vers une limite asymptotique d’environ 1,4 x 106/S qui est due aux limites du collecteur, ou S est la largeur de bande en centimetres. On demontre aussi que toutefois cette limite est approchee de pres a une densite de courant raisonable par la triode SMS seulement. Cette limite est comparee avec une valeur de 5-12 x lOs/S pour le transistor au germanium. A une densite de courant emetteur de 1000 A/cm2 et une largeur de bande de 10 p, les produits gainlargeur de bande maxima ou les frequences d’oscillations maxima sont de 60 kMc/s pour la triode SMS, 38 pour la triode a Cmetteur de charge d’espace limitee et 10 pour la triode a Cmetteur tunnel. Zusammenfassung-Die Frequenzleistung verschiedener mit heissen Elektroden arbeitenden Trioden-VerstPrkern mit Metallbasis, die sich durch den Emitter der heissen Elektronen unterscheiden, wird besprochen. Zu diesen Trioden gehoren: (1) Die SMS oder Halbleiter-MetallHalbleiter-Triode mit einem Sperremitter nach Schottky: (2) Die Triode mit durch Raumladung begrenztem Emitter (3) Die Tunnel-Emitter-Triode. Die Ergebnisse werden mit der Leistung eines Es wird gezeigt, dass fiir die mit bipolaren Transistors mit Germaniumiibergang verglichen. heissen Elektroden arbeitende Triode das maximale Bandbreitengewinn-Produkt mit der Stromdichte zunimmt und asymptotisch einem Grezwert von 1,4x 106/S zustrebt, was auf der Begrenzung durch den Kollektor beruht, und wo S die Breite des Streifens in cm ist. Es ergibt sich ferner, dass bei annehmbarer Stromdichte nur die SMS-Triode diesem Grenzwert einigermassen nahe kommt. Fiir einen Germanium-Transistor ist der entsprechende Grenzwert 5-12 x 106/S. Fur eine Streifenbreite von 10 p und eine Emitterstromdichte von 1000 A/cm2 sind die maximalen Bandbreitengewinn-Produkte oder die maximalen Schwingungsfrequenzen 60 kMHz fur die SMS-Triode, 38 fiir die Triode mit durch Raumladung begrenztem Emitter und 10 fiir die TunnelEmitter Triode. * This work is supported by Contract No. AF19(628)-1637, Cambridge Research Laboratory, Office of Aerospace Research, 245
Electronic Research Directorate, USAF, Bedford, Massachusetts.
Air Force
246
M.
M.
ATALLX
and
R.
W.
SOSHEA Comparison
I. INTRODUCTION
of triodes
CONSIDERABLE interest has recently been generated
in solid-state triode amplifiers based on hot-carrier transport in thin metal films. Various structures have been proposed,(r+ and evidence of hotcarrier triode action has been demonstrated.(3,5*s) Furthermore, independent measurements of transport of hot carriers in various metal films have been carried out,(T) indicating ranges as high as several hundred angstroms in the l-eV energy range. Three principal hot-carrier triode structures have been proposed. These are listed in Table 1, together with other more conventional triode amplifiers. The basic operation of the three hotcarrier triodes indicated is essentially the same. They differ, however, in one all-important respect, namely the structure of the emitter and the mechanism of hot-carrier injection into the metal base. The consequences of utilizing the various emitters indicated, on the general amplifier characteristics, and particularly its high-frequency limitations, are developed and presented in this report. Comparisons are also made with the performance of the more conventional bipolar transistor. Table 1. Someproposed or existing triode amplifiers
.._A I Bipolar transistors II Unipolar transistors
III Hot-carrier
triodes
(1) n-p-n or p-n-p (2) Field-effect transistor (a) junction transistors (b) surface transistors (3) Analogue transistor -___
(1) n-p-n- Junction triode
I
StI --_ ‘“k .&
----
‘/
W
_-a-
(2) Tunnel-emitter
triode
w
---
(3) Space-charge-limited
1
emitter triode
I
(4) Tunnel-emitter triode (5) Space-charge-limited emitter triode (6) (SMS) Schottky emitter triode
II. COMPARISON
OF TRIODES
11.1 Mechanisms of operation Fig. 1 is a schematic presentation of the energyband diagram for each of the triodes compared. a conventional n-p-n Diagram 1 represents transistor. Diagram 2 represents a tunnelemitter hot-electron triode. Hot electrons are into the metal base by quantuminjected mechanical tunneling through a thin insulating
(4) Semiconductor-metal
emitter triode (SMS)
FIG. 1. Schematic energy-band diagrams for a bipolar transistor and three hot-electron metal-base triode amplifiers.
layer W. Hot electrons transported across the metal base are collected by passing over a lowerenergy base-collector barrier into the space
HOT-CARRIER
TRIODES
WITH
charge of the reverse-biased collector. Diagram 3 represents a hot-electron triode with space-chargelimited emitter. Hot electrons are injected into the metal base by flowing from a metal (extreme left) into the conduction band of an insulating film W (or high-resistivity semiconductor) and finally into the metal base. The electron flow in the emitter region Win this case is determined by the space charge of the flowing electrons. Diagram 3 represents the SMS or semiconductor-metalsemiconductor hot-electron triode. The emitter is essentially a Schottky-type barrier, which is so chosen that, in forward bias, current flow is primarily due to majority carriers in the semiconductor (in this case electrons). This current will flow into the metal base as hot electrons. II.2
Basic emitter characteristics
The emitter characteristics pertinent to our discussion are the capacitance-voltage and currentdensity-voltage characteristics under forward bias. These are summarized in Table 2. The assumptions and notations used are as follows : (1) For the n-p-n-transistor emitter, the
THIN-FILM
METAL
247
BASE
emitter junction is a step n+-p junction of unity injection efficiency. The base region has width wb and concentration Nb. A unity base-transport factor is assumed. q is the electron charge, vb is the barrier height, U is the applied forward bias, K is the semiconductor dielectric constant, rzt is its intrinsic carrier density and D, is the diffusion coefficient of electrons in the base region. (2) For the tunnel-emitter triode, it is assumed that current flow obeys a Fowler-Nordhiem relation of field emission or tunneling through a triangular potential barrier.(s) W, is the thickness of the insulating emitter film through which tunneling occurs, 4 is the metal-insulator barrier height, and K is the insulator dielectric constant. The numerical constants given correspond to T = 300°K. (3) For the space-charge-limited emitter, it is assumed that the emitter region W, is free of fixed charges or traps, and only a single carrier is present. It is also assumed that throughout the region the carrier velocity equals @, where p and 15 are the carrier mobility and electric field, respectively. (4) For the SMS triode, the emitter-barrier efficiency is unity (i.e. no minority carriers are
Table 2. Comparison of basic emitter characteristics* Capacitance
Triode
(1) n-p-n Transistor
Current density (je)
(Ce)
Voltage (U)
Voltage (U) c, =
(sn/‘C)(vb-
nf
l/2
qNb
Dn
j, = q ,*-&exp(qU/kT)-11 u>
1
b
(2) Tunnel-emitter
b
1 c
je = 1.54 x 10-s
triode x exp
-
6.82
u w,
a
O( 1 1 X
lO’$s’s
( Ul We) (3) Space-chargelimiter emitter triode (4) SMS
triode
c, =
qNe gr/K[vb - W/q) - u]
* All equations are in e.s.u. except where noted. ? Units are amperes, volts and centimeters.
l/2
1
j, = qnoN, exP[-qVb/kT] kxP W/W
-
11
248
M.
M.
ATALLA
and
R.
W.
SOSHEA
injected into the semiconductor), the emitter is uniformly doped to a concentration Ne, the barrier height is vb, and 00 is the electron thermal velocity (kT/Znm)l~s in the semiconductor. II.3
Emitter
conductance
Based on the relations given in Table 2, the emitter conductanceg, = (dje/dUe) was calculated for each triode at different current densities. The results are shown in Fig. 2 as gm versus emitter current density. It is seen that the transistor and the SMS triode have the highest emitter conductantes due to their strong exponential dependence of emitter current on voltage. The tunnel-emitter triode follows with intermediate values of gm and finally the space-charge-limited emitter triode with the lowest emitter conductance due to its weak current-voltage dependence( j, oc Us). At 1000 A/cm2 emitter current density, the respective values of gm at 300°K are : mho/cms SMS 40,000 Transistor
Space-charge-limited =
10,
p
=
emitter 200
10’
FIG. 2. Comparison of emitter conductance vs. emitter current density for various triodes.
Emitter$gure
12,000 triode
cm2/v-set,
W, = 1CF4 cm) II.4
10
40,000
Tunnel-emitter triode (fee = 4, IV, = 20 A) (Ke
_.
900
of merit, g,,/C,
For the four triode structures under consideration, comparisons were made of their emitter figure of merit, g,/Ce, which is the reciprocal of the emitter charging time TV. The results are given in Fig. 3 as gm/C, versus emitter current density. The calculations were carried out at the specific conditions indicated at the top of Fig. 3. It is to be noted that here again both the SMS triode and the transistor have essentially the same emitter performance, as expected, both having the highest figures of merit. They are followed by the space-charge-limited emitter triode, and finally by the tunnel-emitter triode, which exhibits the most serious emitter limitation. It should be further pointed out for the case of the tunnel emitter that, for given emitter current density, an increase in emitter width IV, will not change its g,/Ce, since the resulting decrease in emitter canacitance decrease --or - is offset bv_I a nronortionate I I
10
10’
10’
i e : amp/cm* Emitter figure of merit (g,/Ce) (1) Semiconductor-metal: Si-Au, N, = 101s/cm3 (2)‘n-p-n: Nb = 1017/cm3, 7.06= lo-” cm (3) Space-charge-limited: we = 10e4 cm (4) Tunnel emitter: 4 = 1 eV, ZL’~= 20 A FIG. 3. Comparison of emitter figures of merit vs. emitter current density for various triodes (g,/C’c is the reciprocal of the emitter charging time).
HOT-CARRIER
TRIODES
WITH
in g, (as can be readily verified from the relations in Table 2). At 1000 A/cm2 emitter current density, the figures of merit g,/Ce for the various emitters are as follows: SMS Transistor Space-charge-limited emitter triode Tunnel-emitter triode II.5 Triode of merit
ampliJier gain-band
c/s 2.2 x 1011 1.7 x 1011
Jigure
We shall now compare the frequency performance of the triodes under consideration. A convenient form of gain-band product expression(s) is K = (power gain)l/s(bandwidth) = fmax.osc.
= 3&cLhl”’
(l)
where a is the triode current-transport ratio, ?‘b is the base resistance, CJ, is the collector capacitance, and Q-~~is the emitter-to-collector signal delay time. 76(3 is the sum of three terms: (1) the emitter charging time 7ec = Ce/gnz, where g, and C, are the emitter conductance and capacitance per unit area, respectively; (2) the base transit time 7b = Wb/‘Uth.m., where Wb is the metal base width, and vth.m. is the velocity of hot electrons in the metal; and (3) the collector transit time 7c = Xm/2z’sc~rrm., where X, is the width of the collector depletion region, and vge.rrm is the scatter limiting drift velocity of the carrier’ in the collector. For all three hot-electron triodes considered, the base transit time is small and can be generally neglected (for Wb = 10-a cm, and vth.rn. 1: 108 cm/set, 71, = lo-14 set). Hence
Tee =
(
Cc?/gm+~
&I
2Vsc. lim.
METAL
1
The dependence of gain-band product K on base width wb is, therefore, only through the dependence of a and r’b on wb. Following EARLY'S treatment of the bipolar junction triode,(le) consider a simple linear stripe geometry of unit length with an emitter stripe
BASE
249
width s, spaced s/2 from the base stripes. The collector capacitance is then sCc, and the base resistance r’b = &+,&/Wb, where Ce is the collector capacitance per unit area [= (K/h)(l/xm)], and pnais the resistivity of the metal base. For a hot-electron triode with unity emitter efficiency, its gain is given by M = (1 -R)
6 x 101” 4x 109 product
THIN-FILM
exp( - wb/L)
(3)
where L is the hot-electron range in the metal base, and R is its reflection coefficient at the collector. Substituting for r’b, Cc&, and a in equation (l), gives
K, obviously, has a maximum, which is reached when Wb = L/2, i.e. when the base width is just one-half the hot-electron range
(5) Substituting K max=-
for T~(: from equation (2) gives 1-R S
(3/8re)L/qh [ l/%c.lim. +2/x&m/Ce)
1
I.12 (6)
This relation is applicable to all three hot-electron triodes under consideration. It indicates the dependence of Kmax on the figure of merit (gm/Ce) of the specific type of emitter that the triode utilizes. From the dependence of (gnz/Ce) on emitter current density je, as discussed in Section II.4 and presented in Fig. 3, and from equation (6)) one obtains the dependence of Kmax on emitter current density. This calculation was carried out, and the results are given in Fig. 4 as Kmax versus emitter current density for the three hot-electron triodes under consideration. For comparison, EARLY'S value of gain-band product of 5-12 x lOa/S for the bipolar germanium transistor is also indicated on the figure. From the results, the following conclusions may be made: (1) The highest-frequency performance should be obtainable by the SMS triode, followed by the space-charge-limited emitter triode and finally by the tunnel-emitter triode. (2) While
250
M.
M.
ATALLA
and
R.
W.
35Oi GOLD
SOSHEA
BASE-
Si Collector
e Width
10 Microns
FIG. 4. Comparison of gain-band product vs. emitter current density for three hot-electron triodes. The corresponding performance of the germanium transistor is also indicated.
both the SMS triode and the space-chargelimited emitter triode have high-frequency performance superior to that of the bipolar transistor, the tunnel-emitter triode performance will not exceed that of the bipolar transistor except at rather excessive emitter current densities. (3) For all three hot-electron triodes, K,,, approaches an asymptotic limit with current density that is due to collector limitations. As shown in Fig. 4, however, only the SMS triode closely approaches this limit at a reasonable current density. This limit is readily obtainable from equation (6) by setting g,/Ce = co. Under the conditions of Fig. 4, one obtains 1.4 x 10s (Kmsx)rss,.So c/Is (7) which is one to two orders of magnitude higher than calculated for the bipolar transistor.(rs) Finally, at an emitter current density of 1000 A/ems, the maximum oscillating frequencies for the triodes under consideration are as follows:
SMS triode Space-charge-limited emitter triode Tunnel-emitter triode (Bipolar transistor
kMc/s 60 38 10 5-12)
REFERENCES 1. C. A. MEAD, Proc. I.R.E. 48, 1359 (1960). 2. J. P. SPRATT, R. F. SCHRARZ and W. M. KANE, Phys. Rev. Letters 6, 341 (1961). 3. M. M. ATALLAand D. KAHNG, IRE-AIEEDevice Research Conference, University of New Hampshire (1962). 4. D. V. GEPPERT, Proc. I.R.E. 50, 1527 (1962). 5. D. KAHNG, Proc. I.R.E. 50, 1534 (1962). 6. M. M. ATALLA, NEREM Rec. p. 162 (1962). 7. W.G. SPITZER,C.R.CROWELL~~~M.M.ATALLA, Phys. Rev. Letters 8, 57 (1962). 8. A. G. CHYNOWETH, Progr. Semicond. 4, 97 (1959). 9. R. L. PRITCHARD, Frequency Response of Grounded Base and Grounded Emitter Transistors, AIEE Winter Meeting, New York January (1954). 10. J. M. EARLY, Proc. I.R.E. 46. 1924 (1958).