Middlebrook, R. D.

Richer, I.

Caltech Authors - Main

[Authors' Comment on] Power-Law Nature of Field-Effect Transistor Characteristics

314 PROCEEDINGS OF THE IEEE March 
and We<<I, , , ,  respectively. Therefore, T,  of 
the mesa type  transistor  can  be  reduced re- 
markably  by  doping  trap  impurities  into  the 
collector region or by  reducing TVc by  an  epi- 
taxial  structure,  and  the  reduction  factor of 
T, can be estimated quantitatively by ( 4 )  
and  (S), respectively. 
The authors with to thank Dr. Takeda 
of Sippon  Electric Co. Ltd. for his support 
of the program. 
H. YANAI 
T. SUGAXO 
K. TADA 
Dept. of Electronic  Engrg. 
Pniversity of Tokyo 
Tokyo,  Japan 
Feedback in Cyclotron-Wave 
Frequency Multipliers* 
Frequency multiplication at microwave 
frequencies by fast cyclotron-wave  inter- 
action  through  the use of multipole  cavities 
has been studied by Cuccia,’ Ashkin2 and 
more recently  by  Dain  and T h ~ m p s o n . ~   T h e  
general scheme of the  operation is to intro- 
duce a beam  carrying a fast  cyclotron  wave 
into a multipole cavity. The beam rotates 
like a metallic conductor around the inside 
of the  cavity.  Interaction between the  beam 
(which is rotating at an angular frequency 
wc) and  the  slot field of the  multipole  cavity 
excites a *-mode oscillation. An output at 
angular frequency me can be coupled from 
the  cavity.  (The  number of poles of the  cav- 
ity  equals 2n . )  As power is drawn from the 
cavity, the rotating beam loses its energy 
and  its  radius of rotation is decreased.  Due 
to  the  fact  that  the  interaction field in the 
neighborhood of the slot varies as ( ~ / u ) ~ - I ,  
where a is the radius to the vane tip, the 
field decreases very  rapidly with the  distance 
away from the slot. This places a limit on 
the  amount of power that  can be withdrawn 
from the  cavity.  For  instance, in an 18-pole 
cavity multiplier, if half of the rotational 
energy of the  beam is withdrawn,  the  radius 
of rotation reduces to (u/@). At  this 
radius,  the  interaction field has been reduced 
to  (l/dZ)g-* (or &,) of the  slot field, which 
is far too weak  for  useful interaction. Cuccia’ 
obtained a “transfer efficiency“ of 1.5 per 
cent using an 8-pole cavity. In  Dain and 
Thompson’s3  computation, 7 7  per cent of 
the  rotational  beam power is collected (and 
wasted) at the collector. 
The present scheme proposes the use of 
supported by the C .  S. S a w  Bureau of Ships under 
*Received September  26,  1963.  Thi3 wolk was 
Contract Nohsr;89274. 
1 C L. Cuccla ‘The electron coupler-a develop- 
mentai tube for ’amplitude modulation andn power 
control at ultra-high  frequencies,  Part 11. RCA 
Rm.. vol. 14.  pp. 72-99. March 1953. 
: A .  Ashkin YA microwaLe  Adler tube,” 1960 
l+tfnnnf’ l .  Conbrcss on Minowarc T u b a  Record. - .. . . .~ ~ 
Munich, Germany. 
, W i n  2nd R .   R .  Thomoson. ‘A cvclotron 
resonahce  frequency  multiplier.” IEEE T R ~ S S .  OS 
ELECTRON DEVICES, vol. EDIO. PP. 195-200; May, 
1963. 
a A ... ~ . .  ~ ~~~ 
Fig. 1-Sketch of a fast cyclotron  wave  frequency 
multiplier  using  modified  Cuccia  coupler  with 
feedback. 
feedback to  enhance  the conversion effi- 
ciency. The  schematic  diagram of the device 
is shown in Fig. 1. 
-4 Cuccia coupler [ s e e  (2 )  in Fig. 11 is 
used at   the exit  end of the  beam  to pick up 
its  residual  rotational  energy  and feed back 
to  the  input  through a  second  Cuccia coupler 
arranged  in  space  and  time  quadrature with 
respect to the input Cuccia  coupler. This 
modified Cuccia coupler [see (1) in Fig. 21 
excites the fast cyclotron wave through a 
circularly polarized wave. Part of the exci- 
tation power is supplied  by  the  input signal 
and  part  by  the  feedback  coupler.  The power 
that would have been wasted is thus utilized. 
This  means that for the  same  output power, 
the  input power supplied  by  the signal 
source can be reduced. In other words the 
conversion efficiency of the device can be 
increased. 
Let 
V1=input coupler efficiency (both cou- 
72 =extraction coupler efficiency [Cuc- 
q3 = multipole  cavity coupling efficiency, 
b-electronic  conversion efficiency (due 
to left over  rotational  energy),  and 
7 = the over-all efficiency. 
plers), 
cia coupler (2)], 
Then the over-all efficiency of a frequency 
multiplier  with  feedback is given by 
? =  
h 1 7 3  . 
1 - (1 - t)?l?? (1) 
On the other hand, without feedback, ;.e., 
q;=O, (1) reduces to 
11 = b11111n. (2) 
The  “transfer efficiency” in Cuccia’s and 
the  ”output coupler efficiency” in Dain  and 
Thompson’s papers both correspond to rqa 
by  this definition. 
In  an ideal  case  inwhich 11‘Vqz‘Vq~‘VlOO 
per cent, an overall efficiency of PI = 100 per 
cent  can  be  achieved  irrespective of the in- 
herent inefficient mechanism of the multi- 
pole cavity multiplier as expressed by r. 
The electronic conductance of a Cuccia 
coupler4 is given by 
Get = s 1 12 
mental tube for  amplitude  modulatio?  and power con- 
4 c .  L. Cuccia ‘The electron coupler- develop 
trol at ultra-high frequencies, Part I. RCA Rev., ~ 0 1 .  
IO. pp. 270-303; June, 1949. 
where 10 is the  beam  current  and VO is the 
beam  voltage; 12 and d0 are  the  length  and 
separation of the Cuccia coupler [(2) of 
Fig. 11 plates, respectively. For a modified 
Cuccia coupler used to excite a circularly 
polarized wave described in (1) Fig. 1, the 
electronic  conductance seen by  each  coupler 
is found to be 
Thus if it is intended to feed back half of the 
rotational power to  the  input,  the  impedance 
matching can be accomplished by letting 
G,,=Gel. If ll=Zt,  it is found that  the sepa- 
ration of the  plates of the  extracting  coupler 
d l  should be (l/&‘)d,, that of the input 
coupler. 
C. YEA 
J. C. LEE 
, Electron  Physics  Lab. 
The  University of Michigan 
Ann Arbor. Mich 
Power-Law  Nature of Field-Effect 
Transistor Characteristics* 
I t  is interesting  to see in Richer  and 
Middlebrook’s communication‘ the experi- 
mental justification of a power-law relation- 
ship between drain  current  and  gate  voltage. 
LVe have already proposed similar for- 
mulas for cylindrical structure field effect 
transistors  (tecnetron).*  Taking n = 2  in (2) 
of Richer  and Middlebrook,’  we obtain 
Our  “parabolic  approximation,”* using 
the  same symbolism,  gives exactly  the  same 
result (third line, p. 88A2). However, as it 
has been shown in our publication,  this  ap- 
proximation is very  rough in the  case of cy- 
lindrical structures, giving results some- 
times which are twice the  exact  value,  as  in 
the case of the maximum drain current. In 
fact, our graph 6 ,  p. 7.43 shows the  variation 
of the slope as a function of the  gate  voltage 
for different approsimations. I t  also indi- 
cates  that  the  above  formula is the worst of 
all  the  approximations in the case of cylin- 
drical  structure devices. 
I t  would be  interesting to know with 
what type of geometric structures Richer 
and Middlebrook have been experimenting 
and what changes in the relationships ob- 
tained  experimentally  are  brought  about 
by modifications in the  geometric  structure 
of the device. 
* Received September 23. 1963. 
1 I. Richer and R. D. Middlebrook. “Power law 
nature 0: field-effect transistor experimental charac- 
teristics P R ~ .  IEEE. p.  1145; August, 1963. 
graphique du  fonctionnement  du tecnCtron,“ I .  Phy-  
f A. c. J.  Martm and J. LeMh. AMIYSZ semi- 
SiQue Rad., rol. 22, suppMment au  fawicule 2. P. 1A; 
,of., I I Y L .  
3 A. V. J. Martin and J. L e M k  “Analyse graph- 
ique du fonctionnement du tecnetro?: etude compara- 
tive  des diverses  approximations, J .  Phyr. Rad.. 
vol. 22, SupplCment au  fascicule 6.  P. .SA; 1961. 
1964 Correspondence 315 
Lye have p u b l i ~ h e d ~ , ~  comparisons  be- 
tween characteristics of plane  and cylin- 
drical  structure field effect transistors  in  the 
hypercritical region  where the mobility is 
assumed to  vary  as (E)-1’2, E being the  axial 
electric field. LVe also  have proposed a num- 
ber of approximate  relationships  giving  the 
electrical characteristics of field effect tran- 
sistors.2 
Other  geometric  structures  have been 
studied. rl paper on this  subject will be pub- 
lished shortly. 
JEAS LEAIBE 
Control  Systems  Dept. 
\Vestinghouse Electric Corp. 
Research and  Development  Center 
Pittsburgh, Pa. 
A .  V. J. LIARTIN 
Director,  Electronique et  Automatisme 
et  Electronique Medicale 
Paris,  France 
-4 uthors’ Comment6 
The  details of the theoretical justification 
for our power-law approximation to field- 
effect transistor ( F E T )  characteristics  have 
not yet been published, but a summary of 
some of the results is given in two recent 
articles.7.8 \\-e consider  asimple, planar 
FTE  and show that  its  properties  are essen- 
tially independent of the impurity profile. 
Thus,  the  theory  obviates  the  solution of an 
analytically intractable device, such as one 
with  a diffused junction,  because  such a 
device may be satisfactorily approximated 
by an  analytically simple structure. 
The normalized drain current is espe- 
cially  insensitive to  the  impurity profile, and 
beyond pinch-off may be approximated by 
a power law of the  form 
The  main  ad\-antage of this  approximation 
is  that it permits  determination of the pinch- 
off voltage V ,  from a straight-line plot of ex- 
perimental quantities. If some weak condi- 
tions are imposed on the impurity profile, 
then  the  exponent n is  restricted to  the 
rather  narrow  range 2 1 n 1 2 . 2 5 . 8  Eq. (1) is 
not intended to  be  exact  at  any  one  point, 
but  represents  an  approximation to the 
over-all shape of the actual transfer char- 
acteristics.  Further,  the worst percentage 
errors in (1) occur near V,= - V, where 
I d = o ,  i .e.,  where percentage errors are un- 
important  experimentally. 
The  theory  embraces  sentially  all 
FET’s that are produced domestically, be- 
cause practical impurity profiles generally 
Analysis of Hypercritical Field Oreration andnCom- 
4 A .  V. J. Martin and ,J. L e M k ,  “First Order 
pared Performances of Field Effect Devices, Coll 
Paris. France,  vol. 1 .  p.  516. 
Int. sur les dispositiis B semiconducteurs. UNESCO, 
8 A .  V. J .  Martin and J. Le?%&, “;\nalyse ap- 
champ en region hypercritique.” J. Phys .  Rad. ,  vol. 
prochCe du fonctionnement des drspositifs a effet de 
23, SupplCment au fascicule 12, p. 177A; 1962. 
6 Received Cpober  31, 1963. 
effect transistors, Solid-Stale  Electronics, vol. 6, pp. 
7 I. Richer, B:sic limits on the properties of field- 
539-542; September. 1963. 
power-law exponent for field-effect transistor transfer 
8 R.  D. Middlebrook and I. Richer,  “Limits on the 
characteristics,” Sdid-Stalc Electronics. v01. 6 ,  pp. 
542-544; September, 1963. 
satisfy  the necessary conditions,  and  because 
most  structures  are  planar or approximately 
so. The devices for which experimental re- 
sults were reported in our communication’ 
have  the following geometries: 
Crrstalonics  610 . . . concentric 
Motorola “764 . . planar 
Fairchild FSP 401 . . planar. 
Texas Ins. TIX 691 . . approximately planar 
The functional relations for an FET with 
concentric geometry are identical to those 
for a planar FET. A t  present, the theory 
does not include cylindrical FET’s but un- 
doubtedly  the  method of approach sum- 
marized in Richer7 could be  applied to those 
devices. 
I. RICHER 
R. D. MIDDLEBROOK 
Division of Engineering  and Applied  Science 
California Institute of Technology 
Pasadena, Calif. 
Diocotron Gain Reduction and 
Space Charge Smoothing in 
Crossed-Field Guns* 
Until  recently  it was commonly believed 
that noise in crossed-field devices is increased 
as the operation of the device is changed 
from a temperature-limited operation to a 
space-charge-limited  operation. I t  is only 
recently that both the theoretical1 and ex- 
perimentar results have indicated that the 
space-charge-limitation causes, in fact, a 
considerable reduction in the current fluc- 
tuations, which in  turn  reduces  the noise 
content in the beam. The velocity fluctua- 
tions, however, may vary, depending upon 
the type of beam focusing system used in 
the  gun region, and  Kino gun3 operation 
seems to be quite reasonable in yielding a 
laminar flow. Comparison of the noise char- 
acteristics of a device  under  the  two  operat- 
ing conditions  has also  become questionable 
particularly when the  trajectories  and 
velocity components under the two differ- 
ent operating conditions require two com- 
pletely different gun designs.’ 
I t  has been reported  that  the  reduction 
in noise figure, possibly due  to  space-charge 
smoothing, applies more to larger values of 
beam currentsz which are obtained by in- 
creasing the values of V ,  (the gun-anode 
voltage)  and B (the  magnetic field) in such 
a manner  that ( 1’,/B2) remains  constant so 
that the trajectories in the gun region are 
in this work was supported by the Bureau of Ships, 
* Received October 4, 1963. The research reported 
Department of the Savy.  Washington, D.  C.. under 
Contract No. NObsr-89546. 
calculation of noise transport in electric and  magnetic 
1 R. P. Wadhwa and J. E. Rowe. “Monte Carlo 
fields.”  IEEE TRASS. o s  ELECTROS DEVICES. vol. 10, 
pp. 378-388; November, 1963. 
2 M. S. Raju, T.  Van Duzer and R. D. Harris 
Cros.sed-Field Amplifiers. presented at the Twenty- 
”Calculations  and MeasurFments Concerning Noise i; 
First Conf. on Electron Device Research. Salt Lake 
City;  June, 1963. 
3 G. S. Kino, ‘A design method for crossed-field 
ekctron  gun,’  IEEE TRANS. ON ELECTRON DE- 
characteristics of tempefature  and space-charge- 
4 R. P. Wadhwa and J. E. Row-e, Steady-state 
limited crossed-field flows, to be published. 
VICES. vel. ED-7. PP. 179-185; July, 1 9 y .  
unaltered.  There  are, i n  fact,  several  factors 
causing this extra reduction in noise. From 
the expression  for the  diocotron  gain  in  the 
gun region developed in the following, it is 
shown,  by  operating at a larger  value of gun 
anode  voltage, that  the  value of the  required 
cathode current density is increased, which 
reduces the  diocotron  gain (or excess noise) 
in the  gun region. I t  appears  from  this infor- 
mation that the noise reduction for larger 
values of beam  currents  is  due  mainly  to a 
reduction of excess noise in the gun region 
and not to increased space-charge smooth- 
ing. An  increase in  the  value of the  cathode 
current density also increases the electron 
plasma  frequency at   the  potential  minimum 
and,  as  observed  in  the one-dimensional cal- 
culations, reduces further the current fluc- 
tuations at   the  operating frequency by an 
increased space-charge  smoothing. However, 
the two-dimensional calculations1 have not 
revealed such a dependence on the electron 
plasma  frequency at   the potential  minimum 
for the  various  portions of the  beam  studied 
beyond the potential minimum. 
The expression  for a, the  diocotron gain 
per unit length as  derived  by Gould,s is 
given by 
a=- TIQj  
eokB2c03 
nepers/unit  length, (1) 
where Io =beam  current, f =  operating fre- 
quency,  eo=permittivity of free space, 
h=width of the  beam in the  direction of the 
magnetic field, B =magnetic field intensity 
and uo=beam velocity. This expression is 
valid  for a beam  drifting  between  two  paral- 
lel conducting planes. For the case of the 
Kino gun,3 this formula for the diocotron 
gain  may also he used piecewise when multi- 
plied by a factor F which takes  into  account 
the  contribution  due  to nonparallel  con- 
ducting planes in the gun region (between 
the T and 27r planes of the  Kino  gun 
FE1); thus  the  dependence of the  diocotron 
gain on the various parameters in the gun 
region (assuming  thin  beams)  can  be  deter- 
mined. By using the definitions of @ [the 
normalized voltage, + =(vJv2/eO2wc4)@], and 
2 [the normalized distance, 5 =(vJ,/eqw2)2]; 
as used in the  Kino  gun model, G the over-all 
diocotron  gain in the  gun region is given by 
where  z~l=width of the  cathode, 7 =absolute 
ratio of electron charge to its mass, Ju =cath- 
ode current density, @ and 2 are functions 
of w,T only,  and  the planes a and b are  two 
arbitrary planes  along the beam. The  values 
of a and b are specified by the values of 
w,T. Thus the diocotron gain in the Kino 
gun model is proportional to w and Bz and 
inversely proportional to -Tu. The expression 
for Jy in a Kino  gun is given by6 
where Va=gun  anode  voltage. LVhile main- 
taining ( Va/B2)=constant,  the  value of Jy 
magnetrons, J .  App l .  Phys.,.vol. 28. pp. 594404;  
j R. W. qould. “Space-charge  effects in beam-type 
May, 1957. 
6 T. A. Midford, “Some Expenmenis with New 
Type of Crossed-Field Electron Guns, Microwave 
Laboratory,  Stanford L’niversity, Calif.,  Rept. No. 
885;  February. 1962. 


https://authors.library.caltech.edu/99282/1/01444821.pdf

[Authors' Comment on] Power-Law Nature of Field-Effect Transistor Characteristics

Abstract

Similar works

Full text

Available Versions

Caltech Authors - Main

Caltech Authors - Main