Thermal feedback theory for silicon junction FET operating at low temperature

Churchill, M. J.

Lauritzen, P. O.

English

NASA Technical Reports Server

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THERMAL FEEDBACK I N  S i  JFETs OPERATING AT LOW TEMPERATURES 
M. J. Churchill  
and 
P. 0. Lauritzen 
University of Washington 
Department of Electrical Engineering 
Sea t t l e ,  Washington 98105 
ABSTRACT 
Thermal feedback modifies t h e  dc and ac charac te r i s t ics  of JFETs 
operating a t  temperatures where carrier freeze out.occurs.  
common source operation are analyzed using t h e  thermal feedback theory 
of Mueller. 
Data for 
22 
This work was supported by the  Office of Engineering Research a t  the  
University of Washington and by NASA Grant NGR 28-002-078. 
https://ntrs.nasa.gov/search.jsp?R=19700031984 2020-03-11T23:08:20+00:00Z
Operation of JFETPs  (Junction Field Effect Transis tors)  a t  tempera- 
tures where carrier freeze-out occurs is w e l l  known Ell, [ 2 l S  
t he  dc and ac cha rac t e r i s t i c s  are grea t ly  modified by thermal feedback 
when the  carrier concentrations become strongly temperature dependent 
(below 125OK for Si l icon  JFET's). 
sidered i n  t h e  design of low temperature amplifiers. 
theories  of Burgess C3l and pa r t i cu la r ly  Mueller C41 are d i r e c t l y  applicable 
t o  JFET ' s ,  
only i n  an unusual voltage driven grounded base configuration C41, while 
However, both 
This thermal feedback should be con- 
The thermal feedback 
In bipolar  t r a n s i s t o r s  thermal feedback becomes s ign i f i can t  
i n  J F E T P s  a t  low temperatures it is important i n  t h e  usual common source 
configuration, 
Causes of Thermal Feedback Effects 
The drain current i n  a JFET operating with f ixed bias  is proportional 
t o  the  carrier density i n  the  conducting channel, 
the  shallow donor or acceptor l eve l s  i n  the  channel region begin deion- 
iz ing a t  temperatures below 125OK thus reducing t h e  carrier densi ty  
( ca r r i e r  "freeze-out"). 
of temperature T is approximately 
I n  commercial devices 
Near 77OK t he  c a r r i e r  density n(T) as a function 
n(T) 01 exp (-9 Ecd/2kT) . 
Here Ecd is t h e  energy difference between the  conduction band and t h e  
donor l e v e l  (for an n-channel device) and q E 
a tu re  dependence of n(T) is primarily responsible f o r  t he  la rge  pos i t ive  
temperature coef f ic ien t  of the  dra in  current. The mobility and bu i l t - i n  
voltage change r e l a t i v e l y  slowly with temperature and need not be included 
i n  the  model. 
>> kT, The strong temper- cd 
2 
The ac t ive  region of t h e  JFET i s . thermal ly  coupled t o  the  ambient by 
a frequency dependent the rma l  impedance Z (w) where w is the  angular fre- 
quency. 
t 
The power d iss ipa t ion  P(w) due t o  a s igna l  of frequency w r e s u l t s  
i n  a temperature change T(w) i n  t h e  ac t ive  region given by T ( o )  = Zt(w) e P(W>. 
The thermal impedance decreases at  high frequencies s ince the  device t e m -  
perature can not follow high frequency power d iss ipa t ion  var ia t ions.  The 
dc thermal res i s tance  R = Z (0) was determined experimentally by measuring t t 
the  increase of i n t e rna l  device temperature for various d iss ipa t ion  leve ls .  
A measurement of t he  zero-bias channel conductance g 
pulse was used t o  determine the  in t e rna l  temperature under operating b i a s  
during a 1OMs "off" ds  
conditions by comparing t h i s  g 
perature. 
t o  a curve of equilibrium g ds  ds  versus t e m -  
F'rom a p lo t  of t h e  in t e rna l  temperature as a function of the  
power d iss ipa t ion ,  Rt was found t o  be typ ica l ly  150-960°K/watt depending 
upon t h e  device type and t h e  ambient temperature. 
Effect on dc Characteristics 
Most models f o r  the  dc charac te r i s t ics  assume a constant device tem- 
perature and thus a constant carrier densi ty  i n  the conducting channel 
region, To  include the  thermal effects due t o  the  dependence of n(T) on 
the  device d iss ipa t ion ,  t h e  temperature T is  taken as T = TA + V 
where T is the  ambient temperature and V and I are t h e  dc drain-source 
I R DS D t 
A DS D 
voltage and cwrent respectiveiy.  When (1) is  va l id  the  b a i n  current may 
be wri t ten i n  t h e  forin 
r 
ID =! IDN exp 
L .J 
3 
where IDN is t h e  drain current obtained neglecting heating effects. 
Fig. 1 measurements a t  T 
The cbain current  without heating IDN is measured using short  pulses.  
Agreement is  very good except a t  high d iss ipa t ion  l eve l s  where t h e  high 
I n .  
= 77OK are compared with calculat ions from (2) .  A 
i n t e rna l  temperature makes (1 inval id  e 
Effect on ac Parameters 
Using the  expressions developed by Mueller t he  y-parameters with 
I - 
thermal feedback y21 and y22 are r e l a t ed  t o  the  constant temperature y- 
parameters y21 and y22 by 
- - y21 - 
'21 1 - DDIDVDSZt(u) 
- - y22 + I i D D Z t ( w )  
'2 1 - DDIDVDsZt(u) - 
. The other  JFET y-parameters yll and y are not where D = - - 
s igni f icant ly  affected by thermal feedback. 
1 alD 
12 aT I D  
The voltage gain %(u) f o r  
a common source s tage becomes 
( 3 )  
(4) 
where RD is the  drain load r e s i s t o r .  
Experimental r e s u l t s  f o r  7 and 7 of two e l e c t r i c a l l y  similar 
devices having widely d i f f e ren t  thermal resistances are shown i n  Fig. 2. 
2 1  22 
The device with t h e  lower thermal res i s tance  has a much smaller var ia t ion  
of Y22. 
4 
The voltage gain 
3 for three values of 
for? a 
dra in  
are iden t i ca l  for  each case 
represent d i f f e ren t  thermal 
dependent zv is obtained a t  
common source 
load r e s i s t o r  
JFET s tage is shown i n  Figure 
RDe The dc voltages and currents  
but t he  d i f f e ren t  frequency responses observed 
feedback conditions. 
a sacrifice i n  voltage gain when the  drain 
A nearly frequency in- 
r e s i s t o r  load l i n e  is  tangent t o  the  curve of constant d i ss ipa t ion  a t  t h e  
operating point.  
To avoid thermal feedback a t  low temperatures, devices must. be se- 
lected having low thermal res i s tances  and must be operated a t  low b ias  
levels .  
tures so carrier freeze-out is  not present. 
Alternatively,  devices can be operated a t  higher ambient tempera- 
5 
REFERENCES 
1. E, Elad and M. Nakamura, "High resolution beta and gamma ray spectro- 
meter," IEEE Trans, Nuclear Science, Vol. NS-14, pp. 523-531, 
February, 1967. 
2, T. V. Blalock, "A low noise charge-sensitive preamplifier with a field 
effect transistor in the input stage,s' IEEE Trans. Nuclear Science, 
Vol. NS-11, pp. 365-372, June, 1964. 
3. R. E. Burgess, "The a.c. admittance of temperature-dependent circuit 
elements," Proc. Phys. SOC. (London), Vol. 68B, pp. 766-774, 
1955. 
4, 0. Mueller, "Internal thermal feedback in four poles, especially in 
transistors," Proc. IEEE, V o l .  52, pp. 924-930, August, 1964. 
6 
FIGURE CAPTIONS 
Figure 1: Current-voltage cha rac t e r i s t i c s  for JFETs with d i f f e ren t  
= 420°K/W f o r  2N5475, Rt = 170°K/W Rt thermal res is tances .  
f o r  3N124. TA = 77OK, VGs = 0. 
Figure 2: Frequency dependence of normalized y21 and y 
with d i f f e ren t  thermal res is tances .  
VDs = 20 vo l t s ,  ID e? 1.6mA. 
for  JFETs 22 
Bias VGs = 0, 
TA = 77OK. 
Figure 3: Ratio of frequency dependent common source voltage gain 
- 
Av ( f )  t o  its high frequency value Av f o r  various drain load 
r e s i s t o r s  s. Device 2N5475: VGs = 0 ,  VDs = 20 vo l t s ,  
ID = 0.9 mA, TA = 77OK. 
2.0 
1.8 
1.6 
A 
h 
Q 1.2 
E 
U 
.O 
I- z 
w 
a a 
2 0.8 
2 
m 
4 
a 0.6 
0 
0.4 
0.2 
0 
2 
PULSED 
0 
0 
a. 
, 


Thermal feedback in Si JFETs operating at low temperatures

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