1076
IEEE JOURNAL OF SOLID-STATECIRCUITS, VOL. SC-15, NO. 6, DECEMBER 1980
James D. Beasom received the B.S. (with dis-
tinction) in engirieering science from Permsyl-
vania State University, University Park, and the
M.S. in electrical engineering from the Univer-
sity of Michigan, Ann Arbor.
He joined Harris Semiconductor in July 1966
as a Senior Engineer assigned to a process and
device development group. While a member of
that group, he studied thermal oxides and
developed processes for the fabrication of
n-channel and p-channel MOSFET’S. Subse-
quently, he joined the Product En@eering Group as a Circuit Engineel
working on the development of three custom, radiation-hardened
digital circuits. Later, he transferred to the Device Group of the
Engineering Department, His assignments in that group included linear
p-n-p design; development of complementary finear device processes;
development of processes for the fabrication of n-p-n’s and FET’s in a
monolithic substrate; design of hardened TTL devices; and develop-
ment of a. number of linear and digital circuits employing these pro-
cesses, Currently, he is the Manager of the Analog Technology Depart-
ment. He directs and participates in the design and development of
new linear devices and processes. His group is responsible for the initial
device design and process development for rdl Harris Semiconductor
linear circuits. It is also responsible for pilot wafer fabrication of these
products to prove yields and reliability before they are released for
production. He is currently developing processes for the fabrication of
high-frequency and high-current complementary linear devices and the
fabrication of complementary bipolars and FET’s in a monolithic
substrate.
He is also developing a GHz frequency range MOS IC pro-
cess. His patents include: an improved tield effect transistor, a process
for simultaneous fabrication of n-p-n’s, p-n-p’s, and MOS devices, a pro-
cess for forming buried layers to reduce collector resistance in top
contact transistors, and an improved semiconductor device (quasi-
vertical transistor).
Accurate Analysis of Temperature Effects in /c-l/BE
Characteristics with Application to Bandgap
Reference Sources
YANNIS P. TSIVIDIS, MEMBER,lEEE
Abstract–The inaccuracy of the analyses commonly used for predict-
ing the temperature behavior of the Ic- V~ characteristics of transis-
tors and the output of bandgap reference sources is pointed out. The
problem is traced to a basic assumption implicit, in such analyses,
namely that the variation of the bandgap voltage of silicon with tem-
perature is Iinear; this assumption is shown to be of poor accuracy.
By taking into account the nonlinearity in this variation, new accurate
formulas tire derived. Both the previous analyses and the proposed
analysis tie compared to experiment; a valuable improvement is dem.
onstrated.
Equations which should prove of vake in the design of
bandgap reference sources and bipolar transistor temperature trans-
ducers are given. H@her order effects are discussed.
I.
INTRODUCTION
N accurate evaluation of the temperature effects in lC-
A
VBE
characteristics is needed in the design of bandgap
reference sources and temperature transducers implemented in
Manuscript received April 8, 1980; revised June 16, 1980.
bipolar technology [1] - [8], Bandgap reference sources are
extensively used in A/D and D/A converters, voltage regulators,
and measurement systems; temperature transducers find appli-
cations in instrumentation and measurement.
In the equations usually found in the literature for the tem-
perature dependence of lC-VBE characteristics and the output
of bandgap reference sources [2]- [4], [7], [9]-[11 ], two
parameters appear: the extrapolated bandgap voltage of silicon
to O K, and a process-dependent parameter denoted by ~ [3],
[11 ] or a variety of other symbols. It is found that when the
values expected from physics are used for these parameters,
the equations do not agree with measurements [3], [7],
[11 ]- [16]; for this reason, fictitious values are often used for
these parameters in an attempt to make the equations fit the
experimental data.
In this paper, it will be shown that the above discrepancies
between theory and experiment are due to an assumption
which, explicitly or implicitly, is made in the derivation of the
The author is with the Department of Electrical Engineering and
. . . . .
Computer Science, Massachusetts Institute of Technology, Cambridge,
equations used: that the variation of
the bandgap voltage of
MA 02139, on leave from the Department of Electrical Engineering,
silicon with temperature
Columbia University, New York, NY 10027.
shown to be not justified
is linear. This assumption will be
for the level of accuracy commonly
0018-9200/80/1200 -1076$00.75 @ 1980 IEEE