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11
Bipolar Junction Transistor Compact Models
11.1 Introduction
As described in Chapters 4 and 5, the pn-junctions are integral part of a
MOSFET (metal-oxide-semiconductor field-effect transistor) device structure
as the source and drain regions. Under the appropriate biasing condition of
a MOSFET device, the source of the source-substrate pn-junction provides a
steady supply of mobile carriers to form a conducting channel from the source
to drain and the drain of the drain-substrate pn-junction collects the mobile
carriers generating drain current. Two back-to-back pn-junctions form a bipolar
junction transistor (BJT). BJTs are very often used in VLSI (very-large-scaleintegrated) circuits. Therefore, a basic understanding of BJT modeling is necessary for engineers and researchers involved in device modeling. In this chapter,
we present the basic but widely used BJT compact models for circuit CAD.
BJTs are active three-terminal devices and were the main active elements
for ICs (integrated circuits) in the 1960s [1,2]. The areas of applications of BJTs
include amplifiers, switches, high-power circuits, and high-speed logic circuits for high-speed computers. After the invention of bipolar transistors in
1947 [3], discrete BJTs were used to design circuits on printed circuit boards.
In order to analyze the performance of BJTs, Ebers and Moll in 1954 reported
a physics-based large signal BJT model, referred to as the Ebers–Moll or EM
model [4]. The level 1 EM model, known as the EM1 model, is valid for the
entire operating regime of BJTs from cutoff to active region. However, the
application and accuracy of EM1 model are limited to evaluating the DC
performance of the devices only due to several simplifying assumptions. In
order to improve the modeling accuracy, EM1 model has been extended to
EM2 and EM3 models for predicting the observed physical effects in BJTs
including transient phenomena [5].
Though EM2 and EM3 models accurately predict most of the observed
physical effects in BJTs, a more complete and unified physics-based BJT model
was reported by Gummel and Poon in 1970 [6]. This model is known today
as the Spice Gummel–Poon (SGP) model [7]. The SGP model uses an integrated
charge control approach along with a very clear and standardized description of many observed effects in BJTs such as early effect [8], high current
11
Bipolar Junction Transistor Compact Models
11.1 Introduction
As described in Chapters 4 and 5, the pn-junctions are integral part of a
MOSFET (metal-oxide-semiconductor field-effect transistor) device structure
as the source and drain regions. Under the appropriate biasing condition of
a MOSFET device, the source of the source-substrate pn-junction provides a
steady supply of mobile carriers to form a conducting channel from the source
to drain and the drain of the drain-substrate pn-junction collects the mobile
carriers generating drain current. Two back-to-back pn-junctions form a bipolar
junction transistor (BJT). BJTs are very often used in VLSI (very-large-scaleintegrated) circuits. Therefore, a basic understanding of BJT modeling is necessary for engineers and researchers involved in device modeling. In this chapter,
we present the basic but widely used BJT compact models for circuit CAD.
BJTs are active three-terminal devices and were the main active elements
for ICs (integrated circuits) in the 1960s [1,2]. The areas of applications of BJTs
include amplifiers, switches, high-power circuits, and high-speed logic circuits for high-speed computers. After the invention of bipolar transistors in
1947 [3], discrete BJTs were used to design circuits on printed circuit boards.
In order to analyze the performance of BJTs, Ebers and Moll in 1954 reported
a physics-based large signal BJT model, referred to as the Ebers–Moll or EM
model [4]. The level 1 EM model, known as the EM1 model, is valid for the
entire operating regime of BJTs from cutoff to active region. However, the
application and accuracy of EM1 model are limited to evaluating the DC
performance of the devices only due to several simplifying assumptions. In
order to improve the modeling accuracy, EM1 model has been extended to
EM2 and EM3 models for predicting the observed physical effects in BJTs
including transient phenomena [5].
Though EM2 and EM3 models accurately predict most of the observed
physical effects in BJTs, a more complete and unified physics-based BJT model
was reported by Gummel and Poon in 1970 [6]. This model is known today
as the Spice Gummel–Poon (SGP) model [7]. The SGP model uses an integrated
charge control approach along with a very clear and standardized description of many observed effects in BJTs such as early effect [8], high current