ELEC 3908, Physical Electronics, Lecture 18
The Early Effect, Breakdown
and Self-Heating
Lecture Outline
• Previous 2 lectures analyzed fundamental static (dc) carrier
transport in the bipolar transistor (transistor action,
injection model)
• This lecture looks at three important effects in bipolar
devices, only one of which is included in the model
– The Early Effect: variation of current with base width, which is
included in the injection model implicitly
– Breakdown: increase in current due to impact ionization, the same
process as in the diode (lecture 12)
– Self-heating: an important physical effect discussed here in the
context of bipolar devices, but applicable generally
ELEC 3908, Physical Electronics:
Early Effect, Breakdown and Self-Heating
Page 18-2
Physical Origin of the Early Effect
•
•
When VCE is increased in forward active operation, the collector-base
reverse bias increases, widening the collector-base depletion region
The increases the extent of the collector-base depletion region into the
base, decreasing the neural base width WB
ELEC 3908, Physical Electronics:
Early Effect, Breakdown and Self-Heating
Page 18-3
Effect of Decreased WB In Injection Model
• As VCE increases, WB decreases, increasing the linking
current term of the injection model equation for IC
qAE D pC pCo
qAE DnB nBo qVBE kT
IC = −
e
− 1) +
e
− e qVBC kT )
(
(
WC
WB
14444
244443 14444
4244444
3
qVBC kT
collector hole injection ( I pC )
linking (electron) current ( I nB )
• Note that in the absence of this effect IC would essentially
not be a function of VCE once VBC became reverse biased
by more than -3kT/q
ELEC 3908, Physical Electronics:
Early Effect, Breakdown and Self-Heating
Page 18-4
Physical Origin of IC Increase
• Physically, the IC arises because the decreasing WB
increases the electron spatial gradient in the base, leading
to an increased component of linking current
dn B ( x ) n Bo e qV BE
=
dx
I n , diff = qADn
I nB
− n Bo e qV BC
WB
kT
dn ( x )
dx
qAE DnB n Bo qV BE
=
e
(
WB
ELEC 3908, Physical Electronics:
Early Effect, Breakdown and Self-Heating
kT
kT
− e qV BC
kT
)
Page 18-5
Early Voltage
•
•
•
The result of the Early effect is
to give IC a slope in the
forward active region when
plotted vs VCE
If the individual lines (different
IB’s) are extrapolated back to
the VCE axis, they will intersect
at approximately the same
point, called the Early Voltage
VA
A larger value of VA indicates
less Early effect
ELEC 3908, Physical Electronics:
Early Effect, Breakdown and Self-Heating
Page 18-6
Base-Collector Avalanche Breakdown
•
•
As VCE is increased and WBC
widens, the magnitude of the
peak electric field in the basecollector depletion region
increases
This can lead to the same
avalanche breakdown
mechanism as in the diode, and
similar models can be applied
ELEC 3908, Physical Electronics:
Early Effect, Breakdown and Self-Heating
Page 18-7
Characterization of Breakdown
•
•
Two different figures of merit
are used to characterize
collector-base breakdown
– the collector base breakdown
voltage measured with the
emitter held open, BVCBO
– the collector base breakdown
voltage measured with the base
held open, BVCEO
BVCBO characterizes the normal
pn-junction avalanche
breakdown mechanism in the
collector base junction, the
same mechanism as was
discussed in lecture 12 for the
diode
ELEC 3908, Physical Electronics:
Early Effect, Breakdown and Self-Heating
Page 18-8
Transistor Action in BVCEO
•
•
•
In the BVCEO measurement configuration, impact ionization generated
holes injected into the base must flow to the emitter, since the base
is open
Transistor action (i.e. the large doping difference between the emitter
and base) requires a corresponding large electron current to flow
This effect amplifies the impact ionization current, and hence gives a
lower value for breakdown voltage than the BVCBO measurement
ELEC 3908, Physical Electronics:
Early Effect, Breakdown and Self-Heating
Page 18-9
Example 18.1: BVCBO Calculation
Calculate BVCBO for the transistor shown below, assuming a
critical field of 2x105 V/cm. Will BVCEO be larger or
smaller than this value?
ELEC 3908, Physical Electronics:
Early Effect, Breakdown and Self-Heating
Page 18-10
Example 18.1: Solution
• Using the formula given in the diode avalanche breakdown
discussion (lecture 12)
V BR = BV CBO
2
E crit
ε Si
= Vbi −
2q
⎛ 1
1 ⎞
⎜⎜
⎟⎟ = −26 .5 V
+
⎝ ND NA ⎠
• BVCEO will be less then BVCBO, because transistor action
will amplify the impact ionization current, leading to
breakdown at a lower value of VCB
ELEC 3908, Physical Electronics:
Early Effect, Breakdown and Self-Heating
Page 18-11
Heat Flow Modeling
•
The basic (1D) equation giving heat
flux Φ (W/cm2) in terms of
temperature gradient is
dT
Φ = −κ
dx
•
•
•
κ is the thermal conductivity in
W/cmK
Heat flux is therefore proportional to
temperature gradient, and flows
“down” the gradient (-ve sign)
At a given temperature difference
between two bodies, heat flux is
larger when κ is larger
ELEC 3908, Physical Electronics:
Early Effect, Breakdown and Self-Heating
Page 18-12
Conversion of Energy in an Electrical Circuit
•
•
•
In an electrical circuit, power supplied by sources such as batteries is
absorbed by circuit elements such as resistors, transistors, integrated
circuits, etc. - this absorbed power is dissipated as heat
When electrons travel through a resistor, they are scattered by, and
hence transfer energy to, the resistive material, resulting in a
temperature increase in the resistor and a “voltage drop” (the loss of
energy by the electrons) across the resistor
Circuit elements therefore convert electrical energy to thermal energy
ELEC 3908, Physical Electronics:
Early Effect, Breakdown and Self-Heating
Page 18-13
Self-Heating and Thermal Resistance
•
•
•
The increase in temperature of a circuit element due to the electrical
energy being absorbed and radiated as heat is called self-heating
Self-heating is characterised by the device’s thermal resistance RTH
(K/W), which expresses how well the device can dissipate heat to the
surroundings
The temperature rise above ambient Trise (K) due to a power dissipation
PD is given in terms of the thermal resistance by
Trise = PD RTH
•
Thermal resistance is inversely proportional to κ - a high thermal
resistance indicates a poor ability to dissipate heat, and therefore a
large temperature gradient (i.e. high device temperature) for a given
heat flux (determined by the requirement to dissipate electrical energy)
ELEC 3908, Physical Electronics:
Early Effect, Breakdown and Self-Heating
Page 18-14
Device Thermal Resistance
•
•
The use of thermal resistance allows the thermal properties of a
device’s operating environment to be expressed as the sum of the
thermal resistances of each section
In the example below, the total thermal resistance to ambient is the
sum of the RTH from device to package, and from package to ambient
ELEC 3908, Physical Electronics:
Early Effect, Breakdown and Self-Heating
Page 18-15
Example 18.2: Device Temperature Calculation
Assume the device shown below is a medium power bipolar
transistor operating at VBE=1.0V, IB=2mA, VCE=5V and
IC=100mA. The thermal resistance between the device and
package is 100 K/W and from the package to ambient in
still air is 200 K/W. If the ambient temperature is 25 °C,
what is the operating temperature of the device?
ELEC 3908, Physical Electronics:
Early Effect, Breakdown and Self-Heating
Page 18-16
Example 18.2: Solution
• Using the emitter as a reference terminal, the total power
dissipation in the device is
PD = (1 ⋅ 2 × 10 −3 ) + (5 ⋅ 100 × 10 −3 ) = 0.5 W
• The total thermal resistance to ambient is
RTh = 100 + 200 = 300 K / W
• The temperature rise is therefore
Trise = PD RTh = 0.5 ⋅ 300 = 150 K = 150 ° C
• The operating temperature is therefore 25+150=175 °C.
ELEC 3908, Physical Electronics:
Early Effect, Breakdown and Self-Heating
Page 18-17
Modifying Thermal Resistance
• If RTH is too large and the operating temperature therefore
too high, the component reliability can suffer
• For a discrete (packaged) device, there are several ways to
lower the thermal resistance:
– A different package (i.e. metal (transistor) or ceramic (IC) vs.
plastic) with higher thermal conductivity will reduce the device to
package component of RTH
– A heat sink attached to the outside of the package will increase the
effective surface area, thereby enhancing convective cooling, and
decrease the package to ambient component of RTH
– Fans mounted near (or on) the package surface reduce the package
to ambient component of RTH for the same reason
ELEC 3908, Physical Electronics:
Early Effect, Breakdown and Self-Heating
Page 18-18
Heat Sinks
• A heat sink increases surface area to enhance cooling,
thereby lowering thermal resistance
ELEC 3908, Physical Electronics:
Early Effect, Breakdown and Self-Heating
Page 18-19
Example 18.3: Heat Sinking
It is decided that for reliability reasons the device of example
18.2 should only run at a maximum temperature of 125 °C.
It is therefore proposed to put a heat sink on the outside of
the package, which will lower the package to ambient
thermal resistance to 25 K/W. Will this change reduce the
operating temperature to within the reliability limit?
ELEC 3908, Physical Electronics:
Early Effect, Breakdown and Self-Heating
Page 18-20
Example 18.3: Solution
• With the heat sink in place, the new thermal resistance is
RTh = 100 + 25 = 125 K / W
• The new temperature increase due to self-heating is
therefore
Trise = 0.5 ⋅ 125 = 62.5 K = 62.5 ° C
• The new operating temperature is therefore 25+62.5=87.5
°C. The addition of the heat sink now brings the operating
temperature to well within the limit.
ELEC 3908, Physical Electronics:
Early Effect, Breakdown and Self-Heating
Page 18-21
Importance of Self-Heating in Modeling
• It is important to model the effect of self-heating because
several parameters are functions of temperature
– The intrinsic density ni is an exponential function of temperature,
making the equilibrium minority densities exponential functions of
temperature
– The diffusion coefficients Dn and Dp contain the mobility, which is
a function of temperature, and temperature itself (D=μ⋅kT/q)
– The voltage exponential terms contain temperature explicitly
– The depletion width W depends on Vbi, which contains kT/q,
therefore WBC and WBE, and hence WC, WB and WE are f(T)
qAE D pC pCo
qAE DnB nBo qVBE kT
IC = −
e
− 1) +
e
− e qVBC kT )
(
(
WC
WB
14444
244443 14444
4244444
3
qVBC kT
collector hole injection ( I pC )
linking (electron) current ( I nB )
ELEC 3908, Physical Electronics:
Early Effect, Breakdown and Self-Heating
Page 18-22
Lecture Summary
• This lecture has discussed three important effects in
bipolar devices
– The Early Effect: Variation of current with base width gives rise to
a slope of IC vs VCE in the active region and is normally
characterized by the Early voltage EA.
– Breakdown: BVCBO is the same reverse breakdown across the base
collector junction discussed in lecture 12 for the diode. BVCEO
involves transistor action magnifying the effect of breakdown in
the BC junction. BVCEO < BVCBO because of the magnification.
– Self-Heating: Refers to a device’s operating temperature increasing
when power is dissipated. Self-heating Trise proportional to thermal
resistance RTH, which depends on package and ambient. Some
parameters in the injection model very sensitive to temperature, so
accurate modeling is important for devices with large Trise.
ELEC 3908, Physical Electronics:
Early Effect, Breakdown and Self-Heating
Page 18-23