semiconductor devices - iit bombay
TRANSCRIPT
Semiconductor Devices
Bipolar Junction Transistors: Part 2
M. B. [email protected]
www.ee.iitb.ac.in/~sequel
Department of Electrical EngineeringIndian Institute of Technology Bombay
M. B. Patil, IIT Bombay
Bipolar junction transistors: Ebers-Moll model
* We have considered a BJT in the active mode (B-E junction under forward bias, B-C junction underreverse bias) and obtained α.
The BJT can now be replaced with its equivalent circuit.
IB= (1− α) IEIB= (1− α) IE
IB
IE IC IE IC
IB
IC=αIEIEIC=αIEIE
E C
B
E C
B
E CCE
VEB VBCVBE VCB
B (base)
(emitter) (collector)
B (base)
(emitter) (collector)
* A generalised model valid in all modes can be obtained by removing the conditions of a forward biasacross the E -B junction and a reverse bias across the C -B junction → Ebers-Moll model.
M. B. Patil, IIT Bombay
Bipolar junction transistors: Ebers-Moll model
* We have considered a BJT in the active mode (B-E junction under forward bias, B-C junction underreverse bias) and obtained α.
The BJT can now be replaced with its equivalent circuit.
IB= (1− α) IEIB= (1− α) IE
IB
IE IC IE IC
IB
IC=αIEIEIC=αIEIE
E C
B
E C
B
E CCE
VEB VBCVBE VCB
B (base)
(emitter) (collector)
B (base)
(emitter) (collector)
* A generalised model valid in all modes can be obtained by removing the conditions of a forward biasacross the E -B junction and a reverse bias across the C -B junction → Ebers-Moll model.
M. B. Patil, IIT Bombay
Bipolar junction transistors: Ebers-Moll model
* We have considered a BJT in the active mode (B-E junction under forward bias, B-C junction underreverse bias) and obtained α.
The BJT can now be replaced with its equivalent circuit.
IB= (1− α) IEIB= (1− α) IE
IB
IE IC IE IC
IB
IC=αIEIEIC=αIEIE
E C
B
E C
B
E CCE
VEB VBCVBE VCB
B (base)
(emitter) (collector)
B (base)
(emitter) (collector)
* A generalised model valid in all modes can be obtained by removing the conditions of a forward biasacross the E -B junction and a reverse bias across the C -B junction → Ebers-Moll model.
M. B. Patil, IIT Bombay
Bipolar junction transistors: Ebers-Moll model
* We have considered a BJT in the active mode (B-E junction under forward bias, B-C junction underreverse bias) and obtained α.
The BJT can now be replaced with its equivalent circuit.
IB= (1− α) IEIB= (1− α) IE
IB
IE IC IE IC
IB
IC=αIEIEIC=αIEIE
E C
B
E C
B
E CCE
VEB VBCVBE VCB
B (base)
(emitter) (collector)
B (base)
(emitter) (collector)
* A generalised model valid in all modes can be obtained by removing the conditions of a forward biasacross the E -B junction and a reverse bias across the C -B junction → Ebers-Moll model.
M. B. Patil, IIT Bombay
Outline of derivation for a pnp BJT
Ebers-Moll model:
xCW0xE
n0E
n0E
n0E
n0E
n0C
n0C
n0C
n0C
n(x) p(x) n(x)
cutoff
reverse active
saturation
forward activebias is not shown.Variation of W with
* Boundary conditions:
∆n(xE ) = n0E
[exp
(VEB
VT
)− 1
]∆n(−∞) = 0
∆p(0) = p0B
[exp
(VEB
VT
)− 1
]∆p(W ) = p0B
[exp
(VCB
VT
)− 1
]∆n(xC ) = n0C
[exp
(VCB
VT
)− 1
]∆n(∞) = 0
M. B. Patil, IIT Bombay
Outline of derivation for a pnp BJT
Ebers-Moll model:
xCW0xE
n0E
n0E
n0E
n0E
n0C
n0C
n0C
n0C
n(x) p(x) n(x)
cutoff
reverse active
saturation
forward activebias is not shown.Variation of W with
* Boundary conditions:
∆n(xE ) = n0E
[exp
(VEB
VT
)− 1
]∆n(−∞) = 0
∆p(0) = p0B
[exp
(VEB
VT
)− 1
]∆p(W ) = p0B
[exp
(VCB
VT
)− 1
]∆n(xC ) = n0C
[exp
(VCB
VT
)− 1
]∆n(∞) = 0
M. B. Patil, IIT Bombay
Outline of derivation for a pnp BJT
Ebers-Moll model:
xCW0xE
n0E
n0E
n0E
n0E
n0C
n0C
n0C
n0C
n(x) p(x) n(x)
cutoff
reverse active
saturation
forward activebias is not shown.Variation of W with
* Boundary conditions:
∆n(xE ) = n0E
[exp
(VEB
VT
)− 1
]∆n(−∞) = 0
∆p(0) = p0B
[exp
(VEB
VT
)− 1
]∆p(W ) = p0B
[exp
(VCB
VT
)− 1
]∆n(xC ) = n0C
[exp
(VCB
VT
)− 1
]∆n(∞) = 0
M. B. Patil, IIT Bombay
Outline of derivation for a pnp BJT
Ebers-Moll model:
xCW0xE
n0E
n0E
n0E
n0E
n0C
n0C
n0C
n0C
n(x) p(x) n(x)
cutoff
reverse active
saturation
forward activebias is not shown.Variation of W with
* Boundary conditions:
∆n(xE ) = n0E
[exp
(VEB
VT
)− 1
]∆n(−∞) = 0
∆p(0) = p0B
[exp
(VEB
VT
)− 1
]∆p(W ) = p0B
[exp
(VCB
VT
)− 1
]
∆n(xC ) = n0C
[exp
(VCB
VT
)− 1
]∆n(∞) = 0
M. B. Patil, IIT Bombay
Outline of derivation for a pnp BJT
Ebers-Moll model:
xCW0xE
n0E
n0E
n0E
n0E
n0C
n0C
n0C
n0C
n(x) p(x) n(x)
cutoff
reverse active
saturation
forward activebias is not shown.Variation of W with
* Boundary conditions:
∆n(xE ) = n0E
[exp
(VEB
VT
)− 1
]∆n(−∞) = 0
∆p(0) = p0B
[exp
(VEB
VT
)− 1
]∆p(W ) = p0B
[exp
(VCB
VT
)− 1
]∆n(xC ) = n0C
[exp
(VCB
VT
)− 1
]∆n(∞) = 0
M. B. Patil, IIT Bombay
Outline of derivation for a pnp BJT
Ebers-Moll model:
xCW0xE
n0E
n0E
n0E
n0E
n0C
n0C
n0C
n0C
n(x) p(x) n(x)
cutoff
reverse active
saturation
forward activebias is not shown.Variation of W with
* Solve the minority-carrier continuity
equations in the neutral emitter, base, and
collector regions.
* From the solutions, obtain the following
currents.
InE (xE ) = qADnEdn
dx(xE ).
IpB(0) = −qADpBdp
dx(0).
IpB(W ) = −qADpBdp
dx(W ).
InC (xC ) = qADnCdn
dx(xC ).
M. B. Patil, IIT Bombay
Outline of derivation for a pnp BJT
Ebers-Moll model:
xCW0xE
n0E
n0E
n0E
n0E
n0C
n0C
n0C
n0C
n(x) p(x) n(x)
cutoff
reverse active
saturation
forward activebias is not shown.Variation of W with
* Solve the minority-carrier continuity
equations in the neutral emitter, base, and
collector regions.
* From the solutions, obtain the following
currents.
InE (xE ) = qADnEdn
dx(xE ).
IpB(0) = −qADpBdp
dx(0).
IpB(W ) = −qADpBdp
dx(W ).
InC (xC ) = qADnCdn
dx(xC ).
M. B. Patil, IIT Bombay
Outline of derivation for a pnp BJT
Ebers-Moll model:
xCW0xE
n0E
n0E
n0E
n0E
n0C
n0C
n0C
n0C
n(x) p(x) n(x)
cutoff
reverse active
saturation
forward activebias is not shown.Variation of W with
* Solve the minority-carrier continuity
equations in the neutral emitter, base, and
collector regions.
* From the solutions, obtain the following
currents.
InE (xE ) = qADnEdn
dx(xE ).
IpB(0) = −qADpBdp
dx(0).
IpB(W ) = −qADpBdp
dx(W ).
InC (xC ) = qADnCdn
dx(xC ).
M. B. Patil, IIT Bombay
Outline of derivation for a pnp BJT
Ebers-Moll model:
xCW0xE
n0E
n0E
n0E
n0E
n0C
n0C
n0C
n0C
n(x) p(x) n(x)
cutoff
reverse active
saturation
forward activebias is not shown.Variation of W with
* Obtain the terminal currents, ignoring G-R
in the depletion regions.
IE = InE (xE ) + IpB(0).
IC = InC (xC ) + IpB(W ).
IB = IE − IC .
M. B. Patil, IIT Bombay
Outline of derivation for a pnp BJT
Ebers-Moll model:
xCW0xE
n0E
n0E
n0E
n0E
n0C
n0C
n0C
n0C
n(x) p(x) n(x)
cutoff
reverse active
saturation
forward activebias is not shown.Variation of W with
* Obtain the terminal currents, ignoring G-R
in the depletion regions.
IE = InE (xE ) + IpB(0).
IC = InC (xC ) + IpB(W ).
IB = IE − IC .
M. B. Patil, IIT Bombay
Bipolar junction transistors: Ebers-Moll model
npn transistor
pnp transistor
I′E = IES
[exp
(VEB
VT
)− 1
]
I′C = ICS
[exp
(VCB
VT
)− 1
]
I′E = IES
[exp
(VBE
VT
)− 1
]
I′C = ICS
[exp
(VBC
VT
)− 1
]
I′E
I′C
I′E
I′C
IE IC
IB
IE
IE IC
IB
ICIEIC
IBIB
αRI′C
αRI′C
αFI′E
αFI′E
C
E
E
E CC
E
B
B
B
C
B
VEB VBC
VBE VCB
* Current directions are assigned such that IC , IE , IB are all positive if the BJT operates in the active mode.
M. B. Patil, IIT Bombay
Bipolar junction transistors: Ebers-Moll model
npn transistor
pnp transistor
I′E = IES
[exp
(VEB
VT
)− 1
]
I′C = ICS
[exp
(VCB
VT
)− 1
]
I′E = IES
[exp
(VBE
VT
)− 1
]
I′C = ICS
[exp
(VBC
VT
)− 1
]
I′E
I′C
I′E
I′C
IE IC
IB
IE
IE IC
IB
ICIEIC
IBIB
αRI′C
αRI′C
αFI′E
αFI′E
C
E
E
E CC
E
B
B
B
C
B
VEB VBC
VBE VCB
* Current directions are assigned such that IC , IE , IB are all positive if the BJT operates in the active mode.
M. B. Patil, IIT Bombay
Ebers-Moll model
npn transistor
pnp transistor
I′E = IES
[exp
(VEB
VT
)− 1
]
I′C = ICS
[exp
(VCB
VT
)− 1
]
I′E = IES
[exp
(VBE
VT
)− 1
]
I′C = ICS
[exp
(VBC
VT
)− 1
]
I′E
I′C
I′E
I′C
IE IC
IB
IE
IE IC
IB
ICIEIC
IBIB
αRI′C
αRI′C
αFI′E
αFI′E
C
E
E
E CC
E
B
B
B
C
B
VEB VBC
VBE VCB
* The Ebers-Moll model can be interpreted as two transistors connected in parallel, each acting in the active mode.
* The forward transistor is represented by the E -B diode and the corresponding dependent source (the upper branches),and the reverse transistor by the C -B diode and the corresponding dependent source (the lower branches).
M. B. Patil, IIT Bombay
Ebers-Moll model
npn transistor
pnp transistor
I′E = IES
[exp
(VEB
VT
)− 1
]
I′C = ICS
[exp
(VCB
VT
)− 1
]
I′E = IES
[exp
(VBE
VT
)− 1
]
I′C = ICS
[exp
(VBC
VT
)− 1
]
I′E
I′C
I′E
I′C
IE IC
IB
IE
IE IC
IB
ICIEIC
IBIB
αRI′C
αRI′C
αFI′E
αFI′E
C
E
E
E CC
E
B
B
B
C
B
VEB VBC
VBE VCB
* The Ebers-Moll model can be interpreted as two transistors connected in parallel, each acting in the active mode.
* The forward transistor is represented by the E -B diode and the corresponding dependent source (the upper branches),and the reverse transistor by the C -B diode and the corresponding dependent source (the lower branches).
M. B. Patil, IIT Bombay
Ebers-Moll model
npn transistor
pnp transistor
I′E = IES
[exp
(VEB
VT
)− 1
]
I′C = ICS
[exp
(VCB
VT
)− 1
]
I′E = IES
[exp
(VBE
VT
)− 1
]
I′C = ICS
[exp
(VBC
VT
)− 1
]
I′E
I′C
I′E
I′C
IE IC
IB
IE
IE IC
IB
ICIEIC
IBIB
αRI′C
αRI′C
αFI′E
αFI′E
C
E
E
E CC
E
B
B
B
C
B
VEB VBC
VBE VCB
* The Ebers-Moll model can be interpreted as two transistors connected in parallel, each acting in the active mode.
* The forward transistor is represented by the E -B diode and the corresponding dependent source (the upper branches),and the reverse transistor by the C -B diode and the corresponding dependent source (the lower branches).
M. B. Patil, IIT Bombay
Ebers-Moll model
npn transistor
pnp transistor
I′E = IES
[exp
(VEB
VT
)− 1
]
I′C = ICS
[exp
(VCB
VT
)− 1
]
I′E = IES
[exp
(VBE
VT
)− 1
]
I′C = ICS
[exp
(VBC
VT
)− 1
]
I′E
I′C
I′E
I′C
IE IC
IB
IE
IE IC
IB
ICIEIC
IBIB
αRI′C
αRI′C
αFI′E
αFI′E
C
E
E
E CC
E
B
B
B
C
B
VEB VBC
VBE VCB
* The model has four parameters: IES , ICS , αF , αR (F for forward, R for reverse) which can be related to the geometry(base width, device area) and material parameters (doping densities, diffusion coefficients, lifetimes) of the transistor.
* With the assumptions we have made, αF IES = αR ICS .
M. B. Patil, IIT Bombay
Ebers-Moll model
npn transistor
pnp transistor
I′E = IES
[exp
(VEB
VT
)− 1
]
I′C = ICS
[exp
(VCB
VT
)− 1
]
I′E = IES
[exp
(VBE
VT
)− 1
]
I′C = ICS
[exp
(VBC
VT
)− 1
]
I′E
I′C
I′E
I′C
IE IC
IB
IE
IE IC
IB
ICIEIC
IBIB
αRI′C
αRI′C
αFI′E
αFI′E
C
E
E
E CC
E
B
B
B
C
B
VEB VBC
VBE VCB
* The model has four parameters: IES , ICS , αF , αR (F for forward, R for reverse) which can be related to the geometry
(base width, device area) and material parameters (doping densities, diffusion coefficients, lifetimes) of the transistor.1
* With the assumptions we have made, αF IES = αR ICS .
1R.F. Pierret, Semiconductor Device Fundamentals. New Delhi: Pearson Education, 1996.M. B. Patil, IIT Bombay
Ebers-Moll model
npn transistor
pnp transistor
I′E = IES
[exp
(VEB
VT
)− 1
]
I′C = ICS
[exp
(VCB
VT
)− 1
]
I′E = IES
[exp
(VBE
VT
)− 1
]
I′C = ICS
[exp
(VBC
VT
)− 1
]
I′E
I′C
I′E
I′C
IE IC
IB
IE
IE IC
IB
ICIEIC
IBIB
αRI′C
αRI′C
αFI′E
αFI′E
C
E
E
E CC
E
B
B
B
C
B
VEB VBC
VBE VCB
* The model has four parameters: IES , ICS , αF , αR (F for forward, R for reverse) which can be related to the geometry
(base width, device area) and material parameters (doping densities, diffusion coefficients, lifetimes) of the transistor.1
* With the assumptions we have made, αF IES = αR ICS .
1R.F. Pierret, Semiconductor Device Fundamentals. New Delhi: Pearson Education, 1996.M. B. Patil, IIT Bombay
Ebers-Moll model
* Assumptions made:
- Low-level injection
- Uniform doping densities, non-degenerate carrier statistics
- One-dimensional device, with the emitter and collector regions much longer than
the respective minority carrier diffusion lengths
- No generation/recombination in the depletion regions
- Constant width (W ) of the neutral base region, independent of bias voltages
* In practice, the above assumptions do not hold, e.g., as we have seen, the dopingdensities are not uniform.
Furthermore, several details about the device such as lifetimes, mobilities, and basewidth, are not known.
* The Ebers-Moll model can still be used as a “phenomenological” description of the deviceif model parameters are suitably extracted using measured data.
* More advanced BJT models are available (e.g., the SPICE model) and are used for circuitsimulation.
M. B. Patil, IIT Bombay
Ebers-Moll model
* Assumptions made:
- Low-level injection
- Uniform doping densities, non-degenerate carrier statistics
- One-dimensional device, with the emitter and collector regions much longer than
the respective minority carrier diffusion lengths
- No generation/recombination in the depletion regions
- Constant width (W ) of the neutral base region, independent of bias voltages
* In practice, the above assumptions do not hold, e.g., as we have seen, the dopingdensities are not uniform.
Furthermore, several details about the device such as lifetimes, mobilities, and basewidth, are not known.
* The Ebers-Moll model can still be used as a “phenomenological” description of the deviceif model parameters are suitably extracted using measured data.
* More advanced BJT models are available (e.g., the SPICE model) and are used for circuitsimulation.
M. B. Patil, IIT Bombay
Ebers-Moll model
* Assumptions made:
- Low-level injection
- Uniform doping densities, non-degenerate carrier statistics
- One-dimensional device, with the emitter and collector regions much longer than
the respective minority carrier diffusion lengths
- No generation/recombination in the depletion regions
- Constant width (W ) of the neutral base region, independent of bias voltages
* In practice, the above assumptions do not hold, e.g., as we have seen, the dopingdensities are not uniform.
Furthermore, several details about the device such as lifetimes, mobilities, and basewidth, are not known.
* The Ebers-Moll model can still be used as a “phenomenological” description of the deviceif model parameters are suitably extracted using measured data.
* More advanced BJT models are available (e.g., the SPICE model) and are used for circuitsimulation.
M. B. Patil, IIT Bombay
Ebers-Moll model
* Assumptions made:
- Low-level injection
- Uniform doping densities, non-degenerate carrier statistics
- One-dimensional device, with the emitter and collector regions much longer than
the respective minority carrier diffusion lengths
- No generation/recombination in the depletion regions
- Constant width (W ) of the neutral base region, independent of bias voltages
* In practice, the above assumptions do not hold, e.g., as we have seen, the dopingdensities are not uniform.
Furthermore, several details about the device such as lifetimes, mobilities, and basewidth, are not known.
* The Ebers-Moll model can still be used as a “phenomenological” description of the deviceif model parameters are suitably extracted using measured data.
* More advanced BJT models are available (e.g., the SPICE model) and are used for circuitsimulation.
M. B. Patil, IIT Bombay
Ebers-Moll model
* Assumptions made:
- Low-level injection
- Uniform doping densities, non-degenerate carrier statistics
- One-dimensional device, with the emitter and collector regions much longer than
the respective minority carrier diffusion lengths
- No generation/recombination in the depletion regions
- Constant width (W ) of the neutral base region, independent of bias voltages
* In practice, the above assumptions do not hold, e.g., as we have seen, the dopingdensities are not uniform.
Furthermore, several details about the device such as lifetimes, mobilities, and basewidth, are not known.
* The Ebers-Moll model can still be used as a “phenomenological” description of the deviceif model parameters are suitably extracted using measured data.
* More advanced BJT models are available (e.g., the SPICE model) and are used for circuitsimulation.
M. B. Patil, IIT Bombay
Ebers-Moll model
* Assumptions made:
- Low-level injection
- Uniform doping densities, non-degenerate carrier statistics
- One-dimensional device, with the emitter and collector regions much longer than
the respective minority carrier diffusion lengths
- No generation/recombination in the depletion regions
- Constant width (W ) of the neutral base region, independent of bias voltages
* In practice, the above assumptions do not hold, e.g., as we have seen, the dopingdensities are not uniform.
Furthermore, several details about the device such as lifetimes, mobilities, and basewidth, are not known.
* The Ebers-Moll model can still be used as a “phenomenological” description of the deviceif model parameters are suitably extracted using measured data.
* More advanced BJT models are available (e.g., the SPICE model) and are used for circuitsimulation.
M. B. Patil, IIT Bombay
Ebers-Moll model
* Assumptions made:
- Low-level injection
- Uniform doping densities, non-degenerate carrier statistics
- One-dimensional device, with the emitter and collector regions much longer than
the respective minority carrier diffusion lengths
- No generation/recombination in the depletion regions
- Constant width (W ) of the neutral base region, independent of bias voltages
* In practice, the above assumptions do not hold, e.g., as we have seen, the dopingdensities are not uniform.
Furthermore, several details about the device such as lifetimes, mobilities, and basewidth, are not known.
* The Ebers-Moll model can still be used as a “phenomenological” description of the deviceif model parameters are suitably extracted using measured data.
* More advanced BJT models are available (e.g., the SPICE model) and are used for circuitsimulation.
M. B. Patil, IIT Bombay
Ebers-Moll model
* Assumptions made:
- Low-level injection
- Uniform doping densities, non-degenerate carrier statistics
- One-dimensional device, with the emitter and collector regions much longer than
the respective minority carrier diffusion lengths
- No generation/recombination in the depletion regions
- Constant width (W ) of the neutral base region, independent of bias voltages
* In practice, the above assumptions do not hold, e.g., as we have seen, the dopingdensities are not uniform.
Furthermore, several details about the device such as lifetimes, mobilities, and basewidth, are not known.
* The Ebers-Moll model can still be used as a “phenomenological” description of the deviceif model parameters are suitably extracted using measured data.
* More advanced BJT models are available (e.g., the SPICE model) and are used for circuitsimulation.
M. B. Patil, IIT Bombay
Ebers-Moll model
* Assumptions made:
- Low-level injection
- Uniform doping densities, non-degenerate carrier statistics
- One-dimensional device, with the emitter and collector regions much longer than
the respective minority carrier diffusion lengths
- No generation/recombination in the depletion regions
- Constant width (W ) of the neutral base region, independent of bias voltages
* In practice, the above assumptions do not hold, e.g., as we have seen, the dopingdensities are not uniform.
Furthermore, several details about the device such as lifetimes, mobilities, and basewidth, are not known.
* The Ebers-Moll model can still be used as a “phenomenological” description of the deviceif model parameters are suitably extracted using measured data.
* More advanced BJT models are available (e.g., the SPICE model) and are used for circuitsimulation.
M. B. Patil, IIT Bombay
Ebers-Moll model
* Assumptions made:
- Low-level injection
- Uniform doping densities, non-degenerate carrier statistics
- One-dimensional device, with the emitter and collector regions much longer than
the respective minority carrier diffusion lengths
- No generation/recombination in the depletion regions
- Constant width (W ) of the neutral base region, independent of bias voltages
* In practice, the above assumptions do not hold, e.g., as we have seen, the dopingdensities are not uniform.
Furthermore, several details about the device such as lifetimes, mobilities, and basewidth, are not known.
* The Ebers-Moll model can still be used as a “phenomenological” description of the deviceif model parameters are suitably extracted using measured data.
* More advanced BJT models are available (e.g., the SPICE model2) and are used forcircuit simulation.
2P. Antognetti and G. Massobrio, Semiconductor Device Modeling with SPICE. New York: McGraw-Hill, 1988.M. B. Patil, IIT Bombay
Ebers-Moll model: special cases
npn transistor
I′E = IES
[exp
(VBE
VT
)− 1
]
I′C = ICS
[exp
(VBC
VT
)− 1
]
I′E
I′C
IE IC
IB
IE IC
IB
αRI′C
αFI′E
E E CC
B
B
VBE VCB
* IE = 0, i.e., emitter open-circuited.
IC = −I ′C + αF I′E
= −I ′C + αF (IE + αR I′C )
= −I ′C (1− αFαR) + αF IE .
When the C -B junction is under reverse bias, I ′C ≈−ICS , and with IE = 0, we get
IC ≡ ICBO = ICS (1− αFαR).
M. B. Patil, IIT Bombay
Ebers-Moll model: special cases
npn transistor
I′E = IES
[exp
(VBE
VT
)− 1
]
I′C = ICS
[exp
(VBC
VT
)− 1
]
I′E
I′C
IE IC
IB
IE IC
IB
αRI′C
αFI′E
E E CC
B
B
VBE VCB
* IE = 0, i.e., emitter open-circuited.
IC = −I ′C + αF I′E
= −I ′C + αF (IE + αR I′C )
= −I ′C (1− αFαR) + αF IE .
When the C -B junction is under reverse bias, I ′C ≈−ICS , and with IE = 0, we get
IC ≡ ICBO = ICS (1− αFαR).
M. B. Patil, IIT Bombay
Ebers-Moll model: special cases
npn transistor
I′E = IES
[exp
(VBE
VT
)− 1
]
I′C = ICS
[exp
(VBC
VT
)− 1
]
I′E
I′C
IE IC
IB
IE IC
IB
αRI′C
αFI′E
E E CC
B
B
VBE VCB
* IE = 0, i.e., emitter open-circuited.
IC = −I ′C + αF I′E
= −I ′C + αF (IE + αR I′C )
= −I ′C (1− αFαR) + αF IE .
When the C -B junction is under reverse bias, I ′C ≈−ICS , and with IE = 0, we get
IC ≡ ICBO = ICS (1− αFαR).
M. B. Patil, IIT Bombay
Ebers-Moll model: special cases
npn transistor
I′E = IES
[exp
(VBE
VT
)− 1
]
I′C = ICS
[exp
(VBC
VT
)− 1
]
I′E
I′C
IE IC
IB
IE IC
IB
αRI′C
αFI′E
E E CC
B
B
VBE VCB
* IE = 0, i.e., emitter open-circuited.
IC = −I ′C + αF I′E
= −I ′C + αF (IE + αR I′C )
= −I ′C (1− αFαR) + αF IE .
When the C -B junction is under reverse bias, I ′C ≈−ICS , and with IE = 0, we get
IC ≡ ICBO = ICS (1− αFαR).
M. B. Patil, IIT Bombay
Ebers-Moll model: special cases
npn transistor
I′E = IES
[exp
(VBE
VT
)− 1
]
I′C = ICS
[exp
(VBC
VT
)− 1
]
I′E
I′C
IE IC
IB
IE IC
IB
αRI′C
αFI′E
E E CC
B
B
VBE VCB
* IB = 0, i.e., base open-circuited.
IC = −I ′C (1− αFαR) + αF IE = −I ′C (1− αFαR) + αF (IC + IB)
=−I ′C (1− αFαR)
1− αF+
αF
(1− αF )IB =
−I ′C (1− αFαR)
1− αF+ βF IB .
When the C -B junction is under reverse bias, I ′C ≈−ICS , and with IB = 0, we get
IC ≡ ICEO =ICS (1− αFαR)
(1− αF )=
ICBO
(1− αF ),
which is much larger than ICBO since αF is close to 1.
M. B. Patil, IIT Bombay
Ebers-Moll model: special cases
npn transistor
I′E = IES
[exp
(VBE
VT
)− 1
]
I′C = ICS
[exp
(VBC
VT
)− 1
]
I′E
I′C
IE IC
IB
IE IC
IB
αRI′C
αFI′E
E E CC
B
B
VBE VCB
* IB = 0, i.e., base open-circuited.
IC = −I ′C (1− αFαR) + αF IE = −I ′C (1− αFαR) + αF (IC + IB)
=−I ′C (1− αFαR)
1− αF+
αF
(1− αF )IB =
−I ′C (1− αFαR)
1− αF+ βF IB .
When the C -B junction is under reverse bias, I ′C ≈−ICS , and with IB = 0, we get
IC ≡ ICEO =ICS (1− αFαR)
(1− αF )=
ICBO
(1− αF ),
which is much larger than ICBO since αF is close to 1.
M. B. Patil, IIT Bombay
Ebers-Moll model: special cases
npn transistor
I′E = IES
[exp
(VBE
VT
)− 1
]
I′C = ICS
[exp
(VBC
VT
)− 1
]
I′E
I′C
IE IC
IB
IE IC
IB
αRI′C
αFI′E
E E CC
B
B
VBE VCB
* IB = 0, i.e., base open-circuited.
IC = −I ′C (1− αFαR) + αF IE = −I ′C (1− αFαR) + αF (IC + IB)
=−I ′C (1− αFαR)
1− αF+
αF
(1− αF )IB =
−I ′C (1− αFαR)
1− αF+ βF IB .
When the C -B junction is under reverse bias, I ′C ≈−ICS , and with IB = 0, we get
IC ≡ ICEO =ICS (1− αFαR)
(1− αF )=
ICBO
(1− αF ),
which is much larger than ICBO since αF is close to 1.
M. B. Patil, IIT Bombay
Ebers-Moll model: special cases
npn transistor
I′E = IES
[exp
(VBE
VT
)− 1
]
I′C = ICS
[exp
(VBC
VT
)− 1
]
I′E
I′C
IE IC
IB
IE IC
IB
αRI′C
αFI′E
E E CC
B
B
VBE VCB
* IB = 0, i.e., base open-circuited.
IC = −I ′C (1− αFαR) + αF IE = −I ′C (1− αFαR) + αF (IC + IB)
=−I ′C (1− αFαR)
1− αF+
αF
(1− αF )IB =
−I ′C (1− αFαR)
1− αF+ βF IB .
When the C -B junction is under reverse bias, I ′C ≈−ICS , and with IB = 0, we get
IC ≡ ICEO =ICS (1− αFαR)
(1− αF )=
ICBO
(1− αF ),
which is much larger than ICBO since αF is close to 1.
M. B. Patil, IIT Bombay
Ebers-Moll model: special cases
npn transistor
I′E = IES
[exp
(VBE
VT
)− 1
]
I′C = ICS
[exp
(VBC
VT
)− 1
]
I′E
I′C
IE IC
IB
IE IC
IB
αRI′C
αFI′E
E E CC
B
B
VBE VCB
* IB = 0, i.e., base open-circuited.
IC = −I ′C (1− αFαR) + αF IE = −I ′C (1− αFαR) + αF (IC + IB)
=−I ′C (1− αFαR)
1− αF+
αF
(1− αF )IB =
−I ′C (1− αFαR)
1− αF+ βF IB .
When the C -B junction is under reverse bias, I ′C ≈−ICS , and with IB = 0, we get
IC ≡ ICEO =ICS (1− αFαR)
(1− αF )=
ICBO
(1− αF ),
which is much larger than ICBO since αF is close to 1.
M. B. Patil, IIT Bombay
BJT I -V description
pnp transistor npn transistor
E E
ICIE
IB
IE IC
IB
C
B
C
B
VEB VBCVBE VCB
* Unlike the diode (where there is only one current and one voltage), the BJT has
three currents and three voltages.
* The current-voltage relationship is described in the form of a “family” of curves,
with a current selected as the y variable, a voltage as the x variable, and a third
variable as a quantity to be held constant for each I -V curve.
* Two descriptions, which are related to the “common-base” and “common-emitter”
configurations, are commonly used.
M. B. Patil, IIT Bombay
BJT I -V description
pnp transistor npn transistor
E E
ICIE
IB
IE IC
IB
C
B
C
B
VEB VBCVBE VCB
* Unlike the diode (where there is only one current and one voltage), the BJT has
three currents and three voltages.
* The current-voltage relationship is described in the form of a “family” of curves,
with a current selected as the y variable, a voltage as the x variable, and a third
variable as a quantity to be held constant for each I -V curve.
* Two descriptions, which are related to the “common-base” and “common-emitter”
configurations, are commonly used.
M. B. Patil, IIT Bombay
BJT I -V description
pnp transistor npn transistor
E E
ICIE
IB
IE IC
IB
C
B
C
B
VEB VBCVBE VCB
* Unlike the diode (where there is only one current and one voltage), the BJT has
three currents and three voltages.
* The current-voltage relationship is described in the form of a “family” of curves,
with a current selected as the y variable, a voltage as the x variable, and a third
variable as a quantity to be held constant for each I -V curve.
* Two descriptions, which are related to the “common-base” and “common-emitter”
configurations, are commonly used.
M. B. Patil, IIT Bombay
BJT I -V description
pnp transistor npn transistor
E E
ICIE
IB
IE IC
IB
C
B
C
B
VEB VBCVBE VCB
* Unlike the diode (where there is only one current and one voltage), the BJT has
three currents and three voltages.
* The current-voltage relationship is described in the form of a “family” of curves,
with a current selected as the y variable, a voltage as the x variable, and a third
variable as a quantity to be held constant for each I -V curve.
* Two descriptions, which are related to the “common-base” and “common-emitter”
configurations, are commonly used.
M. B. Patil, IIT Bombay
Common-base configuration
ICIE
C
I′E
I′C
IE IC
IB
αRI′C
αFI′E
IES = 1× 10−14 A
ICS= 2× 10−14 A
αF= 0.99
αR= 0.5
0.8mA
0.6mA
0.4mA
0.2mA0mA
VBE (volts) VCB (volts)
IE= 1mA
I E(m
A)
I C(m
A)E
B
B B
CE
0 0.7 −1 0 1 2 3 4 5
0
11
0
* VCB > 0 V:
C-B junction is reverse biased, I ′C ≈−ICS , which is negligibly small.
IE ≈ I ′E , IC ≈αF IE → for a given IE , IC is a constant.
On the input side, the IC versus VBE curve (for a positive VCB value) is like a diode I -V relationship.
* VCB < 0 V:
C-B junction is forward biased, but I ′C becomes substantial only when VCB ≈−0.5 V.
Beyond this point, IC drops sharply since IC =αF I′E − I ′C → saturation mode.
M. B. Patil, IIT Bombay
Common-base configuration
ICIE
C
I′E
I′C
IE IC
IB
αRI′C
αFI′E
IES = 1× 10−14 A
ICS= 2× 10−14 A
αF= 0.99
αR= 0.5
0.8mA
0.6mA
0.4mA
0.2mA0mA
VBE (volts) VCB (volts)
IE= 1mA
I E(m
A)
I C(m
A)E
B
B B
CE
0 0.7 −1 0 1 2 3 4 5
0
11
0
* VCB > 0 V:
C-B junction is reverse biased, I ′C ≈−ICS , which is negligibly small.
IE ≈ I ′E , IC ≈αF IE → for a given IE , IC is a constant.
On the input side, the IC versus VBE curve (for a positive VCB value) is like a diode I -V relationship.
* VCB < 0 V:
C-B junction is forward biased, but I ′C becomes substantial only when VCB ≈−0.5 V.
Beyond this point, IC drops sharply since IC =αF I′E − I ′C → saturation mode.
M. B. Patil, IIT Bombay
Common-base configuration
ICIE
C
I′E
I′C
IE IC
IB
αRI′C
αFI′E
IES = 1× 10−14 A
ICS= 2× 10−14 A
αF= 0.99
αR= 0.5
0.8mA
0.6mA
0.4mA
0.2mA0mA
VBE (volts) VCB (volts)
IE= 1mA
I E(m
A)
I C(m
A)E
B
B B
CE
0 0.7 −1 0 1 2 3 4 5
0
11
0
* VCB > 0 V:
C-B junction is reverse biased, I ′C ≈−ICS , which is negligibly small.
IE ≈ I ′E , IC ≈αF IE → for a given IE , IC is a constant.
On the input side, the IC versus VBE curve (for a positive VCB value) is like a diode I -V relationship.
* VCB < 0 V:
C-B junction is forward biased, but I ′C becomes substantial only when VCB ≈−0.5 V.
Beyond this point, IC drops sharply since IC =αF I′E − I ′C → saturation mode.
M. B. Patil, IIT Bombay
Common-base configuration
ICIE
C
I′E
I′C
IE IC
IB
αRI′C
αFI′E
IES = 1× 10−14 A
ICS= 2× 10−14 A
αF= 0.99
αR= 0.5
0.8mA
0.6mA
0.4mA
0.2mA0mA
VBE (volts) VCB (volts)
IE= 1mA
I E(m
A)
I C(m
A)E
B
B B
CE
0 0.7 −1 0 1 2 3 4 5
0
11
0
* VCB > 0 V:
C-B junction is reverse biased, I ′C ≈−ICS , which is negligibly small.
IE ≈ I ′E , IC ≈αF IE → for a given IE , IC is a constant.
On the input side, the IC versus VBE curve (for a positive VCB value) is like a diode I -V relationship.
* VCB < 0 V:
C-B junction is forward biased, but I ′C becomes substantial only when VCB ≈−0.5 V.
Beyond this point, IC drops sharply since IC =αF I′E − I ′C → saturation mode.
M. B. Patil, IIT Bombay
Common-base configuration
ICIE
C
I′E
I′C
IE IC
IB
αRI′C
αFI′E
IES = 1× 10−14 A
ICS= 2× 10−14 A
αF= 0.99
αR= 0.5
0.8mA
0.6mA
0.4mA
0.2mA0mA
VBE (volts) VCB (volts)
IE= 1mA
I E(m
A)
I C(m
A)E
B
B B
CE
0 0.7 −1 0 1 2 3 4 5
0
11
0
* VCB > 0 V:
C-B junction is reverse biased, I ′C ≈−ICS , which is negligibly small.
IE ≈ I ′E , IC ≈αF IE → for a given IE , IC is a constant.
On the input side, the IC versus VBE curve (for a positive VCB value) is like a diode I -V relationship.
* VCB < 0 V:
C-B junction is forward biased, but I ′C becomes substantial only when VCB ≈−0.5 V.
Beyond this point, IC drops sharply since IC =αF I′E − I ′C → saturation mode.
M. B. Patil, IIT Bombay
Common-base configuration
ICIE
C
I′E
I′C
IE IC
IB
αRI′C
αFI′E
IES = 1× 10−14 A
ICS= 2× 10−14 A
αF= 0.99
αR= 0.5
0.8mA
0.6mA
0.4mA
0.2mA0mA
VBE (volts) VCB (volts)
IE= 1mA
I E(m
A)
I C(m
A)E
B
B B
CE
0 0.7 −1 0 1 2 3 4 5
0
11
0
* VCB > 0 V:
C-B junction is reverse biased, I ′C ≈−ICS , which is negligibly small.
IE ≈ I ′E , IC ≈αF IE → for a given IE , IC is a constant.
On the input side, the IC versus VBE curve (for a positive VCB value) is like a diode I -V relationship.
* VCB < 0 V:
C-B junction is forward biased, but I ′C becomes substantial only when VCB ≈−0.5 V.
Beyond this point, IC drops sharply since IC =αF I′E − I ′C → saturation mode.
M. B. Patil, IIT Bombay
Common-emitter configuration
C
VBE (volts)
VCE=
1V
IC
I B(µ
A)
0 V
IB
IES = 1× 10−14 A
ICS = 2× 10−14 A
αF= 0.99
αR= 0.5
I′E
I′CIB
αRI′C
αFI′E
IE IC
6µA
4µA
8µA
2µA0µA
I C(m
A)
IB = 10µA
VCE (volts)
VBC=0.4 V
VBC=0VVBC=−1V
C
EE
B
B
E
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
0
20
10
0
1
0 1 2 3 4 5
* In the active region (where IC is constant for a given IB), the B-C junction is reverse biased.
→ I ′C ≈ 0→ IC =αF IE =βIB , irrespective of VCE .
* When VBC becomes greater than about 0.4 V, I ′C becomes significant, and IC =αF I′E − I ′C decreases → IC < βIB .
* In the active region (e.g., VCE = 1 V), VBE is nearly constant (∼ 0.65 V).
* In the saturtion region, VCE is 0.2 V or smaller. This is generally true for all low-power BJTs.
M. B. Patil, IIT Bombay
Common-emitter configuration
C
VBE (volts)
VCE=
1V
IC
I B(µ
A)
0 V
IB
IES = 1× 10−14 A
ICS = 2× 10−14 A
αF= 0.99
αR= 0.5
I′E
I′CIB
αRI′C
αFI′E
IE IC
6µA
4µA
8µA
2µA0µA
I C(m
A)
IB = 10µA
VCE (volts)
VBC=0.4 V
VBC=0VVBC=−1V
C
EE
B
B
E
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
0
20
10
0
1
0 1 2 3 4 5
* In the active region (where IC is constant for a given IB), the B-C junction is reverse biased.
→ I ′C ≈ 0→ IC =αF IE =βIB , irrespective of VCE .
* When VBC becomes greater than about 0.4 V, I ′C becomes significant, and IC =αF I′E − I ′C decreases → IC < βIB .
* In the active region (e.g., VCE = 1 V), VBE is nearly constant (∼ 0.65 V).
* In the saturtion region, VCE is 0.2 V or smaller. This is generally true for all low-power BJTs.
M. B. Patil, IIT Bombay
Common-emitter configuration
C
VBE (volts)
VCE=
1V
IC
I B(µ
A)
0 V
IB
IES = 1× 10−14 A
ICS = 2× 10−14 A
αF= 0.99
αR= 0.5
I′E
I′CIB
αRI′C
αFI′E
IE IC
6µA
4µA
8µA
2µA0µA
I C(m
A)
IB = 10µA
VCE (volts)
VBC=0.4 V
VBC=0VVBC=−1V
C
EE
B
B
E
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
0
20
10
0
1
0 1 2 3 4 5
* In the active region (where IC is constant for a given IB), the B-C junction is reverse biased.
→ I ′C ≈ 0→ IC =αF IE =βIB , irrespective of VCE .
* When VBC becomes greater than about 0.4 V, I ′C becomes significant, and IC =αF I′E − I ′C decreases → IC < βIB .
* In the active region (e.g., VCE = 1 V), VBE is nearly constant (∼ 0.65 V).
* In the saturtion region, VCE is 0.2 V or smaller. This is generally true for all low-power BJTs.
M. B. Patil, IIT Bombay
Common-emitter configuration
C
VBE (volts)
VCE=
1V
IC
I B(µ
A)
0 V
IB
IES = 1× 10−14 A
ICS = 2× 10−14 A
αF= 0.99
αR= 0.5
I′E
I′CIB
αRI′C
αFI′E
IE IC
6µA
4µA
8µA
2µA0µA
I C(m
A)
IB = 10µA
VCE (volts)
VBC=0.4 V
VBC=0VVBC=−1V
C
EE
B
B
E
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
0
20
10
0
1
0 1 2 3 4 5
* In the active region (where IC is constant for a given IB), the B-C junction is reverse biased.
→ I ′C ≈ 0→ IC =αF IE =βIB , irrespective of VCE .
* When VBC becomes greater than about 0.4 V, I ′C becomes significant, and IC =αF I′E − I ′C decreases → IC < βIB .
* In the active region (e.g., VCE = 1 V), VBE is nearly constant (∼ 0.65 V).
* In the saturtion region, VCE is 0.2 V or smaller. This is generally true for all low-power BJTs.
M. B. Patil, IIT Bombay
Common-emitter configuration
C
VBE (volts)
VCE=
1V
IC
I B(µ
A)
0 V
IB
IES = 1× 10−14 A
ICS = 2× 10−14 A
αF= 0.99
αR= 0.5
I′E
I′CIB
αRI′C
αFI′E
IE IC
6µA
4µA
8µA
2µA0µA
I C(m
A)
IB = 10µA
VCE (volts)
VBC=0.4 V
VBC=0VVBC=−1V
C
EE
B
B
E
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
0
20
10
0
1
0 1 2 3 4 5
* In the active region (where IC is constant for a given IB), the B-C junction is reverse biased.
→ I ′C ≈ 0→ IC =αF IE =βIB , irrespective of VCE .
* When VBC becomes greater than about 0.4 V, I ′C becomes significant, and IC =αF I′E − I ′C decreases → IC < βIB .
* In the active region (e.g., VCE = 1 V), VBE is nearly constant (∼ 0.65 V).
* In the saturtion region, VCE is 0.2 V or smaller. This is generally true for all low-power BJTs.
M. B. Patil, IIT Bombay
Common-emitter configuration
C
VBE (volts)
VCE=
1V
IC
I B(µ
A)
0 V
IB
IES = 1× 10−14 A
ICS = 2× 10−14 A
αF= 0.99
αR= 0.5
I′E
I′CIB
αRI′C
αFI′E
IE IC
6µA
4µA
8µA
2µA0µA
I C(m
A)
IB = 10µA
VCE (volts)
VBC=0.4 V
VBC=0VVBC=−1V
C
EE
B
B
E
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
0
20
10
0
1
0 1 2 3 4 5
* Comparison of IB versus VBE for VCE = 0 V and VCE = 1 V:
- VCE = 1 V (active region):
VBC = VBE − VCE ≈ 0.7− 1 = −0.3 V → I ′C ≈ 0 → IB = I ′E − αF I′E ≈ (1− αF ) IESe
VBE/VT .
- VCE = 0 V (saturation region):
VBC = VBE − VCE = VBE → I ′C is comparable to I ′E .
→ IB = (1− αF )I ′E + (1− αR)I ′C → IB -VBE curve shifts left.
M. B. Patil, IIT Bombay
Common-emitter configuration
C
VBE (volts)
VCE=
1V
IC
I B(µ
A)
0 V
IB
IES = 1× 10−14 A
ICS = 2× 10−14 A
αF= 0.99
αR= 0.5
I′E
I′CIB
αRI′C
αFI′E
IE IC
6µA
4µA
8µA
2µA0µA
I C(m
A)
IB = 10µA
VCE (volts)
VBC=0.4 V
VBC=0VVBC=−1V
C
EE
B
B
E
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
0
20
10
0
1
0 1 2 3 4 5
* Comparison of IB versus VBE for VCE = 0 V and VCE = 1 V:
- VCE = 1 V (active region):
VBC = VBE − VCE ≈ 0.7− 1 = −0.3 V → I ′C ≈ 0 → IB = I ′E − αF I′E ≈ (1− αF ) IESe
VBE/VT .
- VCE = 0 V (saturation region):
VBC = VBE − VCE = VBE → I ′C is comparable to I ′E .
→ IB = (1− αF )I ′E + (1− αR)I ′C → IB -VBE curve shifts left.
M. B. Patil, IIT Bombay
Common-emitter configuration
C
VBE (volts)
VCE=
1V
IC
I B(µ
A)
0 V
IB
IES = 1× 10−14 A
ICS = 2× 10−14 A
αF= 0.99
αR= 0.5
I′E
I′CIB
αRI′C
αFI′E
IE IC
6µA
4µA
8µA
2µA0µA
I C(m
A)
IB = 10µA
VCE (volts)
VBC=0.4 V
VBC=0VVBC=−1V
C
EE
B
B
E
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
0
20
10
0
1
0 1 2 3 4 5
* Comparison of IB versus VBE for VCE = 0 V and VCE = 1 V:
- VCE = 1 V (active region):
VBC = VBE − VCE ≈ 0.7− 1 = −0.3 V → I ′C ≈ 0 → IB = I ′E − αF I′E ≈ (1− αF ) IESe
VBE/VT .
- VCE = 0 V (saturation region):
VBC = VBE − VCE = VBE → I ′C is comparable to I ′E .
→ IB = (1− αF )I ′E + (1− αR)I ′C → IB -VBE curve shifts left.
M. B. Patil, IIT Bombay
Common-emitter configuration
C
VBE (volts)
VCE=
1V
IC
I B(µ
A)
0 V
IB
IES = 1× 10−14 A
ICS = 2× 10−14 A
αF= 0.99
αR= 0.5
I′E
I′CIB
αRI′C
αFI′E
IE IC
6µA
4µA
8µA
2µA0µA
I C(m
A)
IB = 10µA
VCE (volts)
VBC=0.4 V
VBC=0VVBC=−1V
C
EE
B
B
E
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
0
20
10
0
1
0 1 2 3 4 5
* Comparison of IB versus VBE for VCE = 0 V and VCE = 1 V:
- VCE = 1 V (active region):
VBC = VBE − VCE ≈ 0.7− 1 = −0.3 V
→ I ′C ≈ 0 → IB = I ′E − αF I′E ≈ (1− αF ) IESe
VBE/VT .
- VCE = 0 V (saturation region):
VBC = VBE − VCE = VBE → I ′C is comparable to I ′E .
→ IB = (1− αF )I ′E + (1− αR)I ′C → IB -VBE curve shifts left.
M. B. Patil, IIT Bombay
Common-emitter configuration
C
VBE (volts)
VCE=
1V
IC
I B(µ
A)
0 V
IB
IES = 1× 10−14 A
ICS = 2× 10−14 A
αF= 0.99
αR= 0.5
I′E
I′CIB
αRI′C
αFI′E
IE IC
6µA
4µA
8µA
2µA0µA
I C(m
A)
IB = 10µA
VCE (volts)
VBC=0.4 V
VBC=0VVBC=−1V
C
EE
B
B
E
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
0
20
10
0
1
0 1 2 3 4 5
* Comparison of IB versus VBE for VCE = 0 V and VCE = 1 V:
- VCE = 1 V (active region):
VBC = VBE − VCE ≈ 0.7− 1 = −0.3 V → I ′C ≈ 0
→ IB = I ′E − αF I′E ≈ (1− αF ) IESe
VBE/VT .
- VCE = 0 V (saturation region):
VBC = VBE − VCE = VBE → I ′C is comparable to I ′E .
→ IB = (1− αF )I ′E + (1− αR)I ′C → IB -VBE curve shifts left.
M. B. Patil, IIT Bombay
Common-emitter configuration
C
VBE (volts)
VCE=
1V
IC
I B(µ
A)
0 V
IB
IES = 1× 10−14 A
ICS = 2× 10−14 A
αF= 0.99
αR= 0.5
I′E
I′CIB
αRI′C
αFI′E
IE IC
6µA
4µA
8µA
2µA0µA
I C(m
A)
IB = 10µA
VCE (volts)
VBC=0.4 V
VBC=0VVBC=−1V
C
EE
B
B
E
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
0
20
10
0
1
0 1 2 3 4 5
* Comparison of IB versus VBE for VCE = 0 V and VCE = 1 V:
- VCE = 1 V (active region):
VBC = VBE − VCE ≈ 0.7− 1 = −0.3 V → I ′C ≈ 0 → IB = I ′E − αF I′E
≈ (1− αF ) IESeVBE/VT .
- VCE = 0 V (saturation region):
VBC = VBE − VCE = VBE → I ′C is comparable to I ′E .
→ IB = (1− αF )I ′E + (1− αR)I ′C → IB -VBE curve shifts left.
M. B. Patil, IIT Bombay
Common-emitter configuration
C
VBE (volts)
VCE=
1V
IC
I B(µ
A)
0 V
IB
IES = 1× 10−14 A
ICS = 2× 10−14 A
αF= 0.99
αR= 0.5
I′E
I′CIB
αRI′C
αFI′E
IE IC
6µA
4µA
8µA
2µA0µA
I C(m
A)
IB = 10µA
VCE (volts)
VBC=0.4 V
VBC=0VVBC=−1V
C
EE
B
B
E
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
0
20
10
0
1
0 1 2 3 4 5
* Comparison of IB versus VBE for VCE = 0 V and VCE = 1 V:
- VCE = 1 V (active region):
VBC = VBE − VCE ≈ 0.7− 1 = −0.3 V → I ′C ≈ 0 → IB = I ′E − αF I′E ≈ (1− αF ) IESe
VBE/VT .
- VCE = 0 V (saturation region):
VBC = VBE − VCE = VBE → I ′C is comparable to I ′E .
→ IB = (1− αF )I ′E + (1− αR)I ′C → IB -VBE curve shifts left.
M. B. Patil, IIT Bombay
Common-emitter configuration
C
VBE (volts)
VCE=
1V
IC
I B(µ
A)
0 V
IB
IES = 1× 10−14 A
ICS = 2× 10−14 A
αF= 0.99
αR= 0.5
I′E
I′CIB
αRI′C
αFI′E
IE IC
6µA
4µA
8µA
2µA0µA
I C(m
A)
IB = 10µA
VCE (volts)
VBC=0.4 V
VBC=0VVBC=−1V
C
EE
B
B
E
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
0
20
10
0
1
0 1 2 3 4 5
* Comparison of IB versus VBE for VCE = 0 V and VCE = 1 V:
- VCE = 1 V (active region):
VBC = VBE − VCE ≈ 0.7− 1 = −0.3 V → I ′C ≈ 0 → IB = I ′E − αF I′E ≈ (1− αF ) IESe
VBE/VT .
- VCE = 0 V (saturation region):
VBC = VBE − VCE = VBE → I ′C is comparable to I ′E .
→ IB = (1− αF )I ′E + (1− αR)I ′C → IB -VBE curve shifts left.
M. B. Patil, IIT Bombay
Common-emitter configuration
C
VBE (volts)
VCE=
1V
IC
I B(µ
A)
0 V
IB
IES = 1× 10−14 A
ICS = 2× 10−14 A
αF= 0.99
αR= 0.5
I′E
I′CIB
αRI′C
αFI′E
IE IC
6µA
4µA
8µA
2µA0µA
I C(m
A)
IB = 10µA
VCE (volts)
VBC=0.4 V
VBC=0VVBC=−1V
C
EE
B
B
E
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
0
20
10
0
1
0 1 2 3 4 5
* Comparison of IB versus VBE for VCE = 0 V and VCE = 1 V:
- VCE = 1 V (active region):
VBC = VBE − VCE ≈ 0.7− 1 = −0.3 V → I ′C ≈ 0 → IB = I ′E − αF I′E ≈ (1− αF ) IESe
VBE/VT .
- VCE = 0 V (saturation region):
VBC = VBE − VCE = VBE
→ I ′C is comparable to I ′E .
→ IB = (1− αF )I ′E + (1− αR)I ′C → IB -VBE curve shifts left.
M. B. Patil, IIT Bombay
Common-emitter configuration
C
VBE (volts)
VCE=
1V
IC
I B(µ
A)
0 V
IB
IES = 1× 10−14 A
ICS = 2× 10−14 A
αF= 0.99
αR= 0.5
I′E
I′CIB
αRI′C
αFI′E
IE IC
6µA
4µA
8µA
2µA0µA
I C(m
A)
IB = 10µA
VCE (volts)
VBC=0.4 V
VBC=0VVBC=−1V
C
EE
B
B
E
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
0
20
10
0
1
0 1 2 3 4 5
* Comparison of IB versus VBE for VCE = 0 V and VCE = 1 V:
- VCE = 1 V (active region):
VBC = VBE − VCE ≈ 0.7− 1 = −0.3 V → I ′C ≈ 0 → IB = I ′E − αF I′E ≈ (1− αF ) IESe
VBE/VT .
- VCE = 0 V (saturation region):
VBC = VBE − VCE = VBE → I ′C is comparable to I ′E .
→ IB = (1− αF )I ′E + (1− αR)I ′C → IB -VBE curve shifts left.
M. B. Patil, IIT Bombay
Common-emitter configuration
C
VBE (volts)
VCE=
1V
IC
I B(µ
A)
0 V
IB
IES = 1× 10−14 A
ICS = 2× 10−14 A
αF= 0.99
αR= 0.5
I′E
I′CIB
αRI′C
αFI′E
IE IC
6µA
4µA
8µA
2µA0µA
I C(m
A)
IB = 10µA
VCE (volts)
VBC=0.4 V
VBC=0VVBC=−1V
C
EE
B
B
E
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
0
20
10
0
1
0 1 2 3 4 5
* Comparison of IB versus VBE for VCE = 0 V and VCE = 1 V:
- VCE = 1 V (active region):
VBC = VBE − VCE ≈ 0.7− 1 = −0.3 V → I ′C ≈ 0 → IB = I ′E − αF I′E ≈ (1− αF ) IESe
VBE/VT .
- VCE = 0 V (saturation region):
VBC = VBE − VCE = VBE → I ′C is comparable to I ′E .
→ IB = (1− αF )I ′E + (1− αR)I ′C
→ IB -VBE curve shifts left.
M. B. Patil, IIT Bombay
Common-emitter configuration
C
VBE (volts)
VCE=
1V
IC
I B(µ
A)
0 V
IB
IES = 1× 10−14 A
ICS = 2× 10−14 A
αF= 0.99
αR= 0.5
I′E
I′CIB
αRI′C
αFI′E
IE IC
6µA
4µA
8µA
2µA0µA
I C(m
A)
IB = 10µA
VCE (volts)
VBC=0.4 V
VBC=0VVBC=−1V
C
EE
B
B
E
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
0
20
10
0
1
0 1 2 3 4 5
* Comparison of IB versus VBE for VCE = 0 V and VCE = 1 V:
- VCE = 1 V (active region):
VBC = VBE − VCE ≈ 0.7− 1 = −0.3 V → I ′C ≈ 0 → IB = I ′E − αF I′E ≈ (1− αF ) IESe
VBE/VT .
- VCE = 0 V (saturation region):
VBC = VBE − VCE = VBE → I ′C is comparable to I ′E .
→ IB = (1− αF )I ′E + (1− αR)I ′C → IB -VBE curve shifts left.
M. B. Patil, IIT Bombay
BJT: second-order effects
* The Ebers-Moll model does remarkably well in capturing the basic transistor action.
* For a higher accuracy in circuit simulation, second-order effects need to be considered.
* We will consider
- base width modulation
- breakdown phenomena
M. B. Patil, IIT Bombay
BJT: second-order effects
* The Ebers-Moll model does remarkably well in capturing the basic transistor action.
* For a higher accuracy in circuit simulation, second-order effects need to be considered.
* We will consider
- base width modulation
- breakdown phenomena
M. B. Patil, IIT Bombay
BJT: second-order effects
* The Ebers-Moll model does remarkably well in capturing the basic transistor action.
* For a higher accuracy in circuit simulation, second-order effects need to be considered.
* We will consider
- base width modulation
- breakdown phenomena
M. B. Patil, IIT Bombay
BJT: second-order effects
* The Ebers-Moll model does remarkably well in capturing the basic transistor action.
* For a higher accuracy in circuit simulation, second-order effects need to be considered.
* We will consider
- base width modulation
- breakdown phenomena
M. B. Patil, IIT Bombay
Base width modulation
0
n(0)
W0
n(x)
C-Bdepletionregion
E-Bdepletionregion
B (p) C (n)E (n)
x (µm)0 1.5 3
1020
1018
1016
1014
Dopingdensity(cm
−3)
Nd (E)Nd (C)
Na (B)
We have assumed so far that the width of the neutral base region
(in the active mode) is independent of VBE and VBC .
This is a reasonable assumption for the following reasons.
- The B-E junction voltge is nearly constant, say 0.6 to 0.75 V
for a silicon BJT, and the variation of the B-E depletion
width is negliglble.
- Since VCB – the reverse bias across the B-C junction – can
vary substantially, the B-C depletion width can also change
significantly.
However, the change occurs mostly on the collector side since
Na(B) � Nd (C).
M. B. Patil, IIT Bombay
Base width modulation
0
n(0)
W0
n(x)
C-Bdepletionregion
E-Bdepletionregion
B (p) C (n)E (n)
x (µm)0 1.5 3
1020
1018
1016
1014
Dopingdensity(cm
−3)
Nd (E)Nd (C)
Na (B)
We have assumed so far that the width of the neutral base region
(in the active mode) is independent of VBE and VBC .
This is a reasonable assumption for the following reasons.
- The B-E junction voltge is nearly constant, say 0.6 to 0.75 V
for a silicon BJT, and the variation of the B-E depletion
width is negliglble.
- Since VCB – the reverse bias across the B-C junction – can
vary substantially, the B-C depletion width can also change
significantly.
However, the change occurs mostly on the collector side since
Na(B) � Nd (C).
M. B. Patil, IIT Bombay
Base width modulation
0
n(0)
W0
n(x)
C-Bdepletionregion
E-Bdepletionregion
B (p) C (n)E (n)
x (µm)0 1.5 3
1020
1018
1016
1014
Dopingdensity(cm
−3)
Nd (E)Nd (C)
Na (B)
We have assumed so far that the width of the neutral base region
(in the active mode) is independent of VBE and VBC .
This is a reasonable assumption for the following reasons.
- The B-E junction voltge is nearly constant, say 0.6 to 0.75 V
for a silicon BJT, and the variation of the B-E depletion
width is negliglble.
- Since VCB – the reverse bias across the B-C junction – can
vary substantially, the B-C depletion width can also change
significantly.
However, the change occurs mostly on the collector side since
Na(B) � Nd (C).
M. B. Patil, IIT Bombay
Base width modulation
0
n(0)
W0
n(x)
C-Bdepletionregion
E-Bdepletionregion
B (p) C (n)E (n)
x (µm)0 1.5 3
1020
1018
1016
1014
Dopingdensity(cm
−3)
Nd (E)Nd (C)
Na (B)
We have assumed so far that the width of the neutral base region
(in the active mode) is independent of VBE and VBC .
This is a reasonable assumption for the following reasons.
- The B-E junction voltge is nearly constant, say 0.6 to 0.75 V
for a silicon BJT, and the variation of the B-E depletion
width is negliglble.
- Since VCB – the reverse bias across the B-C junction – can
vary substantially, the B-C depletion width can also change
significantly.
However, the change occurs mostly on the collector side since
Na(B) � Nd (C).
M. B. Patil, IIT Bombay
Base width modulation
VCB=VCB1
VCB=VCB2
0
0
n(0)
n(0)
W0
0
n(x)
n(x)
W
B (p) C (n)E (n)
B (p) C (n)E (n)
IC
IB8µA
6µA
4µA
0µA
2µA
VCE (volts)
I C(m
A)
IB= 10µA
VsatCE
C
EE
B
0 1 2 3 4 5
2.5
2.0
1.5
1.0
0
0.5
- As VCB ↑, the B-C depletion region expands, W ↓
→ IC ∝dn
dx(W ) ↑
- This “base width modulation” effect (also called the “Early
effect”) gives rise to a finite slope of the IC -VCE curves in the
active region.
(VCE ↑ → VCB (= VCE − VBE ) ↑ → W ↓ → IC ↑)
M. B. Patil, IIT Bombay
Base width modulation
VCB=VCB1
VCB=VCB2
0
0
n(0)
n(0)
W0
0
n(x)
n(x)
W
B (p) C (n)E (n)
B (p) C (n)E (n)
IC
IB8µA
6µA
4µA
0µA
2µA
VCE (volts)
I C(m
A)
IB= 10µA
VsatCE
C
EE
B
0 1 2 3 4 5
2.5
2.0
1.5
1.0
0
0.5
- As VCB ↑, the B-C depletion region expands, W ↓
→ IC ∝dn
dx(W ) ↑
- This “base width modulation” effect (also called the “Early
effect”) gives rise to a finite slope of the IC -VCE curves in the
active region.
(VCE ↑ → VCB (= VCE − VBE ) ↑ → W ↓ → IC ↑)
M. B. Patil, IIT Bombay
Base width modulation
VCB=VCB1
VCB=VCB2
0
0
n(0)
n(0)
W0
0
n(x)
n(x)
W
B (p) C (n)E (n)
B (p) C (n)E (n)
IC
IB8µA
6µA
4µA
0µA
2µA
VCE (volts)
I C(m
A)
IB= 10µA
VsatCE
C
EE
B
0 1 2 3 4 5
2.5
2.0
1.5
1.0
0
0.5
- As VCB ↑, the B-C depletion region expands, W ↓
→ IC ∝dn
dx(W ) ↑
- This “base width modulation” effect (also called the “Early
effect”) gives rise to a finite slope of the IC -VCE curves in the
active region.
(VCE ↑ → VCB (= VCE − VBE ) ↑ → W ↓ → IC ↑)
M. B. Patil, IIT Bombay
Base width modulation
VCB=VCB1
VCB=VCB2
0
0
n(0)
n(0)
W0
0
n(x)
n(x)
W
B (p) C (n)E (n)
B (p) C (n)E (n)
IC
IB8µA
6µA
4µA
0µA
2µA
VCE (volts)
I C(m
A)
IB= 10µA
VsatCE
C
EE
B
0 1 2 3 4 5
2.5
2.0
1.5
1.0
0
0.5
- As VCB ↑, the B-C depletion region expands, W ↓
→ IC ∝dn
dx(W ) ↑
- This “base width modulation” effect (also called the “Early
effect”) gives rise to a finite slope of the IC -VCE curves in the
active region.
(VCE ↑ → VCB (= VCE − VBE ) ↑ → W ↓ → IC ↑)
M. B. Patil, IIT Bombay
Base width modulation
IC
IB
8µA
6µA
4µA
0µA
2µA
VCE (volts)
I C(m
A)
IB= 10µA
VsatCE
C
EE
B
0 1 2 3 4 5
2.5
2.0
1.5
1.0
0
0.5
VCE−VA
IB1
IB2
IB3
IB4
IC
0
* When the active region parts of the IC -VCE curves are extended backwards, they intersect
the VCE axis approximately at the same point, −VA.
* VA is called the Early voltage.
M. B. Patil, IIT Bombay
Base width modulation
IC
IB
8µA
6µA
4µA
0µA
2µA
VCE (volts)
I C(m
A)
IB= 10µA
VsatCE
C
EE
B
0 1 2 3 4 5
2.5
2.0
1.5
1.0
0
0.5
VCE−VA
IB1
IB2
IB3
IB4
IC
0
* When the active region parts of the IC -VCE curves are extended backwards, they intersect
the VCE axis approximately at the same point, −VA.
* VA is called the Early voltage.
M. B. Patil, IIT Bombay
Base width modulation
IC
IB
8µA
6µA
4µA
0µA
2µA
VCE (volts)
I C(m
A)
IB= 10µA
VsatCE
C
EE
B
0 1 2 3 4 5
2.5
2.0
1.5
1.0
0
0.5
VCE−VA
IB1
IB2
IB3
IB4
IC
0
* When the active region parts of the IC -VCE curves are extended backwards, they intersect
the VCE axis approximately at the same point, −VA.
* VA is called the Early voltage.
M. B. Patil, IIT Bombay
Base width modulation
IC
IB
8µA
6µA
4µA
0µA
2µA
VCE (volts)
I C(m
A)
IB= 10µA
VsatCE
C
EE
B
0 1 2 3 4 5
2.5
2.0
1.5
1.0
0
0.5
VCE−VA
IB1
IB2
IB3
IB4
IC
0
* When the active region parts of the IC -VCE curves are extended backwards, they intersect
the VCE axis approximately at the same point, −VA.
* VA is called the Early voltage.
M. B. Patil, IIT Bombay
Breakdown phenomena
* We have seen that a pn junction diode cannot withstand arbitrarily large reverse voltages,
it breaks down at some point.
* Similarly, if the reverse bias across the B-C junction of a BJT is increased, it breaks down
at some point, i.e., the collector current becomes very large.
* We will look at two breakdown mechanisms:
- punchthrough
- avalanche breakdown
M. B. Patil, IIT Bombay
Breakdown phenomena
* We have seen that a pn junction diode cannot withstand arbitrarily large reverse voltages,
it breaks down at some point.
* Similarly, if the reverse bias across the B-C junction of a BJT is increased, it breaks down
at some point, i.e., the collector current becomes very large.
* We will look at two breakdown mechanisms:
- punchthrough
- avalanche breakdown
M. B. Patil, IIT Bombay
Breakdown phenomena
* We have seen that a pn junction diode cannot withstand arbitrarily large reverse voltages,
it breaks down at some point.
* Similarly, if the reverse bias across the B-C junction of a BJT is increased, it breaks down
at some point, i.e., the collector current becomes very large.
* We will look at two breakdown mechanisms:
- punchthrough
- avalanche breakdown
M. B. Patil, IIT Bombay
Punchthrough
Ec
Ev
E B
VCE=10V
VCE=5V
E-Bdepletionregion
C-Bdepletionregionn p n
Ec
Ev
E
VCE=30V
VCE=40V
E-B and C-Bdepletion regionsmerged together
* As the reverse bias VCB is increased,
the C-B depletion region expands
→ the neutral base region shrinks.
* At some point, the E-B and C-B
depletion regions consume the entire
base region. This condition is called
punchthrough.
(The band bending in the emitter
region is due to non-uniform doping in
the simulated structure.)
M. B. Patil, IIT Bombay
Punchthrough
Ec
Ev
E B
VCE=10V
VCE=5V
E-Bdepletionregion
C-Bdepletionregionn p n
Ec
Ev
E
VCE=30V
VCE=40V
E-B and C-Bdepletion regionsmerged together
* As the reverse bias VCB is increased,
the C-B depletion region expands
→ the neutral base region shrinks.
* At some point, the E-B and C-B
depletion regions consume the entire
base region. This condition is called
punchthrough.
(The band bending in the emitter
region is due to non-uniform doping in
the simulated structure.)
M. B. Patil, IIT Bombay
Punchthrough
Ec
Ev
E B
VCE=10V
VCE=5V
E-Bdepletionregion
C-Bdepletionregionn p n
Ec
Ev
E
VCE=30V
VCE=40V
E-B and C-Bdepletion regionsmerged together
* As the reverse bias VCB is increased,
the C-B depletion region expands
→ the neutral base region shrinks.
* At some point, the E-B and C-B
depletion regions consume the entire
base region. This condition is called
punchthrough.
(The band bending in the emitter
region is due to non-uniform doping in
the simulated structure.)
M. B. Patil, IIT Bombay
Punchthrough
Ec
Ev
E B
VCE=10V
VCE=5V
E-Bdepletionregion
C-Bdepletionregionn p n
Ec
Ev
E
VCE=30V
VCE=40V
E-B and C-Bdepletion regionsmerged together
* As the reverse bias VCB is increased,
the C-B depletion region expands
→ the neutral base region shrinks.
* At some point, the E-B and C-B
depletion regions consume the entire
base region. This condition is called
punchthrough.
(The band bending in the emitter
region is due to non-uniform doping in
the simulated structure.)
M. B. Patil, IIT Bombay
Punchthrough
Ec
Ev
E B
VCE=10V
VCE=5V
E-Bdepletionregion
C-Bdepletionregionn p n
Ec
Ev
E
VCE=30V
VCE=40V
E-B and C-Bdepletion regionsmerged together
* As the reverse bias VCB is increased,
the C-B depletion region expands
→ the neutral base region shrinks.
* At some point, the E-B and C-B
depletion regions consume the entire
base region. This condition is called
punchthrough.
(The band bending in the emitter
region is due to non-uniform doping in
the simulated structure.)
M. B. Patil, IIT Bombay
Punchthrough
Ec
Ev
Ec
Ev
E B E
VCE=30V
VCE=40VVCE=10V
VCE=5V
E-Bdepletionregion
E-B and C-Bdepletion regionsmerged together
C-Bdepletionregionn p n
* Prior to punchthrough, an increase in
the C-B reverse bias only affects the
bands in the base and collector
regions, leaving the E-B barrier (for
electron flow) unchanged.
* After punchthrough, any further
increase in VCB lowers the E-B
potential barrier. The number of
electrons injected from the emitter
increases dramatically. They get swept
away toward the collector, resulting in
a large collector current.
M. B. Patil, IIT Bombay
Punchthrough
Ec
Ev
Ec
Ev
E B E
VCE=30V
VCE=40VVCE=10V
VCE=5V
E-Bdepletionregion
E-B and C-Bdepletion regionsmerged together
C-Bdepletionregionn p n
* Prior to punchthrough, an increase in
the C-B reverse bias only affects the
bands in the base and collector
regions, leaving the E-B barrier (for
electron flow) unchanged.
* After punchthrough, any further
increase in VCB lowers the E-B
potential barrier. The number of
electrons injected from the emitter
increases dramatically. They get swept
away toward the collector, resulting in
a large collector current.
M. B. Patil, IIT Bombay
Punchthrough
Ec
Ev
Ec
Ev
E B E
VCE=30V
VCE=40VVCE=10V
VCE=5V
E-Bdepletionregion
E-B and C-Bdepletion regionsmerged together
C-Bdepletionregionn p n
* Prior to punchthrough, an increase in
the C-B reverse bias only affects the
bands in the base and collector
regions, leaving the E-B barrier (for
electron flow) unchanged.
* After punchthrough, any further
increase in VCB lowers the E-B
potential barrier. The number of
electrons injected from the emitter
increases dramatically. They get swept
away toward the collector, resulting in
a large collector current.
M. B. Patil, IIT Bombay
Avalanche breakdown
A
Ec
Ev
Eg
x
E pn n
W
B
C
EFp
Ev
Ec
EFn
qVBE
qVCB
EFn
* Avalanche multiplication because of impact ionisation can take place in a semiconductor
if the electric field is high (∼ critical field Ec ).
* In a BJT operating in the active mode, the C-B junction is under reverse bias. If the
reverse voltage is sufficiently large, avalanche breakdown can take place.
M. B. Patil, IIT Bombay
Avalanche breakdown
A
Ec
Ev
Eg
x
E pn n
W
B
C
EFp
Ev
Ec
EFn
qVBE
qVCB
EFn
* Avalanche multiplication because of impact ionisation can take place in a semiconductor
if the electric field is high (∼ critical field Ec ).
* In a BJT operating in the active mode, the C-B junction is under reverse bias. If the
reverse voltage is sufficiently large, avalanche breakdown can take place.
M. B. Patil, IIT Bombay
Avalanche breakdown
A
Ec
Ev
Eg
x
E pn n
W
B
C
EFp
Ev
Ec
EFn
qVBE
qVCB
EFn
* Avalanche multiplication because of impact ionisation can take place in a semiconductor
if the electric field is high (∼ critical field Ec ).
* In a BJT operating in the active mode, the C-B junction is under reverse bias. If the
reverse voltage is sufficiently large, avalanche breakdown can take place.
M. B. Patil, IIT Bombay
Avalanche breakdown
E pn n
W
B
C
EFp
Ev
Ec
EFn
qVBE
qVCB
EFn
VBR
VR (volts)
m=5m=4
m=6
M
10
5
050 1000
* The avalanche multiplication process is characterised by a multiplication factor M.
* Let I0 = current through the high-field region without multiplication
I = current through the high-field region with multiplication
Then, M =I
I0.
* Empirically, it is observed that M =1
1−(
VR
V BR
)m , where 3 < m < 6 (depending on the semiconductor),
VR is the reverse bias, and V BR is the breakdown voltage.
M. B. Patil, IIT Bombay
Avalanche breakdown
E pn n
W
B
C
EFp
Ev
Ec
EFn
qVBE
qVCB
EFn
VBR
VR (volts)
m=5m=4
m=6
M
10
5
050 1000
* The avalanche multiplication process is characterised by a multiplication factor M.
* Let I0 = current through the high-field region without multiplication
I = current through the high-field region with multiplication
Then, M =I
I0.
* Empirically, it is observed that M =1
1−(
VR
V BR
)m , where 3 < m < 6 (depending on the semiconductor),
VR is the reverse bias, and V BR is the breakdown voltage.
M. B. Patil, IIT Bombay
Avalanche breakdown
E pn n
W
B
C
EFp
Ev
Ec
EFn
qVBE
qVCB
EFn
VBR
VR (volts)
m=5m=4
m=6
M
10
5
050 1000
* The avalanche multiplication process is characterised by a multiplication factor M.
* Let I0 = current through the high-field region without multiplication
I = current through the high-field region with multiplication
Then, M =I
I0.
* Empirically, it is observed that M =1
1−(
VR
V BR
)m , where 3 < m < 6 (depending on the semiconductor),
VR is the reverse bias, and V BR is the breakdown voltage.
M. B. Patil, IIT Bombay
Avalanche breakdown
E pn n
W
B
C
EFp
Ev
Ec
EFn
qVBE
qVCB
EFn
VBR
VR (volts)
m=5m=4
m=6
M
10
5
050 1000
* The avalanche multiplication process is characterised by a multiplication factor M.
* Let I0 = current through the high-field region without multiplication
I = current through the high-field region with multiplication
Then, M =I
I0.
* Empirically, it is observed that M =1
1−(
VR
V BR
)m , where 3 < m < 6 (depending on the semiconductor),
VR is the reverse bias, and V BR is the breakdown voltage.M. B. Patil, IIT Bombay
Avalanche breakdown
IE IEIC
IB
IC
IB
I′E
I′CαRI
′C
αFI′E
C
B
Epn n
B
CE
* Collector current without multiplication is αF I′E − I ′C .
* Collector current with multiplication is M(αF I′E − I ′C
), i.e.,
IC = M(αF I′E + ICS
)∵ I ′C ≈ −ICS
= M[αF
(IE + αR I
′C
)+ ICS
]= M αF IE + M ICS (1− αFαR)
= M αF IE + M ICBO .
M. B. Patil, IIT Bombay
Avalanche breakdown
IE IEIC
IB
IC
IB
I′E
I′CαRI
′C
αFI′E
C
B
Epn n
B
CE
* Collector current without multiplication is αF I′E − I ′C .
* Collector current with multiplication is M(αF I′E − I ′C
), i.e.,
IC = M(αF I′E + ICS
)∵ I ′C ≈ −ICS
= M[αF
(IE + αR I
′C
)+ ICS
]= M αF IE + M ICS (1− αFαR)
= M αF IE + M ICBO .
M. B. Patil, IIT Bombay
Avalanche breakdown
IE IEIC
IB
IC
IB
I′E
I′CαRI
′C
αFI′E
C
B
Epn n
B
CE
* Collector current without multiplication is αF I′E − I ′C .
* Collector current with multiplication is M(αF I′E − I ′C
), i.e.,
IC = M(αF I′E + ICS
)∵ I ′C ≈ −ICS
= M[αF
(IE + αR I
′C
)+ ICS
]= M αF IE + M ICS (1− αFαR)
= M αF IE + M ICBO .
M. B. Patil, IIT Bombay
Avalanche breakdown
IE IEIC
IB
IC
IB
I′E
I′CαRI
′C
αFI′E
C
B
Epn n
B
CE
E Cpn n
B
IC = M αF IE + M ICBO .
* Emitter open:
IC = MICBO = ICBO ×1
1−(
VR
V BRBC
)m .
Breakdown voltage: As VR → V BRBC , IC →∞, and therefore
the breakdown voltage with the emitter open (denoted by
VCBO) is simply VCBO =V BRBC .
M. B. Patil, IIT Bombay
Avalanche breakdown
IE IEIC
IB
IC
IB
I′E
I′CαRI
′C
αFI′E
C
B
Epn n
B
CE
E Cpn n
B
IC = M αF IE + M ICBO .
* Emitter open:
IC = MICBO = ICBO ×1
1−(
VR
V BRBC
)m .
Breakdown voltage: As VR → V BRBC , IC →∞, and therefore
the breakdown voltage with the emitter open (denoted by
VCBO) is simply VCBO =V BRBC .
M. B. Patil, IIT Bombay
Avalanche breakdown
IE IEIC
IB
IC
IB
I′E
I′CαRI
′C
αFI′E
C
B
Epn n
B
CE
E Cpn n
B
IC = M αF IE + M ICBO .
* Emitter open:
IC = MICBO = ICBO ×1
1−(
VR
V BRBC
)m .
Breakdown voltage: As VR → V BRBC , IC →∞, and therefore
the breakdown voltage with the emitter open (denoted by
VCBO) is simply VCBO =V BRBC .
M. B. Patil, IIT Bombay
Avalanche breakdown
IE IEIC
IB
IC
IB
I′E
I′CαRI
′C
αFI′E
C
B
Epn n
B
CE
E Cpn n
B
IC = M αF IE + M ICBO .
* Emitter open:
IC = MICBO = ICBO ×1
1−(
VR
V BRBC
)m .
Breakdown voltage: As VR → V BRBC , IC →∞, and therefore
the breakdown voltage with the emitter open (denoted by
VCBO) is simply VCBO =V BRBC .
M. B. Patil, IIT Bombay
Avalanche breakdown
IE IEIC
IB
IC
IB
I′E
I′CαRI
′C
αFI′E
C
B
Epn n
B
CE
E Cpn n
B
IC = M αF IE + M ICBO .
* Emitter open:
IC = MICBO = ICBO ×1
1−(
VR
V BRBC
)m .
Breakdown voltage: As VR → V BRBC , IC →∞, and therefore
the breakdown voltage with the emitter open (denoted by
VCBO) is simply VCBO =V BRBC .
M. B. Patil, IIT Bombay
Avalanche breakdown
IE IEIC
IB
IC
IB
I′E
I′CαRI
′C
αFI′E
C
B
Epn n
B
CE
E Cpn n
B
IC = M αF IE + M ICBO .
* Base open:
IC = M αF (IC + IB) + M ICBO
= M αF IC + M ICBO
→ IC (1−MαF ) = M ICBO → IC =M ICBO
1−MαF.
Breakdown condition: MαF → 1 or M → 1
αF.
→ 1
1−(
VR
V BRBC
)m =1
αF=βF + 1
βF
→ VR ≡ VCEO =V BRBC
(βF + 1)1/m≈ VCBO
β1/mF
.
M. B. Patil, IIT Bombay
Avalanche breakdown
IE IEIC
IB
IC
IB
I′E
I′CαRI
′C
αFI′E
C
B
Epn n
B
CE
E Cpn n
B
IC = M αF IE + M ICBO .
* Base open:
IC = M αF (IC + IB) + M ICBO
= M αF IC + M ICBO
→ IC (1−MαF ) = M ICBO → IC =M ICBO
1−MαF.
Breakdown condition: MαF → 1 or M → 1
αF.
→ 1
1−(
VR
V BRBC
)m =1
αF=βF + 1
βF
→ VR ≡ VCEO =V BRBC
(βF + 1)1/m≈ VCBO
β1/mF
.
M. B. Patil, IIT Bombay
Avalanche breakdown
IE IEIC
IB
IC
IB
I′E
I′CαRI
′C
αFI′E
C
B
Epn n
B
CE
E Cpn n
B
IC = M αF IE + M ICBO .
* Base open:
IC = M αF (IC + IB) + M ICBO
= M αF IC + M ICBO
→ IC (1−MαF ) = M ICBO → IC =M ICBO
1−MαF.
Breakdown condition: MαF → 1 or M → 1
αF.
→ 1
1−(
VR
V BRBC
)m =1
αF=βF + 1
βF
→ VR ≡ VCEO =V BRBC
(βF + 1)1/m≈ VCBO
β1/mF
.
M. B. Patil, IIT Bombay
Avalanche breakdown
IE IEIC
IB
IC
IB
I′E
I′CαRI
′C
αFI′E
C
B
Epn n
B
CE
E Cpn n
B
IC = M αF IE + M ICBO .
* Base open:
IC = M αF (IC + IB) + M ICBO
= M αF IC + M ICBO
→ IC (1−MαF ) = M ICBO → IC =M ICBO
1−MαF.
Breakdown condition: MαF → 1 or M → 1
αF.
→ 1
1−(
VR
V BRBC
)m =1
αF=βF + 1
βF
→ VR ≡ VCEO =V BRBC
(βF + 1)1/m≈ VCBO
β1/mF
.
M. B. Patil, IIT Bombay
Avalanche breakdown
IE IEIC
IB
IC
IB
I′E
I′CαRI
′C
αFI′E
C
B
Epn n
B
CE
E Cpn n
B
IC = M αF IE + M ICBO .
* Base open:
IC = M αF (IC + IB) + M ICBO
= M αF IC + M ICBO
→ IC (1−MαF ) = M ICBO → IC =M ICBO
1−MαF.
Breakdown condition: MαF → 1 or M → 1
αF.
→ 1
1−(
VR
V BRBC
)m =1
αF=βF + 1
βF
→ VR ≡ VCEO =V BRBC
(βF + 1)1/m≈ VCBO
β1/mF
.
M. B. Patil, IIT Bombay
Avalanche breakdown
IE IEIC
IB
IC
IB
I′E
I′CαRI
′C
αFI′E
C
B
Epn n
B
CE
E Cpn n
B
IC = M αF IE + M ICBO .
* Base open:
IC = M αF (IC + IB) + M ICBO
= M αF IC + M ICBO
→ IC (1−MαF ) = M ICBO → IC =M ICBO
1−MαF.
Breakdown condition: MαF → 1 or M → 1
αF.
→ 1
1−(
VR
V BRBC
)m =1
αF=βF + 1
βF
→ VR ≡ VCEO =V BRBC
(βF + 1)1/m≈ VCBO
β1/mF
.
M. B. Patil, IIT Bombay
Avalanche breakdown
IE IEIC
IB
IC
IB
I′E
I′CαRI
′C
αFI′E
C
B
Epn n
B
CE
E Cpn n
B
IC = M αF IE + M ICBO .
* Base open:
IC = M αF (IC + IB) + M ICBO
= M αF IC + M ICBO
→ IC (1−MαF ) = M ICBO → IC =M ICBO
1−MαF.
Breakdown condition: MαF → 1 or M → 1
αF.
→ 1
1−(
VR
V BRBC
)m =1
αF=βF + 1
βF
→ VR ≡ VCEO =V BRBC
(βF + 1)1/m≈ VCBO
β1/mF
.
M. B. Patil, IIT Bombay
Avalanche breakdown
IE IEIC
IB
IC
IB
I′E
I′CαRI
′C
αFI′E
C
B
Epn n
B
CE
E Cpn n
B
IC = M αF IE + M ICBO .
* Base open:
IC = M αF (IC + IB) + M ICBO
= M αF IC + M ICBO
→ IC (1−MαF ) = M ICBO → IC =M ICBO
1−MαF.
Breakdown condition: MαF → 1 or M → 1
αF.
→ 1
1−(
VR
V BRBC
)m =1
αF=βF + 1
βF
→ VR ≡ VCEO =V BRBC
(βF + 1)1/m≈ VCBO
β1/mF
.
M. B. Patil, IIT Bombay
Avalanche breakdown
IE IEIC
IB
IC
IB
I′E
I′CαRI
′C
αFI′E
C
B
Epn n
B
CE
E Cpn n
B
* Base open: VCEO =V BRBC
(βF + 1)1/m≈ VCBO
β1/mF
.
As an example, for βF = 200 and m = 4, VCEO =VCBO/3.8, which is
significantly smaller than VCBO .
M. B. Patil, IIT Bombay
Avalanche breakdown
IE IEIC
IB
IC
IB
I′E
I′CαRI
′C
αFI′E
C
B
Epn n
B
CE
E Cpn n
B
* Base open: VCEO =V BRBC
(βF + 1)1/m≈ VCBO
β1/mF
.
As an example, for βF = 200 and m = 4, VCEO =VCBO/3.8, which is
significantly smaller than VCBO .
M. B. Patil, IIT Bombay
IE IC
IB
pn n
B
CE
IE= 1mA
0.8mA
0.6mA
0.4mA
0.2mA
∼ 0mA
VCBO
without impact ionisation
with impact ionisation
I C(m
A)
VCB (volts)
0
0.5
1.0
1.5
0 50 100 150 200 250
IB = 10µA
4µA
∼ 0µA2µA
6µA
8µA
VCEO
VCE (volts)
I C(m
A)
0
1
2
3
4
5
0 50 100
Significance of VCBO and VCEO :
* When IE = 0, the breakdown voltage (VCB) is given by VCBO .
In the above example, it is ∼ 230 V.
* When IB = 0, the breakdown voltage (VCE ) is given by VCEO .
In the above example, it is ∼ 90 V, which is significantly
lower, as we would expect.
* Note that the slope of the IC -VCE curves in the linear region
without impact ionisation is because of base width
modulation.
M. B. Patil, IIT Bombay
IE IC
IB
pn n
B
CE
IE= 1mA
0.8mA
0.6mA
0.4mA
0.2mA
∼ 0mA
VCBO
without impact ionisation
with impact ionisation
I C(m
A)
VCB (volts)
0
0.5
1.0
1.5
0 50 100 150 200 250
IB = 10µA
4µA
∼ 0µA2µA
6µA
8µA
VCEO
VCE (volts)
I C(m
A)
0
1
2
3
4
5
0 50 100
Significance of VCBO and VCEO :
* When IE = 0, the breakdown voltage (VCB) is given by VCBO .
In the above example, it is ∼ 230 V.
* When IB = 0, the breakdown voltage (VCE ) is given by VCEO .
In the above example, it is ∼ 90 V, which is significantly
lower, as we would expect.
* Note that the slope of the IC -VCE curves in the linear region
without impact ionisation is because of base width
modulation.
M. B. Patil, IIT Bombay
IE IC
IB
pn n
B
CE
IE= 1mA
0.8mA
0.6mA
0.4mA
0.2mA
∼ 0mA
VCBO
without impact ionisation
with impact ionisation
I C(m
A)
VCB (volts)
0
0.5
1.0
1.5
0 50 100 150 200 250
IB = 10µA
4µA
∼ 0µA2µA
6µA
8µA
VCEO
VCE (volts)
I C(m
A)
0
1
2
3
4
5
0 50 100
Significance of VCBO and VCEO :
* When IE = 0, the breakdown voltage (VCB) is given by VCBO .
In the above example, it is ∼ 230 V.
* When IB = 0, the breakdown voltage (VCE ) is given by VCEO .
In the above example, it is ∼ 90 V, which is significantly
lower, as we would expect.
* Note that the slope of the IC -VCE curves in the linear region
without impact ionisation is because of base width
modulation.
M. B. Patil, IIT Bombay
IE IC
IB
pn n
B
CE
IE= 1mA
0.8mA
0.6mA
0.4mA
0.2mA
∼ 0mA
VCBO
without impact ionisation
with impact ionisation
I C(m
A)
VCB (volts)
0
0.5
1.0
1.5
0 50 100 150 200 250
IB = 10µA
4µA
∼ 0µA2µA
6µA
8µA
VCEO
VCE (volts)
I C(m
A)
0
1
2
3
4
5
0 50 100
Significance of VCBO and VCEO :
* When IE = 0, the breakdown voltage (VCB) is given by VCBO .
In the above example, it is ∼ 230 V.
* When IB = 0, the breakdown voltage (VCE ) is given by VCEO .
In the above example, it is ∼ 90 V, which is significantly
lower, as we would expect.
* Note that the slope of the IC -VCE curves in the linear region
without impact ionisation is because of base width
modulation.
M. B. Patil, IIT Bombay
IE IC
IB
pn n
B
CE
IE= 1mA
0.8mA
0.6mA
0.4mA
0.2mA
∼ 0mA
VCBO
without impact ionisation
with impact ionisation
I C(m
A)
VCB (volts)
0
0.5
1.0
1.5
0 50 100 150 200 250
IB = 10µA
4µA
∼ 0µA2µA
6µA
8µA
VCEO
VCE (volts)
I C(m
A)
0
1
2
3
4
5
0 50 100
Significance of VCBO and VCEO :
* When IE = 0, the breakdown voltage (VCB) is given by VCBO .
In the above example, it is ∼ 230 V.
* When IB = 0, the breakdown voltage (VCE ) is given by VCEO .
In the above example, it is ∼ 90 V, which is significantly
lower, as we would expect.
* Note that the slope of the IC -VCE curves in the linear region
without impact ionisation is because of base width
modulation.
M. B. Patil, IIT Bombay
IE IC
IB
pn n
B
CE
IE= 1mA
0.8mA
0.6mA
0.4mA
0.2mA
∼ 0mA
VCBO
without impact ionisation
with impact ionisation
I C(m
A)
VCB (volts)
0
0.5
1.0
1.5
0 50 100 150 200 250
IB = 10µA
4µA
∼ 0µA2µA
6µA
8µA
VCEO
VCE (volts)
I C(m
A)
0
1
2
3
4
5
0 50 100
Significance of VCBO and VCEO :
* When IE = 0, the breakdown voltage (VCB) is given by VCBO .
In the above example, it is ∼ 230 V.
* When IB = 0, the breakdown voltage (VCE ) is given by VCEO .
In the above example, it is ∼ 90 V, which is significantly
lower, as we would expect.
* Note that the slope of the IC -VCE curves in the linear region
without impact ionisation is because of base width
modulation.
M. B. Patil, IIT Bombay
IE
IB = 10µA
4µA
∼ 0µA2µA
6µA
8µA
IE= 1mA
0.8mA
0.6mA
0.4mA
0.2mA
∼ 0mA
VCBO
VCEO
IC
IB
VCE (volts)
I C(m
A)
I C(m
A)
VCB (volts)
without impact ionisation
with impact ionisationpn n
B
CE
0
1
2
3
4
5
0
0.5
1.0
1.5
0 50 100 150 200 250
0 50 100
IC = M αF IE + M ICBO
=MαF IB
1−MαF+
MICBO
1−MαF, with M =
1
1−(
VR
V BRBC
)m
* Common-base characteristics: For the same VCB , i.e., the
same multiplication factor, the increase in IC due to
multiplication is larger for larger IE .
* Common-emitter characteristics: For the same VCE (∼ VCB),
i.e., the same multiplication factor, the increase in IC due to
multiplication is larger for larger IB .
M. B. Patil, IIT Bombay
IE
IB = 10µA
4µA
∼ 0µA2µA
6µA
8µA
IE= 1mA
0.8mA
0.6mA
0.4mA
0.2mA
∼ 0mA
VCBO
VCEO
IC
IB
VCE (volts)
I C(m
A)
I C(m
A)
VCB (volts)
without impact ionisation
with impact ionisationpn n
B
CE
0
1
2
3
4
5
0
0.5
1.0
1.5
0 50 100 150 200 250
0 50 100
IC = M αF IE + M ICBO
=MαF IB
1−MαF+
MICBO
1−MαF, with M =
1
1−(
VR
V BRBC
)m* Common-base characteristics: For the same VCB , i.e., the
same multiplication factor, the increase in IC due to
multiplication is larger for larger IE .
* Common-emitter characteristics: For the same VCE (∼ VCB),
i.e., the same multiplication factor, the increase in IC due to
multiplication is larger for larger IB .
M. B. Patil, IIT Bombay
IE
IB = 10µA
4µA
∼ 0µA2µA
6µA
8µA
IE= 1mA
0.8mA
0.6mA
0.4mA
0.2mA
∼ 0mA
VCBO
VCEO
IC
IB
VCE (volts)
I C(m
A)
I C(m
A)
VCB (volts)
without impact ionisation
with impact ionisationpn n
B
CE
0
1
2
3
4
5
0
0.5
1.0
1.5
0 50 100 150 200 250
0 50 100
IC = M αF IE + M ICBO
=MαF IB
1−MαF+
MICBO
1−MαF, with M =
1
1−(
VR
V BRBC
)m* Common-base characteristics: For the same VCB , i.e., the
same multiplication factor, the increase in IC due to
multiplication is larger for larger IE .
* Common-emitter characteristics: For the same VCE (∼ VCB),
i.e., the same multiplication factor, the increase in IC due to
multiplication is larger for larger IB .
M. B. Patil, IIT Bombay
VCEO < VCBO : qualitative exaplnation
E Cpn n
B
* VCEO is sbustantially smaller than VCBO although, in both cases, the
breakdown is related to the same junction (the C-B junction). Why?
* With the emitter open, the breakdown process is really no different than an
isolated C-B junction.
* With the base open, the situation is different.
M. B. Patil, IIT Bombay
VCEO < VCBO : qualitative exaplnation
E Cpn n
B
* VCEO is sbustantially smaller than VCBO although, in both cases, the
breakdown is related to the same junction (the C-B junction). Why?
* With the emitter open, the breakdown process is really no different than an
isolated C-B junction.
* With the base open, the situation is different.
M. B. Patil, IIT Bombay
VCEO < VCBO : qualitative exaplnation
E Cpn n
B
* VCEO is sbustantially smaller than VCBO although, in both cases, the
breakdown is related to the same junction (the C-B junction). Why?
* With the emitter open, the breakdown process is really no different than an
isolated C-B junction.
* With the base open, the situation is different.
M. B. Patil, IIT Bombay
VCEO < VCBO : qualitative exaplnation
E
E
E
C
C
1
2
pn n
EFp
VCBEv
Ec
EFn
VBE
E B C
C
EFn
E3 C
E4 C
Consider an electron undergoing impact ionisation with the base
open.
* A hole generated by impact ionisation experiences an electric
field pointing toward the base, and it enters the neutral base
region.
* Since the base is open, the hole gets injected to the emitter
side.
* The electron and hole components at the B-E junction are
related by
γ =InE
IE=
InE
InE + IpE
→ InE
IpE=
γ
1− γ .
→ injection of one hole into the emitter region causes
injection ofγ
1− γ electrons from the emitter into the base
region.
→ multiplication of carriers is enhanced → lower breakdown
voltage [Pierret].
M. B. Patil, IIT Bombay
VCEO < VCBO : qualitative exaplnation
E
E
E
C
C
1
2
pn n
EFp
VCBEv
Ec
EFn
VBE
E B C
C
EFn
E3 C
E4 C
Consider an electron undergoing impact ionisation with the base
open.
* A hole generated by impact ionisation experiences an electric
field pointing toward the base, and it enters the neutral base
region.
* Since the base is open, the hole gets injected to the emitter
side.
* The electron and hole components at the B-E junction are
related by
γ =InE
IE=
InE
InE + IpE
→ InE
IpE=
γ
1− γ .
→ injection of one hole into the emitter region causes
injection ofγ
1− γ electrons from the emitter into the base
region.
→ multiplication of carriers is enhanced → lower breakdown
voltage [Pierret].
M. B. Patil, IIT Bombay
VCEO < VCBO : qualitative exaplnation
E
E
E
C
C
1
2
pn n
EFp
VCBEv
Ec
EFn
VBE
E B C
C
EFn
E3 C
E4 C
Consider an electron undergoing impact ionisation with the base
open.
* A hole generated by impact ionisation experiences an electric
field pointing toward the base, and it enters the neutral base
region.
* Since the base is open, the hole gets injected to the emitter
side.
* The electron and hole components at the B-E junction are
related by
γ =InE
IE=
InE
InE + IpE
→ InE
IpE=
γ
1− γ .
→ injection of one hole into the emitter region causes
injection ofγ
1− γ electrons from the emitter into the base
region.
→ multiplication of carriers is enhanced → lower breakdown
voltage [Pierret].
M. B. Patil, IIT Bombay
VCEO < VCBO : qualitative exaplnation
E
E
E
C
C
1
2
pn n
EFp
VCBEv
Ec
EFn
VBE
E B C
C
EFn
E3 C
E4 C
Consider an electron undergoing impact ionisation with the base
open.
* A hole generated by impact ionisation experiences an electric
field pointing toward the base, and it enters the neutral base
region.
* Since the base is open, the hole gets injected to the emitter
side.
* The electron and hole components at the B-E junction are
related by
γ =InE
IE=
InE
InE + IpE
→ InE
IpE=
γ
1− γ .
→ injection of one hole into the emitter region causes
injection ofγ
1− γ electrons from the emitter into the base
region.
→ multiplication of carriers is enhanced → lower breakdown
voltage [Pierret].
M. B. Patil, IIT Bombay
VCEO < VCBO : qualitative exaplnation
E
E
E
C
C
1
2
pn n
EFp
VCBEv
Ec
EFn
VBE
E B C
C
EFn
E3 C
E4 C
Consider an electron undergoing impact ionisation with the base
open.
* A hole generated by impact ionisation experiences an electric
field pointing toward the base, and it enters the neutral base
region.
* Since the base is open, the hole gets injected to the emitter
side.
* The electron and hole components at the B-E junction are
related by
γ =InE
IE=
InE
InE + IpE
→ InE
IpE=
γ
1− γ .
→ injection of one hole into the emitter region causes
injection ofγ
1− γ electrons from the emitter into the base
region.
→ multiplication of carriers is enhanced → lower breakdown
voltage [Pierret].
M. B. Patil, IIT Bombay
VCEO < VCBO : qualitative exaplnation
E
E
E
C
C
1
2
pn n
EFp
VCBEv
Ec
EFn
VBE
E B C
C
EFn
E3 C
E4 C
Consider an electron undergoing impact ionisation with the base
open.
* A hole generated by impact ionisation experiences an electric
field pointing toward the base, and it enters the neutral base
region.
* Since the base is open, the hole gets injected to the emitter
side.
* The electron and hole components at the B-E junction are
related by
γ =InE
IE=
InE
InE + IpE
→ InE
IpE=
γ
1− γ .
→ injection of one hole into the emitter region causes
injection ofγ
1− γ electrons from the emitter into the base
region.
→ multiplication of carriers is enhanced → lower breakdown
voltage [Pierret].
M. B. Patil, IIT Bombay
VCEO < VCBO : qualitative exaplnation
E
E
E
C
C
1
2
pn n
EFp
VCBEv
Ec
EFn
VBE
E B C
C
EFn
E3 C
E4 C
Consider an electron undergoing impact ionisation with the base
open.
* A hole generated by impact ionisation experiences an electric
field pointing toward the base, and it enters the neutral base
region.
* Since the base is open, the hole gets injected to the emitter
side.
* The electron and hole components at the B-E junction are
related by
γ =InE
IE=
InE
InE + IpE→ InE
IpE=
γ
1− γ .
→ injection of one hole into the emitter region causes
injection ofγ
1− γ electrons from the emitter into the base
region.
→ multiplication of carriers is enhanced → lower breakdown
voltage [Pierret].
M. B. Patil, IIT Bombay
VCEO < VCBO : qualitative exaplnation
E
E
E
C
C
1
2
pn n
EFp
VCBEv
Ec
EFn
VBE
E B C
C
EFn
E3 C
E4 C
Consider an electron undergoing impact ionisation with the base
open.
* A hole generated by impact ionisation experiences an electric
field pointing toward the base, and it enters the neutral base
region.
* Since the base is open, the hole gets injected to the emitter
side.
* The electron and hole components at the B-E junction are
related by
γ =InE
IE=
InE
InE + IpE→ InE
IpE=
γ
1− γ .
→ injection of one hole into the emitter region causes
injection ofγ
1− γ electrons from the emitter into the base
region.
→ multiplication of carriers is enhanced → lower breakdown
voltage [Pierret].
M. B. Patil, IIT Bombay
VCEO < VCBO : qualitative exaplnation
E
E
E
C
C
1
2
pn n
EFp
VCBEv
Ec
EFn
VBE
E B C
C
EFn
E3 C
E4 C
Consider an electron undergoing impact ionisation with the base
open.
* A hole generated by impact ionisation experiences an electric
field pointing toward the base, and it enters the neutral base
region.
* Since the base is open, the hole gets injected to the emitter
side.
* The electron and hole components at the B-E junction are
related by
γ =InE
IE=
InE
InE + IpE→ InE
IpE=
γ
1− γ .
→ injection of one hole into the emitter region causes
injection ofγ
1− γ electrons from the emitter into the base
region.
→ multiplication of carriers is enhanced → lower breakdown
voltage [Pierret].
M. B. Patil, IIT Bombay
VCEO < VCBO : qualitative exaplnation
E
E
E
C
C
1
2
pn n
EFp
VCBEv
Ec
EFn
VBE
E B C
C
EFn
E3 C
E4 C
Consider an electron undergoing impact ionisation with the base
open.
* A hole generated by impact ionisation experiences an electric
field pointing toward the base, and it enters the neutral base
region.
* Since the base is open, the hole gets injected to the emitter
side.
* The electron and hole components at the B-E junction are
related by
γ =InE
IE=
InE
InE + IpE→ InE
IpE=
γ
1− γ .
→ injection of one hole into the emitter region causes
injection ofγ
1− γ electrons from the emitter into the base
region.
→ multiplication of carriers is enhanced → lower breakdown
voltage [Pierret].
M. B. Patil, IIT Bombay
A typical discrete transistor: 2N3904 (npn)
* VCEO = 40 V, VCBO = 60 V, VEBO = 6 V:
We have already seen why VCEO is smaller than VCBO .
VEBO , the E -B breakdown voltage is substantially lower because of the larger doping
density in the emitter region.
x (µm)0 1.5 3
(representative plot)1020
1018
1016
1014
Dopingdensity(cm
−3)
Nd (E)Nd (C)
Na (B)
In the active or saturation modes, the E-B junction is under forward bias, and a low VEBO
is not a concern.
* Maximum collector current (continuous) ImaxC : 200 mA (DC).
M. B. Patil, IIT Bombay
A typical discrete transistor: 2N3904 (npn)
* VCEO = 40 V, VCBO = 60 V, VEBO = 6 V:
We have already seen why VCEO is smaller than VCBO .
VEBO , the E -B breakdown voltage is substantially lower because of the larger doping
density in the emitter region.
x (µm)0 1.5 3
(representative plot)1020
1018
1016
1014
Dopingdensity(cm
−3)
Nd (E)Nd (C)
Na (B)
In the active or saturation modes, the E-B junction is under forward bias, and a low VEBO
is not a concern.
* Maximum collector current (continuous) ImaxC : 200 mA (DC).
M. B. Patil, IIT Bombay
A typical discrete transistor: 2N3904 (npn)
* VCEO = 40 V, VCBO = 60 V, VEBO = 6 V:
We have already seen why VCEO is smaller than VCBO .
VEBO , the E -B breakdown voltage is substantially lower because of the larger doping
density in the emitter region.
x (µm)0 1.5 3
(representative plot)1020
1018
1016
1014
Dopingdensity(cm
−3)
Nd (E)Nd (C)
Na (B)
In the active or saturation modes, the E-B junction is under forward bias, and a low VEBO
is not a concern.
* Maximum collector current (continuous) ImaxC : 200 mA (DC).
M. B. Patil, IIT Bombay
A typical discrete transistor: 2N3904 (npn)
* VCEO = 40 V, VCBO = 60 V, VEBO = 6 V:
We have already seen why VCEO is smaller than VCBO .
VEBO , the E -B breakdown voltage is substantially lower because of the larger doping
density in the emitter region.
x (µm)0 1.5 3
(representative plot)1020
1018
1016
1014
Dopingdensity(cm
−3)
Nd (E)Nd (C)
Na (B)
In the active or saturation modes, the E-B junction is under forward bias, and a low VEBO
is not a concern.
* Maximum collector current (continuous) ImaxC : 200 mA (DC).
M. B. Patil, IIT Bombay
A typical discrete transistor: 2N3904 (npn)
* VCEO = 40 V, VCBO = 60 V, VEBO = 6 V:
We have already seen why VCEO is smaller than VCBO .
VEBO , the E -B breakdown voltage is substantially lower because of the larger doping
density in the emitter region.
x (µm)0 1.5 3
(representative plot)1020
1018
1016
1014
Dopingdensity(cm
−3)
Nd (E)Nd (C)
Na (B)
In the active or saturation modes, the E-B junction is under forward bias, and a low VEBO
is not a concern.
* Maximum collector current (continuous) ImaxC : 200 mA (DC).
M. B. Patil, IIT Bombay
A typical discrete transistor: 2N3904 (npn)
* VCEO = 40 V, VCBO = 60 V, VEBO = 6 V:
We have already seen why VCEO is smaller than VCBO .
VEBO , the E -B breakdown voltage is substantially lower because of the larger doping
density in the emitter region.
x (µm)0 1.5 3
(representative plot)1020
1018
1016
1014
Dopingdensity(cm
−3)
Nd (E)Nd (C)
Na (B)
In the active or saturation modes, the E-B junction is under forward bias, and a low VEBO
is not a concern.
* Maximum collector current (continuous) ImaxC : 200 mA (DC).
M. B. Patil, IIT Bombay
A typical discrete transistor: 2N3904 (npn)
IC
IEIB
B
C
E
VCE
I C
VCEO
P=PD
0
ImaxC
0
* Maximum power dissipation PD = 625 mW:
The power dissipated by a BJT (as heat) is
P =VBE IB + VCE IC .
In the active mode, IC =βIB is much larger than IB .
→ P ≈VCE IC .
In the common-emitter output characteristics (IC -VCE ), the
constraint P =PD is therefore a hyperbola.
In designing a BJT amplifier, the DC bias values are subject
to the constraints due to ImaxC , VCEO , and PD .
M. B. Patil, IIT Bombay
A typical discrete transistor: 2N3904 (npn)
IC
IEIB
B
C
E
VCE
I C
VCEO
P=PD
0
ImaxC
0
* Maximum power dissipation PD = 625 mW:
The power dissipated by a BJT (as heat) is
P =VBE IB + VCE IC .
In the active mode, IC =βIB is much larger than IB .
→ P ≈VCE IC .
In the common-emitter output characteristics (IC -VCE ), the
constraint P =PD is therefore a hyperbola.
In designing a BJT amplifier, the DC bias values are subject
to the constraints due to ImaxC , VCEO , and PD .
M. B. Patil, IIT Bombay
A typical discrete transistor: 2N3904 (npn)
IC
IEIB
B
C
E
VCE
I C
VCEO
P=PD
0
ImaxC
0
* Maximum power dissipation PD = 625 mW:
The power dissipated by a BJT (as heat) is
P =VBE IB + VCE IC .
In the active mode, IC =βIB is much larger than IB .
→ P ≈VCE IC .
In the common-emitter output characteristics (IC -VCE ), the
constraint P =PD is therefore a hyperbola.
In designing a BJT amplifier, the DC bias values are subject
to the constraints due to ImaxC , VCEO , and PD .
M. B. Patil, IIT Bombay
A typical discrete transistor: 2N3904 (npn)
IC
IEIB
B
C
E
VCE
I C
VCEO
P=PD
0
ImaxC
0
* Maximum power dissipation PD = 625 mW:
The power dissipated by a BJT (as heat) is
P =VBE IB + VCE IC .
In the active mode, IC =βIB is much larger than IB .
→ P ≈VCE IC .
In the common-emitter output characteristics (IC -VCE ), the
constraint P =PD is therefore a hyperbola.
In designing a BJT amplifier, the DC bias values are subject
to the constraints due to ImaxC , VCEO , and PD .
M. B. Patil, IIT Bombay
A typical discrete transistor: 2N3904 (npn)
IC
IEIB
B
C
E
VCE
I C
VCEO
P=PD
0
ImaxC
0
* Maximum power dissipation PD = 625 mW:
The power dissipated by a BJT (as heat) is
P =VBE IB + VCE IC .
In the active mode, IC =βIB is much larger than IB .
→ P ≈VCE IC .
In the common-emitter output characteristics (IC -VCE ), the
constraint P =PD is therefore a hyperbola.
In designing a BJT amplifier, the DC bias values are subject
to the constraints due to ImaxC , VCEO , and PD .
M. B. Patil, IIT Bombay
A typical discrete transistor: 2N3904 (npn)
IC
IEIB
B
C
E
VCE
I C
VCEO
P=PD
0
ImaxC
0
* Maximum power dissipation PD = 625 mW:
The power dissipated by a BJT (as heat) is
P =VBE IB + VCE IC .
In the active mode, IC =βIB is much larger than IB .
→ P ≈VCE IC .
In the common-emitter output characteristics (IC -VCE ), the
constraint P =PD is therefore a hyperbola.
In designing a BJT amplifier, the DC bias values are subject
to the constraints due to ImaxC , VCEO , and PD .
M. B. Patil, IIT Bombay
A typical discrete transistor: 2N3904 (npn)
IC
IEIB
B
C
E
VCE
I C
VCEO
P=PD
0
ImaxC
0
* Maximum power dissipation PD = 625 mW:
The power dissipated by a BJT (as heat) is
P =VBE IB + VCE IC .
In the active mode, IC =βIB is much larger than IB .
→ P ≈VCE IC .
In the common-emitter output characteristics (IC -VCE ), the
constraint P =PD is therefore a hyperbola.
In designing a BJT amplifier, the DC bias values are subject
to the constraints due to ImaxC , VCEO , and PD .
M. B. Patil, IIT Bombay
A typical discrete transistor: 2N3904 (npn)
* DC current gain (βF ) = 100 to 300 at IC = 10 mA, VCE = 1 V:
- A range of values for βF is specified because of device-to-device
variation in the doping profiles and geometric parameters
(especially the base width).
- Since βF varies in practice with bias conditions, the specification
includes the bias values.
M. B. Patil, IIT Bombay
A typical discrete transistor: 2N3904 (npn)
* DC current gain (βF ) = 100 to 300 at IC = 10 mA, VCE = 1 V:
- A range of values for βF is specified because of device-to-device
variation in the doping profiles and geometric parameters
(especially the base width).
- Since βF varies in practice with bias conditions, the specification
includes the bias values.
M. B. Patil, IIT Bombay
A typical discrete transistor: 2N3904 (npn)
* DC current gain (βF ) = 100 to 300 at IC = 10 mA, VCE = 1 V:
- A range of values for βF is specified because of device-to-device
variation in the doping profiles and geometric parameters
(especially the base width).
- Since βF varies in practice with bias conditions, the specification
includes the bias values.
M. B. Patil, IIT Bombay
A typical discrete transistor: 2N3904 (npn)
(substrate)
p+n+
p
n
n+
Collector
BaseEmitter
rb
IC1
IC2
IC, IB (log scale)
VBE
logβF
IC
IB
IC2IC1 log IC
logβF
Ebers-moll model (active mode):
IC = αF IESeVBE/VT , IB = (1− αF ) IESe
VBE/VT .
* At lower values of VBE , the diffusion component of the E -B diode
current becomes small, and recombination in the emitter-depletion
region, which adds to the base current, cannot be neglected any
more. This causes IB to be larger than that predicted by the above
equation.
* At high values of VBE (large IC ),
- The voltage drop across the base resistance rb becomes
significant.
- The minority carrier concentration in the base becomes
comparable to the majority carrier concentration (high-level
injection)
As a result, βF =IC
IBis constant only for a range of IC values.
M. B. Patil, IIT Bombay
A typical discrete transistor: 2N3904 (npn)
(substrate)
p+n+
p
n
n+
Collector
BaseEmitter
rb
IC1
IC2
IC, IB (log scale)
VBE
logβF
IC
IB
IC2IC1 log IC
logβF
Ebers-moll model (active mode):
IC = αF IESeVBE/VT , IB = (1− αF ) IESe
VBE/VT .
* At lower values of VBE , the diffusion component of the E -B diode
current becomes small, and recombination in the emitter-depletion
region, which adds to the base current, cannot be neglected any
more. This causes IB to be larger than that predicted by the above
equation.
* At high values of VBE (large IC ),
- The voltage drop across the base resistance rb becomes
significant.
- The minority carrier concentration in the base becomes
comparable to the majority carrier concentration (high-level
injection)
As a result, βF =IC
IBis constant only for a range of IC values.
M. B. Patil, IIT Bombay
A typical discrete transistor: 2N3904 (npn)
(substrate)
p+n+
p
n
n+
Collector
BaseEmitter
rb
IC1
IC2
IC, IB (log scale)
VBE
logβF
IC
IB
IC2IC1 log IC
logβF
Ebers-moll model (active mode):
IC = αF IESeVBE/VT , IB = (1− αF ) IESe
VBE/VT .
* At lower values of VBE , the diffusion component of the E -B diode
current becomes small, and recombination in the emitter-depletion
region, which adds to the base current, cannot be neglected any
more. This causes IB to be larger than that predicted by the above
equation.
* At high values of VBE (large IC ),
- The voltage drop across the base resistance rb becomes
significant.
- The minority carrier concentration in the base becomes
comparable to the majority carrier concentration (high-level
injection)
As a result, βF =IC
IBis constant only for a range of IC values.
M. B. Patil, IIT Bombay
A typical discrete transistor: 2N3904 (npn)
(substrate)
p+n+
p
n
n+
Collector
BaseEmitter
rb
IC1
IC2
IC, IB (log scale)
VBE
logβF
IC
IB
IC2IC1 log IC
logβF
Ebers-moll model (active mode):
IC = αF IESeVBE/VT , IB = (1− αF ) IESe
VBE/VT .
* At lower values of VBE , the diffusion component of the E -B diode
current becomes small, and recombination in the emitter-depletion
region, which adds to the base current, cannot be neglected any
more. This causes IB to be larger than that predicted by the above
equation.
* At high values of VBE (large IC ),
- The voltage drop across the base resistance rb becomes
significant.
- The minority carrier concentration in the base becomes
comparable to the majority carrier concentration (high-level
injection)
As a result, βF =IC
IBis constant only for a range of IC values.
M. B. Patil, IIT Bombay
A typical discrete transistor: 2N3904 (npn)
(substrate)
p+n+
p
n
n+
Collector
BaseEmitter
rb
IC1
IC2
IC, IB (log scale)
VBE
logβF
IC
IB
IC2IC1 log IC
logβF
Ebers-moll model (active mode):
IC = αF IESeVBE/VT , IB = (1− αF ) IESe
VBE/VT .
* At lower values of VBE , the diffusion component of the E -B diode
current becomes small, and recombination in the emitter-depletion
region, which adds to the base current, cannot be neglected any
more. This causes IB to be larger than that predicted by the above
equation.
* At high values of VBE (large IC ),
- The voltage drop across the base resistance rb becomes
significant.
- The minority carrier concentration in the base becomes
comparable to the majority carrier concentration (high-level
injection)
As a result, βF =IC
IBis constant only for a range of IC values.
M. B. Patil, IIT Bombay
A typical discrete transistor: 2N3904 (npn)
(substrate)
p+n+
p
n
n+
Collector
BaseEmitter
rb
IC1
IC2
IC, IB (log scale)
VBE
logβF
IC
IB
IC2IC1 log IC
logβF
Ebers-moll model (active mode):
IC = αF IESeVBE/VT , IB = (1− αF ) IESe
VBE/VT .
* At lower values of VBE , the diffusion component of the E -B diode
current becomes small, and recombination in the emitter-depletion
region, which adds to the base current, cannot be neglected any
more. This causes IB to be larger than that predicted by the above
equation.
* At high values of VBE (large IC ),
- The voltage drop across the base resistance rb becomes
significant.
- The minority carrier concentration in the base becomes
comparable to the majority carrier concentration (high-level
injection)
As a result, βF =IC
IBis constant only for a range of IC values.
M. B. Patil, IIT Bombay
A typical discrete transistor: 2N3904 (npn)
(substrate)
p+n+
p
n
n+
Collector
BaseEmitter
rb
IC1
IC2
IC, IB (log scale)
VBE
logβF
IC
IB
IC2IC1 log IC
logβF
Ebers-moll model (active mode):
IC = αF IESeVBE/VT , IB = (1− αF ) IESe
VBE/VT .
* At lower values of VBE , the diffusion component of the E -B diode
current becomes small, and recombination in the emitter-depletion
region, which adds to the base current, cannot be neglected any
more. This causes IB to be larger than that predicted by the above
equation.
* At high values of VBE (large IC ),
- The voltage drop across the base resistance rb becomes
significant.
- The minority carrier concentration in the base becomes
comparable to the majority carrier concentration (high-level
injection)
As a result, βF =IC
IBis constant only for a range of IC values.
M. B. Patil, IIT Bombay
A typical discrete transistor: 2N3904 (npn)
(substrate)
p+n+
p
n
n+
Collector
BaseEmitter
rb
IC1
IC2
IC, IB (log scale)
VBE
logβF
IC
IB
IC2IC1 log IC
logβF
Ebers-moll model (active mode):
IC = αF IESeVBE/VT , IB = (1− αF ) IESe
VBE/VT .
* At lower values of VBE , the diffusion component of the E -B diode
current becomes small, and recombination in the emitter-depletion
region, which adds to the base current, cannot be neglected any
more. This causes IB to be larger than that predicted by the above
equation.
* At high values of VBE (large IC ),
- The voltage drop across the base resistance rb becomes
significant.
- The minority carrier concentration in the base becomes
comparable to the majority carrier concentration (high-level
injection)
As a result, βF =IC
IBis constant only for a range of IC values.
M. B. Patil, IIT Bombay
A typical discrete transistor: 2N3904 (npn)
0.1 1 10010IC (mA)
βF
101
102
103
VCE= 1V
(Note: βF varies from device to device.)
M. B. Patil, IIT Bombay
A typical discrete transistor: 2N3904 (npn)
* V satCE = 0.2 V at IC = 10 mA, V sat
CE = 0.3 V at IC = 50 mA.
IC
IB
VsatCE
0VVCE
IC
IB5
IB1
IB2
IB3
IB4
IB6
C
E
B
E
M. B. Patil, IIT Bombay
A typical discrete transistor: 2N3904 (npn)
* Output conductance hoe = 1 to 40 µf at IC = 1 mA, VCE = 10 V:
The slope of the IC versus VCE curve at a constant IB is defined as the output
conductance hoe .
VCE0
−VA
slope= hoe
VCE1
IC1
IC
IB= constant
From hoe , we can get an idea of the Early voltage VA of the device. For example, with
hoe = 10µf, IC1 = 1 mA, VCE1 = 10 V, we get
Ic1
VA + VCE1= hoe → VA =
1× 10−3
10× 10−6− 10 = 90 V.
M. B. Patil, IIT Bombay
A typical discrete transistor: 2N3904 (npn)
* Output conductance hoe = 1 to 40 µf at IC = 1 mA, VCE = 10 V:
The slope of the IC versus VCE curve at a constant IB is defined as the output
conductance hoe .
VCE0
−VA
slope= hoe
VCE1
IC1
IC
IB= constant
From hoe , we can get an idea of the Early voltage VA of the device. For example, with
hoe = 10µf, IC1 = 1 mA, VCE1 = 10 V, we get
Ic1
VA + VCE1= hoe → VA =
1× 10−3
10× 10−6− 10 = 90 V.
M. B. Patil, IIT Bombay
A typical discrete transistor: 2N3904 (npn)
* Output conductance hoe = 1 to 40 µf at IC = 1 mA, VCE = 10 V:
The slope of the IC versus VCE curve at a constant IB is defined as the output
conductance hoe .
VCE0
−VA
slope= hoe
VCE1
IC1
IC
IB= constant
From hoe , we can get an idea of the Early voltage VA of the device. For example, with
hoe = 10µf, IC1 = 1 mA, VCE1 = 10 V, we get
Ic1
VA + VCE1= hoe → VA =
1× 10−3
10× 10−6− 10 = 90 V.
M. B. Patil, IIT Bombay