Semiconductor Devices - IIT Bombay

172
Semiconductor Devices Bipolar Junction Transistors: Part 2 M. B. Patil [email protected] www.ee.iitb.ac.in/~sequel Department of Electrical Engineering Indian Institute of Technology Bombay M. B. Patil, IIT Bombay

Transcript of Semiconductor Devices - IIT Bombay

Page 1: Semiconductor Devices - IIT Bombay

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

Page 2: Semiconductor Devices - 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

Page 3: Semiconductor Devices - 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

Page 4: Semiconductor Devices - 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

Page 5: Semiconductor Devices - 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

Page 6: Semiconductor Devices - 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

Page 7: Semiconductor Devices - 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

Page 8: Semiconductor Devices - 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

Page 9: Semiconductor Devices - 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

Page 10: Semiconductor Devices - 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

Page 11: Semiconductor Devices - 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

Page 12: Semiconductor Devices - 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

Page 13: Semiconductor Devices - 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

Page 14: Semiconductor Devices - 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

Page 15: Semiconductor Devices - 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

Page 16: Semiconductor Devices - 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

Page 17: Semiconductor Devices - 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

Page 18: Semiconductor Devices - 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

Page 19: Semiconductor Devices - 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

Page 20: Semiconductor Devices - 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

Page 21: Semiconductor Devices - 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

Page 22: Semiconductor Devices - 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

Page 23: Semiconductor Devices - 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

Page 24: Semiconductor Devices - 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

Page 25: Semiconductor Devices - 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

Page 26: Semiconductor Devices - 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

Page 27: Semiconductor Devices - 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

Page 28: Semiconductor Devices - 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

Page 29: Semiconductor Devices - 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

Page 30: Semiconductor Devices - 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

Page 31: Semiconductor Devices - 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

Page 32: Semiconductor Devices - 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

Page 33: Semiconductor Devices - 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

Page 34: Semiconductor Devices - 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

Page 35: Semiconductor Devices - 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

Page 36: Semiconductor Devices - 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

Page 37: Semiconductor Devices - 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

Page 38: Semiconductor Devices - 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

Page 39: Semiconductor Devices - 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

Page 40: Semiconductor Devices - 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

Page 41: Semiconductor Devices - 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

Page 42: Semiconductor Devices - 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

Page 43: Semiconductor Devices - 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

Page 44: Semiconductor Devices - 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

Page 45: Semiconductor Devices - 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

Page 46: Semiconductor Devices - 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

Page 47: Semiconductor Devices - 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

Page 48: Semiconductor Devices - 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

Page 49: Semiconductor Devices - 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

Page 50: Semiconductor Devices - 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

Page 51: Semiconductor Devices - 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

Page 52: Semiconductor Devices - 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

Page 53: Semiconductor Devices - 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

Page 54: Semiconductor Devices - 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

Page 55: Semiconductor Devices - 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

Page 56: Semiconductor Devices - 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

Page 57: Semiconductor Devices - 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

Page 58: Semiconductor Devices - 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

Page 59: Semiconductor Devices - 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

Page 60: Semiconductor Devices - 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

Page 61: Semiconductor Devices - 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

Page 62: Semiconductor Devices - 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

Page 63: Semiconductor Devices - 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

Page 64: Semiconductor Devices - 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

Page 65: Semiconductor Devices - 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

Page 66: Semiconductor Devices - 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

Page 67: Semiconductor Devices - 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

Page 68: Semiconductor Devices - 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

Page 69: Semiconductor Devices - 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

Page 70: Semiconductor Devices - 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

Page 71: Semiconductor Devices - 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

Page 72: Semiconductor Devices - 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

Page 73: Semiconductor Devices - 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

Page 74: Semiconductor Devices - 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

Page 75: Semiconductor Devices - 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

Page 76: Semiconductor Devices - 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

Page 77: Semiconductor Devices - 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

Page 78: Semiconductor Devices - 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

Page 79: Semiconductor Devices - 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

Page 80: Semiconductor Devices - 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

Page 81: Semiconductor Devices - 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

Page 82: Semiconductor Devices - 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

Page 83: Semiconductor Devices - 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

Page 84: Semiconductor Devices - 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

Page 85: Semiconductor Devices - 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

Page 86: Semiconductor Devices - 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

Page 87: Semiconductor Devices - 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

Page 88: Semiconductor Devices - 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

Page 89: Semiconductor Devices - 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

Page 90: Semiconductor Devices - 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

Page 91: Semiconductor Devices - 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

Page 92: Semiconductor Devices - 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

Page 93: Semiconductor Devices - 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

Page 94: Semiconductor Devices - 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

Page 95: Semiconductor Devices - 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

Page 96: Semiconductor Devices - 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

Page 97: Semiconductor Devices - 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

Page 98: Semiconductor Devices - 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

Page 99: Semiconductor Devices - 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

Page 100: Semiconductor Devices - 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

Page 101: Semiconductor Devices - 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

Page 102: Semiconductor Devices - 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

Page 103: Semiconductor Devices - 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

Page 104: Semiconductor Devices - 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

Page 105: Semiconductor Devices - 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

Page 106: Semiconductor Devices - 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

Page 107: Semiconductor Devices - 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

Page 108: Semiconductor Devices - 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

Page 109: Semiconductor Devices - 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

Page 110: Semiconductor Devices - 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

Page 111: Semiconductor Devices - 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

Page 112: Semiconductor Devices - 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

Page 113: Semiconductor Devices - 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

Page 114: Semiconductor Devices - 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

Page 115: Semiconductor Devices - 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

Page 116: Semiconductor Devices - 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

Page 117: Semiconductor Devices - 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

Page 118: Semiconductor Devices - 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

Page 119: Semiconductor Devices - 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

Page 120: Semiconductor Devices - 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

Page 121: Semiconductor Devices - 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

Page 122: Semiconductor Devices - 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

Page 123: Semiconductor Devices - 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

Page 124: Semiconductor Devices - 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

Page 125: Semiconductor Devices - 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

Page 126: Semiconductor Devices - 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

Page 127: Semiconductor Devices - 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

Page 128: Semiconductor Devices - 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

Page 129: Semiconductor Devices - 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

Page 130: Semiconductor Devices - 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

Page 131: Semiconductor Devices - 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

Page 132: Semiconductor Devices - 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

Page 133: Semiconductor Devices - 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

Page 134: Semiconductor Devices - 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

Page 135: Semiconductor Devices - 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

Page 136: Semiconductor Devices - 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

Page 137: Semiconductor Devices - 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

Page 138: Semiconductor Devices - 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

Page 139: Semiconductor Devices - 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

Page 140: Semiconductor Devices - 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

Page 141: Semiconductor Devices - 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

Page 142: Semiconductor Devices - 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

Page 143: Semiconductor Devices - 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

Page 144: Semiconductor Devices - 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

Page 145: Semiconductor Devices - 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

Page 146: Semiconductor Devices - 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

Page 147: Semiconductor Devices - 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

Page 148: Semiconductor Devices - 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

Page 149: Semiconductor Devices - 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

Page 150: Semiconductor Devices - 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

Page 151: Semiconductor Devices - 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

Page 152: Semiconductor Devices - 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

Page 153: Semiconductor Devices - 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

Page 154: Semiconductor Devices - 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

Page 155: Semiconductor Devices - 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

Page 156: Semiconductor Devices - 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

Page 157: Semiconductor Devices - 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

Page 158: Semiconductor Devices - 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

Page 159: Semiconductor Devices - 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

Page 160: Semiconductor Devices - 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

Page 161: Semiconductor Devices - 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

Page 162: Semiconductor Devices - 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

Page 163: Semiconductor Devices - 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

Page 164: Semiconductor Devices - 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

Page 165: Semiconductor Devices - 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

Page 166: Semiconductor Devices - 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

Page 167: Semiconductor Devices - 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

Page 168: Semiconductor Devices - 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

Page 169: Semiconductor Devices - 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

Page 170: Semiconductor Devices - 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

Page 171: Semiconductor Devices - 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

Page 172: Semiconductor Devices - 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