band are filled with electrons and the 4N states in the conduction band are empty. E_c and E_v represent the maximum electron energy in the conduction band and maximum hole energy

in the valence band respective.

· To simplify integration Boltzmann approximation is introduced and the unity is dropped from Fermi function.

· Boltzmann approximation is restricted to the range of Fermi energies extending from 3kT above the top of the valence band and 3kT below the bottom of the conduction band. Based on this classification we have generate and non-degenerate semiconductors.

P-type impurity	N-type impurity
Boron	Phosphorous
Aluminum	Arsenic
Gallium	Antimony

· FERMI-DIRAC FUNCTION functions give the probability that an electron occupies a quantum state with energy E.

Carrier-Densities 2

Densities of state in the conduction band

Densities of state in the valence band

Density of electrons in the conduction band

Semiconductor
Si	3
Ge
GaAs

Density of holes in the valence band

Semiconductor
Si
Ge
GaAs

Intrinsic carrier density

· increases with increase in temperature

· decreases with increase in

Charge neutrality

Location of Fermi level in n-type and p-type

For intrinsic semiconductors

Degenerate & Non-Degenerate Semiconductor

Intrinsic & Extrinsic Silicon

P-type impurity	N-type impurity
Boron	Phosphorous
Aluminum	Arsenic
Gallium	Antimony
Semiconductor	Energy Gap (eV)
Ge	0.67 eV
Si	1.12 eV
GaAs	1.42 eV

Carrier Currents 1

· Thermal velocity does not result in current.

· Drift velocity results in drift current.

· Drift velocity is much smaller in magnitude than thermal velocity.

· Drift velocity does not increase with increase in electric field because of scattering.

· Scattering occurs because of the following:

1. Lattice vibration (effective at high temperature).

2. Presence of ionized impurity (effective at low temperature).

· It is also known as Impurity scattering.

3. Lattice imperfection

· Scattering is represented by scattering time (the time between two successive collisions)

Carrier Currents 2

Drift Current
Drift velocity of electrons		is called the relaxation time. It is of the order .
Drift velocity of holes
Mobility & Drift velocity
Mobility (electrons)		Dimension [
Mobility (holes)
Conductivity (due to holes)
Conductivity (due to electrons)
Total conductivity
Total resistivity
Total drift current density
Diffusion current due to electrons		Dimension
Diffusion current due to holes
Diffusion current
Total current density

Direct Generation & Recombination

Causes of Direct-generation of electron-hole pairs:

1. Exposure to thermal energy.

2. Exposure to light energy.

3. Impact ionization.

Cause of Indirect-generation of electron-hole pairs:

1. Lattice imperfection

· Traps=Gold & Iron in silicon and Copper in Ge.

· Recombination-generation occurs through traps.

· Expression for rate of change of carrier density with time for indirect-generation-recombination

· Low Level Injection: Any perturbation such that the change in minority carrier density is much smaller than the majority carrier density is called a low-level injection.

· Most devices work in this condition when excess minority carriers are injected.

· Change in majority carrier density is so small that it is considered constant.

Direct/ Indirect Band Gap Semiconductor

Eg: GaAs

Eg: Si & Ge

Equation of Continuity

· Equation of continuity

for holes in the N-region

for electrons in the P-region

· Haynes Shockley Experiment gives:

1. Lifetime of minority carriers.

2. Mobility.

3. Diffusion constant.

· Hall's Effect experiment gives:

1. Carrier concentration.

2. Type of the semiconductor.

DIODE

PN Junction Diode

Barrier Potential

Constancy of Fermi

Level

Electrostatic in the space

Charge region

Width of the space charge region

is positive in forward bias.

is negative in reverse bias

Diode Currents

Diffusion current (with bias voltage)

Carrier density of holes and electrons in the

n-region and p-region respectively for

for

Diffusion current density at the boundary

Current in the diode at the space charge boundary for ( and )

If then I can be approximated as

Current in the diode at the space charge boundary for ( and )

Diffusion current in the diode (at equilibrium)

The magnitude of diffusion current at equilibrium is much larger than that at forward bias.

Diode Capacitance

Capacitance

1. Transition Capacitance.

2. Diffusion (Storage)Capacitance.

· Transition capacitance exists in both forward and reverse bias.

· It is due to the accumulation of ions in the depletion region.

· It is bias voltage dependent

· It is of the order of 10^-12 Farad.

· Diffusion (storage) capacitance exist only in forward bias.

· It is the excess minority carriers stored on the other side that give rise to this capacitance;

· It is also a measure of the change of area under minority carrier distribution with change in voltage

· There is time delay involved in storing the charges.

· It is of the order of 10^-9 Farad.

Short Base Diode

Base of a diode is the region with weaker doping.. In N is the base and

Short Base and a regular PN (long base diode)

Switching characteristics of short base diode

Turn-on time of P+N long base diode = lifetime of holes in the N legion

Turn-on time of P+N short base diode= transition time of holes in the N region

Diode Characteristics Curve

Avalanche/Zener Breakdown

Avalanche Breakdown

Avalanche breakdown occurs due to impact ionization of atoms by electrons that have acquired high energy from the high electric field in the depletion region.

· Total reverse current get multiplied by multiplication factor

· The critical electric field which can cause this breakdown is

· The breakdown voltage is given by

Zener breakdown

Zener breakdown occurs due to tunneling.

Tunneling occurs if the valence band of P is directly opposite to an empty conduction band of N. This kind of alignment happens if the depletion width is very small.

Diode Fabrication

Fabrication of a planar JN Diode

Epitaxial Growth
Oxidation
Addition of Photoresist
Placement of mask
Exposure to UV
Etching
Diffusion
Metal Contacts

Small signal model

is the dynamic ac resitance

BJT

BJT Currents 1

Injection Efficiency
Transport Factor
DC common base current gain
DC common emitter current gain
Collector current

BJT Currents 2

PNP

NPN

Currents Equation

Ebers-Moll Equation

(for PNP and NPN)

β_R=α_R/(1−α_R )

*subscript F and R stands for active and inverse-active mode of operation respectively

β_R=α_R/(1−α_R )

*subscript F and R stands for active and inverse-active mode of operation respectively

Eber Moll Model

Eber Moll model for pnp BJT Transistor

Eber Moll model for pnp BJT Transistor expressed in matrix A=BC form

Though Eber Moll model is simple but it is not very accurate. In circuit simulation Gummel-Pool model is used

BJT Breakdown

Early Effect

PNP

The difference between the actual and ideal curves is because of the following: .

1. is fixed so any increase in increases .

2. increase the width of the base-collector depletion layer which reduces the effective width of the base (also known as base-width modulation)

3. This increases the gradient of holes in the base.

4. Consequently collector current increases.

Base width modulation is also known as Early effect.

Avalanche Breakdown

PNP

M= avalanche multiplication factor.

Punch-through

Punchthrough occurs when the reverse bias base-collector depletion region reaches the emitter-base junction.

Generally punchthrough happens after avalanche breakdown. But if base width is very small punchthrough may precede avalanche breakdown.

In punchthrough base looses its current controlling property and collector current increases rapidly and is limited only by the external circuit resistance.

Charge Control Equations

Charge Control Equation		Charge control equation is a tool for calculating turn-ON and turn-OFF time of transistors.
Solution of charge control equation		is the amplitude of current pulse applied at base to turn the transistor ON
Turn-ON Time		=transit time of holes(or electrons as the case may be) across the base
Turn-OFF Time	=

BJT DC- Biasing (NPN)

Fixed Bias

Emitter

Bias

Voltage

Divider

Bias

Collector

Feedback Bias

Stability Factor

· Stability Factor S is the rate of change of collector current with respect to or .

· It lies between unity and infinity. S=1 is stable and S is unstable.

BJT Small Signal Model

Small Signal Model of PNP CE Transistor taking into effect the change in magnitude of

only.

Small Signal Model of PNP CE Transistor taking into effect the change in magnitude of and capacitances.

Small Signal Model of PNP CE Transistor taking into effect the change in magnitude of , and capacitances.

	transconductance
	CE current gain
	CE input resistance
	CE output resistance
	Storage capacitance (
	Storage capacitance (
	Junction capacitance (E-B)
	Junction capacitance (C-B)
	Emitter ohmic resistance
	Collector base resistance
	Base ohmic resistance
	Collector ohmic resistance

Figure of merit

Also known as gain-bandwidth product.

· It is a measure of quality of a high frequency transistor.

· If proper amplification is required at high frequency then capacitances should be small.

FET

Current Voltage Equation

Relation between Gate source voltage and Drain source saturation voltage
Relationship among Drain current, Drain source voltage and gate source voltage	Valid only for the linear region i.e.
Pinch off Voltage
Conductance
Channel-conductance [ valid only in the linear region]
Trans-conductance [ valid only in the saturation region]

NJFET CURRENT VOLTAGE

JFET properties:

1. Only one type of majority carrier is the cause of the current.

2. Insensitive to temperature and radiation.

3. Simple to fabricate.

4. Low noise.

5. Operates satisfactorily at high frequency.

6. Very high input impedance.

7. Low gain (compared to bipolar transistor).

· Pinch-off voltage ( is a property of the device.

· It depends on physical dimension and doping densities.

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Drain to Gate Voltage		To find out region of operation compare with the actual .
Drain Current
Breakdown voltage
Threshold Voltage (also called Turn-OFF voltage		It is defined as the gate source voltage at which and

JFET Small Signal Model

Low frequency model

High frequency model

where

* Unity gain bandwidth.

*Capacitance is difficult to determine as it is distributed along the channel. An approximate guess about the frequency is made by taking into account total channel capacitance and total channel resistance.

Capacitance

Cut off frequency for NJFET

Total channel capacitance
Total channel resistance
RC time constant

Pinch off Voltage

· Pinch-off voltage is the voltage at which current in JFET saturates. It is a property of the device

· Given a JFET with defined the drain voltage at which saturation occurs is given by (neglecting barrier potential )

· Compare with the drain voltage .

· JFET is operating in LINEAR region

· JFET is operating in the SATURATION region.

Shockley's Equation for Drain Current

Machine generated alternative text:
Transfer
Charactertisics
GSI
‘D ‚4T(1 ,
=
P)
VG
‘D
Input
Characteristics
VDS

Shockley's Equation for drain current in JFET for linear region

MESFET

MES Junction

· Work function (energy actually) is defined as the energy gap between

· is the energy at vacuum.

· An electron or hole at energy is said to be in a free state

· Work function of metal

· Work function of semiconductor

· Electron affinity

Junction Type	Work-function	Type of contact ( Rectifying / Non Rectifying )
Metal-N		Rectifying contact or Schottky Barrier Diode or Rectifier diode
Metal-N		Non-rectifying contact or Ohmic contact
Metal-P		Rectifying contact or Schottky Barrier Diode or Rectifier diode
Metal-P		Non-rectifying contact or Ohmic contact

MESFET	JFET
Gate is metal. Gate-channel is a metal-semiconductor junction (Schottky diode)	Gate is semiconductor. Gate-channel is a normal PN junction (PN diode)
High-gain bandwidth product	Low-gain bandwidth product
Channel is N-GaAs in which electron mobility is few orders higher.	Channel is semiconductor with normal electron mobility

· Lift-off is one of the various techniques used in the fabrication of very small channel width MESFET.

Rectifying Contacts

Junction Type	Work-function	Type of contact
Metal-N		Rectifying contact or Schottky Barrier Diode or Rectifier diode
Metal-N		Non-rectifying contact or Ohmic contact
Metal-P		Rectifying contact or Schottky Barrier Diode or Rectifier diode
Metal-P		Non-rectifying contact or Ohmic contact

Current in MES

Surface carrier density
Current from Metal to semiconductor
Current from Semiconductor to Metal		is a constant and does not depend upon forward or reverse bias . Its value is the value of at thermal equilibrium with
Total current in MES

Schottky Diode

Schottky barrier potential (

It is the amount of potential an electron in the metal has to overcome to cross into the semiconductor.

· If it is positive, electrons can cross into semiconductor on their own.

· If it is negative, electrons cannot cross into semiconductor on their own.

Schottky barrier (

It is the energy corresponding to Schottky potential.

Barrier Potential (

It is the amount of potential an electron in the semiconductor has to overcome to cross into the metal.

· If it is positive, electrons can cross into metal on their own.

· If it is negative, electrons cannot cross into metal on their own.

Schottky Diode	PN Diode
High current at low voltages. (E.g.: 0.28mA at 0.4 V)	Same current at a higher voltage (E.g.: 0.28mA at 0.6 V)
High reverse saturation current (4 orders of magnitude greater than normal)	Low reverse saturation current
Current only due to majority carriers	Current due to both majority and minority carriers
No storage capacitance hence very small turn- off time	Turnoff time is not so small due to storage capacitance
Characteristic curves

MOS

Depletion Type

Enhancement Type

n-MOS

is positive. Positive increases the drain current whereas negative decreases it. This is an ON device by default.

Machine generated alternative text:
Internal External Alternate
Substrate Substrate Symbol

is positive. This is an OFF device by default. turns the device ON.

p-MOS

is negative. Negative increases the drain current whereas positive decreases it. This is an ON device by default.

Machine generated alternative text:
Internal External Alternate
Substrate Substrate Symbol

is negative. This is an OFF device by default. turns the device ON.

MOS Junction

Metal Oxide semiconductor junctions have some special properties. When voltage is applied to metal-oxide-semiconductor charges accumulate on either side of the oxide.

· On the metal-oxide side charge appears on the surface.

· On the semiconductor-oxide side charges appear inside semiconductor along the boundary with the oxide.

· The density of charges accumulating on the semiconductor-oxide junction depends on the intensity and type of bias applied to the metal.

Let us consider a metal-oxide-P semiconductor junction.

1. For a negative bias the charge accumulating on the semiconductor-oxide junction is positive. This is called accumulation

2. For a positive bias the charge accumulating on the semiconductor-oxide junction is negative. This is called depletion

3. For an even more positive bias the charge accumulating on the semiconductor-oxide junction is negative. This is called inversion.

4. Increasing the bias even further increases the density of electrons beyond the density of acceptor ions. This is called strong inversion.

5. At strong inversion a depletion region of negative acceptor ions is formed just next to the inversion layer. The rest of the semiconductor is neutral.

Threshold Voltage

Surface carrier density
Width of the depleted region
Maximum width of the depletion region
Charge density
Maximum charge density
Threshold Voltage
Gate voltage
Oxide voltage

Inversion

Modes of operation

Accumulation

Depletion

Inversion

Capacitance

Capacitance-Voltage Measurement Graph
Capacitance in the inversion
Capacitance in the depletion
Capacitance in the accumulation