Contents
Degenerate & NonDegenerate Semiconductor
Direct Generation & Recombination
Direct/ Indirect Band Gap Semiconductor
Fabrication of a planar JN Diode
Shockley's Equation for Drain Current
· The densities of electrons and holes in the conduction and valence bands depend on two factors
1. Density of states available for occupancy (given by N(E)).
2. Probability of occupancy of states (given Fermi function).
· Density of states
·
· Fermi Function
· There are about atoms/cm^{3} in silicon. At T=0K, the 4N quantum states in the valence
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 nondegenerate semiconductors.
Ptype impurity 
Ntype impurity 
Boron 
Phosphorous 
Aluminum 
Arsenic 
Gallium 
Antimony 
· FERMIDIRAC FUNCTION functions give the probability that an electron occupies a quantum state with energy E.
Densities of state in the conduction band 



Densities of state in the valence band 



Density of electrons in the conduction band 



Density of holes in the valence band 



Intrinsic carrier density 

· increases with increase in temperature · decreases with increase in 

Charge neutrality 



Location of Fermi level in ntype and ptype
For intrinsic semiconductors





Ptype impurity 
Ntype impurity 
Boron 
Phosphorous 
Aluminum 
Arsenic 
Gallium 
Antimony 
Semiconductor 
Energy Gap (eV) 
Ge 
0.67 eV 
Si 
1.12 eV 
GaAs 
1.42 eV 


· 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)
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 


Causes of Directgeneration of electronhole pairs:
1. Exposure to thermal energy.
2. Exposure to light energy.
3. Impact ionization.
Cause of Indirectgeneration of electronhole pairs:
1. Lattice imperfection

· Traps=Gold & Iron in silicon and Copper in Ge. · Recombinationgeneration occurs through traps.

· Expression for rate of change of carrier density with time for indirectgenerationrecombination
· Low Level Injection: Any perturbation such that the change in minority carrier density is much smaller than the majority carrier density is called a lowlevel 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.
Eg: GaAs 
Eg: Si & Ge 
· Equation of continuity
for holes in the Nregion
for electrons in the Pregion
· 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.
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


Diffusion current (with bias voltage) 
Carrier density of holes and electrons in the nregion and pregion respectively for
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. 

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 

Turnon time of P+N long base diode = lifetime of holes in the N legion Turnon time of P+N short base diode= transition time of holes in the N region 
Diode Characteristics Curve 


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. 

Epitaxial Growth 


Oxidation 


Addition of Photoresist 


Placement of mask 


Exposure to UV 


Etching 


Diffusion 


Metal Contacts 



is the dynamic ac resitance


is the dynamic ac resitance



Injection Efficiency 


Transport Factor 


DC common base current gain 


DC common emitter current gain 


Collector current 



PNP 
NPN 
Currents Equation 


EbersMoll Equation (for PNP and NPN) 
β_R=α_R/(1−α_R )
*subscript F and R stands for active and inverseactive mode of operation respectively 
β_R=α_R/(1−α_R )
*subscript F and R stands for active and inverseactive mode of operation respectively 
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 GummelPool model is used
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 basecollector depletion layer which reduces the effective width of the base (also known as basewidth 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. 
Punchthrough 
Punchthrough occurs when the reverse bias basecollector depletion region reaches the emitterbase 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 Equation 

Charge control equation is a tool for calculating turnON and turnOFF time of transistors. 
Solution of charge control equation 

is the amplitude of current pulse applied at base to turn the transistor ON 
TurnON Time 

=transit time of holes(or electrons as the case may be) across the base 
TurnOFF Time 
=


Fixed Bias 



Emitter Bias 



Voltage Divider Bias 



Collector Feedback Bias 



· 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.
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. 



Figure of merit
Also known as gainbandwidth 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. 
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 

Channelconductance [ valid only in the linear region] 

Transconductance [ valid only in the saturation region] 

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).

· Pinchoff 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 TurnOFF voltage 

It is defined as the gate source voltage at which and 
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.
Cut off frequency for NJFET
Total channel capacitance 


Total channel resistance 


RC time constant 


· Pinchoff 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 in JFET for linear region
· 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 
Workfunction 
Type of contact ( Rectifying / Non Rectifying ) 
MetalN 

Rectifying contact or Schottky Barrier Diode or Rectifier diode 
MetalN 

Nonrectifying contact or Ohmic contact 
MetalP 

Rectifying contact or Schottky Barrier Diode or Rectifier diode 
MetalP 

Nonrectifying contact or Ohmic contact 
MESFET 
JFET 
Gate is metal. Gatechannel is a metalsemiconductor junction (Schottky diode) 
Gate is semiconductor. Gatechannel is a normal PN junction (PN diode) 
Highgain bandwidth product 
Lowgain bandwidth product 
Channel is NGaAs in which electron mobility is few orders higher. 
Channel is semiconductor with normal electron mobility 
· Liftoff is one of the various techniques used in the fabrication of very small channel width MESFET.
Junction Type 
Workfunction 
Type of contact 
MetalN 

Rectifying contact or Schottky Barrier Diode or Rectifier diode 
MetalN 

Nonrectifying contact or Ohmic contact 
MetalP 

Rectifying contact or Schottky Barrier Diode or Rectifier diode 
MetalP 

Nonrectifying contact or Ohmic contact 
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 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 


Depletion Type 
Enhancement Type 
nMOS 
is positive. Positive increases the drain current whereas negative decreases it. This is an ON device by default. 
is positive. This is an OFF device by default. turns the device ON.

pMOS 
is negative. Negative increases the drain current whereas positive decreases it. This is an ON device by default. 
is negative. This is an OFF device by default. turns the device ON. 
Metal Oxide semiconductor junctions have some special properties. When voltage is applied to metaloxidesemiconductor charges accumulate on either side of the oxide.
· On the metaloxide side charge appears on the surface.
· On the semiconductoroxide side charges appear inside semiconductor along the boundary with the oxide.
· The density of charges accumulating on the semiconductoroxide junction depends on the intensity and type of bias applied to the metal.
Let us consider a metaloxideP semiconductor junction.
1. For a negative bias the charge accumulating on the semiconductoroxide junction is positive. This is called accumulation
2. For a positive bias the charge accumulating on the semiconductoroxide junction is negative. This is called depletion
3. For an even more positive bias the charge accumulating on the semiconductoroxide 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.
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 


Modes of operation 


Accumulation 


Depletion 


Inversion 


CapacitanceVoltage Measurement Graph 

Capacitance in the inversion 

Capacitance in the depletion 

Capacitance in the accumulation 
