Chapter 3 OVERVIEW OF ELECTRONIC DEVICES

8/14/2019 Chapter 3 OVERVIEW OF ELECTRONIC DEVICES

http://slidepdf.com/reader/full/chapter-3-overview-of-electronic-devices 1/117

Electronic Materials and

Processing IChapter 3

OVERVIEW OF ELECTRONIC

DEVICES



3.1 DIFFUSION AND DRIFT OF CARRIERS

3.1.1 Chemical Potential

-Consider a thermodynamic system containing n constituent species. Its total internal energy U is to be a

function of the entropy S , the volume V , and the number

of particles of each species N 1, ..., N n

U : the internal energy ,

The chemical potential of the i -th species, µ i isdefined as the partial derivative

Where the subscripts emphasize that the entropy,volume, and the other particle numbers are to be

kept constant.

1 2( , , , ,....., )nU U S V N N N =

, , j i

i

i S V N

U

N µ

≠

⎛ ⎞∂= ⎜ ⎟

∂⎝ ⎠



-In real systems, it is usually difficult to hold the entropy

fixed, since this involves good thermal insulation. It istherefore more convenient to define the Helmholtz energy

A, which is a function of the temperature T , volume, and

particle numbers:

In terms of the Helmholtz energy, the chemical

potential is

-Under conditions of constant temperature and pressure,

the chemical potential is the partial derivative of the Gibbsenergy with respect to number of particles

1 2( , , , ,....., )n

A A T V N N N =

, , j i

i

i T V N

A

N µ

≠

⎛ ⎞∂= ⎜ ⎟∂⎝ ⎠

, , j i

i

i T p N

G

N µ

≠

⎛ ⎞∂= ⎜ ⎟

∂⎝ ⎠



-A chemical potentials associated with "external" force

fields (Electric potential energy differences, gravitationalpotential energy differences, etc.), and with "internal"

factors (density, temperature, etc.)

-Total chemical potential: internal chemical potential and

external chemical potentialµtot = µint + µext

where

i.e., the external potential is the sum of electric potential,

gravitational potential, etc. (q and m are the charge andmass of the species, respectively, V and h are the

voltage and height of the container, respectively, and g

is the acceleration due to gravity.)

...ext qV mghµ = + +



-The chemical potential is the generalized potentialenergy of a particle at a given position that describes

the driving force for particle movement .

-Real particles always move to lower their chemical

potential.

-When any two systems are allowed to interact, they

will always exchange matter or energy in such a way as

to equalize the chemical potentials of the systems.-Equilibrium is defined as equal chemical potential

between the two systems.

-The Fermi energy in a solid gives a measure of thechemical potential of the lowest energy free electron or

the highest energy free hole.



3.1.2 Carrier Motion in a Chemical Potential Gradient

-The force, F, on a particle is expressed through thecorresponding gradient in the chemical potential, µ:

where C is a constant.

-The force on an electron due to a chemical potential gradient

produces a current density J,

.

Here µn is the electron mobility , µ is the chemical potential

.

- Electron chemical potential gradients may result from

electric fields and concentration gradients.

-The presence of an electric field, E, corresponds to a voltage

(potential) gradient dV/dx and contributes to the chemical

potential gradient dµ /dx at constant concentration of electrons

as:

3.2

3.3

3.1

dV E

x dx

∂= − =∂



-A change in electron concentration, n, in the absence of an

electric field causes a change in chemical potential:

-The general chemical potential gradient in the system :

-Substituting for chemical potential gradient in Equation 3.2

gives:

3.7

3.6

3.5

3.4

-Using the Einstein relation between mobility and diffusivity

D=µnkBT/q :

-The first term is a current due to a concentration gradient

:diffusion current

-The second term is due to the electric field: a drift current.



3.2 SIMPLE DIODES

-To consider the effect of joining a semiconductor

doped n- with semiconductor p-type:

The n-type material has higher concentration of electrons.

The p-type material has higher concentration of holes

-Two materials are brought into contact:The large electron concentration gradient across

the junction causes electrons to diffuse from the n-type

to the p-type side, leaving positively-charged donor

dopant atoms behind.

The similar process for holes.



Figure 3.1: Electrons diffuse and drift across a junction between unlike materials.Before contact the Fermi energies (chemical potentials) of

electrons in the two materials do not match.After contact, electrons flow until the Fermi energy is matched across the junction.This electron diffusion produces an electric field. At equilibrium the

drift current balances the diffusion current and no net electron transfer occurs.



3.2.1 The Junction Contact Potential

-The diffusion of charged species causes an electrostatic potential tobuild up, which opposes further diffusion of electrons.

-The initial difference in chemical potential of the electrons on

the two sides of the junction is gradually reduced and finally

eliminated. At this point, diffusion stops.

-An accumulation of positive charge on the n-type side and negativecharge on the p-type side, causing an electric field at the junction.

-The magnitude of the field can be calculated by setting J=0 in

Equations 3.6 :

3.8

-Substituting E=-dV/dx, and integrating across all x in the electric field:

where Vbi is the “built in” voltage (contact potential) across the

junction ; nn and np are the electron concentrations on the n and p

sides of the junction,



For a shallow dopant at high temperature:

nn~Nd

where Nd is the donor concentration on the n-type side of the junction.

np=ni2 /pp

or

Substituting nn~ND and using Equation 3.10 for np:

3.10

Or

Substituting 3.12 into 3.9

3.11

3.12

3.13



-Vbi is zero volts if both sides of the junction are

undoped and increases with NA and ND.

-The built in voltage can be determined from a diagram of the band edges of a junction at equilibrium.

Figure 3.2: The difference in Fermi energies (dashed lines) before contact establishes a band edge bending and a contact potential V bi after contact.

-The built-in voltage can also be written in terms of the

intrinsic carrier concentration ni:3.14



Figure 3.3: The depletion region and

the charge associated with it showing how the depletion is primarily on the lightly-doped side of the junction. The charges on the two sides of the

junction must balance. The electric field that results is due to the charge on

the two sides of the junction. The maximum electric field is directly related to the total charge on each side of the junction.

-The number of free carriers decreases exponentially with

the distance of the Fermi energy from the band edge,

-A well-defined zone (the “depletion region”) around the

junction contains no free carriers.

-The electric field, present in this region, sweeps out the

mobile carriers (resulting in a drift current that balances

diffusion).

-The charge giving rise to the built-in voltage on each side of

the junction : the number of ionized impurities in the

depletion region on that side of the junction. (Figure 3.3).



where xp is the depletion width on the p-type side,

NA is the ionized acceptor concentration

q is the acceptor charge,

ε is the dielectric constant of the semiconductor.

-The voltage is the integral of the field over a distance. Graphically,it is the area under the electric field vs. position .

-The electric field E0 of the junction is found by integration of the

charge Q across either side of the depletion region.

For example, on the p-type side:

As

W=xn+xp

The balance of the charges accumulated on the both sides of the

juntions

3.15

3.16



Solving for xp

Substituting for xp in Equation 3.16 in turn, gives

3.18

3.17

Substituting for Vbi from Equation 3.14 and solving for

W leads eventually to:

3.19

The depletion lies on the lightly-doped side of the

junction



-When a voltage is applied to a p-n junction, the

total voltage across the junction is

V= Vbi - Vapplied.

A voltage that is the opposite sign as the built in

voltage increases the depletion width.

A voltage of the same sign decreases thedepletion width

3.20



- The resulting capacitance is voltage dependent and

depends primarily on the concentration of dopant on

the lightly-doped side of the junction

Where Nnet is the difference between the

number of ionized majority carrier dopant atoms andthe number of minority carrier dopants on the lightly-

doped side of the junction.

3.21

-Diode junctions have a significant capacitance. The

effective separation of the “capacitor plates” in the

junction is the depletion width, W.



-The doping concentration on the lightly doped side

can be determined as a function of depth bymeasuring the capacitance of an asymmetric

junction as a function of voltage,

- For an applied reverse bias voltage VR:

3.22

- This relationship is used in the capacitance-voltage

technique for profiling carrier concentrations near diode

junctions



Figure 3.4: Band edge diagrams for biased junctions

The band edge

diagrams for biased

junctions are shown inFigure 3.4.

3.2.2 Biased junctions

-To consider the biased junction.-The majority of an applied voltage adds to or subtracts from

the field in the depletion region

-The amount of band bending is increased or reduced.



-The current density includes both carrier types to

completely describe the situation in a p-n junction:

where np and pn are the electron concentration on the p-type side

and the hole concentration on the n-type side: concentrations of the

minority carriers (np<<pp and pn <<nn ).

-The first term is the total diffusion current

-The second term is the total drift current.

-In a biased junction the chemical potential barrier

associated with the junction is changed.-Drift current flows in unchanged but diffusion current

changes dramatically with the applied bias.

3.23



3.2.2.1 Drift current

-The drift current is relatively insensitive to the junction

electric field.

-This field sweeps away mobile electrons and holes.

-This sweeping effect does not depend upon how large the

field is as long as it is not too small.

-The drift current does not change under reverse bias

Figure 3.5: A schematic of the motion of minority carriers

by drift across a junction. Drift current does not depend significantly on the electric field magnitude.



-The number of minority carriers reaching the edge of the

depletion region per unit area depends upon the equilibriumnumber of minority carriers on each side of the junction (pn or

np for the n- and p-type sides of the junction, respectively)

multiplied by the effective velocity at which they reach the

edge of the depletion region.-The effective velocity depends upon their diffusivity (or

mobility) and inversely on the average distance they can

diffuse before recombining with a majority carrier:

veff =Dp /Lp.The resulting drift minority carrier current density :

where Dp and Dn are the minority carrier diffusivities and Lp and Ln

are the carrier diffusion lengths for holes in the n-type and

electrons in the p-type materials

3.24



-Reverse current density is important in determining the

power that a device consumes when in the “off ” state as

it determines the effective resistance of the device in

reverse bias.

-Reverse current is also referred to as leakage current.

-The reverse current is carried by drift of minoritycarriers from the lightly doped side of the junction

toward the heavily-doped side.

-Case: p+-n diode (the p-type side is very heavily doped)

:

-The hole current can be related to the doping level on

the n-type side and the intrinsic carrier concentration(nnpn=ni

2):

3.25

3.26



-Reverse saturation current density increases

exponentially with decreasing energy gap.-Ge semiconductor: small energy gap of 0.6 eV,

produces a far higher reverse current density and

consequently much greater “off ” currents.

-Ge devices consume too much power.

Assuming n ~ND, and using expression of ni

3.27



3.2.2.2 Diffusion current

-The diffusion current is a majority carrier current.

-Diffusion current is carried by electrons leaving the n-

type side of the junction and by holes leaving the p-type

side.

-It depends upon the potential barrier opposing motion

of majority carriers and on the velocity with which

these carriers can diffuse into the material of oppositetype, and their concentration gradient. As the Fermi

energy is at mid-gap, carriers switch from being in the

majority to being in the minority and are to recombine.

-Rapid recombination the region far end of thedepletion region where the majority carriers are not

depleted.

-No recombination occurs in the space-charge region in

a good diode.



-The concept of the quasi-Fermi level:

The normal Fermi level or Fermi energy, EF, describesthe equilibrium situation in a junction, where np=ni

2.

When the junction is forward biased, electrons and

holes diffuse into the depletion region faster than they

can recombine locally. In this region np>ni2.

-The Fermi level for electrons cannot lie at the same

location as for holes in this case.

-To distinguish these non-equilibrium and bias-

dependent levels from the equilibrium Fermi level :

quasi-Fermi levels, Fn and Fp for electrons and holes.

Fn

− Ei

= kB

Tln(n /ni

)

Ei − Fp = kBTln(p /ni )

.

Ei is the intrinsic energy, near midgap,

3.28



Figure 3.6: Shows the quasi-Fermi levels for a forward biased junction. The deviation of the quasi-Fermi levels from the Fermi level indicates the excess number of

injected carriers that changes exponentially with the difference in these levels.



-The current density for the junction is given by theinjected carrier densities,

-The number of electrons increases exponentially as

the potential barrier decreases.

- As the barrier decreases the number of injected

carriers increases exponentially.

Diffusion current :

3.29



3.2.2.3 Total current in a junction

The total current in a junction is just the sum of the driftcurrent and the diffusion current

This current/voltage relationship known as the diodeequation.

Figure 3.7: The current voltage curve for an ideal diode obeying the diode equation.

The current density in reverse bias is nearly constant,

while it rises exponentially in forward bias

3.30



Figure 3.8: Comparison of forward currents asa function of reverse current J0.

Minority carrier devices: the magnitude of both the forward

and reverse currents in a homojunction diode depend uponthe minority carrier properties.



3.2.3 Non-ideal diode behaviors

Series resistance:

Resistance of the semiconductor on the lightly-doped side of the junction outside of the depletion

region.

Contact resistances

Figure 3.9: Compares an ideal diode behavior with a non-ideal diode

exhibiting series resistance.



- In reverse bias an ideal diode has an extremely high

resistance. Series resistance in the remainder of thedevice is irrelevant as the diode junction is the most

significant resistance in the circuit.

-In forward bias : the resistance of the diode will drop

below that of some other circuit element.- A series resistance leads to a linear current-voltage

curve in forward bias

-The final current : voltage divided by the net

resistance:

R=dV/dJ is the resistance of an ideal diode

3.31



3.2.3.2 Shunt resistance

A shunt resistance in the diode :

A top contact punches through the device andmake a direct connection to the back contact,

Figure 3.10: A non-ideal behavior due to shunt resistance

compared with an ideal diode.



-The origine:

physical defects such as holes in the device layer,high conductivity paths such as grain boundaries

or dislocations

-The shunt resistance allows current to flow in spite of

the high resistance of the good portion of the diode in

reverse bias.

-In forward bias the shunt only has an effect at very low

voltages where the diode resistance is still high.- Current density flowing through Shunt resistances :

Jshunt=Vapplied /Rshunt

- Total Current density3.32



-No obvious effect on reverse (drift) current : the injected

carrier begins as a minority carrier and becomes a

majority carrier upon transiting the depletion region.

It effectively reduces J0.

-A a large effect on forward current: Recombination in

the space charge region dramatically increases thevoltage needed to achieve a given level of current

injection

The added term “a” is called the diode ideality factor

-The value of the ideality factor ranges from 1 for an

ideal diode to at most 2.-The latter occurs when the minority carrier diffusion

lengths (before recombination) are small relative to the

depletion width, W.



3.2.3.4 Reverse breakdown

There are three forms of breakdown failure in reverse

bias:

tunneling breakdown,

avalanche breakdown,

the soft breakdown associated with current flowthrough defects.

-Avalanche breakdown is generally catastrophic because

the resistance of the diode drops as the process begins.The resulting increased current flow heats the diode

Tunneling breakdown is used in Zener diodes to provide

voltage control..



Figure 3.12: A schematic of the avalanche breakdown process.

Avalanche breakdown occurs when the depletion width

is relatively large (light doping on both sides of the junction). It is most obvious when the semiconductor is

of high quality.

The basic process is shown in Figure 3.12



Avalanche breakdown occurs when the depletion width

is relatively large (light doping on both sides of the

junction); the semiconductor is of high quality.The basic process :

A single minority carrier (1) enters the depletion region

and is accelerated.

The carrier gains more kinetic energy than the energy gapand experiences a collision with a valence band electron,

losing its kinetic energy and transferring the valence band

electron to the conduction band, resulting in an additional

free electron (2) and a free hole (3).Both the free electron and the free hole can go on to

experience additional ionizing collisions.

The original electron (1) and the newly free electron (2)

are accelerating and undergoing such additionalcollisions, creating two more electrons (4 and 5) and two

more holes (6 and 7).

Thus, beginning from a single electron, a continuously

increasing current is created.



As the reverse bias rises, at some point the cascade begins.

The additional current and non-ionizing collisions heat the

system and increase minority carriers which increase the

the reverse current. This leads to the diode acting as a fuse

and burning out.

Th bilit f l t



The mobility of an electron

µe=qτe /me*

where τe is the mean time between scattering events.A mean length between scattering events of electron

l = vτe

l = me* vµe /q.

For silicon, l = 1.1x10-6 cm (11 nm).The breakdown field EBR is that field at which an electron

accumulates at least the energy of energy gap over a

distance of l.

qEBR l = Egap.For silicon, the energy gap is ~1.1 eV at 300 K. EBR~ 1x106

V/cm.

EBR=VBR /W

where VBR is the breakdown voltage and is a negative value.As the doping rises and the depletion region shrinks, the

voltage for breakdown decreases.

Thus, the breakdown field is inversely related to the

square root of the doping concentration.



The relationship of breakdown voltage to doping isshown schematically in Figure 3.13.

Assuming VBR>>Vbi and noting that VBR<0,

Figure 3.13: Typical

breakdown voltages as afunction of doping level

calculated from Equation

3.34 and 3.20. Note: the

curvature at low

breakdown voltage

shows the correction for

non-zero Vbi.

3.34

3.35



Tunneling breakdown occurs in heavily-doped junctions

where the depletion region is relatively narrow.Before the avalanche breakdown process can begin,

electrons can tunnel through the depletion region from

filled states into empty adjacent states

Figure 3.14: A schematic of the tunneling

breakdown process.

The tunneling probability PT through the barrier is given



The tunneling probability, PTu, through the barrier is given

by:

where C is a constant, and E is the electric field of the

junction [E=(Vbi -Vappl)/W].

The tunneling current is proportional to the tunnelingprobability and the number of empty states adjacent to

filled states.

It increases exponentially with applied voltage.

Higher energy gap materials have lower tunneling currents,as do junctions with higher depletion widths.

Semiconductors with higher densities of states at the band

edges have higher tunneling currents.



The important points :-as current begins to flow, other resistances in the

circuit drop more of the applied voltage. This reduces

the voltage across the diode and consequently

limits the tunneling current.

-the tunneling current does not increase

significantly with increasing temperature. This is

less to cause the diode to fail in coparision toavalanche breakdown.



Soft breakdown occurs by generation of carriers through

defect states in the energy gap.Carriers may tunnel through defect states rather than moving

directly band-to-band.

Collisions with energies too low to excite carriers across the

entire energy gap can move electrons into states in the middleof the gap or from there on into the higher energy band edge,

resulting in avalanche-like breakdown

As the reverse voltage is increased, more and more defects

come into the depletion region.

The Fermi energy, shifts with bias. This leads to changes

in the charge state of defects in the energy gap.

These effects combine to increase the amount of reverse

current flowing in a diode with increasing reverse bias.



Figure 3.15: Combined effects of soft breakdown

and avalanche breakdown on the current/voltagecharacteristic of a diode. The soft breakdown is

shown as might be observed in a very poor diode.

Tunneling has a very similar behavior to avalanche

breakdown but is not self-amplifying.



The avalanche and tunneling mechanisms have very abrupt

onsets.

where n normally ranges from 3 to 6.Higher quality materials produce more abrupt onsets and

larger values of n.

3 3 SCHOTTKY BARRIERS AND OHMIC CONTACTS



3.3 SCHOTTKY BARRIERS AND OHMIC CONTACTS

Metal/semiconductor junctions have either linear (ohmic)

or diode-like current voltage characteristics : ohmic

contacts or Schottky diodes,

3.3.1 Ideal Metal/Semiconductor Junctions

The electron chemical potential in metals is the workfunction, Φ.

It measures the position of the Fermi energy with respect to

the vacuum level .

The work function of a semiconductor also measures theposition of the Fermi level.

However, this value changes with doping .

The energies of the band edges with respect to the vacuum

level do not depend significantly upon doping so they aremuch better choices.

The conduction band energy relative to the vacuum level

(the electron affinity, χs) is therefore used to quantify the

general properties of semiconductors .



Figure 3.16: Shows the definitions of the electron affinity χs of the

semiconductor and the work functions of the semiconductor, Φs

and metal, Φm. Also indicated are the depletion width, W, the

Fermi levels, band edges, and the Schottky barrier heights, ΦB.

Note that Schottky barriers to both n and p-type semiconductorsexist but that to calculate the barrier for the p-type semiconductor

you need to compare the valence band edge with the metal work

function while for the n-type material it is the conduction band

that is compared to the work function.

Wh t t i d b t t l d



When contact is made between a metal and a

semiconductor, electrons flow from one material to the other as determined by their relative Fermi levels. This flow can

lead to depletion or enhancement of the majority carriers.

There are four possible situations to consider:

a low work function metal in contact with (1) a p-type or (2)

an n-type semiconductor, and the same cases for a high work

function metal.

“High” and “low” work function here simply indicate whether

the Fermi level for the metal lies above or below the Fermi

level of the semiconductor before contact is made.



Figure 3.17: The four possible metal-semiconductor cases

before and after contact. Two of the four produce ohmic

contacts (resistors) while the others produce Schottky

diodes.



These four possibilities are shown schematically in Figure

3.17.When the direction of electron flow is into n-type material

or out of p-type material,

it increases the majority carrier concentration of the

semiconductor. This increasesthe conductivity of the semiconductor near the junction

and is described as "ohmic"

because the junction acts only as a resistor. Such

junctions are desired for contacts to microelectronicdevices.

Unfortunately, it is often impossible to find a metal of

sufficiently high or low work function to arrange the

electron flow in the correct direction to obtain an ohmiccontact, especially to wide-gap semiconductors and

organic electronic materials



When charge flowing into the semiconductor is of the

opposite sign as the majority carrier type, the majoritycarriers are depleted near the junction forming a resistive

depletion region (Figure 3.17).

An applied bias voltage appears across this relatively

insulating depletion region, modifies the chemical potential of

electrons across the junction and induces current flow as

shown in Figure 3.18.

For positive applied voltages the barrier for majority electrons

is decreased, causing them to diffuse into the metal over the

barrier.

The diffusion current changes exponentially with bias

voltage, as it does in a p-n junction.



Figure 3.18: The effects

of bias voltage onSchottky diode band

edges and band

bending.



In reverse bias the barrier height for electron motion from an

n-type semiconductor or hole motion from a p-typesemiconductor to a metal is increased.

The flow of electrons/holes in this direction decreases

exponentially to near zero.

Charge flow from the metal to the semiconductor faces aconstant barrier height, ΦB (Fig 3.18).

This height is characteristic of any metal-semiconductor

junction independent of the semiconductor doping, and is

known as the Schottky barrier height,ΦB= ΦM - χS.

Compare the metal work function with the valence band

edge

ΦB= χS+Egap-ΦM.

The current voltage curve for the resulting metal-



The reverse saturation current depends upon a

Boltzmann factor describing the probability that anelectron will have sufficient energy to overcome the

barrier height rather than the semiconductor energy gap.

Thermionic emission: electrons are emitted from a hot

filament.The final form of the reverse saturation current is:

g g

semiconductor junction has the same form as a

homojunction diode:

where A and B are constants.Significant advantage : diode operation does not depend

upon the minority carrier properties of the

semiconductor. The only carriers injected across the

unction are ma orit carriers.



A Schottky diode can be made to operate as an ohmic

contact by increasing the doping level of thesemiconductor near the junction.

The depletion width in the semiconductor becomes very

small which lead to very low tunneling breakdown

voltages.

Once breakdown occurs the diode operates as an ohmic

contact.

3 3 2 Real schottky diodes



3.3.2 Real schottky diodes

- Clean surfaces of semiconductors typically have a

large number of defect states.

Because of the limited doping and carrier

concentration of the semiconductor, the Fermi level atthe surface is determined by the energy of these

defects, rather than by the dopant atoms.

A surface Fermi level measurement usually gives

an unreliable estimate of the barrier height.The typical barrier potential in a real Schottky

diode is shown schematically in Figure 3.19.



Figure 3.19: A defective Schottky contact, typical of real

barriers. The small lines indicate defect states in thesemiconductor.

-Thin layers of compounds can form at the junction or



Thin layers of compounds can form at the junction or

short-range diffusion can broaden the effective interface.This spreads out or changes the potential at the

boundary and causes a change in the effective barrier.

Advantage of such reactions in forming metal-Si

Schottky barriers by reacting the metal with thesemiconductor to form a silicide.

This gives a very reliable contact because the

junction is formed by solid phase reaction within the Si

rather than at the original semiconductor surface resultingin few interfacial defects.

-Finally, interfacial defects can permit reverse current to

flow by tunneling through the resulting states (see Figure3.19), which can lead to an unexpectedly high current

(an anomalously low apparent barrier).



3.4 SEMICONDUCTOR HETEROJUNCTIONS

Heterojunctions are any electrical junctions between

dissimilar materials.

Semiconductor heterojunctions are very useful : one

semiconductor can be used to emit light while a

second can be used as a top contact

3.4.1 Heterojunctions at equilibrium



-The critical points in determining the electronicproperties of a semiconductor heterojunction :

The energy gaps,

Electron affinities,

Doping types and levels.

-To consider the case: the Fermi levels of two

semiconductors are arranged to be at the same energy

before contact.-This “flat band” condition means that upon contact there

is no net flow of electrons across the junction and the

band edges remain flat.

-The energy gaps and electron affinities of flat bandsemiconductor heterojunctions lead to three possible

band-edge configurations, shown in Figure 3.20.



Figure 3.20: the band edges in

the flat band condition for thetypes of semiconductor

heterojunctions.



-“Straddling” : the conduction and valence band edges

of the narrow-gap semiconductor lie within the energy

gap of the wide-gap semiconductor.

-To obtain a straddling gap :One gap to be significantly larger than the other:

EgA > EgB

The electron affinity of the smaller gap material isslightly larger than that of the wider gap material:

EgA-EgB > χB

- χA > 0.

A typical example of a straddling gap configuration is

the AlAs-GaAs heterojunction



.- Offset-gap heterojunction :the energy gaps are roughly equal:

EgA~EgB

the electron affinities are differentχA > χB.

The difference is less than the energy gap of either

constituent: both band edges of one semiconductor lieabove both band edges of the other but where a

portion of the energy gap overlaps across the interface.

An example of an offset-gap heterojunction is

between InSb and InP.

- “Broken gap” semiconductor heterojunctions are



composed of semiconductors with such extremedifferences in electron affinity that the band gaps do

not overlap at all.

-In this case the valence band edge of one

semiconductor lies above the conduction band edge of the other.

-An example of this type of junction is between InAs

and GaSb.

- Such semiconductor heterojunctions usually involveat least one relatively narrow-gap material in order to

achieve sufficient difference in electron affinities.



-Transitivity principle:



y

If the discontinuities between any twosemiconductors and a third semiconductor are

known, the discontinuity between the first two

can be inferred.

3.41

The Common Anion Rule:

When the anion (the electron accepting atomsuch as As in GaAs and InAs) is in common across a

semiconductor heterojunction, the change in the

conduction band edge is greater than the change in the

valence band edge across the semiconductor

heterojunction.

∆EV<∆EC.



The Common Cation Rule:When the cation (e.g. Ga in GaAs or GaSb) is in

common across the junction, the valence band edge

energies scale with the anion electronegativities.

For example, the valence band edge of phosphide

semiconductors will lie below those for arsenides which

will lie below those of antimonides.

EV(CA1) < EV(CA2) < EV(CA3),

where C designates a cation, and A1, A2, and A3

designate three anions with decreasing

electronegativities.



Figure 3.21: Recommended

steps in drawing asemiconductor heterojunction.

Step 5 shows the complete band

edges for this junction.

A series of steps for making sketches :



1. Mark a vertical line on a page to indicate the junctionand a horizontal line to indicate the flat-band vacuum

level.

2. Based on a constant vacuum level, mark the band

edge positions on the vertical line using the electronaffinity and energy gap values for the two materials.

These positions are doping-independent and fix the band

edges in relation to one another at the junction.

3.Draw a horizontal dashed line indicating the Fermi levelat equilibrium.

4. Far from the junction, mark the band edges relative to

the Fermi level as appropriate to the doping in each

semiconductor.



5. Connect the band edges far from the junction to the

band edges you marked in Step 2 as appropriate.

-Requirements to be met in this step are:

I. the slopes of the connecting segments must matchwhere they intercept the points marked in Step (2) to

satisfy the electrostatic continuity equation.

II. the energy gaps must be constant on each side of the

junction because the gap for a given semiconductor doesnot change.

III. the depletion widths are fixed by the doping levels.

These are calculated as in Equation 3.19.

-The major question is where to put the Fermi level with

respect to the flat band band edges (step 3)



respect to the flat-band band edges (step 3).

Marking this position will determine on which side

of the heterojunction most of the band bending occurs.

When one semiconductor is very heavily doped :

Mark the Fermi level with respect to the flat band edge of

the heavily-doped material. There will be very little band

bending in that material (see Figure 3.22).

When the doping levels are nearly equal (see

Figure 3.21), the resulting electric field will be distributed

roughly equally across the heterojunction and the bandbending is nearly symmetric. In this case the Fermi level

must be drawn close to the middle of the distribution of

flat band points (Figure 3.21).



Figure 3.22: Shows the formulas for calculation of

various energies in the heterojunction. This case issimilar to that shown in Figure 3.21, but with very

heavy doping in the AlAs layer to produce the electron

gas.

-The potentials (as shown in Figure 3.21) are distributed

approximately, assuming fully ionized dopants, as:



where ΦD indicates the potential energy difference

associated with band bending on the designated side of

the junction.

- The contact potential (difference in Fermi energies of thesemiconductors before contact).

approximately, assuming fully ionized dopants, as:

As in the flat band picture there are discontinuities in

the band edges at the hetero-junction.



The discontinuities result from the fact that not onlythe doping and the electron density are changing

across the interface, but that the atoms themselves are

changing.

The effective charges on the cores of the atoms makingup the lattice on the two sides of the junction change as

one goes across the interface. This leads to a step

function in electron potential. The magnitudes of the

band edge discontinuities can be calculated from the

electron affinities and energy gaps of the two materials,

as shown in Figure 3.21

3.4.2 Heterojunctions as diodes

To consider a perfect abrupt semiconductor



heterojunction (p-GaAs/n-AlAs),-A “forward” applied bias will reduce the potential

between the layers, narrow the depletion region, and lower

the barrier for carrier injection (by diffusion) across the

junction.

-As the opposite signs of the band gap discontinuities

(one is a step upward, the other a step downward),

electrons emitted into the GaAs, will have a much lower barrier to overcome than will holes injected from the GaAs

into the AlAs.

Thus, most of the forward diffusion current will be carried

by electrons.

-In reverse bias the currents are simply the thermally-

generated carriers in the GaAs which reach the depletion

region and are swept into the AlAs.



g

The much larger energy gap of the AlAs :few minority carriers in this material

no significant contribution of minority carrier drift

from the AlAs to the GaAs.

The barriers at the heterojunction will usually have little

effect on the reverse current drift process in high-quality

materials, as the carriers will generally gain enough

energy to pass over them.In a lightly-doped junction where the depletion region is

broad, and where the scattering of carriers is rapid for

any reason, the spike in the conduction band can

influence the behavior of the device.The minority carrier properties in the GaAs will generally

affect this type of device as current injection and

recombination processes are very similar to the

homo unction case.

- The behavior of the junction shown in Figure 3.22

responds in general in the same way as described above



except that now the AlAs is very heavily doped.This further enhances the dominance of injection of

electrons into the GaAs.

The injected electrons come from the electron gas

induced in the GaAs, and the spike at the interface is

truly irrelevant (except that it is responsible for the

formation of the electron gas in the first place).

The behavior now becomes that of an n

++

-p GaAshomojunction.



Figure 3.23: An n-n heterojunction with offset gap. Thisheterojunction may show Schottky diode-like behavior

based on injection of electrons across the spike in the

conduction band.

The larger potential barrier in the valence band reduceshole injection from the narrow gap material into the wider

gap material. An applied voltage reduces band bending in

both semiconductors.

a heterojunction such as shown in Figure 3.23, the

current is carried primarily by injection of electrons



across the spike.both semiconductors are n-type but even so, a depletion

region occurs on one side of the junction

Electrons moving from the electron gas into the wide-gap

material face a barrier that does not change significantlyfor modest bias voltages.

Forward bias reduces the scale of the field causing the

electron gas to accumulate and reduces the barrier for

electron injection from the wide-gap material across thespike.

In reverse bias the behavior is determined by injection of

electrons from the electron gas across the spike.

Thus, there will be a Schottky-like behavior for at least

modest bias voltages.

3.5 TRANSISTORS

3.5.1 Bipolar junction transistors



Figure 3.24: An example of the

connection of an n-p-n typetransistor. The circuit schematic

shows the transistor in forward

bias. Electrons are injected

from emitter to base due to theforward bias. Some electrons

flow across the base and reach

the collector. A minority are lost

through recombination in thebase. These are few and far

more reach the collector.

The bipolar transistor consists of two diodes joined back

to back by a thin common semiconductor layer (the



base).bipolar transistors are referred to as p-n-p or n-p-n

depending upon whether the common base layer is n or p

type.

Consider a typical n-p-n bipolar junction transistor,shown schematically in Figure 3.24

When the emitter junction is forward biased, electrons are

injected into the base and holes into the emitter.

The holes injected into the emitter recombine there andare of no value to operation of the device.

The electrons emitted into the base may either

recombine, contributing to base current, or transit the

base.

If the base is thin, most of the electrons pass through it

without recombining, reach the reverse-biased collector

junction, and are accelerated into the collector

As the time required for the injected electrons to diffuse

through the base to the collector is less than the



minority carrier lifetime, the transistor will permit morecurrent to flow emitter to collector, icollector than from

emitter to base, iba

The current gain of the transistor is approximately:

where τn and τn are the electron lifetime in the baseregion and the transit time required for an electron to

pass through the base.

If the base is wider than the mean-free-path between

collisions, then the carrier must diffuse across the base.By removal of the forward biased emitter junction, there

is no injection and therefore no current emitter to

collector.

3.43

the current emitter to collector is controlled by current

emitter to base as much as by the voltage emitter to base.



The collector current increases rapidly with base currentbut the base current increases exponentially with base

voltage.

Therefore the emitter-to-base resistance is moderate and

decreases with increasing voltage.A bipolar junction transistor has a low input impedance

(resistance) and is a current amplifier .

-BJT’s are known as minority carrier devices:

performances are controlled by the minority carrier

ti



properties.-Two require:

The minority carrier lifetime in the base is critical

to achieving high gains.

To achieve low transit times by diffusion of carriers

through the base, a high carrier mobility is needed.

-Very good quality material with relatively low doping

concentrations and no unintended defects.- Some impurities such as Fe in Si cause such significant

loss of minority carrier properties that degradation in

bipolar transistor performances can be detected at Fe

concentrations of parts per trillion.This has been a major driving force for improved purity in

Si wafers.

-BJT gains and switching speed are controlled by base

t it ti G A d i



transit times : GaAs devices.-GaAs has a higher electron mobility than Si, which

should lead to higher speed n-p-n devices.

-It is difficult to work with very brittle GaAs and to form a

good contact to and insulator on it- Si transistors outperform most GaAs devices. : the

devices can be made smaller , contact resistance and

surface and interface states are less of an issue.

-This compensates for the reduced carrier mobility and

results in similar net performances.

-Only with great care and effort can GaAs outperform Si,

which makes GaAs devices expensive and their applications limited.

3.5.2 Field-effect transistors

-A typical structure of the field-effect transistor (FET) is

h i Fi 3 25



shown in Figure 3.25.

Figure 3.25: A schematic of a typical enhancement-mode n-p-n

“metal-insulator-semiconductor” field effect transistor. The device is

normally off and conduction is enhanced by application of a negative

gate voltage relative to the source, creating an n-type channel. Thesource-to-drain voltage adds to the gate bias when turned on, which

is why the channel is wider at one side. The hatched area under the

gate indicates an optional heavily-doped

polycrystalline semiconductor region as part of the gate .

T o hea il n t pe regions in a lightl p t pe s bstrate



-Two heavily n-type regions in a lightly p-type substrate,fabricated in such a way as to leave a short p-type barrier

separating the n-type areas.

-The heavily doped materials are called the “source”

(from which electrons are flowing when on) and the“drain” (into which the electrons drain).

-A gate electrode provides the current control by causing

majority carrier depletion and ultimately inversion of the

channel in the substrate, drawing charge into the hannelas in a capacitor.

This allows current to flow easily from source to drain.

-More bias voltage produces a wider and more conductive

channel, leading to a lower resistance from source to

drain.

-The FET is considered a majority carrier device because,

the source, drain, and channel all conduct majority

carriers



carriers-FETs are sensitive to majority carrier properties and are

less influenced by defects in the materials than are BJTs.

“junction” field effect transistors (JFET’s):

The type conversion, providing the conducting channel,

can be achieved by creating a heterojunction or

Schottky contact to the surface of the transistor



Schottky contact to the surface of the transistor.The depletion region of such a junction provides type

conversion in the channel.

This depletion region can be increased or decreased

depending upon the gate bias voltage used.

These are used for GaAs-based devices : high quality

heterojunction diodes are relatively easy to fabricate

The major problem with the JFET design is that somegate current can occur even in a reverse-biased junction.

Therefore, the gate resistance is limited by the

conductivity of the reverse biased gate junction.

The most common form of the field-effect transistor uses

a metal-insulator-semiconductor (MISFET) structure .

Metal oxide semiconductor FET’s or MOSFETS when



Metal-oxide-semiconductor FET s or MOSFETS whenSiO2 is used for the gate insulator

Silicon oxynitride gate dielectric can be a remarkable

insulator, withstanding fields of more than 107 V cm-1 with

very low leakage currents.Gate dielectrics less than 5 nm thick , as thin as 1 nm.

The effects of bias voltage

on the electric fields in the



Figure 3.26: Shows the change in carrier concentration in a

semiconductor near the gate of a MISFET for three applied fields.

Under accumulation conditions the majority carrier concentration of the channel region is enhanced. Depletion conditions reduce the

majority carriers without causing the majority carrier type to change.

In the inversion regime the majority carrier type near the insulator is

reversed.

on the electric fields in the

gate insulator and the

underlying semiconductor

are shown in Figure 3.26.

FETs can operate in a number of modes:

Enhancement mode devices are normally off: Therei h l d th t d t d t fl



Enhancement mode devices are normally off: Thereis no channel under the gate and current does not flow

unless a bias voltage is applied to turn conduction on.

Depletion-mode devices are normally on, having a

pre-existing channel. In these devices a voltage must beapplied to deplete the channel of charge and turn them

off.

Depletion-mode device must have an underlying

insulating layer against which the channel can be closed.



Figure 3.27: A schematic diagram of a typical MISFET structure with a

conventional gate metal with spontaneous band bending due to

electron flow (right) and the situation with a heavily-doped

semiconductor gate using the same semiconductor as in the channel

(left). The strong depletion of carriers in the contact to the gate metal

now happens at the contact with the doped gate semiconductor. The

latter is doped sufficiently that the contact breaks down at essentially

zero volts, leading to an effectively ohmic contact.

The control of threshold voltage has largely been solved

by making the gate of a very-heavily-doped



by making the gate of a very-heavily-doped

semiconductor of the same type as the barrier between

source and drain (Figure 3.27).

In silicon devices, polycrystalline silicon (poly-Si) can beused.

It is polycrystalline because it is deposited on a non-

single-crystal substrate (typically amorphous SiO2) and

so there is no template for formation of a single crystalmaterial.

Fortunately, the polycrystalline form works well when

heavily doped.

Using a poly-Si gate, the equilibrium Fermi energy isessentially constant between the gate and the channel

(Figure 3.27).

The most significant advantages of poly-Si gates in Si

devices :

(1) They can be doped the same type as the underlying



(1) They can be doped the same type as the underlyingmaterial, resulting in very little and very predictable band

bending in the adjoining Si channel region for either

channel type.

(2) Any of a wide variety of metals can be used for contactto the semi-conductor gate material, regardless of the

carrier type, because the gate semiconductor is heavily

doped and so the resulting Schottky diode breaks down

at very low voltages.

(3) Metal contacts to poly-Si are relatively stable and

predictable, and the poly-Si/SiO2 interface is very stable

and reproducible.

3.6 LIGHT-EMITTING DEVICES

3.6.1 Light-emitting diodesOne of the most basic solid-state optical devices is the



3.6.1 Light emitting diodesOne of the most basic solid-state optical devices is the

light emitting diode: a p-n homojunction

In forward bias, minority carriers are injected across the

junction.Recombination increases within the depletion region

when the quasi-Fermi levels are more widely separated.

In a direct-gap semiconductor this recombination often

releases the excess energy in the form of light.The critical issues relate to the probability of light

emission and the possible recombination of carriers

through non-radiative processes.



Figure 3.28: (a) A band edge diagram for light emission in a forward-

biased homojunction diode. Fn and Fp indicate the quasi Fermi

levels. The difference between these levels and the equilibrium Fermi

level Ef indicates the excess hole or electron minority carrier

populations.

(b) A schematic of a typical light emitting diode in a standardmounting. The reflector and lens focus almost all of the emitted light

out of the front of the lens providing high efficiency and brightness in

the forward direction.

3.6.1.1 Radiative recombination

Light emission requires that electrons and holes

recombine in a single step, satisfying requisiteconservation laws and with allowed quantum-mechanical



g p, y g qconservation laws and with allowed quantum-mechanical

selection rules.

The rate at which radiative recombination, Rradiative, takes

place between free electrons and holes across the energygap of a semiconductor depends upon the product of the

number of electrons and the number of holes in the

material.

The rate at which these interact depends also upon their thermal velocity vth (the velocity of carriers with a kinetic

energy near kBT), the cross section for the recombination

process SR

, and a factor due to internal reflection in the

material.

where η is the index of refraction of the semiconductor. -

-The cross section is the apparent size of an electron to a

moving hole, or vice versa, and gives a measure of howeffectively one particle is captured by the other



g , , geffectively one particle is captured by the other.

where T is the temperature in Kelvin, and α is the

absorption coefficient in cm-1

For Si the radiative recombination cross section at 300

K is 1.8x10-19

cm2

for GaP : 9.3x10-18 cm-2

-Some points to notice are the following:



p gThe radiative recombination rate scales as

np. Therefore, the more carriers that can be

injected across the junction and the more heavily-

doped the junction, the higher the radiative

recombination rate.

Materials with higher energy gaps and

lower absorption coefficients have higher crosssections , more rapid radiative recombination.

Finally, radiative recombination goes up as

the temperature goes down.

-Radiative recombination normally occurs from band



edge to band edge.

- Radiative recombination by excitons

- An exciton: the electron and hole becoming bound

together by electrostatic attraction.

A rough approximation of the exciton, as a

hydrogen atom in a dielectric medium

Typically the exciton binding energy is of theorder of 10±6 meV for common inorganic

semiconductors. In organic materials it can be 1 eV.

The emitted photon has a lower energy than

the gap of the semiconductor and is therefore notsignificantly reabsorbed as it leaves the material.

3.6.1.2 Non-radiative recombinationAuger processes : the electron recombining with a



- Auger processes : the electron recombining with a

hole passes its energy to

another electron which then gives up the energy to

heat-Trap mediated recombination : Trap-related

recombination only occurs when the material contains

a defect of some sort.

3.6.2 Laser diodes

Stimulated emission : wave emitted with samel th h d i di ti th



wavelength, phase and in same direction as the

driving wave.

the phenomenon of population inversion needed for

lasing

3

21

3

21

(stim)( )

(spon) 8

R ch

R h

ρ ν

π ν

=

-The ratio of stimulated to spontaneous emission



107

-The ratio of stimulated emission to absorption is

-There are two important conclusions:

For stimulated photon emission to exceed photonabsorption we need to achieve population inversion, that is

N 2 > N 1 .

-For stimulated emission to far exceed spontaneousemission, we must have a large photon concentration which

is achieved by building an optical cavity to contain the

photons.

21 2

12 1

(stim)

(absorp)

N

N =

It is important to point that the population inversionrequirement N > N means that we depart from thermal



108

requirement N 2 > N 1 means that we depart from thermal

equilibrium.

According to Boltzmann statistics in :

N 2 > N 1 implies a negative absolute temperature!

The laser principle is based on non-thermal equilibrium.

2 2 1

1

( )exp

B

N E E

N k T

⎡ ⎤−= −⎢ ⎥

⎣ ⎦



In a Fabry-Perot laser, feedback is provided by

mirrors separated by length d. This results in the

modal spacing in frequency of c/2d.

-Laser oscillation condition (amplification).

1 1lnhg γ

⎛ ⎞= + ⎜ ⎟



-Phase Condition and Laser Modes

The round-trip phase change ∆φround-trip must be a

multiple of 2π

∆φround-trip =m2πwhere m is an integer, 1, 2,…. This condition ensures

self-replication

1 2

ln2

thg L R R

γ + ⎜ ⎟⎝ ⎠

where γ is the attenuation coefficient of the medium threshold

gain g th, reflectances R 1 and R 2 of the facets

(a) A double heterostructure

diode has two junctions which

are between two differentbandgap semiconductors (GaAs

and AlGaAs)



111

and AlGaAs).

(b) Simplified energy band

diagram under a large forward

bias. Lasing recombination

takes place in the p-GaAs layer,

the active layer .

(c) Larger bandgap materials

have a lower refractive index.

(d) AlGaAs layers provide

lateral optical confinement.



Figure 15 Schematic illustration of the structure of a double heterojunction stripe contact laser

diode.



•The active layer (GaAs) is effectivelyburied

within a wider bandgapmaterial (AlGaAs) and the structure is hence called buried double

heterostructure laser diode.

Chapter 3 OVERVIEW OF ELECTRONIC DEVICES

Documents

Transcript of Chapter 3 OVERVIEW OF ELECTRONIC DEVICES