NJIT ECE-271 Dr. S. Levkov Chap 2 - 1 ECE 271 Electronic Circuits I Topic 2 Semiconductors Basics.

NJIT ECE-271 Dr. S. Levkov Chap 2 - 1

ECE 271

Electronic Circuits I

Topic 2Semiconductors Basics


Chapter Goals

• Characterize resistivity of insulators, semiconductors, and conductors.• Develop covalent bond and energy band models for semiconductors.• Understand band gap energy and intrinsic carrier concentration.• Explore the behavior of electrons and holes in semiconductors.• Discuss acceptor and donor impurities in semiconductors.• Learn to control the electron and hole populations using impurity

doping.• Understand drift and diffusion currents in semiconductors.• Explore low-field mobility and velocity saturation.• Discuss the dependence of mobility on doping level.


The Inventors of the Integrated Circuit

Jack KilbyAndy Grove, Robert Noyce, and

Gordon Moore with Intel 8080 layout.


Solid-State Electronic Materials

• Electronic materials fall into three categories (WRT resistivity):– Insulators > 105 -cm (diamond = 1016 )– Semiconductors 10-3 < < 105 -cm– Conductors < 10-3 -cm (copper = 10-6 )




• Elemental semiconductors are formed from a single type of atom of column IV, typically Silicon.





• Compound semiconductors are formed from combinations of elements of column III and V or columns II and VI.






• Germanium was used in many early devices.






• Germanium was used in many early devices.• Silicon quickly replaced germanium due to its higher bandgap

energy, lower cost, and ability to be easily oxidized to form silicon-dioxide insulating layers.


Solid-State Electronic Materials (cont)• Bandgap is an energy range in a solid where no electron

states can exist. It refers to the energy difference between the top of the valence band and the bottom of the conduction band in insulators and semiconductors

http://en.wikipedia.org/wiki/Solid

http://en.wikipedia.org/wiki/Electron

http://en.wikipedia.org/wiki/Valence_band

http://en.wikipedia.org/wiki/Conduction_band


Semiconductor Materials (cont.)

SemiconductorBandgap

Energy EG (eV)

Carbon (diamond) 5.47

Silicon 1.12

Germanium 0.66

Tin 0.082

Gallium arsenide 1.42

Gallium nitride 3.49

Indium phosphide 1.35

Boron nitride 7.50

Silicon carbide 3.26

Cadmium selenide 1.70


Covalent Bond Model

Silicon diamond lattice unit cell.

Corner of diamond lattice showing four nearest

neighbor bonding.

View of crystal lattice along a crystallographic

axis.

• Silicon has four electrons in the outer shell.• Single crystal material is formed by the covalent bonding of each

silicon atom with its four nearest neighbors.


Silicon Covalent Bond Model (cont.)

Silicon atom



Silicon atom Silicon atom

Covalent bond



Silicon atom Covalent bonds in silicon



• Near absolute zero, all bonds are complete • Each Si atom contributes one electron to

each of the four bond pairs • The outer shell is full, no free electrons,

silicon crystal is an insulator

• What happens as the temperature increases?



• Increasing temperature adds energy to the system and breaks bonds in the lattice, generating electron-hole pairs.

• The pairs move within the matter forming semiconductor

• Some of the electrons can fall into the holes – recombination.

• Near absolute zero, all bonds are complete • Each Si atom contributes one electron to

each of the four bond pairs • The outer shell is full, no free electrons,

silicon crystal is an insulator


Intrinsic Carrier Concentration

• The density of carriers in a semiconductor as a function of temperature and material properties is:

• EG = semiconductor bandgap energy in eV (electron volts)

• k = Boltzmann’s constant, 8.62 x 10-5 eV/K• T = absolute termperature, K• B = material-dependent parameter, 1.08 x 1031 K-3 cm-6 for Si

• Bandgap energy is the minimum energy needed to free an electron by breaking a covalent bond in the semiconductor crystal.

2 3 -6exp cmGi

En BT

kT


Intrinsic Carrier Concentration (cont.)

• Electron density is n (electrons/cm3) and for intrinsic material n = ni.

• Intrinsic refers to properties of pure materials.

• ni ≈ 1010 cm-3 for Si• The density of silicon

atoms is na ≈ 5x1022 cm-3 • Thus at a room

temperature one bond per about 1013 is broken

Intr

insi

c ca

rrie

r de

nsit

y (c

m-3)


Electron-hole concentrations

• A vacancy is left when a covalent bond is broken. • The vacancy is called a hole.



• A vacancy is left when a covalent bond is broken. • The vacancy is called a hole. • A hole moves when the vacancy is filled by an electron from

a nearby broken bond (hole current).




a nearby broken bond (hole current).• The electron density is n (ni for intrinsic material)





• Hole density is represented by p.





• Hole density is represented by p.• For intrinsic silicon, n = ni = p.





• Hole density is represented by p.• For intrinsic silicon, n = ni = p.

• The product of electron and hole concentrations is pn = ni2.

• The pn product above holds when a semiconductor is in thermal equilibrium (not with an external voltage applied).


Drift Current

• Charged particles move or drift under the influence of the applied field.• The resulting current is called drift current.


Drift Current

• Charged particles move or drift under the influence of the applied field.• The resulting current is called drift current.• Electrical resistivity and its reciprocal, conductivity , characterize current

flow in a material when an electric field is applied.


Drift Current


flow in a material when an electric field is applied.• Drift current density is

j = Qv [(C/cm3)(cm/s) = A/cm2]


Drift Current


flow in a material when an electric field is applied.• Drift current density is

j = Qv [(C/cm3)(cm/s) = A/cm2] j = current density, (Coulomb charge moving through a unit area) Q = charge density, (Charge in a unit volume) v = velocity of charge in an electric field.

Note that “density” may mean area or volumetric density, depending on the context.


Mobility

• At low fields, carrier drift velocity v (cm/s) is proportional to electric field E (V/cm). The constant of proportionality is the mobility, :


Mobility


• vn = - nE and vp = pE , where

• vn and vp - electron and hole velocity (cm/s),

• n and p - electron and hole mobility (cm2/Vs)


Mobility


• vn = - nE and vp = pE , where

• vn and vp - electron and hole velocity (cm/s),

• n and p - electron and hole mobility (cm2/Vs)

• n ≈ 1350 (cm2/Vs), p ≈ 500 (cm2/Vs),

• Hole mobility is less than electron since hole current is the result of multiple covalent bond disruptions, while electrons can move freely about the crystal.


Velocity Saturation

At high fields, carrier velocity saturates and places upper limits on the speed of solid-state devices.


Intrinsic Silicon Resistivity

• Given drift current and mobility, we can calculate resistivity (Q is the charge density) :

jndrift = Qnvn = (-qn)(- nE) = qn nE A/cm2

jpdrift = Qpvp = (+qp)(+ pE) = qp pE A/cm2

jTdrift = jn + jp = q(n n + p p)E = E

This defines electrical conductivity:

= q(n n + p p) (cm)-1

Resistivity is the reciprocal of conductivity:

= 1/ (cm)

E

jTdrift

V /cm

A /cm2 cm


Example: Calculate the resistivity of intrinsic silicon

Problem: Find the resistivity of intrinsic silicon at room temperature and classify it as an insulator, semiconductor, or conductor.

Solution:• Known Information and Given Data: The room temperature motilities. For intrinsic

silicon, the electron and hole densities are both equal to ni.

• Unknowns: Resistivity and classification.• Assumptions: assume “room temperature” with ni = 1010/cm3.

• Analysis: Charge density of electrons is Qn = -qni and for holes is Qp = +qni. Thus:

= (1.60 x 10-10)[(1010)(1350) + (1010)(500)] (C)(cm-3)(cm2/Vs)

= 2.96 x 10-6 (cm)-1 ---> = 1/ = 3.38 x 105 cm

Recalling the classification in the beginning, intrinsic silicon is near the low end of the insulator resistivity range

• Conclusions: Resistivity has been found, and intrinsic silicon is a poor insulator.

= q(n n + p p)


Semiconductor Doping

• The interesting properties of semiconductors emerges when impurities are introduced.




• Doping is the process of adding very small well controlled amounts of impurities into a semiconductor.





• Doping enables the control of the resistivity and other properties over a wide range of values.





• Doping enables the control of the resistivity and other properties over a wide range of values.

• For silicon, impurities are from columns III and V of the periodic table.


Donor Impurities in Silicon

• Phosphorous (or other column V element) atom replaces silicon atom in crystal lattice.

• Since phosphorous has five outer shell electrons, there is now an ‘extra’ electron in the structure.

• Material is still charge neutral, but very little energy is required to free the electron for conduction since it is not participating in a bond.


Donor Impurities in Silicon

• Phosphorous (or other column V element) atom replaces silicon atom in crystal lattice.

• Since phosphorous has five outer shell electrons, there is now an ‘extra’ electron in the structure.

• Material is still charge neutral, but very little energy is required to free the electron for conduction since it is not participating in a bond.

A silicon crystal doped by a pentavalent element (f. i. phosphorus). Each dopant atom donates a free electron and is thus called a donor. The doped semiconductor becomes n type.

q

q

e


Acceptor Impurities in Silicon

• Boron (column III element) has been added to silicon.

• There is now an incomplete bond pair, creating a vacancy for an electron.

• Little energy is required to move a nearby electron into the vacancy.

• As the ‘hole’ propagates, charge is moved across the silicon.


Acceptor Impurities in Silicon

• Boron (column III element) has been added to silicon.

• There is now an incomplete bond pair, creating a vacancy for an electron.

• Little energy is required to move a nearby electron into the vacancy.

• As the ‘hole’ propagates, charge is moved across the silicon.

A silicon crystal doped with a trivalent impurity (f.i. boron). Each dopant atom gives rise to a hole, and the semiconductor becomes p type.

Vacancyq

qe


Acceptor Impurities – Hole propagation

Hole is propagating through the silicon.



e

Hole




Hole




e



Doped Silicon Carrier Concentrations(how to calculate)

• In doped material, the electron and hole concentrations are no longer equal.



• In doped material, the electron and hole concentrations are no longer equal.• If n > p, the material is n-type.

If p > n, the material is p-type.




If p > n, the material is p-type.• The carrier with the largest concentration is the majority carrier, the smaller is

the minority carrier.





the minority carrier.• ND = donor impurity concentration

NA = acceptor impurity concentration atoms/cm3







• Charge neutrality requires q(ND + p - NA - n) = 0:

positive charge: p (holes) + ND (ionized donors)

negative charge: n (electrons) + ND (ionized acceptors)









negative charge: n (electrons) + ND (ionized acceptors)

• It can also be shown that pn = ni2, even for doped semiconductors in thermal

equilibrium.









negative charge: n (electrons) + NA (ionized acceptors)

• It can also be shown that pn = ni2, even for doped semiconductors in thermal

equilibrium.Explanation. The rate of e/h recombination is Cnp (kind of a number of possibilities of each electron to recombine with each hole). At the thermal equilibrium, rate of e/h recombination is equal to the rate of e/h pairs creation, thus np is the constant for certain temperature. Since creation recombination is the thermal process (depends on temperature, not doping), np should be the same as for intrinsic material, so np = ni pi = ni

2.


n-type Material

• Substituting p = ni2/n into q(ND + p - NA - n) = 0

yields n2 - (ND - NA)n - ni2 = 0.


n-type Material



• Solving for n

n (N D N A ) (N D N A )2 4ni

2

2 and p

ni2

n


n-type Material



• Solving for n

• For (ND - NA) >> 2ni, n (ND - NA) .

n (N D N A ) (N D N A )2 4ni

2

2 and p

ni2

n


p-type Material

• Similar to the approach used with n-type material we find the following equations:

p (N A N D ) (N A N D )2 4ni

2

2 and n

ni2

p


p-type Material


• For (NA - ND) >> 2ni, p (NA - ND) .

p (N A N D ) (N A N D )2 4ni

2

2 and n

ni2

p


p-type Material


• For (NA - ND) >> 2ni, p (NA - ND) .

• We find the majority carrier concentration from charge neutrality and find the minority carrier concentration from the thermal equilibrium relationship.

p (N A N D ) (N A N D )2 4ni

2

2 and n

ni2

p


Practical Doping Levels

• Majority carrier concentrations are established at manufacturing time and are independent of temperature (over practical temp. ranges).




• However, minority carrier concentrations are proportional to ni

2, a highly temperature dependent term.






• For practical doping levels (dopant concentration usually is quite larger then ni):

n (ND - NA) for n-type material

p (NA - ND) for p-type material.






• For practical doping levels:

n (ND - NA) for n-type material

p (NA - ND) for p-type material.

• Typical doping ranges are 1014/cm3 to 1021/cm3.Example here


Mobility and Resistivity in Doped Semiconductors

• Impurities degrade mobility (different size disrupt the lattice, atoms ionized – electrons scatter ) – see on the left.

• However, doping vastly increases the density of majority carriers dramatically decreases resistivity despite the lower mobility.

• = qn (ND – NA) for n-type

• = qp (NA – ND) for p-type

Example here


Diffusion Current

• In practical semiconductors, it is quite useful to create carrier concentration gradients by varying the dopant concentration and/or the dopant type across a region of semiconductor.

• This gives rise to a diffusion current resulting from the natural tendency of carriers to move from high concentration regions to low concentration regions.

• Diffusion current is analogous to a gas moving across a room to evenly distribute itself across the volume.


Diffusion Current (cont.)

A bar of silicon (a) into which holes are injected, thus creating the hole concentration profile along the x axis, shown in (b). The holes diffuse in the positive direction of x and give rise to a hole-diffusion current in the same direction.

If the electrons are injected and the electron-concentration profile shown is established in a bar of silicon, electrons diffuse in the x direction, giving rise to an electron-diffusion current in the negative -x direction.



• Carriers move toward regions of lower concentration, so diffusion current densities are proportional to the negative of the carrier gradient.

Diffusion currents in the presence of a concentration

gradient.

2

2

A/cm )(

A/cm )(

x

nqD

x

nDqj

x

pqD

x

pDqj

nndiffn

ppdiffp

Diffusion current density equations



• Dp and Dn are the hole and electron diffusivities with units cm2/s. Diffusivity and mobility are related by Einsteins’s relationship:

• The thermal voltage, VT = kT/q, is approximately 25 mV at room temperature. We will encounter VT many times throughout this course.

Dn

n

kT

q

Dp

p

VT Thermal voltage

Dn nVT , Dp pVT


Total Current in a Semiconductor

• Total current is the sum of drift and diffusion current:

Tn n n

Tp p p

j q n qD

j

E

E

n

x

qx

qp

p D


Total Current in a Semiconductor

• Total current is the sum of drift and diffusion current:

Rewriting using Einstein’s relationship (Dp = nVT),

Tn n n

Tp p p

j q n qD

j

E

E

n

x

qx

qp

p D

1

1

Tn n T

Tp p T

nj q n E V

n x

pj q p E V

p x

In the following sections, we will use these equations, combined with Gauss’ law, (E)=Q, to calculate currents in a variety of semiconductor devices.

Example here


Semiconductor Energy Band Model

Semiconductor energy band model. EC and EV are energy levels at the edge of the conduction and valence bands.




Electron participating in a covalent bond is in a lower energy state in the valence band. This diagram represents 0 K.

What happens as temperature increases?




Electron participating in a covalent bond is in a lower energy state in the valence band. This diagram represents 0 K.

Thermal energy breaks covalent bonds and moves the electrons up into the conduction band.


Energy Band Model for a Doped Semiconductor

Semiconductor with donor or n-type dopants. The donor atoms have free electrons with energy ED. Since ED is close to EC, (about 0.045 eV for phosphorous), it is easy for electrons in an n-type material to move up into the conduction band.


Energy Band Model for a Doped Semiconductor

Semiconductor with donor or n-type dopants. The donor atoms have free electrons with energy ED. Since ED is close to EC, (about 0.045 eV for phosphorous), it is easy for electrons in an n-type material to move up into the conduction band and create negative charge carriers.

Semiconductor with acceptor or p-type dopants. The aaacceptor atoms have unfilled covalent bonds with energy state EA. Since EA is close to EV, (about 0.044 eV for boron), it is easy for electrons in the valence band to move up into the acceptor sites and complete covalent bond pairs, and create holes – positive charge carriers.


Integrated Circuit Fabrication Overview

Top view of an integrated pn diode.


Integrated Circuit Fabrication (cont.)

(a) First mask exposure, (b) post-exposure and development of photoresist, (c) after SiO2 etch, and (d) after implantation/diffusion of acceptor dopant.


Integrated Circuit Fabrication (cont.)

(e) Exposure of contact opening mask, (f) after resist development and etching of contact openings, (g) exposure of metal mask, and (h) After etching of aluminum and resist removal.

NJIT ECE-271 Dr. S. Levkov Chap 2 - 1 ECE 271 Electronic Circuits I Topic 2 Semiconductors Basics.

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