ECE 250 – Electronic Devices 1

ECE 250

Electronic Device Modeling

ECE 250 – Electronic Devices 2

Introduction to Semiconductor Physics

• You should really take a semiconductor device physics course.

• We can only cover a few basic ideas and some simple calculations.

ECE 250 – Electronic Devices 3

Electronic Devices

• Most electronic devices are made out of semiconductors, insulators, and conductors.

• Semiconductors– Old Days – Germanium (Ge)

– Now – Silicon (Si)

– Now – Gallium Arsenide (GaAs) used for high speed and optical devices.

– New – Silicon Carbide (SiC) – High voltage Schottky diodes.

ECE 250 – Electronic Devices 4

Elements

• Elements in the periodic table are grouped by the number of electrons in their valence shell (most outer shell).– Conductors – Valence shell is mostly empty (1

electron)– Insulators – Valence shell is mostly full– Semiconductors – Valence shell is half full

(Or is it half empty?)

ECE 250 – Electronic Devices 5

Semiconductors

• Silicon and Germanium are group 4 elements – they have 4 electrons in their valence shell.

Si

Valence Electron

ECE 250 – Electronic Devices 6

Silicon

• When two silicon atoms are placed close to one another, the valence electrons are shared between the two atoms, forming a covalent bond.

Si

Covalent bond

Si

ECE 250 – Electronic Devices 7

Silicon

Si SiSi

Si

Si

ECE 250 – Electronic Devices 8

SiliconSi SiSi

Si

Si

•An important property of the 5-atom silicon lattice structure is that valence electrons are available on the outer edge of the silicon crystal so that other silicon atoms can be added to form a large single silicon crystal.

ECE 250 – Electronic Devices 9

Si Si Si Si Si Si

Si Si Si Si Si Si

Si Si Si Si Si Si

Si Si Si Si Si Si

Si Si Si Si Si Si

ECE 250 – Electronic Devices 10

Si Si Si Si Si Si

Si Si Si Si Si Si

Si Si Si Si Si Si

Si Si Si Si Si Si

Si Si Si Si Si Si

•At 0 ºK, each electron is in its lowest energy state so each covalent bond position is filled.•If a small electric field is applied to the material, no electrons will move because they are bound to their individual atoms.=> At 0 ºK, silicon is an insulator.

ECE 250 – Electronic Devices 11

Silicon

• As temperature increases, the valence electrons gain thermal energy.

• If a valence electron gains enough energy, it may break its covalent bond and and move away from its original position.

• This electron is free to move within the crystal.

ECE 250 – Electronic Devices 12

Si Si Si Si Si Si

Si Si Si Si Si Si

Si Si Si Si Si Si

Si Si Si Si Si Si

Si Si Si Si Si Si

+

-

ECE 250 – Electronic Devices 13

Si Si Si Si Si Si

Si Si Si Si Si Si

Si Si Si Si Si Si

Si Si Si Si Si Si

Si Si Si Si Si Si

+

-

Since the net charge of a crystal is zero, if a negatively (-) charged electron breaks its bond and moves away from its original position, a positively charged “empty state” is left in its original position.

ECE 250 – Electronic Devices 14

Semiconductors• As temperature increases, more bonds are

broken creating more negative free electrons and more positively charged empty states. (Number of free electrons is a function of temperature.)

• To break a covalent bond, a valence electron must gain a minimum energy Eg, called the energy band gap. (Number of free electrons is a function of Eg.)

ECE 250 – Electronic Devices 15

Insulators

• Elements that have a large energy band gap of 3 to 6 eV are insulators because at room temperature, essentially no free electrons exist.

• Note: an eV is an electron volt. It is the amount of energy an electron will gain if it is accelerated through a 1 volt potential.

ECE 250 – Electronic Devices 16

Electron Volt

joulescoulomb

joulecoul

voltcouleV

19

19

19

10602.1

110602.1

110602.11

Also, 1 eV = 1.518 10-22 BTU, but who cares.

ECE 250 – Electronic Devices 17

Conductors

• Elements that have a small energy band gap are conductors.

• These elements have a large number of free electrons at room temperature because the electrons need very little energy to escape from their covalent bonds.

ECE 250 – Electronic Devices 18

Semiconductors

• Semiconductors have a band gap energy of about 1 eV– Silicon = 1.1 eV– GaAs = 1.4 eV– Ge = 0.66 eV

ECE 250 – Electronic Devices 19

Empty States

• An electron that has sufficient energy and is adjacent to an empty state may move into the empty state, leaving an empty state behind.

ECE 250 – Electronic Devices 20

Si Si Si Si Si Si

Si Si Si Si Si Si

Si Si Si Si Si Si

Si Si Si Si Si Si

Si Si Si Si Si Si

+

Empty state originally here.

This electron can fill the empty

state.

ECE 250 – Electronic Devices 21

Si Si Si Si Si Si

Si Si Si Si Si Si

Si Si Si Si Si Si

Si Si Si Si Si Si

Si Si Si Si Si Si

+

Empty state now here.

ECE 250 – Electronic Devices 22

Si Si Si Si Si Si

Si Si Si Si Si Si

Si Si Si Si Si Si

Si Si Si Si Si Si

Si Si Si Si Si Si

+

ECE 250 – Electronic Devices 23

Si Si Si Si Si Si

Si Si Si Si Si Si

Si Si Si Si Si Si

Si Si Si Si Si Si

Si Si Si Si Si Si

+

ECE 250 – Electronic Devices 24

Empty States

• Moving empty states can give the appearance that positive charges move through the material.

• This moving empty state is modeled as a positively charged particle called a hole.

• In semiconductors, two types of “particles” contribute to the current: positively charged holes and negatively charged electrons.

ECE 250 – Electronic Devices 25

Carrier Concentrations

• The concentrations of holes and free electrons are important quantities in the behavior of semiconductors.

• Carrier concentration is given as the number of particles per unit volume, or

• Carrier concentration = 3

#cm

ECE 250 – Electronic Devices 26

Intrinsic Semioconductor

• Definition – An intrinsic semiconductor is a single crystal semiconductor with no other types of atoms in the crystal. – Pure silicon– Pure germanium– Pure gallium arsenide.

ECE 250 – Electronic Devices 27

Carrier Concentration

• In an intrinsic semiconductor, the number of holes and free electrons are the same because they are thermally generated.

• If an electron breaks its covalent bond we have one free electron and one hole.

• In an intrinsic semiconductor, the concentration of holes and free electrons are the same.

ECE 250 – Electronic Devices 28

Intrinsic Semiconductors

• = the concentration of free electrons in an intrinsic semiconductor.

• = the concentration of holes in an intrinsic semiconductor.

in

ECE 250 – Electronic Devices 29

Intrinsic Carrier Concentration

• B and Eg are determined by the properties of the semiconductor.

• Eg = band gap energy (eV)

• B = material constant

KT

EgBTni 2

exp23

23

3

#

Kcm o

ECE 250 – Electronic Devices 30

Intrinsic Carrier Concentration

• T = temperature (ºK)

• K = Boltzmann’s constant = 86.2×10-6 eV/ºK

KT

EgBTni 2

exp23

ECE 250 – Electronic Devices 31

Material Constants

Material Eg (eV) B

Silicon 1.12 5.231015

Gallium Arsenide

1.4 2.101014

Germanium 0.66 1.661014

23

3

#

Kcm o

ECE 250 – Electronic Devices 32

Important Note:Book uses a slightly different

Notation!

KT

EgBTni exp3

ECE 250 – Electronic Devices 33

Book Material Constants

Material Eg (eV) B

Silicon 1.12 5.41031

36

#

Kcm o

ECE 250 – Electronic Devices 34

Example

• Find the intrinsic carrier concentration of free electrons and holes in a silicon semiconductor at room temperature.

ECE 250 – Electronic Devices 35

MathCAD

eV 1.602 1019 coul 1 volt KB 86.2 10

6eV

K

T 300 KBsi 5.23 10

151

cm3

K1.5

Egsi 1.12 eV

ECE 250 – Electronic Devices 36

MathCAD

ni Bsi T1.5 exp

Egsi

2 KB T

ni 1.5 1010

1

cm3

The concentration of silicon atoms in an intrinsic semiconductor is 51022 atoms/cm3.

ECE 250 – Electronic Devices 37

Extrinsic Semiconductors

• Since the concentrations of free electrons and holes is small in an intrinsic semiconductor, only small currents are possible.

• Impurities can be added to the semiconductor to increase the concentration of free electrons and holes.

ECE 250 – Electronic Devices 38

Extrinsic Semiconductors

• An impurity would have one less or one more electron in the valance shell than silicon.

• Impurities for group 4 type atoms (silicon) would come from group 3 or group 5 elements.

ECE 250 – Electronic Devices 39

Extrinsic Semiconductors

• The most common group 5 elements are phosphorous and arsenic.

• Group 5 elements have 5 electrons in the valence shell.

• Four of the electrons fill the covalent bonds in the silicon crystal structure.

• The 5th electron is loosely bound to the impurity atom and is a free electron at room temperature.

ECE 250 – Electronic Devices 40

Si Si Si Si Si Si

Si Si Si Si Si Si

Si Si P Si Si Si

Si Si Si Si Si Si

Si Si Si Si Si Si

-

ECE 250 – Electronic Devices 41

Extrinsic Semiconductors

• The group 5 atom is called a donor impurity since it donates a free electron.

• The group 5 atom has a net positive charge that is fixed in the crystal lattice and cannot move.

• With a donor impurity, free electrons are created without adding holes.

ECE 250 – Electronic Devices 42

Extrinsic Semiconductors

• Adding impurities is called doping.

• A semiconductor doped with donor impurities has excess free electron and is called an n-type semiconductor.

ECE 250 – Electronic Devices 43

Extrinsic Semiconductors

• The most common group 3 impurity is boron which has 3 valence electrons.

• Since boron has only 3 valence electrons, the boron atom can only bond with three of its neighbors leaving one open bond position.

ECE 250 – Electronic Devices 44

Si Si Si Si Si Si

Si Si Si Si Si Si

Si Si B Si Si Si

Si Si Si Si Si Si

Si Si Si Si Si Si

ECE 250 – Electronic Devices 45

Extrinsic Semiconductors

• At room temperature, silicon has free electrons that will fill the open bond position, creating a hole in the silicon atom whence it came.

• The boron atom has a net negative charge because of the extra electron, but the boron atom cannot move.

ECE 250 – Electronic Devices 46

Si Si Si Si Si Si

Si Si Si Si Si Si

Si Si B Si Si Si

Si Si Si Si Si Si

Si Si Si Si Si Si

+

ECE 250 – Electronic Devices 47

Extrinsic Semiconductors

• Since boron accepts a valence electron, it is called an acceptor impurity.

• Acceptor impurities create excess holes but do not create free electrons.

• A semiconductor doped with an acceptor impurity has extra holes and is called a p-type semiconductor.

ECE 250 – Electronic Devices 48

Carrier Concentrations

• For any semiconductor in thermal equilibrium nopo=ni

2, where

• no = the concentration of free electrons.

• po = the concentration of holes.

• ni = the intrinsic carrier concentration

KT

EgBTni 2

exp23

ECE 250 – Electronic Devices 49

Extrinsic Carrier Concentrations

• For an n-type semiconductor with donor impurities, the concentration of donor impurities is Nd with units #/cm3.

• If Nd >> ni, then the concentration of free electrons in the n-type semiconductor is approximately no Nd.

ECE 250 – Electronic Devices 50

Extrinsic Carrier Concentrations

• Since nopo=ni2 for any semiconductor in thermal

equilibrium, and• For an n-type semiconductor, no Nd

• Where po is the concentration of holes in the n-type semiconductor.

d

io N

np

2

ECE 250 – Electronic Devices 51

Extrinsic Carrier Concentrations

• For a p-type semiconductor with acceptor impurities, the concentration of acceptor impurities is Na with units #/cm3.

• If Na >> ni, then the concentration of holes in the p-type semiconductor is approximately po Na.

ECE 250 – Electronic Devices 52

Extrinsic Carrier Concentrations

• Since nopo=ni2 for any semiconductor in thermal

equilibrium, and• For a p-type semiconductor, po Na

• Where no is the concentration of free electrons in the p-type semiconductor.

a

io N

nn

2

ECE 250 – Electronic Devices 53

Current in Semiconductors

• The two processes that cause free electrons and holes to move in a semiconductor are drift and diffusion.

• Drift – the movement of holes and electrons due to an electric field

• Diffusion – the movement of holes and electrons due to variations in concentrations.

ECE 250 – Electronic Devices 55

Drift Current-Electrons

• Electrons – The Electric field creates a force in the opposite direction of the electric field – Attractive.

• vdn is the drift velocity of electrons.

• Jn is the current density due to electrons.

E

dnv� e

nJ

n-type

ECE 250 – Electronic Devices 56

Drift Current-Electrons

• The electrons acquire a drift velocity of

• Where n is the mobility of electrons with units of cm2/(volt-sec).

• The units of vdn are cm/sec.• For low-doped silicon, a typical number is

n=1350 cm2/volt-sec.

Ev ndn

�

ECE 250 – Electronic Devices 59

Drift Current Density-Electrons

• e = the charge on an electron = 1.60210-19 coulombs.

• n=concentration of electrons = #/cm3.en=charge/cm3.

EenenvJ ndnn

223 sec

charge

seccm

charge

cm

amp

cm

cmenvdn

ECE 250 – Electronic Devices 60

Drift Current - Holes

• Holes – The Electric field creates a force in the same direction of the electric field.

• vdp is the drift velocity of holes.

• Jp is the current density due to holes.

E

dpvh

pJ

n-type

ECE 250 – Electronic Devices 61

Drift Current-Holes• The holes acquire a drift velocity of

• Where p is the mobility of holes with units of cm2/(volt-sec).

• The units of vdp are cm/sec.• For low-doped silicon, a typical number is

dp=480 cm2/volt-sec.

Ev pdp

�

ECE 250 – Electronic Devices 63

Drift Current Density-Holes

• e = the charge on an electron = 1.60210-19 coulombs.

• p=concentration of holes = #/cm3.ep=charge/cm3.

EepepvJ pdpp

223 sec

charge

seccm

charge

cm

amp

cm

cmenvdp

ECE 250 – Electronic Devices 64

Drift Current

E

dpvh

pJ

n-type

E

dnv� e

nJ

n-type

Drift current due to holes and electrons is in the same direction.

ECE 250 – Electronic Devices 65

Total Drift Current

• Since the hole current and the electron current are in the same direction, the currents add.

• The total drift current is:

EepEenJ pn

ECE 250 – Electronic Devices 66

Ohm’s Law

• Another form of Ohm’s law is J=E is the conductivity of the material.

• Noting that

• and

EepEenJ pn

EJ

ECE 250 – Electronic Devices 67

Conductivity

We can find the conductivity of a semiconductor as

pn epen

ECE 250 – Electronic Devices 68

Diffusion Currents

(Cover Them)

ECE 250 – Electronic Devices 69

Excess Carriers

• So far we have assumed that the semiconductor is in steady state.

• Suppose that we shine light on a semiconductor.

• If the photons have sufficient energy, valence electrons may break their covalent bonds and create pairs of free electrons and holes.

ECE 250 – Electronic Devices 70

Excess Carriers• These additional holes and electrons are

called excess holes (δp) and excess free electrons (δn).

• When excess holes and free electrons are created, these concentration of holes and free electrons increase above the thermal equilibrium value

n = no+ δn p = po + δp

ECE 250 – Electronic Devices 71

Excess Carriers

• In steady state, the generation of excess carriers will not cause the carrier concentration to increase indefinitely due to a process called recombination.

• Electron-Hole Recombination – a free electron combines with a hole and both disappear.

ECE 250 – Electronic Devices 72

Excess Carriers

• Generation – Creates free electrons – hole pairs.

• Recombination – Eliminates free electrons and holes in pairs.

• Excess Carrier Lifetime – The mean time over which an excess free electron and hole exist before recombination.