Modern Semiconductor DevicesSummer Semester 2010Prof. Dr.-Ing. Hermann Schumacher

H. Schumacher | 23.04.10 | Modern Semiconductor Devices

Title graphics: http://www.wirelessdesignmag.com/images/0512/wd511_f2_1_lrg.jpg

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In this lecture ...

we will review Silicon as a semiconductor material, along with some basics in semiconductor physics.

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All semiconductors ...

… are crystalline structures with atoms arranged periodically in a lattice

Graphics: http://newton.ex.ac.uk/research/qsystems/people/sque/images/diamond-conventional-unit-cell.gif

a0: lattice constant

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Periodic potential as the origin of the forbidden gap

Now assume:Outer electron leaves its host atom and moves through the lattice.

EC: conduction bandEV: valence band

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Energy band structure - definitions

Conduction band EC

Vacuum level Evac

Valence band EV

In a semiconductor:

Conduction band empty at T=0K,partially filled with electrons atT>0K.

No allowed energy states in thebandgap for pure semiconductors.

Valence band completely filled atT=0K, partially filled at T>0K.

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Energy band structure - definitions

Conduction band EC

Vacuum level Evac

Valence band EV

electron affinity χ

bandgap energy Eg

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Semiconductor materials in the periodic table of elements

Single-element semiconductorsfrom the fourth column

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Semiconductor materials in the periodic table of elements

“III-V” compound semiconductorswill be discussed later.

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Key advantages of SiliconSilicon

Cheap, supply almost limitless

Mechanically robust

High thermal conductivity

Most important: highly stable native oxide

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Use of SiO2 in a MOSFET

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Band gap of selected solids

Material Band Gap Property

Ge 0.68 eV Semiconductor

Si 1.12 eV Semiconductor

0.36 eV Semiconductor

NaCl 8.97 eV

Sn 0.00 eV Metal

C 5.4 eV

ZnSe

GaN

GaAs

InSb

Semiconductor1.42 eV

Semiconductor

Semiconductor

3.4 eV

2.71 eV

Insulator

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Density of states

EC, EV are boundaries, not exact energy levels.

The bands are made up of a dense distribution of energy levels.

Integral over the energy distributions: density of states in the conduction band (EC) and valence band (EV).

The densities of states are material properties.

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Intrinsic carrier density

Consider a perfectly pure semiconductor at T>0K:

Thermal excitation of electron from valence band to conduction band: creation of free (unbound) electron creation of defect electron (hole) in valence band – also unbound.

Density of electrons and holes:

Boltzmann's constant

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Doping

Doping is the deliberate introduction of foreign elementsinto the lattice.

Example:As atom (Vtht

column) replaces Si atom (IVth column)

Extra electron in the outer shell, not needed for chemical bondavailable as free electron in the conduction band,n-type doping.

Creation of ionized donor (fixed charge) locatedjust below the conduction band.

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Doping

Doping is the deliberate introduction of foreign elementsinto the lattice.

Example:B atom (IIIrdt

column) replaces Si atom (IVth column)

Not enough electrons in outer shell for chemical bond,defect electronavailable as free hole in the valence band,p-type doping.

Creation of ionized acceptor (fixed charge) locatedjust above the valence band.

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Doping

Mass action law: n⋅p=ni2 also in doped semiconductors.

ND≫ni or NA≫ni

Typical assumptions:

all doping atoms are ionized (cf. activation energy to thermal energy kT)

doping concentrations far exceed the intrinsic carrier concentration

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Doping - example

Arsenic doping, 1017 cm -3 – compare total density of Si atoms in lattice: 5 x 1022 cm-3

intrinsic carrier density of Si: 1.5 x 1010 cm-3

Hence: n ≈ ND = 1017 cm-3 free electrons – majority carriers

Hole density – use mass action law:

Holes are here the minority carriers.

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Fermi energy

Fermi-Dirac statistics describes the likelihood of a permissible state to be occupied.

Parameter EF: Fermi energy

In a semiconductor in thermodynamic equilibrium: EF=const.

Also called “electrochemical potential of the electron”.

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Fermi-Dirac Function

-0.10 -0.05 0.00 0.05 0.100.0

0.2

0.4

0.6

0.8

1.0

kTE

Aeef

+=

11)(

Temperature 5K 20K 50K 100K 300K 600K

Dis

tribu

tion

f(E)

Energy (eV)

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Fermi-Dirac and Boltzmann DistributionsCommonly: Fermi-Dirac distribution approximated by the Boltzmann distribution:

f E = 1

1eE−EF

kT

≈e−E−EF

kT

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Specific locations of the Fermi energy in the band gap

Using the Boltzmann approximation:

in an intrinsic semiconductor:

in an n-type doped semiconductor:

in a p-type doped semiconductor:

EC

EV

n-typekT ln

NC

ND

kT lnNV

N Ap-type

intrinsic

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Things you need to remember ...

Drawing band diagrams will be a frequent task in this course – band diagrams are essential to the understanding of semiconductor device concepts.

At this point, you should be able to

distinguish between intrinsic and doped semiconductors

understand the importance of the Fermi energy

calculate the position of valence and conduction band with respect to the Fermi energy

calculate majority and minority carrier concentrations for doped semiconductors.