ENG2000: R.I. Hornsey Semi: 1 Engineering 2000 Chapter 8 Semiconductors.

ENG2000: R.I. Hornsey Semi: 1

Engineering 2000 Chapter 8Semiconductors


Overview• We need to know the electrical properties of Si• To do this, we must also draw on some of the

physical properties and we return to our ideas about atomic bonding

• These will enable us to understand the difference between: insulators conductors metals

• As a start, we can try to answer a seemingly unrelated question why is a diamond transparent?


Why is a diamond transparent?• The process required to answer this question

brings out several points which we can then apply to Si

• So, transparent to what? We usually mean “visible light” but we have to a bit more specific photons pf a particular energy Ephoton = hc/ light: 400nm < < 700nm giving Ephoton ≈ 4 x 10-19J = 2.5eV

(recall, 1eV = 1.6 x 10-19J)


• So we can now say that diamond does not absorb photons with energies corresponding to visible light. So what would happen if a photon was absorbed?

• Since the nucleus of the atoms is very small compared to the overall diameter, we would expect the photon to be absorbed by transferring the energy to the electrons

• Electrons tightly bound to the nucleus cannot readily change states so the photon energy is mostly given to the outer electrons


• Since the same electrons are also involved with bonding – we’ll get to that soon – photon are only absorbed if they have enough energy to break the bonds

• So a very simplistic picture of the variation of light absorption with photon energy might look like:

EphotonEbond

% absorbed


• The idea we have formed is that an electron can be moved between two states: “loose” and “bound”

• For diamond, Ebond is approximately 7eV which is a wavelength of about 180nm (x-ray)

• The source of energy to provide Ebond does not have to be optical, it could be thermal “electrical”

• Once the electron is “freed” from the bond, it could move if a voltage was applied. The diamond could then conduct electricity

Ebond


• If we try to obtain Ebond from thermal excitation, the energy available is of the order of kT k = Boltzmann constant = 1.38 x 10-23 J/K T = absolute temperature in K (kT = 25.9meV at room temperature)

• Since this is much less than Ebond, we can assume that diamond is a good insulator

• Important assumptions we made above include material is a perfect crystal electrons are in bonds that can be broken electrons can become loose enough to conduct

• We can now look at some of these issues in a bit more detail and for Si now rather than diamond [By the way, the reasons why gases and liquids are

transparent are not the same ... ]


Energy levels• Recall the silicon COVALENT BONDING that

arose from the sharing of the outer electrons• A simple – but incorrect – view of the energy

levels would now be:

• We might now also imagine that we can create a “loose” electron by supplying enough energy to move an electron from 3 to 4

• This is essentially a good picture; we will refine it further in a little while

4

3

2

1

original electron

shared electron


More on bonding• If this picture of the energy levels is really true

then we would get optical absorption only at a single wavelength because the electron can only be at an existing allowed

energy level

• Since optical absorption occurs for a large range of photon energies above the critical value, the upper level must in fact be a band of energy

• You can imagine that any of the photon energy left over after breaking the bond gives the “loose” electron some energy which will later be released as heat


Band diagram• A better picture of the allowed energies of the

electrons would therefore be:

• This is a vital and standard representation – it is called the BAND DIAGRAM of a material.

EC

EV

EG

x

energy


• The “forbidden” region between the bands – the energy required to “free” the electron from the bond – is formally called the BAND GAP, EG, of the material

• Since we presume that the “free” electrons can move – can contribute to electrical conduction – the upper band is known as the CONDUCTION BAND, EC

• The lower band is called the VALENCE BAND, EV, because it arises from the valence (outer) electrons of the atom


The differences …• So now we can formally state the differences

between insulators, semiconductors and conductors

• The terms insulator, semiconductor and conductor are based on everyday experience the energy to get an electron into the conduction band is

usually gained from thermal energy

• An insulator is therefore a material for which the band gap is large compared with kT e.g. diamond with EG = 7eV

• A semiconductor is a material for which the band gap is medium! e.g. Si (1.1ev), Ge (0.7eV), GaAs (1.4eV)


• And a conductor has essentially no energy gap• A metal is not bonded covalently and we don’t

think of it as having a band gap at all while it is possible to think in terms of energy bands, the

conduction and valence bands of a metal overlap, allowing free transition of electrons

• HOWEVER, we have not yet determined the origin of the energy bands ...

• There are several levels of explanation, from handwaving to a full quantum-mechanical treatment! we will look at the handwaving argument!


Formation of bands• The easiest way to think of the formation of

bands is due to interactions between the shared electrons in the covalent bonds

• A conceptual picture would look something like:

[note: it doesn’t have to be the same electron in the same bond – they can swap over provided there is no net movement]


• [Don’t worry about the handwavyness of these pictures – this is the way everyone thinks of things! The real situation is very complex and only weird people like chemists do the whole treatment]

• Now, the electrons in the bonds interact due to electrostatic (Coulomb) forces

• The strength of the interactions depends on the electrons’ separations which are not constant.

• Therefore the energy level associated with these bonds broadens into a band all the levels for all the atoms in the material are slightly

different from each other, but lie in a defined range


• The same is true for all of the atomic levels – they all form bands, including the “loosely” bound outer levels we think of as being “free”

• Obviously, the amount of interaction between electrons in different atoms depends on how close the atoms are to each other

from Callister


• In fact, the band gap etc of semiconductors can be changed by STRAINING the material i.e. changing the inter-atomic distance

• This is an important area of advanced semiconductor research for materials such as SiGe alloys


Electrons and holes• When the electron is excited to the conduction

band – by whatever means – it leaves behind a space

• This is called a HOLE:

EC

EV

EG

hole


• In our bonding picture, this looks like:

• Just like electrons in the conduction band, holes in the valence band are mobile and act just like positive particles (with +e of charge) except that they cannot exist outside a

material– a hole is the absence of an electron

hole

e-

Si


• Electrical conduction in a semiconductor therefore involves the movement of both holes and electrons electrons in the conduction band holes in the valence band

• We can picture the motion of a hole as follows:

http://www.vislab.usyd.edu.au/photonics/devices/semic/images/car_hole_an.gif


hole

e-

+ –

QuickTime™ and aGraphics decompressor

are needed to see this picture.

http://www.vislab.usyd.edu.au/photonics/devices/semic/movies/electron_hole_move.mov

Si


Intrinsic semiconductor• A pure semiconductor is known as intrinsic

material because its properties are intrinsic to the Si

• One very important property of an intrinsic semiconductor is that electrons and holes can only be created in pairs termed electron-hole pairs (EHPs)

• And therefore must be present in equal numbers

• Mathematically, this is expressed as n = p = ni

n = concentration (or density) of electrons (# / cm3) in conduction band

p = concentration (or density) of holes (# / cm3) in valence band

ni = intrinsic carrier concentration


Recombination• The opposite of electron-hole pair generation is

also important to maintain the steady-state balance i.e. equilibrium

• When an electron and hole meet, they can recombine with the release of energy usually heat in Si, but could be light in other materials

• This is shown the band diagram as:

EC

EV

EG


• For this simple situation we can say that the rate of recombination, ri, is proportional to: n0 ( the equilibrium electron concentration)

p0 ( the equilibrium hole concentration)

• Thus ri = const. x n0p0 = const. x ni2

• n0p0 = ni2 is a fundamental equation for

semiconductors rather confusingly known as the mass action law

• In steady state, this must also equal the rate of generation of e-h pairs, gi

• Recombination is a very important mechanism in many devices, including anything with a p-n junction in it It may take many forms and may emit useful things, like light in

LEDs for example


Conduction• So, our picture of the energy bands now allows

us to say that conduction can take place when electron-hole pairs are created which usually occurs under illumination – photoconductivity

– or by temperature

• At room temperature, the number of e-h pairs (= ni) is about 1.5 x 1010 cm-3 for Si there are >1022 Si atoms per cm3! comparable for metals, where all electrons conduct

• But if kT ≈ 25meV and EG = 1.1eV, why are there any e-h pairs at all in the dark? because kT is the average thermal energy; some electrons

have much more and this relatively small number that does the conduction


• The net result is that intrinsic Si is not a good conductor at room temperature unless it is illuminated.

• This appears in the values of the resistivity, a material property enabling resistance to be calculated by R = l/A: Si: = 2.3 x 105 Ωcm diamond: ~ 1016 Ωcm metal: = 2 x 10-6 Ωcm

• We need to find a way to control this ...


Doping • Probably the most useful property of

semiconductors is the ability to control the conductivity ( = 1/)

• In fact, what we will control directly is the carrier concentrations

• To do this, we somehow have to escape from the limitations of the intrinsic material

• The aim, therefore, is to gain extra charge carriers (electrons and/or holes) at room temperature

• This is achieved by adding impurities into the Si crystal lattice - which is called DOPING


• The resultant doped material is now known as EXtrinsic because the material’s properties are now dependent on the

impurities rather than its intrinsic properties

• Moreover, we can control the doping so that a material can have more electrons or more holes

• The equilibrium electron and hole concentrations are denoted by n0 and p0 as before

• n and p are now the instantaneous – non steady state – values


N-type material• A semiconductor with an excess of electrons is

called n-type we will see later that this does not mean that there are no

holes

• n-type extrinsic Si is obtained by adding in a material such as phosphorus (P), arsenic (As) or antimony (Sb) into the lattice.

• These are Group V elements each of these elements likes to bond with 5 bonds

• In the Si crystal, however, the dopant atoms are forced to bond with the 4 bonds preferred by Si atoms


• This leaves a “spare” bond, and hence an extra, “free” electron

• The bonding picture of this process looks like:

• Therefore, we can “add” electrons to the conduction band - this type of dopant is called a DONOR

e-

P

Si


• It still takes a little energy to separate the electron from the donor atom, so the band diagram looks like:

EC

EV

EG

EC

EV

EG

ED ED

T = 0K T ≈ 50K

Donors become positively ionised


Activating dopants• Because we still need this small energy (30 -

60meV), at T = 0K there will be no electrons in the conduction band

• At higher temperatures (> ~50K), most of the donors will be ionized when the donor atom contributes its electron to the

conduction band, it becomes positively charged

• This is an important point to note; when the electron has left the donor, the principle of charge neutrality says that the remaining dopant is positively charged we cannot, therefore, gain charges but the electron is mobile

while the ionized donor is fixed.


P-type material• The complement to n-type material is p-type,

which has an excess of holes which are mobile in the valence band

• By analogy with n-type, we can dope Si to be p-type by adding an impurity element with only 3 bonds such dopants include boron (B), aluminium (Al), gallium (Ga)

and indium (In)


• In the bonding picture, this is represented by:

hole

B

Si


• Since the dopant atom is missing a bond, it can accept an electron which is the same as adding a hole.

• This type of dopant is therefore called an acceptor

• Again, it takes a little energy to force the electron from the valence band onto the acceptor atom, so the band diagram at T > 0K is:

EC

EV

EGEA

T ≈ 50K

Ea - Ev = 30 - 60meV

Acceptors become negatively ionised


• The type of doping described above for Si is known as substitutional doping because the dopant atom substitutes for a Si atom

• Typical dopant concentrations are 1016 - 1020 cm-3

• At room temperature, almost all dopants are ionized so doping changes the carrier concentration by 6 – 10 orders of magnitude

• The terminology for carriers in n-type or p-type materials is

electrons holes

n-type majority minority

p-type minority majority


Conductivity• Once they are able to move, electrons and holes

can contribute to electrical conduction• The current they can carry depends on

how many carriers how fast they move how much charge they carry

• So

where J = current density (A/cm2), and q is the electronic charge

note: vn and vp are in opposite directions because the charges are opposite

€

J n =nqvnJ p=pqvp


€

v=με

€

vn =−μnε

vp=+μpε

Mobility• At low electric fields, the carrier velocity is

proportional to the applied field

• The constant of proportionality (as defined above) is called the MOBILITY

• Hence:

• So the total current density is

• Where is the electrical conductivity for Si, n = 1350 cm2/Vs, p = 480 cm2/Vs

€

J =q nμn+pμp( )ε=σε=ερ


Electron drift• The electrons have two components of velocity• Thermal velocity is very high

~107 cm/s but has no net direction and contributes nothing to a current

• The net drift imposed by the applied electric field is what leads to the current flow drift velocity is of the order of 1 cm/s


Temperature dependence• Like many energy-activated processes, the

variation of ni with temperature is exponential

• The variation of ni with temperature is shown on the next slide …

• Followed by n(T) for an extrinsic material

€

ni =const×e−EG 2kT


From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap (© McGraw-Hill, 2002)http://Materials.Usask.Ca

Fig. 5.16: The temperature dependence of the intrinsicconcentration.

Si

Ge

GaAs

0 °C200 °C400 °C600 °C 27 °CLLLL

1018

1 1.5 2 2.5 3 3.5 41000/T (1/K)

1015

1012

103

106

109 1.45×1010 cm-3

2.4×1013 cm-3

2.1×106 cm-3Intrinsic Concentration (cm-3)

Intrinsic carrier concentration, ni (cm-3)


ln(n)

1/T

Ti

Ts

Intrinsic

Extrinsic Ionization

ni(T)

ln(Nd)slope = -ΔE/2k

slope = -Eg/2k


Fig. 5.15: The temperature dependence of the electronconcentration in an n-type semiconductor.

dopants are activated as T > 50 - 100K so carrier concentration increases

provided Nd >> ni the number of carriers is dominated by Nd

At very high temperatures, ni increases beyond Na


€

p0 +ND+ =n0 +NA

−

Charge neutrality• Earlier on, we said that when a donor gives up its

electron to the conduction band it becomes positively charged

• More generally, we can say that whatever we do with doping – n, p or both – the material must remain electrically neutral

• Thus in all circumstances

• A result of this is that a material doped equally with donors and acceptors at the same time becomes intrinsic again!


Application to p-n diode

+ –

+–

hole flow

electron flow

recombination zone

depletion zone

zero bias

forward bias

reverse bias

hole

electron


Diode I-V characteristic

Fig.6.4: Schematic sketch of the I-V characteristics of Ge, Si andGaAs pn Junctions


G e S i G a A s

C u r r e n t

V o l t a g e~ 0 . 1 m A

0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0


Summary• We have scratched the surface of how

semiconductors work the picture is much more complex than we have assumed and these complexities are actually important in how practical

devices are made

• We have learned how to distinguish conductors, insulators and semiconductors in terms of their band structure

• And we now know control the carrier concentrations and hence the conductivity

• The next step, were we to take it, would be to use the band diagrams for different pieces of semiconductor to design devices such as transistors

ENG2000: R.I. Hornsey Semi: 1 Engineering 2000 Chapter 8 Semiconductors.

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Transcript of ENG2000: R.I. Hornsey Semi: 1 Engineering 2000 Chapter 8 Semiconductors.