Baca A.G., Ashby C.I.H. Fabrication of GaAs Devices

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Semiconductor properties

a solid are derived from the physical equations governing elec-

trical charges through the interactions of protons and electrons in

the solid. Solid materials come in three types of atomic ordering:

amorphous, poly-crystalline and single crystal. Useful semicon-

ductor properties are most often obtained from single crystal or

polycrystalline solids, though amorphous Si is very important in

solar cell applications and display technology. The energy states

of many crystalline solids have been determined both theoretically

and experimentally. These energy states, the crystalline analogues

to energy levels in individual atoms, are commonly referred to as

the band structure of the material. The details of the band structure

of solids and its relation to the details of the crystalline lattice is the

subject of solid state physics; we have listed both introductory [6]

and advanced references [7]. In this section, some important semi-

conductor properties, concepts and equations will be introduced

at a very basic level. The concepts chosen are those that will lead

to a greater understanding of semiconductor contacts, the semi-

conductor surface, and devices such as the ﬁeld effect transistor

and the heterojunction bipolar transistor and issues related to their

interaction with processing techniques. No attempt will be made to

derive important equations and any attempt to explain these equa-

tions or certain physical concepts is only with the intent of later

introducing related device concepts. A minimum of topics will

be presented to enable a better understanding of semiconductor

materials, useful characterisation techniques, electronic devices

and common processing techniques. Our goal is not to provide

a comprehensive discussion but rather to introduce the reader to

relevant topics that may be pursued further using other resources,

if necessary.

2.2.1 Energy levels and band structure in semiconductors

Using the electron energy levels of atoms as a starting point, the

bonding of molecules will be extended to the case of solids. The

electrons are attracted to the protons in a nucleus due to elec-

trostatic forces but they are repelled from other electrons due to

these same forces. The energy level of an electron state is the

energy required to remove the electron to a position far away

from the atom (such that the electrostatic attraction with the nuc-

leus is negligible) and this energy state can be calculated from

the quantum-mechanical equations governing the system. From

quantum mechanics, it is found that the energy levels of electrons

in the atoms are organised into shells, beginning with those closest

to the nucleus of the atom. The ﬁrst shell can accommodate up to

two electrons in the 1s state. The second shell can accommodate

up to eight electrons, which are called the 2s and 2p states. The

Semiconductor properties

third shell accommodates up to two 3s electrons, six 3p electrons

and ten 3d electrons. Heavier atoms have additional shells. The

actual number of electrons in a neutral atom is equal to the num-

ber of protons in the nucleus. In the neutral atom’s ground (or

lowest energy) state, the electrons ﬁll each shell in sequence, with

the outermost shell being only partially ﬁlled up to the number of

available electrons. The difference between electron energy states

is much greater between shells than within a shell. Atomic energy

states are illustrated in FIGURE 2.1 for a three-shell atom.

FIGURE 2.1 An illustration of

electron energy states in an atom.

1s 1s

FIGURE 2.2 Energy levels of a

molecule are derived from the outer

atomic levels.

Molecules are built up from atoms by quantum mechanically

combining their atomic orbitals that correspond to the atomic

energy levels to produce molecular orbitals with different energy

levels. A chemical reaction accompanies this process leading to

pairing electrons in unﬁlled shells to lower the overall energy state.

Atoms with completely ﬁlled shells cannot lower their energy state

in this way and are generally unreactive. The process of forming a

molecule is illustrated in FIGURE 2.2. Paired electrons in bonding

orbitals have a lower energy state than the original electrons in the

atomic orbitals. Energy levels of the molecule are calculated by

similar methods as for atoms.

A solid can be thought of as an extremely large molecule, but it

is not useful to think of it that way because calculating and keeping

track of upward of 10

valence energy states per cubic centimetre

is very unwieldy. In the case of ordered solids, the calculation of

energy states is greatly simpliﬁed by crystalline symmetry. Gener-

ally speaking, the properties of a unit cell (with several to dozens

of atoms) is sufﬁcient to describe the whole crystalline solid, since

many of the properties can be accounted for by translation. Such

a calculation will give a “band structure” for a solid, so named

because large numbers of energy states are naturally grouped into

bands that can be related back to the atomic energy levels. Rather

than accounting for each paired electron energy state as is done

in molecular-energy-state descriptions, the energy states in an

ordered solid are classiﬁed according to the number of states in

a given energy range, which is termed the density of states. An

example of a band structure is shown in FIGURE 2.3.

Similar to the case for atomic energy or molecular states, the

lower lying energy “bands” describe the core electrons that are

localised to speciﬁc atoms (although this is not always obvi-

ous from band structure terminology). The upper lying energy

bands describe electrons (valence electrons) that form the chem-

ical bonds that hold the solid together. However, rather than

speciﬁc electrons being associated with speciﬁc chemical bonds,

many electrons in a given “band” are associated with many sim-

ilar chemical bonds. For example, in a two-atom molecule such

Semiconductor properties

4.5

ΛΓ Δ Γ

–2

–4

–6

–8

–10

GaAs

ΣX U,K

wave vector k

–12

energy (eV)

FIGURE 2.3 Band structure of GaAs. (Properties of GaAs, IEE, 1996,

reprinted with permission.)

as hydrogen ﬂuoride, the outermost valence electron of ﬂuor-

ine occupies an energy state shared with the hydrogen electron

to form a localised chemical bond. In a Cu solid, the outer-

most valence electron of many Cu atoms combine to form an

energy band that represents Cu-Cu chemical bonds. Each Cu bond

can be thought of as having localised character, but the band

describing those bonding electrons does not specify any partic-

ular origin of an electron occupying a particular state. Without

getting into a philosophical discussion of the implications of the

band-structure model for bonding, we will merely state that this

concept will have important implications when the band struc-

tures of insulators and conductors are contrasted later in this

section.

As is the case for atoms and molecules, electrons from the solid

occupy the available states starting with the lowest energies avail-

able. The states are shown in FIGURE 2.3 as energy states as

a function of k, which is a solid state analogue of the electron

momentum and has units of inverse length. Separately from the

energystates shown in FIGURE 2.3, one must account for the num-

ber or density of states at a given energy, since electrons are allowed

to occupy a state only if it is “empty”. The state-ﬁlling process

(a thought process only, since electrons in reality do not ﬁll the

states sequentially in time) proceeds until all available electrons

in the solid have ﬁlled the available states. These are the occu-

pied bands. At this point the electrical properties of the solid are

Semiconductor properties

determined by the character of the remaining unﬁlled bands and

their density of states.

Before describing the electrical implications of a given band

structure, a few qualitative comments about the band structure are

in order. In the band structure of a solid, as in atomic and molecular

states, transitions may occur from the occupied to the unoccupied

bands. These may occur in all of the usual ways: thermally assisted

(according to the equations governing the probability of a thermal

transfer with that energy separation), by absorption of radiation

or by inelastic charged-particle scattering. The occupied bands

are termed the valence bands, while the unoccupied bands are

called the conduction band, for reasons that will become apparent

shortly. At zero temperature and in the absence of transitions to

higher levels, the bands are ﬁlled strictly according to energy levels

from the lowest to the highest. The remaining unﬁlled levels may

be continuous with the ﬁlled levels or they may have an energy

gap separating ﬁlled and unﬁlled states. In the latter situation, no

electrical conduction can occur in the presence of an electric ﬁeld.

The reason for this situation is that an electron’s properties are

governed by its energy state and these states represent chemical

bonds whose attractive forces with atomic nuclei are greater than

an externally applied electric ﬁeld. At ﬁnite temperatures some

electrons have a reasonable probability of occupying upper states.

Due to ﬁnite temperature or the presence of transitions to higher

energy bands through photonic excitation or scattering, electrons

in these higher states may move in response to an external electric

ﬁeld. The reasons are two-fold. First, the non-valence states are

not associated with bonding (they are analogues of non-bonding,

or antibonding orbitals). Second, and perhaps more importantly,

the states in ordered solids tend to be delocalised over many atoms

and readily allow carriers to respond to an external ﬁeld. Rather

than dwell on this point or attempt to be more precise, it will be

taken as a given that electrons in upper states (higher than the

ground state) can respond to an electric ﬁeld. These states are

called conduction bands in the terminology of solid-state physics,

electrical engineering and materials science.

Unﬁlled valence band states can also conduct electrical current

in response to an electric ﬁeld, as will become apparent in the

discussion of “hole” conduction.

Ordered solids are grouped into conductors, insulators and semi-

conductors based on the energy separation of the valence and

conduction bands. Materials with no energy separation between

the valence and conduction bands are conductors (usually metals).

The energy bands form a single continuum in energy. Mater-

ials with large separation between the valence and conduction

bands are insulators. Those with intermediate energy separation

Semiconductor properties

TABLE 2.1 Bandgaps at 300 K.

Semiconductor Bandgap (eV) Semiconductor Bandgap (eV)

AlN 6.2 ZnS 3.8

AlP 2.43 ZnSe 2.58

AlAs 2.16 ZnTe 2.28

AlSb 1.6 CdS 2.53

GaP 2.25 CdSe 1.74

GaAs 1.42 CdTe 1.50

GaN 3.35 Si 1.12

GaSb 0.69 Ge 0.67

InAs 0.36 Ga

4.3

InN 1.89 Al

8–10

InP 1.28 SiO

InSb 0.17

are called semiconductors. The deﬁnition of the energy separation

of the valence and conduction bands is called the “bandgap”. As

a general guideline, conductors have bandgaps less than 0.2 eV,

semiconductors have bandgaps from 0.2 to about 4 eV, and insu-

lators have higher bandgaps. TABLE 2.1 lists some of the more

common semiconductors and their bandgaps. In practice some

insulators can be grown in the same crystal as semiconductors for

“bandgap engineering” and are then considered semiconductors.

An example of the latter is the aluminium nitride/gallium nitride

combination. AlN with abandgap of 6.2 eV is considered a ceramic

in many applications, but is also a semiconductor when combined

with GaN. Partly, these designations came from the early days

of electronics where one’s imagination as to how to use semi-

conductors was limited by prevailing materials technology. The

reality nowadays is that many insulators can be engineered to have

semiconducting properties.

Two more comments about semiconductor band structures (such

as that of FIGURE 2.3) are in order. First is the concept of direct

and indirect semiconductors. When the conduction minimum and

the valence-band maximum line up at the k = 0 (inverse length

units) momentum point, termed the Γ point, electrons and holes

can recombine directly with the emission of light and the semi-

conductor is termed direct, as is the case for GaAs and a number

of other III–V semiconductors. When the conduction band min-

imum does not line up in k with the valence band maximum, the

semiconductor is termed indirect and electrons at the conduction

band minimum recombine with holes in the valence band through

the emission of phonons (lattice vibrations) rather than light. Such

materials are indirect semiconductors. Second, the curvature of

the bands (the dE/dk derivative) is inversely proportional to the

Semiconductor properties

effective mass of the electron for the conduction band and of the

hole for the valence band. Higher curvature in a band results in

better transport properties (Section 2.2.3).

Another important semiconductor concept is that of the Fermi

level. Whereas the density of states tells us how many states exist

at a given energy, the Fermi function f(E) speciﬁes how many of

the existing states at the energy E will be occupied. More precisely,

f(E) speciﬁes the probability that an available state at an energy E

will be occupied by an electron and is given by the relation

f(E) = (1 + exp((E − E

)/kT))

−1

(2.1)

where E

is the Fermi level, k is the Boltzmann constant and T is

the absolute temperature. As the temperature goes to 0, f(E) goes

to 1 for E < E

and to 0 for E > E

, i.e. the Fermi level deﬁnes

the energy below which electron states are occupied and above

which they are unoccupied. At non-zero temperatures, the Fermi

function f(E) gives the probability of electrons occupying higher

energy states. The Fermi function plot is given in FIGURE 2.4,

where the x-axis is plotted in units of kT. The Fermi function is

0.5 at E = E

, approaches 1 for (E − E

)<3kT, and approaches

0 for (E − E

)>3kT. At room temperature, kT is approximately

0.026 eV and 3kT is approximately 0.078 eV. Compared to the

bandgap of GaAs (1.42 eV), these are small numbers and very few

carriers will be in the conduction band. In order to calculate the

carrier distributions (electron and hole occupancy versus energy),

the Fermi function is multiplied by the density of states.

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

–10 –5 0 5 10

(E–E

)/kT

f (E)

FIGURE 2.4 A plot of the Fermi

function.

2.2.2 Charged carriers in semiconductors

Next the conducting properties of semiconductors will be dis-

cussed. A pure semiconductor such as Si with a bandgap of

1.12 eV can conduct electrons if they reach the conduction band.

An interesting situation arises if the electron’s thermal energy,

which at room temperature is 0.026 eV, allows it to reach the

conduction band. Although the thermal energy is only a small

fraction of the bandgap, some electrons nevertheless reach the

conduction band because their numbers are so large. A Si atom

has 14 electrons, 4 of which are valence electrons and a Si crystal

has more than 10

atoms per cubic centimetre. The equation gov-

erning the equilibrium (meaning the semiconductor has had plenty

of time to respond to a perturbation such as a temperature change

and has reached its lowest energy state) electron concentration in

the conduction band is given by

= (N

)

1/2

exp(−E

/2kT) (2.2)

Semiconductor properties

where n

is the intrinsic (meaning for a pure semiconductor) carrier

concentration, N

is the density of states of the valence band, N

the density of states of the conduction band, E

is the bandgap,

k is the Boltzmann constant and T is the absolute temperature.

The density of states is calculated by theoreticians and reasonable

estimates are available. For Si, n

is about 10

−3

and for GaAs,

is about 10

−3

at room temperature. Although these numbers

seem large, in terms of current they are actually quite small due

to the unit of charge of an electron (1.6 × 10

−19

C) in relation

to an ampere (coulomb/s). It is seen that pure semiconductors

with bandgaps greater than 1 eV are excellent insulators at room

temperature, but that their conductivity will rise exponentially with

temperature. At 300

◦

C, for example, n

rises to about 10

−3

for Si and 10

−3

for GaAs.

Si Si Si

–

Si Si Si

–

Si Si Si

(a)

(b)

FIGURE 2.5 Impurity doping in

Si. The donor electron of P is free

to move about the crystal, while the

P remains with a ﬁxed positive

charge.

Pure semiconductors can be manipulated by adding atomic

impurities to change their electron concentrations. First one con-

siders a pure silicon crystal with four-fold bonding symmetry (one

bond for each unpaired valence electron). Rather than the band

structure description of the bonding (which is accurate but hope-

lessly complicated for a brief discussion), simple chemical pictures

will be used. The ideal bonding conﬁguration for four-fold sym-

metry is the tetrahedron, in which four points equally spaced on

a sphere represent the nucleus of the four atoms bonded to the

centre Si. Each bond comprises one valence electron from each

silicon atom. Next, consider the introduction of a P impurity. Phos-

phorus occupies a tetrahedral site in place of a Si atom. Instead

of four valence electrons it has ﬁve, so four of these are used in

chemical bonding and a ﬁfth is left over and allows P to be an elec-

tron “donor” to the crystal. The lattice has an extra proton which

stays ﬁxed at the P atom. The leftover electron is free to move over

the whole crystal, subject to relevant physical effects including the

(weak) attractive force from the ﬁxed positive charge that is left

with the phosphorus. In the case of P and several other dopants,

the weak attractive force to the donor ion is easily overcome by

thermal energy and the electron freely conducts in response to an

electric ﬁeld. This situation is illustrated in FIGURE 2.5, where for

convenience, the tetrahedral three-dimensional bonds are shown

as if in a single plane. If, instead of phosphorus, boron is used

to dope the silicon, only three valence electrons are added to the

crystal at the place where boron replaced a Si. One of the sil-

icon bonds will be missing a valence electron. In such a case the

valence band can participate in electron conduction. The unpaired

silicon bond can take an electron from its neighbour in response to

an electric ﬁeld leaving a ﬁxed negative charge with the boron and

a mobile positively charged “hole” in the neighbouring Si atom.

The electron “hopping” process can repeat itself leading to “hole”

Semiconductor properties

mobility in response to an electric ﬁeld. Rather than call this an

electron conduction mechanism through the valence band, it is

more useful to think of this transport and its energetics in terms

of particles called holes. GaAs is doped by an analogous method

using a wide variety of dopants. For example, Si with four valence

electrons provides electrons to the crystal if it replaces Ga and

provides holes if it replaces As.

The preceding discussion can be summarised as follows. Semi-

conductors can be made more conductive by introducing impurities

that occupy lattice sites normally occupied by the elements of the

original semiconductor. Those that add an extra electron to the

lattice contribute to electron conduction and those that are missing

an electron contribute to hole conduction. Because an electron

is negatively charged by convention, electron-adding impurit-

ies are called n-type dopants. Likewise, impurities that add

holes are called p-type dopants. Whereas pure semiconductors

with a bandgap greater than 1 eV have no more free carriers than

−3

at room temperature, it is fairly common to dope semi-

conductors with donor or acceptor impurities to levels greater than

−3

, leading to a 10

or greater increase in conductivity.

In fact, the situation of a doped semiconductor is not quite so

simple because the electron does not necessarily go into the con-

duction band of a pure semiconductor (because of the attraction

to the ﬁxed ion), but the states of an n-type semiconductor are

recalculated with the perturbation of an impurity dopant and there

may be slight changes to the band structure. Any impurity atom

and other things like crystal defects will usually add energy states

to the bandgap of the semiconductor. The case of the impurity

dopant, for example, can be modelled most simply as a hydrogen-

like atom in a dielectric matrix. The atomic hydrogen states are

known from free-space calculations:

= m

∗

/2(4πnεh)

(2.3)

where m

is the electron mass, q is the electron charge, ε is

the dielectric constant and h

is Planck’s constant divided by 2π.

The dielectric constant of GaAs is 13 times greater than the free-

space dielectric constant and the electron mass in GaAs is about

13 times smaller than the free-space electron mass. E

in free

space is 13.6 eV for n = 1, representing the ground-state ion-

isation energy of hydrogen. In GaAs, the hydrogen-like model

gives E

of approximately 6 meV. Coupled with the band structure

model, the donor state is placed 6 meV below the conduction band

and the donor electron is said to have a binding energy of 6 meV.

More sophisticated calculations are, of course, used for this and

other states involving impurities and defects in semiconductors

Semiconductor properties

when accuracy is needed. The hydrogen-like structure is called

a bound exciton, to describe the ﬁxed ion and the loosely bound

electron. Unbound excitons describe the situation where mobile

electron-hole pairs are loosely bound in such an arrangement.

If we recall the interpretation of the Fermi function of EQN (2.1),

and its plot in FIGURE 2.4, we can see that hydrogen-like donor

binding energies fall well within 3kT of the conduction band at

room temperature, indicating that this type of donor impurity gives

up its electrons to the conduction band at room temperature. In

fact many common donors and acceptors in GaAs have binding

energies less than 30 meV and are assumed to be fully ionised at

room temperature.

EQN (2.2) gives the free-electron concentration for a pure semi-

conductor. Similar equations can be generalised for pure or doped

semiconductors. Some of the most useful results are quoted here:

n = (N

)

1/2

exp(E

− E

/kT) (2.4)

p = (N

)

1/2

exp(E

− E

/kT) (2.5)

np = (N

)

1/2

exp(−E

/kT) = n

(2.6)

where n and p are the free electron and free hole concentrations and

the other terms have been deﬁned previously. EQNS (2.4)–(2.6)

are derived under the assumption that E

lies at least 3kT below

the conduction band and at least 3kT above the valence band, i.e.

+ 3kT < E

< E

− 3kT (2.7)

If these assumptions are met, the semiconductor is said to be non-

degenerate and if they are not met, the semiconductor is said to be

degenerate. EQNS (2.4)–(2.5) have twounknowns, E

and n (or p).

The reader is directed to the references for methods of solving

these equations [1,6,7]. However, some general comments are in

order. E

is roughly in the middle of the energy gap for an intrinsic

semiconductor (its actual position depends on the values of N

and N

).E

moves logarithmically towards E

as n increases

from the intrinsic value towards values determined by the number

of ionised donors. E

reaches (E

− 3kT) at about 10

−3

for

GaAs, which makes the doping degenerate, or more commonly,

the GaAs is said to have n

doping. In a similar way, E

moves log-

arithmically towards E

with increasing p-type doping and GaAs

is said to be degenerate for p

hole concentrations generally above

−3

. One last comment relates to unintentional doping. The

intrinsic carrier concentration of GaAs is near 10

−3

at room

temperature, but GaAs cannot be made pure enough to realise

Semiconductor properties

this condition. Today’s highest purity GaAs will have n- or p-type

donors in the low 10

−3

range which come from impurities

incorporated during the growth process (Sections 2.3 and 2.4).

Other energy levels that exist in the bandgap of GaAs and other

semiconductors are related to crystal imperfections or substitu-

tional incorporation of complex impurities such as metals. These

energy levels are often termed “deep levels” to contrast their ener-

gies with those of shallow donors and acceptors. Potentially large

numbers of defects can fall into this category and their study keeps

material scientists busy. The importance of these types of deep

levels stems from their ability to trap mobile carriers. Consider a

semiconductor with shallow donors and acceptors in the presence

of a deep level, as illustrated in FIGURE 2.6. Four processes can

occur: electron capture (a), electron emission (b), hole capture (c)

and hole emission (d). Processes (b) and (d) are also referred to

as carrier generation events. The carrier capture events (a) and (c)

depend on factors such as the density of the deep levels, spa-

tial overlap of carriers and deep levels, and electric ﬁelds in the

semiconductor. The carrier capture events are often referred to as

“trapping” of mobile carriers. The term “trap” relates to the fact

that thermal emission of electrons or holes occupyingthe deep level

is improbable due to the energy separation from the conduction or

valence bands. Because of the importance of trapping effects in

active devices, much effort has gone into the study and character-

isation of deep levels in GaAs and other semiconductors, including

speciﬁc types of growth (Section 2.3), measurement (Section 2.5),

and device modelling (Section 8.2.2).

(a) (b) (c) (d)

FIGURE 2.6 Four processes that

can occur in the presence of a deep

level.

As an example, let’s consider the most important defect in GaAs,

EL2. EL2 is identiﬁed by its energy location 0.76 eV below the

conduction band edge and is generally believed to be related to an

antisite defect, an As atom on a Ga site, perhaps complexed with a

nearby vacancy (empty lattice site). Its concentration in most types

of bulk crystal growth (Section 2.3) is near 10

−3

, although

it is much lower than that in epitaxial growth (Section 2.4). EL2

and other deep levels are thought to compensate impurity donors

and acceptors to make GaAs semi-insulating and insensitive to

impurities at levels below 10

−3

. EL2 may also trap electrons

in GaAs devices when they are accelerated into the semi-insulating

regionsof thedevice and may create regions of ﬁxedtrappedcharge

that can be detrimental to devices (Section 8.8). Its presence and

that of other deep levels must be accounted for in device design and

operation to minimise detrimental effects. Detrapping of electrons

(or holes) may also occur and generally happens on a timescale

that is long compared to device transit times that correspond to

high-frequency operation.