Table Of Content1 Introduction: Fundamental Aspects
CMOS (Complementary Metal Oxide Semiconductor) circuitry dominates
the current semiconductor market due to the astonishing power of silicon
electronic integration technology. In contrast to the dominance of silicon in
electronics, photonics utilizes a diversity of materials for emitting, guiding,
modulatinganddetectinglight.Inthelasttenyearsmuchresearcheffortwas
aimed at rendering Si an optically active material so that it can be turned
fromanelectronicmaterialtoaphotonicmaterial.ForsomethefutureofSi-
basedphotonicsliesin“hybrid”solutions,forothersintheutilizationofmore
photonicfunctionsbysiliconitself.Manybreakthroughsinthefieldhavebeen
made recently. Nevertheless, the major deficiency in Si based optoelectronic
devices remains the lack of suitable light emitters. In this chapter starting
fromtheanalysisoftheelectronicandopticalpropertiesofsilicon,compared
to other semiconductors, we present the strategies that have been employed
to overcome the physical inability of bulk silicon to emit light efficiently.
1.1 Electronic and Optical Properties
of Bulk Silicon
Silicon, the most important elemental semiconductor, crystallizes in the di-
amond structure. The diamond lattice consists of two interpenetrating face-
centeredcubicBravaislatticesdisplacedalongthebodydiagonalofthecubic
cellbyonequarterofthelengthofthediagonal.ThesymmetrygroupisO7h-
Fd3m. The lattice constant is 0.5341 nm.
Theenergybandstructureofsolidsdependsnotonlyonthecrystalstruc-
turebutalsoonthechemicalspecies,thebondingbetweentheatomsandthe
bond lengths. This results in severaldifferences in the electronic band struc-
ture ofthe varioussemiconductors.As anexample the bandstructuresof Si,
Ge and GaAs are compared in Fig. 1.1, which shows the results of electron
energy band calculations within the empirical pseudopotential method [1, 2]
(forasurveyonbandstructurecalculationsseeSect.2.1).Notethatwhereas
Ge has the same diamond lattice structure of Si, the compound semiconduc-
torGaAscrystallizesinthezinc-blendstructure.Inthislatticetheatomsare
arrangedas in the diamond case but the two species alternate: the Ga atom
StefanoOssicini,LorenzoPavesi, FrancescoPriolo:Light EmittingSiliconfor Microphotonics,
STMP194,1–35(2003)
(cid:1)c Springer-VerlagBerlinHeidelberg2003
2 1 FundamentalAspects
Fig. 1.1. Topleft:BandstructureofGecalculatedwithintheempiricalpseudopo-
tentialmethod.Spin–orbitcouplingisincludedinthecalculations.Topright:Band
structureofSicalculatedwithintheempiricalpseudopotentialmethod.Tworesults
areshown: nonlocal pseudopotential (solid line)and local pseudopotential(dashed
line).Spin–orbitcouplingisincludedinthecalculations.Bottom:Bandstructureof
GaAscalculatedwithintheempiricalpseudopotentialmethod.Spin–orbitcoupling
is included in thecalculations. After [1]
occupiestheoriginalsitesofthefacecenteredcubiclattice,whiletheAsatom
is located at the tetrahedral site.
Qualitatively the bands of all three materials are similar in shape, as ex-
pectedfromtheircommoncrystalstructureandclosepositionsintheperiodic
table. The main difference in the valence band structure is the degeneracy
atthetopofthevalencebandattheΓ point,thecenteroftheBrillouinzone
(BZ).TheΓ25(cid:1) pointoftheSicaseissplitbythespin–orbitinteractionatthe
Γ andΓ points in the case ofGe andGaAs.The spin–orbitsplitting ∆ at
8 7 0
the zone center is a relativistic effect and increases with the atomic number
1.1 Electronic and Optical Properties of Bulk Silicon 3
of the element. In Si it is negligible (0.044 eV), while in Ge it has the value
of about 0.29 eV and in GaAs of 0.34 eV. The two Γ and Γ bands have
8 7
differenteffectivemasses,termedlightandheavyholes,forsmallwavevector.
Moreover,attheX point,someofthosestatesthataredoublydegeneratein
SiandGearesplitinGaAs,bothinthe valenceandinthe conductionband.
The main striking difference is related to the peculiar properties of the
conductionbandextremainthethreecases.Thevalencebandsexhibitamax-
imumattheΓ pointoftheBrillouinzoneforthethreesemiconductors;while
the conduction band for GaAs has an absolute minimum at the Γ point, for
Si it lies away from the high symmetry points near the X point along the
(cid:1)001(cid:2) directions and for Ge it occurs at the zone boundaries in the (cid:1)111(cid:2)
directions.
ThedispersionoftheconductionbandinGaAsisparabolicneartheband
edges.The effective massforthe electronis about0.067m ,wherem is the
0 0
electron mass in vacuum. The low value of the electron effective mass is one
of the reasonsfor the high mobility in GaAs and of its use in high-frequency
transistors.InSitheconductionbandhassixsymmetry-relatedminimainthe
(cid:1)100(cid:2)directions.Eachoftheseminimagivesrisetoaconductionbandvalley.
Theconstant-energysurfacesneartheconductionbandminimaareellipsoids
elongated in the (cid:1)100(cid:2) directions (see Fig. 1.2). For each valley a parabolic
approximation can be used. Due to symmetry considerations this leads to
different effective masses for the electron, one for the longitudinal x-direc-
tion, the other for the transverse y- and z-directions. The high anisotropy
of the valleys for Si results in very different masses for the longitudinal and
transverse mass, 0.916 and 0.19 m .
0
For Ge the minima, which are located at the L points along the (cid:1)111(cid:2)
directions,originate in four equivalentvalleys or eighthalf-valleys.Also here
the electron effective masses are highly anisotropic, 1.64 and 0.092 m (see
0
Fig. 1.2).
Fig. 1.2. Left: Brillouin zone of Ge with constant-energy surfaces for the four
equivalent L valleys. Right: Brillouin zone of Si with constant-energy surface for
thesix equivalent X valleys
4 1 FundamentalAspects
Theenergygap(the energydifferencebetweenthe conductionbandmin-
imum and the valence band maximum) is termed direct in the case of GaAs,
because an electronic transition between the two extrema can occur without
change in wavevector. The energy gap is termed indirect when a change in
wavevector is needed, as for Si and Ge. The value of the energy gaps ranges
from the infrared (Ge) to the near infrared (Si) to the visible (GaAs). Some
general properties of the three semiconductors are given in Table 1.1 [4, 5].
Table 1.1. Properties of Si, Ge, and GaAs
Prop- Si Ge GaAs Units Name
erty
a 0.5431 0.5658 0.5653 nm Lattice constant
ρ 2.329 5.323 5.318 g cm−3 Density
hω 64 37 36 meV Optical phonon energy
LO
E 1.12 0.66 1.42 eV Energy gap at 300 K
g
E 1.17 0.74 1.52 eV Energy gap at 0 K
g
E(min) X L Γ Conduction band minimum
c
EΓ 3.5 0.80 1.42 eV Energy gap at Γ
c
∆ 0.044 0.296 0.341 eV Spin–orbit splitting
0
χ 4.05 4.01 4.07 eV Electron affinity
m 0.49 0.33 0.51 Heavy hole mass
hh
m 0.16 0.043 0.082 Light hole mass
lh
mΓ 0.063 Electron mass
m 0.916 1.64 Longitudinal electron mass
L
m 0.19 0.092 Transverse electron mass
T
µ 0.15 0.39 0.85 m2V−1s−1 Electron mobility at 300 K
n
µ 0.045 0.19 0.04 m2V−1s−1 Hole mobility at 300 K
p
(cid:10) 11.7 16.2 12.9 Dielectric constant
b
n 3.42 4.0 3.3 Static refractive index
R 1.1 6.4 7×104 ×10−14 cm3s−1 Radiative recombination coeff.
C 16.6 12.6 11.9 ×10−11 dyn cm−2 Elastic constant at 300 K
11
C 6.4 4.4 5.34 ×10−11 dyn cm−2 Elastic constant at 300 K
12
C 7.96 6.77 5.96 ×10−11 dyn cm−2 Elastic constant at 300K
44
T 1685 1210 1513 K Melting temperature
m
The optical properties reflect the electronic ones. Figure 1.3 shows the
real and imaginary parts of the dielectric function of the three considered
semiconductors. They have been determined from reflectivity measurements
and the use of Kramers–Kronigrelations [3]. They are directly connected to
the optical parameters (see Sect. 2.1); the imaginary part is correlated with
the absorption coefficient, the real part with the dielectric constant. In the
caseof a directbandgapsemiconductor like GaAs the energygapis directly
givenbytheopticalthreshold.ThisisnottrueinthecaseofSiandGewhere
the onset of absorptionis related to the first direct transition:0.80 eV in Ge
1.1 Electronic and Optical Properties of Bulk Silicon 5
Fig.1.3.Real(cid:10) (thecurvethatalsoshowsnegativevalues)andimaginaryparts(cid:10)
1 2
of the dielectric function (cid:10) between 1.5 and 6 eV. Left: Crystalline Ge. Middle:
Crystalline Si. Right: Crystalline GaAs. After [3]
and 3.5 eV in Si (see Table 1.1). Moreover for a direct semiconductor the
absorptioncoefficientαnear the bandedge has asquarerootdependence on
the energy E, whereas a linear dependence of (αE)1/2 versus E is indicative
of an indirect band gap semiconductor.
InGaAs anelectronwhich has been excited in the conduction band atΓ
caneasilydecayradiativelyatthesameΓ pointinthevalencebandproducing
a photon of the same energy as the band gap. Under these conditions the
radiative recombination rate is large, of the order of 2×107 s−1, and the
radiative lifetime is short, of the order of nanoseconds. In the case of Ge
and Si, where the minima and maxima occur at different points of the BZ,
a phonon must participate in the process in order to conserve the crystal
momentum, hence the term indirect transition.
The three-particle process (electron, hole and phonon) has for Si a very
lowrate,about102s−1,andtherelativeradiativelifetimesareinthemillisec-
ondrange.The luminescence efficiency, defined asthe ratio ofthe number of
photons emitted to the number of electron–hole pairs excited, is typically of
the order 10−4–10−5 in bulk Si; for a direct semiconductor it can be of the
orderof10−1.Thus in orderto overcomethe inability ofSito emit lighteffi-
ciently one must defeat the tyranny of the k vector,e.g. by trying to reverse
the indirect nature of the Si band gap into a direct one.
The presence of an indirect gap is not, however, the only reason for the
poor luminescence efficiency [6, 7]. The luminescence efficiency, due to the
low radiative recombination rate, is determined by the competition among
alternateelectron–holerecombinationprocesses.Onecandefinetheradiative
efficiency of a semiconductor η as
τ
η = nr , (1.1)
τ +τ
r nr
where τ is the lifetime of the radiative transition and τ is the lifetime
r nr
relativeto the recombinationmechanismsthatdo notinvolvethe creationof
aphoton.Fromthisequationitisclearthatinordertohavealargeη,τ must
r
6 1 FundamentalAspects
be much shorter than τ . As stated above, τ for direct gap semiconductors
nr r
isveryshort(intherangeofns);forSi,τ ismuchlonger(oftheorderofms).
r
Extremely pure Si is needed to have a long nonradiative lifetime. There are
several possible nonradiative recombination processes [8]. Just to cite a few:
• Intrinsic defect or impurity recombination that involves the trapping of
an electron (or hole) by a deep trap level and the subsequent capture of
a hole (or electron), thus originating a recombination process. This mech-
anism is usually termed Shockley–Read–Hall recombination. For this, the
lifetime depends onthe concentrationsofdeepstatesandisofthe orderof
nanoseconds [9].
• Augerrecombinationwhereanelectronrecombineswithaholetransferring
its energy and momentum as kinetic energy to another electron and/or
hole. Depending on the doping level the radiative lifetime associated with
the Auger process ranges between 1 ns and 0.5 ms [10].
• Finally dislocations and surface mediated recombinations are possible. In
these cases it is difficult to establish characteristic lifetimes because they
vary depending on the quality of the surface. Good surface passivation
via a naturally grownoxide removesalmostcompletely these nonradiative
recombinations.
The totalrecombinationratefor allthe differentnonradiativepathways,τ ,
nr
can be obtained by the sum of the individual rates τnri:
(cid:1)
1 1
= . (1.2)
τ τ
nr i nri
For Si, τ is at least of the order of µs, three orders of magnitude smaller
nr
than the radiative lifetime τ . Bulk silicon has a very low quantum efficiency
r
and thus it is very unattractive as a light emitting device.
1.1.1 Light Emitting Diode Efficiency
In this and the next sections we will discuss light emitting diodes (LEDs)
basedonbulkSi.RecentlyareviewonSibasedLEDshasbeenpublished[14].
The performances of light emitting diodes could be given with different pa-
rameters: maximum brightness, quantum efficiency, wall plug-in efficiency,
peak power, on-set voltage, etc. A classification of the various efficiencies is
reported in Table 1.2.
Thepracticalperformanceofalightsourceisprimarilyevaluatedthrough
itspower efficiency η ,whichistheratiobetweentheradiantfluxP emitted
P
by the LED and the input electrical power W flowing into the LED.1 The
e
externalpowerefficiencyissometimesreportedinlumensperwatt.η isalso
P
1 The radiant flux P is the power carried by the light beams. Given a flux of
photonsΦ,atagivenphotonfrequencyν,P =Φ×hν =Φ×hc/λ,wherecisthe
speedoflightinvacuumandλisthewavelengthoflightinvacuum.Theluminous
1.1 Electronic and Optical Properties of Bulk Silicon 7
Table 1.2. Definitionof thevariousefficiencies. τ and τ are theradiativeand
rad nr
nonradiative lifetimes, respectively. P and P are the optical power as
op(int) op(ext)
measured in and outof thedevice. W , I andV aretheelectrical powerabsorbed,
e
current and voltage of the operating LED. (cid:1)ω is theemission energy of the LED
internal quantum numberof photonsemitted
τ eP
efficiency ηint versusthe numberof electron– ηint = τ +nrτ = Io(cid:1)p(ωint)
hole pairs generated nr rad
external quantum numberof photonsdetected eP
efficiency ηext versusnumbersof charge ηext = Iop(cid:1)(ωext)
injected
power efficiency η watts of light detected P η (cid:1)ω
P η = op(ext) = ext
versuswatts of electricity used P W eV
e
calledwall–plug-inefficiency because it is intendedthat the powershouldbe
directlytakenbytheplug-in.Itshouldbenoticedthatthisgeneraldefinition
can also be used for nonelectrically pumped luminescence mechanisms. In
any case, the power efficiency value will always be between 0 and 1.
The mechanism of electrically pumped light generation involves the gen-
eration of a photon by the radiative recombination of electrical carriers (one
electronandonehole).Thecapabilityofasingleelectron–holepairtogener-
ateaphotoniscalledthe internalquantumefficiency,η .η isthenumber
int int
ofphotonsgenerateddividedbythenumberofminoritycarriersinjectedinto
the region where recombination mostly occurs. By definition
(Rate of radiative recombination)
η = ,
int
(Total rate of recombination (radiative and nonradiative))
or
1/τ
η = r ,
int (1/τ )+(1/τ )
r nr
where τ is the mean lifetime of a minority carrier before it recombines ra-
r
diatively and τ is the mean lifetime before it recombines without emitting
nr
flux F is the power of light weighted by the human eye responsivity V(λ), as
defined in 1924 by CIE [11]. The conversion factor F/P, called the efficacy, has
the same spectral shape as the eye responsivity V(λ), with the convention that
the efficacy is 683 lm/W at λ =555 nm. The radiant intensity J is P per unit
solidangleandismeasuredinwattspersteradian.Theluminousintensity I isF
per unit solid angle. It is measured in candela, which are lumens per steradian.
TheradianceListhesurfacedensity(withrespecttothesurfaceofthesource)of
radiantintensityJ.Itismeasuredinwattspersquarecentimeterpersteradian.
The luminance or brightness B is its photometric counterpart, i.e. the surface
density of the luminous intensity I, and it can be measured in candelas per
square meters, or nits (nt). Radiance and brightness are important when the
source cannot be assumed as a point source.
8 1 FundamentalAspects
a photon. If one considers that the number of carriers per unit time elec-
trically injected by a current I is I/e, where e is the electrical charge of
one electron, and that the number of photons per unit time carried by the
internally generated optical power P is P /(cid:1)ω, where (cid:1)ω is the
op(int) op(int)
emissionenergy,thenη =eP /I(cid:1)ω.Theinternal quantumefficiency
int op(int)
(IQE),η ,isusedtocharacterizetheinternalgenerationofphotons.Itdoes
int
not take into account(1) how many electricalcarriers injected into the LED
do not excite the material to the emitting excited state, and (2) how many
generated photons get lost before exiting the device (e.g. by reabsorption
processes). In fact, for those photons that are generated, there can still be
loss through absorption within the LED material, reflection loss when light
passes from a semiconductor to air due to differences in refractive index and
total internal reflection of light at angles greater than the critical angle de-
finedby Snell’s law.Forthese reasonsoneintroducesa moregeneralconcept
to measure the efficiency of a LED, the external quantum efficiency (EQE),
η , which is the ratio of the number of photons actually exiting the LED
ext
and the number of electrical carriers entering the LED per unit time. Thus,
the following relation holds:
ηext =ηj ×ηint×ηx (1.3)
where ηj and ηx are by definition the carrier injection efficiency and the
photonextractionefficiencies,respectively[12,13].Onecangiveestimatesof
these last quantities for a LED based on a plane p/n junction.
(cid:2) (cid:3)
µ N L −1
ηj = 1+ µhNALe (1.4)
e D h
whereµ andµ arethemobilitiesofelectronsandholes,N andN arethe
e h A D
dopingdensitiesonthep-typeandn-typesideofthejunction,andL andL
e h
arethediffusionlengthsoftheelectronsandholes,respectively.Ontheother
hand, the extraction efficiency can be estimated by considering the fraction
of light which is transmitted through a plane interface between a medium of
index of refraction n and one of index of refraction n with respect to the
1 2
total light impinging on the interface at any angle:
(cid:2) (cid:3)(cid:4) (cid:2) (cid:3) (cid:5)
1 n n −n 2
F = 2 1− 1 2 . (1.5)
T 4 n n +n
1 1 2
Finally,byusingtheEQEonecanalsoderiveη .Infact,η =η (cid:1)ω/eV,
P P ext
where V is the working voltage of the LED. The power efficiency of a LED
should be at least 1% for display applications, whereas for optical intercon-
nects it should be at least 10%, due to the requirement of a small thermal
budget on the chip. The operating voltage can be high for display applica-
tions, while it should be low (1–5 V) for interconnects. An operating life of
more than severaltens of thousand hours with no degradation is a must.
1.2 Electroluminescence in Bulk Crystalline Si 9
1.2 Electroluminescence in Bulk Crystalline Si
AreviewofLEDsbasedonSiandSicompatiblematerialsisreportedin[14].
Here we discussthose LEDs made frombulk Si; the other approachesto a Si
LED are discussed in the following chapters.
1.2.1 Bulk-Si pn Junction LED
EL from bulk crystalline Si can be obtained in the most basic way both by
forwardor by reverse biasing a pn junction at room temperature (RT), thus
injectingminoritycarriersacrossthepnjunction,andrealizingband-to-band
radiativerecombinationoffreeexcessminoritycarriersaftertheinjection[15].
A pn junction shows a power efficiency of about 10−4 at 1.1 µm in forward
bias,andofabout10−8inthevisibleandinreversebiaswhileintheavalanche
breakdown regime [16].
The power quantum efficiency of an ordinary Czochralski (CZ) direct-
biased pn junction is low, typically of the order of 10−4% or lower [17].
The most important recombination mechanisms are schematically shown in
Fig. 1.4 [13].
EL in bulk Si was first reported by R. J. Haynes and H. B. Briggs in
1952 [19] by direct biasing a Si pn junction at room temperature (RT), and
explainedby R.J. Haynes andW. C. Westphal in 1956[18] reporting exper-
iments both at RT and at 77 K (see Fig. 1.5). At 77 K, the emission is not
only due to free carriers, but also to exciton recombination [15]. The main
feature of Fig. 1.5 at 77 K is the peak at hν = 1.100 eV (vacuum wave-
1
length 1127 nm). The emission line shape is the product of the Boltzmann
occupation factor times the density of states.
Forpracticalapplications,however,itisnecessarytoprovidemechanisms
which work at RT. By raising the temperature to RT, several changes are
observed.The first is a loweringof the peak intensity andofη . This is due
int
(1) to an increase of nonradiative recombination rates, and (2) to exciton
ionization. Since the exciton binding energy is of the order of 15 meV, at
RT exciton dissociation is significant (kT is about 25.8 meV at RT). It has
been shown that the radiative recombination rate, which is dominated by
excitonrecombinationallow temperature(under 26K),decreasesby raising
the temperature. The drop is over an order of magnitude from 100 K to
300 K [20]. The second change is a shift to lower energy because of thermal
band-gap shrinkage [17, 18, 21]. The third effect is the broadening of the
luminescence band, as a consequence of the rise in the free carrier kinetic
energy:thefull-width-half-maximum(FWHM) ofluminescenceisfittedwith
1.795 kT. The ratio between the free carrier concentration (n ) and exciton
c
concentration (n ) increases with the temperature according to the mass
x
actionlaw.AtRT,variousspectralfeaturesareobserved,whoseoriginisnot
yetclearandseveralmodelshavebeenpresented[22].Theyinclude:interband
10 1 FundamentalAspects
Fig. 1.4. Schematics of selected radiative (a) and nonradiative (b) recombina-
tion mechanisms in Si. (a) (1) Intrinsic free electron–hole (eh) and free exciton
(X),which both also involvecreation or annihilation of a phonon(not shown); (2)
extrinsic recombination (in the presence of a neutral acceptor), of a free electron
to bound hole (eAo) and of a bound exciton (AoX) (a similar situation can exist
with neutral donors); (3) extrinsic recombination, bound electron (neutral donor)
toboundhole(neutralacceptor)(DoAo).(b):Similarmechanismsoftype(1),(2),
(3) can give rise to nonradiative (Auger) recombination. In this case the released
energy is transferred to a free (or bound) carrier rather than generating a photon.
(4) is Shockley–Read–Hall recombination. After [13]
Fig. 1.5. First reported electroluminescence spectrum due to recombination of
electrons and holes in Si, as published by J. R. Haynes and W. C. Westphal in
1956. The solid line shows the emission at 77 K, whereas the dashed line and the
line with circles show emission at room temperature (the two spectra correspond
to slightly different conditions). After[18]
