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2. Point Defects
R. Krause-Rehberg
2. Point Defects
2.1 Introduction
2.2 Classification2.3 Notation
2.4 Examples
2.5 Peculiarities in Semiconductors
2.6 Determination of Structure and Concentration
2.7 Vacancies in thermodynamic Equilibrium
2.8 Irradiation-induced Point Defects
2.9 Aspects of Defect Chemistry(F-center in NaCl)
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2.1 Introduction
point defects: vacancies, interstitials, impurities, antisite
defects, and their complexes
many physical properties are governed by point defects:
Conductivity and conduction type
Color
Transparency
Diffusion
Mechanical properties
Formation of precipitation
without vacancies: with 0.001% vacancies
transparent opaque
1 defect in 100000 atoms!
Galliumphosphide1 cm
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2.2 Classification
Types of Point Defects:
Vacancies
Interstitials
wrong species at
regular lattice site
Schottky defect
Frenkel pair
self-interstitial
impurity at interstitial Position
antisite atom
impurity at regular lattice position
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Another way of Classification
point defectsnative
induced extrinsic
intrinsic
native: defects in crystal after growth (intrinsic and extrinsic defects)
induced: generated in crystal after growth (e.g. by irradiation and plasticdeformation, or diffusion, precipitation growth)
intrinsic: self-defects of crystal without impurities (e.g. VGa, GaAs, Asi inGaAs)
extrinsic: defects including impurities (e.g. B- acceptor and V-O defect in Si;SiGa-VGa in GaAs)
however, this notation is not used uniformly in literature
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Still another Classification
Point De
fec
ts
Equilibrium Defec ts Excess Defec ts
thermal
vacancies
structural
defec ts
elec tronically
induced
ir radiation plastic
deformation
vacancies
in metals close
to melting point
AsGa
in LT-GaAs
Hg vacancies
in CdHgTe
SiGa-VGa in
n-doped GaAs
electron irradiation
ion implantation
cold-rolled metals
high-T deformed Si
lubrication
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Vacancies
vacancy of Schottky type Frenkel pair (here: close Frenkel pair)
note: relaxation of lattice at vacancy vacancies: - dominating defect at high temperature
- most important (primary) irradiation defect
- generated during plastic deformation (but often not stable)
in compounds and intermetallic phases: two different types of vacancies with
different properties
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Vacancies
defect reactions lead to defect complexes:
formation of divacancies and vacancy clusters
VAl-MgAl in Al-Mg-alloys
TeAs-VGa in GaAs:Te
V-Oi in Cz-Si (so-called A center)
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Interstitials
a) and b) interstitial in octahedral and tetrahedral position in a bcc crystal
EFFERG\FHQWHUHGFXELF
c) interstitial as dumbbell (deutsch: Hantel)
interstitial atoms are often small (e.g. B, C, N, O in metals)
often built-in in octahedral position (C in Fe): lattice distortion leads to
increased hardness
H is always built-in as interstitial
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Interstitials
important defect in silicon: Oi [O] is about 1018 cm-3 in Cz-Si
Oi has six equivalent positions
during annealing: formation of O-
precipitates; important for gettering of
impurities
self-interstitials often in dumbbell
FRQILJXUDWLRQLHDPROHFXOHRIWZR
identical atoms shares a regular lattice
site
Oxygen forms varies defect complexes in Si
with Si interstitials and Si vacancies
proposed structure of the I-O2 complex in Si
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Impurities
important defect in semiconductors (but also in metals, remember C in Fe)
intentionally used as dopants for the generation of carriers in high-resistive material
(Si, GaAs)
important acceptors: B in Si Zn or C in GaAs
important donors: P and As in Si Te, Si in GaAs
effect of a donor dopant
dopant levels in bandgap of Si
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Antisite Defects
prerequisite: ordered structure
in compound semiconductors and
intermetallic compounds
antisite defects compensate partly
deviations from stoichiometry
superlattice in system Au-Cu
a) (100)-plane in ordered Cu3Au
b) same plane at T > 390C
in existence region: deviation compensated
by point defects; outside: formation of
different phases, starting with small
precipitations
maximum deviation in compound
semiconductors very small at room
temperature
in LT-GaAs (grown at 200C): up to 1% of
point defects (mainly AsGa) extremely highconcentration
0.50000 0.50004 0.50008 0.50012900
1000
1100
1200
1300
TF
Melt
GaAss
GaAss+ Ga(As)
l
GaAss+ As(Ga)
l
solidus line
liquidus line
p6As
= 0.1 1 3 6 9 12 18 barT/
oC
xAs
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2.3 Notation of Point Defects
twofold negatively charged As vacancy2AsV
0
GaAs
iSi
SiB
neutral As antisite defect
Si atom at interstitial position
negatively charged boron atom at Si position
2AsV
speciescharge
position
often used in defect chemistry: .U|JHUVQRWDWLRQ
Au A' A'' acceptor neutral, negative, twofold negative
donor neutral, positive, twofold positive DDDu
e' electron in conduction band
GHIHFWHOHFWURQRUKROHLQYDOHQFHEDQG
h
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2.4 Examples: Color Centers
DONDOLKDORJHQLGHV1D&O.&ODUHFOHDUDQGWUDQVSDUHQW
coloring is obtained by point defects: color centers
possible defects: chemical impurities, excess metallic ions (e.g. Na+ in NaCl)
so-called F-bands: optical
absorption as function of wave
length; a part of optical
spectrum is cut, so the crystal
appears colored
the simple anion vacancy with a bound electron is the
F-center (absorption in UV region)
absorption: electric dipole transition to a bound exited
state of the defect
missing anion acts as positive charge and binds a
valence electron (which was delocalized before)
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other Color Centers
the FA-center in KCl; one of six K+
ions is replaced by another alkali ion(here Na+)
the M-center consists of two F-centers
the R-center consists of three F-centers
which are in an [111] plane of the NaCl
structure
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EL2 in GaAs: important antisite defect
probably the most frequently studied point defect in semiconductors: EL2 in GaAs
EL2 = electrical active defect II (as found in DLTS measurements)
used to obtain semi-insulating GaAs (auto-compensation of unwanted impurities)
self-compensation works only when [EL2] > [shallow acceptors] > [shallow donors]
VWHSQHHGVWRRKLJKWHPSHUDWXUHWKXVDOOFDUULHUVDUHFRPSHQVDWHGDWQRUPDOWHPSHUDWXUHV
condition can be fulfilled in pure semi-LQVXODWLQJ*D$VE\GRSLQJZLWK&
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EL2 in GaAs: important Antisite Defect
interesting feature: EL2 exhibits metastability
illumination at low temperature oproperties changes (e.g. no IR absorption any more)
many structural models were discussed
Dabrowski/Scheffler and Chadi/Chang: EL2 is isolated AsGa and in metastable state the
antisite atom moves outward and leaves a VGa Metastability is lost during warming-up to 115 K
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EL2 in GaAs: important Antisite Defect
positron annihilation is a method to detect
vacancy-type defects in solids
before annihilation, diffusing positrons can be
trapped by such defects
as a consequence: positron lifetime increases due
to the reduced electron density in the vacancy
experiment shows the existence of a Ga vacancy
in the metastable state of GaAs, which does not
exist in stable ground state
was prove of AsGa model of EL2
R. Krause, K. Saarinen, P. Hautojrvi, A. Polity, G. Grtner, and C. Corbel
Observa tion of a monovacancy in the metastablesta te of the E L2 defect
in GaAs by positron annihilation
Phys. Rev. Lett. 65 (26), 3329-32 (1990).
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DX Center in GaAlSb
defect appears in doped quasi-ternary III-V compound
semiconductors (e.g. AlxGa1-xAs, AlxGa1-xSb)
is complex: donor-? (so-called DX center)
also shows metastable state at low temperatures
model of Dabrowski/Scheffler predicted vacancy in
stable state and the disappearance of this vacancy in
metastable state
also proved by positron annihilation
Ga GaAl Al
Te Te
Sb Sb
metastable stable
Illumination
Illumination
10 2
10 3
10 4
10
5Photoconductivity[S]
279
278
277
276
275
274Averagepo
sitronlifetime[ps]
20 40 60 80 100 120Annealing temperature [K]
GaAlSb:Te
R. Krause-Rehberg et al., Phys. Rev. B 48 (1993) 11723
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Compensating Defects in GaAs:Te
Te is typical donor in GaAs
is built-in only as TeAs experimental finding: with increasing
donor doping concentration
acceptor density simultaneously
increases
VHOI-FRPSHQVDWLRQ
degree of compensation about 25%
confirmed model:
donor acceptor
TeAs
+
VGaTeAs
-
driving force for generation of defect
clusters: so-FDOOHG)HUPL-OHYHOHIIHFW
it is energetically favorable to form
additional acceptors in n-type GaAsresult of Hall-effect measurements
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Compensating Defects in GaAs:Si
Si is also often used as donor in GaAs
Si is built-in as SiGa+ and also as SiAs
-
(amphoteric behavior)
thus: situation is different from GaAs:Te
degree of compensation not constant, butgrowing
result: doping only possible up to 1019 cm-3
at higher Si content: almost complete auto-
compensation
model for additional compensating center(acceptor): VGaSiGa-
result of positron annihilation spectroscopy (by K. Saarinen et. al, Helsinki UT)
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Compensating Defects in GaAs:Si
model was proven by correlated STM and positron experiments
STM shows at cleavage planes of GaAs:Si the VGaSiGa- defect (but possibly formed
during cleavage)
positron annihilation found the same number of vacancies in the volume of the identical
crystals
conclusion: both methods detect the identical defects
J. Gebauer et al.
Phys. Rev. Lett. 78 (1997) 3334
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22
1 2 3 4 5 6 7 8 90.00.1
0.2
1 2 3 4 5 6 7 8 9
lattice spacing in [110] direction
Heigh
t[nm]
-2.0 V +1.4 V
occupied empty states
Scanning tunneling microscopy at GaAs (110)-
cleavages planes (by Ph. Ebert, Jlich)
Defect complex identified as VGa-SiGa
1018
1019
1017
1018
1019
Si concentration (cm-3)
Positrons - cvac
STM - [SiGa
-VGa
]
Defectconcentration(cm
-3)
Quantification o Agreement
Mono-vacancies in GaAs:Si are VGa- SiGa-complexes
Identification of VGa-SiGa-Complexes in GaAs:Si
Gebauer et al., Phys. Rev. Lett. 78 (1997) 3334
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two-zone-furnace: Control ofsample temperature and Aspartial pressure in quartz tube
TAs: determines As-partialpressure
navigate freely in phase diagram(existence area of compound)
Tsample: 1100 C
GaAs: annealing under defined As-partial pressure
Jurisch, Wenzl; 2002
0.50000 0.50004 0.50008 0.50012
900
1000
1100
1200
1300
TF
Melt
GaAss
GaAss+ Ga(As)
l
GaAss+ As(Ga)
l
solidus line
liquidus line
p6As
= 0.1 1 3 6 9 12 18 barT/
oC
xAs
Equilibrium Phase Diagram of GaAs
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0,01 0,1 1 10
1017
GaAs:Si
Linear fit
Vacancyc
oncen
tra
tion
(cm
-3)
Arsenic pressure (bar)
0,1 1 10
1016
1017
1018
[Te] in cm-3
9x1016
4x1017
6x1018
2x1018
231
GaAs:Te
250
235
240
245
Wav
at550K(ps)
Vacancyconcentration(cm
-3)
Arsenic pressure (bar)
SiGa-VGa
TeAs
-VGa
Fit: [VGa-Dopant] ~ pAsn
o n = 1/4
Thermodynamic reaction:1/4 As4
gaslAsAs + VGa
Mass action law:
[VGa] = KVG upAs1/4
J. Gebauer et al.,Physica B 273-274, 705 (1999)
GaAs: Annealing under defined As pressure
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Thermodynamic reaction:AsAs l VAs + 1/4As4
gas
Mass action law:
[VAs] = KVAs upAs-1/4
Fit: [V-complex] ~ pAsn
o n = -1/4
undoped GaAs: As vacancy
Comparison of doped and undoped GaAs
Bondarenko et al., 2003
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2.5 Peculiarities in Semiconductors
defects in semiconductors can be
charged (e.g.: +, 0, -)
charge depends on position of
Fermi level
electronic configuration and
structure of a defect depend on
charge state a different charge leads to
different lattice distortions
is so-FDOOHGJahn-Teller Effect
thus: distortion energy depends
on charge state influence may be so strong that
normal charge sequence (2-, -, 0,
LVFKDQJHGnegative-U
behavior
electron configuration of V0 in Si
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negative-U behavior
example: theoretical calculations of
ionization levels
a) to c) are calculated without lattice
relaxation
calculations g) to h): lattice distortion
was taken into account
Jahn-Teller Effect is frequently foundin semiconductors
Defec ts in InP
GaAs in Ga As
relaxedunrelaxed
relaxed
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2.6 Determination of structure and concentration
range of concentration: about 1010 cm-3 (metallic impurities in Si)
> 1020 cm-3 (some dopants in Si, AsGa in LT-GaAs)
defect identification difficult due to large variety of species
in GaAs: 6 intrinsic defects in many charge states; they form defect complexes; in
addition: they can form complexes with impurities
there is no universal method many methods give information about ionization levels in
band gap, but no structural information (e.g. DLTS, Hall, IR absorption)
other methods have structural information, but can only be applied to a restricted number
of defects or materials (e.g. EPR, Positron Annihilation)
topic of lec tures in next course!
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2.7 Vacancies in thermodynamic equilibrium
VVV STWNF ''
!)!(
!
!
)1()1(
VVV
V
NNN
N
N
NNNNG
!)!(
!lnln
VV
BBVNNN
NkGkS
'
statistical considerations change of free enthalpy during formation of NV Schottky-type vacancies (N .. number of
atoms; WV YDFDQF\IRUPDWLRQHQHUJ\
(positive energy term can be compensated by gain of entropy!)
'SV is entropy gain; is calculated in the following (from statistics: S= kB ln G):
probability Gto form NV vacancies in N atoms is equal to probability to
choose NV atoms out of N atoms (numerator):
The factor NV! (speak: factorial) in the denominator excludes those cases which differ onlyby the different order of pick-out of atoms.
using the Boltzmann-Equation and the Stirling approximation:
xxxx # ln!ln
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!)!(
!lnln
VVBBV
NNN
NkGkS
' xxxx # ln!ln
Tk
W
NN
N
B
V
V
V
ln
]ln)ln()(ln[ VVVVBV NNNNNNNNkS '
0ln
w
'w
V
VBV
TV N
NNTkW
N
F
it follows:
in thermal equilibrium: 'F is extreme value (minimum)
in the lattice: NV 103)
Tk
WNN
B
VV exp
thus: vacancies must exist in an ideal crystal at T>0 !
[1]
VVV STWNF ''
!
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example: T=1000K and WV = 1 eV NV/N 10-5
T=1000K and WV = 3 eV NV/N 10-15
not detectable
real example: vacancies in Au: WV = 0.98 eV, but in Si: WV > 3.6 eV
vacancy concentration is slightly larger compared to Eq. [1]
further factors to be taken into account:
- interaction of vacancies
- influence of point defects to 'S
- volume work for dilatation of lattice
- electronic effects
defect density often much larger: crystal far from being in thermal equilibrium
excess vacancies due to e.g. irradiationby fast particles
also: vacancies can be quenched-inby very fast quenching
quenching rate must be about 104 Ks-1, then a large fraction of thermal vacancies remain
during slow warming-up: vacancies become mobile (migration energy required 0.5mm)
ions produce extended defect cascades; energy large enough for 104 displacement events
however: only a few defects survive (stationary state reached after 1 ps)
also larger point defect clusters are generated
computer-simulated defect cascade in {100} plane of Cu. T=250 eV, ta = 0.06 ps, tb = 0.35 ps, tc = 1.5 psstationary result after 1.5 ps: 5 vacancies and 5 interstitials
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ion implantation
important dopant species in Si are As and B
in order to obtain homogenous doping depth profiles: multiple implantation steps with
different energy
depth distribution of implanted B
(As) atoms in silicon
depth distribution of displaced
atoms in B-implanted Si
when implantation dose large enough: lattice becomes amorphous
amorphisation dose is function of ion mass, target species, and temperature
6LPXODWLRQZLWKIUHHFRGH65,0ZZZVULPRUJ 7KH6WRSSLQJDQG5DQJHRI,RQVLQ
0DWWHU
projected range Rp
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Example of SRIM simulation
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temperature dependence of amorphisation
dose for different ions in Si
Doping by ion-implantation
KDVPDQ\DGYDQWDJHVEXW
defects must be annealed
temperature dependence ofamorphisation dose is strong
at elevated temperature:
defects anneal during
irradiation
at room temperature: boron
implantation will not lead to
amorphisation at all
in technology: defects must be
annealed
often: rapid thermal annealing
(RTA) in Si: 30s at 950C
done by light illumination by
strong halogen lamps (few
kW)
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Rutherford Backscattering
classical method to investigate ion implantation defects:
Rutherford Backscattering
probe atoms (H, He) penetrate into the sample into low-
index directions (channels)
defects which are present scatter the probe atoms and raise
the backscattered intensity
defect depth profiles can be determined
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41
FLA = Flash Lamp Annealing
short light pulses of Xe flash lamps may melt surface of Si
heating period some ms
RTA-Annealing (Rapid thermal annealing) of semiconductors after ionimplantation
Problem: measurement of temperature
P h ti f s l b h l l s d th
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42
Pre-heating of sample by halogen lamps and then:light pulse by flash lamps
Pulse-forming network (PFN).
Ground switch
Xenon flash-lampsPulse-forming network (PFN).
Ground switch
Xenon flash-lamps
Temperature up to 2000C electrical power: 12 MW (for 20ms)
Pre-heating necessary
temperature gradient: 5105 K/s
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2.8.2 Annealing of excess point defects
irradiation defects far from thermal equilibrium but still stable (frozen-in)
increasing temperature: defects start migration
energymigration...exp0 mB
m ETk
ENN
electri
calresistance
annealing of irradiation defects in Cu
electrical residual resistance at low temperature: sensitive for defects (electrons are
scattered during movement in electric field)
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Annealing of excess point defects
annealing starts at very low temperatures (in metals: interstitials have smallest migration energy)
many annealing stages; during annealing: defect reaction (e.g. formation of vacancy clusters)
often: several mechanisms lead to
disappearance of same defect: vacancies
vanish due to migration of interstitials and
vacancies itself
several stages (A-E) for interstitials: close
Frenkel pairs (A-C) and separated interstitials
(D+E)
curve b: electron irradiation
curve k: plastic deformation
curve a: quenched sample
stage I + II: interstitial annealing stage III: vacancy annealing
isochronal annealing curve of Cu after 3-
MeV-electron irradiation (Tirr=4.5 K)
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Annealing of excess point defects
example: defects after electron irradiation in
Ge (Ee-=2 MeV, Tirr=4K)
distinct annealing stage at 200K
sample with highest dose: formation of
divacancies during annealing (they anneal at
about 400K)
formation of divacancies prove: it is nomovement of interstitials but vacancies
this is further supported by the fact that the
vacancies disappear completely in this stage;
interstitial stage always incomplete
(Polity et al., 1997)
Defect annealing in electron irradiated Si
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Positron study of defect annealing after 4K-
electron irradiation of Cz-Si
Monovacancies disappear around room
temperature and divacancies are formed
Annealing is more complex: several stages
in intensity
Cz-Si contains about 1018 cm-3 oxygen Oxygen-vacancy complexes are formed
which can be transferred into more
complex defects during course of annealing
Defect reactions occur
(Polity et al., 1998)
Defect annealing in electron irradiated Si
f
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2.8.3 Defect reactions
defect reactions during annealing sequence is a normal
effect
defect complexes could be rather complicated
typical example: defect annealing in Cz-Si after low-
temperature electron irradiation
Cz-Si contains about 1018 cm-3 oxygen
many different oxygen-vacancy complexes are formed
most simple defect is theso-called A-center (VO)
during annealing:
sequence of different
VxOy complexes are
formed
defects stable up to
800C, although an
isolated monovacancy
anneals at about 200K
oxygen stabilizes the
defects
V-O complex (A-center)
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2.9 Aspects of defect chemistry
chemical or defect reaction
i
DCBA DCBA
:indexreaction
molesofQXPEHU
DCO
prior to reaction: O = 0 ; complete reaction O = 1
in thermodynamic equilibrium: 0 < O < 1
equilibrium condition:
T,p
G0 minimum of free entalphy G
w
w
reaction runs spontaneously only when:
0
,
w
w
pT
G
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The mass action law
DCBA mo chemical or defect reactionk1
k2
ki ... reaction velocity coefficientsci ... concentrations
BABA
cckdt
dc
dt
dc 1 DC
DCcck
dt
dc
dt
dc 2and for return reaction:
in case of thermodynamic equilibrium: velocity in both directions identical
dt
dc
dt
dc CA and thus: mequilibriuinionconcentrat...2
1i
BA
DCck
k
k
cc
cc
equation is called mass action law not only for chemical reactions: intrinsic conductivity in semiconductors
kN
pnpn
m
o :lawactionmass0 N ... number of all electrons
and thus: 'kpn
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Example: Defect chemistry in HgCdTe
HgCdTe is used as infrared detector; dominating defect is VHg2- (twofold ionized acceptor)
vacancies are in equilibrium with vapor pHg over crystal
HgHg HggasHghV
he
l
l
)(2
0
2
electrical conductivity is sum of intrinsic
conduction and ionization of VHg acceptors
QQXPEHURIIUHHHOHFWURQV
KQXPEHURIIUHHKROHV
mass action laws:
(1)][ v
22kphV
khn
HgHg
i
(2)0][22
HgVhn
neutrality condition: intrinsic part
extrinsic part (3)][2 2 hVHg
ratures)high tempe(athn
technical use at T < 100K (no intrinsic conduction); combination of (1) to (3) gives:
(4)02
22
v77
2
77
v
2
3
77
Hg
KiK
Hgi
Kp
khkh
k
pkh
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Defect chemistry in HgCdTe
is equation which defines
correlation between Hg partial
pressure and concentration of
Hg vacancies in crystal(because h77K= 2 [VHg])
constants ki and kv were
determined by electrical
measurements (Hall effect)
lines in figure: result ofsimulation by eq. (4);
measured points: experimental
data of Hg vacancy
concentration obtained by
positron annihilation
(4)02
22
v77
2
77
v
2
3
77
Hg
KiK
Hgi
K
p
khkh
k
pkh
f h
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Defect chemistry
treatment of quasi-ternary compounds
becomes rather difficult
very large number of intrinsic defects
but in special regions: only a few
defects dominate
calculation of the dominating defects
requires the knowledge ofthermodynamic constants which are
usually only roughly known
diagram only valid for a constant
temperature
CuInSe2
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