Point defects ionic crystals Electronic defects in semiconductors
Transcript of Point defects ionic crystals Electronic defects in semiconductors
University of Virginia, MSE 6020: Defects and Microstructure in Materials, Leonid Zhigilei
Point defects ionic crystals
Ionic bonding and ionic crystals: Brief reviewDefects in ionic crystal and oxides. Kröger-Vink Notation Site, mass, and charge balanceFrenkel and Schottky defects Extrinsic point defects in ionic crystals - impuritiesNon-stoichiometry in ionic crystals
References:Allen & Thomas, Ch. 5, pp. 263-270Swalin: Ch. 14, pp. 317-350
Electronic defects in semiconductorsElectronic defects in intrinsic semiconductorsExtrinsic electronic defects in semiconductors - doping
optional reading(not tested)
University of Virginia, MSE 6020: Defects and Microstructure in Materials, Leonid Zhigilei
Ionic bonding: Brief reviewIonic bonding - typical between elements from horizontal extremities of the periodic table
Electronegativity - a measure of how willing atoms are to accept electrons
give
up
1e-
give
up
2e-
give
up
3e-
iner
t
acce
pt 1
e-
acce
pt 2
e-
Electropositive elements: Readily give up electrons to become positive ions (cations)
Electronegative elements: Readily acquire electrons to become negative ions (anions)
IA: Alkali metals (Li, Na, K…) - one electron in outermost occupied s subshell - eager to give up electronVIIA: Halogens (F, Br, Cl...) missing one electron in outermost occupied p subshell - want to gain electronMetals are electropositive – they can give up their few valence electrons to become positively charged ions
University of Virginia, MSE 6020: Defects and Microstructure in Materials, Leonid Zhigilei
Example: table salt (NaCl)
Na has 11 electrons, 1 more than needed for a full outer shell (Neon)
Cl has 17 electron, 1 less than needed for a full outer shell (Argon)
11 Protons Na 1S2 2S2 2P6 3S1
11 Protons Na+ 1S2 2S2 2P6
donates e-
10 e- left
17 Protons Cl 1S2 2S2 2P6 3S2 3P5
17 Protons Cl- 1S2 2S2 2P6 3S2 3P6
receives e-
18 e-
Na Cle-
Cl-Na+
Na (gas) + 5.14 eV (ionization energy) → Na+ + e-
e- + Cl (gas) → Cl- + 3.61 eV (electron affinity)
energy of (long-range) interaction among the ionsNa+ + Cl- → NaCl (crystal) + 7.9 eV
balance: ΔE = 7.9 eV - 5.1 eV + 3.6 eV = 6.4 eV per NaCl formula unit
Cohesive energy of NaCl crystal (energy needed to convert NaClcrystal into individual Na and Cl atoms):
< 0 → it costs energy to transfer e from Na to Cl
Ionic bonding: Brief review
University of Virginia, MSE 6020: Defects and Microstructure in Materials, Leonid Zhigilei
Ionic crystals: Brief review• Charge neutrality: the total charge in the base must be zero• There are no free electrons, ionic crystals are insulators• Interatomic bonding is mostly defined by long-range inter-ionic Coulomb interactions ±q2/r
and is rather strong (Ec ~ 600-1000 kJ/mol ~ 6-10 eV/atom) and has no directionality
fcc with 2 atoms in the base: at (0, 0, 0) and (½, 0, 0)
NaCl structure
KCl, AgBr, KBr, PbS, MgO, FeO
Na+ ions filling octahedral holes in the fcc structure
fcc with 3 atoms in the base:cations at (0,0,0) and two anions at (¼, ¼, ¼), and (¼, ¾, ¼)
fluorite structure
F- ions filling tetrahedral holes in the fcc structure
CaF2 or ZrO2
University of Virginia, MSE 6020: Defects and Microstructure in Materials, Leonid Zhigilei
Ionic crystals: Brief review
simple cubic with two atoms in the base at (0,0,0) and (½, ½, ½)
CsCl structure
CsCl, TlI, TlClAlNi, CuZn - intermetallic comp.
fcc with two atoms in the base at (0,0,0) and (¼, ¼, ¼)
zinc blende structure
ZnS, CuF, CuClGaAs, GaP, InP- semiconductors
tetrahedral sites are preferred because of the relative sizes of the positive and negative ions, but not all of them are filled to maintain stoichiometry
spinel structurenamed after the mineral spinel (MgAl2O4)
can contain vacancies as an integral part of the structure to satisfy the charge balance, Fe21,67Vac2,33O32 if all Fe converted to Fe+3
Fe3+( Fe2+ Fe3+)O4, Mg2+( Al23+)O4, Fe3+(Cr2
3+)O4
University of Virginia, MSE 6020: Defects and Microstructure in Materials, Leonid Zhigilei
Defects in ionic crystal and oxides. Kröger-Vink Notation Introduction of a concentration α of vacancies to Na+ sites (or the same concentration of Cl- interstitials) creates net charge of -eαN charge in a crystal with N lattice sites → very high energy → Na1-αCl cannot exist
pure ionic crystals must be perfectly stoichiometric (?)
introduction of impurities with different valence and electronegativity than the host ions can require additional point defects to charge balance
The concentration of vacancies can be much higher than required by thermal equilibrium -electrochemical equilibrium must be maintained. How to incorporate point defects into chemical reaction equations?
Kröger-Vink Notation:
X – nature of species located on a site: element symbol for an atom, V for vacancy
Y – type of the site occupied by X: (i for an interstitial, element symbol for site normally occupied by this element)
Z – charge relative to the normal ion charge on the site′ negative relative charge• positive relative chargex zero relative charge (x is often omitted)
ZYX
University of Virginia, MSE 6020: Defects and Microstructure in Materials, Leonid Zhigilei
Kröger-Vink Notation ZYX
Examples:
interstitial Ag ion in AgCl:
vacancy on a Ag site in AgCl:
Ca2+ ion on a Na site in NaCl:
vacancy on an O site in Al2O3:
Cu+ on a Cu2+ site CuO:
•iAg
'AgV•NaCa••
OV'CuCu
i siteO siteU site
Pu4+ ionVacancyO2- ionU4+ ionY X
''''UV••
OVxiV
xOO
''''''UO
''iO
xUU
••••••OU
••••iU
xUPu
••••••OPu
••••iPu
Intrinsic point defects and Puimpurity in UO2 crystal
In a generic discussion of defect reactions, M and X are often used:M - atom of electropositive elementX - atom of electronegative element
University of Virginia, MSE 6020: Defects and Microstructure in Materials, Leonid Zhigilei
Site, mass, and charge balance
1. Site balance– Ratios of regular lattice sites must be conserved, i.e., fixed proportion of M
and X sites must be created regardless of whether they are occupied or not. Total number of sites may change, but the ratio must remain constant.
Formation and annihilation of point defects in ionic crystals must satisfy the following 3 rules:
Example: Al2O3: by oxidation of aluminum create 3OO then 2AlAl must also be created, although they may be vacant.
2. Mass balance– Total number of atoms of each species on right and left side of defect formation reaction
must be equal– Vacancies and electronic defects do not affect mass balance
3. Charge balance (electroneutrality)– Compounds are assumed to remain neutral
Any charge inbalance, global or local, leads to high electrostatic energy that exceed any other contributions to the Gibbs free energy, making the charged state to be strongly nonequilibrium one.
University of Virginia, MSE 6020: Defects and Microstructure in Materials, Leonid Zhigilei
Frenkel defects
+
Frenkel defect (Frenkel pair) = vacancy + interstitial in close proximityfirst discussed in 1926 by Frenkel for AgCl
two types of Frenkel defects:
• cation Frenkel pair: cation vacancy + cation interstitial
• anion Frenkel pair: anion vacancy + anion interstitial
Typically, the enthalpies of formation are very different for the two types and, in a given crystal, one type of Frenkel defect is prevalent.
'VAgAg AgixAg +↔ •formation reaction for a cation Frenkel pair in AgCl:
this reaction satisfies the mass, charge, and site balance
Analysis of the equilibrium concentration of Frenkel defects can be done similarly to our derivation for vacancies. We just have to keep in mind that both vacancy and self-interstitial are generated and ni = nv = nFP
University of Virginia, MSE 6020: Defects and Microstructure in Materials, Leonid Zhigilei
Frenkel defects
⎟⎟⎠
⎞⎜⎜⎝
⎛ Δ−⎟⎟
⎠
⎞⎜⎜⎝
⎛ Δ⎟⎟⎠
⎞⎜⎜⎝
⎛=
Tkh
ks
NN
Nn
B
FPf
B
FPv
iFPeq
2exp
2exp
2/1
FPvi nnn ==
( ) ( )!!!ln
!!!ln iii
i
BvvBnc nNn
NknNn
NkS−
+−
=
nc
FPf
FPf
FP STsThnG Δ−Δ−Δ=Δ )(Equilibrium concentration of Frenkel defects:
where Ni is the number of interstitial sites (may depend on configuration, e.g., dumbbell vs. octahedral)
0ln =⎟⎟⎠
⎞⎜⎜⎝
⎛+Δ−Δ=
∂Δ∂
=i
eqeqB
FPv
FPf
nnFP N
nNn
TksThn
GFPeq
FP
2.5ZnO9.53.0
UO2
128.7
TiO2
2.3Li2O7
2.3-2.8CaF2
1.1AgBrreactioncompound eV ,FP
fhΔ
''iO
xO OVO +↔ ••
''''Ui
xU VUU +↔ ••••
'Agi
xAg VAgAg +↔ •
'iF
xF FVF +↔ •
''Cai
xCa VCaCa +↔ ••
'Lii
xLi VLiLi +↔ •
''iO
xO OVO +↔ ••
''''Tii
xTi VTiTi +↔ ••••
''iO
xO OVO +↔ •• from Allen & Thomas
many more anion Frenkel defects than cation ones
to measure the concentration of intrinsic point defects, ionic crystals of high purity have to be made, e.g., by zone refining
includes energy of electrostatic interactionsFPfhΔ
University of Virginia, MSE 6020: Defects and Microstructure in Materials, Leonid Zhigilei
Schottky defects
6.4UO2
2.2-2.4NaCl
5.2TiO2
5.5CaF2
2.6KCl
6BeO
26α-Al2O3
Schottky defectcompound eV ,SDfhΔ
••+ o'''
Al V32V
from Allen & Thomas
electrostatic attraction between cation and anion vacancies → binding energy of the Schottky defect and temperature dependent degree of association
Schottky defect = cation vacancy + anion vacancy in close proximity
xO
xBeO
''Be
xO
xBe OBeVVOBe +++↔+ ••
formation reaction for a Schottky defect in BeO:
this reaction satisfies the mass, charge, and side balance
⎟⎟⎠
⎞⎜⎜⎝
⎛ Δ−⎟⎟
⎠
⎞⎜⎜⎝
⎛ Δ=
Tkh
ks
Nn
B
SDf
B
SDv
SDeq
2exp
2exp
equilibrium concentration:•+ F
''Ca V2V
••+ O''
Be VV••+ O
''''Ti V2V
••+ O''''
U V2V•+ Cl
'Na VV
•+ Cl'K VV relative low Δhf → Schottky defects dominate
University of Virginia, MSE 6020: Defects and Microstructure in Materials, Leonid Zhigilei
Extrinsic point defects in ionic crystals - impuritiesIntroduction of impurities may require simultaneous introduction of additional defects, e.g., in addition to the thermally-induced (intrinsic) vacancies, some additional extrinsic vacancies may be induced by impurity ions with valence different from the one of the ions in the host crystal.
Let’s consider incorporation of CaCl2 to KCl crystal as a substitutional impurity:
2KCl(g)2ClVCa2Cl2K)s(CaCl xCl
'KK
xCl
xK2 +++↔++ •
Site balance: the 1:1 ratio of K and Cl sites must be maintained. Two Cl anions occupy the existing Cl sites → two cation sites must be created. One of the cation sites is occupied by Ca2+
and one is left vacant.
xCl
'Ki2 2ClV2CaCaCl ++↔ ••or
Mass balance: the numbers of atoms of each species on both sides of the equation are equal.
Charge balance: placing Ca2+ on a K+ gives a net charge of +1 that has to be compensated by a vacancy.
If Ca2+ occupies an interstitial site, the equation has to be modified:
2KCl(g)2ClV2Ca2Cl2K)s(CaCl xCl
'Ki
xCl
xK2 +++↔++ ••
xCl
'KK2 2ClVCaCaCl ++↔ •or
University of Virginia, MSE 6020: Defects and Microstructure in Materials, Leonid Zhigilei
Extrinsic point defects in ionic crystals - impuritiesDifferent schemes of impurity incorporation can be sometimes distinguished from experimental measurements of the effect of impurity concentration on material density.
Let’s consider incorporation of ZrO2 to Y2O3 crystal
Two simplest options: (1) Zr4+ fully occupy Y sites and anion defects take care of the charge balance
''i
xOY2 OO32Zr2ZrO ++↔ •
(2) O2- fully occupy O sites and cation defects take care of the charge balance '''
YYxO2 V3ZrO63ZrO ++↔ •
Experimental observation that density of Y2O3 increases with addition of ZrO2 is in favor of option (1), since appearance of vacancies would decrease density and Zr has slightly higher atomic mass and smaller ionic radius than Y.
University of Virginia, MSE 6020: Defects and Microstructure in Materials, Leonid Zhigilei
Extrinsic point defects in ionic crystals - impuritiesLet’s consider incorporation of CaO to ZrO2
We have two possible scenarios:
(1) charge compensation by anion vacancy ••++↔ OxO
''Zr VOCaCaO
(2) charge compensation by Zr interstitials
Solid solutions produced by these different reactions will have different densities. For reaction (1), the defective formula unit is made up of one Ca, one O, and one vacancy. For reaction (2), the defective formula unit is made up of one Ca, two O, and one half of a Zr (in an interstitial site). Thus, the formulas for weight and density of each solid solution are:
••••++↔+ ixO
''Zr
xZr ZrO2Ca2Zr2CaO
2ZrOCaO )M(1)(M (1) xx −+22 ZrOZrCaO )M(1)M
21(M (2) xx −++
where M is the molecular weights of the corresponding species, Vcell is the volume of the unit cell, and Z is the number of formula units per unit cell.
cellaVNxxZ ])M(1)(M[
2ZrOCaO −+×=ρ
cellaVNxxZ ])M(1)M5.0(M[
22 ZrOZrCaO −++×=ρ
need an extra Zr sitesite balance: 1Zr = 2Zr + 2Onull = ZrO2
2ixO
''Zr
xZr
xO
xZr ZrOZr2O2CaZr2OZr2CaO +++↔+++ ••••
Ca2+ cation, Zr4+ cation, O2- anion
University of Virginia, MSE 6020: Defects and Microstructure in Materials, Leonid Zhigilei
Extrinsic point defects in ionic crystals - impurities
cellaVNxxZ ])M(1)(M[
2ZrOCaO −+×=ρ
cellaVNxxZ ])M(1)M5.0(M[
22 ZrOZrCaO −++×=ρ
••++↔ OxO
''Zr VOCaCaO ••••++↔+ i
xO
''Zr
xZr ZrO2Ca2Zr2CaO
Experiments by Diness and Roy [Solid State Commun. 3, 123, 1965]
Thus, the two hypothetical models predict ~8% difference in the density. When mass and volume measurements can be done with sufficient accuracy, it is possible to distinguish themodels.
small amount of CaO stabilizes cubic fluorite structure a4×(ZnO2) per unit cell
For x = 0.15, Z = 4, MCaO = 56.2 g/mole, MZrO2 = 123.2 g/mole, MCaO2 = 72.1 g/mole, MZr = 91.2 g/mole, and the cubic latticeconstant a = 5.15 Å, we calculate densities of ρ = 5.5 g/cm3 and ρ = 5.95 g/cm3 for the vacancy and interstitial models, respectively.
ρ, g
/cm
3
(we are neglecting changes in the size of the unit cell with composition)
University of Virginia, MSE 6020: Defects and Microstructure in Materials, Leonid Zhigilei
Extrinsic point defects in ionic crystals - impurities
from Allen & Thomas
extrinsic defects dominate at low T
concentration of point defects in KCl with 0.1 ppm CaCl2
⎟⎟⎠
⎞⎜⎜⎝
⎛ Δ−⎟⎟
⎠
⎞⎜⎜⎝
⎛ Δ=
Tkh
ks
Nn
B
SDf
B
SDv
SDeq
2exp
2exp
xCl
xKCl
'K
xCl
xK ClKVVClK +++↔+ •
intrinsic (Schottky) defects:
eV 6.2=Δ SDfh
xCl
'KK2 2ClVCaCaCl ++↔ •
extrinsic defects
ln(10-7) = 16.12
University of Virginia, MSE 6020: Defects and Microstructure in Materials, Leonid Zhigilei
Non-stoichiometry
This scenario works for transition metals (e.g., Fe, Ti, Cu, Ni), where the ionization energy is low, but not for metals with high ionization energy (e.g. Na or K)
Ni2+ can then transform into Ni3+ (2 Ni ions have to be transformed for each vacancy)
While some of the compounds become unstable at small deviations from stoichiometric composition (e.g. NaCl), other compounds can exhibit large deviations from stoichiometric composition or even be unstable at the stoichiometric composition (e.g. FeO - wüstitephase).
MxO2 VO)(O
21
+↔gFor a transfer of oxygen to a metal oxide MO:
cation vacancy + 2 holes
(transfer of neutral O)
But if the crystal is ionic, O will accept 2 e- that should come from metal that is already ionized, e.g., for NiO:
''Ni
xO2 V2O)(O
21
++↔ •hg
-2O-2O-2O-2O
-2O-2O-2O-2O
•h
+2Ni+2Ni+2Ni+2Ni
+2Ni+2Ni+2Ni+2Ni
''NiV
-2O-2O-2O-2O
-2O-2O-2O-2O
+2Ni+2Ni+2Ni+2Ni
+2Ni+2Ni+2Ni+2Ni
•h
-2O)(O
21
2 g
(equivalent to solution of Ni2O3 in NiO)
OM δ1−MO
University of Virginia, MSE 6020: Defects and Microstructure in Materials, Leonid Zhigilei
Non-stoichiometry
University of Virginia, MSE 6020: Defects and Microstructure in Materials, Leonid Zhigilei
Electronic defects in semiconductors
Electronic defects in intrinsic semiconductorsExtrinsic electronic defects in semiconductors - doping
optional reading(not tested)
University of Virginia, MSE 6020: Defects and Microstructure in Materials, Leonid Zhigilei
insulators - semiconductors - metals
σ (Ωcm)-1
n ≈ 1.4×1010 cm-3 (Si at 300 K)n - number of “free” or conduction electrons per unit volume
n ≈ 1.8×1023 cm-3 (Al)n ~ 1 cm-3
σ = n|e|μe + p|e|μh
filled band
Energy
partly filled band
empty band
GAP
fille
d st
ates
partially filled band
filled band
Energy
partly filled band
empty band
GAP
fille
d st
ates
filled band
Energy
partly filled band
empty band
GAP
fille
d st
ates
partially filled band
Energy
filled band
filled band
empty band
fille
d st
ates
overlapping bandsEnergy
filled band
filled band
empty band
fille
d st
ates
Energy
filled band
filled band
empty band
fille
d st
ates
overlapping bands
Energy
filled band
filled valence band
fille
d st
ates
empty
bandconductionempty
bandconduction
Energy
filled band
filled valence band
fille
d st
ates
?
empty
bandconductionempty
bandconduction
Mg: 1s22s22p63s2Cu: 1s22s22p63s23p63d104s1
Eg > 2 eV Eg < 2 eV
University of Virginia, MSE 6020: Defects and Microstructure in Materials, Leonid Zhigilei
Electronic defects in intrinsic semiconductors
conduction band
Eg
T = 0 K
material Eg, eV
Si 1.1
SiC 2.9
ZnO 3.3
Al2O3 9.5
Thermal generation of electron-hole pairs.Electrons excited to the conduction band leave holes in the valance band
electrons, e
holes, h
EF represents probability of ½ that an available energy state is occupied by an electronEF = electrochemical potential of electrons
valence band
Fermi level, EF
f(ε)
ε
T > 0 K
f(ε)
ε
10 0 1
The concentration of electrons, n, in the conduction band
⎟⎟⎠
⎞⎜⎜⎝
⎛ −−⎟⎟
⎠
⎞⎜⎜⎝
⎛ π≈ε⎥
⎦
⎤⎢⎣
⎡⎟⎟⎠
⎞⎜⎜⎝
⎛ −ε+ε=εεε=
−∞∞
∫∫ TkEE
hTkmd
TkEgdTfg
B
FCBe
B
F
EE CC
exp22exp1)(),()(n2/3
2
*1
EV
EC
2/12/3
2
*
)(24)( Ce E
hmg −ε⎟⎟
⎠
⎞⎜⎜⎝
⎛π=ε
⎟⎟⎠
⎞⎜⎜⎝
⎛ −ε≈⎟⎟
⎠
⎞⎜⎜⎝
⎛ −ε+
TkE
TkE
B
F
B
F expexp1
We used the free electron gas model approximations:
( ) 2/exp0
π=−∫∞
xxas well as and
University of Virginia, MSE 6020: Defects and Microstructure in Materials, Leonid Zhigilei
Electronic defects in intrinsic semiconductors
- effective densities of state at the conduction and valence band edges
⎟⎟⎠
⎞⎜⎜⎝
⎛ −−=⎟⎟
⎠
⎞⎜⎜⎝
⎛ −−⎟⎟
⎠
⎞⎜⎜⎝
⎛ π=
TkEEN
TkEE
hTkmn
B
FCCeff
B
FCBe expexp222/3
2
*
Similarly, the concentration of holes, p, in the valence band
⎟⎟⎠
⎞⎜⎜⎝
⎛ −−=⎟⎟
⎠
⎞⎜⎜⎝
⎛ −−⎟⎟
⎠
⎞⎜⎜⎝
⎛ π=
TkEEN
TkEE
hTkmp
B
VFVeff
B
VFBh expexp222/3
2
*EV
g(ε)
ε
EC
for an intrinsic semiconductor:
pnni ==2
Eln
43
2E
E g*
*g ≈+=
e
hBF m
mTk
Veff
Ceff and NN
intrinsic concentration of charge carriers:
⎟⎟⎠
⎞⎜⎜⎝
⎛−==
TkE
NNnpnB
gVeff
Ceffi 2
exp
depends only on T and Eg = EC -EV
n = C T3/2 exp(-Eg/2kT)
University of Virginia, MSE 6020: Defects and Microstructure in Materials, Leonid Zhigilei
Electronic defects in intrinsic semiconductors
Js 10626.6 34−×=h
surprisingly good semi-quantitative agreement, given that very rough
approximations are used, e.g. g(ε) for free electron model,
decrease of Eg with increasing T is neglected…
Eg = 0.67 eV for GeEg = 1.11 eV for Si
3-262/3
2
*
m 108.222 ×=⎟⎟⎠
⎞⎜⎜⎝
⎛ π=
hTkmN BeC
eff
⎟⎟⎠
⎞⎜⎜⎝
⎛−=⎟⎟
⎠
⎞⎜⎜⎝
⎛−⎟⎟
⎠
⎞⎜⎜⎝
⎛ π=
TkE
NTk
Eh
TkmnB
gCeff
B
gBe
2expexp22
2/3
2
*
J/K 10381.1 23−×=Bkkg 1011.9 31* −×≈em
for T = 1500 K
014.02
exp =⎟⎟⎠
⎞⎜⎜⎝
⎛−
TkE
B
g
- can find Eg from the temperature dependence of intrinsic carrier concentration
University of Virginia, MSE 6020: Defects and Microstructure in Materials, Leonid Zhigilei
Electronic defects in extrinsic semiconductorsExtrinsic semiconductors - electrical conductivity is defined by impurity atoms. Si is considered to be extrinsic at room T if impurity concentration is one impurity per 1012 lattice sites
molar volume of Si ≈12 cm3/molNA ≈ 6×1023 atoms/mol6×1023 / 12×10-6 = 5×1028 atoms/m3
fraction of excited intrinsic electrons per atom ~10-13
intrinsic: n ≈ 1.4×1016 m-3 (Si at 300 K)Unlike intrinsic semiconductors, an extrinsic semiconductor may have different concentrations of holes and electrons.
p-type if p > n and n-type if n > p
One can engineer conductivity of extrinsic semiconductors by controlled addition of impurity atoms – doping (addition of a very small concentration of impurity atoms). Two common methods of doping are diffusion and ion implantation.
n-type: excess electron carriers are produced by substitutional impurities that have more valence electron per atom than the semiconductor matrix (elements in columns V and VI of the periodic table are donors for semiconductors in the IV column, Si and Ge)Example: P (or As, Sb..) with 5 valence electrons, is an electron donor in Si since only 4 electrons are used to bond to the Si lattice when it substitutes for a Si atom. Fifth outer electron of P atom is weakly bound in a donor state (~ 0.01 eV) and can be easily promoted to the conduction band.
p-type: excess holes are produced by substitutional impurities that have fewer valence electrons per atom than the matrix (elements in columns III of the periodic table (B, Al, Ga) are donors for semiconductors in the IV column, Si and Ge)
University of Virginia, MSE 6020: Defects and Microstructure in Materials, Leonid Zhigilei
Electronic defects in extrinsic semiconductors
donor dopant creates energy level near conduction band easy to promote electron from donor level to conduction bandFermi level moves toward conduction band
Ec
EV
T = 0K
EdEc
EV
T > 0K
EdEF EF
acceptor dopant creates energy level near valence band easy to promote electrons from valence levels to acceptor band (create holes are in valence band)Fermi level moves toward valence band.
Ec
EV
T = 0K
Ea
Ec
EV
T > 0K
EaEF EF
Out of the total number of dopants (substitutional extrinsic point defects), some will be neutral and some ionized. For example, for P in Si, the total concentration [P] = [P]0 + [P]+
{ } ⎟⎟⎠
⎞⎜⎜⎝
⎛ −≈−=+
TkEEf
B
dFexp]P[)T,E,E(1]P[]P[ Fd
vacancies can also introduce energy levels within the band gap and can be ionized