chap 2 energy absorption of luminescent materials 2-1 general...

Chap 2 Energy Absorption of Luminescent Materials

2-1 General/Theoretical Considerations2-2 Effect of Host Lattice (主體晶格效應)2 2 Effect of Host Lattice (主體晶格效應)

(a) covalence effect (共價效應)(b) crystal field effect (結晶場效應)

2-3 Energy level diagrams of Individual Ions 個別稀土離子之能階圖簡介

(a) Transition metal ions (dn, d0: W6+, Mo6+, Nb5+,V5+; d10: Zn2+,Cd2+, Ga3+, Sb3+)(b) Rare earth ions (fn→fn, fn→ fn-15d與電荷遷移)(c) Main group ion (s2)(c) Main group ion (s )(d) Other charge transfer (LMCT, MLCT, MMCT)(e) Color Center (F-center)

(2-4 Host lattice absorption (主體晶格對能量之吸收- 兩類光學躍遷機制 )(a) Those generate free carriers (electrons and holes)(能產生電子電洞等自由載子者) examples: ZnS, ZnSe,ZnTe, CdS, CdTep(b) Those generate free carriers (紫外照射CaWO4, 激子存在於WO42-中; NaCl) 1

HL: Host lattice

CT E 3+ O2 ChCT: Eu3+→O2- Charge transfer

f f absorptionf – f absorption

2

Symmetrical Stretching Mode (breathing mode)Symmetrical Stretching Mode (breathing mode)

3

Vibration motion – harmonic*F: Restoring forceF = -k (R-Ro) Crossing point:

E

*Potential energyE = 1/2k (R-Ro)2

Crossing point: possible to return to ground state non-radiatively.( o)

*Energy of vibrational levelEn = (n+1/2)hνEn (n 1/2)hν

R

Th f f ib ti l d (聲子) i d t i d b h tThe frequency of vibrational modes (聲子) is determined by host lattice (H) in which a luminescent center (A) is located ! 4

Calculated energy level terms f f R E th I (4f )for free Rare Earth Ions (4fn)

(自由態稀土3+離子理論能階圖)

Incompletely filled 4f shell, 4f is shielded by 5s2 5p6 orbitals5s2, 5p6 orbitals.

5D0

Host Lattice effect on optical transitions within 4f n configuration is4f configuration is small (but essential)

1 2 3 4 5 6 7 8 9 10 11 12 13 n =5

Highest (vibronic)

Electronic state

Lowest (vibronic)( )

6

How to Understand the Probability of Optical Transitions between v = 0 and v =1 vibrational states?

The probability (P) is proportional to

P ∞ P ∞ e: excited state wavefunction (Ψe) g: ground state wavefunction (Ψg)r: electric-dipole operator (電雙極運算子) that drives the transition

1.When one considers the absorption bands, ∑ χv (v = 0 → n)

χv’,χo: vibrational states wavefunctions

must be considered2.上式中 : electronic matrix elements, independent of vibration 決定 ground → excited state 的intensityvibration. 決定 ground → excited state 的intensity3. : vibrational overlap of Ψ‘s決定absorption band 的形狀

一般而言, Electronic-vibrational coupling係指

electronic與vibration of optical centers之間的交互作用, 可以用 ΔR ( = Ro＇– Ro)表示表示

ΔR大, 則為強交互作用; ΔR 小, 則為弱交互作用 7

(1) ΔR = 0 時, the vibrational overlap is maximized for v = 0 and v’= 0

代表∴ absorption spectrum 由line 所組成(線光譜),代表v = 0 → v’= 0之遷移(其中無振動遷移牽涉其中)，故又稱之為zero-vibrational或non-phonon transition (i.e., zero-phonon lines)

(2) ΔR ≠0 時 v = 1 level與 v＇ > 0 level之間有maximal overlap∴ absorption spectrum is broad, ΔR越大,則激發光譜中吸收峰越寬, 此時兩個states 所對應之化學鍵性質差異越大states,所對應之化學鍵性質差異越大

通常稱 ΔR = 0 weak coupling 弱偶合作用

ΔR > 0 intermediate coupling

ΔR >> 0 strong coupling 強偶合作用

上述coupling係指電子與發光中心(optical center)之振動兩者交互作用。之振動兩者交互作用

At high temperature, 高溫時基態可能為 v> 0 而非 0 此時會造成光譜中吸收峰變寬!而非 v = 0, 此時會造成光譜中吸收峰變寬!

8

Coupling 係指電子與vibration center之間的交互作用,而ΔR決定此交互作用之強弱定此交互作用之強弱

ΔR = 0 the weakest 溫度升高 absorption

高溫

coupling scheme溫度升高 absorption band broadened

ΔR > 0 the intermediate coupling schemescheme

ΔR 0 th t t

決定band 寬度

ΔR >> 0 the strongest coupling

9

Intensity of Optical Transition (absorption) related to matrix elements

Selection Rules (光學躍遷選擇律)1. The spin selection rule which forbids electronic transition between levels with different spin states (ΔS = 0, forbidden).

2. Parity selection rule which forbids electronic (electric-dipole) transitions between levels with the same parity. (Same parity forbidden, 如: d → d or f → f)

In solids, selection rules NOT absolute, some forbidden transitions slightly relaxed. Why? y

It is related to

(a) Wavefunctions admixture into the original, unperturbed wavefunctions.

(b) Spin-orbit coupling, electronic-vibrational coupling and uneven crystal field terms.

Reference1. Henderson (1989) “Optical Spectroscopy of Inorganic Solids”. O f d U i it POxford University Press.2. DiBartolo (1968)”Optical Interaction in Solids”, Wiley. 10

HL: Host lattice3 2CT: Eu3+-O2- Charge transfer

f – f absorption

Highest occupied level of ground state: 2p, 3s of oxygenLowest unoccupied level of exc state: mixture of 3s of oxygen and 4d of YLowest unoccupied level of exc. state: mixture of 3s of oxygen and 4d of Y. (顯示基態與激發態兩者有極大之差異,兩者之間躍遷牽涉相當大ΔR值及bonding差異) 11

Y2O3: crystal structure in the solid state 2 3 yGeometry of Y3+: 6 coordinate: octahedral

Eu2O3 doped with 1 mol% Eu3+ can be represented as Y2O3:0.01Eu or(Y0.99Eu0.01)2O3

1%Y3+ is replaced by Eu3+Eu

Y2O3:Eu

activator 12

The Influence of Host Lattice on Absorption of Luminescent Materials(a) Covalency effect

當共價性增加時由於電子密度更分散於軌域中電子間斥力減弱不同能階當共價性增加時,由於電子密度更分散於軌域中,電子間斥力減弱,不同能階間電子躍遷對應能量減小, 故產生紅位移.

(b) Crystal field effect(b) Crystal field effect結晶場係指發光中心離子周圍環境的電場強度，某些光學躍遷對結晶場顯示高度依存度。

- Higher covalency: 組成元素離子間 electronegativity 差異小,故 charge transfer (CT) transition between these ions shifted to lower energy,transfer (CT) transition between these ions shifted to lower energy, CT absorption band of Eu3+ in YF3 is at higher energy than that in Y2O3

I Y O S E 3+ E t d t b t i 2+ d 3+ t t th th- In Y2O2S:Eu3+, Eu tends to be present in 2+ and 3+ states, thus, the maximal Eu2+ CT is much lower than the rest .

13

Examples: - Host:Bi3+ (6s2, 6s2→ 6s16p1), 6s, 6p electrons residing on the surface

of Bi3+ ion, the repulsion effect is large.of Bi ion, the repulsion effect is large. - Host:Gd3+ (4f7, 4f→ 4f), f electrons lie inside the Gd3+ ion, the effect is

small- Covalency Y2O3 > YF3, thus, Eu3+ f → f energy is lower (longer labs)y 2 3 3, , gy ( g )

weakweak

covalency

weak

covalency

weakSmall and negligible

Large variation

strongstrong

negligible variation

14

- Higher covalency: 組成元素離子間 electronegativity 差異小,故 charge transfer (CT) transition between these ions shifted to lower energy, CT absorption band of Eu3+ in YF is at higher energy than that in Y Oabsorption band of Eu3 in YF3 is at higher energy than that in Y2O3- In Y2O2S:Eu3+, Eu tends to be present in 2+ and 3+ states, thus, the maximal Eu2+ CT is much lower than the rest .

weak large

covalency

weak

CT Energy

largeCT: charge transfer

Oxygen to Eu3+

strong small

Oxygen to Eu

15

(b) Crystal field (C.F.) effect- the electric field at the site of luminescent center due to surrounding,some optical transitions are highly dependent on strength of C.F. – Cr3+

例如: Al2O3:Cr3+ is red while Cr2O3:Cr3+ is green. Both hosts are isostructural.

In Al2O3:Cr3+ - Cr3+ occupies Al3+ site, stronger crystal field is expectedthan in Cr2O3. ti l t iti i b (紅寶石 i t hi h th th t i C O∴optical transition in ruby(紅寶石)is at higher energy than that in Cr2O3

(即紅寶石吸收較短波長可見光而所顯示波長較長之紅色互補光)

此外, 由於結晶場強度決定optical transition 之劈裂 (splitting)

∵不同主體晶格造成不同晶場強度導致不同splitting,因此optical center的光譜可被利用以探討site symmetry.

另一方面,若有非對稱結晶場存在,則往往可以不遵守selection rules.

16

Nephelauxetic Effect (電子雲擴散效應)

With increasing covalency and weakening of the electronic repulsion between electrons, the transition between energy levels with an energy difference shifted to lower energy

(共價性增加, 電子間作用力降低,)

weakweak

covalency

weak

covalency

weakSmall and negligible

Large variation

strongstrong

negligible variation

17

EFFECT OF HOST LATTICE

IONIC CHARACTER

YF > Y OYF3 > Y2O3

Covalency

YF3 < Y2O3

1.YF3:Eu中主體吸收峰消失可能出現在更短波長.2.波長為250nm之Y2O3:Eu CT band在YF3:Eu中偏移至150nm.

中之躍遷出現了而在中則無3. YF3:Eu中, 4f-5d之躍遷出現了! 而在YF3:Eu中則無.4.兩者中Eu3+之吸收峰為尖銳weak lines (因為4f 軌域遮蔽良好)相對於O2 E 3+ h t f F E 3+CT 吸收更難相對於O2- → Eu3+ charge transfer, F- → Eu3+CT 吸收更難,應出現在更高能量) 18

Spectral Inhomogeneous Broadening

實驗值

Example:

The optical transition energy of Eu3+ on the surface and in the interior are different:

1 Y O E 3+中 Y3+離子具有2種結晶學上獨立的格位(l tti it ) 故產1. Y2O3:Eu3+中, Y3+離子具有2種結晶學上獨立的格位(lattice sites), 故產生兩種Eu3+之放射/吸收峰.

2 當主體物質為玻璃態時因為缺乏translational symmetry 因此放射/吸2.當主體物質為玻璃態時, 因為缺乏translational symmetry,因此放射/吸收峰產生寬化現象(broadening). 19

Parity(宇稱): The molecular orbitals of homonuclear molecules (同核分子)are labelled with a subscript g or u that specifies their parity, that is, their behavior

d i i t tiunder inversion symmetry operation.

The parity designation applies only to homonuclear diatomic molecules, since heteroatomic molecules do not have an inversion center (i).( )

Term symbol The total angular momentum of all electrons around the internuclear axis is denoted by symbols Σ, Π, Spin multiplicityXg,u

y y , ,Δ…..corresponding to the S, P, D, F, G, H, I, ……of atoms.

Overall parity: g x g = g, u x u = g, g x u = u

H2+: 2Σg Neutral H2: 1Σg O2: 3Σg 20

Spectroscopic TerminologyOptically active cations having electrons external to the closed shellOptically active cations having electrons external to the closed shell which can be excited by a photon of proper energy, e.g., Sn2+(5s25p0)is optically active, Sn4+ (5s0) is NOT

Russell-Sanders Coupling (L=S coupling)- valid for light atomsL = Σ li S = Σ si J = L + S (J can also be obtained as J = Σi jiis used because it agrees well with experimental values most of the time

L = 0 1 2 3 4 5 6 7 2S+1 LJ Term S P D F G H I J (S: total spin quantum no.; L: total orbital angular quantum no.; Degeneracy(S: total spin quantum no.; L: total orbital angular quantum no.; Degeneracy (2L+1) and maybe lifted by crystal field)

R-S coupling adequately describes the optically active E states for nearly all t d i ith th ti f th th

For crystal field levels: 2S+1 X

atoms and ion, with the exception of the rare earths

X: A, no degeneracy E, two fold degeneracy T, three fold degeneracy21

Metal Complexes with d1 configuration

d1 – Octahedral symmetry

Δo

Δt

而在 tetrahedraL d1 complexes中並不具有“i ”的反轉對稱,因此selection rule is relaxed by mixing small amount of opposite-parity wave function into the d wavefunctioninto the d wavefunction

因此 Color of tetrahedral transition-metal ions is stronger, as compared to octahedral cases. f (oscillator strength) = kA.

22

4T2

Cr3+ ground state: 4A2 4A24T1(F)

2S + 1 = 2(3/2) + 1 = 4

L = 2+1+0 = 3 → 光譜項 F4F

(基態)

Absorption transitions from 4A24T1(P)

4Fp

obey spin selection rules.23

Energy Level Diagrams of Individual Ions – the transition metal ions (dn)

Transition Metals: incompletely filled d-shell; d1, d3, d5 ions with incompletely filled shells (0

Mn2+ (d5): parity forbidden d → d (基態為6A1)

For d5 ions (基態為6A1) all possible transitions arepossible transitions are spin-forbidden and parity-forbidden.

25

400 nm 750 nm

25 000 1 13 225 1

Δ = 2E – 2T2 (crystal field strength)

Δ = 20000 cm-1 for M3+ visible

~25,000 cm-1 13,225 cm-1

3.10 eV 1.65 eV

E (eV) = 1240/ λ(nm)

1 eV = 8064.5 cm-1


Strength of crystal field determines Δvaluesvalues

Charge transfer

2T2 → 2E

水溶液中Ti3+(d1)之UV-Vis吸收光譜 26

400 nm 750 nm

25 000 1 13 225 1 Δ = 2E – 2T2 (crystal field strength)


~25,000 cm-1 13,225 cm-1

3.10 eV 1.65 eV

E (eV) = 1240/ λ(nm)

1 eV = 8064.5 cm-1Strength of crystal field determines Δvalues

水溶液中Ti3+(d1)之

Charge transfer

水溶液中Ti3+(d1)之UV-Vis吸收光譜 2T2 → 2E

27

Observations and Rationalizations of Band Width in Mn2+ Absorption SpectraMn2+: - 源自於t23e2 excited state的 4A1, 4EΔR is vanishing, thus, transitions from 6A1→4A1, 4E should appear as lines- 然而 4T1 4T2係源自於t24e1之電子組態 6A1→ 4T1 or 4T2- 然而 4T1, 4T2係源自於t24e1之電子組態, 6A1→ 4T1 or 4T2ΔR ≠ 0, observed as a band in the absorption spectra

28

In the U V region transition metal ions 通常顯示broad and strongIn the U.V. region transition metal ions 通常顯示broad and strong absorption due to

(a) Ligand-to-metal charge transfer (LMCT)- d0 ions: Cr6+, Mn7+ strongly ( ) g g ( ) , g ycolored in oxides due to charge transfer transitions; 如: MnO4- and Cr2O72- are deeply colored

(b)Oth i t t LMCT i V5+ Nb5+ W6+ (d0) d0 YVO YNbO(b)Other important LMCT species: V5+, Nb5+, W6+ (d0) d0: YVO4, YNbO4, CaWO4

Compounds with anions that are optically active or “self-activated” (自身活化化合物)self activated (自身活化化合物)CaWO4, CaMoO4,YVO4, YNbO4ZnGa2O4Zn2SnO4

29

Molecular energy levels for the tetrahedral VO43- groupExcited state consists of an increased e density in the vicinity of V ion, along

Excitation: 3t2 → 3a1

the Td bonds → Charge Transfer (CT)

Emission: 4t2 → 3t2

excitation

Oxide anionMn+

30

Transition Metal Ions with d0 configurationYVO4, YNbO4, CaWO4- Strong, broad bands in the Ultraviolet region.

Charge transfer from Oxygen to Mn+ (d0 ion)- Charge transfer from Oxygen to Mn (d0 ion)- Electrons are excited from a non-bonding orbital to antibonding orbital 造成 Metal-Oxygen bonding 減弱- M-O Bonding is strongly weakened after optical absorption- M-O Bonding is strongly weakened after optical absorption 此時造成ΔR >> 0 and band width is large

Absorption transition Energy or λ relies on(a) d1→d0之ionization energy, (b) number and nature of the ligands, (c) lattice 中ion-ion interaction

CaWO4(with WO42-) CaMoO4 Ca3WO6 (with isolated WO66-)CT ν (cm-1) 40,000 34,000 35,000 (286 nm)

(CT: M6+ + e- (氧-鉬)→M5+)(CT: M6 + e (氧-鉬)→M5 )WO3結構中具有WO66- groups sharing O2-則吸收出現在可見光範圍Ca3WO6結構中具有isolated WO66- groups ,此為optical center與CT bands交互作用所形成所形成

31

Comparison of ground-state energy levels and optical terms for f l th id i (III)free lanthanide ions (III)

(鑭系(lanthanide)自由離子之電子組態基態能級與光譜項之比較)

32

Calculated energy level terms f f R E th I (4f )for free Rare Earth Ions (4fn)

(自由態稀土3+離子理論能階圖)

Incompletely filled 4f shell, 4f is shielded by 5s2 5p6 orbitals5s2, 5p6 orbitals.

5D0

Host Lattice effect on optical transitions within 4f n configuration is4f configuration is small (but essential)

1 2 3 4 5 6 7 8 9 10 11 12 13 n =33

Experimentally observed 4f n energy level diagrams for trivalent p y f gy glanthanides in the range 40,000-70,000 cm-1(250 - 142 nm). Levels from which emission is observed are marked with a semicircle. 34

E ( V) 1240/ λ( ) 1 V 8064 5 1E (eV) = 1240/ λ(nm) 1 eV = 8064.5 cm-135

Rare earth 4fn ions (f→ f transitions)

1)R3+電子組態 4fn..5s2..5p6.. 4fn electrons are well shielded by 5s, 5p..Crystal field splitting強度之數量級遠較dn之過渡金屬為小

R O hit (∵ it f bidd ) 其中僅 Nd O f i t i l t Tb O- R2O3: white (∵ parity forbidden)，其中僅 Nd2O3: faint violet; Tb4O7, Pr4O7, Pr6O11 dark color(∵ R3+/R4+共存之緣故) -Eu3+(aq)具有 low molar absorptivity, sharp lines f-f transition and ΔR = 0( q)具有 p y, p

2)此時parity selection rule並非因振動摻入而產生relaxation,而是因uneven component of crystal field (如R3+ ions位於一不具反轉對稱中心的格位)

3) Uneven component 將具有opposite parity之5d混入R3+之4f 波函數之中因此造成躍遷產生因此光譜學家說

component of crystal field (如R ions位於一不具反轉對稱中心的格位)

之中, 因此造成4f - 4f 躍遷產生。因此光譜學家說: 4f-4f transitions steal some intensity from allowed 4f-5d transitions。

Rare earth ions (interconfiguration 4f-5d CT transitions)

1. CT transitions (4fn-4fn+1L-1)1. CT transitions (4f 4f L )2. 4fn-4fn-15d transitions (allowed by selection rule) 36

(a)CT transitions 4fn-4fn+1L-1 (由L至4f的遷移)

allowed and ΔR ≠ 0, broad absorption bands

occurs in easily reduced R4+ ions (R4+ + e- → R3+), examples: y ( )Ce4+,Pr4+,Tb4+ – CT broad absorption bands; orange Y2O3:Tb3+(CT absorption band in visible)

另一方面, R2+亦易發生4f-5d transitions (Sm2+ -可見光; Eu2+,Yb2+-長波長之紫外範圍)

(b) 4fn-4fn-15d transitions

1)發生於傾向被氧化之R2+離子( R = Sm, Eu,Yb,傾向被氧化成R3+離子); 2)另一方面,傾向被氧化成R4+ ( R = Ce, Pr,Tb)之離子則常在紫外光範圍產生4f – 5d吸收帶; 3)傾向被還原成Sm2+, Eu2+, Yb2+之R3+離子,則在紫外範圍產生CT absorption bands.

(Ref. Structure and Bonding, vol. 26, p. 43(1976))37

The absorption and PL spectra and the relevant energy levels for Y3Al5O12:Ce3+at 295K

38

CaSO4(s):Ce3+ The five observed peaks are attributed to the 4f –5d absorption transitions induced by crystal field splitting 由於5d晶場分裂造成吸收光譜中4f – 5d 吸收躍遷形成5 peaks

Ce3+: 4f1 (ground state) 5d1 (excited state)

39

Order of energy level splitting strength for rare earth ionsstrength for rare earth ions 稀土離子能階的劈裂(splitting)強度順序

Crystal field (102-103cm-1)< Spin-orbit y ( ) p(103-104 cm-1) < Interelectronic repulsion (>105 cm-1) 41

Ions with d10 Configuration (e.g., Zn2+, Ga3+, Sb5+)

-Showing intense and broad absorption bands in the short wavelength UV (strong broad bands 高強度寬吸收帶 !!)

- Luminescence of d10 ions – the exact nature is unclear, but

wavelength UV (strong broad bands 高強度寬吸收帶 !!)

mainly consisting of a CT transition from the ligands (oxygen 2p orbital) to an anti-bonding orbital (partly on d10 ions and partly on ligands)partly on ligands)

(Blasse, G.: Chem Phys. Lett. (1990) 175, 237)

Examples: ZnGa2O4Self activatedZn2GeO4

M2SnO4

Self-activated luminescence

M2SnO4

Oxygen vacancies, cation defects, 42

Color Centers (色心) F-Center

-Consisting of an electron in a halide vacancy in KCl.

-The first optical transition is parity-allowed 1s → 2p (similar to thatThe first optical transition is parity allowed 1s → 2p (similar to that of hydrogen atom).

In KCl its absorption maximum is red, so KCl crystals containing F-center is strongly and deeply blue colored

Synthetic quartz

Smoky quartzIrradiated glassCentury-

Synthetic quartz

yold desert amethyst

紫水晶 43

Comparison of absorption spectra for color centers formed by chlorides with different alkali metals (不同鹼金屬氯化物中所形成色心之吸收光譜之比較)

44

Absorption of host lattice (主體晶格之吸收)

Levels with Zn character

Levels with S character

Scheme illustrating possible absorption and emission between energylevels attributed to donor, acceptor and traps in the energy gap.(能隙中含有施體受體與陷坑能階的螢光體之中可能的吸收與放射躍遷示意圖)(能隙中含有施體、受體與陷坑能階的螢光體之中可能的吸收與放射躍遷示意圖)

46

Delocalized luminescence centerdonor-acceptor pair ZnS:Ag,Cl or

ZnS:Cu,AlZnS:Cu,AlConduction band

0.1eVelectronAlS

luminescenceDonor (Cl, Al)Zn

C luminescence

Acceptor (Cu, Ag)3.7eV

hole

Cup ( , g)

Valence band1eV

o e

luminescence Valence band

Th t ti f d t (C A Cl) l l f Z S b dThe representation of dopants (Cu,Ag, Cl) levels for ZnS-based phosphors. 48

chap 2 energy absorption of luminescent materials 2-1 general...

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