Photometric characterization of OLEDs

Photometric characterization of OLEDs1

1. General definitions ď Ž

dW W Energetic flux (radiant): ÎŚ e = e , if the flux is uniform over time ‘t’ then ÎŚ e = e and is t dt expressed in watts (W).

ď Ž

Luminous flux ÎŚ v is defined with respect to the sensitivity of the human eye to different wavelengths of light. The value is expressed in lumen (lm). To convert from energetic to luminous scales the constant Km = 683 lm W-1 is multiplied by the diurnal photo-response V(đ?œ†đ?œ†) of human eye. ď Ź V(đ?œ†đ?œ†) 2: CIE (1924) Photopic V(Îť) 1 0.8 0.6 0.4 0.2 0 350

450

550

650

750

850

Wavelength (nm)

ď Ź

Relationship between energetic and luminous flux for a monochromatic or pseudo

= ÎŚ v K mV ( Îťd ) ÎŚ e . monochromatic source: ď Ź

Relationship between energetic and luminous flux for a polychromatic source: ď ˇ

ď ˇ

δ Ό′ ( Ν ) = lim  Ό δ Ν →0 δ  Ν

  , where δΌ is the fraction of flux Ό contained in a spectral band of size 

đ?›żđ?›żđ?œ†đ?œ† about the wavelength Îť;

Ό′e = (Ν )

ÎŚe â‹… S ( Îť ) = ÎŁ

ÎŚe â‹… S ( Îť )

âˆŤ

∞

0

= ÎŁ normalized spectra;

1 2

S (Îť ) â‹… dÎť ∞

, where ÎŚđ?‘’đ?‘’ is the total energetic flux; S(Îť) is the

âˆŤ S (Îť ) â‹… dÎť 0

corresponding to the sum over the area of an

Optoelectronics of Molecules and Polymers, Moliton AndrĂŠ, Springer-Verlag New York, 2006. http://www.cvrl.org/lumindex.htm 1/5

empirical normalized spectra; ÎŚ e = aÎŁ , in which ‘a’ is a constant,

a = ď ˇ ď Ž

Ό′e ( Ν ) = aS ( Ν ) , that is

Ό e Ό′e ( Ν ) ; = S (Ν ) Σ

The luminous flux is ÎŚ v =

Energetic intensity (radiant): I e =

âˆŤ Ό′ ( Îť ) d Îť = K âˆŤ V ( Îť ) Ό′ ( Îť ) d Îť . v

m

e

d Όe . If the emitted flux within a given solid angle (Ί) is dℌ

Όe ; the radiant intensity is thus expressed as watt per steradian (W sr-1). ℌ Ό d Όv ; when Ό�� is a constant within Ί, I v = v (lm sr-1), also denoted Luminous intensity: I v = ℌ dℌ as the candela (cd).

constant, then I e =

ď Ž

ď Ź ď Ź

For a monochromatic/pseudo-chromatic (Îť = đ?œ†đ?œ†đ?‘‘đ?‘‘ ) ray,

I v = K mV ( Îťd ) I e .

For a polychromatic source: ď ˇ

I v = K m âˆŤ V ( Îť )I e′ ( Îť ) d Îť

I e′ ( Îť ) ď ˇ =

Ie â‹… S ( Îť ) = ÎŁ

Ie â‹… S ( Îť ) ∞

âˆŤ S (Îť ) â‹… dÎť 0

ď Ž

Energetic luminance (đ??żđ??żđ?‘’đ?‘’ ) is defined as the ratio of the emitted energetic intensity to the area of

= apparent emitting surface (���� ): L e

ď Ž

Visual luminance:

Ie 1 d ÎŚe 1 ÎŚe = ; for a constant flux, Le = (W sr-1 m-2).

Sa â„Ś Sa Sa d â„Ś

ÎŚv Iv 1 d ÎŚv L= = , when the flux is constant, Lv = (cd m-2). v â„ŚS a Sa Sa d â„Ś

ď Ź

For a monochromatic/pseudo-monochromatic source= Lv

ď Ź

For a polychromatic source ď ˇ

K mV ( Îťd ) ÎŚ e ÎŚv = â„ŚS a â„ŚS a

Lv = K m âˆŤ V ( Îť ) Le′ ( Îť ) d Îť

Le′ ( Îť ) ď ˇ =

Le â‹… S ( Îť ) = ÎŁ

Le â‹… S ( Îť ) ∞

âˆŤ S (Îť ) â‹… dÎť 0

2. Internal and external quantum yields ď Ž

At the OLED interior, in the recombination zone, emissions going towards the frontal surface

âˆŤ

θ =π /2

âˆŤÎ¸

sin θ dθ 2Ď€ . occur in a half space, that= is â„Ś1 = d â„Ś1 2Ď€= ď Ž

=0

The portion of flux which can leave the OLED is emitted from the emission zone within a solid

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= 2Ď€ angle limited to â„Ś 2

θ =θ1

âˆŤÎ¸

=0

θ 2Ď€ (1 − cos θ1 ) . Given that sin θ d=

(

calculated by through C =1 − cos θ1 =1 − 1 − sin θ1 2

)

12

sin đ?œƒđ?œƒ1 = 1/đ?‘›đ?‘›, the term C can be 12

1   =1 − 1 − 2   n 

1  1  ≈ 1 − 1 − 2  = 2 . đ?œƒđ?œƒ1 is  2n  2n

the critical angle, in which ‘n’ is the refractive index of the organic material.

ď Ž ď Ž

Ď€

â„Ś1 .

2n 2 n If we also bring into play emissions towards the back of the device, that is towards the cathode,

Thus â„Ś 2=

2

=

then Ί1 and Ί2 are simply multiplied by 2, however, the relationship between them remains

unchanged. ď Ž

The luminous intensity directly emitted by the source is denoted as đ??źđ??ź0đ?‘–đ?‘–đ?‘–đ?‘–đ?‘–đ?‘– . Assuming the material

to be homogeneous and having no internal interface, the internal emission from the

recombination zone is isotropic and the total emitted flux inside the forward half space can be written in the for: = ÎŚT int ď Ž

âˆŤ

Ď€ 2

= I 0int d â„Ś 2Ď€ I 0int âˆŤ = sin θ dθ 2Ď€ I 0int .

1 2 space

0

By denoting ÎŚđ?‘–đ?‘–đ?‘–đ?‘– as the flux from the interior towards the exterior, we now have:

θ1 1 1 = ÎŚ ie 2Ď€ I 0int âˆŤ sin= = θ dθ 2Ď€ I 0int (1 − cos θ1 ) 2Ď€ I 0int= Ď€ I 0int 2 .

2 0 2n n

ď Ž

If luminous intensity emitted with respect to the normal to the surface of the OLED is denoted by đ??źđ??ź0đ?‘’đ?‘’đ?‘’đ?‘’đ?‘’đ?‘’ , then the emission follows Lambert’s law ( I ext = I 0 ext cos Ď• ) and the total external flux (ÎŚđ?‘’đ?‘’đ?‘’đ?‘’đ?‘’đ?‘’ )

emitted over the forward half space is thus in the form:

= ÎŚ ext ď Ž

âˆŤ

Ď€ 2

0

1 = π I 0 ext , from which can be deduced that I 0int = I 0ext n 2 , then n2 1 or Ό ext = ΌT int .

2n 2

Ό ie =Ό ext and thus π I 0int 2π n 2 I 0 ext ΌT int =

ď Ž

Ď€ 2

0

= I cos Ď• d â„Ś 2Ď€ I 0 ext âˆŤ = cos Ď• sin Ď• dĎ• 2Ď€ I 0 ext âˆŤ = sin Ď• d ( sin Ď• ) Ď€ I 0 ext .

1 2 space 0 ext

External quantum yield (đ?œ‚đ?œ‚đ?‘’đ?‘’đ?‘’đ?‘’đ?‘’đ?‘’ ) is defined as the ratio of the number of photons emitted by an

OLED (đ?‘ đ?‘ đ?‘?đ?‘?â„Žđ?‘’đ?‘’đ?‘’đ?‘’đ?‘’đ?‘’ ) in to the external half space over a time t divided by the number of electrons injected (đ?‘ đ?‘ đ?‘’đ?‘’đ?‘’đ?‘’ ) over the same period of time. = Ρext

ď Ź

ď Ź

N phext t N phext . = t N el N el

If đ??źđ??źđ?‘?đ?‘? represents the current injected into an electroluminescent structure, we have

= I c Q= t qN el t , where ‘q’ is the elementary charge (1.6 Ă— 10−19 đ??śđ??ś). Thus

For a given đ?œ†đ?œ†đ?‘‘đ?‘‘ , the energy of the photons is determined by E ph = hc Îťd . With the emitted

external flux being ÎŚđ?‘’đ?‘’đ?‘’đ?‘’đ?‘’đ?‘’ = đ?‘Šđ?‘Šđ?‘’đ?‘’ â „đ?‘Ąđ?‘Ą, now N phext = ď Ź

N el I c = . t q

For (pseudo-)monochromatic ray, Ρext =

N phext Îťd We , that is = ÎŚ ext .

E ph t hc

qΝd Ό ext 1 = 2 Ρint . hc I c 2n 3/5

3. Measuring luminance and yields with a photodiode ď Ž

Typically, a photo-detector (or photodiode) gives to a responsive current (đ??źđ??źđ?‘?đ?‘?đ?‘?đ?‘? ) in a form arising

from two origins: dark current (đ??źđ??ź0 ) (arise from thermal excitation and ambient beam effects) and photoelectric current (đ??źđ??źđ?‘?đ?‘? ). For a given photo-detector subject to a luminous flux, consisting not

necessarily of monochromatic light, there is I pd= I 0 + I p . ď Ž

Normally, đ??źđ??ź0 remains constant, however, đ??źđ??źđ?‘?đ?‘? will change proportionally with the received flux

(ÎŚđ?‘’đ?‘’ ). So I pd= I 0 + Ďƒ â‹… ÎŚ e . For a linear photo-detector, the sensitivity is a constant Ďƒ =

dI pd ( Îť )

Ip

ÎŚe

.

dI p ( Ν ) I ′p ( Ν ) = . d Ό e ( Ν ) Ό′e ( Ν )

ď Ž

The spectral sensitivity is defined by the relationship Ďƒ ( Îť ) = =

ď Ž

For a photo-detector exposed to a monochromatic beam of a given wavelength đ?œ†đ?œ†đ?‘‘đ?‘‘ and flux

d ÎŚe ( Îť )

ÎŚđ?‘’đ?‘’ (đ?œ†đ?œ†đ?‘‘đ?‘‘ ), the total number of photons received by the detector per second is n p =

Îťd ÎŚ e ( Îťd ) hc

. If T

is the transmission coefficient of the photo-detector window and Ρ the quantum efficiency of the

detector, the actual number of electron-hole pairs generated per second is of the form

= G Ρ= Tn p ΡT ď Ž

Îťd ÎŚ e ( Îťd )

= G ( Îťd ) . hc

For a linear detector, the photoelectric current component is in the form I p = FqG where F is a factor of amplification. Hence,= I p ( Νd ) FqG = ( Νd ) FqΡT

= Ďƒ ( Îťd )

Îťd ÎŚ e ( Îťd ) hc

. We arrive at

dI p ( Νd ) Ν = FqΡT d . d Ό e ( Νd ) hc

I p ( Îťd )

ď Ž

The above can also be written Ďƒ ( Îťd ) =

ď Ž

If the light is polychromatic, the current đ??źđ??źđ?‘?đ?‘? is therefore such that:

ÎŚ e ( Îťd )

.

I p = âˆŤ dI p = âˆŤ Ďƒ ( Îť )d ÎŚ e ( Îťd ) = âˆŤ Ďƒ ( Îť )Ό′e ( Îťd ) d Îť = âˆŤ I ′p ( Îť )d Îť .

ď Ž

Ip

We= thus have

ÎŚe

( Îť ) Ό′ ( Îť ) d Îť âˆŤ Ďƒ ( Îť ) S ( Îť ) d Îť âˆŤ Ďƒ= = ÎŚ âˆŤ S (Îť ) dÎť e

e

Ďƒ av ; and the value đ?œŽđ?œŽđ?‘Žđ?‘Žđ?‘Žđ?‘Ž then obtained

for the ratio đ??źđ??źđ?‘?đ?‘? â „ÎŚđ?‘’đ?‘’ appears as an effective sensitivity. Furthermore, we can get

ÎŚ e =I p

ď Ž

âˆŤ S (Îť ) dÎť

âˆŤĎƒ (Îť ) S (Îť ) dÎť

In addition, I ′p ( Ν ) = I p

and Ό′e ( Ν ) = Ip

S (Îť )

âˆŤĎƒ (Îť ) S (Îť ) dÎť

Ďƒ (Îť ) S (Îť )

âˆŤĎƒ (Îť ) S (Îť ) dÎť

.

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.

ď Ž

In general terms, ���� is the apparent emitting diode surface, and practically speaking, the

measurement of a bean emitted by an OLED is effected by placing a photodiode at the window of the measuring cell. The surface of the photodiode is perpendicular to the beam direction, so if we ď Ž

designate the surface of the OLED by đ?‘†đ?‘†đ??ˇđ??ˇ , the apparent surface đ?‘†đ?‘†đ?‘Žđ?‘Ž is such that đ?‘†đ?‘†đ?‘Žđ?‘Ž = đ?‘†đ?‘†đ??ˇđ??ˇ .

đ?‘&#x;đ?‘&#x; 2

The half angle at the apex (φ) is such that tan đ?œ‘đ?œ‘ = đ?‘&#x;đ?‘&#x;â „đ??ˇđ??ˇ . The solid angle is Ί = đ?‘†đ?‘†đ?‘?đ?‘?đ?‘?đ?‘? â „đ?‘…đ?‘…2 = Ď€ ďż˝ ďż˝ .

R Source (SD)

Ίđ?‘?đ?‘?â„Ž đ?œ‘đ?œ‘

r

D

Photo-detector (Spd)

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đ??ˇđ??ˇ