• 검색 결과가 없습니다.

Carrier mobility of Si and Organic Materials

N/A
N/A
Protected

Academic year: 2024

Share "Carrier mobility of Si and Organic Materials"

Copied!
21
0
0

로드 중.... (전체 텍스트 보기)

전체 글

(1)

Organic Semiconductor EE 4541.617A 2009. 1stSemester

2009 5 12

K. C. Kao and W. Hwang, Electrical Transport in Solids, (Pergamon, New York, 1981), p.159

Changhee Lee, SNU, Korea 1/41

Changhee Lee

School of Electrical Engineering and Computer Science Seoul National Univ.

chlee7@snu.ac.kr 2009. 5.12.

Organic Semiconductor EE 4541.617A 2009. 1stSemester

Electron mobility of Si

Carrier mobility of Si and Organic Materials

hole mobility of Perylene hole mobility of MPMP

Changhee Lee, SNU, Korea 2/41

370 nm thick perylene crystal 8.7 um thick unordered layer of

MPMP ( sublimed).

(2)

Organic Semiconductor EE 4541.617A 2009. 1stSemester

d

2

Mobility Measurement Techniques

10

2

)

/ ( cm

2

Vs

μ 10

−4

10

6

10

8

10

0

10

2

TOF Mobility in the bulk

d = 0.5~5 mm

FET

Mobility in a thin layer d ~ 50 nm

μ τ V d

2

=

∴ V d τ = μ

2

Changhee Lee, SNU, Korea 3/41

d 0.5 5 mm

Other mobility measurement techniques

• Dark injection in the space-charge limited current regime

• I-V characteristics of space charge limited current

• Transient EL

• SHG measurement [T. Manaka, E. Lim, R. Tamura, M. Iwamoto, Nature Photon.1, 581–584 (2007).]

……

Organic Semiconductor EE 4541.617A 2009. 1stSemester

Mobility Measurement Techniques : Organic TFT

Changhee Lee, SNU, Korea 4/41

T. N. Jackson, Penn State U.

(3)

Organic Semiconductor EE 4541.617A 2009. 1stSemester

Light (hν)

μ τ V

d

2

= Mobility measurement techniques: TOF-PC

Time-of-flight photoconductivity t =0

-- - - - - ++ ++ ++

-- - - - -

++ ++ + +

0 < t

< τ

---- - -

++ ++ + +

t

= τ

rrent

g p y

N2laser

Vacuum Cryostat

B/S

Sample Si-PD

Trigger

Changhee Lee, SNU, Korea 5/41

t =0 t

= τ 0 < t

< τ Time

Photocu r

Oscilloscope Bias V

PC

gg

TOF Signal RL

Organic Semiconductor EE 4541.617A 2009. 1stSemester

Transport of charge carriers in organic materials

60 40 20 0

Photocurrent (arb. units)

10 08 06 04 02 00

0.20 0.15 0.10 0.05 hotocurrent (arb. units) 0.00

a-NPD Alq3

Gaussian transport Dispersive transport Fast

Slow

P 1.00.80.60.40.20.0

Time (μs)

Ph 806040200

Time (μs)

Dispersive transport Gaussian transport

er Densit y

Trapping and release Band States

Changhee Lee, SNU, Korea 6/41

Distance

Carri e

Localized states

Hopping Deep trap

Ref.) Harvey Scher, Michael F. Shlesinger and John T. Bendler, Physics today, Jan. p.26 (1991)

(4)

Organic Semiconductor EE 4541.617A 2009. 1stSemester

Mobility Measurement Techniques: Transient EL

30

25

20

rb.unit)

57V

Al

PPP

15

10

5

0

Light (x10-3 ar

500 450 400 350 300 250 200 150 100 50 0

Time (x10-9 s) 57V

19V 27V 39V 42V 46V 52V

240 220

Mobility from the delay time τ=d

2

/ μV

ITO glass

PMT

Changhee Lee, SNU, Korea 7/41

220 200 180 160 140 120 100

Time Delay (ns)

60 50 40 30 20 10

1/V (x10-3 V-1)

Hole mobility

in the vacuum-deposited PPP:

ITO/PPP/Al: μ=4.5x10

-6

cm

2

/Vs

G. W. Kang, C. H. Lee, W. J. Song, and C. Seoul, SPIE 4105, 362 (2001).

Organic Semiconductor EE 4541.617A 2009. 1stSemester

Transient EL Mobility vs TOF-PC mobility in Alq3

Changhee Lee, SNU, Korea 8/41

S. C. Tse, H. H. Fong, and S. K. So, J. Appl. Phys. 94, 2033 (2003)

For a thin layer of Alq3 (d<180 nm), it is found that tdis affected by both the charging effect and carrier transit time through the Alq3 layer. For a thicker layer of Alq3 (d>200 nm), td approaches the intrinsic electron transit time through Alq3 .

(5)

Organic Semiconductor EE 4541.617A 2009. 1stSemester

Space-charge-limited current

Hole only device

0.3 μm d=0.13 μm

0.7 μm

OC

1

C

10

-PPV

Electron only device

3 2

8 9

d JSCLC= εoεrμV

d=0 22 m

ITO + Au

OC

1

C

10

-PPV -

Changhee Lee, SNU, Korea 9/41

d=0.22 μm 0.37 μm

0.31 μm 2 1

1 +

mm+

d J V

Ca (a) Ca

Poly(dialkoxy-p-phenylene vinylene) (OC1C10-PPV)

P. W. M. Blom M. J. M. de Jong, and J. J. M. Vleggaar, Appl. Phys. Lett. 68, 3308 (1996).

Organic Semiconductor EE 4541.617A 2009. 1stSemester d

T it ti

V R

+ + + + + +

Dark injection SCL transient current

Transient SCLC

Transit time

Ohmic contact tp=

0 . 787 τ

PTPB

poly (tetraphenylbenzidine) PTPB 1.0

0.8

0.6

i(t) (arb. unit) 0.4

Dark injection SCL transient current τ

787 .

=0 tp

t

Changhee Lee, SNU, Korea 10/41

M. Abkowitz, J. S. Facci, and M. Stolka, Appl. Phys. Lett. 63, 1892 (1993).

0.2

0.00.0 0.2 0.4 0.6 0.8 1.0

Time (ms) 787 . 0

tp

τ= TOF-PC

S.C. Tse, S.W. Tsang, and S.K. So, J. Appl. Phys. 100, 063708 (2006).

(6)

Organic Semiconductor EE 4541.617A 2009. 1stSemester

Mobility Measurement Techniques: dark charge injection

ITO/300nm m-MTDATA/Ag with ITO biased positively.

E t

tr

= 0 . 786 d

In a monopolar and single-layer configuration, the carrier transit time is shorter than in the absence of space-charge effects due to the enhancement of the electric field at the leading edge of the carrier packet.

tr

μ E

The transient current overshoots its steady-state value by a factor of 1.21 and starts at 0.44 times the

steady-state value.

Changhee Lee, SNU, Korea 11/41

M. Stossel et al, Phys. Chem. Chem. Phys.1, 1791 (1999) A. Many and G. Rakavy, Phys. Rev. 126, 1980 (1962)

Organic Semiconductor EE 4541.617A 2009. 1stSemester

nj.

Carrier injection efficiency

contact limiting - current for 1

contact ohmic for 1

current injected : efficiency Injection

<

=

= η

η

η SCLC 3

2

8 9

d J

SCLC

= ε

o

ε

r

μ V

Injection Ef ficiency η

in

Changhee Lee, SNU, Korea 12/41

Hole

Hole Injection Barrier (eV)

M. Abkowitz, J. S. Facci, J. Rehm, J. Appl. Phys. 1998, 83, 2670.

(7)

Organic Semiconductor EE 4541.617A 2009. 1stSemester

Mobility Measurement Techniques: TRM-SHG

Vs cm

/ 25 .

0

2

=

μ

Changhee Lee, SNU, Korea 13/41

T. Manaka, E. Lim, R. Tamura, M. Iwamoto, Nature Photon.1, 581 (2007).

T. Manaka, M. Nakao, D. Yamada, E. Lim and M. Iwamoto, Optics Express 15, 15964 (2008).

Organic Semiconductor EE 4541.617A 2009. 1stSemester

(1) Poole-Frenkel Model

Conduction band x = x

m

x

) (x V )

(x V

Charge Transport in Disordered Organic Solids

E e E

PF 2

/ 1

0 3

PF

β

φ πεε ⎟⎟ ⎠ =

⎜⎜ ⎞

= ⎛ Δ

Conductio n band edge at E Tunneling

φ

PF

edge at E=0 Δ

Zero field (E=0) E≠0

x

− eEx x

e

o

ε πε 4

2

Changhee Lee, SNU, Korea 14/41

Zero field (E 0) E≠0

⎟⎟ ⎠

⎜⎜ ⎝

⎟⎟ ⎛

⎜⎜ ⎞

⎛ − Δ

= k T

E T

k μ E

F,T

B PF B

PF

exp exp

)

( β

μ Δ E : Activation energy at

E=0

: PF Mobility : PF constant

μ

PF

β

PF 0

3

PF

πεε

β = e

(8)

Organic Semiconductor EE 4541.617A 2009. 1stSemester

0

1 1 1

T T

T

eff

= − : Empirical parameter

T

0

(2) Gill’s modified Poole-Frenkel model

⎟ ⎟

⎜ ⎜

⎟ ⎟

⎜ ⎜

⎛ − Δ

=

eff

eff

k T

E T

k μ E

F,T

B PF B

PF

exp exp

)

( β

μ

Charge Transport in Disordered Organic Solids

PVK

poly-n-vinylcarbazole (hole conductor)

N n

O2N C

O

NO2

Changhee Lee, SNU, Korea 15/41

TNF

2,4,6-trinitro-9-fluorenone (electron acceptor)

NO2

W. D. Gill, J. Appl. Phys. 43, 5033 (1972).

Organic Semiconductor EE 4541.617A 2009. 1stSemester

(3) Bassler’s Gaussian Disorder Model

• The energy of each site is distributed in accordance with the Gaussian distribution

• Energies of adjacent sites are uncorrelated and motion between sites is Markovian (no phase memory)

• The transition rates for phonon-assisted tunneling (Miller and Abrahams):

⎪⎬

⎪ ⎫

⎧ − >

− −

=v R ikT j i j

W ε ε ε ε

α

) exp( ), 2

exp(

εεj

Charge Transport in Disordered Organic Solids

α= inverse localization length, Rij = distance between the localized states, εi= energy at the state i.

• Since the hopping rates are strongly dependent on both the positions and the energies of the localized states,

hopping transport is extremely sensitive to structural as well as energetic disorder.

σ

LUMO

⎪⎭⎬

⎪⎩⎨

>

=

j i ij j

ph

ij v R kT

W α ε ε

, 1 ) 2

exp(

εi

A. Miller, E. Abrahams, Phys. Rev.120(1960) 745. Hopping

0 5

ε

Changhee Lee, SNU, Korea 16/41

H. Bässler, Phys. Status Solidi B 175, 15 (1993).

HOMO

σ

-1 0 1 2 3 4 5

-10

-5 kBT kBT

σ2

ε =−

log (t/t

o

)

T kB

ε

(9)

Organic Semiconductor EE 4541.617A 2009. 1stSemester

T kB σ = σ

Hole mobility of TAPC embedded in BPPC matrix

Charge Transport in Disordered Organic Solids

: Energetic disorder : Positional disorder : Constant 2 9x10-4(cm/V)1/2 σ

CΣ

Changhee Lee, SNU, Korea 17/41

radius on localizati carrier and

distance site - inter average where

), / 2 exp(

)

( 2

=

=

=

o

o o

o a

μ ρ

ρ

ρ ρ ρ ρ

H. Bässler, Phys. Status Solidi B 175, 15 (1993). M. Stolka, J. F. Janus and D. M. Pai, J. Phys. Chem. 88, 4707 (1984).

1.5) ( 3 ,

exp 2 3 exp 2 ) (

1.5) ( 3 ,

exp 2 3 exp 2 ) (

2 2

B 2

B

2 2

B 2

B

⎪⎭ Σ

⎪⎩

⎟⎟ Σ

⎜⎜

⎟⎟

⎜⎜

=

<

⎪⎭ Σ

⎪⎩

⎟⎟ Σ

⎜⎜

⎟⎟

⎜⎜

=

T E C k T μ k E,T

T E C k T μ k E,T

o o

σ μ σ

σ μ σ

: Constant ~2.9x10-4(cm/V)1/2 : High temperature limit of the mobility C

μo

P. M. Borsenberger, L. Pautmeier and H. Bassler, J. Chem. Phys. 94, 5447 (1991).

Organic Semiconductor EE 4541.617A 2009. 1stSemester

MPMP

bis(4-N,N-diethylamino-2-methylphenyl)-4- methylphenylmethane

(thickness~8.7 μm) Hole mobility of MPMP

Charge Transport in Disordered Organic Solids

Changhee Lee, SNU, Korea 18/41

P. M. Borsenberger, L. Pautmeier and H. Bässler, J. Chem. Phys. 95, 1258 (1991)

(10)

Organic Semiconductor EE 4541.617A 2009. 1stSemester Disorder parameters

•σ: The width of the DOS. Random distribution of both permanent and van der Waals dipoles lead to local fluctuations in electric potential Æincrease σby an amount proportional to the square root of the dipole concentration and to the strength of the dipole moment. Æreduce the carrier mobility. The smaller dipolar interaction is better for the carrier transport.

•Σ: The degree of positional disorder. Amorphous morphology of molecular solids or doped polymers lead to the variation in the intermolecular distances.

Disorder parameters

μ TAPC doped polystyrene>> μ TAPC doped polycarbonate

Dipole moment:

• TAPC [1,1-bis(di-4-tolylaminophenyl)cyclohexane] = 1.0 D

• PC (bisphenol-A-polycarbonate) = 1.0 D

• PS (polystyrene) = 0.1 D

• Larger dipolar interaction increases both σand Σ.

• The elimination of random dipolar fields due to

Changhee Lee, SNU, Korea 19/41

P. M. Borsenberger and H. Bässler, J. Chem. Phys. 95, 5327 (1991).

• The elimination of random dipolar fields due to static dipole moments of PC reduces both σand Σ and thereby increases the mobility.

Organic Semiconductor EE 4541.617A 2009. 1stSemester

Disorder parameters

Changhee Lee, SNU, Korea 20/41

A. Dieckmann, H. Bässler and P. M. Borsenberger, J. Chem. Phys. 99, 8136 (1993).

(11)

Organic Semiconductor EE 4541.617A 2009. 1stSemester

Effect of dipolar molecules on carrier mobilities

• Conduction through the dopant.

• Mobility is strongly affected by the dipole moment of the dopant for holes and electrons

Changhee Lee, SNU, Korea 21/41

A. Goonesekera and S. Ducharme, J. Appl. Phys. 85, 6506 (1999)

Organic Semiconductor EE 4541.617A 2009. 1stSemester

Temperature dependence of the hole mobility of PPVs

Changhee Lee, SNU, Korea 22/41

P.W.M. Blom, M.C.J.M. Vissenberg, Materials Science and Engineering 27, 53-94 (2000)

(12)

Organic Semiconductor EE 4541.617A 2009. 1stSemester

⎩ ⎨

⎧ <

=

+

τ

α α

t t

t

t ,

(t)

J

(1 )

) 1 ( ph

(4) Scher-Montroll dispersive transport model

Trapping Band States

α

≈ Ψ ( t ) t

Continuous time random walk (CTRW)

Charge Transport in Disordered Organic Solids

⎩ t

(1+α)

, t > τ

pp g

p

and release Localized states

Deep trap

T

o

= T α Disappearance of plateau

h otocurrent

Slope = -(1- α)

log i

ph

τ ( )

α1

E

∝ L

Changhee Lee, SNU, Korea 23/41

Time

t =0 t =τ Time

P h

Slope = - (1+α)

log t

t =0 t =τ

Scher and Montroll, Phys. Rev. B 12, 2455 (1975)

Organic Semiconductor EE 4541.617A 2009. 1stSemester

τ ( )

α1

E

∝ L

Scher-Montroll model of dispersive transport

) 45 . 0 1 (−

t

) 45 . 0 1 (+

t

2 . 2

45 . 0 1 1

= α=

Changhee Lee, SNU, Korea 24/41

H. Scher and E. W. Montroll, Phys. Rev. B 12, 2455 (1975)

(13)

Organic Semiconductor EE 4541.617A 2009. 1stSemester

Dispersive Transport in a-Selenium

Changhee Lee, SNU, Korea 25/41

G. Pfister, Phys. Rev. Lett. 36, 271 (1976)

Organic Semiconductor EE 4541.617A 2009. 1stSemester

Changhee Lee, SNU, Korea

26/41

(14)

Organic Semiconductor EE 4541.617A 2009. 1stSemester

Charge –voltage characteristics of organic semiconductors

Injection limited

Thermionic emission

] 1 )

[exp( −

= k T

J eV J

B

s * 2

exp( )

T k T e

A J

B bn s

φ

= −

Current

Bulk Limited

Ohmic (Doped semiconductor) E

ep J = μ Tunneling

)

2

exp(

E E b

J ≈ −

qh q b m

3 ) ( 2

8 π

*

φ

3/2

=

Changhee Lee, SNU, Korea 27/41

Bulk Limited

SCLC (undoped semicond. or Insulator)

3 2

8 9

d J

SCLC

= ε

o

ε

r

μ V

Organic Semiconductor EE 4541.617A 2009. 1stSemester

PPV

Au ITO

V=0

V>0

Space-charge-limited current (SCLC)

velocity density)

charge (

J

SCLC

≈ ×

Space-charge-limited current (SCLC) OLED acts as a capacitor

V>0

V>>0 +

PPV

Au ITO +

+ + +

+ + + + +

2

2

) ( area ) (

velocity density)

charge (

V d V V d d E

CV J

r o

r o SCLC

μ ε ε

ε μ ε

μ

=

⋅ ×

=

ε

− ρ

2

=

2

dx V d

potential

Field ~ 0 at contact

Changhee Lee, SNU, Korea 28/41

+

PPV Au

ITO + + +

+ +

+ + + +

+ + +

+ + + +

+

3

d

r

=

o

3 2

8 9

d J

SCLC

= ε

o

ε

r

μ V

x d ohmic

SCLC

(15)

Organic Semiconductor EE 4541.617A 2009. 1stSemester

Ohmic Contact (1)

field.

applied external no is there since

, 0 :

equation flow Current

.

: equation Poisson

dx F - qD dn qn J

qn dx dF

=

=

= μ ε

figure right in the condition boundary

the From

log

used.

is relation

Einstein the where

, pp

0

Fdx . T k

q n

n

q T k μ D T Fdx k Fdx q D

μ n dn

x

B s

B B

=

=

=

=

: cathode virtual

Changhee Lee, SNU, Korea 29/41

law.

Boltzmann i.e.,

], exp[

figure, right in the condition boundary

the From

0

T k

χ) ψ(x)-(φ n

n

. Fdx q χ) ψ(x)-(φ

B s m

x m

− −

=

=

− ∫ .

dx dV 0

: cathode virtual

=

Organic Semiconductor EE 4541.617A 2009. 1stSemester

when 0 condition boundary

the using and

) 2(

g multiplyin after

sides both g Integratin

].

exp[

2 2 2

2

χ φ ψ

dx T k

χ) ψ(x)-(φ n

q n q dx qdF dx

ψ d

B m s

=

=

− −

=

=

=

ε ε

Ohmic Contact (2)

2 )}].

{exp(

2 sin 2 )[

exp(

2 ) ( W

region on accumulati the

of width the

gives equation this

g Integratin

]}.

exp[

] {exp[

) 2 (

, when

0 condition boundary

the using and

1 2

/ 1 2

2 2

T k

φ T

k χ φ N

q T k

T k

) φ ( T

k χ) ψ(x)-(φ T

k n q dx

χ φ dx ψ

B m B

c B

B m B

m B

s

− −

− −

=

− −

− −

=

=

=

ϕ

π ε

ϕ ε

Changhee Lee, SNU, Korea 30/41

2 ).

exp(

2 ) 2 ( W

, level energy discrete a in confined traps shallow containing tors

semiconduc For

2 ).

exp(

2 ) 2 ( W

, 4 If

2 / 1 2

2 / 1 2

T k

E χ φ N

q T k

E T

k χ φ N

q T k

T k φ

B t t

B

t B

c B

B m

≈ −

≈ −

>

ε π

ε

π

ϕ

(16)

Organic Semiconductor EE 4541.617A 2009. 1stSemester

Space-charge-limited current

.) ( ) ( :

equation flow Current

)] . ( ) ( [ )

( : equation Poisson

density trap of function on Distributi

x F x p q J

x p x p q dx

x dF (E)S(x).

N h(E,x)

p

t t

μ ε ε

ρ

=

= +

=

=

φ

oi

'

eV

'

x eVa

0 : electrode Virtual

'

=

=x

dxx

dφ

) 2 (

2 . )]

( [ )]

0 ( [ )]

( [ 2 . )]

( [ ) ) ( ( 2

, 0 ) ( For

. exp

, ) ( )

(

) ( ) ( q

2 2

2 2

J x x F

J x x F x

F x J F

dx x F d dx

x x dF F

x p

T ] k [ E N p(x) dE E h(E,x)f x

p

p q

p p

t

B F v

E

E p

t

p

u p l

εμ εμ

μ

=

=

=

=

=

=

=

=

= ∫

Electrode

Organic semiconductor Electrode

Changhee Lee, SNU, Korea 31/41

law.

Gurney - Mott 8 .

9

) ( condition,

Boundary . )

(

3 2

0

d J V

. dx x F V x x

F

p

d p

εμ εμ

=

=

=

The distance Wabetween the actual electrode surface and the virtual anode (-dV/dx=F=0) is so small that we can assume F(x=WaÆ0)=0for simplicity.

(no trap)

Organic Semiconductor EE 4541.617A 2009. 1stSemester

ITO/PPV/Au hole-only devices

3 2

8 9

d J

SCLC

= ε

o

ε

r

μ V

3

&

/ 10 5 0 i

Fit

6 2

V

Space-charge-limited current

3

&

/ 10 5 . 0 using

Fit μ = ×

6

cm

2

Vs ε

r

=

⎟⎟⎠

⎜⎜⎝

⎛ Δ −

=

eff B oexp PF

)

( k T

F μ E

F,T β

μ

Changhee Lee, SNU, Korea 32/41

P.W.M. Blom, M.C.J.M. Vissenberg, Materials Science and Engineering 27, 53-94 (2000)

(17)

Organic Semiconductor EE 4541.617A 2009. 1stSemester

of onset or the law s Ohm' from departure the of onset The

8 . 9

such that t predominan is

specimen the

inside carriers free

generated thermally of

density the if holds law s ohm' field, low At

3 2 p p

o

o

d V d

qp V

p

εμ μ

>>

J log

Space-charge-limited current

V V at ansit time

carrier tr when the place takes

regime SCL the to ohmic the from n transitio the Therefore,

. or 8 9 8

9 V

have e equation w this

g rearrangin By

9 . V 8 when place takes conduction SCL

the

2 t d t 2

2

o p o p

o

d qp

d

d qp

τ τ σ τ

ε μ ε μ

ε

=

=

=

=

Ω Ω

Ω

V J ∝

V

2

J ∝

Changhee Lee, SNU, Korea 33/41

. time relaxation dielectric

the to equal ely approximat is

V

d o p

σ τ ε μ

=

Ω

K. C. Kao and W. Hwang, Electrical Transport in Solids, (Pergamon, New York, 1981), p.159

t.

predominan is

conduction SCLC

, At

t.

predominan is

conduction ohmic

, At

d t

d t

τ τ

τ τ

<

> ε

2

9 V 8 qp

o

d

Ω

= log V

0

Organic Semiconductor EE 4541.617A 2009. 1stSemester

, equation

Continuity

. time relaxation

dielectric

d

σ τ ε

t J ) p q (p

o

o

−∇

∂ = +

=

Space-charge-limited current

ignored.

be can term 2nd the , time relaxation dielectric

the to comparable

time a in specimen over the

uniformly spreads

p and If

. )

(

).

( )

( J by given is current where

d 2

μ

σ τ ε ε

μ

μ

qp p p

p D qp p

t p

p p qD F p p q t

o o

p p

o p p o

=

<

∇ +

∂ =

∴ ∂

+

− +

=

Changhee Lee, SNU, Korea 34/41

m.

equilibriu establish

- re carrier to for the

required time the of measure a is

. exp 0

. ) ( τ

d

ε τ

μ p p(t) p(t ) (-t/ ) qp

t p

d p

o

∴ = =

∂ ≈

∴ ∂

(18)

Organic Semiconductor EE 4541.617A 2009. 1stSemester

) , ( / 1

) ) (

( density charge

Trapped

) ( ) ( ) , (

levels energy discrete

multiple or

single in confined Traps

x p N

x S x N

p x S E E N x E h

t t t t

t t

θ δ

≈ +

=

Space-charge-limited current

traps of on distributi spatial

uniform -

non Ignoring

8 . 9

. where

) ( / 1

3 2

d θ V J

N e N θ g

x p N

eff t r o SCLC

kT E

t v p t

t t

t

μ ε ε

θ

=

=

+

E

CB

Changhee Lee, SNU, Korea 35/41

8 . 9

,

3 2

d θ V J

d p d

p θ p

t r o SCLC

eff t t

μ ε ε

= + =

=

E

VB

Discrete trap levels

Organic Semiconductor EE 4541.617A 2009. 1stSemester

Space-charge-limited current

Changhee Lee, SNU, Korea

36/41

(19)

Organic Semiconductor EE 4541.617A 2009. 1stSemester

DOS Energy

Space-charge-limited current: analytic solution

kT E E c f

F c

e N n

− −

=

c c

E

kT FD E E t

t

e f E dE

T k n N

− −

= ∫ ( )

Space-charge-limited current

E

C

(E

LUMO

) E

F

t c

kT E E

t t

e

kT E N G

− −

= ) ( E

t F c

F c

kT E E t

E kT

E E

t B

t t B

e N

dE T e

k N

T k

− −

− −

=

≈ ∫

T 1

Changhee Lee, SNU, Korea 37/41

kT

t

Exponential trap distribution

T m T

N N n N

N n n

t

m c f t T T

c f t

t t

=

=

∴ ( ) ( )

1

Organic Semiconductor EE 4541.617A 2009. 1stSemester

N J N d

x F dF

x F x n q J

N qN n x x qn n x n q dx

x dF

t m m

f

m c f o

t o t o

t f

=

=

≈ + ≈

=

/ 1 /

1

/ 1

. ) ) (

(

.) ( ) ( : equation flow Current

. ) ) (

)] ( ( ) ( ) [ ( : equation Poisson

μ

ε ε ε ε ε

ε log J

Law Gurney Mott

Space-charge-limited current

. dx x F V

N q

J N m x m F

N x q

J F N

m m

N q dx

d m c m

m

o t

m c o m t m

c o

=

= +

∴ + =

+ +

+

0 1 1 1

/ 1 1

) ( condition, Boundary

. ) ( 1 ) ( ) (

. ) 1 (

) (

μ ε ε

μ ε ε

μ ε ε

3 2

d V 8 J 9

Law Gurney - Mott

εμ

=

Changhee Lee, SNU, Korea 38/41

. , 1 )

( 1 )

1

( 2

2 1

1 1

1

T m T d

V N m

m m

N m q

J

m t

m m t m o

c

m

=

+ +

=

μ +

+

ε ε

++

V

Ω

log V

0

V

TFL

. 1 ) 2 )( 1 ( 1 ) (

SCLC Trapped

Ohmic

1 2 1

m m m

v o r o

t

m m m m N

p N V qd

+

Ω +

+

= +

⇒ ε

ε [89 ( 1) (2 11) ] .

SCLC free - Trap SCLC Trapped

1 1 1 2

+

+ +

= +

m m m v m t r o

TFL m

m m m N N V qd

ε ε

(20)

Organic Semiconductor EE 4541.617A 2009. 1stSemester

Ca/PPV/Ca electron-only devices

Space-charge-limited current

Trap-limited SCLC Trap-free SCLC

Changhee Lee, SNU, Korea 39/41

P.W.M. Blom, M.C.J.M. Vissenberg, Materials Science and Engineering 27, 53-94 (2000)

Organic Semiconductor EE 4541.617A 2009. 1stSemester

. , SCLC limited - Trap

1 2

1

T m T d N V N

J

m t

m m t

v

=

∝ μ

++

3 18

eV 15 .

≈ 0 E

t

SCL current with an exponential trap distribution

3 -

18

cm

≈ 10 N

t

Changhee Lee, SNU, Korea 40/41

P. E. Burrows, Z. Shen, V. Bulovic, D. M. McCarty, S. R. Forrest, J. A. Cronin and M. E. Thompson, J. Appl. Phys. 79, 7991 (1996).

(21)

Organic Semiconductor EE 4541.617A 2009. 1stSemester

Trap-limited SCL current with field-dependent μ

Changhee Lee, SNU, Korea 41/41

W. Brütting, S. Berleb and A. G. Mückl, Org. Electronics 2, 1 (2001)

참조

관련 문서

5 MeV proton-irradiation with total dose of 10 15 /cm 2 was performed on AlGaN/GaN-on-Si high electron mobility transistors (HEMTs) with various gate metals including Ni, TaN,

In this study, tensile properties of the ~130 nm- and ~320 nm-thick SiN x thin films were successfully measured by coating a ~190 nm-thick organic nano-support-layer (PMMA, PS,

temperature of MgB 2 thin films grown at various growth temperatures on silicon substrate with (a) 80-nm-thick alumina and (b) 300-nm- thick alumina buffer. Magnetizations

Effect of Carrier Gases on the Microstructure and Properties of Ti Coating Layers Manufactured by Cold Spraying.. Myeong-Ju Lee, Hyung-Jun Kim a , Ik-Hyun Oh b and Kee-Ahn

It was also shown that the photoacoustic effects in GaAs of a direct band gap were governed by all three processes and those in Si of an indirect band gap were produced by

For this, the study presented a methodology to evaluate the driving safety and mobility of personal mobility devices, and measured acceleration and speed in

When a strong negative potential (−4 V) is applied to the Si/SiO 2 , the 6-nm thick SiO 2 film loses its dielectric properties and conduction spots are produced within

A Study on the Perception of Personal Mobility Vehicle for the Improvement of Pedestrian Environment for the Disabled.. Joohyung Lee a ,