p. stallinga (universidade do algarve) · pf “wins”, current is exponentially growing vds =...

MONA-LISA Würzburg 2003, P. Stallinga, UAlg

P. Stallinga (Universidade do Algarve)MONA-LISA Wuerzburg, 3-VII-2003


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MONA-LISA Würzburg 2003, P. Stallinga, UAlgMONA-LISA Würzburg 2003, P. Stallinga, UAlg

Intro

Transfer curves

Spectroscopy

Poole-Frenkel

TSC

Conclusions

Introduction


• An FET needs VT to start working:

VT = … NA½

• From then on it is a capacitor:

Q = Cox (VG−VT)

• In the linear region the current is proportional to the field and the charge density:

Ids = Vds Q µ

Result:

Ids = a Vds Cox (VG−VT) µ

IntroductionIntro

Transfer curves

Spectroscopy

Poole-Frenkel

TSC

Conclusions


Ids = a Cox (VG−VT) µ Vds

a

Cox (VG−VT)

µ

Vds

device dimensions

charge density

response of a carrier to the field

field

IntroductionIntro

Transfer curves

Spectroscopy

Poole-Frenkel

TSC

Conclusions


Special Effects

• Mobility depends on longitudinal field (Vds)

• Mobility appears to depend on transversal field (Vg)

• Mobility appears to depend on the frequency (ν)

• Threshold voltage not constant (Vg, t, T)

IntroductionIntro

Transfer curves

Spectroscopy

Poole-Frenkel

TSC

Conclusions


Transfercurves

Intro

Transfer curves

Spectroscopy

Poole-Frenkel

TSC

Conclusions


LIN: Ids = (W/L) Cox µ (Vg−Vt)1+γ Vds

SAT: Ids = (1/2)(W/L) Cox µ (Vg−Vt)2+γ

This implies that the amount of free charge in the channel grows faster-than-linear with the gate voltage, i.e. no longer a simple “parallel metal plates” device

Alternatively: define an as-measured (parametric) mobility that depends on Vg, example (LIN)

Ids = (W/L) Cox µ(Vg) (Vg−Vt) Vds

Mobility appears to depend on VgIntro

Transfer curves

Spectroscopy

Poole-Frenkel

TSC

Conclusions


Vissenberg

g(ε) = (NT/kT0) exp (ε/kT0))

γ = 2(T0/T−1)

Vissenberg et al, PRB 57, 12964 (1998)

Intro

Transfer curves

Spectroscopy

Poole-Frenkel

TSC

Conclusions


Mobility appears to depend on Vg

Failure of the VRH/MTR theory, which cannot adequately describe the behavior of γ as a function of temperature.

γ depends on T

Intro

Transfer curves

Spectroscopy

Poole-Frenkel

TSC

Conclusions


The Meyer-Neldel rule (MNR)

MNR holds, with a phase transition at 200 K

MNR: In Arrhenius plot all mobilities lie on line going through the same point (TMR, µMN)

Intro

Transfer curves

Spectroscopy

Poole-Frenkel

TSC

Conclusions

Nano-FET


Currentspectroscopy

Intro

Transfer curves

Spectroscopy

Poole-Frenkel

TSC

Conclusions


0 5 10 15 20

0

0.2

0.4

0.6

0.8

1

Time (µs)

Bia

s (V

)

T = 10 µsT = 20 µs

Fourrier transform of pulse:

Shorter pulse: higher frequencies

Examples: Pulse 20 µs = 0.25 MHz Pulse 10 µs = 0.5 MHz

When doing pulsed measurement, you are doing FTCS (Fourrier-transform current-spectroscopy)

Important if µ depends on ν.

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2-5

0

5

10

15

20

Frequency (MHz)

Spe

ctra

l Den

sity

(s)

T = 10 µsT = 20 µs

Pulsed measurementsIntro

Transfer curves

Spectroscopy

Poole-Frenkel

TSC

Conclusions


Current Spectroscopy

Amplitude of response proportional to µ

Using lock-in detection

Intro

Transfer curves

Spectroscopy

Poole-Frenkel

TSC

Conclusions


Experimetal SetupIntro

Transfer curves

Spectroscopy

Poole-Frenkel

TSC

Conclusions


100 200 300 400 500 600 700 800 900 10000.5

1

1.5

2

2.5x 10

-4 Mobilidade em Função da Frequência

Frequencia(Hz)

Mob

ilida

de(c

m2 /V

s)

Primeiro Directamente a seguir

The as-measured mobility depends on the frequency!

Current Spectroscopy

sample: T635, RT, bias: Vds = −1 V, Vg= −5 V, modulation: ∆Vg = 40 mV di

a3_7

.m

Intro

Transfer curves

Spectroscopy

Poole-Frenkel

TSC

Conclusions


Stressing effects (VT changes)

100 200 300 400 500 600 700 800 900 10000.5

1

1.5

2

2.5x 10

-4 Mobilidade em Função da Frequência

Frequencia(Hz)

Mob

ilida

de(c

m2 /V

s)


Spectroscopy resultsIntro

Transfer curves

Spectroscopy

Poole-Frenkel

TSC

Conclusions


102 103 104 105

10-4

10-3

10-2

Mobilidade em Função da Frequência

Frequencia(Hz)

Mob

ilida

de(c

m2 /V

s)


Extrapolation to pulsed measurements

Pulsed experiments give 500x mobility

∆t = 10 µs µ = 10−2 cm2/Vs


Transfer curves

Spectroscopy

Poole-Frenkel

TSC

Conclusions


0 100 200 300 400 500 600 700 800 900 10000

0.5

1

1.5

2

2.5x 10-4 Mobilidade em Função da Frequência

Frequencia(Hz)

Mob

ilida

de(c

m2 /V

s)

Primeiro Directamente a seguirExpected t=infinite

Expected for t = ∞: DC mobility = 0 because VT = VG. AC mobility is not 0 (?)


Transfer curves

Spectroscopy

Poole-Frenkel

TSC

Conclusions


Transient of mobility vs. time.

sample: T6-35

Tempo (ks)

Rel

ativ

e m

obili

ty---- Fit µ(t) = µ0 exp(-√t/τ) + µoffset

dia7

_1.m

ν = 570 Hz

Note that in this experiment Vg is always on

Intro

Transfer curves

Spectroscopy

Poole-Frenkel

TSC

Conclusions


Poole-Frenkel

Intro

Transfer curves

Spectroscopy

Poole-Frenkel

TSC

Conclusions


Poole-Frenkel Conduction model

For low-conductivity materials, the conducting model might be “field-assisted hopping”.

The as-measured mobility then depends on the longitudinal field (Vds)

Images and equations: Sze, “Physics of Semiconductor Devices”, 2nd ed., p403.

Intro

Transfer curves

Spectroscopy

Poole-Frenkel

TSC

Conclusions


Waragai, “Charge transport in thin films of semiconducting oligothiophenes”, PRB 52, 1786 (1995).

Poole-Frenkel conduction in literatureIntro

Transfer curves

Spectroscopy

Poole-Frenkel

TSC

Conclusions


Sample: LO27 (Tobias), RT, LV

Experimental observation of Poole-Frenkel conduction

C:\d

ata\

TNT\

lo02

7\no

vo2\

dia1

\iv18

.m

Intro

Transfer curves

Spectroscopy

Poole-Frenkel

TSC

Conclusions


Sample: LO23 (Tobias)

Poole-Frenkel: Effect of temperature

C:\d

ata\

tobi

as\lo

023_

8m\d

ay4\

iv_2

m6.

m

C:\d

ata\

tobi

as\lo

023_

8m\d

ay4\

iv_2

n6.m

T = 340 KT = 210 K

Intro

Transfer curves

Spectroscopy

Poole-Frenkel

TSC

Conclusions


Simulation of Poole-Frenkel conduction

1: Simple model: field (and µ) constant in space

E = Vds/Lµ = µ0 exp(γE½ )Ids = a Cox (VG−VT) µ Vds

0 1 2 3 4 5 6 7 8 9 100

1

2

3

4

5

6

7

8x 10-8

Vg=0 Vg=1 Vg=2 Vg=3 Vg=4 Vg=5 Vg=6

Vg=7

Vg=8

Vg=9

Vg=10

Vds (V)

Ids

(A)

Poole Frenkel

waragai3.m

Intro

Transfer curves

Spectroscopy

Poole-Frenkel

TSC

Conclusions



2: Full simulation. System of differential equations

Differential equations:1. E(x) = dV(x)/dx2. µ(x) = µ0 exp[γE(x)½ ]3. Q(x) = Cox [Vg−Vt−V(x)]4. I(x) = W Q(x) µ(x) E(x)

Boundary conditions:• I constant in space, I(x) = Ids• V(0) = 0• V(L) = Vds (or I = Ids)

Intro

Transfer curves

Spectroscopy

Poole-Frenkel

TSC

Conclusions



2: Full simulation. System of differential equations

0 1 2 3 4 5 6 7 8 9 100

1

2

3

4

5

6

7

8

9x 10

-6

Vg=1 Vg=2

Vg=3

Vg=4

Vg=5

Vg=6

Vg=7

Vg=8

Vg=9

Vg=10

Vds (V)

Ids

(A)

Poole Frenkel, Ids/Vg vs. Vds

γ = 0

0 1 2 3 4 5 6 7 8 9 100

0.5

1

1.5

2

2.5x 10-5

Vg=1 Vg=2 Vg=3

Vg=4

Vg=5

Vg=6

Vg=7

Vg=8

Vg=9

Vg=10

Vds (V)

Ids

(A)

Poole Frenkel, Ids vs. Vds

γ = 0.2

0 1 2 3 4 5 6 7 8 9 100

2

4

6x 10

-5

Vg=1 Vg=2 Vg=3 Vg=4

Vg=5

Vg=6

Vg=7

Vg=8

Vg=9

Vg=10

Vds (V)

Ids

(A)


γ = 0.4

0 1 2 3 4 5 6 7 8 9 100

0.2

0.4

0.6

0.8

1x 10

-4

Vg=1 Vg=2 Vg=3 Vg=4

Vg=5

Vg=6

Vg=7

Vg=8

Vg=9

Vg=10

Vds (V)

Ids

(A)


γ = 0.6

Note: γ ∼ 1/T

Intro

Transfer curves

Spectroscopy

Poole-Frenkel

TSC

Conclusions


Alternative: Schottky Barrier Contacts

• But: maximum current through device would be reverse-bias saturation current of a Schottky diode.

• Very similar to Poole-Frenkel emission• Can be modeled by diodes in series with the FET

Intro

Transfer curves

Spectroscopy

Poole-Frenkel

TSC

Conclusions


Schottky Barrier Contacts

• But: connection to a physical model is lost.

• Very similar to Poole-Frenkel emission• Can be electrically simulated by 4 diodes in series with the FET

Intro

Transfer curves

Spectroscopy

Poole-Frenkel

TSC

Conclusions


Conclusions: • Region at contact is highly resistive or entiresample is controlled by hopping conduction(MTR: multi-trap and release?).

• correlation seen with other effects? (non-lineartransfer curves)

Poole-Frenkel Conduction modelIntro

Transfer curves

Spectroscopy

Poole-Frenkel

TSC

Conclusions


TSC

Intro

Transfer curves

Spectroscopy

Poole-Frenkel

TSC

Conclusions


http://www.ualg.pt/fct/adeec/optoel/fet/

VT = (4qεsψBNA−)1/2 / Cox + 2ψB

YesYesψB

YesNoNA−

Organic½-con

Classic½-con

Dependence on temperature

p452 of Sze

Temperature Scanned CurrentIntro

Transfer curves

Spectroscopy

Poole-Frenkel

TSC

Conclusions


T35_

T5.M

A

A:

• VT decreases reversibly because ψBchanges (linear)

• Poole-Frenkel: µ = exp(−EA/kT)

PF “wins”, current is exponentially growing

Vds = −0.5 V, Vg = −9 V

180 K

140 K

160 K

Vds = −0.5 V (−1 V @ 140 K)


Transfer curves

Spectroscopy

Poole-Frenkel

TSC

Conclusions


EA = 0.167 eV

PF: EA = q φB – 2 a k √Vds


Transfer curves

Spectroscopy

Poole-Frenkel

TSC

Conclusions


T35_

T5.M

BVds = −0.5 V, Vg = −9 V

VT = (4qεsψBNA−)1/2 / Cox + 2ψB

B:

• VT increases irreversibly because NA appear/ionize. Stressing!

• τ = τ0 exp(−EA/kT), NA−(t) = NA

−(∞)[1−Exp(t/τ)]

Stressing wins because of slow scanning.


Transfer curves

Spectroscopy

Poole-Frenkel

TSC

Conclusions


T35_

T5.M

?

Vds = −0.5 V, Vg = −9 V


Transfer curves

Spectroscopy

Poole-Frenkel

TSC

Conclusions


C:\d

ata\

tnt\t

6_35

\t2\te

mp\

pjot

r\pf_

i31.

m

Sample 35 Τ = 180 K

RP = 20 GΩ

Vg = −10 V

Temperature, Poole-FrenkelIntro

Transfer curves

Spectroscopy

Poole-Frenkel

TSC

Conclusions


C:\d

ata\

tnt\t

6_35

\t2\te

mp\

pjot

r\pf_

i52.

m


Vg = −20 V


Transfer curves

Spectroscopy

Poole-Frenkel

TSC

Conclusions


C:\d

ata\

tnt\t

6_35

\t2\te

mp\

pjot

r\pf_

i64.

m


Vg = −20 V


Transfer curves

Spectroscopy

Poole-Frenkel

TSC

Conclusions


Conclusions

Intro

Transfer curves

Spectroscopy

Poole-Frenkel

TSC

Conclusions


Magical temperature (phase transition?) at 200 K

Behavior up to 250 K well understood

VRH doesn’t work

MNR applies

Poole-Frenkel can explain a lot Is it the same as MTR (multi-trap-and-release)? Gilles Horowitz ….

Mobility spectra. Careful with pulsed measurements, µ depends on ν

ConclusionsIntro

Transfer curves

Spectroscopy

Poole-Frenkel

TSC

Conclusions


Current Spectroscopy: José Almada, Nelson Pimenta Final-year project students

Henrique Gomes

Thanks

All the partners in the MONA-LISA project

Intro

Transfer curves

Spectroscopy

Poole-Frenkel

TSC

Conclusions

The Callas (re)insurance group for giving this computer

p. stallinga (universidade do algarve) · pf “wins”, current is exponentially growing vds =...

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