Post on 27-Jul-2020
MONA-LISA Würzburg 2003, P. Stallinga, UAlg
P. Stallinga (Universidade do Algarve)MONA-LISA Wuerzburg, 3-VII-2003
MONA-LISA Würzburg 2003, P. Stallinga, UAlg
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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
MONA-LISA Würzburg 2003, P. Stallinga, UAlg
• 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
MONA-LISA Würzburg 2003, P. Stallinga, UAlg
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
MONA-LISA Würzburg 2003, P. Stallinga, UAlg
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
MONA-LISA Würzburg 2003, P. Stallinga, UAlg
Transfercurves
Intro
Transfer curves
Spectroscopy
Poole-Frenkel
TSC
Conclusions
MONA-LISA Würzburg 2003, P. Stallinga, UAlg
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
MONA-LISA Würzburg 2003, P. Stallinga, UAlg
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
MONA-LISA Würzburg 2003, P. Stallinga, UAlg
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
MONA-LISA Würzburg 2003, P. Stallinga, UAlg
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
MONA-LISA Würzburg 2003, P. Stallinga, UAlg
Currentspectroscopy
Intro
Transfer curves
Spectroscopy
Poole-Frenkel
TSC
Conclusions
MONA-LISA Würzburg 2003, P. Stallinga, UAlg
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
MONA-LISA Würzburg 2003, P. Stallinga, UAlg
Current Spectroscopy
Amplitude of response proportional to µ
Using lock-in detection
Intro
Transfer curves
Spectroscopy
Poole-Frenkel
TSC
Conclusions
MONA-LISA Würzburg 2003, P. Stallinga, UAlg
Experimetal SetupIntro
Transfer curves
Spectroscopy
Poole-Frenkel
TSC
Conclusions
MONA-LISA Würzburg 2003, P. Stallinga, UAlg
Experimetal SetupIntro
Transfer curves
Spectroscopy
Poole-Frenkel
TSC
Conclusions
MONA-LISA Würzburg 2003, P. Stallinga, UAlg
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
MONA-LISA Würzburg 2003, P. Stallinga, UAlg
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)
Primeiro Directamente a seguir
Spectroscopy resultsIntro
Transfer curves
Spectroscopy
Poole-Frenkel
TSC
Conclusions
MONA-LISA Würzburg 2003, P. Stallinga, UAlg
102 103 104 105
10-4
10-3
10-2
Mobilidade em Função da Frequência
Frequencia(Hz)
Mob
ilida
de(c
m2 /V
s)
Primeiro Directamente a seguir
Extrapolation to pulsed measurements
Pulsed experiments give 500x mobility
∆t = 10 µs µ = 10−2 cm2/Vs
Spectroscopy resultsIntro
Transfer curves
Spectroscopy
Poole-Frenkel
TSC
Conclusions
MONA-LISA Würzburg 2003, P. Stallinga, UAlg
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 (?)
Spectroscopy resultsIntro
Transfer curves
Spectroscopy
Poole-Frenkel
TSC
Conclusions
MONA-LISA Würzburg 2003, P. Stallinga, UAlg
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
MONA-LISA Würzburg 2003, P. Stallinga, UAlg
Poole-Frenkel
Intro
Transfer curves
Spectroscopy
Poole-Frenkel
TSC
Conclusions
MONA-LISA Würzburg 2003, P. Stallinga, UAlg
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
MONA-LISA Würzburg 2003, P. Stallinga, UAlg
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
MONA-LISA Würzburg 2003, P. Stallinga, UAlg
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
MONA-LISA Würzburg 2003, P. Stallinga, UAlg
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
MONA-LISA Würzburg 2003, P. Stallinga, UAlg
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
MONA-LISA Würzburg 2003, P. Stallinga, UAlg
Simulation of Poole-Frenkel conduction
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
MONA-LISA Würzburg 2003, P. Stallinga, UAlg
Simulation of Poole-Frenkel conduction
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)
Poole Frenkel, Ids vs. Vds
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)
Poole Frenkel, Ids vs. Vds
γ = 0.6
Note: γ ∼ 1/T
Intro
Transfer curves
Spectroscopy
Poole-Frenkel
TSC
Conclusions
MONA-LISA Würzburg 2003, P. Stallinga, UAlg
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
MONA-LISA Würzburg 2003, P. Stallinga, UAlg
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
MONA-LISA Würzburg 2003, P. Stallinga, UAlg
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
MONA-LISA Würzburg 2003, P. Stallinga, UAlg
TSC
Intro
Transfer curves
Spectroscopy
Poole-Frenkel
TSC
Conclusions
MONA-LISA Würzburg 2003, P. Stallinga, UAlg
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
MONA-LISA Würzburg 2003, P. Stallinga, UAlg
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)
Temperature Scanned CurrentIntro
Transfer curves
Spectroscopy
Poole-Frenkel
TSC
Conclusions
MONA-LISA Würzburg 2003, P. Stallinga, UAlg
EA = 0.167 eV
PF: EA = q φB – 2 a k √Vds
Temperature Scanned CurrentIntro
Transfer curves
Spectroscopy
Poole-Frenkel
TSC
Conclusions
MONA-LISA Würzburg 2003, P. Stallinga, UAlg
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.
Temperature Scanned CurrentIntro
Transfer curves
Spectroscopy
Poole-Frenkel
TSC
Conclusions
MONA-LISA Würzburg 2003, P. Stallinga, UAlg
T35_
T5.M
?
Vds = −0.5 V, Vg = −9 V
Temperature Scanned CurrentIntro
Transfer curves
Spectroscopy
Poole-Frenkel
TSC
Conclusions
MONA-LISA Würzburg 2003, P. Stallinga, UAlg
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
MONA-LISA Würzburg 2003, P. Stallinga, UAlg
C:\d
ata\
tnt\t
6_35
\t2\te
mp\
pjot
r\pf_
i52.
m
Sample 35 Τ = 160 K
Vg = −20 V
Temperature, Poole-FrenkelIntro
Transfer curves
Spectroscopy
Poole-Frenkel
TSC
Conclusions
MONA-LISA Würzburg 2003, P. Stallinga, UAlg
C:\d
ata\
tnt\t
6_35
\t2\te
mp\
pjot
r\pf_
i64.
m
Sample 35 Τ = 140 K
Vg = −20 V
Temperature, Poole-FrenkelIntro
Transfer curves
Spectroscopy
Poole-Frenkel
TSC
Conclusions
MONA-LISA Würzburg 2003, P. Stallinga, UAlg
Conclusions
Intro
Transfer curves
Spectroscopy
Poole-Frenkel
TSC
Conclusions
MONA-LISA Würzburg 2003, P. Stallinga, UAlg
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
MONA-LISA Würzburg 2003, P. Stallinga, UAlg
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