leakage mechanisms - microwave electronics...

© 2000, S.K. Streiffer, Argonne National Laboratory, All Rights ReservedNC State

Leakage Mechanisms

Thin films, fully depleted Leakage controlled by combined thermionic /

field emission across the Schottky barrier at the film-electrode interfaces. Film quality effects barrier height, and mobilities of carriers.

Thicker films of interest for higher voltage applications

Poorly understood


Much effort has gone into studying the leakage of perovskite-type titanate thin films, including SrTiO3, (Ba,Sr)TiO3, and Pb(Zr,Ti)O3:

J.F. Scott, et al., Proc. of the 1992 IEEE Int. Symp. Appl. Ferro., 356 (1992). T. Makita, et al., Mat. Res. Soc. Symp. Proc. 284, 529 (1993). T. Kuroiwa, et al., Ceramic Transactions 43, 219 (1994). C.S. Hwang, et al., Jpn. J. Appl. Phys. 34, 5178 (1995). M. Kiyotoshi and K. Eguchi, Appl. Phys. Lett. 67, 2468 (1995). R. Waser, in Science and Technology of Electroceramic Thin Films: NATO ASI

Series Vol. 284, ed. O. Auciello and R. Waser (London: Kluwer Academic Publishers, 1995) pp. 223-248.

G. Dietz, et al., J. Appl. Phys. 78, 1 (1995). S. Dey, et al., Jpn. J. Appl. Phys. 34, 3142 (1995). G. Dietz, et al., J. Appl. Phys. 82, 2359 (1997). G. Dietz and R. Waser, Thin Solid Films 299, 53 (1997) S. Zafar, et al., Appl. Phys. Lett. 73, 3533 (1998)


Proposed conduction mechanisms for BST thin films:

Fowler-Nordheim tunneling (interface, bulk) Poole-Frenkel effect (bulk) Thermionic emission across Schottky barriers

(interface)

The most favored mechanism:Schottky-barrier limited current flow


“ELECTRICAL C ONDUCTION MECHANISMS IN SOLIDS”Hamann, Burghardt, and Frauenheim

“Bulk” -Controlled vs. “Interface” -Controlled(Injection-Limited)

________________________________________________________________________Ionic (high T, long time) Schottky Emission

Tunneling (through film) (High E) Field Emission

Bulk Doping (acceptors, donors, etc.) Contact Photoexcitation

Photoexcitation (light effect) Fowler-Nordheim Tunneling(can be bulk as well)

Trapping/Detrapping (Poole Frenkel) Space-Charge-Limited(can be bulk as well)

Hopping Conduction (Localization)________________________________________________________________________

Thin Films Thick(er) Films Failure Mode


Lack of complete and careful analyses of leakage in BST thin films

Experimental: Using a ramp or voltage step technique.

– danger of relaxation currents contribution in the analyses

Field and temperature dependencies:– Only field- or temperature-dependent data not sufficient

for understanding the mechanism !

Assumed values for the parameters in the model such as Richardson constant.

Inhomogeneity of Schottky barrier, interfacial roughness, etc.


W

²W

WB

metal insulator

xxm

Evac

Ec

EF

Evmetal metal

insulator


Leakage vs. A:B Site Ratio

-20

-15

-10

-5

400 500 600 700 800 900 1000 1100

51% Ti @200°C51% Ti @125°C53% Ti @200°C53% Ti @125°C

ln (J

)

E1/2 (V/cm) 1/2

t = 30 nm; T = 125, 150, 175, & 200°C, 0 < V < 3.5V



-32

-30

-28

-26

-24

-22

-20

-18

-16

-32 -30 -28 -26 -24 -22 -20 -18 -16

Pred

icte

d ln

(J/T

2 )

ln(J/T 2)

51% Ti

-32

-30

-28

-26

-24

-22

-20

-18

-16

-32 -30 -28 -26 -24 -22 -20 -18 -16

Pred

icte

d ln

(J/T

2 )

ln(J/T 2)

53% Ti

ln JT 2

= ln A∗∗ + αE1/ 2 − Wb

kBT



Ti Content Wb (eV) α A (A/cm2K2)

51% 1.05 0.00085 4.0e-6

51.5 1.28 0.00066 4.2e-3

52 1.44 0.00080 1.2e-2

53 1.17 0.00069 9.1e-5

53.5 0.92 0.00084 3.3e-9

J = A∗∗ T 2 exp αE1/ 2 − WbkBT


Depletion Widths Issue: What are the depletion lengths?

5 – 10 nm > film thickness (i.e. > 100 nm)

Why is this an issue? Explanation of C-V behavior Affects development directions and ultimate performance predictions

Case for fully depleted film Field dependence in a thickness series:

J(E,T) is almost independent of thickness !!!!Field dropping across entire film thickness

Frequency dependence of permittivity Depletion layer !!!! step frequency dependence


Consider 2 cases for a 200 nm filmdi = 10 nmτ = Ci × R

Case 1: τ < 10-4 Hz

!!!! Rb ~ 1011 Ω!!!! n ~ 1011 m-3

Not high enough carrier density to cause band bending Case 2:

τ > 109 Hzσb = ~ 30 (Ωm)-1

This is strongly semiconducting.

Electrode ElectrodeDepletionLayer

DepletionLayer

FilmBulk

d − 2diARb


BST Depletion Widths

M. Copel et al., Appl. Phys. Lett. 70, 3227 (1997): W = 70nm for CVD films


Failure Modes: Resistance Degradation Change in resistivity of a sample caused by migration of

charged point defects, leading to increased leakage and eventually breakdown

Bulk and single crystals: R. Waser, T. Baiatu, and K.-H. Härdtl, J. Am. Cer. Soc. 73, 1645 (1990); 73, 1654 (1990); J. Am. Cer. Soc. 73, 1663 (1990).

10-5

10-4

10-3

10-2

10-1

10-1 100 101 102 103 104

Cur

rent

Den

sity

(A/c

m2 )

Time (s)

(-) (+)

53.3 at%TiThickness: 40 nmField: 875 kV/cmT = 225°C Resistance degradation in a

polycrystalline (Ba,Sr)TiO3 film, after C. Basceri et al., Ferroelectric Thin Films VI, MRS Symp.Proc. 493 (1998)


Resistance Degradation and Lifetime: Thickness Dependence

10-5

10-4

10-3

10-2

10-1

100

101

10-1 100 101 102 103 104 105

Cur

rent

Den

sity

(A/c

m2 )

Time (s)

53.3 at%TiField: 750 kV/cmT = 225°C

24 nm

40 nm80 nm

160 nm

101

102

103

104

105

106

0 20 40 60 80 100

@200°C@225°C@250°C

Mea

sure

d L

ifetim

e, t

d (s)

Thickness (nm)

n=1.85

n=1.48

n=1.47

Observed thickness dependence manifests itself as a decrease in the activation energy with respect to temperature.

Waser: bulk SrTiO3, n ~ 2.5 @ 2 kV/cm, 270°CJ. Am. Ceram. Soc. 73, 1645-1663 (1990).


Resistance Degradation and Lifetime: Composition Effect

The measured resistance degradation lifetime at this temperatureand in this field increases as the Ti content is increasedto 52.0 at%Ti, and then decreases with higher at%Ti.

100

101

102

103

104

105

106

400 600 800 1000 1200 1400

51.0 at%Ti (n=10.7)52.0 at%Ti (n=9.5)53.0 at%Ti (n=8.3)53.5 at%Ti (n=8.1)

Mea

sure

d L

ifetim

e, t

d (s)

Field (kV/cm)

T = 225°CThickness: 30 nm


Resistance Degradation and Lifetime: Temperature Dependence

Temperature dependence clearly follows an Arrhenius-type behavior:

dt = 0t exp QT (V)kT

101

102

103

104

105

106

1.8 1.9 2 2.1 2.2 2.3M

easu

red

Life

time,

td (s

)

1000/T (1/K)

53.3 at%TiThickness: 40 nmField: 875 kV/cm


Resistance Degradation and Lifetime: Voltage/Field Dependence

It is difficult to distinguish the different functional forms ofvoltage/field dependence, given the electric field range investigated:

dt = 0t exp − qVvQ (T)

dt = 0t exp vQ (T)qV

dt = 0t −nV

most conservative

least conservative


Resistance Degradation and Lifetime: Estimation of Lifetimes

51.0 at%Ti BST Films

102

104

106

108

1010

1012

1014

1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0

30 nm BST70 nm BST150 nm BST

Ext

rapo

late

d L

ifetim

e, t

d (s)

1000/T (1/K)

85°C

10 years

(Previously extrapolated to 1.6 V)

51.0 at%Ti

102

104

106

108

1010

1012

1014

0 2 4 6 8 10 12 14

30 nm BST70 nm BST150 nm BST

Ext

rapo

late

d L

ifetim

e, t

d (s)

Voltage (V)

1.6 V

10 years

51.0 at%Ti

(Previously extrapolated to 85°C)


Resistance Degradation and Lifetime: Modification Of Leakage Behavior

Oxygen vacancies are mobile defects under the given experimentalconditions: electromigration toward cathode.

“Modification of Schotky barrier heights/band structure”(different than bulk resistance degradation mechanism)

Also: Spatial modification of carrier concentrations due to the spatial variation in the oxygen vacancy concentration between the two electrode: change in conductivity of the bulk film.

The accumulation of oxygen vacancies in front of the cathode creates an internal built-in potential at the interface. This space charge modifies the band structure and thus interfacial energy barriers: The difference in barrier heights then appears as an internal bias in the film.



The differences in barrier heights:

-20

-16

-12

-8

-4

700 800 900 1000 1100 1200

lnJ

(A/c

m2 )

E1/2 (V/cm) 1/2

Fresh

4xts (- deg.)

5xts (- deg.)

53.0 at%TiThickness: 40 nmT = 25°C

(-) Polarity

-20

-16

-12

-8

-4

700 800 900 1000 1100 1200

lnJ

(A/c

m2 )

E1/2 (V/cm) 1/2

Fresh

7xts (+ deg.)


(+) Polarity

4xts: 0.13 eV5xts: 0.21 eV 7xts: 0.22 eV



The peak shift in C-V: 0.12 V

15

20

25

30

35

40

45

50

55

-5 -4 -3 -2 -1 0 1 2 3 4 5

Fresh4xt

s (-deg.)

C/A

(fF/

µm2 )

Bias (V)

PeakShift: 0.12 V

53.0 at%Tit: 40 nmT = 25°C

0.0000

0.0020

0.0040

0.0060

0.0080

0.0100

-5 -4 -3 -2 -1 0 1 2 3 4 5

tan δδ δδ

Bias (V)




15

20

25

30

35

40

45

50

55

-5 -4 -3 -2 -1 0 1 2 3 4 5

Fresh5xt

s (-deg.)

C/A

(fF/

µm2 )

Bias (V)

PeakShift: 0.20 V

53.0 at%Tit: 40 nmT = 25°C

0.0000

0.0020

0.0040

0.0060

0.0080

0.0100

-5 -4 -3 -2 -1 0 1 2 3 4 5

tan δδ δδ

Bias (V)




15

20

25

30

35

40

45

50

55

-5 -4 -3 -2 -1 0 1 2 3 4 5

Fresh7xt

s (+ deg.)

C/A

(fF/

µm2 )

Bias (V)

PeakShift: 0.20 V

53.0 at%Tit: 40 nmT = 25°C

0.0000

0.0020

0.0040

0.0060

0.0080

0.0100

-5 -4 -3 -2 -1 0 1 2 3 4 5

tan δδ δδ

Bias (V)



Recovery anneal studies:Negative polarity currents were completely recovered.Positive polarity currents decreased further ?

10-10

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

0 0.5 1 1.5 2 2.5

Fresh Contact (+)After 11 cycles (+)550°C, 40 min, Air (+)Fresh Contact (-)After 11 Cycles (-)550°C, 40 min, Air (-)

Cur

rent

Den

sity

(A/c

m2 )

V1/2




C-V behavior indicates that resistance degradation is recoverable.

15

20

25

30

35

40

45

50

55

-4 -2 0 2 4

Fresh ContactAfter 11 CyclesAfter Air Anneal(550°C, 40 min)

C/A

(fF/

µm2 )

Bias (V)

53.3 at%Tit: 40 nmT = 25°C

0.0000

0.0020

0.0040

0.0060

0.0080

0.0100

-4 -2 0 2 4

tan δδ δδ

Bias (V)

leakage mechanisms - microwave electronics...

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