www.elsevier.com/locate/mee

Microelectronic Engineering 75 (2004) 316–320

Electrical characteristics of (Ba,Sr)TiO3 films accountedby partially depleted model

Toru Hara *

R&D Center, Taiyo Yuden Co. Ltd., 1037 Oazasasoh, Shinji-Town, YatsukaGun 6990406, Japan

Received 30 April 2004; received in revised form 14 June 2004; accepted 15 June 2004

Available online 26 June 2004

Abstract

We investigated the leakage current versus voltage (I–V) characteristics, the capacitance versus thickness of

(Ba0:5Sr0:5)TiO3 film (C–t) characteristics, and the relaxation currents of sputtered (Ba0:5Sr0:5)TiO3 films with the

thickness of 40–166 nm. The I–V characteristics can be explained by the partially depleted model especially when the

thickness of (Ba0:5Sr0:5)TiO3 film exceeds 62 nm. The C–t characteristics indicate that the relative dielectric constant in

the internal layer (out of the depletion layer) does not change by applied voltages. This can be explained by assuming

that the electric field is concentrated at the partially depleted layer, and that the relative dielectric constant in the

depletion layer decreases in accordance with the increasing of applied voltage. The relaxation currents may be explained

by assuming that the relative dielectric constant in the depletion layer decreases in accordance with the increasing of

applied voltage.

� 2004 Elsevier B.V. All rights reserved.

Keywords: (Ba0:5Sr0:5)TiO3; Thin film; Partially depleted model

1. Introduction

(Ba,Sr)TiO3 thin films are prime candidates ascapacitors for dynamic random-access memories

(DRAMs), and for tunable microwave devices.

Though a lot of work has been reported explaining

the electrical characteristics of (Ba,Sr)TiO3 thin

films, a complete overall picture is yet to be uni-

versalized. In this paper we present a partially

* Corresponding author. Tel./fax: +81-0852-66-2735.

E-mail address: thara@m6.dion.ne.jp.

0167-9317/$ - see front matter � 2004 Elsevier B.V. All rights reserv

doi:10.1016/j.mee.2004.06.003

depleted model, which is able to explain the leak-

age current versus voltage (I–V) characteristics,

the capacitance versus film thickness (C–t) char-acteristics, and the relaxation currents. Previously,

Hwang et al. [1] explained the I–V characteristics

of Pt/(Ba,Sr)TiO3/Pt capacitors using the partially

depleted model. Fukuda et al. [2] explained the

relaxation mechanism of Pt/(Ba,Sr)TiO3/Pt ca-

pacitor using the partially depleted model. Ma-

runo et al. [3] explained the I–V characteristics and

C–V characteristics of Pt/(Ba,Sr)TiO3/Pt capacitorusing the wholly depleted model. However, the

schematic band structure described in [3] shows the

ed.

T. Hara / Microelectronic Engineering 75 (2004) 316–320 317

partially depletion when the voltage is applied. We

reported the degradation mechanism of Au/

(Ba,Sr)TiO3/Pt capacitor using the partially de-

pleted model [4]. We add the new aspects for the

partially depleted model in this paper.

2. Experiment

The 100-nm thick Pt films were deposited as

bottom electrodes on TiO2(2 nm) coated SiO2(80

nm)/Si substrates by dc sputtering in an ambient of

argon (Ar) gases at a constant pressure of 0.7 Pa,

and at a constant substrate temperature of 250 �C,and at a fixed dc power of 100 W. The

(Ba0:5Sr0:5)TiO3 films were deposited on the bot-

tom Pt electrodes by rf magnetron sputtering in an

ambient of oxygen (O2) and Ar gases with O2/Ar

ratio of 5/5 at a constant pressure of 0.035 Pa, at a

constant substrate temperature of 600 �C, at a

fixed rf power of 1 kW, and at a fixed dc power of

200 W. The 250-nm thick Pt films were depositedas top electrodes with a diameter of 0.5 mm on the

(Ba0:5Sr0:5)TiO3 films by electron beam evapora-

tion at 120 �C through a metal shadow mask.

After a series of depositions, the capacitors were

annealed at 600 �C in oxygen ambient for 30 min.

Thickness measurements were performed using a

spectroscopic ellipsometer. The current versus

voltage (I–V) characteristics were measured usingan I–V meter (ADVANTEST R62469) through a

step voltage technique with stair-shaped dc-bias

-8

-6

-4

-2

0.5

log

(J)

at 3

13[K

]J:

Cur

rent

Den

sity

[A

cm-2

]

Electric Field

102n

1

166nm

Fig. 1. Plots of leakage current versus voltage

voltage applied to the top electrode, while the

bottom electrode was grounded. The value of each

voltage step and the hold time were 0.1 V and 1 s,

respectively. In order to minimize the influence of

the relaxation current on the leakage current data,

measurement was performed after sweeping thevoltage to the maximum value of each biased di-

rection. The capacitance at 10 kHz versus thick-

ness of (Ba0:5Sr0:5)TiO3 film (C–t) characteristics

were obtained using an HP4284A precision LCR

meter under the dc bias voltages (0, 1, 2, 2.5, and 3

V). The relaxation currents were measured using a

pA-meter (ADVANTEST R62469) with a con-

stant voltage (2–3 V) applied to the top electrode,while the bottom electrode was grounded. The

value of each measuring time was 0.1 s. The

measurements of electrical characteristics were

performed at 40 �C.

3. Results and discussion

Fig. 1 shows the results of I–V measurements

for (Ba,Sr)TiO3 films. The leakage currents ex-

hibit no dependence on the film thickness be-

tween 40 and 62 nm. However when the film

thickness exceeds 62 nm, the leakage current

exhibits the dependence on the film thickness.

This may be the evidence that the (Ba,Sr)TiO3

film is fully depleted when the film thickness isless than or equal to 62 nm, and that the

(Ba,Sr)TiO3 film is partially depleted when the

1.0 1.5 [MV cm-1]

40nm

62nm

89nm

m

17nm

(I–V) characteristics of (Ba,Sr)TiO3 films.

318 T. Hara / Microelectronic Engineering 75 (2004) 316–320

film thickness exceeds 62 nm. The leakage cur-

rents exhibit no dependence on the film thickness

(89–117 nm) when the applied electric field in-

creases. We assume that it is due to the in-

creasing of electric field in the partially depleted

0

100

200

300

400

500

0 50 10

t: Thickness of

Rel

ativ

e D

iele

ctri

c C

onst

ant

2.5V

0V

1V

2V

3V

0.0

0.2

0.4

0.6

0.8

1.0

0 50 10

t: Thickness of (B

t/ εr

t / ε r = (t - nW DL ) / εODL + nW

n = 2at 0V, n = 1 when the bias

Pt Pt

at 0V

Tcd

Vbi = 1.0eV

εODL = 578

(a)

(b)

(c)

Fig. 2. (a) Plots of relative dielectric constant versus thickness of (Ba,S

(Ba,Sr)TiO3 film. er denotes the relative dielectric constant of (B

eODL þ nWDL=eDL. WDL denotes the depletion width. eODL denotes the re

layer. eDL denotes the relative dielectric constant of (Ba,Sr)TiO3 film in

band structure with or without the applied voltage. ‘‘eODL’’ is calcula

layer, and due to the slightly decreasing of de-

pletion width, and due to the increase of tun-

neling current through the thin depletion layer.

Fig. 2(a) shows the plots of relative dielectric

constant versus thickness of (Ba,Sr)TiO3 films.

0 150 200

(Ba, Sr)TiO3 [nm]

0 150 200

a, Sr)TiO3 [nm]

0V

1V

2V

2.5V

3V

DL / ε DL

voltage is applied.

Pt

Pt

at 1-2V

he electric field isoncentrated at the partiallyepleted layer.

2.0eV at 1V

3.0eV at 2V

εODL = 595

Vbi =

r)TiO3 films; (b) Plots of t=er versus t. t denotes the thickness ofa,Sr)TiO3 film. The data were fitted by t=er ¼ ðt � nWDLÞ=lative dielectric constant of (Ba,Sr)TiO3 film out of the depletion

the depletion layer. n ¼ 2 at 0 V. n ¼ 1 at >0 V; (c) Schematic

ted from the slope in Fig. 2.

T. Hara / Microelectronic Engineering 75 (2004) 316–320 319

Fig. 2(b) shows the plots of t=er versus t. t de-

notes the thickness of (Ba,Sr)TiO3 film. er de-

notes the relative dielectric constant of

(Ba,Sr)TiO3 film. The data were fitted by

t=er ¼ ðt � nWDLÞ=eODLþ nWDL=eDL. WDL denotes

the depletion width. eODL denotes the relativedielectric constant of (Ba,Sr)TiO3 film out of the

depletion layer. eDL denotes the relative dielectric

constant of (Ba,Sr)TiO3 film in the depletion

layer. Fig. 2(c) shows the schematic band

structure with or without the applied voltage.

eODL is calculated from the slope in Fig. 2. n ¼ 2

at 0 V. n ¼ 1 at >0 V. As we can see from

Fig. 2(c), eODL does not change by appliedvoltages. This may be the evidence that the

(Ba,Sr)TiO3 film is partially depleted, and

that the electric field is concentrated at the

partially depleted layer. The relative dielectric

constant of partially depleted layer is assumed to

decrease in accordance with the increasing of

electric field.

Fig. 3 shows the results of relaxation currentsmeasurements for 62-nm thick (Ba,Sr)TiO3 films

at applied voltages of 2–3 V. (At applied volt-

ages of <2 V, the slowest relaxation was hidden

due to the lower limit of current detection.)

Three kinds of relaxations (s1 ¼ 0:36 s, s2 ¼ 5:45s, and s3 ¼ 237 s at 2 V, s1 ¼ 0:24 s, s2 ¼ 4:90 s,

and s3 ¼ 151 s at 3 V) were observed. These are

given by

1.00E-12

1.00E-11

1.00E-10

1.00E-09

1.00E-08

1.00E-07

0 20 40 60

Lea

kage

Cur

rent

[A

]

Fig. 3. Plots of relaxation currents of

Itotal ¼X3

n¼1

I0;n exp��� tM

sn

��; ð1Þ

where Itotal is the total leakage current, I0;n is the

constant, sn is the relaxation time, and tM is the

measuring time, respectively. We assumed that

the relaxation is due to the electron-detrapping

in the depletion layer. Fukuda et al. [2] suggested

that the relaxation of (Ba,Sr)TiO3 thin film is in-

duced by the electron-detrapping in the depletionlayer. Ang et al. [5] assumed that the dielectric

relaxation and relaxation current for the

(Sr1–1:5xBix)TiO3 ceramic are induced by electrons

trapped by oxygen vacancies. Lu et al. [6] reported

the trapped-carrier-induced impedance relaxation

in ferroelectric ceramic Pb2KNb4TaO15. The de-

crease of relaxation time in accordance with

the increasing of bias voltage is probably due tothe decreasing of relative dielectric constant in the

depletion layer. The depletion width is propor-

tional to ðVbi þ V Þ1=2; Vbi denotes the built-in

voltage, and proportional to e1=2DL, as given by

WDL ¼ 2eDLe0ðVbi þ V ÞqNSC

� �1=2

; ð2Þ

where e0 is the dielectric constant of free space, q is

the electric charge of a donor-like defect (oxygen

vacancy) in the depletion layer, and NSC is the

donor-like defect density in the depletion layer. We

assumed the relaxation time is given by

80 100 120 140

Time [s]

3V

2V

62-nm thick (Ba,Sr)TiO3 films.

320 T. Hara / Microelectronic Engineering 75 (2004) 316–320

s ¼ WDL

mdrift¼ WDL

lðVbi þ V Þ=WDL

¼ 2eDLe0qNSCl

; ð3Þ

where vdrift is the drift velocity of electron and l is

the electron mobility. s decrease in accordance

with the decreasing of eDL. This is the assumption

for the first discussion.

Generally, the relative dielectric constant de-

creases exponentially in accordance with the in-

creasing of applied voltage when the applied

voltage is low. Therefore, we speculate that thedepletion width decreases in accordance with the

increasing of electric field when the applied voltage

is low.

4. Conclusions

The leakage current versus voltage (I–V) char-acteristics, the capacitance versus film thickness

(C–t) characteristics, and the relaxation currents of

sputtered (Ba0:5Sr0:5)TiO3 films imply that the

partially depleted model is reliable especially when

the bias voltage is applied.

References

[1] C.S. Hwang, B.T. Lee, C.S. Kang, J.W. Kim, K.H. Lee, H.-

J. Cho, H. Horii, W.D. Kim, S.I. Lee, Y.B. Roh, J. Appl.

Phys. 83 (1998) 3703.

[2] Y. Fukuda, K. Numata, K. Aoki, A. Nishimura, Jpn. J.

Appl. Phys. 15 (1996) 5178.

[3] S. Maruno, T. Kuroiwa, N. Minami, K. Sato, S. Ohmura,

M. Kaida, T. Yasue, T. Koshikawa, Appl. Phys. Lett. 73

(1998) 954.

[4] T. Hara, IEEE Trans. Device and Materials Reliability 4,

No. 2 (June 2004).

[5] C. Ang, Z. Yu, L.E. Cross, Phys. Rev. B 62 (2000) 228.

[6] Z. Lu, J.P. Bonnet, J. Ravez, P. Hagenmuller, Solid State

Ionics 57 (1992) 235.