Using JPF1 format

JOURNAL OF APPLIED PHYSICS

VOLUME 89, NUMBER 6

15 MARCH 2001

Effects of annealing conditions on optical and electrical characteristics of titanium dioxide films deposited by electron beam evaporation V. Mikhelashvili and G. Eisensteina) Electrical Engineering Department, Technion, Haifa, 32000, Israel

共Received 10 November 2000; accepted for publication 20 December 2000兲 We report measured evolutions of the optical band gap, refractive index, and relative dielectric constant of TiO2 film obtained by electron beam gun evaporation and annealed in an oxygen environment. A negative shift of the flat band voltage with increasing annealing temperatures, for any film thickness, is observed. A dramatic reduction of the leakage current by about four orders of magnitude to 5⫻10⫺6 A/cm2 共at 1 MV/cm兲 after 700 °C and 60 min annealing is found for films thinner than 15 nm. An equivalent SiO2 thickness of the order of 3–3.5 nm is demonstrated. An approach is presented to establish that at different ranges of applied voltage the hopping, space charge limited current, and Fowler–Nordheim are the basic mechanisms of carrier transport into the TiO2 film. © 2001 American Institute of Physics. 关DOI: 10.1063/1.1349860兴

I. INTRODUCTION

in silicon devices. Detailed data of TiO2 films obtained by electron beam gun evaporation has not been reported before although some results concerning single layer TiO228 and double layer TiO2 /Ta2O529 or TiO2 /Y2O330 systems have been published. The second part of the article presents a comprehensive procedure for analyzing current density versus voltage (J – V) characteristics based on analysis of the power exponent parameter. This general procedure, which can be used for any dielectric thin film, serves to determine the charge transport nature under different bias conditions as well as various aspects that limit metal–oxide–semiconductor device performance. For each charge transport mechanism governing the behavior in a respective bias regime we present general formalisms and use our experimental results to confirm it.

The use of high dielectric constant 共⑀兲 materials in small scale metal–insulator–semiconductor 共MIS兲 devices has been considered in numerous recent publications. These materials enable to maintain the capacitance density of thin 共less than 5 nm thick兲 SiO2 films while providing low leakage currents. Examples of such materials include, Y2O3, Ta2O5, 1–9 and TiO2 which has the highest ⑀ value.10 Room temperature grown TiO2 can have three structural forms: two crystalline, anatase and rutile, and an amorphous phase. Annealing at temperatures between 350 and ⬃800 °C initiates a transition from primary anatase to the rutile phase.11–13 The relative dielectric constant of TiO2 depends on the crystalline form and changes from ⬃31 to 60–100, for crystalline anatase and rutile respectively.10,14 Some structural and optical characteristics of TiO2 obtained by the sol–gel method and by oxidation of sputtered Ti were described in Refs. 15 and 16. Electrical characteristics of MIS structures with a TiO2 insulator deposited by chemical vapor deposition method and postannealed in oxygen or oxygen/hydrogen ambient have been studied and reported.17–24 Composite films of Ta2O5 :TiO2 used to enhance the relative dielectric constant and lower leakages were also investigated.25–27 This article contains two related parts. First, we describe detailed optical and electrical characterizations of TiO2 films obtained by electron beam gun evaporation. We present measurements of absorption spectra, refractive index and thickness, relative dielectric constant, and charge transport. The dielectric properties in field effect devices, the leakage current, and the interface properties are closely related to carrier trapping processes as well as defects, composition, and microstructure aspects of the thin films. In the systematic study presented here, we emphasize therefore dependencies on annealing conditions, film thickness, and morphology. Such detailed understanding of the film properties are imperative if TiO2 is to be developed to a degree which will enable its use

II. EXPERIMENTAL PROCEDURE

P-type Si wafers 共100兲 with resistivity of 8–10 ⍀ cm were used to prepare the MIS structures. TiO2 films with thickness in the range of 15–130 nm were deposited on unheated Si substrates without additional oxygen. Fused silica was used as a substrate for 153 nm thick TiO2 film for the optical measurement. The deposition was carried out at a pressure of (2 – 3)⫻10⫺6 Torr and a rate of 0.05 nm/s. Following the deposition, the films were annealed in an O2 environment at several temperatures in the range of 350– 750 °C and for different times up to 120 min. MIS capacitor structures with different areas (2 ⫻10⫺5 – 3⫻10⫺4 cm2) were patterned using standard lithography. The top contact was Al/Ti while Al was used for the back contact. The deposited film thickness was determined from step height measurements by ␣-step stylus profilometer and ellipsometry. The refractive index was also measured by ellipsometry. The optical absorption of the films was studied at a wavelength range of 250–900 nm. The surface features were examined by an atomic force microscope 共AFM兲 operating in the tapping mode. High frequency capacitance–

a兲

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© 2001 American Institute of Physics

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J. Appl. Phys., Vol. 89, No. 6, 15 March 2001

V. Mikhelashvili and G. Eisenstein

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FIG. 1. The change of the absorption spectra of 153 nm thick TiO2 film with annealing temperature. t ann⫽60 min. Curve 1—as deposited; curve 2—T ann⫽350; curve 3—550; and curve 4—750 °C.

voltage (C – V) and current density–voltage (J – V) measurements were performed using standard techniques and instruments. All electrical and optical measurements were carried out at room temperature. III. RESULTS A. Optical properties

Room temperature optical absorption spectra of TiO2 films: as deposited and after a 60 min anneal at different temperatures in an oxygen environment are shown in Fig. 1 1/2 as ␣ abs versus photon energy (h ␯ ). The absorption coefficient above the threshold of fundamental absorption follows the (h ␯ ⫺E g ) 2 energy dependence corresponding to indirect transitions with absorption or emission of phonons. The optical band gap (E g ) values near the absorption edge were extrapolated 共see for example the dash line along curve 4兲 for the as deposited 共amorphous state, curve 1兲, partially or full crystallized films 共curves 2 to 4, respectively兲, and were found to be in the range of 3.12–3.25 eV. The E g values of the annealed films are close to those reported for polycrystalline anatase and rutile films 共3.2 and 3.05 eV, respectively兲.10 However, they are lower than those obtained for an anatase of single crystal31 and for reactive sputtered TiO2 film.13 The modification of the crystalline structure is supported by the measured changes of refractive index 共n兲 and physical thickness 共L兲 with annealing temperature and time. These facts are illustrated in Fig. 2 for a 25 nm thick film. The most dramatic change of L and n occurs in the range of 400– 550 °C and at annealing times shorter than 20 min. The refractive index change from 2.15, for as deposited films to 2.35 for annealed films, and the thickness decrease by 6%–7% denote a densification of the annealed films due to a transition from the amorphous state to the crystalline form.32,33 This is consistent with known densities of TiO2 in its amorphous state 共3.2–3.65 gr/cm3兲, crystalline–anatase 共3.84–3.9 gr/cm3兲, and rutile 共4.25–4.26 gr/cm3兲 phases.32,33 The change of the refractive indexes correlates quantitatively with the index increase following annealing in reactive

FIG. 2. Thickness and refractive index dependencies on annealing temperature 共a兲 and time 共b兲 of 25 nm thick TiO2 film. 共a兲 t ann⫽60 min; 共b兲 T ann ⫽700 °C.

ion sputtered rutile films reported in Ref. 34. Reported refractive indices of crystalline anatase or rutile TiO2 are higher than found here (n⬎2.35), 35 indicating that film densification after annealing at 750 °C might not be complete in our samples. B. AFM image and roughness parameters

A roughness study experiment was performed on a set of as deposited and annealed TiO2 films of different thickness. Figure 3 shows examples of surface image changes with annealing temperature. The change in height and size of the roughs, specially in the thicker films is obvious. The 100 nm film when annealed above 550 °C also reveals a consolidation of the grains and cracks 关see Fig. 3共f兲兴. The AFM images were analyzed by calculating two roughness parameters: the root mean square value for roughness (R q ) and the maximum difference between the highest and lowest points in the scan range (R max). The variation of R q and R max with annealing temperature and film thickness are summarized in Fig. 4 which shows a nonmonotonic change of R q and R max with temperature. For the 450– 550 °C the surface quality improves, especially for films with


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FIG. 3. AFM images of as deposited 共a兲, 共c兲, and 共e兲 and annealed 共b兲, 共d兲, and 共f兲 TiO2 films of various thickness. 共a兲, 共b兲—L⫽15 nm; 共c兲, 共d兲—L ⫽25 nm; 共e兲, 共f兲—L⫽100 nm. t ann⫽60 min; T ann⫽700 °C.

thickness of less than 50 nm. At an annealing temperature of 550 °C the values of R q and R max , of films thinner than 50 nm, decrease respectively to 0.1–0.15 nm and 1–1.5 nm, values which are comparable with the silicon substrate surface. At temperatures above 550 °C a relatively sharp increase of both R q and R max is observed for all thickness. This is generally attributed to relaxation of the thermal expansion

mismatch stresses between the silicon substrate and the crystallized TiO2 film. C. Electrical characteristics 1. C – V dependence

Typical C – V characteristics of MIS structure with 15 and 25 nm thick TiO2 films are shown in Fig. 5. The flat




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FIG. 5. C – V characteristics of as deposited and annealed 15 共a兲 and 25 nm 共b兲 thick TiO2 films. t ann⫽60 min; T ann⫽700 °C.

FIG. 4. The change of the roughness and the maximum grain height difference of TiO2 film surface with annealing temperature 关共a兲 and 共b兲兴 and thickness 共c兲. 共a兲 and 共b兲: curve 1—L⫽15 nm; curve 2—L⫽25 nm; curve 3—L⫽50 nm; and curve 4—L⫽100 nm. t ann⫽60 min. 共c兲 t ann⫽60 min; T ann⫽700 °C.

band voltage V FB 共see Fig. 6兲 is always negative and it shifts to larger values with increasing annealing temperature and time, from ⫺0.3 to ⫺1.1 and ⫺0.25 to ⫺0.8 V for, retively, 15 and 25 nm films. The negative value of V FB sug-

gests that positive charges accumulate at the oxide–semiconductor interface. The relatively large change of V FB for annealing temperatures of 350–550 °C is accompanied by an insignificant variation of the flat band capacitance. The sharp change of V FB in the annealing time range of 10–20 min is similar to the behavior of the film thickness and refractive index 关see Fig. 2共b兲兴. For the 25 nm films we observe in Fig. 5 a saturation of the C – V curve indicating complete accumulation. The depletion layer in the silicon has no effect of the C – V curve. In contrast, for the 15 nm film the voltage dependent depletion layer in the Si causes an incomplete accumulation and an unsaturated C – V curve, typical of thin film.19 The estimated value of the total fixed charge density N tf 共the sum of the nonmobile charges: fixed and trapped in bulk and interface兲 increases with annealing temperature from 1.33⫻1012 to 6.8⫻1012 and from 5.2⫻1011 to 5.1 ⫻1012 cm⫺2 for 15 and 25 nm thick films, respectively. These charge densities when recalculated to bulk concentration (⬃N tf3/2) yield the values of 1.54⫻1019, 1.8⫻1019, and 3.7⫻1018, 1.1⫻1019 cm⫺3, respectively. The effect of thickness and annealing conditions on the relative dielectric constant is described in Figs. 7 and 8. Fig-


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FIG. 6. The change of the flat band voltage value with annealing temperature 共a兲 and time 共b兲 of 15 and 25 nm thick TiO2 film. 共a兲 t ann⫽60 min; 共b兲 T ann⫽700 °C.

FIG. 7. Thickness dependencies of the relative dielectric constant of as deposited and annealed TiO2 films. t ann⫽60 min; T ann⫽700 °C.


FIG. 8. The change of the relative dielectric constant with annealing temperature 共a兲 and time 共b兲 of TiO2 films. Curve 1—L⫽15 nm; curve 2—L ⫽25; and curve 3—L⫽50 nm. 共a兲 t ann⫽60 min; 共b兲 T ann⫽700 °C.

ure 7 shows ⑀, extracted from saturated capacitance values in the accumulation mode of the C – V characteristics, as a function of thickness for as deposited and samples annealed at 700 °C for 60 min. As deposited and annealed films with thicknesses up to 30 nm exhibit a fast increase in ⑀ and then saturation. The ⑀ value of as deposited thin 共less than 30 nm兲 films is actually higher than that of the corresponding annealed film. This is possibly due to the formation of a 1.5– 2.5 nm SiO2 layer at the Si surface during the annealing process which adds a series capacitor.36–38 The sharper change of ⑀ with thickness in the annealed films occurs because of: 共i兲 a decrease of the contribution of the SiO2 interface capacitance in thicker films because of a slow down in oxidization and 共ii兲 an increase of the relative dielectric constant due to a thermally induced 共in the oxygen ambient兲 homogenization of different crystalline phases of the TiO2 film. The ⑀ values for the annealed films, with the exception of the 15 nm sample are close to those of crystalline anatase ( ⑀ ⬇31) and rutile ( ⑀ ⬎40). 10 A monotonic reduction of ⑀ with temperature for a 15 nm film is seen in Fig. 8 curve 1. The value of ⑀ for 25 and




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of the leakage current density with annealing conditions depends on the film thickness and 共iii兲 the shift towards negative voltages of the inflection point as the annealing temperature increases is larger for the thinner film as seen when comparing Figs. 9共a兲 and 9共b兲. Several carrier transport mechanisms of charge flow in MIS structures biased in the accumulation mode are discussed in Ref. 39. These include double injection, hopping of the carriers into trapping levels, thermionic emission over the barriers, and field ionization of trapping levels based on, respectively, Schottky, Poole–Frenkel, and Fowler–Nordheim tunneling through insulator and space charge limited current 共SCLC兲. Determination of the dominant mechanism is usually achieved by graphical linearization of the J – V dependencies in accordance with theoretical formalisms. However, the semi- or double logarithmic representation of J – V characteristics averages over peculiarities of the characteristics which leads in turn to inaccurate conclusions about current transport mechanisms and wrong determination of the physical parameters. The analysis we present uses the power exponent a⫽

FIG. 9. Current density–voltage characteristics of 15 共a兲 and 25 nm 共b兲 thick TiO2 films. t ann⫽60 min; T ann⫽700 °C.

50 nm films 共curves 2 and 3 in Fig. 8, respectively兲 goes through a maximum and starts to decrease above 550 °C. The critical value of the annealing time 关see Fig. 8共b兲兴 is almost the same for all thickness, 10–20 min. The reduction of ⑀ for films thicker than 20 nm is partially due to the growth of a SiO2 interfacial layer. A second reason is an incorrect calculation of the capacitance which comes about due to the roughness enhancement in those films when annealed at high temperatures 共above 550 °C兲共see Figs. 3 and 4兲. This leads to a decrease of the contact area in comparison with the patterned geometrical size as the inner surface of the deposited metallic layer is contacting only the tops of the rough film areas. 2. J – V dependence and current flow mechanisms

The J – V curves of Al/Ti/TiO2 /Si/Al structures with two different dielectric thickness, negatively biased to set the accumulation mode, are shown in Fig. 9. Three important observations can be made: 共i兲 the leakage current decreases considerably at all applied fields when the amorphous TiO2 films are annealed at temperatures higher than the crystallization temperature, namely, above 350 °C, 共ii兲 the reduction

d 关 ln共 J 兲兴 , d 关 ln共 V 兲兴

共1兲

which describes the voltage dependent slope of the J – V characteristic in log–log scale.7,40–45 The transformation of the experimental J – V dependencies of Fig. 9 to the ␣ – V domain, using Eq. 共1兲 is shown in Fig. 10. The ␣ – V characteristic is more sensitive to changes taking place as different current flow mechanisms dominate in different ranges of applied voltage. The revelation of peculiar regions 共extrema, bends, or asymptotes兲 on the ␣ – V curves and their relation to known mathematical formalism of different current transport processes alows a discrimination among the mechanisms as well as an accurate extraction of some physical parameters. This is demonstrated below for the MIS structures we fabricated with 15 and 25 nm thick TiO2 films. 3. Low and moderate electric field range

a. The hopping mechanism: In dielectric materials with extremely low densities of thermally generated free charge carriers and correspondingly low carrier mobilities, the hopping conduction becomes probable. This process that uses incoherent jumps of carriers between isolated states is characterized by the formation of a small polaron at each occupied site.46,47 Experimental evidence of the polaron driven conductivity in rutile type single-crystal TiO2 is given in Ref. 48. We find that the carrier flow at low voltages through as deposited TiO2 films as well as postannealed 25 nm films has a hopping nature described by46

冉冊

qFR 1 J Mott⫽ ␴ 0 F exp , 2 kT

共2兲

or using Eqs. 共1兲 and 共2兲

␣ Mott⫽1⫹

qFR . kT


共3兲

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FIG. 11. J – V in Mott scale and corresponding to it the ␣ – V curves of as deposited 25 nmTiO2 film. Points and solid lines respectively describe the measured and calculated data. Curve 1—J – V; curve 2—␣ – V. Parameters of calculation are: R⫽4.7 nm and ␴ 0 ⫽5.8⫻10⫺12 ⍀ ⫺1 cm⫺1.

FIG. 10. ␣ – V dependencies of 15 共a兲 and 25 nm 共b兲 thick TiO2 films. t ann⫽60 min; T ann⫽700 °C.

The value ␴ 0 in Eq. 共2兲 is the impurity conductivity, q, T, k, and F denote the elementary charge, absolute temperature, Boltzmann constant, and the electric field, respectively. Equation 共3兲 enables us to estimate of the carrier hopping distance 共R兲. Figure 11 shows J – V and ␣ – V curves for a 25 nm structure. It is seen that for weak electric fields, F⬍5 ⫻104 V/cm, the experimental J – V characteristic 共plotted in a semilogarithmic scale兲 is linear 共see curve 1兲. The initial values of the power exponent is one 共at a condition F ⰆkT/qR兲 and ␣ increases linearly with applied voltage, curve 2 in Fig. 11. Solving Eqs. 共2兲 and 共3兲 alows us to extract the impurity conductivity

␴ 0 ⫽2

J . F exp共 ␣ Mott⫺1 兲

共4兲

The average hopping distance between localized states and the impurity conductivity of as deposited films are 2.5–3.5, 4–5 nm, and 1.5⫻10⫺11, 1⫻10⫺11 ⍀ ⫺1 cm⫺1 respectively, for 15 and 25 nm thick TiO2 films. The solid lines in Fig. 11 are calculated J – V and ␣ – V dependencies 关using Eqs. 共2兲 and 共3兲 with the extracted values of R and ␴ 0 兴. Annealing in

an oxygen ambient at 600 °C changes the value of R in a 25 nm film to 6 nm while ␴ 0 decreases significantly to ⬃1 ⫻10⫺16 ⍀ ⫺1 cm⫺1. The drastic change of the impurity conductivity of the annealed 25 nm film may also be due to several mechanisms other than a hopping current flow. For example, an enhancement of the probability for carrier trapping by deep levels can lead to an increase of the activation energy of the hopping process. The J – V characteristics of a 15 nm annealed film cannot be described by Eq. 共2兲 as the annealing process adds a native oxide SiO2 film and it is difficult to separate the actual mechanism in the TiO2 under a weak applied electric field. b. Schottky and Poole–Frenkel mechanisms. The Schottky and Poole–Frenkel mechanisms are commonly used to describe current transport under low and moderate electric fields. The current densities due to Schottky emission for an ideal contact 共no gap and no surface states on the metal–insulator or metal–semiconductor boundary兲 and the Poole–Frankel model are expressed by

冉

J Sch⫽A * T 2 exp ⫺ J PF⫽

冉

冊冉

冊

q⌽ Sch 1 exp ␤ V 0.5 , kT 2

冊

AV q⌽ PF exp ⫺ exp共 ␤ V 0.5兲 . L kT

共5兲共6兲

The ⌽ Sch and ⌽ PF are the thermionic barrier height and ionization energy of levels, respectively. A * is the Richardson coefficient and A is related to the density of ionized traps. The coefficient ␤ depends on the relative dielectric constant and interelectrode distance d according to

␤⫽

冉冊

q q kT ␲ ⑀ d

0.5

.

共7兲

The distance d is the dielectric thickness for ideal metal– insulator and metal–semiconductor contacts and in this case equals the interelectrode distance L. Previously, we have shown7 that an ␣ – V 0.5 presentation of the experimental J – V characteristic is advantageous compared to the common




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differs from the value determined by C – V characteristics. These results demonstrate that the current flow in our samples does not follow the Schottky or Poole–Frenkel processes. c. Space charge limited current. At moderate electric fields, carrier movement in the MIS structure may be limited by capture of carriers at electron traps in the dielectric.1,7,39,42 Here we use the theoretical analysis of SCLS dominated J – V characteristics40,49 to explain the peculiarities observed on the experimental and ␣ – V characteristics. The analysis40,41,49 allows the establishment 共from experimental J – V and ␣ – V data兲 of the dependencies on the applied voltage 共or current density兲 of the charge density 兩 ␳ a 兩 /q and free carrier concentration n a at the back contact, that is near the anode. These characteristics, in contrast to Refs. 50–52, can be derived for any type of trap distribution 共monoenergetic, exponential, etc.兲 provided that the usual conditions for SCLC are satisfied.40 The method49 is based on two assumptions: 共i兲 the carrier mobility 共␮兲 and interelectrode distance are bias independent and 共ii兲 the trap distribution is homogeneous across the sample area. The values of 兩 ␳ a 兩 /q and n a take the form

冉冊冉冊

1 J L n a⫽ , q␮ V d 2 J d

兩 ␳ a兩 ⑀ ⫽ 2 q L q

FIG. 12. Schottky 共a兲 and Poole–Frenkel 共b兲 plots, experimental and calculated 关Eqs. 共8兲 and 共9兲兴 power exponent characteristics of 15 nm thick as deposited TiO2 film. Curve 1—J – V; curves 2 and 3—experimental and calculated ␣ – V 0.5, respectively. Calculation for ⑀ ⫽25 was carried out. The dash lines denote the linearity of J – V curves in Schottky and Poole– Frenkel scales.

ln(J)–V0.5 or ln(J/V)–V0.5 scales since the ␣ – V 0.5 curve reveals the different transport mechanisms and enables to determine ⑀ from Eq. 共7兲. The parameter ␤ may be calculated using the expressions

␣ Sch⫽ 41 ␤ V 0.5

共8兲

␣ PF⫽1⫹ 21 ␤ V 0.5

共9兲

or derived from Eqs. 共5兲 and 共6兲 using Eq. 共1兲. Figure 12 shows an example of experimental J – V and ␣ – V characteristics for an as deposited 15 nm thick TiO2 film. The curves are shown in the Schottky and Poole– Frenkel scales. The J – V curves actually follow the linear dependence dictated by the Schottky and Poole–Frenkel laws 共see dash lines兲. However, the experimental characteristic 共curve 2 in Fig. 12兲 plotted as ␣ – V 0.5 varies from the curve calculated according to Eqs. 共8兲 and 共9兲共curve 3 in Fig. 12兲. The relative dielectric constant extracted by Eq. 共7兲

共10兲

冋册

冉冊冉冊冉冊

1 d 1 d J

V J2 1 d J

d

,

共11兲

Using the ␣ – V transformation of the J – V characteristics Eqs. 共10兲 and 共11兲 become n a⫽

J L ␣ , q ␮ 共 2 ␣ ⫺1 兲 V

兩 ␳ a兩 ⑀ 共 2 ␣ ⫺1 兲共 ␣ ⫺1 兲 ⫺ ␥␣ V, ⫽ 2 q L q ␣2

共12兲共13兲

where ␥ stands for

␥⫽

d 关 ln共 ␣ 兲兴 . d 关 ln共 J 兲兴

共14兲

The space charge limited current density can be calculated from Eqs. 共12兲 and 共13兲 J SCL⫽

共 2 ␣ ⫺1 兲 2 共 ␣ ⫺1 兲 ⫺ ␣␥ 共 2 ␣ ⫺1 兲 ⑀␮ V 2 , ␣3 Qa L3

共15兲

where Q a ⫽ 兩 ␳ a 兩 /q/n a accounts for the difference between the current densities in the trap-charge limited and trap-free SCL cases.52 For a monoenergetic trap distribution and for ␣ ⫽2 共that is ␥ ⫽0兲 when 兩 ␳ a 兩 /q⫽q t n a , Eq. 共15兲 transforms to the well known current–voltage relationship52 J SCL⫽

9 ⑀␮ V 2 , 8 qt L3

共16兲


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where the value q t ⫽1⫹ t兺 (N t /N ct ) is the trap occupation coefficient, N t is the trap concentration, and N ct ⫽N c ⫻exp(⫺Et /kT) represents the concentration of carriers which are thermally generated from traps. The effective density of states in the conduction band is N c and E t is the trap depth measured from the bottom of the conduction band. If Q a ⫽1 共or q t ⫽1兲, Eq. 共16兲 yields the expression for a trap free SCL J – V, characteristic52 9 V2 J SCL⫽ ⑀␮ 3 . 8 L

共17兲

In the case of more than one trap level 共with a level separation larger than several kT兲, the J – V characteristic may include several abrupt current changes caused by full population of partially occupied trap levels with different depths and densities.51 This is represented in the ␣ – V curve by extrema and bends 共that is d ␣ /dJ⫽0 or d 2 ␣ /dJ 2 ⫽0兲. For an exponential distribution, the traps fill up gradually with voltage and this yields a broad maximum on the ␣ – V curve. The case of closely separated trap levels 共with energy differences smaller than kT兲 is characterized by a slow change in ␣, as is the case for lightly populated trap levels. A discrimination criterion to diagnose the mechanisms causing the abrupt rise of current with voltage 共exhibited on ␣ – V curves by maxima兲, was suggested in Refs. 40 and 42. It follows from Eq. 共14兲 for ␥ ⫽0, Q am⫽

2 共 2 ␣ m ⫺1 兲 2 共 a m ⫺1 兲 ⑀␮ V m , L 3 J SCLm ␣ m3

共18兲

where ␣ m is the value of ␣ at the maximum point and J SCLm and V m are the corresponding values of current density and voltage. In accordance with Refs. 40 and 42, if Q amⰇ1, a large part of the injected carriers are trapped so that they are not contributing to the conductivity. If Q am is on the order of or equal to one, field ionization of trap levels 共the Poole– Frenkel law, for example兲 or trap-free SCL take place. A value of Q amⰆ1 denotes the absence of trapping and the dominant process becomes double injection of free carriers 共recombination limited current兲. In the double injection case the value of Q am is the ratio of the recombination to the actual mobility unlike in the SCLC case.40 The value of trapped charge density leading to the abrupt rise of the current with voltage can be calculated from Eq. 共13兲 using the same conditions as were used to develop Eq. 共18兲兩 ␳ am兩 ⑀ 共 2 ␣ m ⫺1 兲共 ␣ m ⫺1 兲 V m ⫽ . q q L2 ␣ m2

共19兲

The equation is the same as the one given in Ref. 52, for a single trap level provided that 兩 ␳ am兩 /q and V m in 共19兲 are substituted, respectively by N t and V TFL . The voltage V TFL 共trap fill limited voltage兲 is that for which the the traps are filled and the currents rises sharply becoming a SCL current.52 The values of Q am and 兩 ␳ am兩 /q are estimated from Eqs. 共18兲 and 共19兲 and the data of Figs. 9 and 10. A high value of the discrimination coefficients 共above 108 兲 is obtained for all 25 nm samples and for 15 nm films annealed at below

FIG. 13. Trapped charge density and free carrier concentration versus applied voltage of 15 共a兲 and 25 nm 共b兲 thick TiO2 films. Curves 1, 2—as deposited; curves 1⬘, 2⬘—annealed. Curves 1, 1⬘—charge density; curves 2, 2⬘—free carrier concentration. 共a兲 t ann⫽60 min; T ann⫽450 °C; 共b兲 t ann ⫽60 min; T ann⫽700 °C.

450 °C. This denotes a limitation of the carrier injection due to charges which accumulate on the traps distributed in the TiO2 band gap close to the anode 共that is near the Si/TiO2 or TiO2 /SiO2 boundary兲. In the case of field ionization of the trapping levels, Q m must be less than 12 and 10 关see Eq. 共8兲 in Ref. 7兴 for 15 and 25 nm as deposited films, respectively. This result confirms once more the conclusion made above that a Poole–Frenkel contribution to the current transport is absent in our experiments. The dependencies of the carrier concentration and trapped charge density on applied voltage, calculated by Eqs. 共12兲 and 共13兲, using the experimental data of Figs. 9 and 10 are shown in Fig. 13. The results are for 25 and 15 nm thick films, as deposited and annealed at 700 and 450 °C, respectively. These curves exhibit a decrease in carrier concentration in the bulk of the 25 nm TiO2 film by almost two orders of magnitude, accompanied by an increase of the trapped charge density by a factor of 2–3, as the annealing temperature increases. For the 15 nm TiO2 film, the change in free carrier concentration is by a factor of about 104 while the




variation of the charge concentration with annealing temperature is similar to that of the 25 nm film. The distinguishing features are observed in the voltage range below 1 V. The carrier concentration at the inflection voltage 共see Figs. 9 and 10兲 sharply decreases, while the charge concentration reveals a jumping nature. Assuming that the two separated maxima 关see Fig. 10共b兲兴 and the single maximum accompanied by two bends 关right and left side of the extremum in Fig. 10共a兲兴 seen in the ␣ – V curves for structures with as deposited 25 and 15 nm films are caused by occupation of trapping levels at different energy levels within the TiO2 band gap, we may estimate their energy and concentration according to Ref. 40. The levels responsible for the maxima and bends are located in the energy range of 0.475–0.55 eV. The annealing process shifts the voltage location of the maxima and their merger to 450 °C and more than 650 °C, respectively for 15 and 25 nm films 共see Fig. 10兲. The trap level energy defining the single maxima is 0.61–0.63 eV for both thicknesses. Thus, the annealing process deepens the levels and simultaneously increases the charge density from 9.6⫻1018 to 2.17⫻1019 and from 3⫻1018 to 7.4⫻1018 cm⫺3, respectively for 15 and 25 nm thick films. The estimated charge concentration is of the same order as the values determined from C – V data 共N if recalculated in volumetric units兲. Finally, we address very thin films where the basic process limiting the current may be somewhat ambiguous and difficult to determine. A common technique is to analyze J – V data as a function of temperature and plot the current density in the 关 (J/T 2 )⫺(1/T) 兴 scale 共see, for example Ref. 21兲. This type of measurement characterizes thermionic emission in accordance with Schottky theory. For TiO2 film annealed in an oxygen ambient, a change of the activation energy from 0.5 to 1 eV was determined and the barrier was associated with the Si/TiO2 boundary.19 This conclusion requires additional verification however, as the linearity of the (J/T 2 )⫺(1/T) function it not sufficient to prove that the of the Schottky mechanism dominates. Almost the same value of activation energy may be obtained when it is determined from J⫺(1/T) dependencies. The observed variation of activation energy may actually be connected with processes in the bulk of the TiO2, namely, it may reflect the change of trap level depth due to the annealing process, as in TiO2 films thinner then 15 nm which were annealed at temperatures above 450 °C such as the films we are describing in this article. 4. High electric field range: Fowler – Nordheim tunneling

The Fowler–Nordheim type tunneling process is usually considered as the most probable current flow mechanism in MIS structures under high bias levels. The J – V characteristic is described in those cases by39,53 J FN⫽

冉

冊

1.5 C⌽ FN BF 2 exp ⫺ . ⌽ FN F

共20兲

For a semiconductor 共or metal兲–single dielectric boundary, ⌽ FN represents the tunneling barrier height. For a double

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dielectric system 共for example in the boundary between a deposited dielectric and a native SiO2 layer兲 ⌽ FN represents the valence and conduction band offsets between the neighboring films. The coefficient B⫽1.54⫻10⫺6 and C⫽6.83 ⫻107 (m * /m) 0.5, 54,55 where m * /m is the ratio between the average effective electron mass in the band gap of the insulator layer and the free electron mass. The value of m * /m for SiO2 is equal to 0.42–0.5.54,56 A pure Fowler–Nordheim current flow mechanism is possible only for very thin dielectric films 共on order of several nanometers兲 which enables the required high field (⬃1⫻107 V/cm). However, the thickness can not be less than 2–3 nm as direct tunneling from the gate electrode to the silicon substrate or vice versa will dominate.39,56,57 The ␣ – V dependence derived from Eq. 共20兲 using Eq. 共1兲 is

␣ FN⫽2⫹

1.5 C⌽ FN

F

共21兲

.

1.5 It follows from Eq. 共21兲 that at electric field F⬍C⌽ FN , ␣ FN⬎2 and ␣ approaches 2 for large fields, say for F⬎1 ⫻107 V/cm. In accordance with Eq. 共21兲 a reciprocal relationship between ␣ FN and F in the proper range of electric field determines the dominance of the Fowler–Nordheim mechanism. The barrier height ⌽ FN and the field F may be derived from Eqs. 共20兲 and 共21兲

exp ⌽ FN⫽ 共 ␣ FN⫺2 兲

F⫽ 共 ␣ FN⫺2 兲

0.5

冉

冊

␣ FN ⫺1 2 , CB 0.5

exp关 43 共 ␣ FN⫺2 兲兴 C 0.5B 0.75

共22兲

.

共23兲

Equations 共22兲 and 共23兲 enable us to estimate independently the tunneling barrier height and the electric field and therefore the thickness of the single dielectric film. Equation 共21兲, on the other hand, permits the extraction of one of these parameters when the second one is known. When a noncontrollable thermal oxide exists on the semiconductor boundary, the field F develops partially across the low ⑀ material so that charge balance conditions within the double layer is satisfied.39,57–59 Since Eq. 共22兲 does not require knowledge of the electric field distribution, ⌽ FN can still be extracted. The J – V characteristics of MIS structures with as deposited 15 and 25 nm layers plotted in the conventional Fowler–Nordheim scale (ln(J/F2)⫺(1/F)) are illustrated in Fig. 14, curves 1. We note that the curves are indeed linear in the large bias regime 共dash line兲. The barrier height estimated using Eqs. 共21兲 or 共22兲, ⌽ FN⫽0.1– 0.15 eV, differs from the value needed to limit the current transport by the Fowler–Nordheim tunneling mechanism.53–57 The electric field F used in Eq. 共21兲 was estimated for the 25 and 15 nm films assuming that there is no native oxide so that the voltage drops only across the single TiO2 layer. The resulting field of 1 – 3⫻106 V/cm is lower than the minimum field required to cause carrier transport through the insulator by the Fowler–Nordheim mechanism.54–56 Besides the value of ␣ in this field range is 3–4, 共see Fig. 10 or curves 2 in Fig.


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FIG. 15. The Fowler–Nordheim tunneling barrier height 关Eq. 共22兲兴 and calculated SiO2 thickness 关Eq. 共24兲兴 dependencies on annealing temperature of 15 nm thick TiO2 film. Curve 1—L SiO2 ; curve 2—⌽. t ann⫽60 min.

where L SiO2 , L TiO2 and ⑀ SiO2 , ⑀ TiO2 are, respectively, the thickness and relative dielectric constant of the SiO2 and TiO2 films. The annealing temperature dependence of the SiO2 thickness, calculated by Eq. 共24兲, is illustrated in Fig. 15 curve 1. Here the relative dielectric constants of the TiO2 and SiO2 were assumed to be 30 and 3.85, respectively. Note the significant increase of the SiO2 thickness at 450 °C. The electric field distribution across a double layer dielectric under the condition of charge balance within the double dielectric stack is described by39 FIG. 14. The Fowler–Nordheim plots of experimental J – V and ␣ – V characteristics of as deposited 15 共a兲 and 25 nm 共b兲 thick TiO2 films. Curve 1— J – V; curve 2—␣ – V. The dash line denotes the linearity of J – V curve in Fowler–Nordheim scale.

14兲 while according to Eq. 共21兲 it must be larger. Hence, all as deposited and annealed TiO2 films, expect for those thinner than 15 nm and annealed above 450 °C, do not satisfy the conditions for Fowler–Nordheim-type characteristic and carriers transport across them has the character of direct tunneling. In order to explain the J – V curves of annealed 15 nm films we assume, as in Ref. 21 that the Si substrate is covered with a thin interfacial SiO2 film. The data in Fig 8共a兲 curve 3, where a reduction in ⑀ with annealing temperature is observed 共for a 15 nm TiO2 film兲 serves as evidence for the formation of the interfacial SiO2 layer. Considering a simple series capacitance model of a double layer TiO2 /SiO2 capacitor the SiO2 thickness may be estimated from the extracted accumulation capacitance

冉冊 1⫺

L SiO2⫽L TiO2

⑀

⑀ TiO2

⑀

⑀ SiO2

⫺1

,

共24兲

⑀ F⫽ ⑀ SiO2F SiO2 ⫹

Q ⫽ ⑀ TiO2F TiO2 . ⑀0

共25兲

Assuming, now, that carriers injected from the gate metal pass through the double layer with no charge being accumulated at the TiO2 /SiO2 interface (Q/ ⑀ 0 ⬍ ⑀ F), we derive from Eqs. 共24兲 and 共25兲 the electric field in the SiO2 and TiO2 films F SiO2⫽

V

⑀ SiO2 ⑀ TiO2

F TiO2⫽

⑀ SiO2

共26兲

,

共27兲

L TiO2⫹L SiO2 V

⑀ TiO2

,

L SiO2⫹L TiO2

where Q is the charge density and ⑀ 0 is the permittivity of vacuum. According to Eqs. 共26兲 and 共27兲, the electric field across the ultrathin interfacial layer is quite high, even at moderate voltages, while the electric field across the thicker, higher ⑀ TiO2 layer is low. The electric field in the SiO2 film is sufficiently high to satisfy the conditions for Fowler–Nordheim tunneling. In Fig. 16 共curves 1 and 2兲 we show J – V and ␣ – V characteristics of a 2.3 nm SiO2 film plotted in the Fowler–Nordheim scale. The curves in Fig. 16 were calculated by Eqs. 共25兲 or 共26兲 using J – V date of an MIS structure with a 15 nm TiO2




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FIG. 16. The Fowler–Nordheim plots of measured and calculated J – V and ␣ – V characteristics of annealed 15 nm thick TiO2 film. Parameters of calculation are: ⌽ FN⫽0.89 eV and m * /m⫽0.5. The value of the electric field for L SiO2⫽2.3 nm was calculated in accordance with Eq. 共26兲. Curves 1, 2—measured; curves 1⬘, 2⬘—calculated. t ann⫽60 min; T ann⫽700 °C.

film, annealed at 700 °C and assuming an effective relative dielectric constant of 17 关see curve 3 in Fig. 8共a兲兴. The barrier height for this case is 0.89 eV, calculated by Eqs. 共21兲关or 共22兲兴 and 共26兲 and the data of Fig. 16 共curve 2兲, where ␣ is linear. The variation of the obtained barrier height with annealing temperature is shown in Fig. 15 共curve 2兲 with significant changes seen abobe 500 °C. However, the obtained values of ⌽ FN are lower than the actual band offset between TiO2 and SiO2 共which is approximately 2.4 eV兲.21 In addition, the quantity of ␣ at an electric field of ⬃1 ⫻107 V/cm must be ⬃18 for an ⌽ FN on the order of 2.4 eV. Experimental values of ␣ in the high voltage range, where the calculated ␣ – V dependence 共curve 2⬘ in Fig. 16兲 fits experimental data 共curve 2 in Fig. 16兲, do not exceed 7. Experimental evidence of the sharp change of the Fowler– Nordheim tunneling current in a 4–4.5 nm SiO2 based MIS structure together with an estimated ␣ above 20–25 at electric field of ⬃1⫻107 V/cm is described in Refs. 54–56 共see Fig. 4 in Ref. 54 and Fig. 1 in Ref. 56兲. The low effective barrier heights obtained here may be due to the existence of a current mechanism in addition to Fowler–Nordheim tunneling, causing a lowering of the theoretical band offset between TiO2 and thermal oxide at high electric fields. Such a mechanism may be the direct tunneling between Si and the traps at the SiO2 /TiO2 interface or in the TiO2 bulk as considered for similar double insulator structures in Refs. 1, 39, 57, and 59. A second explanation may be the internal electric field which develops on the interface of the TiO2 /SiO2 due to a double charge layer 共the observed inflection on the J – V characteristics or the minimum on the ␣ – V curves of the annealed films, see Figs. 9 and 10兲, aiding the penetration of carriers into the interfacial layer. 5. Leakage current dependence on annealing conditions

Leakage current densities at an electric field F ⫽106 V/cm versus annealing temperature and time, are de-

FIG. 17. Leakage current density, measured at F⫽1⫻106 V/cm vs annealing temperature 共a兲 and time 共b兲 of TiO2 films. 共a兲 t ann⫽60 min; 共b兲 T ann ⫽700 °C.

scribed in Fig. 17. For both 15 and 25 nm TiO2 films we observe an initial sharp reduction of the leakage current and a saturation in the temperature range of 400–500 °C. The most drastic change occurs after 10–20 min at annealing temperatures above 700 °C. The total leakage current for the 25 nm film is reduced from 1 to ⬃10⫺2 A/cm2 while in the 15 nm structure, it is reduced from 1 to 5⫻10⫺6 A/cm2. The sharp change in the leakage current density occurs in the range of annealing temperature where the variation of the optical parameters and the morphology of the TiO2 film and the interface characteristics of the TiO2 /Si boundary, obtained from C – V measurement take place. A phenomenological model is assumed to explain the reduction of leakage current with annealing in an oxygen ambient. The oxygen molecules, broken by the high temperature, produce excited atoms in single states which have one unoccupied electron orbital and therefore are thought to be strong electron trap levels. The excited oxygen atoms are adsorbed on the surface of the TiO2 film and diffuse into it.


3268


Diffused excited atoms fill the oxygen vacancies in the TiO2 which are sources of free electrons in the conduction band, accept free electrons, and occupy the lattice site. As the annealing temperature rises, the concentration of the excited oxygen atoms increases, the number of vacancies decreases and the leakage current lowers. The value of the oxygen diffusion coefficient estimated from the data of the leakage current density dependence on annealing time 关see curve of the 15 nm film in Fig. 17共b兲兴 is 10⫺15 cm2 s⫺1. This value was obtained assuming that the time necessary for oxygen atoms to transit across the TiO2 film is determined by the condition of achieving the required lowering in leakage current. The large reduction of the leakage current is caused by the formation of an interfacial silicon dioxide layer that dominates for films thinner than 15 nm. With thin SiO2 film, some of the injected carriers can tunnel through as occurs for all 25 nm samples and for 15 nm films annealed above 450 °C. The increase of the SiO2 layer thickness leads to a change in the local electric field distribution within the TiO2 关see Eq. 共27兲兴 and reduces the energy of carriers, while their barrier increases due to the annealing 共see curve 2 in Fig. 15兲. Note that the increase of the roughness value of thick films annealed at high temperatures 共see Figs. 3 and 4兲 causes an enhancement of the local electric field distribution at the metal contact/roughed TiO2 interface 共similar to the data of Al/Ta2O5 samples兲.60 The result is an additional difference between the achieved leakage current of relatively thick and thin TiO2 films. IV. CONCLUSION

We have shown a correlation between structural transformations in TiO2 films and its optical and electrical characteristics—interfacial and current flow properties. A large change in all the parameters at an annealing range of 350–550 °C and 10–20 min has been determined. The leakage current decrease in thick films is basically caused by diffusion of excited oxygen atoms which fill vacancies of oxygen that are the source of free electrons in the conduction band of the TiO2. The reason for the carrier flow limitation in thin L⬍15 nm films is the additional barrier at the TiO2 /Si boundary which is formed due to the growth during anneling of a 2–2.5 nm thick. Experimental J – V dependencies were analyzed using the power exponent procedure. We find that at low electric fields the charge flow into as deposited and annealed 25 nm TiO2 have a hopping nature. The average values of the hopping distance between localized states and the impurity conductivity were found to be 2.5–3.5, 4–5 nm and 1.5 ⫻10⫺11, 1⫻10⫺11 ⍀ ⫺1 cm⫺1, respectively for 15 and 25 nm thick as deposited films. Annealing in an oxygen environment changes R and ␴ 0 to 6 nm and 1 ⫻10⫺16 ⍀ ⫺1 cm⫺1 for the 25 nm thick film. At a moderate electric field for any as deposited film the current transport seems to be limited by space charges accumulated on trap levels which are located at an energy of 0.475–0.55 eV with density ⬃8⫻1018 cm⫺3. After annealing they becomes deeper, up to 0.61–0.63 eV with concentration on the order of ⬃2⫻1019 cm⫺3. At high electric fields, conventional tun-


neling may be the basic mechanism for carrier transport trough thin interfacial SiO2 layers in all 25 nm films and low temperature annealed 15 nm structures. Direct tunneling together with Fowler–Nordhein penetration of the SiO2 seems to be the current limiting mechanism in structures with 15 nm TiO2 annealed above 450 °C. A. C. Rastogi and R. N. Sharma, J. Appl. Phys. 71, 5041 共1992兲. C. H. Ling, J. Bhaskaran, W. K. Choi, and L. K. Ah, J. Appl. Phys. 77, 6350 共1995兲. 3 M. Agarwal, M. R. DeGuire, and A. H. Heuer, Appl. Phys. Lett. 71, 891 共1997兲. 4 F.-C. Chui, J.-J. Wang, J. Y. Lee, and S. C. Wu, J. Appl. Phys. 81, 6911 共1997兲. 5 W. S. Lau, L. Zrong, Allen Lee, and C. H. See, Appl. Phys. Lett. 71, 500 共1997兲. 6 H.-J. Lee, R. Sinclair, M.-B. Lee, and H.-D. Lee, J. Appl. Phys. 83, 139 共1998兲. 7 V. Mikhelashvili, Y. Betzer, I. Prudnikov, M. Orenstein, D. Ritter, and G. Eisenstein, J. Appl. Phys. 84, 6747 共1998兲. 8 V. Mikhelashvili and G. Eisenstein, Appl. Phys. Lett. 75, 2836 共1999兲. 9 C. Chaneliere, J. L. Autran, B. Balland, and R. A. B. Devine, Mater. Sci. Eng., R. 22, 269 共1998兲. 10 H. Tang, K. Prasad, R. Sanjines, P. E. Schmid, and F. Levy, J. Appl. Phys. 75, 2042 共1994兲. 11 D. G. Howitt and A. B. Harker, J. Mater. Sci. 2, 201 共1987兲. 12 F. Edelman, A. Rotshild, Y. Komem, V. Mikhelashvili, A. Chack, and F. Cosandey, Electron Technology 共Institute of Electron Technology, Warszawa, 2000兲, Vol. 33, p. 89. 13 J. D. Deloach, G. Scarel, and C. R. Aita, J. Appl. Phys. 85, 2377 共1999兲. 14 P. Alexandrov, J. Koprinarova, and D. Todorov, Solid-State Electron. 47, 1333 共1996兲. 15 M. Mosaddeq-ur-Rahman, G. Yu, T. Soga, T. Jimbo, H. Ebisu, and M. Umeno, J. Appl. Phys. 88, 4634 共2000兲. 16 C. Ting, S. Chen, and D. Liu, J. Appl. Phys. 88, 4628 共2000兲. 17 T. Fuyiki and H. Matsunami, Jpn. J. Appl. Phys., Part 1 25, 1288 共1986兲. 18 N. Rausch and E. P. Burte, J. Electrochem. Soc. 140, 145 共1993兲. 19 J. Yan, D. C. Gilmer, S. A. Campbell, W. L. Gladfelter, and P. G. Schmid, J. Vac. Sci. Technol. B 14, 1706 共1996兲. 20 H.-S. Kim, D. C. Gilmer, S. A. Campbell, and D. L. Polla, Appl. Phys. Lett. 69, 3860 共1996兲. 21 S. A. Campbell, H. S. Kim, D. C. Gilmer, B. He, T. Ma, and W. L. Gladfelter 共unpublished兲. 22 S. A. Campbell, D. C. Gilmer, X.-C. Wang, M.-T. Hsieh, H.-S. Kim, W. L. Gladfelter, and J. Yan, IEEE Trans. Electron Devices 44, 104 共1997兲. 23 H.-S. Kim, S. A. Campbell, and D. C. Gilmer, IEEE Electron Device Lett. 18, 465 共1997兲. 24 H.-S. Kim, S. A. Campbell, D. C. Gilmer, V. Kaushik, J. Conner, L. Prabhu, and A. Anderson, J. Appl. Phys. 85, 3278 共1999兲. 25 R. F. Cava, W. F. Peck, Jr., and J. J. Krajewski, Nature 共London兲 377, 215 共1995兲. 26 J.-Y. Gan, Y. C. Chang, and T. B. Wu, Appl. Phys. Lett. 72, 332 共1998兲. 27 A. Cappellani, J. L. Keddie, N. P. Barradas, and S. M. Jeckson, SolidState Electron. 43, 1095 共1999兲. 28 W. D. Brown and W. W. Grannemann, Solid-State Electron. 21, 837 共1978兲. 29 V. Mikhelashvili and G. Eisenstein, Microelectron. Reliab. 40, 657 共2000兲. 30 V. Mikhelashvili and G. Eisenstein, IEEE Trans. Electron Devices 共to be published兲. 31 H. Tang, F. Levy, H. Berger, and P. E. Schmid, Phys. Rev. B 52, 7771 共1995兲. 32 H. Tang, H. Berger, P. E. Schmid, and F. Levy, Solid State Commun. 87, 847 共1993兲. 33 A. C. Adams, in VLSI Technology, edited by S. M. Sze 共McGraw-Hill, New York, 1983兲. 34 L. S. Hsu, R. Rujkorakarn, J. R. Sites, and C. Y. She, J. Appl. Phys. 59, 3475 共1986兲. 35 The Encyclopedia of Advanced Materials, Vol. 4, edited by R. W. Cahn 共Elsevier, New York, 1994兲, p. 2880. 36 Y. Jeon, B. H. Lee, K. Zavadzki, W. Qi, and J. C. Lee, Tech. Dig. Int. Electron Devices Meet. 797 共1998兲. 1 2


J. Appl. Phys., Vol. 89, No. 6, 15 March 2001 37

G. B. Alers, D. J. Werder, Y. Chabal, H. C. Lu, E. P. Gusev, E. Garfunkel, T. Gustafsson, and R. S. Urdal, Appl. Phys. Lett. 73, 1517 共1998兲. 38 B. H. Lee, Y. Jeon, K. Zavadzki, W. Qi, and J. Lee, Appl. Phys. Lett. 74, 3143 共1999兲. 39 S. M. Sze, in Physics of Semiconductor Devices 共Wiley Interscience, New York, 1969兲. 40 A. N. Zyuganov and S. V. Svechnikov, Injection Contact Phenomena in Semiconductors 共Naukova Dumka, Kiev, 1981兲, in Russian. 41 A. N. Zyuganov, V. V. Zorikov, M. S. Matinova, V. M. Mikhelashvili, and R. I. Chikovani, Sov. Tech. Phys. Lett. 7, 493 共1981兲. 42 G. D. Bagratishvili, R. B. Dzanelidze, D. A. Jishiashvili, L. V. Piskanovski, A. N. Zyuganov, V. M. Mikhelashvili, and P. S. Smertenko, Phys. Status Solidi A 65, 701 共1981兲. 43 V. Mikhelashvili, G. Eisenstein, V. Garber, S. Fainleib, G. Bahir, D. Ritter, M. Orenstein, and A. Peer, J. Appl. Phys. 85, 6873 共1999兲. 44 V. Mikhelashvili and G. Eisenstein, J. Appl. Phys. 86, 6965 共1999兲. 45 V. Mikhelashvili, G. Eisenstein, and R. Uzdin, Solid-State Electron. 45, 143 共2001兲. 46 N. F. Mott and E. A. Davis, Electron Processes in Non-Crystalline Materials 共Clarendon, Oxford, 1979兲. 47 in Electronic and Structural Properties of Amorphous Semiconductors,


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edited by P. G. LeComber and J. Mort 共Academic, New York, 1972兲. V. N. Bogomolov, E. K. Kudinov, D. N. Mirlin, and Yu. A. Firsov, Sov. Phys. Solid State 19, 1630 共1968兲. 49 J. C. Pfister, Phys. Status Solidi A 24, k15 共1974兲. 50 A. Rose, Phys. Rev. 97, 1538 共1955兲. 51 M. A. Lampert, RCA Rev. 20, 682 共1959兲. 52 M. A. Lampert and P. Mark, Current Injection in Solids 共Academic, New York, 1970兲. 53 J. G. Simmons, J. Appl. Phys. 34, 1793 共1963兲. 54 S. Zafar, Q. Liu, and E. A. Irene, J. Vac. Sci. Technol. A 13, 47 共1995兲. 55 S. Zafar, K. A. Konrad, Q. Liu, E. A. Irene, G. Hames, R. Kuehn, and J. J. Wortmann, Appl. Phys. Lett. 67, 1031 共1995兲. 56 M. V. Fischetti, D. J. DiMaria, L. Dori, J. Batey, E. Tierney, and J. Stasiak, Phys. Rev. B , 4404 共1987兲. 57 in Silicon Integrated Circuits, Part A, edited by D. Cahng 共Academic, New York, 1981兲. 58 G. W. Taylor and J. G. Simmons, Solid-State Electron. 17, 1 共1974兲. 59 Y. Nishioka, S. Kimura, H. Shinriki, and K. Mukai, J. Electrochem. Soc. 13, 410 共1987兲. 60 Y. S. Kim, Y. H. Lee, K. M. Lim, and M. Y. Sung, Appl. Phys. Lett. 74, 2800 共1999兲. 48


Using JPF1 format - Technion - Electrical Engineering

Using JPF1 format - Technion - Electrical Engineering

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