electrical conductivity was substantially different between ultrathin (1500 Ã
). INTRODUCTION. In2O3 is a semiconducting material with ...
ANALELE STIINTIFICE ALE UNIVERSITATII "AL.I.CUZA" DIN IASI Tomul XLV-XLVI, s. Fizica Stării Condensate, 1999 – 2000, p. 166 – 172.
ON THE SIZE EFFECT IN In2O3 THIN FILMS MIHAELA GÎRTAN, G.I. RUSU∗
KEYWORDS: thin films, indium oxide, size effect In2O3 thin films have been prepared by thermal evaporation of Indium in vacuum on unheated glass substrates, followed by thermal oxidation in air. The applicability of FuchsSondheimer model to explain the electronic transport properties in respective films is disscused. The electrical conduction mechanisms were studied as function of temperature, for films with various thicknesses. It was found that the temperature dependence of the electrical conductivity was substantially different between ultrathin (1500 Å).
INTRODUCTION In2O3 is a semiconducting material with a direct band gap of about 3.6 eV [1] and an indirect band gap of about 2.6 eV [2]. In its common form it is a yellow powder but it can be prepared as a thin film which is transparent in the visible spectrum. Generally the films are n type semiconductors as a consequence of deviations from stoiechiometric composition, excess indium atoms or oxygen vacancies serve as donors. The material properties, described in the literature often differ considerably from each other. One important reason for this is that the preparation conditions are different and consequently the oxidation state of the samples is different. Due to its complicated crystal structure (80 atoms in a In2O3 unit cell [3]) the conduction mechanism in indium oxide thin films is still not fully understood. In this study we shall examine the effect of thickness on the electrical conductivity of indium oxide thin films.
EXPERIMENTAL Indium oxide thin films have been prepared by thermal oxidation in an open atmosphere of indium films deposited in vacuum by evaporation onto unheated glass ∗
Faculty of Physics, “Al.I.Cuza” University, Bd. Carol I No 11, Iasi, R-6600, Romania
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ON TH SIZE EFFECT IN IN2O3THIN FILMS
substrates. The thickness, d, of thin films was determined using an interferential microscope MII 4 [4]. Investigated films have the thickness ranged between 500 and 4000Å. Indium thin films were then oxidized by removing them directly at high temperature (480 oC) in an open resistive furnace and maintained them in air at this temperature for different times or heated from room temperature to 480oC with different heating rates. It is known that indium films are completely oxidized at 350 oC [5]. The indium oxide thin films adhesion to the glass was extremely good. The structural characteristic of oxide films were studied by X-ray diffractometry (XRD) from a Philips X-ray generator [6] using a Cu Kα radiation. The electrical conductivity (σ) behavior was investigated by measuring their electrical resistance during two or three cycles of heating and cooling, using surfacetype cells. Thin silver electrodes with thickness of 1.1-1.3 µm were deposited onto substrates by thermal evaporation under vacuum after the oxidation process. The interelectrode distance was about 4.5mm. RESULTS AND DISSCUSION Thickness is one of the most important parameter which affect the physical properties of the films. In our previous paper [7] we showed that, as the thickness increase the crystallynity improved and the grain size increase too. Samples investigated now, were completely oxidized (no traces of indium were observed), they were polycrystalline and retained a cubic bixbyte structure. In this study we shall examine the applicability of Fuchs-Sondheimer theory [8,9] and the conduction mechanisms of these crystalline films as a function of their thickness. For the investigated films we have experimentally established (Fig.1) that the conductivity of In2O3 films decrease with the decrease film thickness. This phenomena is known as “size effect” and it is due to the increase surface scattering with the decrease of films thickness with the respect of volume bulk material. In the n-type degenerate thin semiconducting films electrical conductivity, in Fuchs-Sondheimer model, is give by [8-10]:
σ=
γ σo ϕ( γ )
(1) were σo is the electrical conductivity for the bulk material, γ = d/l, is the ratio between the film thickness d, and the carrier free mean path, l and ϕ (γ) is a function given by: 1 1 3(1 − p) ∞ 1 1 1 − exp[− γa ] = − d a ∫ − ϕ(γ ) γ 2γ 2 1 a3 a5 1 − p exp[− γa]
(2)
M. GÎRTAN, G.I. RUSU
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were a=1/cosθ θ is the integration variable, θ is the angle between the Oz axis (perpendicular to the plane of the film) and the charge carriers velocity direction and p is the scattering parameter [10]. 100
-1 -1 σ (Ω Ω cm )
80 60 40 20 0 0
1000
2000
3000
4000
d (A)
Fig.1. Dependence of the electrical conductivity of indium oxide thin films on the film thickness In particular for ultrathin films (γ 1) these formulas can be expressed by: σ 3 1+ p 1 σ 3 = γ ln , γ 1 (4) σo 4 1− p γ σo 8γ
80
1
σ (Ω cm- )
100
-1
60 40 20 0 0
200
400
600
800
−γln(1/γ) γ) −γ
Fig.2. Study of the applicability of Fuchs-Sondheimer theory for ultrathin indium oxide thin films
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ON TH SIZE EFFECT IN IN2O3THIN FILMS
According to this, we represented the dependences σ = f(γ ln(1/γ) in Fig.2. for ultrathin films and σ = f(1/d) in Fig.3. for thin films, considering for the free mean path the value l = 30Å, which has been determined from Hall measurements [11].
100
-1 -1 σ (Ω cm )
80 60 40 20 0 0
5
10 6
15
20
-1
1/d * 10 (m )
Fig.3. Study of the applicability of Fuchs-Sondheimer theory for thin indium oxide thin films From Figs.2. and 3 and we can observe that the used formulae cannot fit the data. An explanation for this, could be the fact, that one of the hypothesis of FucsSondheimer model is that, the surface states are neglected (flat band approximation). On the other hand, H.S. Kwok et al. [12] related to the relatively rapid decrease in σ as the films get thinner, to the percolative structure of indium oxide thin films. Moreover for the ultrathin films, the small sizes of the islands may lead to a Mott type transition rendering the film non-metallic with a higher resistivity. An interesting feature of In2O3 films is that depending upon the growth conditions (method of preparation, substrate temperature, film thickness etc.) can be prepared films having totally different properties (insulator, metal, semiconductor). The transport properties of thin films strongly depend on their structure (grain size and shape as well as the characteristics of the contact between them, structural defects, etc.) and purity (nature and concentration of the impurities, absorbed and adsorbed gases, etc.). Heating of films may modify these structural characteristics and consequently, the transport properties of the respective film (e.g. electrical conductivity) may vary too. Therefore, the study of the temperature dependence of the electrical conductivity during the heat treatment may provide information on the processes taking place in the films. For the studied films we remarked a qualitative difference between thick (>1500 Å) and thin films (
