2. MARCO TEÓRICO
2.6 VARIABLES DE ESTUDIO
Basics of Hall Effect
The carrier transport properties of TCO materials can be determined using a variety of magneto-optical and standard transport measurements. The most common measure- ments are based on the Hall effect. Since the discovery of the Hall effect by Edwin Hall in 1879 [189], it has became an important characterization method for semiconductors. This is not only possible to determine the dominant charge carrier type (electrons or holes), but also its concentration and charge carrier mobility can be obtained.
Figure 4.16: Schematic representation of the Hall effect geometry, adapted for n type semi-
conductors. Current flowing in the x - direction with the current density jx; the coordinate
system (x, y, z) ; magnetic field in Z direction BZ and charge carriers are moving with the drift velocity vd,x, which will be deflected by Lorentz force ~F in y - direction, are given [193].
4.2 Materials Characterizations
of Marius Grundmann [190] and Donald Neamen [191]. Schematic representation of the Hall effect geometry, adapted for n type semiconductors, is shown in Fig. 4.16. The semiconductor has charge carrier of charge q, charge carrier density n, and charge carrier drift velocity vd,x. A current Ix flow due to an applied voltage in x-direction.
The drift velocity is an average velocity of the charge carriers over the volume of the semiconductor. Each charge carrier may move in a seemingly random way within the conductor, but under the influence of applied fields there will be a net transport of carriers along the length of semiconductor. The current Ix is the current density Jx
times the cross-sectional area (bd) of semiconductor. The current density Jx is charge
density nq times the drift velocity vd,x. In other words
Jx = Ix/bd = nqvd,x (4.11)
Where, b and d are the width and thickness of the sample, respectively.
When a perpendicular magnetic field ~B is applied to a semiconductor, the charge carriers
will experience a Lorenz force ~F = q~v ~B that will deflect them towards one side of the
conductor. This deflection will cause an accumulation of charges along one side and create a transverse electric field Ey, which counteracts the force of the magnetic field.
When steady state is reached, there will be no net flow of charge in the y direction, since the electrical and magnetic forces on the charge carriers in that direction must be balanced. Assuming these conditions, it is easy to show that:
~
F = q ~E + q(~v × ~B) = qEy+ qvd,xBz = 0 (4.12)
InFig. 4.16, Ey points in negative y-direction and is therefore negative. By considering
the semiconductor is n - type with electrons e as charge carriers and taking into account equationEq. 4.11 of current density, Eq. 4.12 can be rewritten as:
Ey = vd,xBz = − Bzjx ne = − 1 ne Bzjx = RHBzjx (4.13)
The term in parenthesis is known as Hall coefficient and the charge carrier concentration n can thus be calculated directly from RH
RH = −
1
In an experiment, the potential difference across the sample namely the Hall voltage VH, is measured. The Hall voltage is related to the electric field by:
VH = −
Z d
0
Eydy = −Eyd (4.15)
Thus, from equations4.11,4.13, and4.15, it is possible to obtain:
VH = −
BzIx
ned (4.16)
If the electrical conductivity σ is also measured, the charge carrier mobility µ can be calculated from measured conductivity (σ) using the relationship σ = enµ.
This simplified approach assumes the same mobility for charge carriers moving along x due to the electric field as for carriers moving along y due to the magnetic field in z. This means the mobility is proportional to a uniform, average scattering time τ . However, this is only true at very large magnetic fields, which are typically not encountered in laboratory-based Hall effect equipment. In order to understand some of the ideas involved in theory of the Hall effect in real materials, it is instructive to construct a more careful model for electric currents under electric and magnetic fields from a classical point of view. The charge carriers move in a medium associated to a given resistivity. The resistance could be due to scattering between the carriers and impurities in the material and between the carriers and vibrations of the material’s atoms. Thus, the relaxation time τ depends on dominant scattering mechanism. This results in a more general expression for previously derived Hall coefficient RH by supplementing the Hall
scattering factor rH
RH = −
rH
ne (4.17)
The knowledge of rH allow to distinguish between Hall carrier mobility µH and actual
drift mobility µd of the charge carriers.
4.2 Materials Characterizations
Description of the Equipment
The custom made Hall effect system at TU Darmstadt is described in a publication [192]. The experimental set-up was build during preparation of the PhD theses of Mareike Frischbier and Andr´e Wachau [193]. The schematic representation of the setup is shown inFig. 4.17.
Figure 4.17: Schematic representation of the Hall effect set-up at TU Darmstadt: Hall effect
and relaxation conductivity measurements are performed as a function of temperature and for different atmospheres [192].
The sample in van der Pauw geometry [194] is installed inside a quartz tube, which may be evacuated through a turbo molecular pump down to a pressure of 10−8 mbar.
Alternatively, a gas flow at atmospheric pressure of an argon oxygen mix may be chosen by separate mass flow controllers and an optional oxygen pump. The gas mixture at the outlet is monitored by a potentiometric oxygen sensor. The quartz tube is fit into a furnace, which allows for measurement at temperatures up to 700◦C. The furnace with quartz tube carrying the sample is then placed between the pole shoes of a electromagnet (Type EM4-HVA, Lake Shore Cryotronics), capable of a maximum magnetic field of 1 T. A Hall probe serves to monitor the actual magnetic field in the vicinity of the sample. Several Keithley instruments are responsible for supplying the measurement current, measuring the Hall voltage and performing the permutation among the four contacts of the sample in van der Pauw geometry. A buffer amplifier is included in order to measure high impedance samples. A LabView routine controls the Keithley instruments and the magnet power supply to perform conductivity and Hall effect measurement.
Results, Discussion and Considera-
tions
Based Thin Films
The defect modulation doping approach uses two dissimilar materials to circumvent the alignment of doping limits. The use of dissimilar materials removes the constraint of aligned doping limits. By aligning two dissimilar materials it is therefore, in principle, possible to obtain Fermi levels outside the doping limits in the host material. Such a situation can, from a thermodynamic point of view, only be achieved if defects in the host material cannot form spontaneously when the Fermi energy is raised during deposition of a modulation layer. The detail concept of defect modulation doping are described in subsection 2.4.3.
In this part of the project ultra thin defective and amorphous insulators (Al2O3 and
SiO2−x) are used as a potential dopant and deposited at the surface of TCO ( In2O3,
Sn-doped In2O3, and SnO2). As a result it is expected for them to induce conduction
electrons at the near interface region on TCO and allows to realize defect modulation doping. The energy band diagram of the hetrostructure is schematically illustrated in
Fig. 4.18. In which, the Fermi level of TCO is forced into the conduction band at the
interface and resulting surface band bending-Φbb. Thus, the Fermi level is expected to
be well above the classical doping limit of these TCOs and evident modulation doping effect.
In the following chapters, experimental approach and results of different dissimilar materials will be presented with discussions in the context of defect modulation model.
Chapter 5 will focus on the effect of Al2O3 deposition by ALD on interfacial and electrical
properties of Sn-doped In2O3 (ITO) thin films in order to observe the modulation doping
effect. In Chapter 6 the case for undoped In2O3 with the effect of changing the thickness
of dopant Al2 O3 layer will be discussed. Finally, in Chapter 7 different dopant namely
Figure 4.18: Schematic illustration for energy band diagram of TCO (In2O3, Sn-doped In2O3,
and SnO2) thin films before (left) and after (right) deposition of ultra thin potential dopants
(Al2 O3 and SiO2−x) modulation layers. The Fermi level of TCO forced into the conduction band at the doped interface, but it remains low near the interface to the substrate. At the position of maximum surface band bending (Φbb), the Fermi level is expected to be positioned
well above the classical doping limit of these TCOs and demonstrate the success of defect modulation doping effect.
5
C
h
a
p
t
Surface Modification of Sputtered ITO by ALD-
Al2O3
5.1
Introduction
As it has been discussed earlier in subsection 2.4.3, the deposition of an ultra thin defective and amorphous insulator material on the surface of a TCO ( In2O3, Sn-doped
In2O3, and SnO2) should induce conduction electrons in the interface near region of
TCOs, which is called defect modulation doping. This chapter is designed to assess the viability of defect modulation doping by ultra thin ALD-Al2O3 coated ITO thin
films. For this purpose, different ITO thin film samples were prepared with and without ALD-Al2O3 coating. The prepared samples were examined using in-situ photoelectron
spectroscopy for near surface properties as well as using ex-situ electrical conductivity measurements. The chapter is divided in the following sections.
Section 5.2, shortly describes the experimental procedures followed during thin film preparation and characterization. The photoelectron spectra of uncoated and ALD-