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Work functionmeasurements in single-crystalline In2O3 for conductionmodelling Federico Schipani1,Alexandru Oprea1, Udo Weimar1, Alexandra Papadogianni2, Oliver Bierwagen2, and NicolaeBarsan11Institute of Physical Chemistry, University ofTübingen, Auf der Morgenstelle 15, 72076 Tübingen, Germany2Paul-Drude-Institute fürFestkörperelektronik, Leibniz-Institut im Forschungsverbund Berlin e.V., Hausvogteiplatz 5?7, 10117 Berlin, Germany To date, there areonly a few studies on the gas sensing properties of single crystalline sensors.The preferred study of polycrystalline materials is mainly due to the considerablylarger sensor signals, which are caused by the presence of grain boundaries[1].However, the high quality and controlled growth of single-crystalline materialshas the promise to help the fundamental understanding of sensing: the electricalmeasurements of crystals under in-operando temperatures and different gasatmospheres are an avenue for directly extracting fundamental electronicbehaviour of each material that is essential for building an accurate model ofsensor behaviour. Due to the recent advance in the development of in-operandoinvestigation methods, it seems now possible to combine them with controlledsingle crystalline model sample.Indium oxide is a wide-bandgap semiconducting material with a directbandgap of around 2.8?2.9 eV. It has been extensively used as a transparentconductive oxide (TCO) in electronics, for photovoltaic devices, light emittingdiodes and chemical sensors [3,6]. Nevertheless, the knowledge about sensingwith In2O3 based devices is still insufficient.Here, we present results of investigations performed on an approximately440 nm thick crystalline In2O3 film grown byplasma-assisted molecular beam epitaxy (PA-MBE) on a YSZ substrate. Combined DC resistance and work functionchange measurements performed at an operation temperature of 300 ºC in variousatmospheres were used in order to obtain information about the conduction mechanismsand electronic properties of the material in the same manner that waspreviously employed for the study of polycrystalline samples [2].The work function and resistance changes are measured with the KelvinProbe technique, which is a non-contact, non-destructive method that uses avibrating reference electrode and measures the changes of the contact potentialdifference (CPD) between the sample and the electrode. Variations in the CPDinduced by changes in the gas atmosphere represent relative work functionvariations of the sample [2]. The work function in a semiconductor can beexpressed by Where is thesurface band bending, χ represents the electron affinity, which we assumeconstant when no humidity is present, and is the difference betweenthe conduction band in the bulk and the Fermi level.In Figure 1 thedependence of the sample conductance on work function changes is presented. Experimentalresults will be interpreted using two approaches. First, all changes will beattributed to (surface processes), meaning that no bulkelectron concentration changes are allowed in the model. Next, all changes willbe attributed to bulk-related processes, where only the bulk electronconcentration changes and no band bending at the surface is present. FIG. 1: Conductivityagainst relative work function changes measured at 300 ºC with no humiditypresent. The measured in nitrogen is taken as the flat bandcondition. The green and blue area represent the carrier gas present. The total conductanceof a compact layer is the sum of the part of the layer influenced by surfaceprocesses and the conductance of the layer that is left unchanged, the bulk. In equation 2, L is the length ofthe layer, W its width, D its thickness and the thickness of the surface layer and the mobility. Room temperatureexperiments indicate that a large downwards band bending is present, which iscausing the appearance of a surface electron accumulation layer (SEAL) [4] thatcannot be described using Boltzmann statistic. For that reason, a numerical conductionmodel using Fermi-Dirac statistics, which are valid for all electron densities,has been developed. This was solved with an iterative process to findequilibrium concentration of electrons in the bulk ( and surface properties such as bandbending and surface density of electrons ( . Thefitting parameters (fitting not shown here) would imply a bulk electronconcentration of , which would be very low and not realistic.On the other hand, ifwe apply a flat band approach, where all changes in conductivity and workfunction are due to variations of , the results alsocannot be fully explained. From the experimentally measured conductance in purenitrogen and pure synthetic air (green and blue points in Fig.1), the bulkelectron concentration found is and respectively.From this, the difference between the Fermi Level and the conduction band canbe estimated, using the effective density of states andequation 3: Here, this difference is in pure nitrogen and in synthetic air. These results indicate that the experimentalchanges in conductance (a factor 100 from nitrogen to synthetic air) and workfunction differences (approximately 0.5 eV) are neither purely due to bulkchanges nor purely surface dominated and implies that the atmosphere changesaffect both bulk and surface electron concentration. [1] N. Barsan, J.Electroceram. 7 (2001) pp. 143-167.[2] A. Opreaet alSensors and Actuators B 142 (2009) pp.470?493.[3] D. Zhang et al., Nano Letters 4, 10 (2004) pp. 1919-1924.[4] J. Rombach et al., Sensors and Actuators B 236 (2016) pp. 909?916.[5] N. Barsan et al., Sensors and Actuators B 121 (2007) pp. 18?35.[6] S. Roso et al., ACS Sensors 2, 9 (2017) pp. 1272-1277