The mean inner potential of GaN measured from nanowires using off-axis electron holography
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The mean inner potential of GaN measured from nanowires using off-axis electron holography Andrew S. W. Wong1, Ghim W. Ho2, Rafal Dunin-Borkowski1,3, Takeshi Kasama3,1, Rachel A. Oliver1, Pedro M.F.J. Costa1 and Colin. J. Humphreys1 1
Department of Materials Science and Metallurgy, University of Cambridge, Pembroke Street, Cambridge CB2 3QZ, United Kingdom. 2 Nanoscience Centre, University of Cambridge, 11 JJ Thomson Avenue, Cambridge CB3 0FF, United Kingdom. 3 Frontier Research System, The Institute of Physical and Chemical Research, Hatoyama, Saitama 350-0395, Japan.
ABSTRACT The mean inner potentials of wurtzite GaN nanowires are measured using off-axis electron holography in the transmission electron microscope (TEM). The nanowires have a circular cross-section and are suspended across holes in a holey carbon film, resulting in an accurate knowledge of their thickness profiles and orientations. They are also free of the implantation and damage that is present in mechanically-polished ion-milled TEM specimens. The effect of a thin amorphous coating, which is present on the surfaces of the nanowires, on measurements of their mean inner potential is assessed. A value for the mean inner potential of GaN of (16.7± 0.3) V is obtained from these samples. INTRODUCTION The technique of off-axis electron holography in the transmission electron microscope (TEM), which is described in detail elsewhere [1-3] allows the phase shift φ of a high-energy electron that has passed through a specimen to be measured. In the absence of magnetic fields, the phase shift is, in turn, directly proportional to the electrostatic potential in the specimen V integrated in the electron beam direction, according to the equation
φ (x,y) =
CE
∫
∞
−∞
V ( x, y, z )dz
(1)
where CE takes a value of 6.53 x 106 rad V-1m-1 at a microscope accelerating voltage of 300 kV. If V is constant throughout specimen thickness t, then Eq. 1 can be expressed more simply in the form
φ (x,y) = CE V(x,y) t(x,y)
(2)
A major contribution to V is associated with the mean inner potential Vo. When using off-axis electron holography to quantify piezoelectric fields in InGaN/GaN quantum wells [4-5] an accurate knowledge of Vo is desirable. In most materials, Vo takes a value between 5 and 30V [3], depending on the composition and structure of the material. Its value is highly sensitive to variations in charge density associated with bonding and ionicity. Traditionally, experimental values of Vo in many
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semiconductors have been measured using wedge-shaped cleaved specimens [6-7], which are relatively free of the surface damage that is associated with preparing TEM specimens using ion milling. If the wedge angle is known, then according to Eq. 2 the specimen thickness profile can be correlated precisely with a phase profile measured using electron holography in order to determine Vo. Unfortunately, measurement of Vo for GaN typically suffers from the difficulty of cleaving wedges of epitaxial layers of GaN that have been grown on
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