Simulations of the electrostatic potential in a thin silicon specimen containing a p-n junction
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Simulations of the electrostatic potential in a thin silicon specimen containing a p-n junction P.K. Somodi1, R.E. Dunin-Borkowski1, A.C. Twitchett1, C.H.W. Barnes2 and P.A. Midgley1 1 Department of Materials Science and Metallurgy, University of Cambridge, Pembroke Street, Cambridge CB2 3QZ, U.K. 2 Department of Physics, University of Cambridge, Madingley Road, Cambridge CB3 0HE, U.K. ABSTRACT The measurement of potentials associated with dopant atoms in semiconductors at nanometer spatial resolution using off-axis electron holography is known to be affected by the presence of the surfaces of thin specimens. In particular, the potential across a p-n junction is often found to be lower than would be expected from predicted properties of bulk devices. Here we present simulations of two-dimensional potential profiles within a thin (1017 cm-3). The simulations are compared with experimental data. Although they can account for some of the reduction in the observed potential, they do not fully explain the experimental results. INTRODUCTION The quantitative characterization of electrostatic potential distributions associated with the presence of dopant atoms is of fundamental importance for the development of future generations of nanoscale semiconductor structures and devices. Off-axis electron holography is a technique that offers the prospect of measuring electrostatic potentials at nanometer spatial resolution [1-3]. An electron wave that has passed through an electron-transparent specimen is interfered with another part of the same electron wave that has passed only through the vacuum. Analysis of the resulting interference fringe patterns allows the phase difference between the two parts of the electron wave to be established. This phase difference can then be related to the electrostatic potential within the specimen, V, by making use of the expression
φ ( x, y ) = C E ∫ V ( x, y, z )dz
(1)
where z is the electron beam direction, CE is a constant that depends on the microscope accelerating voltage, and the geometry of the thin (< 1 µm) TEM specimen is defined in figure 1. Given an accurate measurement of the sample thickness it is possible to determine the potential within the specimen, averaged in the electron beam direction. Previous electron holography studies have shown that the potential measured across a p-n junction, determined from measurements of the phase and specimen thickness according to equation 1, is almost always lower than would be predicted using simple theory [4, 5]. There are several possible explanations for this discrepancy including the effects of surface depletion, the implantation of ions during sample preparation and electron-beam-induced charging of oxide
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layers on the specimen surface. By calculating the potential within a thin specimen we aim to show how the surfaces of a finite specimen can partially account for the discrepancies observed. e-
y
C t
A
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p
z
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D Figure 1. Schematic diagram showing the direction of the electron beam relative to a parallel-side
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