By Rainich G. Y.
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Additional resources for Curved Space-Time and Radiation
2). 22), respectively, can be substantial when nc is not (at least) several orders of magnitude smaller than ND . 18) for a variety of nc values. 7) for jn = 0 are shown in Fig. 3 for n(x), (x), F (x), and ψ(x), with nc as family parameter. Space-charge saturation is achieved for curves 3–5 (b). The saturation region, however, is much narrower than the total width of the barrier, even for the lowest value of nc . Nevertheless, the Schottky approximation yields a substantially linear branch of the ﬁeld distribution near the metal/semiconductor interface as long as nc /Nd is below ≈ 10−2 (c).
2b), following the arguments given in Sect. 3. These charges are split between both electrodes in such a way that the ﬁelds (Fig. 2c) created by these charges provide drift current continuity in the bulk parts of regions 1 and 2. 1 for the parameters used in this example). 18) ˚). 18) using the drift current equation, one obtains for the surface charges at the left and right electrodes, respectively Ω1 = − 8 |jn |εε0 ; σ1 Ω2 = + |jn |εε0 . 19) These surface charges balance the net charge of the double layer but do not change the zero space-charge line shown in Fig.
2d, curve 3). For zero current the potential step between regions 1 and 2 (Fig. 22) permitting separation of variables, e 1 dψn = dn. 23) After integration this yields: ψn,D = ψn,10 (j = 0) − ψn,20 (j = 0) = kT ln e n20 . 24) This potential diﬀerence ψn,D for zero currents is called the electron diﬀusion potential. For the given parameters with a density ratio of 10, it is approximately 60 mV. In addition to the electrostatic electron potential ψn (x), one recognizes as a very useful variable the electrochemical potential, also referred to as the Fermi potential, (1/e)EF , which relates to the electrostatic electron 10 11 This does not imply that the eﬀect of the junction on the current (see Sect.