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A High-Field Domain is a band of elevated field orthogonal to the equi-current lines and seen in photoconductive and monochromatic light at the band edge as dark band was discovered by Boer,〔Karl W. Böer, Z. Physik 155, 184 (1959)〕 using the Franz-Keldysh effect. Such domains must appear〔 whenever the conductivity decreases stronger than linearly. This can be caused by the field dependence of the carrier density, as observed in copper-doped caused by Frenkel Poole excitation of holes, causing faster electron recombination, known as field quenching.〔Karl W. Böer and G. A. Dussel Phys. Rev. 154, 291 (1967)〕 These high-field domains, now referred to as Böer-domains, or by field dependence of the mobility,〔Karl W. Böer Monatsber. d. Deutsch Akadem. d. Wissensch. 1, 325 (1959)〕 caused by excitation of electrons into higher conduction bands with lower mobility as observed in , called the Gunn effect.〔J.B.Gunn Solid State Commun. 1, 88 (1963)〕〔H. Kroemer, Proceedings IEEE 52, 1230 (1961)〕 The high-field domains can be identified by periodical field oscillations between high (the domain) and low values, as shown in Fig. 1.〔Cantapediera, I.R., et al. Phys. Rev B48, 12278 (1993)〕 Many other crystals show such domains by typical current oscillations. The high-field domains in copper doped can be easily observed by the Franz-Keldysh effect as stationary, adjacent to the cathode〔Karl W. Böer and P. Voss, Phys. Rev. 171, 899 (1968)〕〔Karl W. Böer and P. Voss, phys. status solidi 28, 355 (1968)〕 or moving.〔E. Schoell,Non-equilibrium Phase Transitions in Semiconductors, Springer, Berlin (1978)〕〔M.P. Shaw, V.V. Mitin, and H.L. Grubin The Physics of Instabilities in Solid State Electerronic Devices Plenum Press New York (1987)〕 These are analyzed as another example below. Theory: Stationary high-field domains can be analyzed from the transport- and Poisson equations: and The projection of any solution curves into an arbitrary plane can be filled with direction arrows at any point of this plane. Two auxiliary curves for which , called and called divide this plane into four quadrants with the same type of directions. This is shown in Fig. 2(left) in a double logarithmic representation.〔 Any solution of an -type semiconductor with blocking cathode must start at the boundary density that is below the density in the bulk, and approaches the singular point at which , that is in the bulk where both and are constant. The solution curve represents a Schottky-blocking contact as shown in Fig. 2(B), curve (a).〔 When decreases at higher fields due to field-quenching cause by Poole-Frenkel excitation of holes from Coulomb attractive hole traps, that consequently enhances electron recombination through recombination centers, and thereby deforms the curve at higher fields as shown in Fig. 2(B). When the bias is increased the current curve is shifted upwards and to the right, and when it crosses again, it produces a second singular point II. With further increased bias this singular point II reaches the value of the boundary density , and the solution curve changes from a monotonic increasing Schottky-solution, to a high-field domain, curve (b): that remains constant near the cathode, and then changes within a few Debye lengths to approach the constant value in the bulk, near the singular point I. The width of the domain increases with bias (Fig. 3a), while the current remains constant (Fig. 3c).〔 The domain is visible as dark part in the transmission picture through the platelett, extending from the cathode as shown in Fig. 3a. The field in the domain can be obtained from the slope of the domain that increases with bias (Fig. 3b).〔 When, with further increased bias the domain fills the entire sample,then it flips to an anode adjacent high-field domain (Fig. 4b). The field at the cathode is now much higher than for the cathode adjacent domain (Fig. 4b and c), while the current still remains essentially constant (Fig. 4c).〔 High-field Domains to determine the work function of blocking contacts Since the high field domain starts at the electron density given by the work-function at the cathode and pulls the Schottky barrier open to a constant field in the domain, this work function can be determined precisely, and it can be used as a tool to determine the changes of the work function, as it varies depending on external parameters. As an example, it can be shown that it depends on the optical excitation in a photoconductor (See Fig. 5).〔R. J. Stirn, K. W. Böer, and G. A. Dussel, Phys. Rev. B 7.4, 1443 (1973)〕 High-field domains as tools to measure the electron density in the field quenched branch and of the electron mobility as a function of the temperature The high-field domain is determined by the boundary density at the cathode and the field within the domain. A shadow band in front of the cathode acts as a pseudo-cathode, as it reduces the electron density within the shadow (Fig. 6).〔 This can be used as an experimental tool to change the boundary density as a function of the light intensity within the shadow. This permits to measure directly the electron density in the field-quenched range, using different pseudo-electron densities, causing a shift of the singular point, and measuring the domain field.〔 The electron Hall mobility can be measured by placing the platelett in a magnet and applying a bias sufficient to create a high-field domain. When the domain is extended to include the Hall electrodes one can determine the Hall mobility within the domain. Different fields in the high-field domain are achieved by using different samples or different cathode metals.〔K. W. Böer and K. Bogus, Phys. Rev. 186, 793 (1968)〕 Stationary domains to explain efficiency improvement of solar cells with a thin cover layer The application of a 200Å thick copper doped layer of on top of a typically 2 μm thick solar cell, increases the open circuit voltage substantially, so that it can reach the theoretical limit of the band gap of the -emitter when extrapolated to 0 . This improvement can be explained by limiting the field in the side of the junction when it reaches the critical value for a high-field domain to appear and thereby limits the maximum junction field to the domain field of typical 50 .〔K. W. Böer, H. J. Hänsch and U Kümmel, Z. für Physik 155, 170 (1959)〕 This field is below a field in which electron leaking from the into occurs, resulting in an increase of the open circuit voltage and thereby an increase of the solar cell conversion efficiency.〔Karl W.Böer, J. Appl.Phys. 107 (2010), 023701〕 Moving high-field domains in copper-doped with a small circular cathode The domains started from the cathode, separates and, with increasing bias increases its radius. When the anode is reached the ring disappeared and a new domain grows from the cathode. The process repeated itself with a period of 10 sec (Fig. 7).〔〔K.W. Böer, Visualization of field and current inhomogeneities, Springer Verlag (2011)〕 Such undeformed moving domains in crystals with slit electrodes are bands parallel to the electrodes, and seen by the oscillating field, when plotted in a diagram give the optical impression of bifurcation (Fig. 8).〔 Such moving high-field domains are measured in p-Ge with (a) local voltage (b) field- and (c) carrier density oscillation (Fig. 9).〔Kahn, A. M. et al., Phys. Rev. B 43, 9742 (1991)〕 Undeformed moving high-field domains and domains with deformation (Chaos) are observed in many other crystals,〔Eckehard Schoell, Non-linear SpatioTemporal Dynamics and Chaos in Semiconductors Cambridge University Press, (2001)〕 and also in nanocrystals〔K.N. Akkeseev et al. Phys. Rev. B 52,7849 (1995)〕 or superlatices.〔L.L. Bonilla et al. Solid State E 140,161 (1996).〕 However, because of the small size they can only be analyzed by the changing shape of the current-voltage characteristics. Böer-domains The high-field domains were renamed Böer-domains at the 50th anniversary of their discovery.〔Klaus Thiessen, Phys. stat. sol.(2011)DOI 10.1002/pssb.20146605〕 == References == 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「High-field domain」の詳細全文を読む スポンサード リンク
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