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In this paper the transmission coefficient for a double-barrier quantum well (DBQW) structure as a function of applied voltage is calculated, for the first time, using WKB approximation: This approach allows to discuss a dependence of several quantities characteristic of the system (e.g. the value of the coefficient, resonance voltage, charge stored in the well) on the barrier and the well parameters.PACS numbers: 73.40. Lq, 73.40.Gk Recent advances in the technology of growth of semiconductor heterostructures have stimulated a great deal of interest, both experimental and theoretical, in the phenomenon of resonant tunneling through double-barrier quantum well (DBQW) structures. Elementary understanding of the resonant tunneling usually bases on the consideration of an one-dimensional potential energy profile created by the bottom of conduction band of the DBQW structure. The general analysis of phenomena occurring in such systems has been given by Ricco and Azbel [1]. In spite of the simplicity of their approach these authors did not avoid repeating the mistake which had already appeared in the early paper by Kane [2] (see the expression for the global transmission coefficient given by Eq. (1) in [1]).In the present work we have calculated the transmission coefficient T for a DBQW stucture given in Fig. 1, using quasi-classical WKB approximation. The calculation is restricted to the electron energies which do not exceed the height f any barrier. The DBQW profile consists of three regions, namely of two barriers with the heights of V1 and V2 and the widths of b1 and b2, respectively, and of the potential well with the width of w confined between the barriers. The applied voltage V results in the electric field F which is assumed being constant over any particular region. The physical quantities in the respective regions are referred by the indices b1, w, b2 in the stucture and outside the stucture -by the indices (441)

In this paper we consider the influence of "mass barrier" and elastic scattering processes on the shape of j(V) and j(B) characteristics. Two scattering mechanisms, i.e. Coulombic on ionized impurities and on potential fluctuations in double-barrier structures are considered. The "mass barrier" shifts the whole j(V) characteristic slightly towards lower voltage and makes the resonant energy ER dependent on magnetic freld. On the other hand, both considered scattering mechanisms change the shape of j(V) and j(B) characteristics by shifting the oscillation maxima towards lower applied voltage.PACS numbers: 73.40.GkResonant magnetotunneling through double-barrier stuctures (DBS) is an important investigation tool providing information on how scattering processes influence the resonant tunneling process. For DBS with degenerate emitter in the resonant tunneling regime, when a magnetic fleld Β is applied parallel to the current j, oscillations are expected in both, j(V) and j(B), characteristics [1]. These oscillations are a result of complete quantization of the electron energy in the DBS well. In an idealized picture, where we take the resonant level ER in the DBS well and the Landau levels as delta functions, the j(V) characteristic, for a given B, would be a series of steepy rises followed by flat regions. Each jump of the current corresponds to an opening of a new tunneling channel when a successive Landau level Εn in the well crosses the Fermi level EF in the emitter. On the other hand, for a fixed bias, due to an increase in the magnetic field, successive Landau levels are pushed out to energies above the emitter Fermi energy, causing sudden falls in the j(B) characteristic. The resonant tunneling conditions for each Landau level, as a function of applied bias and magnetic fleld, are usually summarized in the fan chart. In the idealized picture, maxima of j(V) for various 13 and maxima of j(B) for various applied bias V are lying on straight lines, given by the condition ER -V + Εn -EF = 0. The two factors, the inherent Landau level broadening and the flnite width of the resonant level in the DBS well, would tend to smooth the oscillations. Indeed, the features due to the magnetic quantization are usually (833)