The binding energy of hydrogenic impurites in a quantum well wire has been calculated as a function of the width of the quantum well wire and the location of the impurity with respect to the axis of the wire. The calculations have been preformed using a variational wave function which takes into account the confinement of the carriers in the wire. For the confining potential used in our calculations, we have used the models of either an infinite potential well or a finite potential well whose depth is detemined by the discontinuity of the band gas in the quantum well wire and the cladding. For the infinite potential well model, the binding energy continues to increase as the radius of the wire decreases while in the finite potential well model, the binding energy reaches a peak value as the wire radius decreases and then decreases to a value characteristic of the cladding. The binding energy also depends upon the location of the impurity in the wire and is a maximum when the impurity is located on the axis of the wire.
Equivalence between focused paraxial beams and the quantum harmonic oscillator Am. J. Phys. 73, 625 (2005) Elementary Quantum Mechanics in One Dimension Am. J. Phys. 73, 480 (2005) The wave function and reality Am. J. Phys. 73, 197 (2005) Quantum harmonic oscillator revisited: A Fourier transform approach Am.
Sakaki [Jpn. J. Appl. Phys. 19, L735 (1980)] has investigated the mobility of semiconducting thin wire structures when the mobility of the wire is limited by scattering from ionized impurities which are located a fixed distance outside the wire. We have used a similar model to theoretically calculate the impurity-limited mobility of such semiconducting thin wires for the cases where the impurities are either in the wire itself (background impurities) or are distributed outside the wire (remote impurities) or are distributed uniformly both inside and outside the wire. For the case of scattering from the background impurities, we find that the mobility decreases with decreasing wire radius d as [ln (kd)]−2 where k is either the thermal or Fermi wave vector of the carriers. For the case of scattering from remote impurities, the size dependence of the impurity-limited mobility depends upon how the remote impurities are distributed outside the wire. When the distribution of ionized impurities outside the wire is uniform, the mobility is independent of the wire radius while, if the ionized impurities are separated from the wire by a fixed distance, we recover the results previously obtained by Sakaki. When the impurities are distributed uniformly both inside and outside the wire, the mobility again is size independent.
We have obtain~ t~e ~ielectric response function for a quasi-one-dimensional electron gas (Q 1 D). In .the statIC hIDlt (llJ = 0), we find that the dielectric function has a logarithmic singularity ~ a fun~tlon of wave vector when q = 2k f when the electron gas is degenerate, but that this sm~anty no lo~ge~ ~urs when the electron gas is nondegenerate. This singularity is ~nsld~red to be mdlcatlve of the Peierls transition which has been predicted to occur in a one-dImenSIOnal electron gas. As the radius of our quantum wen wire goes to zero, the dielectric response function is found to diverge logarithmically. This divergence is independent of the d~gene~acy of the ~lectron gas or the value of q or UJ, but is indicative of the divergence of the one-dtmensl~nal Founer transform of the Coulomb potential. We compare our results to other calculatIons of the dielectric function for one-and quasi-one-dimensional systems, and discuss the reas~ns for the differences in the various results. The momentum relaxation rates for scattering of carners by background and remote ionized impurities in a quantum well wire are investigated.
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