SEMICONDUCTOR NANOSTRUCTURES

In 1970, L. Esaki and R. Tsu proposed the fabrication of an artificial heterostructure of nanometric layers of

two semiconductors materials with different energy gaps: a semiconductor superlattice. The energy potential

arising from the periodic alternance of each kind of semiconductor is a succession of quantum wells where

the energy can only take discrete values. When an external electric field is applied to the heterostructure, the

potential bends and electrons can move according to three transport regimes: miniband transport (strongly

coupled superlattices), resonant sequential tunneling (in weakly coupled superlattices), and Wannier-Stark

hopping (not considered here).

A quantum well (AT & T Bell Labs) A periodic superlattice, each period made of a barrier and a well

Miniband transport: when potential barriers are thin (≤ 3 nm) the discrete energy levels overlap leading to

the creation of extended quantum states with energetic width Δ (strongly coupled superlattices).

Resonant sequential tunneling: when potential barriers are large, electrons move from one quantum well

to the next by tunneling to the same energy level, after what they fall, by scattering, to a lower energy level.

(weakly coupled superlattices).

Resonant sequential tunneling under a dc bias

Charge transport in doped semiconductor superlattices

- Generalized drift-diffusion equation: GDDE

A drift-diffusion model of miniband transport in strongly coupled SLs is derived from the single-miniband

Boltzmann-Poisson transport equation with a BGK (Bhatnagar-Gross-Krook) collision term by means of

a consistent Chapman-Enskog method in the hyperbolic limit.

Drift-diffusion equation (to be solved with the constant bias condition + initial and boundary conditions)

and its numerical simulation showing the density current self-sustained oscillations and the periodically

recycling electric field wave: -- right clic for a larger image of the equations --

- Quantum drif-diffusion equation: QDDE

Nonlocal drift-diffusion equations are derived systematically from a Wigner-Poisson kinetic equation

describing charge transport in doped semiconductor SLs with a BGK collision term by means of the

Chapman-Enskog method in the hyperbolic limit.

Quantum drift-diffusion equation (again, coupled to the constant bias condition and initial and boundary

conditions), again exhibiting self-sustained current oscillations and the recycling electric field wave:

-- right clic for a larger image of the equations --

version of the drift-diffusion equation describing the Gunn effect:

- Generalized drift-diffusion equation: GDDE
Relocation dynamics in weakly coupled semiconductor SLs under voltage switching

A numerical study of domain wall relocation during voltage switching is presented for weakly coupled, doped

semiconductor superlattices exhibiting multistable domain formation in the first plateau of their current-voltage

characteristics. Unusual relocation scenarios are found including changes of the current that follow adiabatically

the stable I-V branches, different faster episodes involving charge tripoles and dipoles, and even small amplitude

oscillations of the current near the end of static I-V branches followed by dipole-tripole scenarios.

The experimental figures are taken from:*"Relocation time of the domain boundary in weakly coupled SLs"*

K. J. Luo, H. T. Grahn, and K. H. Ploog, Phys. Rev. B 57, R6838-R6841 (1998)*"Statistics of the domain-boundary relocation time in SLs"*

M. Rogozia, S.W. Teitsworth, H.T. Grahn, K.H. Ploog, Phys. Rev. B 64 R041308 (R) (2001)*"Time distribution of the domain-boundary relocation in SLs"*

M. Rogozia, H.T. Grahn, S.W. Teitsworth, K.H. Ploog, Physica B 314, 427-430 (2002)

- Equations and electric field domain wall relocation

In the following figure, the electric field domain wall is relocated from the 31^{th}quantum well (QW)

to the 29^{th}QW after the sudden increase of the applied voltage from 1 V to 1.2 V at time t=0.

The relocation of the electric field domain wall is done by the injection of an electric field wave.

-- right clic for a larger image of the equations --

- Time evolution of current density during the electric field domain wall relocation showed above

Left: numerical simulation -- Right: experimental results

Note that we represent the current density (A/cm^{2}), whereas experiments show the current (μA)

-- right clic for a larger image --

Detail (note again that we depicted the current density (A/cm^{2}), whereas experimental figures show the current (μA)

- Current density
*vs.*voltage characteristic curve (current-voltage in the experimental figure)

Left: numerical simulation -- Right: experimental results

Note that we represent the current density (A/cm^{2}), whereas experiments show the current (μA)

-- right clic for a larger image --

Detail (note again that we depicted the current density (A/cm^{2}), whereas experimental figures show the current (μA)

End of page