Transcript Dynamic of one-dimensional transport in semiconductors

Instability in one-dimensional transport
of electrons in ungated semiconductors
Williams R. Calderón Muñoz
Advisor: Dr. Mihir Sen
Acknowledgements:
Universidad de Chile
CONICYT-Chile
Outline
 Motivation and previous works
 Mathematical model
 Linear stability analysis
 Conclusions
 Future work
Motivation and previous works
 Currently, the study of mechanism of
terahertz emissions from semiconductor
devices is getting attractive and important
 Compact, tunable and small THz sources
are required to detect a wide range of
process and chemical reactions to
characterize a variety of chemical and
biological systems
Motivation and previous works
Souce: http://www1.sura.org/news/docs/sura_electromagnetic_spectrum_full_chart.pdf
Motivation and previous works
 Dyakonov and Shur (1993,2005) have used
capacitor approximation and zero ac voltage
at the source and zero ac current at the
drain
 Instead consider Poisson, continuity and
momentum equations and just the
semiconductor
Mathematical model
 Boltzmann Equation
Hydrodynamic model for electrons.
 Hydrodynamic model for electrons
+ Energy balance equations for phonons
 Mathematical Model
Mathematical model (1D)
Mathematical model (1D)

Interaction with the phonon field is neglected (small
Te approximation)
Mathematical model (1D)

Diagram of semiconductor
Linear stability analysis
 By linearization of the equations and boundary conditions
Linear stability analysis
Linear stability analysis
Linear stability analysis
Linear stability analysis
 Asymptotic approximation
Linear stability analysis
 Spectrum of Eigenvalues (case: b=1, g=(20)^0.5)
a=2
a=20
Conclusions
 With small Te approximation, unstable
eigenvalues indicate terahertz frequencies
 The spectrum of eigenvalues describes the
branches of an out of phase Lambert W
function
 As the applied voltage through the
semiconductor decreases, the spectrum is
getting more stable
Work on going
 Study of the nonlinear system
 Set up the two-dimensional problem