1. in collaboration with:
Noise of hot electrons in anisotropic semiconductors in the presence of a magnetic field
Francesco Ciccarello
in collaboration with:
S. Zammito and M. Zarcone
CNISM & Dipartimento di Fisica e Tecnologie Relative, University of Palermo (Italy)
UPON 2008, École Normale Supérieure de Lyon (France), June 2–6, 2008

2. a sketch of this work problem our outcomes
in an anisotropic seminconductor:
how hot-electron velocity fluctuations are affected by the presence of a static magnetic field?
our outcomes
1. the relative importance of noise can be reduced
2. partition noise can be strongly attenuated
3. a simultaneous increase of conductivity can take place

3. conduction band of Si ml=0.916 m0 > mt=0.19 m0
3 pairs of energetically-equivalent
ellipsoidal valleys along:
<100> (“valleys 1” )
<010> (“valleys 2” )
<001> (“valleys 3” )
ml=0.916 m0 > mt=0.19 m0
electrons’ inertia does depend on the direction and valleys

4. we apply an intense electric field (~ kV/cm)
valleys cold & less populated
valleys 2,3 hot & most populated

5. v1x< v2x,v3x v1x < vd < v2x=v3x
velocity fluctuations
heavy valleys slow electrons
light valleys 2,3 fast electrons
v1x< v2x,v3x
v1x < vd < v2x=v3x
longitudinal velocity
autocorrelation function
partition noise
in the <100> case

6. let us add a magnetic field in a Hall-geometry
<001> B EH EA
<010>
B= B≠0
valleys cold & most populated hot & less populated
valleys 2, hot & less populated cold & most populated
also: conductivity is enhanced
Asche M and Sarbei O G, Phys. Stat. Sol. 37, 439 (1970)
Asche M et al., Phys. Stat. Sol. (b) 60, 497 (1973)

7. how are velocity fluctuations affected?
n-GaAs (isotropic)
Ciccarello F and Zarcone M, J. Appl. Phys. 99, (2006)
Ciccarello F and Zarcone, AIP Conf. Proc. 800, 492 (2005 )
Ciccarello F and Zarcone, AIP Conf. Proc. 780, 159 (2005 )

8. our Monte Carlo approach
free-flight Newtonian equation
scattering processes
3 f -type intervalley processes
3 g -type intravalley processes
acoustic scattering
(valley i j)
(valley i i)
Brunetti R, et al., J. Appl. Phys. 52, 6713 (1981)
Jacoboni C, Minder R and Majni ,J. Chem. Phys. Solids 36,1129 (1975)
Hall field
we iteratively look for EH such that
Raguotis R A, Repsas K K and Tauras V K, Lith. J. Phys. 31, 213 (1991)
Raguotis R, Phys. Stat. Sol. (b) 174 K67 (1992)
regime
T=77 K; stationary conditions; maximum magnetic-field strengths
allowing magnetic-field effects competing with electric-field ones

9. central result the magnetic-field action yields
drift velocity
velocity variance
EA=10 kV/cm
EA=10 kV/cm
EA=6 kV/cm
EA=6 kV/cm
average energy
standard deviation/drift velocity
EA=10 kV/cm
EA=10 kV/cm
~20~%
EA=6 kV/cm
EA=6 kV/cm
the magnetic-field action yields
a more intense & cleaner current

10. insight into the mechanism behind
valley average energies
valley occupation probabilities
valley average velocities
EA=6 kV/cm
EA=6 kV/cm
valleys 2, 3
valleys 1
valleys 2, 3
drift velocity
EA=6 kV/cm
mean
valleys 2, 3
valleys 1
valleys 1
the magnetic field increases
population of high-velocity valleys

11. isotropic case: free-flight motion
A. D. Boardman et al., Phys. Stat. Sol. (a), 4, 133 (1971)
cyclotron frequency
center magnitude
measures the
maximum amount
of gainable energy

12. K*-space Herring-Vogt transformation dispersion law in each valley
Herring C and Vogt E, Phys. Rev. 101, 944 (1956)
dispersion law in each valley
velocity vs. wavevector
nonparabolicity effects

13. free-flight equation in each valley more & more significant
fields*
free-flight equation in each valley
isotropic
in k *-space fields
are valley-dependent
as B grows the
effect of EH becomes
more & more significant
measures the
maximum energy
that can be gained

14. fields*
valleys 1
valleys 2
valleys 3

15. autocorrelation functions
longitudinal B=0 vs. B=4.5 T
EA=5 kV/cm
partition-noise
attenuation
is partition noise lost?
transversal average velocity
longitudinal vs. transversal
partition-noise
is shifted towards the transversal direction
EA=5 kV/cm
B=4.5 T
valleys 1
valleys 3
different valleys
have different
transversal velocities
valleys 2

16. conclusions ∙ B can give rise to a more ordered conductive state with:
- higher mobility
- reduced importance of fluctuations
- attenuated partition noise
- moderate electron heating

17. open questions & outlook thanks for your attention!
∙ what about different Hall geometries such as
EA ll <011> & B ll <100> or EA ll <111> & B ll <110>??
∙ what’s the optimal geometry in order to
minimize noise?
∙ is there a statistical procedure able to filter out mere fluctuations from cyclotronic oscillations?
∙ is there a better system able to exhibit such phenomena (if possible, at room temperature)?
∙ noise spectrum analysis
thanks for your attention!