|Title:||Terahertz oscillations of hot electrons in graphene
|Author(s):||Sekwao, Samwel Kedmon
|Director of Research:||Leburton, Jean-Pierre
|Doctoral Committee Chair(s):||Dahmen, Karin A.
|Doctoral Committee Member(s):||Eckstein, James N.; Stelzer, Timothy J.
|Department / Program:||Physics
|Degree Granting Institution:||University of Illinois at Urbana-Champaign
|Abstract:||Once a uniform electric field is turned on in graphene, carriers accelerate ballistically until they are scattered
by optic phonons and the process repeats itself. In this dissertation, I will show that the oscillatory nature
of the motion of the carrier distribution function manifests in damped oscillations of carrier drift velocity
and average energy. In appropriate fields, the frequency of such oscillations can be in the terahertz (THz)
range. The randomizing nature of optical phonon scattering on graphene’s linear band structure further
limits terahertz observation to a range of sample lengths.
I will also show that when an ac field is superimposed onto the appropriate dc field, hot carriers in
graphene undergo an anomalous parametric resonance. Such resonance occurs at about half the frequency
ωF = 2πeF/~ωOP , where 2π/ωF is the time taken for carriers to accelerate ballistically to the optic phonon
energy ~ωOP in a dc field F. For weak elastic scattering, the phase difference between the current and the
ac field has a nonzero minimum at resonance. Dephasing increases with ac frequency for stronger elastic
scattering. The overall effect could also be seen in long-range spatially periodic potentials under steady state
This dissertation also shows that the soft parametric resonance (SPR) at ω = ηωF is temperature
independent, and the resonance factor η ∼ 0.56 is weakly dependent on the dc field Fo. This ensures
tunability of resonant frequencies in the terahertz range by varying Fo. A small signal analysis (SSA) of the
time-dependent Boltzmann transport equation (BTE) reveals a second resonance peak at η ∼ 1. This peak
is prevalent at temperatures T ≤ 77 K, and appears as a weak shoulder at T = 300 K.
Finally, this dissertation shows that in graphene, the motion of carriers under the influence of temporarily
and spatially modulated scattering is characterized by sharp resonances. Such resonances occur when the
period of the ac field applied equals the time taken by the quasi-ballistic carriers to travel a spatial distance
corresponding to the wavelength of the field. I will also show that such scattering can be realized on graphene
sheets on periodically spaced gates energized by an a-c bias. Appropriate fields and gate separation will
result in high Q-factor resonances in the THz range. The resonant frequencies are tunable with the gate
separation, and higher harmonics with large Q-factors can also be achieved.
|Rights Information:||Copyright 2015 Samwel Kedmon Sekwao
|Date Available in IDEALS:||2015-09-29
|Date Deposited:||August 201