Terahertz oscillations of hot electrons in graphene
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 conditions. 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.
University of Illinois - Urbana-Champaign
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University of Illinois at Urbana-Champaign