Notes on "Carrier Dynamics and THz radiation in Photoconductive Antennas"

Zhisheng Piao et al's paper consists of calculating the effects of certain parameters (capture time, carrier density, momentum relaxation time, etc) on THz waveforms generated and detected by photoconductive (PC) antennas. They mention how their results agree with experimental work shown in other papers.

• Interaction between electrons e^- and holes h⁺
• Carrier trapping in mid-gap states (due to material defects)
  
• Scattering of carriers
• Dynamical space-charge effects (particularly screening)

Their conclusions were
Using the Drude-Lorentz model (electron pinball classical treatment) for carrier transport in semiconductors they discuss

• Major contributor to THz radiation is due to ultrafast change in n (carrier density)
• At high n the local electric field (active area of PC antenna between the electrodes) oscillates and induces E&M radiation
• When using a PC antenna as a detector there is a discrepancy between the transmitted and detected THz signal.

Why are PC antennas a good source of THz

They exhibit instantaneous polarization arising from optical excitation, and transport of photoexcited carriers in E field. Low temperature grown gallium arsenide, LT GaAs, in particular has short carrier lifetime, high mobility, and high break down E field. These characteristics lead to intense, large bandwidth THz radiation.

How does the THz radiation come about

The radiation arises from an ultrafast change in semiconductor photocurrent. The change in photocurrent can be attributed to

• Change in n (via optical pumping)
• Carrier acceleration (E^­_loc ~bias + polarization effects)

Calculations
Assumptions include

• free carrier trapping time is much smaller than carrier recombination time thus carrier trapping time determines carrier lifetime
  
• neglect LT GaAs nonlinear absorption effects
  

Based on Maxwell's equations and Hertzian Dipole far-field regime the transmitted THz field can be defined asThe different terms in this equation can be related to different material, pump pulse, and bias parameters.

Results

You definitely want to view this in a separate window

1. Plots (a) and (b) show the effect of varying the capture time on dn/dt and dv/dt. A larger effect can be observed in the dv/dt plots. The dn/dt plot (shape and magnitudes) reveals how much more influential the change in carrier density is to the THz signal. Without the inclusion of a bias, E&M radiation can still be emitted from the PC antenna as long as dn/dt does not equal 0. However the inclusion of a bias allows for a shortening of the time scale, which in turn leads to wider bandwidths.
2. Plots (a) and (b) show the effect of carrier density on the local E field and THz signal. As n₀ increases the THz signal starts to oscillate. This is due to screening caused by the polarization term in E_loc. The field becomes comparable to the restoring force between the electrons and holes and thus causes them to move around switching the polarization of the field (positive and negative peaks).
   
3. Plots (a) and (b) show temporal and spectral profiles of THz signals when the pump laser pulse width is varied. Here you can see the shorter the pulse duration, the wider the spectrum. This can be exploited for spectroscopic experiments.
4. Plot (a) shows an emitted THz pulse profile and the detected pulse with varying detector capture times. As you can see, the shorter the capture time, the truer to the original the detected pulse is. This is because the detector has a faster response time to changes in photocurrent supplied by the THz radiation. There is distortion because the photocurrent response is a convolution of the detected E field and the detector's carrier density and lifetime. In plot (b) it seems that a longer capture time leads to a better spectral profile. I am not particularly sure why just yet. In practice the detector can act as a filter, cutting off a part of the signal. The THz pulse has a Gaussian distribution with shorter wavelengths towards the center and longer wavelengths towards the outer rim (so usually smaller frequencies can get cut off).

This paper answers a lot of important questions on how these PC antennas work, what's the source of the THz radiation and how it's influenced by different parameters, and what to be conscious of especially when doing spectroscopy. So that is what I know!