Photoconductivity in GaAs

How fast does a semiconductor become conductive when illuminated with above band-gap light? How long does it stay conductive after illumination? How conductive is it? How mobile are the photogenerated carriers? These are some of the questions we answer using time-resolved THz spectroscopy (TRTS).

TRTS is a useful probe of semiconductors because THz photon energies are very low, 1-10 meV. Therefore, THz radiation is only absorbed by free carriers, those carriers which have been photoexcited into the conduction band. We use a visible pulse to excite interband transitions and then probe the intraband transitions with the THz pulse. The picture to the right is not drawn to scale: The visible pump pulse energy should be 400 times larger then that of the THz probe pulse, but due to space limitations we have shown it to be only about 10 times larger.

GaAs is of particular interest for several reasons. It has a very fast turn-on time, that is, it becomes conductive almost immediately after photoexcitation. The electron mobility in GaAs is very high, about 8 times greater than that of silicon, and the lifetime of the photogenerated carriers is about 10 ns, compared to 10 ms for silicon. GaAs has been extensively studied and the physics are fairly well understood, which makes GaAs attractive as a benchmark system for TRTS.

The average change in THz transmission is shown to the left. Upon creating carriers in the conduction band by photoexcitation at 800 nm, the THz probe pulse is strongly absorbed. The total absorption of THz radiation is directly related to the conductivity of the sample. The more conductive a sample is, the more THz light is absorbed. The rise of the signal occurs in less then 1 ps and decays on the time scale of several hundred picoseconds. The decay of the signal is due to both surface recombination (100's of ps) and bulk recombination (several ns).

Photoexcitation at shorter wavelengths allows the photoexcited carriers to scatter into the high lying L and X valleys as shown in the diagram. The mobility in these valleys is lower then in the central G valley. The THz response is then governed by the return of carriers into the G valley, this effectively slows the onset of the photoconductivity.

The scans shown above on the right, only show the average change in THz absorption, and are collected by monitoring one point in the THz waveform as a function of pump-delay time. It is clear that it takes longer for the sample to become conductive when exciting with short wavelength light. More information is available in a TRTS experiment by collecting the entire THz waveform at each pump-delay time. In particular we can obtain the frequency dependent complex conductivity s(w) by a Fourier transform of the transmitted THz waveform. We can then compare the measured conductivity to that predicted from a model.

The simplest model of conduction electrons is the Drude model, which treats the electrons as free to move under the influence of an applied electric field, but subject to collisional damping forces, (see the figure to the right). The small dot represents an electron, and the larger dots are scattering centers. This is very similar to the drag experience by a particle in a viscous medium. The scattering centers are not nuclei of the background material, but rather, they are phonons, impurities, holes, or even other electrons.

The time between scattering events is known as the scattering time, or relaxation time t  . The mobility m is related to t   by m = et /m. Where e is the charge of an electron and m is the effective mass of the carrier. In the Drude model all scattering events are assumed to have the same scattering time, however, a generalization of the Drude model is achieved by allowing a distribution of relaxation times. Photoconductivity in GaAs is well described by a Generalized Drude model. For a generalized Drude model, the mobility m is related to the average relaxation time <t >.

The mobility is higher at lower temperatures because the scattering probability is lower (smaller number of phonons) at the lower temperature. This results in a larger scattering time and a larger mobility, and is manifested in the peak of the imaginary conductivity shifting to lower frequencies.