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UCSB ECE 594 - Photoconductive Switches and Photomixers

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Notes#13, ECE594I, Fall 2009, E.R. Brown 179 THz Photoconductive Devices: Photoconductive Switches and Photomixers Researchers in the THz field struggled mightily during the 1960s through the 1980s to develop fundamental coherent sources. Among the many devices explored were IMPATT diodes, resonant tunneling diodes, Josephson-junction oscillator (arrays), and superlattice Block oscillators. Amongst the laser devices were cyclotron resonance (Landau level) intersubband lasers, coupled-quantum-well intersubband lasers, and spin-flip Raman lasers. All of these proved very difficult, even at cryogenic temperatures, so never gained widespread use, let alone commercial viability. Then in the late 1980s and early 1990s a big breakthrough occurred with the advent of subpicosecond-lifetime (aka “ultrafast”) photoconductors, as summarized quickly in Notes#5. These offered a means of generating useful levels of THz power using all room-temperature components, and took advantage of parallel developments in photonics technology. The first breakthrough was the photoconductive (i.e., “Auston”) switch. The Auston switch cleverly utilized mode-locked laser technology. The second breakthrough was the photoconductive mixer (or “photomixer” for short) that took advantage of single-frequency, tunable solid-state (e.g., Ti:sapphire) and semiconductor (e.g., GaAs/AlGaAs heterojunction DBR) lasers. Before discussing these devices in detail, we will first address two important effects in all photoconductors: square-law absorption and the Shockley-Ramo effect. The photoconductor in both the Auston switch and photomixer occur in bulk form; that is, they are a homogeneous material with two metal contacts. As in any semiconductor device, the coupling to the external circuit is a critical issue. On first glance, one might expect the coupling of photogenerated electrons and holes to the external circuit to be delayed by their respective transit times to the contacts – clearly a significant delay for any THz device. But this turns out to not be the case. In fact, the external circuit begins to respond to the effect of the photogenerated electron-hole pair immediately after the dc bias field begins to separate the two carrier types through the effect of carrier drift. This coupling to the external circuit was explained first in an elegant theorem due two separate papers in the late 1930s – one by Shockley and one by S. Ramo (the same Ramo comprising the “R” of TRW). Internal Photoelectric Effect in Semiconductors From fundamental semiconductor physics we know that the generation of electron-hole pairs by cross-gap photon absorption can be described semi-classically with the carrier wave functions expressed as quantum-mechanical (e.g. Bloch) wave functions and the electromagnetic energy expressed through the classical Poynting vector or, equivalently, the intensity. What results (from Fermi’s golden rule) is an expression for the photocarrier generation rate g(t) νhZtEhtrItrg02)(),(),(α=να=rr [m-3–s-1] (1)Notes#13, ECE594I, Fall 2009, E.R. Brown 180 where α is the absorption coefficient, E is the time-dependent optical electric field measured in the medium at the point rrwhere absorption occurs, Z0 is the intrinsic impedance of the medium, and hv is the optical photon energy. In going from I to E, the electric field is being treated classically, so (1) is generally regarded as “semiclassical”. The first equality in (1) is sometimes called the photoelectric law, first deduced by Einstein and the primary citation for his Nobel Prize in 1921. It is interesting that all of the early work on the photoelectric effect pertained to the creation of photoelectrons at air-solid interfaces, otherwise known as photocathodes. Later this effect was discovered to occur within solids and was called the “internal photoelectric effect.” When it occurred in materials such as semiconductors having good electron transport properties (i.e., high mobility), significant changes in the electrical conductivity were found to occur. This led to the description “photoconductivity.” The second equality is critical for THz ultrafast photoconductive devices because of the quadratic dependence on electric field. This is what makes the ultrafast photoconductors “self-rectifying.” So in response to a mode-locked laser, the photocarrier density can be computed in terms of the “envelope” of the optical pulse rather than the instantaneous electric field. And in response to two frequency-offset cw lasers, the photocarrier density shows a time-varying term at the difference frequency – the same effect as occurs in microwave mixers in which the current has a quadratic dependence on voltage. Shockley-Ramo Effect and Current Impulse Response Function Suppose one has a parallel-plate capacitor in which the internal electric field is uniform and the plates are separated by distance D. If an electron or hole is suddenly created somewhere inside the capacitor, it will initially have zero velocity but immediately be accelerated by the electrostatic force eE. In the process, its velocity v(t) will increase rapidly as will the kinetic energy. The interesting question addressed independently by Shockley and Ramo is what effect this acceleration process has on the current i(t) in the external circuit connected to the capacitor. They showed that the effect is immediate and can be expressed in simplest form as i(t) = ev(t)/D. If a carrier traverses the entire thickness of the capacitor and the velocity is constant or nearly constant during the entire process (not a bad assumption if the velocity quickly saturates, as it tends to do in semiconductors), then i(t) = ev/D = e/T where T is the transit time between the plates. In Notes#6 we derived the electron-hole pair concentration ρ(t) in response to a short pulse in photon power that generates electron-hole pairs. If this generation occurs in the parallel-plate capacitor under high bias field and starts at time t = 0 (for simplicity), then ρ(t) must be combined with the Shockley-Ramo effect to get the external-circuit electrical-current response. The response function of greatest use for circuits and systems calculations is the current impulse response, h(t) which is related to the photocarrier impulse response ρi(t) by h(t)= [(e/T)ρi(t)]θ(t) (2) where θ(t) is the unit step function, needed to


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UCSB ECE 594 - Photoconductive Switches and Photomixers

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