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Pulses of coherent terahertz radiation can be efficiently generated by a lateral diffusion current after ultrafast generation of photo-carriers near a metal interface on the surface of a semiconductor, this is known as the lateral photo-Dember effect. We investigate how the emission depends on the pump spot position, size, power and how it is affected by the application of an applied external bias. We study the role of the metallic mask and how it suppresses emission from the carriers diffusing under it due to a reduction of available radiation states both theoretically and experimentally.
© 2013 optical society of america
1. Introduction
Ultrafast generation of photo-carriers near the surface of a semiconductor produces picosecond lifetime surge currents that radiate a broadband THz pulse propagating parallel to the surface. At low fluencies there are two different mechanisms identified as being responsible for surface emission, surface field emission where carriers are accelerated by a surface field due to band bending and the photo-Dember effect where a net diffusion current forms perpendicular to the surface due to the difference in diffusivity of electrons and holes and a break in symmetry at the surface [1–5]. Both phenomena however suffer from low out-coupling from the semiconductor device, this led to a decline in interest owing to the high performance of photo-conductive (PC) devices. It has however been recently demonstrated that lateral photo-Dember (LPD) devices can efficiently generate THz radiation that is easily out-coupled [6–10] making them both comparable and competitive with state of the art PC devices in both power and bandwidth. The major advantage LPD devices have over PC devices is that they do not require a high-voltage bias to be maintained across a semiconductor, this increases the lifetime of LPD emitter devices.
As shown in Fig. 1, by partially masking a semiconductor surface with a deposited metal layer, and focusing an ultralfast laser, with above band-gap energy, half on the metallic mask and half on the semiconductor surface, an asymmetrical distribution of photo-generated carriers forms near the metal-semiconductor interface that is free to diffuse. Such a device gives intense THz emission as observed by [6–9], where this is attributed to an asymmetrical diffusion current because of the initial asymmetrical carrier distribution. The argument is that because the carrier population is steeper at the interface there must be a greater diffusion current moving towards and under the metal mask than that going away from it, leading to a net diffusion current. This explanation however is not physically plausible because regardless of initial symmetry any population density across an unbounded space where the concentration starts at zero and ends at zero must result in zero net diffusion current at all times. In the case of the traditional PD effect that is simulated in [2] the surface is a boundary condition which gives the needed asymmetry. We investigated this phenomenon theoretically and found that indeed the net diffusion current is zero and such a device would radiate in a quadrupole pattern which gives theoretically zero THz emission in the direction that the detector is placed [10]. We proposed an alternative explanation in [10] where we argue the current that forms parallel to the surface under the metal mask will not emit, due to dipole quenching. A dipole formed under the metal experiences destructive interference from a reflected wave off the metal mask because the dipole is much closer to the surface than THz wavelengths and the emitted wave experiences a π phase shift on reflection [11], whereas the currents that form elsewhere not under the mask are free to radiate; this changes the configuration making this a dipole current that can be the source of the detected THz emission. This alternative explanation predicted an opposite sign of the THz emission, which we then measured finding it in our favour in [10].
Fig. 1 A schematic showing the geometry of an LPD emitter; a semiconductor surface partially masked by a deposited metal layer, where an ultralfast band gap matched laser is focused half on the metallic mask and half on the semiconductor surface creates a distribution of photo-generated carriers near the metal-semiconductor interface which radiate in the same direction as the optical excitation.
Here we further investigate the mechanism involved in LPD emitters both theoretically and experimentally. Our theoretical model uses finite element analysis of the emitter geometry with and without a gold mask incorporating results from a 1D numerical drift-diffusion model of the ultrafast generation of an asymmetrical carrier distribution and its evolution showing how the radiation is affected by the metallic layer. For our experiments we are using a THz-TDS setup where our emitter is an LPD device and our receiver a PC antenna (from Menlo GMBH). A sketch showing how our emitter is held on a printed circuit board (PCB) and in contact with a silicon lens is shown in Fig. 2(a); all elements can be aligned using translation stages. Using our experimental apparatus we first measure the THz emission from a LPD emitter with two gold layers deposited on a low temperature (LT) grown GaAs substrate separated by a 200 μm semiconductor gap as a function of an applied external electric field finding it in good agreement with our model. We then show the emission dependency on spot position observing the expected sign dependency of the THz pulse electric field. We investigate the evolution of the radiation pattern and the radiation strength; THz emission can still be detected when the laser beam is illuminating the semiconductor surface far away from the metal edge, we explain the mechanisms of the detected THz radiation depending on the laser beam position. Next, we experimentally generate different asymmetrical carrier concentrations away from any gold layer by shadow masking the laser beam with a knife edge demonstrating that regardless of shape it does not change the sign or shape of the emitted THz electric field. And finally we investigate the fluence dependency of THz emission from LT-GaAs in order to find the optimum parameters of illumination and saturation fluence.
Fig. 2 (a) A sketch showing how our emitter is held on a printed circuit board (PCB) then touching on a silicon lens, all elements can be aligned using translation stages. A model of the dynamic electric field (z-axis) produced by drift-diffusion after an asymmetric distribution of carriers is generated in GaAs; red is a positive field, blue is a negative field. In (b), a layer of gold is on top the GaAs indicated by the yellow rectangle. In (c), there is no gold layer and the horizontal white line denotes the surface of the semiconductor.
2. Results from drift diffusion modelling and finite element analysis
Using a simple 1D drift diffusion model described in [10, 12] we model the evolution of carrier concentration during and after photo-excitation from a subpicosecond ultrafast laser pulse. The equation describing the evolution of the electron density, including both electric field and diffusion terms is,
where the electron density is ne, the hole density is nh, the electric field is E and G(x, t) is the optical generation term, determined by the laser spot shape, size and length. The mobility, μ, and the diffusion coefficient, D, follow the Einstein relation assuming quasi-thermal equilibrium. τ1 is the carrier density lifetime due to carrier recombination and τ2 is carrier density lifetime due recombination via fast traps. A similar equation was used for hole evolution. During this investigation we used the material properties of LT-GaAs [13–15]. The resulting current density evolution from this drift-diffusion model was used within a finite element analysis application (COMSOL Multiphysics) to study the resulting THz emission from the same asymmetrical carrier distribution with and without a gold mask. Figure 2(b) shows the dynamic electric field 1 ps after photo-excitation on a structure with a metal mask where a dipole emission is shown and Fig. 2(c) shows the same situation but without the metal mask where a quadrupole radiation pattern is observed that would give no radiation in the direction of our detector. This clearly demonstrates that we expect to see THz emission along the laser propagation axis, if and only if, there is a metal mask present near the carrier concentration.3. Experiments and results
In order to investigate the validity of our numerical model we determined experimentally how an applied electric field suppresses or enhances the LPD effect. We fabricated a LPD emitter with two Cr:Au contacts separated by a 200 μm semiconductor gap on the surface of a LT-GaAs substrate. These metal contacts were used as both electric contacts to apply an external bias and metal mask for the LPD effect. This emitter was used as the emitter in a typical transmission THz-TDS system with a strip-line PC LT-GaAs detector. In order to study the LPD effect the optical beam was modulated using a mechanical chopper, rather than a modulated electric bias, allowing for synchronous detection with a lock-in amplifier. A 100 fs Ti:Saphire laser centred at 800 nm and repetition rate of 80 MHz was focused onto the LPD emitter half on the gold mask and half on the semiconductor with a spot size of ∼ 60 μm FWHM and average power of 150 mW. The gold contacts were connected to a DC variable power supply. We then measured the THz emission from the LPD emitter as a function of applied external electric field from −0.75 kV/cm to +0.75 kV/cm. In Fig. 3 we plot the time domain scans of the detected THz pulse with a DC electric field of −0.75 kV/cm, +0.75 kV/cm and 0 kV/cm showing a clear enhancement and suppression of the THz emission. Using our drift-diffusion model described in Section 2 we added the applied electric field to the electric field in Equation 1 such that E = Ebias + Eϕ where Ebias is the applied electric field across the region not under the metal contacts and Eϕ is the electric field found by solving Possion’s equation for the carrier densities in the model. The resulting peak amplitude of the predicted THz emission is plotted in the insert of Fig. 3 with the measured peak amplitude as a function of DC electric field. A clear linear dependency was discovered that is in good agreement with the theoretical diffusion model showing that the drift-diffusion equation adequately describes the LPD emitter geometry. We found that for our parameters we are still in the linear regime of THz emission as a function of bias voltage, where we do not yet experience enhancement of photoconductive emission due to trap enhanced electric fields [16, 17]. This is due to our lower voltage bias and large beam waist, however in [16, 17] SI-GaAs was used, whereas here we use LT-GaAs so a simple comparison of the electric fields is not possible. According to [18] where an LT-GaAs strip line emitter has been tested we are still using a much lower bias than what would have been ideal for a strip line emitter with a gap of 200 μm.
Fig. 3 Time domain of detected THz emission from LPD emitter biased at −0.75 kV/cm, 0 kV/cm and +0.75 kV/cm; the sign of the electric field corresponds to the sign of the charge of the irradiated electrode. Insert shows experimental and theoretical results of the amplitude of THz pulse peak from LPD emitter as a function of applied electric field.
Experimentally, an impedance matched hyper-hemispherical Si-Lens is used to help out-couple the THz from the semiconductor device and minimise internal reflections and beam dispersion. The alignment of the Si-lens is critical and we have found that for optimal performance with LPD emitters we have to position the lens slightly away from the laser beam path, the reason for this is apparent in Figure 2(a) where it can be seen that the peak emission occurs slightly off axis. However, when having the Si-Lens centred away from the laser beam axis we could detect THz radiation when the laser illumination was away from a metal mask, the detected radiation is almost 50 times less than that from the LPD effect when it is illuminated near a gold mask. This weak detected radiation due to surface fields can be seen in Fig. 4(a) in comparison to the radiation of the LPD effect. The origin of this weak THz signal is likely to be due to the out-coupling of the quadrupole radiation generated by the LPD effect, as seen in, 2(b) and of the radiation generated from the surface emission effect which is quite prominent in GaAs [2, 5]. With the Si-Lens fixed to the LPD emitter and centred in between the two deposited gold layers, the sample was translated so the laser spot moved across the surface of the emitter. The signal amplitude of the main peak of the emitted THz was recorded as a function of spot position and is shown in Fig. 4(b) where the two gold edges are positioned at x = 0 & 200 μm. As expected, the THz signal detected depends on the position with respect to the gold edges. The sign of the THz electric field flips when the laser is centred on the left or right metal mask. Half way across the gap the signal completely vanishes as the Si-Lens and laser spot are perfectly aligned and thus no emission is observed. This electric field sign change is characteristic of LPD currents and is consistent with both the explanation given by Klatt et.al [6] and ours [10]. However, the expected sign of the THz electric field signal on either side, when measured, is opposite to what is predicted by Klatt et. al. [6] but consistent with our explanation [10].
Fig. 4 (a) The peak THz signal detected as a function of position across the semiconductor surface which is enclosed between two parallel gold regions separated by 200 μm. (b) The THz radiation from a Gaussian pump spot on bare LT-GaAs in comparison to the radiation observed from radiation of the metal edge (LPD effect). THz radiation from bare LT-GaAs originates from diffusion current and surface fields, due to the strong focusing provided from the combination of the Si-lens and parabolic mirrors.
Next we aligned the same LPD emitter with the Si-Lens fixed to the beam and translated the sample such that the laser spot with a spotsize of ∼ 30 μm FWHM was more than 50 μm away from the metal edge on the semiconductor surface where we could only measure the weak THz radiation explained above. The TDS scan of this type of emission from an un-masked guassian laser spot is shown as one of the scans in Fig. 5 and is similar to the surface field effects scan shown in Fig. 4(a). A knife edge was then imaged onto the surface and used to shadow-mask the laser spot such that we formed a semicircular, half-guassian spot, thus, creating an asymmetrical carrier distribution similar to that when using a metal mask, a schematic of this is shown in Fig. 6(a); a THz-TDS scan was then measured at this configuration. The knife edge was then rotated such that it masked only the opposite half of the laser spot and again a scan was acquired. The results of this experiment are shown in Fig. 5, if the explanation given by Klatt et. al. [6] is correct then we would have expected to see an enhancement of the THz emission from the shadow mask configuration and a flip in the sign of the electric field when we rotated the geometry. However this was not found to be the case as the THz emission does not increase and nor does the sign of the emission flip. This, further demonstrates that an asymmetrical carrier distribution does not produce a net diffusion current, this conclusion is valid even if we take into account that diffraction will not permit us to make a perfect half gaussian, because it still permits us to create an asymmetric carrier distribution. Furthermore, we translated the metal edge of the LPD emitter under the half Gaussian as shown in Fig. 6(a), and took THz-TDS scans every 2 μm until the spot was completely on the metal mask. Figure 6(b)(c)(d) shows the central frame from ( Media 1) where these results are presented. The result supports our theoretical argument as it can be seen that the THz emission is increasing as the metal edge is moved underneath the part of the half-Gaussian that is not illuminated; the THz radiation reaches its maximum exactly when the metal edge reaches the beginning of the illuminated part of the half-Gaussian. This clearly demonstrates that the metal is not really used to create an asymmetrical carrier distribution but to quench part of the carrier distribution shifting the radiation pattern from a quadrupole to a dipole.
Fig. 5 The THz radiation from bare LT-GaAs from a whole spot and two half-masked Gaussians, by shadow-masking opposite sides of the Gaussian laser spot. The insert shows a photo of an image of the shadow masked spot on the bare semiconductor surface, we found the spot to have a HWHM on one side to be ∼ 3 μm and the other to be ∼ 12 μm.
Fig. 6 (a) Schematic of experiment where the metal-semiconductor interface of the LPD emitter (extending to the left) is translated underneath the shadow masked semicircular pump spot. The rest of the figure is the central frame from ( Media 1). (b) Shows an image and scale of the semicircular pump spot on the surface of the LPD emitter (c) time scan of detected THz signal (d) peak amplitude of detected THz emission for different metal mask positions, highlighted spot is the current position. In this case the metal-semiconductor interface is at the sharp edge of the semicircular pump spot, which we define as mask position 0. Position −20 μm is when the metal edge is to the far left of the image; position 20 μm is when the metal edge is to the far right and all the illuminated spot is covered by the metallic region.
We present here how the peak to peak amplitude of emitted THz from a LPD emitter on LTGaAs depends on fluence. Again using the same LPD emitter with gold layers evaporated on LT-GaAs we measured the peak to peak amplitude of the emitted THz electric field from one metal edge for different spot sizes and average pump powers, from these data we calculated the fluence for each measurement. We used a neutral density filter wheel to vary the average pump power and translated the focusing optics to vary the spot sizes. Knife edge measurements were used to calculate the 1/e2 spot size radius. Figure 7(a) shows the recorded data from this experiment for different spot sizes and fluence. The data fits the saturation formula ETHz (F) = AωF/(F + Fsat), where A is a coefficient of conversion and alignment efficiency, ω is the 1/e2 spot radius and Fsat is the saturation fluence, the average saturation fluence was found to be Fsat = 0.116 mJ/cm2. The saturation arises due to the finite density of states in the conduction band and trap saturation. As it can be seen in Fig. 7(a), higher THz peak to peak current was observed for larger spots for the same average fluence, this demonstrates that for optimal performance large spot sizes are needed with high average pump powers. Figure 7(b) shows the calculated efficiency curve using the saturation formula and fitting parameters obtained from Fig. 7(a) and a constant fluence of 0.01 mJ/cm2 with increasing spot size, we see an initial increase in efficiency of our device before reaching roll-over. The increase in efficiency is expected because we are extending the region along the metal interface that is taking part in generating radiation and thus increasing the number of participating carriers. We attribute roll-over to a loss in out coupling efficiency with the Si-Lens as the spot size approaches the wavelength of THz radiation and we move away from a point dipole approximation.
Fig. 7 (a) Peak to Peak amplitude of detected THz emission for different spot size radii (1/e2) and average powers plotted as a function of fluence. The solid lines are saturation curve fits. (b) Calculated efficiency curve using the saturation formula and fitting parameters from the fits shown in Fig. 7(a) for a constant fluence of 0.01 mJ/cm2 with increasing spot size.
4. Discussion and conclusion
LPD devices as demonstrated in [6–10] can efficiently generate THz radiation that is easily out-coupled. A single LPD emitter can give comparable THz bandwidth to a PC antennae albeit approximately a tenth of the peak THz current [6, 10]. LPD emitters can be also multiplexed making them both comparable and competitive with state of the art PC devices in both power and bandwidth [6]. An advantage of LPD devices over PC devices is that they do not require a high-voltage bias to be maintained across the semiconductor, this increases the lifetime of LPD emitter devices. Furthermore, emitters based on lateral diffusion currents and dipole radiation suppression are simple to fabricate, opening up possibilities for easier THz integration and interfacing with other THz elements. Previously, we investigated the sign of the emitted THz emission from LPD emitters and proposed an alternative explanation [10] that the metal masking is suppressing part of the dipole emission thus creating the required asymmetry for the LPD effect to produce efficient THZ emission. Here we have further investigated the role of the metal mask used for LPD emitters and how it affects the THz emission changing it from a weak THz radiation originating from surface field effects to THz radiation from the diffusion current of the LPD effect. Using a drift-diffusion model incorporated with a finite element analysis model of the geometry we found that without metal mask we would expect no THz emitted along the laser beam direction. Furthermore, experimentally we were able to suppress or enhance the emitted THz radiation by applying a DC electric field across the LPD emitter and found good agreement with results from our model. We demonstrated that regardless of the symmetry of the carrier distribution without a metal mask no dipole emission was generated from lateral diffusion currents. However, we were able to observe quadrupole radiation from diffusion and surface emission effects when in a lateral transmission geometry depending on the alignment of the hyper-hemispherical Si-Lens with the beam axis. Finally we have taken saturation measurements of the LT-GaAs samples finding the saturation fluence for the effect and showing that the optimal parameters are high powers and large spot sizes making the emitters very easy to align. In future work we will further investigate the dependency of the THz power with optical fluence for LPD emitters and characterise the dependence on emitter material.
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