Unbiased continuous wave terahertz photomixer emitters with dissimilar Schottky barriers

We are introducing a new bias free CW terahertz photomixer emitter array. Each emitter consists of an asymmetric metal-semiconductormetal (MSM) that is made of two side by side dis-similar Schottky contacts, on a thin layer of low temperature grown (LTG) GaAs, with barrier heights of difference (ΔΦB) and a finite lateral spacing (s). Simulations show that when an appropriately designed structure is irradiated by two coherent optical beams of different center wavelengths, whose frequency difference (∆f) falls in a desired THz band, the built-in field between the two dis-similar potential barriers can accelerate the photogenerated carriers that are modulated by ∆ω, making each pitch in the array to act as a CW THz emitter, effectively. We also show the permissible values of s and ΔΦB pairs, for which the strengths of the built-in electric field maxima fall below that of the critical of 50 V/μm— i.e., the breakdown limit for the LTG-GaAs layer. Moreover, we calculate the THz radiation power per emitter in an array. Among many potential applications for these bias free THz emitters their use in endoscopic imaging without a need for hazardous external biasing circuitry that reduces the patient health risk, could be the most important one. A hybrid numerical simulation method is used to design an optimum emitter pitch, radiating at 0.5 THz. ©2015 Optical Society of America OCIS codes: (040.2235) Far infrared or terahertz; (040.5150) Photoconductivity; (230.6080) Sources. References and links 1. P. H. Siegel, “Terahertz Technology,” IEEE Trans. Microw. Theory Tech. 50(3), 910–928 (2002). 2. I. S. Gregory, C. Baker, W. R. Tribe, I. V. Bradley, M. J. Evans, E. H. Linfield, A. G. Davies, and M. Missous, “Optimization of photomixers and antennas for continuous-wave terahertz emission,” IEEE J. Quantum Electron. 41(5), 717–728 (2005). 3. M. C. Teich, “Field-theoretical treatment of photomixing,” Appl. Phys. Lett. 14(6), 201–203 (1969). 4. D. Saeedkia and S. Safavi-Naeini, “A comprehensive model for photomixing in ultrafast photoconductors,” IEEE Photonics Technol. Lett. 18(13), 1457–1459 (2006). 5. E. R. Brown, “THz generation by photomixing in ultrafast photoconductors,” Int. J. High Speed Electron. Syst. 13(2), 497–545 (2003). 6. S. Verghese, K. A. McIntosh, and E. R. Brown, “Optical and terahertz power limits in the low-temperaturegrown GaAs photomixers,” Appl. Phys. Lett. 71(19), 2743–2745 (1997). 7. S. Verghese, K. A. McIntosh, and E. R. Brown, “Highly tunable fiber-coupled photomixers with coherent terahertz output power,” IEEE Trans. Microw. Theory Tech. 45(8), 1301–1309 (1997). 8. J. T. Darrow, X.-C. Zhang, D. H. Auston, and J. D. Morse, “Saturation Properties of Large-Aperture Photoconducting Antennas,” IEEE J. Quantum Electron. 28(6), 1607–1616 (1992). 9. S. Winnerl, “Scalable microstructured photoconductive terahertz emitters,” J. Infrared Millim. THz W. 33(4), 431–454 (2012). 10. A. Dreyhaupt, S. Winnerl, T. Dekorsy, and M. Helm, “High-intensity terahertz radiation from a microstructured large-area photoconductor,” Appl. Phys. Lett. 86(12), 121114 (2005). 11. M. Awad, M. Nagel, H. Kurz, J. Herfort, and K. Ploog, “Characterization of low temperature GaAs antenna array terahertz emitters,” Appl. Phys. Lett. 91(18), 181124 (2007). #242007 Received 29 May 2015; revised 3 Jul 2015; accepted 3 Jul 2015; published 15 Jul 2015 © 2015 OSA 27 Jul 2015 | Vol. 23, No. 15 | DOI:10.1364/OE.23.019129 | OPTICS EXPRESS 19129 12. S. Jafarlou, M. Neshat, and S. Safavi-Naeini, “A fast method for analysis of guided wave and radiation from a nano-scale slit loaded waveguide for a THz photoconductive source,” IEEE Trans. THz Sci. Technol. 2(6), 652– 658 (2012). 13. G. Klatt, F. Hilser, W. Qiao, M. Beck, R. Gebs, A. Bartels, K. Huska, U. Lemmer, G. Bastian, M. B. Johnston, M. Fischer, J. Faist, and T. Dekorsy, “Terahertz emission from lateral photo-Dember currents,” Opt. Express 18(5), 4939–4947 (2010). 14. V. Apostolopoulos and M. E. Barnes, “THz emitters based on the photo-Dember effect,” J. Phys. D Appl. Phys. 47(37), 374002 (2014). 15. A. Reklaitis, “Crossover between surface field and photo-dember effect induced terahertz emission,” J. Appl. Phys. 109(8), 083108 (2011). 16. M. Nagel, “Photoconductive structure e.g. radiation source, for optical generation of field signals in terahertzfrequency range in bio analysis, has metallic layers formed from locations and provided in direct contact with semiconductor material,” European Patents Office, 2013, DE102012010926 (A1) 17. M. J. Mohammad-Zamani, M. K. Moravvej-Farshi, and M. Neshat, “Modeling and designing an unbiased CW terahertz photomixer emitters,” in The 2014 Third Conference on Millimeter-Wave and Terahertz Technologies (MMWATT), (IEEE, 2014) pp. 1–4. 18. S. Lodha, D. B. Janes, and N.-P. Chen, “Fermi level unpinning in ex situ Schottky contacts on n-GaAs capped with low-temperature-grown GaAs,” Appl. Phys. Lett. 80(23), 4452–4454 (2002). 19. M. Khabiri, M. Neshat, and S. Safavi-Naeini, “Hybrid Computational Simulation and Study of Continuous Wave Terahertz Photomixers,” IEEE Trans. THz. Sci. Technol. 2(6), 605–616 (2012). 20. M. Neshat, D. Saeedkia, L. Rezaee, and S. Safavi-Naeini, “A Global Approach for Modeling and Analysis of Edge-Coupled Traveling-Wave Terahertz Photoconductive Sources,” IEEE Trans. Microw. Theory Tech. 58(7), 1952–1966 (2010). 21. S. Selberherr, Analysis and Simulation of Semiconductor Devices (Springer-Verlag, 1984). 22. C. R. Crowell and S. M. Sze, “Current Transport in Metal-Semiconductor Barriers,” Solid-State Electron. 9(1112), 1035–1048 (1966). 23. S. Jafarlou, M. Neshat, and S. Safavi-Naeini, “A Hybrid Analysis Method for Plasmonic Enhanced Terahertz Photomixer Sources,” Opt. Express 21(9), 11115–11124 (2013). 24. S. Preu, G. H. Döhler, S. Malzer, L. J. Wang, and A. C. Gossard, “Tunable, continuous-wave Terahertz photomixer sources and applications,” J. Appl. Phys. 109(6), 061301 (2011). 25. C. A. Balanis, Antenna Theory: Analysis and Design, 3rd ed. (John Wiley & Sons, Hoboken, 2005). 26. A. Eshaghi, M. Shahabadi, and L. Chrostowski, “Radiation characteristics of large area photomixer used for generation of continuous-wave terahertz radiation,” J. Opt. Soc. Am. B 29(4), 813 (2012).


Introduction
Generation and detection of terahertz radiation, commonly defined as 0.1-10 THz, has attracted ample academic and industrial attentions, in recent years.Introducing potentially compact, low cost, low power consuming, and highly tunable photomixers, generating coherent continuous wave (CW) THz radiation at room temperature [1][2][3], has made photomixing a popular generation method among its rivals, during the past decade.In a conventional photomixer, basically, two CW infrared laser beams are mixed in a DC biased fast photoconductive material, generating a CW photocurrent with a THz beat frequency that can be either a direct source for THz radiation or can excite a THz antenna [4].The photogenerated THz power in a photomixer can be raised by increasing the incident optical power and applied DC bias, below the device breakdown limit.In a low temperature as grown (LTG)-GaAs photomixer, as an example, the limiting breakdown DC field is ~50 V/μm [5,6].Besides, intensity of the incident optical beam should be limited to 1 mW/µm 2 , to prevent the device failure due to the associated thermal damage.In fact, an incident optical power density in excess of this can cause a temperature gradient of ~110 K/10 μm within the surface of the active region, which is large enough to cause material to fracture and hence a permanent device failure [6,7].Alternative approaches such as large aperture emitters (LAEs), capable of handling high optical powers with reduced optical intensity, have been proposed to prevent the device failure due to the thermal degradation [8].Nevertheless, LAEs, suffer from the drawback of requiring high DC biases in the range of kV, for efficiently accelerating photogenerated carriers through the existing large gaps between their electrodes.This drawback, however, has been overcome by introducing scalable microstructured photoconductive emitters whose electrode structures can provide high bias fields with moderate applied voltages [9].These scalable emitters consist of arrays of electrodes, with micro-(nano)-sized pitches, each acting as an individual emitter.
Constructive interference of emissions from individual pitches adds up to the total THz emission from the scalable THz emitters.Although large effective areas of these arrayed emitters allow the usage of the state-of-the-art lasers' full powers [10][11][12], they suffer from a practical shortcoming.That is, a single submicron gap in a large array of metal-semiconductor-metal (MSM) structure can viably become short circuited, deteriorating the entire device operation.This type of failure becomes more probable during the fabrication process, as the interdigitated fingers are increased in number.Nonetheless, introduction of bias-free THz emitters with lateral photo-Dember current has overwhelmed this deficiency [13,14].In this type of structures emitters stay functional even in the presence of short-cut defects.The net photocurrent flowing in a photo-Dember emitter, as a radiating dipole, is diffusion limited and is determined by the difference in the electrons' and holes' mobilities.Nevertheless, the lateral photo-Dember effect also suffers from shortcomings like the complexity in fabrication of suitable electrodes, limitation in the choice of photoconductive materials with high contrast mobilities, and its low emission as compared with the biased emitters [14,15].Moreover, very recently Protemics GmbH, utilizing bi-metallic MSMs structures, has patented new bias free THz emitters operating in the pulse modes [16].This alternative approach, triumphing the shortcomings exhibited by other approaches and yet enjoying their advantages, has enabled pulse mode operation of THz emitters with improved efficiencies, without requiring external biases.Comprehending the overwhelming advantages of such bias free THz emitters, in our most recent presentation [17], we have briefly demonstrated the possibility of the CW radiation of such THz emitters consisting of two side by side interconnected Schottky barriers of dissimilar heights on LTG-GaAs, when irradiated by two lasers with 0.5 THz difference in their center frequencies.Nevertheless, the physical intimacy of the two dis-similar metal contacts, in lateral direction as proposed in [16] and also used in our preliminary study [17], might result in a maximum electric field that is larger than the breakdown DC field in LTG-GaAs.Occurrence of such a limiting phenomenon would certainly deteriorate the emitters operation.In order to overcome such limitation and yet enjoying the advantages of similar THz photomixer emitters with asymmetric MSM gratings, in this paper, we have proposed a new emitters consisting of similar gratings in each of which the two dis-similar Schottky contacts are laterally separated by an optimum distance and yet are interconnected externally.To the best of our knowledge, this is the first instance that such THz emitters have been reported in the literature.

Devices structure and electrostatics
Figure 1 illustrates a cross sectional view of the building block of the model bias-free photomixer made of an asymmetric MSM structure that can also serve as the unit cell of a periodic array of the modeled bias-free THz photomixer emitters.Each emitter pitch, with lateral dimension of Λ, consists of a pair of dissimilar metallic strips (M1 and M 2 ) that are deposited in parallel with lateral spacing s, on top of a 1-μm thick layer of LTG-GaAs to make a pair of dissimilar Schottky barriers Φ B1 >Φ B2 .As can be observed from this figure, the lateral spacing between two contacts is filled by a dielectric stripe, like SiO 2 , and M 1 is extended over on top to interconnect with M 2 , providing the required current path.The constituents' geometrical dimensions shown in the figure and the physical properties of the LTG-GaAs are tabulated in Table 1.Knowledge of the device electrostatic would help us to understand the device operation qualitatively.Hence, before going any further, we briefly revisit the relation between barrier heights of Schottky contacts made on LTG-GaAs and the metals Fermi levels, first.Direct observation of unpinned Fermi levels for three different metals on LTG-GaAs has been reported by [18], studying the heights (Φ B ) of the resulting Schottky barriers versus the metals work functions (Φ M ), experimentally.This is another key point that has motivated us to use dissimilar Schottky contacts formed on LTG-GaAs in designing CW THz photomixers.The data depicted by () in Fig. 2, represent the measured values of Φ B vs. Φ M for Mg, Ti, and Au reported [18].Moreover, the quadratic curve depicted by dashes-dots (-•-•-) shows an excellent numerical fit to these experimental data.From this curve one may readily predict approximate values of the Schottky barriers for other metals of known work functions, like those shown in this figure.The vertical dots () indicate the exact value of Cr work function and ranges of work functions for other metals known to make Schottky contacts on LTG-GaAs are shown by the horizontal dots (⋯).This figure is to demonstrate variety of possibilities for finding various pairs of metals with Schottky barrier differences that may match the desires of various users.Then, to gain insight into the device electrostatics, we calculate the conduction band (CB) diagrams by solving the Poisson's and continuity equations, iteratively.The CB diagrams versus the lateral (x) coordinate, at y = 1 nm (below the LTG-GaAs surface) for four MSM structures similar to Fig. 1, under equilibrium, are shown in Fig. 3(a).The electrodes M 1 in all these four MSMs are taken to be the same, with the largest barrier height, Φ B1 = 1.11 eV, while electrodes M 2 are formed by four different metals making barrier heights of Φ B2 = 0.8, 0.9, 1, and 1.11 eV.3(a).The asymmetry observed in this and the other CB diagrams for the MSM structures with dissimilar electrodes, unlike that of the symmetric MSM, provide potential differences between the electrodes in the range of 110 meV ≤ ∆Φ B ≤ 310 meV.When the device is under appropriate illuminations, the ∆Φ B in each case can cause the photogenerated carriers within the space charge region to flow-in and out through the dissimilar contacts.As indicated by the arrowheads in the figure, the photogenerated electrons () and holes (⊕) move downhill and uphill, respectively.Since the contacts dimensions and the lateral spacing between them are the same, the larger the difference ∆Φ B , the steeper the CB diagram, at any given y, and hence the greater the expected photocurrent flux under illumination would be.As can be seen from Figs. 3(a) and 3(c), in asymmetric MSMs electrons move away from the terminal M 1 and towards the terminal M 2 , resulting in a finite net current flowing between the two terminals.Whereas holes move in opposite directions, resulting in a net current flowing in the same direction as that of electrons flows.On the contrary in the symmetric MSM electrons move away from both terminals while holes moving in opposite direction, each resulting in a net zero current.

Permissible choices for s and ΔΦ B values
At this stage, we need to find a nearly optimum condition, in which the strength of the electric field maxima are below that of the critical electric field− i.e., |E max |≤50 V/μm− beyond which the photogenerated carriers attain enough energy to breakdown the LTG-GaAs [5,6].In doing so, we vary the lateral spacing between the two contacts in the range of 20 nm ≤ s ≤ 600 nm and the barrier height difference between the two Schottky contacts, in the range of 0 eV ≤ ΔΦ B ≤ 0.6 eV and calculate the strength of the maximum electric field in each structure.Numerical results are plotted in Fig. 5.The horizontal white plane specifies the critical electric field strength of 50 V/μm.Hence, it is clear that there is a trade-off limits between the size of s and the value of ΔΦ B , for preventing the breakdown phenomenon that renders the device useless.The dashes in the inset depict the loci of the critical eclectic field strength in the s-ΔΦ B plane− i.e., the border line between the 3D color plot and the horizontal white plane.Any pair of s and ΔΦ B values that falls below this border line is an "allowed" choice.We elaborate further on this issue, in the next section.#242007

CW operation of THz photomixer emitters
At first, we consider an individual asymmetric MSM structure similar to that shown in Fig. 1, having a pair of dissimilar Schottky contacts with a permissible choice of s and ΔΦ B , as determined by Fig. 5. Illuminating the top surface of the structure by two coherent optical beams of different center wavelengths, whose frequency difference (∆f) falls in a desired THz band, generates electron-hole pairs with a time-dependent generation rate, G (x, y, t) = G (x, y) e jωt with ω = 2πΔf being the modulation frequency.Acceleration of these photogenerated carriers by the built-in field is also modulated by the same frequency− i.e., E (x, y, t) = E (x, y) e jωt triggers radiation of the desired CW THz wave, in the absence of an external applied bias.Using the same procedure as reported in [19,20], in order to model the optical generation, we initially obtain the intensity distribution from the time-averaged Poynting vector.In simulating the optical characteristics of the individual Emitter structure, we used absorbing boundary conditions at all sides of the simulation domain.
Moreover, to obtain the THz photocurrent inside the photoconductor, we use G (x, y, t) in the drift-diffusion model to solve the Poisson's and carriers' continuity equations self consistently, employing FEM in the time domain [21].The Shockley-Read-Hall (SRH) and Auger processes, as non-radiative generation-recombination mechanisms, are taken into account in the model.Moreover, along the outer boundaries, homogeneous Neumann (reflecting) boundary conditions are imposed, to imply that the current flows in and out of the device merely through the contacts.In the absence of any surface charges the electric field components normal to these boundaries vanish [21].Nevertheless, the appropriate boundary conditions for the Schottky contacts at the metal/semiconductor interfaces, is based on surface recombination mechanism determined by the thermionic surface recombination velocity near the interface, assuming that the thermionic emission is the dominant source of current across both MS junctions [22].
Knowing the amplitudes of the optical generation rate and the electric field, throughout the LTG-GaAs, we can readily define the photomixer efficiency, in a similar manner as in [23] ( ) ( )

G x y E x y dxdy G x y E x y dxdy
The photomixer efficiency defined in Eq. ( 1) is an indication of the generated power in the photomixer device, and can be used as the goal function to maximize the THz power.Alternatively, one may evaluate the performance of the given THz photomixer, by evaluating its radiation output power that is directly proportional to the magnitude squared of its effective (collective) THz dipole current [24].In doing so one needs to know the local THz photocurrent density, where J DC (x, y) and J AC (x, y) are the DC component and the amplitude of the AC component of the local photocurrent density, respectively.Since the wavelength of the THz radiation (λ THz ) is much longer than the dimensions of the photomixer, under study, the lateral and transverse components of the local currents at all points inside the active region add-up coherently, resulting in the effective dipole current densities for both lateral and transverse directions: where φ represents the phase difference between the two effective components.The magnitude of the dipole current density is an indication of the THz output power.Moreover, for these emitters the total THz power can be obtained by the coherent summation of all elementary Hertzian dipole emissions at various points inside the active region.Hence, we can easily neglect any spatial phase shifts.In other words THz radiated power of a single pitch can be estimated by [24,25]: where is the radiation resistance.Parameter Z 0 and ε eff are the free space impedance and the air/semiconductor interface effective relative permittivity, respectively, and l 0 ( = v sat τ rad ) represents the dipole effective length with v sat and τ rec representing the carriers' saturation velocity and recombination lifetime, respectively.The radiation mechanism in the proposed photomixer is similar to that of biased large area emitters such as large aperture emitters [8,26] and the scalable microstructured THz emitters [9,10].The acceleration and separation of photocarriers induce a time-varying dipole moment within the active region that generates terahertz radiation.For this antenna-less concept, a collection of Hertzian electron and hole dipoles generated by the photomixer, themselves, act as the antenna.

Results and discussions
In this section we first find an optimum condition for an individual THz emitter and illustrate its characteristics.Then we use this optimum emitter to serve as a pitch for periodic arrays of THz emitters.Finally by varying the pitch size we investigate how it can affect the THz dipole radiation.

Efficiency: Individual THz emitter
Here, we calculate the efficiency, η, of an isolated THz emitter similar to that in Fig. 1, with a pair of dis-similar Schottky barriers, with permissible pairs of s and ΔΦ B that fall within the ranges of 20 nm ≤ s ≤600 nm and 0 ≤ ΔΦ B ≤ 0.47 eV, when under illumination of two coherent laser beams with parameters specified in Table 1. Figure 6 illustrates the 3D plot of η versus s and ΔΦ B .The ellipse depicted by dashes encompasses the high efficiency (η ≥90%) region of the plot, where 150 nm ≤ s ≤225 nm and 0.25 ≤ ΔΦ B ≤ 0.35 eV.Appropriate pairs of metals (M 1 and M 2 ) that can provide Schottky barriers with desired height difference can be found from the data given in Fig. 2. A careful inspection shows that the choice of s = 180 nm and ΔΦ B = 0.31 eV, for which the E max < 49.8 V/μm, is an optimum choice with the highest efficiency.From Fig. 1 one can see that the pair Au and Ag are one of the optimum choices for M 1 and M 2 , respectively.This optimum choice for s and ΔΦ B pair is going to be used for the numerical simulations that are going to be reported henceforth.Fig. 6.Efficiency, η, versus s and ΔΦB.The ellipse encompasses the high efficiency region (η ≥90%) of the plot.
As an example, here we present the numerical results, obtained for the distribution of the time-averaged carrier photogeneration rate inside the LTG-GaAs, as shown in Fig. 7.As can be observed from this figure, the incident optical beams are scattered from the contact edges, making the generation distribution non-uniform.It is noticeable that the generation rate maxima almost coincide within the regions where electric field components, E x exhibits large peaks.Knowing this and comparison of the field strengths around the inner boundaries of the asymmetric MSMs with those around their outer boundaries (specifically for the one with largest ∆Φ B ), we anticipate that the expected photocurrents under appropriate illuminations to be flown between M 1 and M 2 terminals mainly laterally.Later, in the following subsection we will show that the transverse component of the net current is much smaller than its lateral counterpart.

THz dipole current: Individual Emitter
Now, we take a snapshot of the 2D distributions of the photo generated electrons and holes densities inside the LTG-GaAs region of the given emitter at a given moment.The corresponding distributions are illustrated in Figs.8(a) and 8(b), respectively.As expected from the results shown in Fig. 7 and can also be observed from these figures, both photogenerated carriers are mainly concentrated around the outer boundaries of M 1 and M 2 .Meanwhile, the same numerical data show that the carrier's concentrations in the regions just below the contacts are insignificant.Then, we take the snapshots of the 2D distributions of the lateral and transverse components of the total local current density (J phx and J phy ) within the LTG-GaAs of the same emitter, as illustrated in Fig. 9. Negative and positive values of the total local current components at any given point shown in Figs.9(a) and 9(b), are determined by the direction of the electric field components (Fig. 4).Knowing the spatial distribution of the lateral and transverse components of the local current at any given moment, we can calculate the time dependence of the effective THz current components according to Eq. ( 2) and Eq.(3). Figure 10 illustrate the time dependence of both effective current components, J eff-x (t) and J eff-y (t), for the given individual emitter.As seen from this figure, amplitude of the transverse component of the effective THz dipole current as compared with that of its lateral rival is negligible.Moreover, the value of the dominant component is negative.

THz dipole current: Pitch Emitter
So far, we have presented the numerical obtained for an individual THz emitter.Nevertheless, when the same emitter serves as a pitch (unit cell) in a periodic array of emitters, the numerical results for the pitch are expected to differ.Because, along the x-direction in the simulation, in this case, domain periodic boundary conditions rather than absorbing boundary conditions must be applied.Now, we present the numerical results for spatial distributions of the photogenerated electrons and holes as well as the distributions of the lateral and transverse components of the total local current densities− i.e., J phx and J phy − at the given moment.Figures 11(a) and 11(b), respectively, illustrate the snap shots of the electrons and holes concentrations, within two unit-cells in the array, as an example.The differences observed by comparing these results with data shown in Fig. 8 is due to the difference in the boundary conditions along the x-direction that is in accordance with our expectations.Figures 11(c) and 11(d) also show the snap shots of the lateral and transverse components of the total local current densities, J phx and J phy , within the same two unit cells, respectively.The differences between these data figures and those shown in Fig. 9 are also noticeable at the boundaries of each emitter, along the x-direction.Otherwise, both sets of data follow the same trend.Nevertheless, the difference observed at the boundaries along the x-direction is expected to make a significant difference in the effective THz dipole current of the emitter.To see this difference, we evaluated the time dependence of the amplitudes of lateral and transverse components of the effective THz dipole currents, J eff-x (t) and J eff-y (t), for the single pitch emitter in the array.
Figure 12 illustrates the results for the pitch shown in Fig. 1, with the same dimensions and under the same illuminations as for the case of individual emitter of In other words, when an emitter serves as a of a periodic array of THz emitters is 36.7%more efficient than it can be as an individual emitter.This can be attributed to the coherent addition of the local current densities in lateral direction.As can be observed from Fig. 12, the effective dipole current densities along the lateral direction (J eff-x ) is much larger than that for the transverse component (J eff-y ).Therefore, the emitter emits perpendicular to the device surface, and mainly into the substrate as its wave impedance is smaller than that of the free space (Z 0 ) due to its higher refractive index.Finally, we have investigated the effect of the pitch size, Λ, on the THz dipole radiation output power.In doing so, we have kept all the constituents dimensions fixed except for the pitch size that has been varied in the range of 800 nm ≤ Λ ≤ 1600 nm, and evaluated the photomixer efficiency (η), first.The numerical results are depicted by the stars in Fig. 13 4) and ( 5), we have also calculated the THz radiation power from a 10-µm wide (in z-direction) pitch emitter.Figure 13(b) illustrates the results.As seen from the results illustrated in Fig. 13(b), the optimum value of 3.5 nW/pitch for the THz radiation power is obtained for the pitch with Λ ≈1400 nm.This relatively small #242007 power observed in Fig. 13, is a of the very radiation resistance of a single Hertzian dipole, as compared to that of antenna-based emitters [24].Nevertheless, the total radiated power can be scaled up by the squared number of cells (N 2 ).Hence, an appropriate choice of N in the array can provide the THz output power for a specific application.These large area unbiased emitters can offer high-power terahertz radiation because of their capacity to handle relatively high optical powers without suffering from the carrier screening effect and thermal breakdown.It is worth noting, if the device dimensions in (x, and z directions) becomes comparable to or larger than the λ THZ , the radiation resistance given in Eq. ( 5) should be modified according to Eq. (88) of [24].
One of the advantages of the proposed design over the microstructured THz emitters [9,10] is that the new design helps to prevent or minimize the creation of opposing photocurrents in two adjacent un-contacted regions that occurs in the later devices.It should be noted that the aforementioned opposing photocurrents leads to destructive interferences in the far field, considerably reducing the radiation efficiency.Therefore, the proposed electrode structure allows for almost uni-directional motion of carriers and a uniform electromagnetic field over a large area with increased radiation efficiency.It also may make the fabrication process simpler by eliminating the etching of the photoconductor in unwanted regions as is necessary in the fabrication of microstructured THz emitters [9,10].
These unbiased antenna-free emitters, with scaled-up with a large number of cells, unlike the antenna-coupled emitters are not vulnerable to the high total laser power.They rather can tolerate much higher optical-power levels than their antenna-coupled rivals do.Moreover, they are capable of offering broadband terahertz radiation.Because, their terahertz radiation is directly generated by time-varying dipole moments induced within the active area, and the radiated spectrum is not affected by the frequency response of any external antenna.Another important advantage of these antenna-less emitters over their antenna-based counter parts, especially in high frequencies, is that their efficiency and THz power are not limited by the RC roll-off.
It is also worth noting that the larger the size of the radiation aperture is, the more collimated the radiated THz beam becomes.In that case, the THz radiation power is mainly emitted along one direction as a highly collimated beam without the need for any extra optics such as silicon lens.If the dimensions of the arrayed emitter structure is small as compare to the terahertz wavelength, λTHz, the device should be mounted on a silicon lens to efficiently couple the terahertz radiation from the back side of the substrate to the free-space similar to the conventional antenna-based emitters with small active area.Otherwise, the THz radiation is collimated enough to eliminate the focusing optics for the THz beam radiated from the large area unbiased emitter [26].Due to the coherent emission of the whole radiating aperture of the active area, the emitter provides a diffraction-limited Gaussian beam, not requiring a silicon lens for out-coupling.This property of large-area emitters can be used to design very simple optics for THz imaging or spectroscopy systems.

Conclusion
We have presented the results of a systematic numerical study for designing a new generation of unbiased CW THz photomixers.In this work, we have shown that an array of asymmetric (bi-metallic) MSM structures, whose unit cell (pitch) is made of a pair of dis-similar Schottky contacts on LTG-GaAs can act as bias free CW THz photomixer emitters.Furthermore, we have developed a systematic procedure for optimizing the emitter efficiency versus the lateral spacing between the two dis-similar Schottky contacts in each array's pitch and the difference in their barrier heights.Moreover, we have found the optimum pitch size too.Emergence of this kind of THz source can be a gateway to many applications, especially in medical applications such as endoscopic imaging without a need for hazardous external biasing circuitry, reducing the patient health risk.

Fig. 1 .
Fig.1.Cross sectional view of the unit cell of the periodic array of the modeled bias-free THz photomixer emitters, each consisting an interconnected pair of dissimilar Schottky contacts on LTG-GaAs layer.The array pitch size is Λ.Geometrical dimensions can be found in Table1.

Fig. 2 .
Fig. 2. Measured Schottky barrier heights () for Mg, Ti and Au contacted LTG-GaAs, versus work-function [18].Dotted-dashes shows a quadratic fit, while () indicate the exact value of Cr work function.The work functions for other metals known to make Schottky contacts on LTG-GaAs are depicted by horizontal dots. #242007

Figure 3 (
c) illustrates a similar energy band diagram for the asymmetric MSM with the largest ∆Φ B ( = Φ B1 −Φ B2 = 310 meV), corresponding to the diagram depicted by (-), in Fig.

Fig. 3 .
Fig. 3. (a) CB diagrams of the MSM structure with a single pair of Schottky contacts along the LTG-GaAs surface (x-direction at y = 1 nm) for Φ B1 = 1.11 eV and 0.08 ≤Φ B2 ≤ 1.11 eV; the corresponding CB diagrams in x-y plane (y ≥ 1 nm) for (b) Φ B2 = 1.11 eV and (c) Φ B2 = 0.8 eV.All drawn under equilibrium.The x-and y-components of the electrostatic electric field (E x and E y ) distributions, for each MSM can be obtained by taking the gradient of the corresponding CB diagram, with respect to x-and y-directions.Figure 4(a) illustrates the 1D distribution of E x versus x at y = 1 nm below the LTG-GaAs surface corresponding to each CB diagram shown in Fig. 3(a).Figure 4(b) shows the 2D distribution of the E x versus x and y (y ≥ 1 nm) within the x-y plane of Figure 4(a) illustrates the 1D distribution of E x versus x at y = 1 nm below the LTG-GaAs surface corresponding to each CB diagram shown in Fig. 3(a).Figure 4(b) shows the 2D distribution of the E x versus x and y (y ≥ 1 nm) within the x-y plane of #242007 Received 29 May 2015; revised 3 Jul 2015; accepted 3 Jul 2015; published 15 Jul 2015 © 2015 OSA the space charge region for the symmetric structure, corresponding to the CB diagram shown in Fig. 3(b).Moreover, Fig. 4(c) illustrates a similar electric field distribution for the asymmetric MSM with the largest ∆Φ B , corresponding to the CB diagram shown in Fig. 3(c).Meanwhile 1D and 2D distributions for E y , similar to those shown in Figs.4(a)-4(c) are illustrated in Figs.4(d)-4(f), respectively.As can be observed from these figures, strengths of E x and E y are significant within 10-nm wide regions about the contacts edges and become negligible outside these regions.Their directions also indicate the direction of their current components.Moreover, diagrams in Figs.4(a) and 4(d) show that the larger the difference ∆Φ B, the greater the strengths of the electric field components around the contacts edges would be, as we have already concluded from the CB diagrams in Fig. 3(a).The symmetry observed in Figs.4(b) and 4(e) is also supporting our earlier comment about the zero net current for both electrons and holes between M 1 and M 2 of the symmetric MSM.

Fig. 5 .
Fig. 5. Strength of the maximum electric versus the size of lateral spacing between M 1 and M 2 , s, and the difference in the barrier heights, ΔΦ B .Dashes depict the loci of the critical eclectic field strength, 50 V/μm.

Fig. 7 .
Fig. 7.The time-averaged carrier photo-generation rate inside the LTG-GaAs layer of the individual emitter.

Fig. 8 .
Fig. 8. Snapshots of the carriers' concentrations: (a) electrons and (b) holes, within the LTG-GaAs substrate, at a given moment.

Fig. 9 .
Fig. 9. Snapshots of the components of the local current densities: (a) J phx and (b) −J phy, within the LTG-GaAs substrate, at a given moment.

Fig. 10 .
Fig. 10.Time dependence of the amplitudes of the components of the effective THz dipole current, J eff-x (-) and J eff-y (---), for the optimized individual emitter.

Fig. 11 .
Fig. 11.Snap shots of the (a) electrons and (b) holes concentrations; and the components of the total local current densities (c) J phx and (d) −J phy , within the LTG-GaAs substrate of the twofinger MSM photomixer, under illumination.

Fig. 10 .
Figures11(a) and 11(b), respectively, illustrate the snap shots of the electrons and holes concentrations, within two unit-cells in the array, as an example.The differences observed by comparing these results with data shown in Fig.8is due to the difference in the boundary conditions along the x-direction that is in accordance with our expectations.Figures11(c) and 11(d) also show the snap shots of the lateral and transverse components of the total local current densities, J phx and J phy , within the same two unit cells, respectively.The differences between these data figures and those shown in Fig.9are also noticeable at the boundaries of each emitter, along the x-direction.Otherwise, both sets of data follow the same trend.Nevertheless, the difference observed at the boundaries along the x-direction is expected to make a significant difference in the effective THz dipole current of the emitter.To see this difference, we evaluated the time dependence of the amplitudes of lateral and transverse components of the effective THz dipole currents, J eff-x (t) and J eff-y (t), for the single pitch emitter in the array.Figure12illustrates the results for the pitch shown in Fig.1, with the same dimensions and under the same illuminations as for the case of individual emitter of Fig.10.Using data shown in Figs. 10 and 12 in Eq. (4), one can see that

Fig. 12 .
Fig. 12.Time dependence of the amplitudes of the components of the effective THz dipole current, J eff-x (-) and J eff-y (---), for a single pitch of arrayed emitters.
(a).The behavior observed from this figure can be attributed to the two counteracting phenomena, as Λ increases: (i) the LTG-GaAs bare area (illuminated by the laser beams) also increases and hence the active volume in which the photogeneration occur increases too; (ii) the electric field around the pitch boundaries decreases significantly (see Fig. 4(a)).The curves for the effective THz dipole current and hence the resultant THz radiation power for each emitter in the array are also expected to follow the same behavior.The calculated data for the effective THz dipole current are depicted by the open circles in the same figure.Using Eqs. (

Fig. 13 .
Fig. 13.(a) The photomixer efficiency (*) read from the left axis, and the effective THz dipole current () read from the right axis, and (b) the THz radiation output power from a 10-μm wide pitch, all versus the pitch size (Λ).