UNIVERSIDAD DE CHILEFACULTAD DE CIENCIAS FSICAS Y MATEMTICASDEPARTAMENTO DE INGENIERA ELCTRICA

Propuesta de Proyecto de Tesis Programa de Doctorado en Ingeniera Elctrica

Simulaciones fsicas de la radiacin de la potencia de salida de radiacin de terahercios desde un fotomezclador verticalmente iluminado UTC y un estudio de la usabilidad de campos magnticos para una mejorada caracterizacin de sus propiedades de transporte de portadores

Thesis ProposalDoctoral Program in Electrical Engineering

Physical simulations on the terahertz radiation output power from a vertically illuminated travelling wave UTC photomixer, and a study of the usability of magnetic fields for improved characterization of its carrier transport properties

Victor Hugo Calle GilThesis Advisor: Ernest Michael

SANTIAGO DE CHILE CHILE 2010

Contents1.Introduction131.1.Introduction and General Context131.2.Thesis Project and State-of-the-Art141.3.Radio astronomy Applications152.Fundamental Theory192.1.Photomixing Theory192.2.PIN Photodiode202.3.Theory of UTC-PD Photodetectors222.3.1.Structure232.3.2.How does it work232.3.3.Performance features242.3.4.Modeling252.3.5.Boundary Conditions292.4.Theory of vertically illuminated Traveling-wave Photomixers312.5.Vertically illuminated UTC-TW-Photodiode332.6.Numerical Analysis of a Vertically Illuminated UTC-TW-Photodiode342.6.1.Finite Difference Methods352.6.2.Finite Element Method362.6.3.Transmission-Line-Matrix Method362.7.Models and Devices372.7.1.CPW-Bowtie Aperture Antenna372.7.2.310 GHz Uni-Traveling-Carrier Photodiode382.7.3.1.5 THz Uni-Traveling-Carrier Photomixer392.7.4.Theoretical 340 GHz Uni-Traveling Carrier Photomixer392.7.5.Theoretical 110 GHz UTC-TW Photodetector402.7.6.Experimental UTC-TW Photomixer402.8.Influence of a magnetic field412.8.1.Magnetotransport423.Proposed Research work453.1.Hypothesis453.2.Goals453.2.1.Main Goal453.2.2.Specific Goals453.3.Methodology453.3.1.Literature Review463.3.2.Carrier Transport Modeling473.3.3.Electromagnetic Modeling483.3.4.Combination of Electromagnetic and Carrier Modeling494.Working Plan514.1.Phases and activities to be performed514.2.Gantt chart525.Expected Results555.1.Physical parameters555.2.Simulations and experiments to be performed555.2.1.Proposed simulations555.2.2.Proposed Publications576.Conclusions597.References61

List of FiguresFigure 1:16Figure 2:20Figure 3:20Figure 4:20Figure 5:21Figure 6:22Figure 7:23Figure 8:24Figure 9:32Figure 10.33Figure 11:34Figure 12:35Figure 13:36Figure 14:37Figure 15:38Figure 16.41Figure 17.43Figure 18:46Figure 19:47Figure 20:48Figure 21:49Figure 22:50Figure 23:50Figure 24:56

List of TablesTable 1: State of the art [23] [36][37][41][42].15Table 2: Layer Composition of the 310 GHz Uni-Traveling-Carrier Photodiode [64].38Table 3: Layer Composition of the 310 GHz Uni-Traveling-Carrier Photomixer [15].39Table 4: Layer Composition of the Theoretical 340 GHz Uni-Traveling-Carrier Photomixer [41].39Table 5: Layer Composition of the Theoretical 110 GHz Uni-Traveling-Carrier Photodetector [37].40Table 6. Layer Composition of the Experimental UTC-TW photomixer [31].40

List of AbbreviationsCPS: Coplanar striplineCPW:Coplanar-wave guideCTA:Carrier Transport AlgorithmCW: Continuous-waveDD: Drift-Diffusion equationsDDM:Drift-Diffusion ModelEA:Electromagnetic Algorithm.EC: Equivalent circuitFEM:Finite Element MethodFDM:Finite Difference MethodGaAs: Gallium ArsenideGHz GigahertzHD: Hydrodynamic-Diffusion equationsHDM:Hydrodynamic-Diffusion ModelHEB: Hot-electron bolometerHECA:Hybrid Electromagnetic-Carrier AlgorithmHEDDA:Hybrid Electromagnetic-Drift-Diffusion AlgorithmHEHDA:Hybrid Electromagnetic-Drift-Diffusion AlgorithmLO: Local OscillatorLT-GaAS: Low Temperature-Grown Gallium ArsenideMSM:Metal-Semiconductor-MetalNIR: Near-infraredPD: PhotodiodeRLT: Receiver Lab TelescopeSIS: Superconductor-Insulator-SuperconductorTEM: Transversal electromagneticTHz: TerahertzTLM:Transmission Line Matrix MethodTLMM:Transmission Line Matrix MethodTW: Traveling-waveTWPD: Traveling-wave photodetectorUTC-PD: Uni-traveling-carrier PhotodiodeUTC-TW-PD:Uni-traveling-carrier Traveling-wave photodetectorYIG: Yttrium-Iron-Garnet

List of Symbols: Absorption coefficient: Angular frequency: Antenna resistance: Bias Voltage, :Constants >0: Carrier transit distance: Carrier drift velocity, , : Constants >0: Electrical Photocurrent: Electric DC current: Effective response time (semiconductor): Electron recombination time: Electron trap time: Electrical photo current at : Electrons photocurrent at : Electron photocurrent saturation: Electron photocurrent of electrons or holes (or): Electron mobility: Admittance matrix of coupled waveguides: Frequency of operation: Frequency difference : 3dB down frequency (cut-off frequency): Hole recombination time: Intrinsic impedance of the medium: Intrinsic mobility: Optical electric field: Optical intensity: Optical electric field from two lasers, : Optical input power: Planck's constant: Photocurrent density in the intrinsic region: Photogeneration rate: Power in terahertz range: Recharge-time capacitance of the lumped elementRCbandwidth limit (in frequency): Recombination time of the intrinsic region: Saturation velocity of electrons: Saturation velocity of holes: Transit time cut-off frequencyTransit time:

IntroductionIntroduction and General ContextThe generation of powerful tunable continuous wave (CW) radiation in the so-calledterahertz gap" has been intensively studied and there is rapid progress in thelast couple of decades[1]-[15]. CW systems based on photoconductive mixers (photomixers) have several attractivefeatures: high spectral resolution, easily tunable in a widefrequency range, and based on the relative cheap semiconductor lasers.Nevertheless, THz photomixers have a substantial disadvantage; so far their output power (efficiency) is very low[16]. The generation of THz power with photonictechnology is promising for new developments in several marked applications, such as high-speed measurements [17], spectroscopy[18],wireless communications[19], security and medicine[17][20][21], as photonic Local Oscillators (LO) in astronomy applications [22] (for a more detailed discussion about the astronomical applications see section 1.3),due to synergies with low-cost photonic techniquesalready available for communication technologies.The development of photonic local LO supplied for heterodyne receivers in radio telescopes, could be regarded as a challenging research because of the difficulty for obtaining high power and ultra wide bandwidth. In order to get such powerful devices, the present research proposal is part of the development of photomixers. The main advantages of this technique over the conventional electronic devices are the extremely wide bandwidth (e.g. 700 GHz for LT-GaAs). In the last years, several research groups have developed new high-speed photodiodes in order to obtain higher conversion efficiency (responsivity) and ultra wide bandwidth. Among them are the Uni-Traveling Carrier (UTC) photodiodes which have been demonstrated as the most efficient for the generation of CW THz signal[23][24][25][16]. On the other hand, the concept of Traveling-Wave (TW) in photomixers [26] has been applied for developing edge-coupled photodetectors with larger bandwidth-efficiency products [9][27][28][29]. However, while edge-coupled devices inherently suffer from velocity mismatch between optical and submm-wave and power limitations due to the small optical cross section [30], vertically illuminated TW-MSM-mixer structures were demonstrated to be in full TW mode due to the in-situ adjustability of the optical fringe velocity and to have high power capabilities if large optical absorption areas are realized.Actually, the Radio Astronomical Instrumentation Group (RAIG) is developing a novel device, which it is a merger of two ideas, the concept of vertically illuminated TW photomixers and the concept of UTC layer systems: vertically pumped TW-UTC structures [31]. It is interesting to take into account the thicknesses used in the manufacture of an UTC-photodiode. For example, the UTC-photodiode developed by Ishibashi et al[32], its device thickness of the most important layer, the absorption layer, is about 220 nm [33]. Therefore, the reduced feature sizes require more complicated and time-consuming manufacturing processes [34]. It means that a pure trial-and-error approach to device optimization will become impossible since it is both time consuming and expensive [34]. Since computers are considerably cheaper resources, simulation is becoming an indispensable tool for device engineering[34]. Besides offering the possibility to test hypothetical devices which have not yet been manufactured, simulation offers unique insight into device behavior by allowing the observation of phenomena that cannot be measured on real devices[34].As it was mentioned above, the RAIG group is developing TW-UTC photodiodes. In order to perform the present proposal research, it is important to understand that it is necessary to perform carrier transport and RF simulations [35][36][37]. Thesis Project and State-of-the-ArtFor the first time in modeling of UTC photodiodes, Ishibashi et al [38] used a Drift-Diffusion model for analyzing carrier dynamics in the absorption layer. They treated carefully the boundary conditions by taking into account the thermionic emission velocity of electron in order to accurately calculate the response in scaled UTC-PD structures. They found that the velocity overshoot effect plays an essential role in broadening the UTP-PD bandwidth.They also concluded that the response of a UTC-PD is dominated by the electron transport in the absorption layer. Moreover, calculations predicted that an UTC-PD with a quasi-field in the absorption layer could generate a much broader bandwidth than a conventional PD with similar internal quantum efficiency.Pasalic et al [39] presented a hybrid method for numerical analysis oftraveling-wave photodetectors (TWPDs). The method is a combination of two-dimensional semiconductor and three-dimensional full-wave electromagnetic (EM) simulators. The time-domain drift-diffusion method is used to determine the photogenerated currents at the cross section of the device to calculate the microwave bandwidth and output current of the device. In the analysis, the effects of the carrier velocity and lifetime, optical power, bias voltage, velocity mismatch, and microwave loss are taken into account. The method is tested in case of GaAs and low-temperature-grown GaAs-based TWPDs. Again, Pasalic et al [37] used their previous work to extend the hybrid drift-diffusion (DD)TLM method to include the analysis ofuni-traveling-carrier (UTC) photodetectors. The extended method considers the overshoot velocityat which electrons in the collector of an UTC photodiode drift. The method is used for large and smallsignal analysis of the UTC traveling-wave photodetector (TWPD) and near-ballistic (NB) UTC TWPD. They showed that there is a trade-off between the UTC TWPDs bandwidth and saturation current that has to be considered in the design. A higher bias voltage reduces the bandwidth, but also increases the saturationcurrent of the photodetector. They presented a UTC TWPD with bandwidths of 110 and 83 GHz andsaturation currents of 15 and 30 mA under 1 and 5 V biases, respectively. Mahmudur et al [40] presented results of a UTC photodiode using the hydrodynamic carrier transport model. A maximum responsivity of 0.25 A/W and a small signal 3-dB Bandwidth of 52 GHz were obtained for a 220-nm-thick InGaAs absorption layer. They investigated the physical properties of the UTC-PD under different optical injection levels. Moreover, they observed a modulation of the energy-band profile due to the space charge effect at high injection level, and a velocity overshoot of 3107 cm/s has been found to effectively delay the onset of the space charge effects. Also, they found that the speed of the photo response of the UTC-PD could be improved by incorporating a graded doping profile in the absorption layer.Banik et al [41]presented a method to optimize the epitaxial layer structure of an InGaAs/InP uni-traveling-carrier photo-diode (UTC-PD) for continuous THz-wave generation. The design approach used is general in that it can be applied for any target frequency while this study focuses on 340 GHz. The photodiode epitaxy is modeled and optimized using a TCAD-software implementing the hydrodynamic semiconductor equations. Their results showed that the UTC-PD can generate ~1 mW at 340 GHz by choosing the optimum absorption layer and collection layer thicknesses.All the above works rely in the modeling and simulation of both electromagnetic and carrier transport phenomena. Table 1 summarizes the State of Art of numerical modeling. As shown in Table 1, the simulation and modeling using drift-diffusion and hydrodynamic carrier transport models were applied only on the UTC-photodiode. Modeling and simulation on UTC-TW photodiodes were realized using only a hybrid drift-diffusion-TLM model. Therefore, the present research proposal suggests a novel hybrid model for the UTC-TW using the hydrodynamic carrier transport model and TLM. The use of hydrodynamic carrier transport model has the advantage that it takes into account more information than the drift-diffusion carrier transport model like carrier temperature dependent parameters such as motilities and diffusion coefficients and thereby it models more accurately the carrier transport [41]. Carrier transport ModelThree-dimensional Full-wave electromagnetic analysis

UTC-PDTW-PDUTC-TW-PD

Drift-Diffusion Carrier Transport ModelIshibashi et al: Drift-Diffusion algorithm.Pasalic et al: TLM Method.Pasalic et al: TLM Method.

Hydrodynamic Carrier transport ModelBanik et al: Sentaurus TCAD.Mahmudur et al: ISE-TCAD (Now is Sentaurus TCAD).Not yet done.Not yet done.

Table 1: State of the art [23][36][37][41][42].Moreover, as an optional development, we will include an additional variable magnetic field in the drift-diffusion carrier transport and hydrodynamic models, with the purpose of investigating the effect of a magnetic field in carrier transport properties of a UTC-TW photodiode. This experimental was not achieved yet. By the optional term I mean if there is enough time, the Hydrodynamic Carrier Transport Model will be extended in order to include the magnetic field parameter.Radio astronomy ApplicationsTerahertz technology is a fast-growing field with a variety of applications in biology, medicine, spectroscopy, astronomical instrumentation, security and communications. Among the different terahertz continuous-wave (CW) devices, photomixers have the best possibilities of small and economical, low power consumption, highly coherent and tunable devices[1]-[13]. A photomixer is a device that employs a heterodyne scheme, in which two laser beams with their frequency difference falling in the terahertz range mix in a medium like aphotoconductor or superconductor, and generate a signal, whose frequency is equal to the frequency difference of the two lasers[11]. This device can exhibit a nonlinear I-V bias curve, but not necessarily. A photomixer can also have linear I-V-curve, an example is illustrated later.The spectral regionfrom 0.3 to 3 THz, located between the radio range, controlled by macroscopic flows of electrons (amplifiers, frequency multipliers), and the infrared range controlled by optical media (lasers), is often called the terahertz gap due to the lack of strong tunable sources. In that scheme, terahertz photonic sources can be considered as an interesting hybrid approach: a direct ultra-high speed control of an electron flow, confined in space as much as possible at the foot-point of a microscopic antenna by means of laser light. One of the most important motivations to develop efficient CWterahertz photomixers is their use as efficient local oscillators. In radio astronomy, they are employed in heterodyne receivers, in which the frequency of detected radiation is down-converted to an intermediate frequency (IF) by mixing with a monochromatic local oscillator signal. The main motivation for terahertz receivers is the study of the terahertz frequency range (1-3 THz, or wavelength: 100-300 m), which provides a vision of the Universe in the far infrared. This window provides unique goals for both the interstellar chemical and star formation studies. For example, the cold interstellar clouds (10-15 K) emit their strongest radiation in the frequency range of 1.0-1.5 THz. Moreover, in the hot cores (50-200 K) where the stars are forming, the species CO, CN, HCN and HCO emit their strongest rotational radiation in this range of frequencies[43].Near both young and evolved stars, molecules exist across a large range of excitation levels, with the more highly-excited states often located closer to the exciting source or protostar[43].An inspection of the objects in theses spectral lines is likely to provide a good discriminator of the various stages of the protostellar evolution[43]. A broad range of atmospheric windows open up to 1500 GHz (see Figure 1), at the uniquely dry Chajnantor altiplano in the Chilean Andes, where the ALMA (Atacama large Millimeter Array) interferometer and many other internationally operated single-dish radio-telescopes are taking advantage of this worldwide unique site. While ALMA has a photonic local oscillator (LO) system already developed and will have ten receiver bands covering all atmospheric windows up to 950 GHz, some of the single-dish telescopes will have instrumentation projects up to the 1500 GHz window (e.g. Receiver-Lab-Telescope (RLT), Nanten 2, Cornell-Caltech-Atacama-Telescope (CCAT), APEX Telescope. While many spectral lines of high scientific interest are falling into these atmospheric windows, these ground-based observatories will offer significant advantages in terms of costs and logisticscompared to aircraft and balloon-based platforms, and therefore open access to technology-pushing experiments. Cooperation with the RLT and CCAT groups is currently being developed.

Figure 1:The leftfigure shows the atmospheric transmission between 200 GHz and 1.6 THz for different PWV values. (source: www.apex-telescope.org). The right figure shows the annual variation of the Precipitable Water Vapor (PWV) content at Chajnantor, based on 10 years of site testing.

Heterodyne receivers provide the spectral high resolution necessary to study these spectral lines. They down-convert the high frequency to one in the gigahertz-range by mixing with a coherent continuous-wave radiation source, called local oscillator. The type of local oscillators most commonly used in radio-astronomical receivers is based on Gunn- and YIG- oscillators, both of them with frequency multiplier chains. Typical terahertz power values provided by frequency multiplier sources based on waveguides are 300 - 1000 W in the range 400 - 500 GHz, 20 - 30 W in the range 900 - 1100 GHz and 2 - 4 W in the range 1300 - 1600 GHz (see company Virginia Diodes). Themain drawbacks are theirsmall relative bandwidth which decreases toward higher frequencies and the possible variations of power within these bandwidths. Therefore, the full coverage up to frequencies above 1 THz is complicated and expensive because it has to be provided by a collection of individual costly local oscillators. Especially for 1 THz or higher, frequency multipliers of the local oscillator are very expensive and often not available for certain frequency ranges.In contrast to this situation, a terahertz photomixer will deliver all the frequencies and the spectrum will be flat except for the overall roll-off in power. The crucial point is that if only enough power is provided to pump SIS junctions (Superconductor-Insulator-Superconductor) or HEB Bolometers (Hot-Electron Bolometer), photonic local oscillator will bring great benefits to radio-astronomy, especially in the higher frequency ranges. 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Start

1D-BC

1D-DDA

1D-SR ~ 1D-DDAR?

Tuning 1D-DDA

2D-BC

2D-DDA

2D-SR ~ 2D-DDAR?

Tuning 2D-DDA

End

No

Yes

No

Yes

Start

1D-BC

1D-HDA

1D-SR ~ 1D-HDAR?

Tuning 1D-HDA

2D-BC

2D-HDA

2D-SR ~ 2D-HDAR?

Tuning 2D-HDA

End

No

Yes

No

Yes

3D-BC

Start

1D-BC

1D-EA

1D-HR ~ 1D-EAR?

Tuning 1D-EA

2D-BC

2D-EA

2D-HR ~ 2D-EAR?

Tuning 2D-EA

End

3D-EA

No

Yes

No

Yes

3D-HR ~ 3D-EAR?

Tuning 3D-EA

No

Yes

Start

BC

HEDDA

HEDDAR ~ PTM?

Tuning HEDDA

End

No

Yes

Start

BC

HEHDA

HEHDAR ~ PTM?

Tuning HEHDA

End

No

Yes