IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 66, NO. 1, JANUARY 2019 349

Thermal Characterization of Quasi-VerticalGaAs Schottky Diodes Integrated on Silicon

Souheil Nadri , Student Member, IEEE, Christopher M. Moore, Student Member, IEEE,Noah D. Sauber, Student Member, IEEE, Linli Xie , Student Member, IEEE,

Michael E. Cyberey, Member, IEEE, John T. Gaskins,Arthur. W. Lichtenberger, Senior Member, IEEE,

N. Scott Barker , Fellow, IEEE, Patrick E. Hopkins,Mona Zebarjadi, and Robert M. Weikle, II , Fellow, IEEE

Abstract— This paper presents the first thermal charac-terization of terahertz quasi-vertical GaAs Schottky diodesintegrated on silicon. The devices are characterized usinga thermoreflectance measurement technique. Heating andcooling temperature profiles and 2-D temperature maps areobtained for 5.5-µm diameter diodes. From the measure-ments, we extracted the device thermal resistances, anodetemperatures, and thermal time constants. Equivalent cir-cuit and finite-element models are developed to study thedevice geometry, and extract unknown material thermalparameters. The devices are also characterized using anelectrical transient method, and the temperature and cool-ing transients found from both techniques are compared.The quasi-vertical diodes show comparable thermal resis-tance and a faster transient response compared to otherterahertz Schottky diodes reported in the literature.

Index Terms— Heterogeneous integration, imaging, junc-tion temperature, Schottky diode, thermal characterization,thermal parameters, thermoreflectance.

I. INTRODUCTION

THERMAL management and design have been under-stood, for many years, as critical factors in the implemen-tation of submillimeter-wave Schottky diode-based circuits and

Manuscript received September 13, 2018; revised October 14, 2018;accepted October 28, 2018. Date of publication November 28, 2018;date of current version December 24, 2018. The work of S. Nadri wassupported in part by the National Ground Intelligence Center underContract W911W5-16-C-0007, in part by the National Science Foun-dation under Grant ECCS-1609411, and in part by the Office of NavalResearch under Grant N00014-16-1-3048. The work of M. Zebarjadi wassupported by NSF under Grant 1653268. The work of P. E. Hopkins wassupported in part by the National Science Foundation under Grant EECS-1509362 and in part by the Air Force Office of Scientific Research underAward FA9550-18-1-0352. The review of this paper was arranged byEditor R. Venkatasubramanian.(Corresponding author: Souheil Nadri.)

S. Nadri, C. M. Moore, N. D. Sauber, L. Xie, M. E. Cyberey,A. W. Lichtenberger, N. S. Barker, M. Zebarjadi, and R. M. Weikle, IIare with the Department of Electrical and Computer Engineering,University of Virginia, Charlottesville, VA 22904-4743 USA (e-mail:sn3t@virginia.edu).

J. T. Gaskins and P. E. Hopkins are with the Department of Mechan-ical and Aerospace Engineering, University of Virginia, Charlottesville,VA 22904-4743 USA.

Color versions of one or more of the figures in this paper are availableonline at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TED.2018.2880915

instruments [1], [2]. Removal of heat is particularly importantfor frequency multipliers, as these circuits generally exhibitlow-to-modest conversion efficiencies, and are usually drivenwith high-power sources to achieve usable output power in thesubmillimeter-wave region of the spectrum [3]. Elevated diodejunction temperature due to inadequate heat sinking is knownto degrade performance, accelerate aging effects (for example,due to electromigration, ohmic contact deterioration, or ther-mally induced stress), and can ultimately lead to device fail-ure [4]–[6]. The relatively low thermal conductivity of GaAs(the predominant material technology for submillimeter-wavediodes) [7], coupled with restrictions on diode anode size andgeometry needed to minimize parasitics and achieve the deviceimpedances required for high-frequency operation, presentsignificant challenges, and tradeoffs between electrical andthermal designs of these devices.

Because they are amenable to realizing integrated compo-nents, planar Schottky diodes represent the most prevalentarchitecture for submillimeter-wavelength components, suchas frequency multipliers. A variety of approaches for realizingplanar diodes have been developed, aimed at optimizing RFperformance. These include flip-chip mounted devices [8],diodes fabricated from epitaxy that has been transferred to low-permittivity substrates [9], membrane-supported diodes [10],as well as substrate-less diodes [11]. Recognition that heatingis a major factor limiting efficiency and output power hasprompted numerous approaches to mitigate excessive tem-perature rise in the diode junction, including the use ofAlN or diamond as low-loss heat spreaders substrates [1], [6].

An alternative diode topology, based on a quasi-verticalgeometry realized through heterogeneous integration of GaAswith high-resistivity silicon, was recently developed forsubmillimeter-wave applications [12]. Unlike planar diodes,this device structure (Fig. 1) consists of a metal contactunder the diode’s anode and epitaxial mesa, thus providinga large-area ohmic cathode contact that also serves as anintegrated heat sink. Measurement of high-efficiency mul-tipliers based on this technology [13] suggest the quasi-vertical architecture provides an effective approach for heat

0018-9383 © 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

https://orcid.org/0000-0002-9722-7361https://orcid.org/0000-0002-9737-9728https://orcid.org/0000-0003-2115-8379https://orcid.org/0000-0002-1774-9769

350 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 66, NO. 1, JANUARY 2019

Fig. 1. Scanning electron micrograph of a quasi-vertical diode fabricatedat the University of Virginia.

Fig. 2. Diagram of the diode cross section and epitaxy. The semiinsu-lating handle and AlGaAs etch stop layers are removed in the fabricationprocess and are not shown. Note the device layers are not shown toscale.

removal and thermal management in Schottky diodes. Thispaper reports on the first experimental characterization ofheating in heterogeneously integrated quasi-vertical diodesusing thermoreflectance as a diagnostic tool.

II. QUASI-VERTICAL SCHOTTKY DIODE GEOMETRY

A scanning electron micrograph of a prototype device isshown in Fig. 1. A cross section of the device epitaxy andstructure is shown in Fig. 2. The diode mesa lies directly onan ohmic metal pedestal that is bonded to a silicon carrierwhich serves as a low-loss substrate for RF signal lines andcircuitry. A metal overlay of the ohmic pedestal provides thecathode contact, as well as a thermal path for removing heatfrom the diode to the substrate. The device shown in Fig. 1 isfabricated using an epitaxy transfer process described in detailin [14].

Development of the quasi-vertical diode structure describedearlier was motivated as an effort to reduce device parasitics(series resistance and shunt capacitance) as well as to fabricatedevices on a suitable low-loss substrate that can be microma-chined to form fully integrated chips with electrical circuitryand contacts. The high efficiency (>25%) and power output(100 mW) of frequency quadruplers implemented with thistechnology, in addition to estimates of the diode temperaturebased on electrical measurements [13], [15], suggest thequasi-vertical geometry offers a number of benefits with regard

Fig. 3. Diagram of the quasi-vertical diode geometry showing the paths(dashed lines) for heat flow from the anode to the thermal ground (siliconsubstrate) and simplified thermal equivalent circuit model.

to thermal management in comparison with standard planardiode configurations. Note that the ohmic contact acts as anintegrated heat sink that underlies the full device mesa and canbe placed in close proximity to the anode. The use of siliconas a substrate (with a thermal conductivity of 150 W/m-K)provides improved heat spreading and thermal grounding tothe circuit housing compared to GaAs (having a thermalconductivity of 55 W/m-K). In addition, the anode finger(Fig. 1) is in direct contact with the silicon substrate, thuspresenting a secondary thermal path that directly shunts theGaAs mesa.

III. THERMAL MODELING

Electrothermal modeling of submillimeter-wave Schottkydiodes has proven invaluable as a tool to inform the designprocess and tailor circuit architectures for the improvementin efficiency and power handling [1], [16]. These thermalmodels typically employ analytical models based on equivalentcircuits, finite-difference time-domain solutions of the heatequation, or finite-element simulations of 3-D models [17].

A. Thermal Equivalent Circuit Model

Equivalent electrical circuit representations for heatflow [18] through semiconductor diodes are a useful andcommonly used tool for understanding thermal transients indevices as well as for identifying thermal bottlenecks. A sim-plified thermal model of the quasi-vertical diode, superim-posed over the device geometry, is shown in Fig. 3. In thismodel, dissipation of electrical power in the diode’s junctionand series resistance generates heat that is represented as a cur-rent source. This dissipation, in conjunction with conductivecooling mechanisms that are modeled with equivalent thermalimpedances, provide paths for heat flow to thermal ground(held at ambient), and determine the instantaneous temperatureof the device. As indicated in Fig. 3, the thermal impedance ofeach material layer comprising the diode may be representedas a parallel combination of a thermal conductance G and ther-mal capacitance C . In the simplified model of Fig. 3, the GaAsand Inx Ga1−x As layers of the diode mesa are combined intoa single effective thermal impedance (Gm || Cm). Likewise,parallel conductances and capacitances represent the thermal

NADRI et al.: THERMAL CHARACTERIZATION OF QUASI-VERTICAL GaAs SCHOTTKY DIODES INTEGRATED ON SILICON 351

TABLE IMATERIAL THERMAL PROPERTIES

impedances of the airbridge finger (Gb || Cb), SU-8 adhesivelayer (GSU-8 || CSU-8), and cathode ohmic contact metaloverlay (Gc || Cc). Heating and cooling transients of thediode depend on thermal time constants (τ ) associated witheach layer (denoted with subscript i), τi = (Ci/Gi ) (1). Theconductance Gi depends on the cross-sectional area, thermalconductivity, and material thickness, whereas the capacitanceCi is the product of the density, volume, and specific heatcapacity [19]. For microscale devices, the thermal bound-ary resistance at material interfaces needs to be considered,since its contribution can sometimes dominate the overallthermal resistance [20]. The diode thermal resistances at theanode/cathode interfaces are, respectively, denoted in Fig. 3as Ra and Rc.

From the thermal model, the steady-state junction tempera-ture is found as [19]: Tj − T0 = Rth Pdis (2), where Rth is thetotal thermal resistance between the diode junction and thermalground, Tj is the junction temperature, T0 is the ambient tem-perature (thermal ground), and Pdis is the power dissipated inthe diode. A circuit model is then constructed using Keysight’sAdvanced Design System. A 6.86-mA thermal current isapplied, which is equivalent to the thermal power deliveredto the device in the measurement. The lumped element circuitvalues are based on the materials’ temperature-independentnominal values, ignoring thermal boundary resistances, andassuming that the diode mesa stack consists only of undopedgallium arsenide (Table I). From this analysis, we can obtaina rough estimate for the total thermal resistance and thermaltime constant of a 5.5-μm-diameter device by fitting the sim-ulated thermal response to an exponentially decaying curve:Rth = 1000 (K/W) and τ = 500 ns.

These estimates are helpful in understanding qualitativelythe dominant heat paths in the quasi-vertical diode structure.The thin and poorly conductive SU-8 layer acts as a thermalopen circuit. On the other hand, the highly conductive ohmicbehaves as a thermal short. The heat temperature of the hotspot (anode) is, therefore, governed by the parallel thermalpaths formed by the mesa stack, and the gold airbridge.

B. Finite-Element Model

While simple lumped equivalent circuit analogs providequalitative information for the thermal properties of theSchottky diode as well as intuitive guidance for thermal

design, finite-element solvers can provide a more completerepresentation of the temperature distribution throughout thegeometric structure of the device. A finite-element solutionis acquired using the ANSYS mechanical [21] simulationtool. The mesh size for the model is adjusted to 3 μmaround the critical features (diode stack and airbridge). Theairbridge length is 17 μm, width is 5.5 μm, and thicknessis 1.35 μm, corresponding to the physical dimensions of thedevices tested in this paper. The rectangular mesa dimension is11 μm × 15 μm.

An input heat flux equal to the net electrical power dissi-pated divided by anode area is applied directly beneath thediode contact. The bottom and side facets of the substrateare fixed to the ambient temperature (293 K) and remainingsurfaces are assumed to be adiabatic. Convection and radiationcooling mechanisms are assumed negligible. The steady stateand transient solutions are obtained by solving the conductionheat equation [16]. The relevant material thermal propertiesused in this analysis are listed in Table I [16]. The thermal con-ductivity for the gold metallization is set to 214 W/m-K, basedon the measured electrical conductivity (3 × 107 S/m) andthe Wiedemann–Franz law. Thermal boundary resistances [22]and other factors described in Section V make the thermalconductivity of the diode mesa stack difficult to estimate.Therefore, these layers are lumped into a single layer ofthickness 1.37 μm. The effective thermal conductivity of thislayer is used as a fitting parameter to model the measuredresults presented in the following section. In an effort to reducethe number of fitting parameters, the ohmic and anode thermalboundary conductances Ga and Gc are estimated using atime-domain thermoreflectance measurement similar to theone described in [2] to a value of 35 MW/m2 − K. The othermaterial parameters are well established values [16].

IV. MEASUREMENT

Experimental characterization of the thermal behavior ofsubmillimeter-wave Schottky diodes have generally includedthe use of electrical techniques, whereby the temperaturedependence of the diode current–voltage (I–V ) characteristicis used to estimate the junction temperature [13], [23]–[25],and imaging methods (thermography) which typically utilizeinfrared microscopes to measure thermal radiation emittedfrom the device [17], [26]. Infrared imaging methods canprovide information on the temperature distribution over adevice (or array of devices), but with diffraction-limited spatialresolution and frame rates that usually limit the ability toresolve thermal time constants less than 1 μs. In this paper,thermoreflectance (optical) and electrical transient measure-ments are used and compared to characterize the thermalperformance of quasi-vertical diodes integrated on silicon.

A. Thermoreflectance Measurements

The thermoreflectance measurement technique is basedon the change in refractive index, and, therefore, surfacereflectivity (�R/R), with changes in temperature (�T ), whichcan be approximated to first order as [27]: (�R/R) =χ�T (3). The thermoreflectance calibration coefficient χ

352 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 66, NO. 1, JANUARY 2019

Fig. 4. (a) Experimental setup for thermoreflectance characterization ofthe diode. (b) Optical image of the device under test.

depends on the sample material, wavelength of the illumi-nating light, angle of incidence (and, by extension, surfaceroughness), and the composition of the sample. The thermore-flectance calibration coefficient typically varies from 10−2 to10−5 K−1 [27], with values reported in the literature for platedgold at 530 nm [27]–[31] varying over a range of −3×10−4 to−2.3 × 10−4 K−1. Because the determination of the exactcoefficient of thermal reflectance for our device was extremelydifficult, the authors decided that measuring this quantitywould be outside the scope of this paper. Instead, a valueof −2.65 × 10−4 K−1 is chosen (an average of the reportedvalues in the literature) and the uncertainty in the temperatureestimation (resulting from this choice) is incorporated in theerror analysis.

The experimental setup for the thermoreflectance measure-ments is shown in Fig. 4(a). The change in the diode’ssurface reflectivity under a voltage pulse heating excitation ismeasured with a Microsanj NT210A unit [32] which includesa signal generator, pulse generator, and a control unit. Thesetup utilizes a green (530 nm) LED light source and acharge-coupled device (CCD) camera to sense the intensity ofthe reflected signal. 530-nm light is chosen because the reflec-tivity of a gold surface is sensitive near this wavelength [27].

As the change in surface reflectivity with temperature issmall, the signal measured by the CCD camera is averagedover many device thermal excitation cycles. The CCD recordsreflectance information only for the duration of the LED illu-mination pulse [30]. Consequently, the measurement requiressynchronizing the device excitation, LED illumination, andimage acquisition (as shown in [30, Fig. 2]). A square-wavevoltage pulse train excites the diode with the ON voltagelevel chosen to deliver the desired heating power to thediode. The diode voltage and current are monitored usingan oscilloscope connected in shunt with the device, and anammeter in series with the setup. For each period, the voltageis ON for 50 μs with a 30% duty cycle. These parameters allowthe diode to cool down completely to ambient temperaturebefore the next heating voltage pulse is applied. From theseparameters, the Microsanj software calculates the minimumwidth of the LED pulse, and therefore, the time resolution ofthe measurement, to be 500 ns. The delay of the illuminationpulse relative to the device excitation pulse is controllableand the full diode thermal transient can be assembled byacquiring a sequence of images as the illumination pulse delayis adjusted in increments relative to the rising edge of the diode

Fig. 5. Thermal maps of the diode obtained at times (a) 49.7, (b) 51.9,(c) 54.6, and (d) 57.3 µs after the removal of the heating excitationusing thermoreflectance measurements. Note the temperature scale isindicated on the right.

excitation pulse [33]. In this paper, for each increment in pulsedelay time, the reflected light intensity measured by the CCDcamera is averaged for 4 min. Temperature maps of 5.5-μmanode diameter diodes are obtained using this procedure.

Fig. 4(b) shows the top view of the diode and Fig. 5shows its 2-D temperature maps at four sample times duringcooling. The input electrical power delivered to heat the diodeis 6.86 mW. A postprocessing shadow algorithm is used toremove data from nonplanar surfaces that result in erroneousintensity readings. Consequently, these areas appear as blackpixels in the 2-D images. The surface of the gallium arsenidemesa is also shadowed as the thermoreflectance of this materialis insensitive to light at 530-nm wavelength. The temperaturereadings of the 2-D images are calibrated to gold using athermoreflectance coefficient of −2.65 × 10−4 K−1.

Heating/cooling curves (Fig. 6) are obtained from the 2-Dtemperatures maps. The temperature has been averaged over arectangular region of interest (ROI) as indicated in Fig. 5(d).This region contains 196 pixels, and is located at the topof the anode pillar, as it is the closest visible region to theanode-mesa contact which is the device’s hottest spot.

The heating and cooling transients at different power excita-tion levels are presented in Fig. 6(a). As the thermoreflectanceimaging measures changes in surface reflectivity, the plotshows the temperature rise relative to ambient (293 K). In thisfigure, as well as all subsequent plots, symbols indicatemeasured values while lines represent the fitted or modeledtemperature. In Fig. 6(a), the lines are fitted (least squaresfitting method in MATLAB) using an exponential functionwith a single-time constant (extracted from the cooling data),used for both the heating and cooling transients. The thermalparameters extracted from these fitted curves are summarizedin Table II. The temperature rise and time constant areobtained from the fitted exponential curves. The total thermalresistance is then calculated using (2). As anticipated, thepeak diode temperature rise scales linearly with dissipatedelectrical power in accordance with (2). The fitted valuefor the temperature rise is in a good agreement with themeasurement. Furthermore, cooling of the quasi-vertical diodeis described with a single-time constant of 2 μs. This is in

NADRI et al.: THERMAL CHARACTERIZATION OF QUASI-VERTICAL GaAs SCHOTTKY DIODES INTEGRATED ON SILICON 353

Fig. 6. (a) Measured and fitted heating and cooling transients ofa 5.5-µm-diameter diode. The fitted curves utilize a single-time constantof ∼2 µs. (b) Measured cooling transient of this diode compared to themodeled transient using ANSYS mechanical finite-element solver (solidline).

TABLE IIEXTRACTED THERMAL PARAMETERS FOR DIODE

(AREA = 23.76 µm2 ) VERSUS POWER

contrast to the planar diodes reported in [25], which exhibitmultiple time constants and much slower thermal processes,as a consequence of their geometry and integration usingflip-chip bonding. Fig. 6(b) compares the measured coolingcurves with the ANSYS model, which are in good agreement.In the model, the thermal conductivity of the mesa stack isadjusted to the value of 9.5 W/m-K to fit the measured data.The physical rationale and validity of this fitted value will bediscussed later in this paper.

Uncertainty in the estimation of the peak temperature riseis comprised of two components: the uncertainty in the choiceof the coefficient of thermoreflectance for gold and measure-ment error. Error due to uncertainty in the thermoreflectance

Fig. 7. (a) Measured and fitted I–V relation for a 5.5-µm-diameterquasi-vertical diode. (b) Measured diode temperature–current calibrationcurves for three different sensing voltages, VM .

coefficient (χ) for gold is found by obtaining the temperaturescorresponding to the ROI region given the minimum andmaximum values for χ found in the literature. Measurementerror is found from the standard error of the mean using seventhermoreflectance measurements based on a 95% confidencelevel. Finally, the fitting error in temperature T and timeconstant τ correspond to a 95% confidence bound with anR-square value of 0.999.

B. Electrical Transient Measurements

The second method for temperature characterization, basedon electrical transient measurements, was implemented toestimate the diode temperature and thermal time constantsas well as to provide a comparison with both the thermore-flectance method presented earlier and other results reportedin the literature [25]. The electrical characterization methodemployed utilizes the approach detailed in [25] and exploitsthe temperature dependence of the I–V relationship of theSchottky diode [34] to estimate junction temperature.

In this paper, diodes with 5.5-μm-diameter anodes weremounted to a temperature-controlled stage, and I–V mea-surements were performed to obtain temperature calibra-tion curves. Fig. 7(a) shows the I–V characteristic of a5.5-μm-diameter anode quasi-vertical diode at ambient tem-perature. At low applied voltages, conduction through thehigh-resistivity silicon substrate dominates the I–V charac-teristic and appears electrically as a 10-K� resistor shuntingthe diode. A sensing voltage VM , between 0.56 and 0.58 V,is selected in the region of the I–V curve where conductionthrough the diode is dominant, but remains sufficiently lowto minimize self-heating. The resulting calibration curves areshown in Fig. 7(b). A third-order polynomial fit (solid line)

354 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 66, NO. 1, JANUARY 2019

Fig. 8. Measured and fitted thermal cooling transients for a5.5-µm-diameter quasi-vertical diode using electrical transient mea-surements. Results obtained from thermoreflectance measurements(triangles) of the same diode are shown for comparison. Deviation ofelectrical transient data from a straight line indicates the necessity oftwo-time constants.

is used to obtain a temperature-current relationship for eachsensing voltage.

Transient current measurements were performed using aKeysight B1500A semiconductor parameter analyzer, with tworemote-sense and switch units (RSUs), each connected to adiode terminal. One RSU is used to apply a transient step volt-age waveform, that is switched between the heating voltage,VH = 0.75 V, to the sensing voltage VM . The heating voltageis chosen to deliver 6.92 mW to the diode, near that used forthe thermoreflectance method, and is held for 50 μs so that thediode heating reaches steady state. After 50 μs, the appliedvoltage is reduced linearly to VM over a 10-ns interval andthe second RSU measures the transient current. A third-orderpolynomial fit for the measured temperature–current curves ofFig. 7 is used to convert the measured transient current totemperature. A 1.4-μs delay is introduced after the voltageis switched to VM before recording the transient current usedfor the temperature curves. This delay allows for electricaltransients to settle. The measured thermal transients shown inFig. 8 are fitted using an exponentially decaying function withtime constants indicated in Fig. 8 (inset). Note that the best fitto the electrical transient method requires two-time constants,in contrast, with the thermoreflectance measurement, whichexhibits a single-time constant. Nevertheless, the two methodsgive comparable results regarding the net time required forthese diodes to cool from their operating temperature toambient—approximately 10 μs—which, notably, is severalorders of magnitude lower than for GaAs flip-chip mounteddiodes reported in the literature [25].

V. DISCUSSION

The cooling transient parameters and time constantsextracted from both measurement techniques, although similar,exhibit some differences that are likely a consequence ofthe specific physical parameters measured in each case andthe inherent limitations of each technique. Thermoreflectanceprovides temperature maps and cooling transients by sampling

the reflectance of visible light from the metallized (gold)surface of the diode’s anode contact. Unlike the electricalcharacterization approach, this technique permits both theheating and cooling transients to be measured. However, as thethermoreflectance method samples the surface temperatureonly, the internal temperature at the junction of the deviceis not directly monitored and must be inferred. In addition,the necessity to average over many heating and coolingcycles restricts the sample rate for measurement and limits itscapacity to observe transients with short time constants. On theother hand, the electrical transient method is an establishedtechnique that utilizes standard electrical instruments andprovides a means for estimating the internal temperature of thediode junction, even if the device is packaged. This techniqueis capable of measuring short time constants but is also subjectto a number of potential sources of error. As the measuredparameter (electrical current) depends on both electrical andthermal transients, the data must be interpreted carefully andnecessitates the introduction of a time delay between theremoval of the electrical stimulus and collection of data toallow the electrical portion of the transient to settle. Thediode junction temperature is estimated through extrapolationand the temperature transient monitored by the change indiode current at a fixed low-level “sensing” voltage, whichpotentially can introduce self-heating of the device. Moreover,this method of thermal characterization is not capable ofproducing temperature maps or accounting for the effects ofnonuniform heating in the device structure.

In this paper, a delay of 1.4 μs was introduced for theelectrical transient measurement to allow sufficient time for theelectrical response of the diode and measurement instrumenta-tion to decay and three different sensing voltages were used tomonitor the thermal response. Extrapolation of these transientsyield similar operating temperatures (27 ◦C ± 1.5 ◦C, Fig. 8)that are in a good agreement with one another and withthe value obtained using thermoreflectance (27.82 ◦C). Theseresults suggest that sufficient time has elapsed and that thetransient response after this delay is dominated by coolingof the device and that the sensing voltage does not introducesignificant self-heating. Interestingly, the electrical transientmeasurement data exhibits two-time constants (of approx-imately 1 and 5 μs), consistent with the results obtainedin [25], while the thermoreflectance data are described witha single-time constant of approximately 2 μs. There areseveral possible explanations for this. The sampling rate of thethermoreflectance technique (0.5 μs) under a 50-μs excitationlimits its capacity to resolve short time constants that could beassociated with rapid thermal processes within the diode. Fur-thermore, thermoreflectance deduces temperature based on theoptical reflectance from the surface metallization of the anodeand finger contact, so the data obtained from this method isnot influenced by the electrical response of the device whichexhibits both electrical and thermal transients. Of particularnote is that the two characterization methods essentially probedifferent regions in the device: thermoreflectance monitors thesurface temperature while the electrical transient measurementestimates the internal temperature of the diode junction andsubstrate.

NADRI et al.: THERMAL CHARACTERIZATION OF QUASI-VERTICAL GaAs SCHOTTKY DIODES INTEGRATED ON SILICON 355

It should be noted that this model utilizes a single fittingparameter, representing the effective thermal conductance ofthe diode mesa epitaxial stack, with a value of 9.5 W/m-K.As the epitaxial stack consists of two n-doped GaAs layers(280 nm and 1 μm) layers, a GaAs/InGaAs interface, anda 90-nm graded InxGa1−xAs layer, it is difficult to predicta priori, the thermal boundary resistance of the interfacesand the thermal resistivity of the thin layers. Using bulkmaterial values for the thermal conductivities (44 W/m-Kfor GaAs, and 5.5 W/m-K for InGaAs), and a measuredvalue (based on time-domain thermal reflectance measure-ments) for the GaAs/InGaAs thermal boundary conductanceof 90 MW/m2 − K, the total thermal resistance of the mesastack Rm (Fig. 3) can be estimated to be 2380 W/m-K. Usingthis value and the expression for thermal resistance [19],the equivalent thermal conductivity for the epitaxial stackis estimated at 24 W/m-K. Note that the values of thermalconductivities for thin films are typically significantly smallerthan their corresponding bulk values (due to size effectsand doping) [35], the thermal conductivity of the mesa(9.5 W/m-K) for the finite-element model is reasonable.

ACKNOWLEDGMENT

The authors would like to thank Dr. N. Alijabbari forhis input on diode fabrication, as well as D. Kendig fromMicrosanj LLC for his help in setting up the thermoreflectancemeasurement. They would also like to thank N. Buonamicoand J. Schuch from Keysight Technologies, Inc. for theirassistance with the electrical transient measurement.

REFERENCES

[1] C. G. Pérez-Moreno, J. Grajal, C. Viegas, H. Liu, J. Powell, andB. Alderman, “Thermal analysis of high-power millimeter-wave Schot-tky diode frequency multipliers,” in Proc. Global Symp. Millim. Waves(GSMM) ESA Workshop Millimetre-Wave Technol. Appl., Espoo, Fin-land, Jun. 2016, pp. 1–4, doi: 10.1109/GSMM.2016.7500307.

[2] S. Nadri et al., “Steady-state thermal analysis of an integrated 160 GHzbalanced quadrupler based on quasi-vertical Schottky diodes,” in Proc.40th Int. Conf. Infr., Millim., Terahertz Waves (IRMMW-THz), HongKong, Aug. 2015, pp. 1–2, doi: 10.1109/IRMMW-THz.2015.7327482.

[3] A. Maestrini et al., “Schottky diode-based terahertz frequency multipli-ers and mixers,” Comp. Rendus Physique, vol. 11, nos. 7–8, pp. 480–495,Aug./Oct. 2010, doi: 10.1016/j.crhy.2010.05.002.

[4] F. Temcamani, J.-B. Fonder, O. Latry, and C. Duperrier, “Electrical andphysical analysis of thermal degradations of AlGaN/GaN HEMT underradar-type operating life,” IEEE Trans. Microw. Theory Techn., vol. 64,no. 3, pp. 756–766, Mar. 2016, doi: 10.1109/TMTT.2016.2519342.

[5] J. Stake et al., “Effects of self-heating on planar heterostructure bar-rier varactor diodes,” IEEE Trans. Electron Devices, vol. 45, no. 11,pp. 2298–2303, Nov. 1998.

[6] C. Lee et al., “Diamond heat-spreaders for Submillimeter-wave GaAsSchottky diode frequency multipliers,” in Proc. 20th Int. Symp. SpaceTerahertz Technol., 2009, pp. 43–46.

[7] S. Adachi, GaAs and Related Materials: Bulk Semiconducting andSuperlattice Properties. Singapore: World Scientific, 1994.

[8] W. L. Bishop, E. R. Meiburg, R. J. Mattauch, T. W. Crowe, andL. Poli, “A micron-thickness, planar Schottky diode chip for terahertzapplications with theoretical minimum parasitic capacitance,” in IEEEInt. Dig. Microw. Symp., vol. 3, May 1990, pp. 1305–1308.

[9] I. Mehdi, M. Mazed, R. Dengler, A. Pease, M. Natzic, andP. H. Siegel, “Planar GaAs Schottky diodes integrated with quartzsubstrate circuitry for waveguide subharmonic mixers at 215 GHz,”in IEEE MTT-S Int. Microw. Symp. Dig., vol. 2, May 1994,pp. 779–782, doi: 10.1109/MWSYM.1994.335240.

[10] P. H. Siegel, R. P. Smith, M. C. Graidis, and S. C. Martin,“A 2.5 THz GaAs monolithic membrane-diode mixer,” IEEE Trans.Microw. Theory Techn., vol. 47, no. 5, pp. 596–604, May 1999,doi: 10.1109/22.763161.

[11] E. Schlecht et al., “200, 400 and 800 GHz Schottky diode ‘sub-strateless’ multipliers: Design and results,” in IEEE MTT-S Int.Microw. Symp. Dig., Phoenix, AZ, USA, May 2001, pp. 1649–1652,doi: 10.1109/MWSYM.2001.967221.

[12] N. Alijabbari, M. F. Bauwens, and R. M. Weikle, “Design and characteri-zation of integrated submillimeter-wave quasi-vertical Schottky diodes,”IEEE Trans. THz Sci. Technol., vol. 5, no. 1, pp. 73–80, Jan. 2015,doi: 10.1109/TTHZ.2014.2361434.

[13] N. Alijabbari, M. F. Bauwens, and R. M. Weikle, “160 GHz balancedfrequency quadruplers based on quasi-vertical Schottky varactors inte-grated on micromachined silicon,” IEEE Trans. THz Sci. Technol., vol. 4,no. 6, pp. 678–685, Nov. 2014, doi: 10.1109/TTHZ.2014.2360983.

[14] L. Xie et al., “An epitaxy transfer process for heterogeneous integrationof submillimeter-wave GaAs Schottky diodes on silicon using SU-8,”IEEE Electron Device Lett., vol. 38, no. 11, pp. 1516–1519, Nov. 2017,doi: 10.1109/LED.2017.2756920.

[15] S. Nadri et al., “A 160 GHz frequency Quadrupler based onheterogeneous integration of GaAs Schottky diodes onto siliconusing SU-8 for epitaxy transfer,” in IEEE MTT-S Int. Microw.Symp. Dig., Philadelphia, PA, USA, Jun. 2018, pp. 769–772,doi: 10.1109/MWSYM.2018.8439536.

[16] A.-Y. Tang et al., “Steady-state and transient thermal analysis of high-power planar Schottky Diodes,” in Proc. 22nd Int. Symp. Space TerahertzTechnol., Tucson, AZ, USA, Apr. 2011, pp. 26–28.

[17] M. A. Saber, “Thermal characterization of THz planar Schottky diodesusing simulations,” M.Sc. thesis, School Elect. Eng., Dept. Radio Sci.Eng., Aalto Univ., Aalto, Finland, 2012.

[18] J. W. Sofia, “Analysis of thermal transient data with synthesized dynamicmodels for semiconductor devices,” IEEE Trans. Compon., Packag.,Manuf. Technol. A, vol. 18, no. 1, pp. 39–47, Mar. 1995.

[19] A. F. Robertson and D. Gross, “An electrical-analog method for transientheat-flow analysis,” J. Res. Nat. Bureau Standard, vol. 61, no. 2,pp. 105–115, 1958.

[20] T. Zhan, Y. Xu, M. Goto, Y. Tanaka, and M. Sasaki, “Thermal boundaryresistance at Au/Ge/Ge and Au/Si/Ge interfaces,” RSC Adv., vol. 5,pp. 49703–49707, May 2015, doi: 10.1039/C5RA04412J.

[21] ANSYS Mechanical, ANSYS, Canonsburg, PA, USA, 2018.[22] K. M. Freedy, A. Giri, B. M. Foley, M. R. Barone, P. E. Hopkins, and

S. McDonnell, “Titanium contacts to graphene: Process-induced vari-ability in electronic and thermal transport,” Nanotechnology, vol. 29,no. 14, p. 145201, Feb. 2018, doi: 10.1088/1361-6528/aaaacd.

[23] T. Kiuru, J. Mallat, A. V. Raisanen, and T. Narhi, “Schottkydiode series resistance and thermal resistance extraction FromS-parameter and temperature controlled I–V measurements,” IEEE Trans.Microw. Theory Techn., vol. 59, no. 8, pp. 2108–2116, Aug. 2011,doi: 10.1109/TMTT.2011.2146268.

[24] S. Khanal et al., “Characterisation of THz Schottky diodes for MetOp-SG instruments,” in Proc. 26th Int. Symp. Space Terahertz Technol.,Cambridge, MA, USA, Mar. 2015, pp. 16–18.

[25] S. Khanal et al., “Thermal characterization of THz Schottky diodes usingtransient current measurements,” IEEE Trans. THz Sci. Technol., vol. 4,no. 2, pp. 267–276, Mar. 2014, doi: 10.1109/TTHZ.2014.2303982.

[26] D. L. Blackburn, “Temperature measurements of semiconductordevices—A review,” in Proc. 20th Annu. IEEE Semicond.Therm. Meas. Manage. Symp., Mar. 2004, pp. 70–80, doi:10.1109/STHERM.2004.1291304.

[27] D. Kendig, K. Yazawa, and A. Shakouri, “Hyperspectral thermore-flectance imaging for power devices,” in Proc. 33rd Therm. Meas.,Model. Manage. Symp. (SEMI-THERM), Mar. 2017, pp. 204–207, doi:10.1109/SEMI-THERM.2017.7896931.

[28] B. Vermeersch, J.-H. Bahk, J. Christofferson, and A. Shakouri, “Ther-moreflectance imaging of sub 100ns pulsed cooling in high-speed ther-moelectric microcoolers,” J. Appl. Phys, vol. 113, p. 104502, Feb. 2013,doi: 10.1063/1.4794166.

[29] A. Shakouri et al., “Stable thermoreflectance thermal imagingmicroscopy with piezoelectric position control,” in Proc. 32ndTherm. Meas., Modeling Manage. Symp. (SEMI-THERM), Mar. 2016,pp. 128–132, doi: 10.1109/SEMI-THERM.2016.7458456.

[30] D. Kendig, K. Yazawa, and A. Shakouri, “High resolution thermalcharacterization of a GaAs MMIC,” in Proc. IEEE Radio Freq. Integr.Circuits Symp. (RFIC), Phoenix, AZ, USA, May 2015, pp. 51–54,doi: 10.1109/RFIC.2015.7337702.

http://dx.doi.org/10.1109/GSMM.2016.7500307http://dx.doi.org/10.1109/IRMMW-THz.2015.7327482http://dx.doi.org/10.1016/j.crhy.2010.05.002http://dx.doi.org/10.1109/TMTT.2016.2519342http://dx.doi.org/10.1109/MWSYM.1994.335240http://dx.doi.org/10.1109/22.763161http://dx.doi.org/10.1109/MWSYM.2001.967221http://dx.doi.org/10.1109/TTHZ.2014.2361434http://dx.doi.org/10.1109/TTHZ.2014.2360983http://dx.doi.org/10.1109/LED.2017.2756920http://dx.doi.org/10.1109/MWSYM.2018.8439536http://dx.doi.org/10.1039/C5RA04412Jhttp://dx.doi.org/10.1088/1361-6528/aaaacdhttp://dx.doi.org/10.1109/TMTT.2011.2146268http://dx.doi.org/10.1109/TTHZ.2014.2303982http://dx.doi.org/10.1109/STHERM.2004.1291304http://dx.doi.org/10.1109/SEMI-THERM.2017.7896931http://dx.doi.org/10.1063/1.4794166http://dx.doi.org/10.1109/SEMI-THERM.2016.7458456http://dx.doi.org/10.1109/RFIC.2015.7337702

356 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 66, NO. 1, JANUARY 2019

[31] P. L. Komarov, M. G. Burzo, and P. E. Raad, “A thermoreflectance ther-mography system for measuring the transient surface temperature fieldof activated electronic devices,” in Proc. 22nd Annu. IEEE Semicond.Therm. Meas. Manage. Symp., Mar. 2006, pp. 199–203.

[32] Microsanj NT210A, Microsanj LLC, Santa Clara, CA, USA.[33] K. Maize, “High resolution thermoreflectance imaging of power transis-

tors and nanoscale percolation networks,” Ph.D. dissertation, UC SantaCruz, Santa Cruz, CA, USA, 2014.

[34] S. M. Sze and K. K. Ng, Physics of Semiconductor Devices. Hoboken,NJ, USA: Wiley, 2007.

[35] C. Jeong, S. Datta, and M. Lundstrom, “Thermal conductivity of bulkand thin-film silicon: A Landauer approach,” J. Appl. Phys. vol. 111,p. 093708, Mar. 2012, doi: 10.1063/1.4710993.

Souheil Nadri (S’13) received the B.S. degreein electrical engineering from the University ofVirginia, Charlottesville, VA, USA, in 2012, andthe Ph.D. degree with a focus on submillimeterwave device fabrication, modeling, and circuitsfrom the University of Virginia.

Dr. Nadri was a recipient of the IEEE MTT-SGraduate Fellowship Award in 2017.

Christopher M. Moore (S’16) received the B.S. degree in electricalengineering from the University of Virgnia, Charlottesville, VA, USA,where he is currently pursuing the Ph.D. degree in electrical engineering,with a focus on submillimeter electronics and metrology.

Noah D. Sauber, photograph and biography not available at the time ofpublication.

Linli Xie (S’10) received the B.S. and M.S.degrees in electrical engineering from the Uni-versity of Electronic Science and Technol-ogy of China, Chengdu, China, in 2008 and2011, respectively. He is currently pursuing thePh.D. degree with the University of Virginia,Charlottesville, VA, USA, with a focus onsubmillimeter-wave electronics.

Michael E. Cyberey (M’04) received thePh.D. degree from the University of Virginia,Charlottesville, VA, USA, in 2014.

He is currently a Principal Scientist withthe University of Virginia. His currentresearch interests include quantum-limitedsuperconducting-insulating-superconductingterahertz mixers, kinetic inductance detectors,and traveling-wave kinetic inductance parametricamplifiers.

John T. Gaskins received the Ph.D. degree inmechanical and aerospace engineering from theUniversity of Virginia, Charlottesville, VA, USA,in 2013.

He is currently a Senior Scientist with theMechanical and Aerospace Engineering Depart-ment, University of Virginia, where he is involvedin nanoscale thermal transport.

Arthur W. Lichtenberger (SM’18) received thePh.D. degree in electrical engineering from theUniversity of Virginia, Charlottesville, VA, USA,in 1987.

He is currently a Professor of electrical engi-neering with the University of Virginia, wherehe is involved in superconducting materials anddevices.

N. Scott Barker, photograph and biography not available at the time ofpublication.

Patrick E. Hopkins is a Professor with theDepartment of Mechanical and Aerospace Engi-neering, University of Virginia, Charlottesville,VA, USA. His current research interests includeheat transport mechanisms in solids, liquids, andgases from nano-to-macro length scales.

Mona Zebarjadi is currently an Assistant Profes-sor with the Electrical Engineering and MaterialsScience and Engineering Department, Universityof Virginia, Charlottesville, VA, USA. Her currentresearch interests include electron and phonontransport in thermoelectric and thermionic mate-rials and devices with a focus on 2-D structures.

Robert M. Weikle, II (S’90–M’91–SM’05–F’18)received the Ph.D. degree in electrical engineer-ing from the California Institute of Technology,Pasadena, CA, USA, in 1992.

He is currently a Professor of electricalengineering with the University of Virginia,Charlottesville, VA, USA, where he is involved insubmillimeter electronics and metrology.

http://dx.doi.org/10.1063/1.4710993

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