applied sciences Article
Thermal Modeling of the GaN-based Gunn Diode at Terahertz Frequencies Ying Wang 1 , Jinping Ao 2, *, Shibin Liu 1 and Yue Hao 2 1 2
*
School of Electronic Information, Northwestern Polytechnical University, Xi’an 710072, China;
[email protected] (Y.W.);
[email protected] (S.L.) The State Key Discipline Laboratory of Wide Band Gap Semiconductor Technology, School of Microelectronics, Xidian University, Xi’an 710071, China;
[email protected] Correspondence:
[email protected]; Tel.: +86-029-88491212
Received: 14 November 2018; Accepted: 17 December 2018; Published: 26 December 2018
Featured Application: This manuscript provides a simulation study on the self-heating effect of the GaN-based terahertz Gunn diode. It would potentially give some guidance to the design of the Gunn diode and other terahertz oscillators. The method in this manuscript can be also used to study the self-heating effect of other semiconductor devices. Abstract: In this paper, a comprehensive evaluation of thermal behavior of the GaN vertical n+ -n− -n-n+ Gunn diode have been carried out through simulation method. We explore the complex effects of various parameters on the device thermal performance through a microscopic analysis of electron movements. These parameters include operation bias, doping level, and length of the active region. The increase of these parameters aggravates the self-heating effect and degrades the electron domains, which therefore reduces the overall performance output of the diode. However, appropriate increase of the doping level of active region makes the lattice heat distribute more uniformly and improves the device performance. For the first time, we propose the transition domain, which is in between the dipole domain and accumulation layer, and stands for the degradation of the electron domain. We have also demonstrated that dual domains occur in the device with longer active region length and higher doping level under EB (Energy balance) model, which enhances the harmonics component. Electric and thermal behaviors analysis of GaN vertical Gunn diode makes it possible to optimize the device. Keywords: GaN Gunn diode; terahertz oscillator; thermal modelling; self-heating effect; III–V semiconductor devices
1. Introduction As one of the excellent candidates for terahertz radiation source, Gunn diodes have attracted much attention [1–8]. Many recent researches demonstrate that the negative-differential-resistance (NDR) based GaN devices possess outstanding power performance at terahertz frequencies due to its unique electronic properties such as large band gap, high breakdown electric field, high electron drift velocity, and large NDR threshold voltage. Although theoretical works predict Gunn oscillations in the THz range in GaN diode [4–7], experimental demonstrations of oscillations have not been achieved due to the technological bottleneck on GaN epitaxial growth and device fabrication. Besides, GaN material would face a serious self-heating problem when it is used for NDR device, because the threshold electric-field for NDR effect is almost 50 times larger than the value of GaAs material. For the Gunn diode, self-heating may trigger the weakening of the NDR effect and even the permanent failure of diode [8–11]. As far as we know, there are many theoretical studies on Gunn diode recent Appl. Sci. 2019, 9, 75; doi:10.3390/app9010075
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years, but without considering the self-heating effect. Some conclusions derived by these studies may not stand when taking the self-heating effect into consideration, particularly when the operation frequency approaches the terahertz regime. It is imperative to thoroughly investigate the relation between the thermal and electrical properties of terahertz Gunn diode in order to optimize the structure of the GaN Gunn diode and prevent or minimize the joule heating. There are great limitations to study the device thermal performance on the experimental method. Firstly, as we mention above, the fabrication and measurement of GaN Gunn diode are still very difficult because of bottlenecks on GaN epitaxial growth and device fabrication and the serious self-heating problem. Secondly, the self-heating effect deteriorates the output characteristics of the Gunn diode by affecting the motion of the electrons. However, it is difficult to provide a microscopic analysis on electron movements (especially the electron domain movements) by experimental method. Therefore, we choose the physical-based modeling and simulation method to achieve accurate device thermal management, which would guide the experiment research in turn. It is of difficulty to clarify the thermal effect on the electron domain in such a short transit region of Gunn diode at such a high electric field by means of traditional device transport theory. In this work, we use the energy balance transport model to explore the self-heating effect on characteristics of GaN vertical Gunn diode by means of a 2-D device simulation platform. The papers published on Gunn diode recent years have been mainly concentrated on the lateral high electron mobility transistor (HEMT)-like Gunn diode, due to its advantages over vertical ones [12–14]. However, the lateral structure still face reliability and integration challenges. Compared with the lateral diode, the vertical one also has its advantages, such as easier package, higher breakdown voltage, and so on [15–17]. Furthermore, the dc-to-ac dispersion induced by the surface states in lateral diode would be mitigated in the vertical one. Therefore, study on vertical Gunn diode is also needed. In this paper, we analyze the effect of the operation bias, the doping level and length of the active region on the performance and heating generation of the diode in detail. The geometry of the vertical diodes and physical model are described in Section 2, results and discussions are given in Section 3, and conclusions are given in Section 4. In order to better understand the thermal and electrical properties of GaN Gunn diode, two transport models, the non-isothermal-energy-balance model (NEB) and the energy-balance model (EB) are compared alternately in the simulation of each device sample. 2. Method of Analysis and Physical Models Compared with the drift-diffusion (DD) model, the EB model is more accurate for spatiotemporal domain and chaos in the short channel. This is because the EB model includes non-localized carrier transport phenomena, such as the velocity overshoot and the non-local impact ionization which are neglected by the conventional DD model. Therefore, the EB model is more suitable for the transient simulation of terahertz devices and is employed in this paper. Indeed, the non-local transport phenomena can be modeled by using Monte Carlo method or using higher order moments of the Boltzmann transport equation, though huge computation times are required by these approaches. In this paper, higher order solution to the general Boltzman transport equation is solved based on the EB model at the Atlas simulation platform, which consists of an additional coupling of the current density to the carrier’ temperature, or energy [18]. MODELS statement is the important part in the device-simulation code, where the physical models of the device is specified. In the simulation code of Gunn diode in Atlas, the energy balance model is selected by specifying the ‘HCTE’ command in the MODELS statement to enable the energy transport model. The energy relaxation time τε is defined as 150 fs based on [4,19]. Meanwhile, the self-heating simulations are incorporated in the GaN Gunn diode structures using GIGA module of Atlas to account for lattice heat flow and general thermal environments. GIGA module accounts for the dependence of material and transport parameters on the lattice temperature. For simulation of self-heating effects, it adds the heat flow equation to the primary equations that are solved by Atlas. The heat flow equation has the following expression:
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∂T C = ∇ κ∇T + H ∂t
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(1)
∂TL volume, κ is the thermal conductivity, H is the heat where C is the heat capacitance per Cunit = ∇(κ∇TL ) + H (1) ∂t generation, and TL is the local lattice temperature. where is thesimulation, heat capacitance per unit volume, κ is the H is the heat generation, InCour the thermal conductivity is thermal set as conductivity, a temperature-dependent thermal α and TL is the local lattice temperature. conductivity: κ = κ300 /(T/300) , where κ300 is the thermal conductivity at the temperature of 300 K and In our simulation, the thermalcoefficient conductivity is set a temperature-dependent α is the temperature dependence [20]. Foras GaN, κ300 is set equal to 1.6thermal W/cm·Kconductivity: and α = 1.4 α , where κ 3 κ = κ /(T/300) is the thermal conductivity at the temperature of 300 K and α isand the 300 heat capacitances C 300are 3.0135 J/cm /K for GaN. All the interfaces between the diode [20]. The temperature dependence [20]. For GaN, κ300 is set equal 1.6 W/cm ·K and = 1.4 [20]. external surroundings are coefficient set to be adiabatic boundary conditions. Into order to simplify theαalgorithm 3 /K for GaN. All the interfaces between the diode and external The heat capacitances C are 3.0135 J/cm and solve the non-convergence problem, the heat transport from the metal contact to external surroundings are set included to be adiabatic conditions. In order to simplify algorithmofand solve surroundings is not in ourboundary simulations, a common practice in the the simulation thermal the non-convergence the heat transport fromtemperature the metal contact surroundings is effect as described in problem, [21–23]. The LAT.TEMP lattice modeltoisexternal added to the MODELS not included in our simulations, a common practice in the simulation of thermal effect as described statement to include heat flow. We have used a non-isothermal energy balance (NEB) model by in [21–23]. both The LAT.TEMP temperature model added to thestatement MODELS to statement to include specifying HCTE. andlattice LAT.TEMP parameters inisthe MODELS solve both energy heat flow. We have and usedheat a non-isothermal energy (NEB) is model by specifying both HCTE. and balance equations flow equations. Thebalance NEB model an extension of stratton’s energy LAT.TEMP parameters in the MODELS statement to solve both energy balance equations and heat flow balance model for the case of nonuniform lattice temperature, which is a set of six partial differential equations. for Theelectrostatic NEB model ispotential, an extension of stratton’s energy balance modelelectron for the case nonuniform equations electron and hole concentrations, andofhole carrier lattice temperature, which is a set of six partial differential equations for electrostatic potential, electron tempertures, and lattice temperature [18]. For the impact ionization model, we adopt Toyabe impact and hole concentrations, electron andwhen hole the carrier tempertures, and lattice temperature [18]. For the ionization model, which is available energy balance transport model is applied [18,24]. A impact ionization model, we isadopt Toyabebalance impact length ionization available when the key parameter of the model the energy LRELmodel, , whichwhich can beiscalculated by LREL = energy balance transport model is applied [18,24]. A key parameter of the model is the energy balance υsat×τε, where υsat are the saturation velocities for electrons, and τε corresponds to the energy length LREL , which can be calculated by LREL = υsat × τε , where υsat are the saturation velocities for relaxation time. + structural GaN Gunn didoes, where a electrons, andpaper, τε corresponds to the energy relaxation time. In this we put an emphasis on n+-n--n-n + -n− -n-n+ structural GaN Gunn didoes, where a In this paper, we put an emphasis on n notch-doped n region adjacent to the cathode of diode aims to create a high electric field zone so as notch-doped n− onset regionofadjacent the cathode diode aims to create a high fieldofzone to promote the electrontodomain in theofcathode. Figure 1 gives the electric schematic the so as to promote the onset of electron domain in the cathode. Figure 1 gives the schematic of the strucuture of the diode we study. As described in Figure 1, we propose a fixed length (Lnotch) of 250 16 −3 strucuture of the diode we study. As described in Figure 1, we propose a fixed length (L ) of 250 nm nm and a fixed doping concentration (Nnotch) of 5 × 10 cm for the notched layer. Thenotch highly doped −3 for the notched layer. The highly doped + ohmic a fixed doping concentration of 5 ×length 1016 cm nand contact region (n+ layer)(N have of 100 nm. The length of transit region (Lac) notcha) fixed + layer) have a fixed length of 100 nm. The length of transit17region n+ ohmic contact region ranges from 0.8 μm to 1.4(nμm, and its doping concentration (Nac) ranges from 1.5 × 10 cm−3 to(L4ac×) 17 cm−3 to 4 × 17 −3 17 cm −3, and ranges 0.8 µmspeciously to 1.4 µm, and its doping from 1.5 the × 10operation ac ) ranges cm from . Without speaking, Lac =concentration 0.8 μm, Nac (N = 1.5×10 bias 10 17 − 3 17 − 3 10 cm Vdc. =Without speaking, Lac =to0.8 µm, Nan = 1.5 × 10 cm filed , and bias ac average voltage 50 V. Inspeciously the simulation, in order sustain electric in the the operation transit region voltage V = 50 V. In the simulation, in order to sustain an average electric filed in the transit region of Gunn diode, we intentionally change the value of Vdc in proposition to Lac, for instance, if Lacof = dc Gunn diode, we intentionally of Vdc to Lac ,toforimprove instance,the if Lcalculation ac = 1.0µm, 1.0μm, then V dc = 62.5 V, andchange if Lac = the 1.4 value μm, then Vdcin=proposition 87.5 V. In order then Vdc =of 62.5 V, and if Lac =simulation, 1.4 µm, thenwe Vdcput = 87.5 V. In order tosinusoidal improve the calculation efficiency efficiency the numerical a single-tone voltage of form Vdc + ofacthe numerical simulation, put aof single-tone sinusoidal voltage of formcircuit Vdc +to Vac sin(2πft)the across V sin(2πft) across the diode we instead embedding it to an RLC resonant calculate RF the diode instead ofoutput embedding circuit to calculate theηRF Frequency) (Radio Frequency) poweritPto RF an andRLC the resonant dc-to-ac conversion efficiency of (Radio the diodes, as the output power and complexity the dc-to-ac conversion efficiencyand η ofeasily the diodes, external circuit adds external circuitPRF adds of the calculation leadsastothethe non-convergence complexity of the calculation and easily leads to the non-convergence problems [25]. problems [25].
−-n-n++ Figure1.1. Schematic Schematicstructure structureof ofnn++-n -n− Figure -n-n structural structuralGaN GaNGunn Gunndidoe. didoe.
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3. Result and Discussion 3. Result and Discussion Figure 2 gives direct current I–V characteristics of the GaN Gunn diode under the EB model 2 givesrespectively. direct currentAI–V characteristics GaN Gunn diode under the EB model and Figure NEB model, serious drop of of thethe saturate current appears when taking and the NEB model, respectively. A serious drop of the saturate current appears when taking the self-heating self-heating problem into consideration in NEB model, which is attributed to the decrease of the problem consideration in NEB model, which is attributed the decrease of the electron velocity electron into velocity in the transit region due to the increasedtolattice temperature. At smaller Vdc, in the transit region due to the increased lattice temperature. At smaller V , however, the differences dc however, the differences in the anode current are almost negligible, because the increment of the in the anode current is aresmall. almostThe negligible, because the the lattice temperature small. lattice temperature heat generation in increment the transitofregion is caused by an isenergy The heat generation the transit region is caused an energy transferring from the electron to the transferring from theinelectron to the lattice, which by is related to inelastic phonon scattering processes lattice, which is related to inelastic phonon scattering processes of the electron. As reported in [26], of the electron. As reported in [26], the scattering processes mainly responsible for the heat the scattering processes mainly responsible for the heat generation are the intra-valley scatterings of generation are the intra-valley scatterings of the electron in the Γ1 and the U valley. The heat the electronoriginated in the Γ1 and thethe U valley. The heat generation originated from the intra-valley generation from intra-valley scattering in the Γ1 valley builds up near thescattering cathode in the Γ1 valley builds up near the cathode side. The electric field peak at the notch layer increases the the side. The electric field peak at the notch layer increases the scattering rate and accelerates scattering to rate and accelerates the electrons to attain to transfer to theasupper U-valley. electrons attain sufficient energy to transfer to sufficient the upperenergy U-valley. Therefore, the electrons Therefore, as the electrons travel towards the anode side, the heat generation originated from travel towards the anode side, the heat generation originated from the intra-valley scattering in the the intra-valley in thebegins U and to other upper valleys to predominate. The variation of lattice U and otherscattering upper valleys predominate. Thebegins variation of lattice temperature throughout temperature throughout transit region can beNEB investigated by using NEB model. Our simulations the transit region can bethe investigated by using model. Our simulations shown that the peak shown that the peak lattice temperature occurs near the notch-doped region where the electric field lattice temperature occurs near the notch-doped region where the electric field has a maximum, has a maximum, approaching 820 K at V = 50 V and 1015 K at V = 60 V, respectively. Therefore, dc Therefore, we suggest using a approaching 820 K at Vdc = 50 V and 1015 dc K at Vdc = 60 V, respectively. we suggest using a pulsed bias operation to reduce the self-heating generation, in consistent with the pulsed bias operation to reduce the self-heating generation, in consistent with the fact that short fact that short bias pulses are normally applied instead of dc biases in order to avoid possible joule in bias pulses are normally applied instead of dc biases in order to avoid possible joule in the the experiments of GaAs Gunn diode HEMT devices [15,27–30]. experiments of GaAs Gunn diode andand HEMT devices [15,27–30].
Figure Simulated direct I–V characteristics GaN diode under NEB Figure 2. 2. Simulated direct I–V characteristics of GaN Gunnof diode underGunn NEB (non-isothermal-energy(non-isothermal-energy-balance model) model model) and EB model. (energy-balance model) model. balance model) model and EB (energy-balance
In the theinstantaneous instantaneoussimulation, simulation, stable oscillations generate when the voltage bias voltage ofGunn GaN stable oscillations generate when the bias of GaN Gunn diode ranges 75 VEB under EBHowever, model. However, stable oscillations only be diode ranges from 50from V to50 75 V V to under model. stable oscillations can only can be obtained obtained at avoltage narrowrange voltage range V of under 50–55 V under NEBwhich model, which attributes to influence of at a narrow of 50–55 NEB model, attributes to influence of thermal thermal generation. both the models, the conversion dc-to-ac conversion η decreases with Vdc, as generation. For bothFor models, dc-to-ac efficiencyefficiency η decreases with Vdc , as shown in shown Figure gives 3, which the η, fosc (oscillation frequency) PRF versus Vdc. Under Figure in 3, which the gives results ofresults η, fosc of (oscillation frequency) and PRFand versus Vdc . Under NEB NEB model, the operation rises 50there to 55isV, is an obvious increase of lattice model, as the as operation voltagevoltage rises from 50 from to 55 V, anthere obvious increase of lattice temperature temperature throughout the especially whole diode, side,in asFigure manifested Figure of 4. throughout the whole diode, nearespecially the anodenear side,the as anode manifested 4. Theinincrease The increase of greatly the electric field the greatly enhances the phonon scatterings of the electrons, which the electric field enhances phonon scatterings of the electrons, which leads to the increase leads the increase of thewith lattice temperature with Vdc , and accordingly the subsequent decrease of of theto lattice temperature Vdc , and accordingly the subsequent decrease of the anode current the current and the conversion efficiency. The serious even heat accumulation even prevents the andanode the conversion efficiency. The serious heat accumulation prevents the formation of stable formation stable oscillation when the biashigher voltagethan becomes 55 V. Atof the50bias voltage of oscillationof when the bias voltage becomes 55 V. higher At the than bias voltage V, we extract 50 we extract the oscillation frequency of around 207.0 GHz and 178.1oscillation GHz from stable the V, oscillation frequency fosc of around 207.0foscGHz and 178.1 GHz from stable currents oscillation currents under EB and NEB model, respectively. We can also find from Figure 3 that fosc
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under NEBunder model, respectively. also increases, find from which Figure can 3 that an Figure uptrend osc shows by showsEB an and uptrend both models as asWe thecan voltage be fexplained explained by 5, shows an uptrend under both models the voltage increases, which can be Figure 5, under both models as the voltage increases, which can be explained by Figure 5, the electric field the electric field profiles derived inside one oscillation period. At the operation voltage of 50 V, the electric field profiles derived inside one oscillation period. At the operation voltage of 50 V, profiles derived at inside onedomain oscillation period. the operation voltage of in 50Figure V, diode at dipole diode operates operates dipole mode underAtEB EB model, as manifested manifested 5a.operates Figure 5b 5b shows diode at dipole domain mode under model, as in Figure 5a. Figure shows domain mode under EB model, as manifested in Figure 5a. Figure 5b shows that under EB model, that under under EB EB model, model, the the electron electron domain domain degrades degrades into into the the mode mode between between dipole dipole domain domain and and that the electron domain degrades into the mode between dipole domain and accumulation domain at accumulation domain at V dc = 75 V, and we call it a transition domain mode for the first time. As accumulation domain at Vdc = 75 V, and we call it a transition domain mode for the first time. As V we 4c calland it a Figure transition mode for time. As compared Figures 4c and 5d, dc = 75 V, and compared Figure 5d,domain we conclude conclude thatthe thefirst joule heating generation accelerates the compared Figure 4c and Figure 5d, we that the joule heating generation accelerates the we conclude that the joule heating generation accelerates the degradation of the domain under NEB degradation of of the the domain domain under under NEB NEB model. model. Only Only transition transition domain domain formed formed under under NEB NEB model model as degradation as model. Only transition domain formed underrises NEB model as Vthe =domain 50 V. When the operation voltage dc V dc = 50 V. When the operation voltage to 55 V, completely degrades to Vdc = 50 V. When the operation voltage rises to 55 V, the domain completely degrades to rises to 55 V, the domain completely degrades to accumulation domain. In theory, the dipole-domain accumulation domain. domain. In In theory, theory, the the dipole-domain dipole-domain mode mode oscillation oscillation is is more more stable stable and and generates generates accumulation mode oscillation iscompared more stable andother generates highermodes RF power compared with other oscillation modes higher RF power with oscillation in the Gunn diodes. As a result, no matter higher RF power compared with other oscillation modes in the Gunn diodes. As a result, no matter in the Gunn diodes. As a result, no matter under EB model or NEB model, the RF output power RF under EB model or NEB model, the RF output power P RF shows a downward trend, although the under EB model or NEB model, the RF output power PRF shows a downward trend, althoughPthe shows a downward trend, although the voltage increases, as shown in Figure 3b The dipole domain voltage increases, increases, as as shown shown in in Figure Figure 3b 3b The The dipole dipole domain domain is is composed composed of of an an excess excess electrons electrons voltage is composed of an excess electrons layer and a depleted electrons layer. However, there is an layer and a depleted electrons layer. However, there is only an excess electrons layer in the the layer and a depleted electrons layer. However, there is only an excess electrons layeronly in excess electronslayer. layer in the accumulation layer. Therefore, dipole-domain mode generatesthan a lower accumulation layer. Therefore, dipole-domain mode generates generates lower frequency than the accumulation Therefore, dipole-domain mode aa lower frequency the frequency than the accumulation-layer mode does. As a conclusion, the degradation of the domain accumulation-layer mode mode does. does. As As aa conclusion, conclusion, the the degradation degradation of of the the domain domain under under both both EB EB and and accumulation-layer under both EB and NEB modelin a decrease in conversion efficiency and RF power andin a NEB model model incurs decrease inincurs conversion efficiency and RF RF output output power andoutput slight increase in NEB incurs aa decrease conversion efficiency and power and aa slight increase slight increase in frequency. frequency. frequency.
Figure 3. 3. (a) (a) Simulation Simulation results results of ofthe theoscillation oscillationfrequency frequencyfffosc osc and dc-to-ac conversion efficiency η η Figure 3. (a) Simulation results of the oscillation frequency Figure osc and dc-to-ac conversion efficiency η versus the anode voltage V dc and (b) RF output power P RF versus V dc under EB and NEB models. versus the the anode anode voltage voltage VVdc dc and (b) RF output power PRF RF versus versus versus V Vdcdcunder underEB EBand andNEB NEBmodels. models.
Figure 4. 4. Lattice Lattice temperature temperature profiles profiles at at different different bias bias voltages voltagesunder underNEB NEBmodel. model. Figure profiles at different bias voltages under NEB model.
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Figure 5. 5. Electric field profiles derived inside one oscillation circle at the same same time time steps, steps, when when the the Figure dc = dc dc = 50 diode is is applied applied at at different different voltage: voltage: (a) (a) V Vdc diode =50 50VVand and(b) (b)VVdcdc= =7575VVunder underEBEBmodel; model;and and(c)(c)VV = V and (d)(d) VdcV=dc55=V55under NEB model. 50 V and V under NEB model.
The doping concentration of transitofregion Nacregion on the output The influence influenceof different of different doping concentration transit Nac oncharacteristics the output and physical mechanism of GaN Gunn diode is also investigated. We get the direct I–V and the global characteristics and physical mechanism of GaN Gunn diode is also investigated. We get the direct I– 17 17 − 3 temperature characteristics for N 10 to 4from × 101.5cm and NEB ac ranging from V and the global temperature characteristics for1.5 Nac×ranging × 1017under to 4 × EB 1017model cm−3 under EB model, as shown in Figure 6. Under EB model, the saturated current characterizing generation model and NEB model, as shown in Figure 6. Under EB model, the saturated currentthe characterizing of NDR oscillation exhibits a nearly uniform increase with a rising N . However the increase of ac a rising Nac. However the the generation of NDR oscillation exhibits a nearly uniform increase with the saturated current obtained under NEB model smaller. At higher doping levels,doping anode increase of the saturated current obtained under becomes NEB model becomes smaller. At higher current cannot become saturated as the voltage increases under NEB model, particularly, it presents levels, anode current cannot become saturated as the voltage increases under NEB model, 17 cm−3 . This is because −3. This obvious upward trend when Nacupward is larger thanwhen 2 × 10 the increase of the particularly, it presents obvious trend Nac is larger than 2 × 1017 cm is because lattice temperature with Ntemperature the negative resistance effect. In Figure 6,effect. the global lattice ac degrades with the increase of the lattice Nac degrades the negative resistance In Figure 6, 17 cm−3 . Our simulation 17 −3 temperature can approach 1080 K when N = 2.5 × 10 also presents the the global lattice temperature can approachac1080 K when Nac = 2.5 × 10 cm . Our simulation also −3 17 upper limit leveldoping of Nac level for stable is 3 × 1017iscm model and 2.5and × presents thedoping upper limit of Nacoscillations for stable oscillations 3 × 10under cm−3EB under EB model 17 − 3 17 −3 10 cm under NEB model. Figure 7 shows the influence of N on dc-to-ac conversion efficiency, ac 2.5 × 10 cm under NEB model. Figure 7 shows the influence of Nac on dc-to-ac conversion oscillation RF output Under EB model, η decreases doping level increases, efficiency, frequency oscillation and frequency and power. RF output power. Under EB model, ηas decreases as doping level 17 − 3 however, is an obvious of ηincrease under NEB Nac model of 2 × 10 cmof 2. ×The increases,there however, there is increase an obvious of ηmodel underatNEB at Nac 1017same cm−3trend . The also on the curves PRFcurves -Nac asofshown 7b.inThe increase of N larger ac results sameappears trend also appears onofthe PRF-NacinasFigure shown Figure 7b. The increase of in Naca results proportion of Nac /Nnotch we set an Nnotch in thisin paper. The notch layer layer near in a larger proportion of Nbecause ac/Nnotch because weunchanged set an unchanged Nnotch this paper. The notch cathode side aims modulate the electric field of theof cathode regionregion and used a nucleation point near cathode side to aims to modulate the electric field the cathode andas used as a nucleation for thefor electron domaindomain to reduce dead the zonedead length. However, a larger proportion Nac /Nnotch point the electron tothe reduce zone length. However, a larger of proportion of leads larger electric fieldelectric and parasitic resistance at resistance the notch layer asnotch well aslayer a smaller electric field in Nac/Nanotch leads a larger field and parasitic at the as well as a smaller the activefield region. Thisactive is whyregion. the dipole a smaller distancewithin and the electric in the Thisdomain is whygets themature dipolewithin domain gets mature a domain smaller size becomes smaller when N increases, which results in a decrease of η and P . In addition, when distance and the domain sizeacbecomes smaller when Nac increases, which results of η RF in a decrease we self-heating effect lattice distribution plays an andtake PRF.the In addition, when we into takeconsideration, the self-heatingthe effect intotemperature consideration, the latticealso temperature important role on plays the output characteristic of the temperaure within thetemperaure device is a distribution also an important role on the device. output The characteristic of profile the device. The reflection of thethe distribution the jouleofheating, which in of turn the electric field profile within device is aof reflection the distribution thereflects joule heating, which in distribution. turn reflects The temprature and heating where theand fieldheating is a maximum. shown Figure the peak electric field distribution. Theoccurs peak at temprature occurs atAs where thein field is 8, a the electric field inside the notch layer enhances at larger N /N , thus the lattice temperature peak maximum. As shown in Figure 8, the electric field inside the ac notch notchlayer enhances at larger Nac/Nnotch, gradually transfers from the anode side to thetransfers notch layer. thus the lattice temperature peak gradually fromThe thelattice anodetemperature side to the distributes notch layer.most The 17 −3 −3 the lattice uniformly at the doping level ofmost 2 × uniformly 1017 cm−3 .atAtthe thedoping dopinglevel levelofof22.5 ×1710cm cm lattice temperature distributes × 10 . At ,the doping temperature transfers to the notch layer. This is why we get η and This PRF at level of 2.5 ×peak 1017 completely cm−3, the lattice temperature peak completely transfers tothe thehighest notch layer. is 17 cm−3 and no oscillation can be obtained −3 and the 2 × 10η at the doping level higher than whydoping we getlevel the of highest and PRF at the doping level of 2 × 1017 cm no oscillation can be −3 . 2.5 × 1017atcm obtained the doping level higher than 2.5 × 1017 cm−3.
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Figure 6. I–V characteristics of GaN Gunn diode under NEB model and EB model, and the global Figure 6. 6. I–V characteristics NEB modeland andEB EBmodel, model,and and the global Figure characteristics GaN Gunn diode under the global Figure 6. I–V I–V characteristicsofof ofGaN GaNGunn Gunndiode diode under under NEB NEB model model and EB model, and the global lattice temperature at different N acunder under NEB lattice temperature atat different NN lattice temperature different NEB acac lattice temperature at different N ac under underNEB NEBmodel. model.
Figure 7. (a) Simulation results of the oscillation frequency osc and and dc-to-ac conversion efficiency ηη η Figure Simulation results the oscillation frequency osc efficiency η Figure 7. 7. (a) Simulation results anddc-to-ac dc-to-acconversion conversion efficiency Figure 7. (a) (a) Simulation resultsofof ofthe theoscillation oscillationfrequency frequency fffosc osc and dc-to-ac conversion efficiency ac and (b) RF (Radio Frequency) output power P RF versus N ac under EB and versus the doping level N and (b) RF (Radio Frequency) output power RF EB and versus doping level N and(b) (b)RF RF(Radio (RadioFrequency) Frequency)output outputpower power PPRF RF versus versus N under EBEB and versus the doping level Nacac versus thethe doping level Nac and versusN Nacacacunder under and NEB models. NEB models. NEB models. NEB models.
Figure 8. Lattice temperature profiles in the active region at different N ac under under NEB NEB model. Figure temperature profiles in the active region model. Figure 8. Lattice Lattice temperatureprofiles profilesin inthe theactive activeregion region at N ac under model. Figure 8. 8. Lattice temperature at different differentN Nac NEB model. ac underNEB
We also investigate the influence of transit region length LLac ac on output performance of GaN also investigate influence of region length L on performance of We also investigate the influence of transit transit region length ac output on output output performance of GaN GaN WeWe also investigate thethe influence of transit region length Lac on performance of GaN Gunn Gunn diode, where L ac changes from 0.8 to 1.4 μm at a step of 0.1 μm in this simulation. Figure Gunn diode, LLacac changes to μm step μm in Gunn diode, where changes from 0.8 toat1.4 1.4 μm at at step ofin0.1 0.1 μm in this this simulation. simulation. Figure diode, where Lacwhere changes from 0.8from to 1.40.8 µm a step ofaa0.1 µmof this simulation. Figure 9 Figure shows 999the shows the influence of LLac ac on dc-to-ac conversion efficiency and oscillation frequency under both EB shows of dc-to-ac and frequency under shows the the influence of L ac on on dc-to-ac conversion conversion efficiency and oscillation oscillation frequency under both EB influence of Linfluence conversion efficiency efficiency and oscillation frequency under both EBboth and EB NEB ac on dc-to-ac models. The dc-to-ac efficiency η and the oscillation frequency fosc decrease as Lac increases under both
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and NEB NEB models. models. The The dc-to-ac dc-to-ac efficiency efficiency ηη and and the the oscillation oscillation frequency frequency ffosc osc decrease decrease as as LLacac increases increases and under both EB and NEB models, as illustrated in Figure 9. It is noteworthy that the oscillation under and NEB models, as illustrated Figure 9. It that is noteworthy that frequency the oscillation EB andboth NEB EB models, as illustrated in Figure 9. It in is noteworthy the oscillation obtained frequency obtained under NEB NEB model becomes larger than than that obtained underLEB EB model when ac frequency under model becomes larger that under model when LL ac under NEBobtained model becomes larger than that obtained under EBobtained model when is larger than 0.9 µm. ac is larger than 0.9 μm. We can explain the phenomenon by using extracted electric field profiles of is larger than 0.9 μm. We can explain the phenomenon by using extracted electric field profiles of We can explain the phenomenon by using extracted electric field profiles of 1.2-µm-long device under 1.2-μm-long device under under EB and and NEB model, model, as shown shown in Figure Figure 10. Gunn Figurediode 10a shows shows thatatthe the 1.2-μm-long EB NEB as in 10. Figure 10a that EB and NEB device model, as shown in Figure 10. Figure 10a shows that the operates dipole Gunn diode operates at dipole domain mode under EB model. Figure 10b indicates that the device Gunn diode operates at dipole under EB model. Figureoperates 10b indicates that the device domain mode under EB model.domain Figure mode 10b indicates that the device at accumulation mode as operates at at accumulation accumulation mode mode as as well well as as the the dead dead zone zone is is enlarged obviously obviously when when we we take take the the operates well as the dead zone is enlarged obviously when we takeenlarged the self-heating effect into consideration self-heating effect effect into consideration consideration under under NEB NEB model. model. The The lattice lattice temperature, temperature, particularly particularly the the self-heating under NEB model.into The lattice temperature, particularly the temperature near the anode side, increases temperature near near the the anode anode side, side, increases increases with with LLacac.. The The dipole dipole domain domain will will become become not not able able to to temperature with Lac . The dipole domain will become not able to sustain at higher lattice temperature, as shown in sustain at higher lattice temperature, as shown in Figure 10b. Based on [9] and [30], in order to allow sustain at higher lattice temperature, as shown in Figure 10b. Based on [9] and [30], in order to allow Figure 10b.domains Based on [9,30], in inthe order to allow the dipole domains forming in thedcGunn diode, design the dipole dipole domains forming in Gunn diode, diode, design design criteria criteria must must be be met: met: (N (Nacac×× LLdc (N ×× L) L)oo≡≡ 33 ×× the forming the Gunn )) >> (N × ≡ criteria must be met: (N L ) > (N × L) 3 × ε × v /qµ (ε: dielectric constant; µ ac constant; o NDR NDR : the dc peak differential peak/qμ /qμNDR NDR (ε: (ε: dielectric dielectric μNDR NDR:: the the peak peak negative negative mobility). The The numerical numerical εε ×× vvpeak constant; μ differential mobility). peak differential mobility). The numerical value fordipole GaN. domains Therefore, mostto references believe valuenegative is for for GaN. GaN. Therefore, most references references believe that is the prefer form at at the the value is Therefore, most believe that the dipole domains prefer to form that the dipole domains prefer to form at the longer transit region with higher doping level, which longer transit transit region region with with higher higher doping doping level, level, which which may may only only hold hold in in ideal ideal situation situation without without longer may only hold in ideal situation without considering the joule heating. In our simulation, we draw considering the the joule joule heating. heating. In In our our simulation, simulation, we we draw draw an an absolutely absolutely opposite opposite conclusion: conclusion: the the an considering absolutely opposite conclusion: the dipole modesmodes easilydue degenerate into accumulation modes dipole domain domain modes easily degenerate degenerate intodomain accumulation modes due to the the self-heating self-heating effect in in the the dipole modes easily into accumulation to effect due to the self-heating effect in the longer channel. A stable oscillation hardly generates under longer channel. A stable oscillation hardly generates under NEB model but there is still oscillation longer channel. A stable oscillation hardly generates under NEB model but there is still oscillationNEB generating underisEB EB model when LLgenerating ac increases increasesunder to 1.4 1.4 μm. μm. model but there still oscillation EB model when Lac increases to 1.4 µm. generating under model when ac to
and dc-to-ac dc-to-ac conversion conversion efficiency efficiency ηη Figure 9. 9. Simulation Simulation results results of the oscillation oscillation frequency frequency ffosc and Figure the Figure 9. Simulation results ofofthe oscillation frequency foscoscand dc-to-ac conversion efficiency η versus versus the active region length L ac under EB and NEB models. versus the region active region Lac under EB NEB and NEB models. the active lengthlength Lac under EB and models.
Figure 10. 10. Electric field profiles the diode diode derived derived inside inside one oneoscillation oscillation circle circleat atthe thesame sametime timesteps, Figure 10. Electric field profiles of of the Figure the diode derived inside one oscillation circle at the same time ac = 1.2 μm, under (a) EB and (b) NEB models. steps, when L when L = 1.2 µm, under (a) EB and (b) NEB models. ac steps, when Lac = 1.2 μm, under (a) EB and (b) NEB models.
If thermal generationis suppressedin the long transit region diode, non-unique dipole If the the thermal thermal generation generation isissuppressed suppressed inin the long transit region diode, non-unique dipole If the the long transit region diode, non-unique dipole domains appear particularly at higher doping level of N ac . By using EB model we have found domains would appear particularly at higher doping level of N . By using EB model we have found ac using EB model we have found domains would appear particularly at higher doping level of Nac. By 17 − 3 17 cm −3, as 17 −3 two dipole domains formed in the diode with L ac of 1.4 μm and N ac of 3 × 10 illustrated in two diodewith withLLacacofof1.4 1.4μm µmand andNN × 10cm cm , as illustrated two dipole dipole domains formed in the diode ac ac ofof 3 ×3 10 , as illustrated in in Figure11a,b. 11a,b.The Thedual-dipole-domain dual-dipole-domainphenomenon phenomenonisis isattributed attributed to two reasons. Firstly, dipole Figure to to two reasons. Firstly, dipole domain Figure 11a,b. The dual-dipole-domain phenomenon attributed two reasons. Firstly, dipole easily generates in the device which has higher Nac × Lac . Secondly, the increase of the Nac /Nnotch enhances the fluctuation of the electric field in the transit region, which promotes the formation of two
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domain easily easily generates generates in in the the device device which which has has higher higher NNacac×× LLacac. . Secondly, Secondly, the the increase increase of of the the domain N ac /N notch enhances the fluctuation of the electric field in the transit region, which promotes the Nac/Nnotch enhances the fluctuation of the electric field in the transit region, which promotes the formation oftwo two dipole domains inside oneoscillation oscillation circle. However, the domain nearthe the notch formation of dipole domains inside one However, the domain notch dipole domains inside one oscillation circle. However,circle. the domain near the notchnear layer differs from layer differsfrom from thedomain. traditional dipoledomain. domain. Normally, the dipoleof domain consists ofan anlayer excess layer differs the traditional dipole Normally, dipole domain consists of excess the traditional dipole Normally, the dipole domainthe consists an excess electrons and a electronselectrons layerand andlayer, depleted electrons layer, but wecannot cannot findelectrons anobvious obvious excess electrons layerside, electrons layer aadepleted electrons but we find an excess electrons layer depleted but we cannotlayer, find an obvious excess layer near the cathode near the cathode side, as shown in Figure 11a. In order to demonstrate it is a dipole domain we near the cathode Figure 11a. In to demonstrate it is a dipole domain we as shown in Figureside, 11a.as In shown order toindemonstrate it isorder a dipole domain we extract electron concentration extract electron concentration and electron velocity profiles at 12.6 ns, as shown in Figure 12a. extract electron concentration velocity profiles at Theoretically, 12.6 ns, as shown in Figure 12a. part and electron velocity profiles atand 12.6electron ns, as shown in Figure 12a. the excess electrons Theoretically, the excess electrons part of the dipole domain forms as the trailing electrons behind Theoretically, the excess electrons part of the dipole domain forms as the trailing electrons behind of the dipole domain forms as the trailing electrons behind the dipole arriving with a higher velocity. thedipole dipolearriving arrivingwith withaahigher highervelocity. velocity. Bythe thesame sametoken, token,the theregion region ofdepleted depletedelectrons electronsalso also the By the same token, the region of depleted By electrons also grows because of electrons ahead of the dipole grows because because electrons electrons ahead ahead of of the the dipole dipole leave leave atat aa higher higher velocity velocity [30]. [30]. The The correspondence correspondence grows leave at a higher velocity [30]. The correspondence between the electron concentration and electron betweenthe theelectron electronconcentration concentrationand andelectron electronvelocity velocityshown shownin inFigure Figure12a 12aexcellently excellentlysupports supports between velocity shown in Figure 12a excellently supports this opinion. The electrons inside the notch layer thisopinion. opinion.The Theelectrons electronsinside insidethe thenotch notchlayer layerexperience experienceaavelocity velocityovershoot, overshoot,as asillustration illustrationin in this experience a velocity overshoot, as illustration in the region 1 of the Figure 12a. So the electrons of the theregion region11of ofthe theFigure Figure12a. 12a.So Sothe theelectrons electronsof ofthe theexcess excesselectrons electronslayer layercomes comesfrom fromthe thenotch notch the excess electronsOne layer comes from the notch layer initially. One onishand, thelower electron concentration layerinitially. initially. onhand, hand,the the electron concentration ofnotch notch layer greatly thanthat thatof ofthe the layer One on electron concentration of layer is greatly lower than ofactive notchchannel; layer is greatly lower than that of the active channel; on the other hand, the excess electrons on the the other other hand, hand, the the excess excess electrons electrons layer layer part part comes comes into into being being immediately immediately active channel; on layer part into being immediately inside the notch layer. Therefore, it results in thelayer. formation inside thecomes notchlayer. layer. Therefore, results inthe the formation ofan an obscureexcess excess electrons layer.At At of inside the notch Therefore, ititresults in formation of obscure electrons an obscure excess At the sameup, time, the of electrons in region 2 speed up, aheadlayer. of which the sametime, time, theelectrons electronslayer. inregion region speed up, ahead ofwhich whichformed formed depleted electrons layer. the same the electrons in 22speed ahead aadepleted electrons formed a depleted electrons layer. Due to the dual-dipole-domain phenomenon inside one oscillation Dueto tothe thedual-dipole-domain dual-dipole-domainphenomenon phenomenoninside insideone oneoscillation oscillationcircle, circle,the theharmonic harmonicfrequency frequencyisis Due circle, the harmonic frequency is greatly enhanced, as shown in Figure 12b where the frequency greatly enhanced, asshown shown inFigure Figure 12bwhere where thefrequency frequency spectrum extracted bymeans means ofthe the greatly enhanced, as in 12b the spectrum isisextracted by of spectrum is extracted by means of algorithm. the fast Fourier transformation (FFT) algorithm. Thefind excellent fast Fourier Fourier transformation (FFT) algorithm. The excellent excellent frequency multiply would find fast transformation (FFT) The frequency multiply would aa promising application in terahertz technology. frequency multiply would find a promising application in terahertz technology. promising application in terahertz technology.
Figure11. 11.Electron Electronconcentration concentration(a) (a) and electric field (b)(b) profiles derived inside oneone oscillation circle Figure and electric field (b) profiles derived inside one oscillation circle Figure Electron concentration (a) and electric field profiles derived inside oscillation circle 1717cm −3−3under 17 − 3 ac==1.4 1.4 μm and N ac==33××10 10 cm under EB model. at the same time step, when L ac μm and N ac EB model. at the same time step, when L at the same time step, when Lac = 1.4 µm and Nac = 3 × 10 cm under EB model.
Figure 12. (a) The relationship of the electron velocity and electron concentration derived inside on oscillation circle at 12.6 ns, when Lac = 1.4 µm, Nac = 3 × 1017 cm−3 ; (b) and its frequency spectrum diagrams.
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4. Conclusion In this paper, we present a numerical analysis on self-heating effect in GaN vertical n+ -n− -n-n+ Gunn diode based on Silvaco-Atlas, by emphasizing the microscopic analysis of the electron domain mode. In order to better understand the thermal and electrical properties of GaN Gunn diode, two models—the non-isothermal energy balance model (NEB) and energy balance model (EB)—are solved and analyzed alternately in the implementation of each sample. Our simulations have demonstrated that self-heating effect degrade the electron domain model and output characteristics of GaN Gunn diode. There is an obvious decrease of the saturation current in the direct I–V characteristics of each sample under NEB model, and peak lattice temperature in the notch region and reaches more than 1015 K at the operation voltage of 60 V. In order to avoid the serious heat generation, pulsed current is suggested instead of direct current. We have also explored the influence of the various parameters, viz. operation bias, the doping level and length of the active region on the heating generation and distribution. The increase of these parameters increases the inelastic phonon scattering processes of the electron, and further enhances the heat generation of the lattice, which weakens the NDR effect and degrades the electron domain as well as the output characteristics. In addition, with self-heating effect taken into consideration, the normal operation range of device is greatly limited, as compared with the ideal situation. We propose the transition domain for the first time, which is in between the dipole domain and accumulation layer, and stands for the degradation of the electron domain. A proper Nac /Nnotch not only makes the notch layer a nucleate layer but also provides a more uniform temperature distribution, which results in higher output characteristics of the device. As demonstrated in our simulation, best performance is obtained in the sample with a doping level of 2 × 1017 cm−3 . Dual-domain phenomenon is formed under EB model in the device with longer active region length and higher Nac /Nnotch , which enhances the harmonic frequency. However, we have not found dual-domain phenomenon under NEB model. The simulation of the structure parameters makes it possible to optimize the device and reduce the self-heating effect. Other engineering approaches to alleviate the heating like using an effective heat-sinking are our future work. Author Contributions: Conceptualization, Y.W. and J.A.; methodology, Y.W.; software, Y.W.; validation, Y.W., J.A. and S.L.; formal analysis, Y.W.; investigation, W.Y.; resources, Y.H.; data curation, Y.W.; writing—original draft preparation, Y.W.; writing—review and editing, S.L., Y.H.; visualization, J.A.; supervision, J.A., Y.H.; project administration, J.A.; funding acquisition, J.A., Y.H. Funding: This work was partially supported by the National Key Research and Development Program (Grant No. 2017 YFB043000) and the National Natural Science Foundation of China (Grant No. 61274092). Acknowledgments: The author Ying Wang thanks the colleagues and her teachers who help her in her research work. Conflicts of Interest: The authors declare no conflict of interest.
References 1.
2.
3. 4. 5.
Maricar, M.I.; Khalid, A.; Dunn, G.; Greedy, S.; Thomas, D.; Cumming, D.R.; Oxley, C.H. An electrical equivalent circuit to simulate the output power of an AlGaAs/GaAs planar gunn diode oscillator. Microw. Opt. Technol. Lett. 2018, 60, 2144. [CrossRef] Glover, J.; Khalid, A.; Cumming, D.; Dunn, G.M.; Kuball, M.; Bajo, M.M.; Oxley, C.H. Thermal profiles within the channel of planar Gunn diodes using micro-particle sensors. IEEE Electron Device Lett. 2017, 1, 99. [CrossRef] Wang, Y.; Yang, L.; Wang, Z.; Ao, J.P.; Hao, Y. The modulation of multi-domain and harmonic wave in a GaN planar Gunn diode by recess layer. Semicond. Sci. Technol. 2016, 31, 025001. [CrossRef] Alekseev, E.; Pavlidis, D. Large-signal microwave performance of GaN-based NDR diode oscillators. Solid-State Electron. 2000, 44, 941–947. [CrossRef] Yang, L.A.; Hao, Y.; Zhang, J.C. Use of AlGaN in the notch region of GaN Gunn diodes. Appl. Phys. Lett. 2009, 95, 143507. [CrossRef]
Appl. Sci. 2019, 9, 75
6.
7. 8. 9. 10. 11. 12. 13.
14. 15.
16. 17.
18. 19. 20.
21.
22.
23. 24. 25. 26. 27. 28.
11 of 12
Song, A.M.; Missous, M.; Omling, P.; Peaker, A.R.; Samuelson, L.; Seifert, W. Unidirectional electron flow in a nanometer-scale semiconductor channel: A self-switching device. Appl. Phys. Lett. 2003, 83, 1881–1883. [CrossRef] Barry, E.A.; Sokolov, V.N.; Kim, K.W.; Trew, R.J. Large-signal analysis of terahertz generation in submicrometer GaN diodes. IEEE Sens. J. 2010, 10, 765–771. [CrossRef] Tang, X.; Rousseau, M.; Dalle, C.; de Jaeger, J.C. Physical analysis of thermal effects on the optimization of GaN Gunn diodes. Appl. Phys. Lett. 2009, 95, 142102. [CrossRef] Lü, J.T.; Cao, J.C. Terahertz generation and chaotic dynamics in GaN NDR diode. Semicond. Sci. Technol. 2004, 19, 451. [CrossRef] Aslan, B.; Eastman, L.F. A THz-range planar NDR device utilizing ballistic electron acceleration in GaN. Solid State Electron. 2011, 64, 57–62. [CrossRef] Pilgrim, N.J.; Khalid, A.; Dunn, G.M.; Cumming, D.R.S. Gunn oscillations in planar heterostructure diodes. Semicond. Sci. Technol. 2008, 23, 075013. [CrossRef] Khalid, A.; Pilgrim, N.J.; Dunn, G.M.; Holland, M.C.; Stanley, C.R.; Thayne, I.G.; Cumming, D.R.S. A planar Gunn diode operating above 100 GHz. IEEE Electron Devices Lett. 2007, 28, 849–851. [CrossRef] Li, C.; Khalid, A.; Caldwell SH, P.; Holland, M.C.; Dunn, G.M.; Thayne, I.G.; Cumming, D.R.S. Design, fabrication and characterization of In0.23 Ga0.77 As-channel planar Gunn diodes for millimeter wave applications. Solid State Electron. 2011, 64, 67–72. [CrossRef] Khalid, A.; Li, C.; Papageorgiou, V.; Pilgrim, N.J.; Dunn, G.M.; Cumming, D.R. A 218-GHz second-harmonic multiquantum well GaAs-based planar Gunn diodes. Microw. Opt. Technol. Lett. 2013, 55, 686–688. [CrossRef] Sugimoto, M.; Ueda, H.; Kanechika, M.; Soejima, N.; Uesugi, T.; Kachi, T. Vertical device oeration of AlGaN/GaN HEMTs on free-standing n-GaN substrates. In Proceedings of the Power Conversion Conference, Nagoya, Japan, 2–5 April 2007; pp. 368–372. Shrestha, N.M.; Wang, Y.Y.; Li, Y.; Chang, E.Y. A novel AlGaN/GaN multiple aperture vertical high electron mobility transistor with silicon oxide current blocking layer. Vaccum 2015, 118, 59–63. [CrossRef] Zhang, Y.; Sun, M.; Liu, Z.; Piedra, D.; Lee, H.S.; Gao, F.; Fujishima, T.; Palacios, T. Electrothermal simulation and thermal performance study of GaN vertical and lateral power transistors. IEEE Trans. Electron Devices 2013, 60, 2224–2230. [CrossRef] Atlas. Atlas User’ Manual; Silvaco International Software: Santa Clara, CA, USA, 2010. Fouz, B.E.; Eastman, L.F.; Bhapkar, U.V.; Shur, M.S. Comparison of high field electron transport in GaN and GaAs. Appl. Phys. Lett. 1997, 70, 2849–2851. Das, J.; Oprins, H.; Ji, H.; Sarua, A.; Ruythooren, W.; Derluyn, J.; Kuball, M.; Germain, M.; Borghs, G. Improved thermal performance of AlGaN/GaN HEMTs by an optimized flip-chip design. IEEE Trans. Electron Devices 2006, 53, 2696–2702. [CrossRef] Sahoo, A.K.; Subramani, N.K.; Nallatamby, J.C.; Sommet, R.; Quéré, R. Thermal Analysis of AlN/GaN/ AlGaN HEMTs grown on Si and SiC substrate through TCAD simulations and measurements. In Proceedings of the Microwave Integrated Circuits Conference, London, UK, 3–4 October 2016. García, S.; Íñiguez-de-la-Torre, I.; Mateos, J.; González, T.; Pérez, S. Impact of substrate and thermal boundary resistance on the performance of AlGaN/GaN HEMTs analyzed by means of electro-thermal Monte Carlo simulations. Semicond. Sci. Technol. 2016, 31, 0650056. [CrossRef] Jones, J.P.; Heller, E.; Dorsey, D.; Graham, S. Transient stress characterization of AlGaN/GaN HEMTs due to electrical and thermal effects. Microelectron. Reliabil. 2015, 55, 2634–2639. [CrossRef] Katayama, K.; Toyabe, T. A new hot carrier simulation method based on full 3D hydrodynamic equations. In Proceedings of the Electron Devices Meeting, Washington, DC, USA, 3–6 December 1989; pp. 135–138. Sevik, C.; Bulutay, C. Gunn oscillations in GaN channels. Semicond. Sci. Technol. 2004, 19, 188. [CrossRef] Fujishiro, H.I.; Mikami, N.; Hatakenaka, M. Monte Carlo study of self-heating effect in GaN/AlGaN HEMTs on sapphire, SiC and Si substrates. Phys. Stat. Sol. 2005, 2, 2696–2699. [CrossRef] Mutamba, K.; Yilmazoglu, O.; Sydlo, C.; Mir, M.; Hubbard, S.; Zhao, G.; Daumiller, I.; Pavlidis, D. Technology aspects of GaN-based diodes for high-field operation. Superlatt. Microstruct. 2006, 40, 363–368. [CrossRef] Barker, J.M.; Ferry, D.K.; Koleske, D.D.; Shur, R.J. Bulk GaN and Al Ga N/Ga N heterostructure drift velocity measurements and comparison to theoretical models. J. Appl. Phys. 2005, 97, 063705. [CrossRef]
Appl. Sci. 2019, 9, 75
29. 30.
12 of 12
Nuttinck, S.; Wagner, B.K.; Banerjee, B.; Venkataraman, S.; Gebara, E.; Laskar, J.; Harris, H.M. Thermal analysis of AlGaN-GaN power HFETs. IEEE Trans. Microw. Theory Tech. 2003, 51, 2445–2452. [CrossRef] Sze, S.M.; Ng, K.K. Physics of Semiconductor Devices, 3rd ed.; Wiley: Hoboken, NJ, USA, 2007. © 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
