Optimum transit-region doping profile for W-band InP Gunn diodes

ph.surrey.ac.uk

Optimum transit-region doping profile for W-band InP Gunn diodes

A theoretical study of differing active region dopingprofiles for W-band (75-110 GHz) InP Gunn diodesG M Dunn (a) and M J Kearney (b)(a)Department of Physics, Fraser Noble Building,King’s College, University of Aberdeen,Aberdeen, AB24 3UE, UK(b)Advanced Technology Institute,School of Electronics and Physical SciencesUniversity of Surrey, Guildford, SurreyGU2 7XH, UKAbstractInP Gunn diodes are widely used as high power microwave sources in the W-band frequency range (75-110 GHz), but interesting questions remain as to theoptimal active-region doping profile for such devices. In this paper we carry out adetailed theoretical study, using Monte Carlo simulations, of three types of dopingprofile; (i) uniform doping, (ii) graded doping (i.e. increasing linearly fromcathode to anode), and (iii) notch doping (a lightly doped region adjacent to thecathode). By studying the effects of varying all the relevant parameters, such asdoping levels, active region length, bias levels, and temperature, under both DCand RF conditions, we argue that the notch doping approach is superior, offeringhigh performance combined with a greater tolerance to doping fluctuations.1


1. IntroductionInP Gunn diodes have long been used as high power microwave sources in theimportant W-band frequency range (75-110 GHz) (see e.g. [1]), the key attractionbeing that fundamental-mode operation is relatively straightforward to achieve (unlikewith GaAs). Over the last few years, increasing attention has been given to extendingfundamental mode operation up to D-band frequencies (110 -170 GHz) [2-4], as wellas to investigating second harmonic mode operation [5, 6]. The experimental resultsdemonstrated have been impressive, e.g. ~ 130 mW output power at ~ 130 GHz (witha DC-RF conversion efficiency of ~ 2.5%), combined with low phase-noise [3].Recent reviews show these results compare very favourably with those obtained fromother types of microwave source [7, 8].The advantages of InP (as opposed to GaAs) lie principally in the higher driftvelocities of electrons, and in the (generally) larger oscillation amplitudes due to themore pronounced negative differential resistance (NDR). However, the greaterdifference between the light and heavy valley energies (~ 0.8 eV, as opposed to ~ 0.3eV in GaAs) also causes a greater dead space than in GaAs and requires a higherthreshold field to instigate oscillations (~ 1.4 10 6 Vm -1 as opposed to ~ 0.4 10 6 Vm -1 ). This is a significant issue, and to achieve high performance operation at highfrequencies requires full optimisation of the device design, as well as recourse totechnological improvements such as the replacement of integral heat sinks withdiamond heat sinks [3, 4]. Whereas early studies concentrated on relatively simplestructures (e.g. uniform doping active regions [1]), it has become clear that gradingthe doping in the active region can improve performance considerably (see the laterdiscussions). Thus the state-of-the-art devices reported in [2-5] have a ~ 1 m activeregion with the doping graded linearly from ~ 7.5 x 10 15 cm -3 at the cathode to ~ 2 x10 16 cm -3 at the anode. In a recent paper [9], Judaschke has theoretically studiedvarious doping profiles with an eye to further improving D-Band operation. Inparticular, Judaschke considers uniform doping, graded doping and notch doping(wherein a lightly doped region is incorporated adjacent to the cathode), andconcludes that the latter is best of all for fundamental-mode operation. Furtherconsideration is given to the so-called ‘mesa’ doping profile (following on from2


earlier work [10, 11]), concluding that it is favourable for improving second-harmonicmode operation up to 260 GHz.The main thrust of this paper is to extend and to expand the work in [9] toconsider optimum doping profiles for fundamental-mode operation at W-Band (ratherthan D-Band) frequencies. Such a study is timely, particularly with regard to thegrowing opportunities for civilian (e.g. automotive radar at 77 GHz [12]) as well asmilitary applications in this frequency range. Our work differs from that in [9] inseveral respects that are worth mentioning from the outset. First, we use a MonteCarlo rather than a hydrodynamic based approach, although where comparisons canbe made, very similar results are obtained. Second, the results we present are morecomprehensive in terms of the wide range of parameters studied, such as dopinglevels, active region length, bias levels, and temperature, under both DC and RFconditions. Of the three types of active region doping profile studied (uniform doping,graded doping and notch doping), our conclusions support the view in [9] that gradeddoping is superior to uniform doping and that notch doping is superior to both. Notonly does notch doping offer higher efficiency and output power, it also appears toprovide a greater tolerance to doping fluctuations. The latter is an importantconsideration, since to realise high frequency InP Gunn devices in practice requirescontrol over growth at the very limit of what is achievable.The paper is organised as follows. In section 2 we give details of the devicemodel used. In section 3 we divide the discussion into sub-sections referring to (i) the(natural) DC response of the devices to variations in potential bias, active regionlength and temperature, and (ii) the RF response at 94 GHz over a range of lengths inorder to find the optimum active region length, and then the frequency response at thisoptimum length. We then discuss the effect of changes in temperature and activeregion doping level. Finally, in section 4 we draw these various strands together anddiscuss the implications for the optimum design of such devices.3


2. Theory and modellingMany approaches to the modelling and simulation of InP Gunn diodes andtheir associated circuits have been advocated over the last twenty years or so. Initialwork relied on explicit solutions of the Boltzmann transport equation in the relaxationtime approximation [13, 14]. Later work extended this to the consideration of moregeneralised hydrodynamic models [9, 11, 15], often with explicit consideration of thecircuit in which the device is embedded. With Monte Carlo simulations, inclusion ofthe external circuit is more difficult to achieve, although some progress has been madein this direction (see e.g. [16]). On the other hand, Monte Carlo simulations (see e.g.[2]) are particularly useful for studying non-equilibrium effects at the cathode and thedetailed physics of domain nucleation and propagation. Thus no single modellingapproach should be viewed as intrinsically superior; each method has an importantrole to play in the overall task of trying to design better-optimised devices.In the present work a one-dimensional self-consistent ensemble Monte Carloapproach is employed, see e.g. [17-19]. Full details of the InP material parametersused are given in [20]. Typically, in each simulation 30,000 ‘super-particles’ werefollowed, the time-step equating to 1.2 x 10 -15 s, and the current was evaluated every10 time-steps. Each ‘super-particle’ represents a number of ‘real’ particles such thatthe charge carried by the super-particles will reproduce the correct charge density.These particles are propagated classically between collisions according to theirvelocity, effective mass and the prevailing electric field in the standard manner [17-20]. The spatial grid-size employed throughout the simulations was 1.8 nm. Thesimulations were all begun with the devices in a charge neutral configuration. Toensure insensitivity to the initial starting configuration, the evolution of each devicewas followed for a minimum of three full domain transits.An important issue is how to address resistive heating, since under normaloperating conditions the junction temperature can easily approach 200 0 C [1-4,13, 14].Lowering this temperature through the use of diamond heat sinks is a major factor inincreasing device efficiency and output power [3, 4]. Hydrodynamic approaches canincorporate thermal modelling self-consistently as an integral part of the simulation, to4


the point of allowing for non-uniform temperatures throughout the device structure(see e.g. [15]). In our particular Monte Carlo approach this is not an option; thusresistive heating is accounted for by considering a range of uniform latticetemperatures up to 500 K. Results in [15] show that the assumption of a uniformtemperature is not unreasonable. In [9] the temperature is fixed at 400 K throughout,but we are interested in how things change with temperature, not least with an eye tohow performance is affected by changes in the ambient operating temperature.A recognised drawback of Monte Carlo modelling is the statistical (noisy)nature of the simulated current. It is this feature (above all others) that makes linking aMonte Carlo model with an external circuit model so difficult [16]. To improve thestatistics in the present study, the current I (t) through the device was evaluated byaveraging the charge output through the anode over 40 output values, which equatesto 0.5 ps. This is much less than the time-period of the oscillations for the frequenciesof interest (e.g. 94 GHz corresponds to a time-period of ~ 10.6 ps). To evaluate theefficiencies and output power levels, a sinusoidal potential of the formV ( t) V V sin(2ft)was imposed on the device, and the appropriate terms in aDCRFFourier expansion of the averaged current response were considered. In a real device,of course, the circuit and cavity within which the device is embedded determine thefrequency and amplitude of oscillation, but it is standard practice to model Gunndevices in this way [2, 9, 15]. The RF power delivered is given by,PRFVTRFT0I( t)sin(2f t)dtwhilst the impedance is given byZ R jX where,R IVIRF R,2 2R IXXVIRF2RI IX2XIR2TT0I(t) cos(2f t)dt,IX2TT0I ( t)sin(2f t)dt5


In what follows, for all the devices studied the impedance of a device of 50 mdiameter is ~ 4 at 94GHz (see below for details). This value is suitable for effectiveand efficient coupling to a cavity, which is an important design consideration.3. Results and analysisGunn diode devices usually work in either an accumulation layer (monopole)mode or a dipole mode. In an accumulation layer mode a density wave of electronstransfers along the active region of the device. In a dipole mode, a depletion layerprecedes the density wave. Previous experimental and theoretical investigations of 94GHz InP devices have largely been concerned with the accumulation layer modewhere the active region was either uniformly doped or contained graded doping (e.g.increasing linearly from the cathode to the anode) [13, 14]. Within these studies arange of optimum device configurations (for 94 GHz operation) are implied withactive region lengths varying between ~ 1.1 m [13, 14] and ~ 1.6 m [2]. Thedisparity between these results may be accounted for (to a certain extent) bydifferences in the material parameters used in each model.In accumulation layer devices the charge monopole usually forms mid-wayalong the device. This effectively means that about half the device operates as anundesirable series resistance, which reduces its efficiency. Much work has been doneto reduce this dead space and to allow the domain to form closer to the cathode, andusually this results in the formation of a charge dipole. One such method is to usegraded doping of the active region. Another method is to provide a doping notch inthe active region adjacent to the cathode [9]. Electrons then diffuse into the notch andcause an upturn in the electric field that is sufficient to increase the energy of the -valley electrons to allow a domain to nucleate. The details of how this works inpractice are, however, still poorly understood.As mentioned in the Introduction, in this paper we present a systematic studyof three types of device, i.e. accumulation layer devices with uniform doping in theactive region, and dipole devices where dipole formation is stimulated using either6


graded doping or a doping notch (see Figure 1). In what follows, the cathode andanode contact layers are taken to be 0.2 m thick and are doped at ~ 2 x 10 18 cm -3 .The latter is a typical value for devices operating at such frequencies and the results ofthe simulations are not sensitive to it. After many hundreds of simulations with manydifferent selections for the active region doping levels and doping profile, thefollowing choices were found to be representative of the optimal and are used initiallyto illustrate the main results and conclusions of the paper. For the uniform dopingprofile, the optimal doping level was found to be ~ 2 x 10 16 cm -3 . For the gradeddevices the optimal doping profile was found to be a linear grading from ~ 1 x 10 16cm -3 at the cathode to ~ 2.25 x 10 16 cm -3 at the anode. For the notch devices theoptimal doping profile was found to be a uniform doping at ~ 1.8 x 10 16 cm -3 apartfrom a 0.2 m notch region adjacent to the cathode which is lightly doped ~ 2 x 10 15cm -3 . These results are principally for 94 GHz operation, which is the representativefrequency we concentrate on. At either end of the frequency band of interest (W-band,75-110 GHz) one would probably adjust them slightly for optimal performance.3.1 DC BiasIn practice, Gunn diodes operate in an RF cavity and consequently experiencean oscillatory feedback potential. It is very useful, however, to establish the naturaltendency and frequency of a given device to oscillate under a constant DC potential(what we will henceforth refer to as the natural frequency). If it does not, it wouldalmost certainly not oscillate in a cavity, and simulating what happens under an RFbias would then be pointless. In addition, understanding what happens under DC biasconditions can often give a clearer impression of what is happening inside the deviceand an idea of how the device is likely to behave under an RF potential. We can, forexample, gain a reasonable idea of what the effects of temperature, bias and activeregion length are likely to be on the frequency response of the device.3.1.1 Uniformly doped devices7


The accumulation layer mode was found to occur in uniformly doped 1 mstructures only when the doping level exceeded 2.0 10 16 m -3 , in agreement with [13,14]. In view of this high doping level, we have assumed a high operating temperatureof about 500 K (a 50 m diameter device might have to carry a current as high as 2A), and this temperature will be used throughout the following analysis unlessotherwise stated. This probably represents the highest possible operating temperatureof the device, though any device that operates at this temperature will almost certainlywork better at a lower temperature. The natural frequency of oscillation (by which wemean the frequency of the current waveform under a DC applied bias) is very high at1 m, i.e. ~ 200 GHz for a 6 V DC bias (Figure 2). Increasing the active region lengthto 1.7 m decreases this frequency to ~ 105 GHz for the same bias. Thus, over thisrange, the frequency change with active region length f / l 165GHz m -1 . Asmentioned previously, there is a substantial NDR slope in InP which causes a shift inthe frequency of about 10 GHz V -1 , all other factors being equal (see Figure 2).Finally, figure 2 shows a temperature dependence of 0.17GHzK -1 in this type ofdevice. This is significant in the context of the range of ambient temperatures overwhich such devices are required to operate.3.1.2 Graded doping profile devicesOur DC simulations, over the range of active region lengths we are interestedin, indicate that charge domains in graded devices are always accompanied bysignificant depletion regions (i.e. they are dipoles as opposed to accumulation layers).These dipoles form closer to the cathode than in the accumulation layer devices andhence the frequency is lower for a given device length (see Figure 3). The variation ofthe natural frequency of oscillation with active region length is f / l 110GHz m -1 at a nominal field of ~ 4 10 6 Vm -1 . The variation with temperature is ~ 0.12GHz K -1 , which is potentially quite significant in terms of controlling frequency driftwith ambient temperature changes in a given application. The origin of this sensitivityis the well-known sensitivity of electron transport processes in InP to temperaturechanges (as compared, for example, to the corresponding situation in GaAs).8


3.1.3 Notch doping profile devicesWe found that we were able to form dipoles in all the devices studied byincorporating a nominally undoped 0.2 m notch adjacent to the cathode. In fact, suchstructures seem very robust and relatively insensitive to other structural details, whichis important from a manufacturability perspective. Smaller notches were found not toalways work, particularly in the shorter devices, resulting in the formation ofaccumulation layers. An active region doped at ~ 2 10 16 cm -3 was found to producestable dipole oscillations for all the device lengths studied (at 500 K). The variation infrequency with active region length (including the 0.2 m notch) was f/ l 116GHz m -1 (assuming a nominal electric field of ~ 3.5 10 6 Vm -1 ) – see Figure 4. Thevariation with temperature is once again ~ 0.12 GHz K -1 .3.2 RF BiasIn order to mimic the effect of placing a device in a resonant cavity, we imposean RF potential (V RF ) on the DC bias (V DC ) in the manner described in section 2.Ideally, one would like the current to be 180 0 out of phase with the driving potentialor, in other words, the current maximum should occur at the potential minimum. Toexamine what this means in terms of the physical nucleation and transit of the chargedomains we will take the graded device as an example, before going on to examinethe frequency response of each type of device in detail.Charge domains will nucleate at the cathode once the electric field at this pointin the device increases beyond a threshold value. This increase can be due to anincrease in external potential (from the RF bias) or from an increase as internalpotential is ‘liberated’ from a previous domain which is passing through the anode. Ifthe RF frequency is too high for the given length of the device (or, alternatively, thedevice is too long for the given frequency) the domain will not have sufficient time totraverse the active region before the RF bias passes through its minimum and beginsto rise, nucleating a new domain and increasing the current. The current waveformwill therefore lag behind the potential by less than 90 0 (see Figure 5) or, in extreme9


cases, might even be in phase with the driving potential (when the response of thedevice will be purely resistive). As the length of the device is decreased, the domainswill have sufficient time to cross the active region and arrive at the anode as thepotential is falling. The release of the potential ‘stored’ in the domain will more thancompensate for the fall in external potential, and the electric field will increase at thecathode causing a new domain to nucleate with a corresponding increase in current(see Figure 6). Comparing the charge density profiles in Figures 5 and 6, at 18 ps(about the potential minimum) we can see that in the shorter 1.5 m device (Figure 6)the charge domain's peak density is less than 0.1 m from the anode and the depletionregion has already passed into the anode, whereas in the longer 1.7 m device (Figure5), the domain's peak density still has about 0.35 m to go and the domain as a wholehas not yet reached the anode. The 1.7 m device is therefore too long and this isreflected in the current waveform which lags the potential by about 100 0 , whereas inthe shorter device the lag is about 145 0 i.e. it has a good negative resistive response.3.2.1 Uniform doping profile devicesImposing a 94 GHz RF potential of V RF = 2 V on a DC bias of V DC = 5 V andmeasuring the efficiency as a function of active region length, we observe a peakbetween 1.5 m and 1.6 m. This is to be expected from our study of the naturalfrequency, which would yield a frequency of 94 GHz under a bias of about 7 V, whichis our peak applied potential. Figure 7 (column a) shows the variation, along with thepower and phase angle (of the peak current to the peak potential). Note how the phaseangle improves as the device becomes shorter and the accumulation layer has a greateropportunity to traverse the length of device and nucleate a new layer on the fall of thepotential. The current oscillation amplitude, however, also falls so that the peak ofefficiency does not occur at 180 0 phase angle but at about 140 0 . Figure 8 (column a)shows the efficiency, power and phase angle as a function of frequency for a 1.5 mdevice over a range of frequencies from 75 GHz to 105 GHz, for two appliedpotentials of V DC = 5 V, V RF = 2 V and V DC = 5 V, V RF = 3 V. A peak efficiency of ~5 % occurs for V RF = 2 V at 94 GHz, with the peak efficiency for V RF = 3 V occurring10


at lower frequency, as would be expected from the reduced drift velocity at this higherpotential.The effect of temperature is very significant. Figure 2 shows the variation inthe natural frequency in a 1.4 m device under a 5 V DC bias. This variation amountsto about 20 GHz per 100 K change in temperature. This quite substantial change isreflected in the RF response of the device where the maximum efficiency at 94 GHz isachieved at 1.5 1.6 m at 500K, whereas at 300 K this maximum efficiency occursfor an active region length of about 1.8 m (see Figure 9), about 0.25 m greater. Thisimplies the necessity of increasing the device length by about 0.25 m for a 200 Kreduction in temperature.All of the above analysis has been done for an active region doping of 2 10 16cm -3 which allows the device to work (by which we mean have a natural DC responseas well as an RF response) in every instance we have examined, whether it be forshort (~ 1 m) or long (~ 2 m) devices or at high or low temperatures. Having settledthat the optimum device length for 94 GHz is ~ 1.5 m we can see how far one canlower the doping whilst making sure that by doing so one does not significantly affectthe frequency response of the device as calculated at 2 10 16 cm -3 . We have examinedthe natural (DC) response of a 1.4 m device under a 5 V bias between temperaturesof 300 K to 500 K at 1 10 16 cm -3 , 1.5 10 16 cm -3 and 2 10 16 cm -3 doping in theactive region. The 1 10 16 cm -3 device worked well at 300 K but stopped oscillatingby 400 K, whereas the 1.5 10 16 cm -3 device sustained natural oscillations over theentire temperature range. At 500 K the natural period was found to be 137 GHzwhich is almost identical to the 139 GHz of the 2 10 16 cm -3 device. Under RFconditions, Figure 10 shows the response of the 1.5 10 16 cm -3 device as a function ofactive region length for a driving frequency of 94 GHz at 500 K, compared to the 2 10 16 cm -3 device. Aside from an ~ 1% reduction in efficiency (and the obviousreduction in power caused by the lower current), the frequency response is verysimilar with a peak efficiency occurring between 1.5 m and 1.6 m.11


In view of this clear similarity in both the DC and RF response of the 1.5 10 16 cm -3 and 2.0 10 16 cm -3 device we can conclude that changes of doping in thisrange have a relatively insignificant effect on the frequency response of suchaccumulation layer devices. But, allowing the doping to fall below 1.5 10 16 cm -3may mean the device will fail to support oscillations at higher temperatures.3.2.2 Graded doping profile devicesFigure 7 (column b) shows the device efficiency, power and phase angleagainst active region length at 94 GHz and 500 K for an imposed potential of V DC = 6V and V RF = 2 V. A peak in efficiency of ~ 6 % occur at 1.45 m. This peak responseat 94 GHz is some 30 GHz less than would be expected from the DC naturalfrequency response, from which we must conclude that the natural response is not asgood a guide to the peak efficiency as it was with the uniformly doped (accumulationlayer) devices. The DC response indicates a change in frequency of ~ 110 GHz m -1and 0.12 GHz K -1 and therefore implies the need to lengthen the device by about 0.11m per 100 K reduction in temperature. This is reasonably consistent with theincrease of 0.14 m indicated in Figure 9.The variation of the efficiency of a 1.4 m device with frequency (Figure 8,column b) shows a full width at half maximum of 25 GHz peaking at 94 GHz for V DC= 6 V, V RF = 2 V. Increasing the RF potential on the V DC = 6 V bias to V RF = 3 V, thefull width at half maximum increases to about 35GHz and the peak reduces down to90GHz (Figure 8, column b). This again shows the strong NDR behaviour of thesedevices and is consistent with our DC analysis which indicates a change in frequencyof about 4 GHz V -1 .3.2.3 Notch doping profile devicesFrom Figure 4, we can see that a device length of ~ 1.5 m should yield anatural frequency of about 94 GHz. The device behaviour under an RF drivingpotential of 94 GHz was, however, found to be almost purely resistive. We must12


therefore conclude that the effect of an RF bias is to slow the transfer of dipoledomains across this type of device structure. Figure 7 (column c) shows the variationof the efficiency, power and phase angle (of the current with respect to the drivingpotential) with active region length for an applied 94 GHz potential of V DC = 4.5 Vand V RF = 2 V. A strong peak of ~ 7 % efficiency occurs at about 1.2 m. Figure 8(column c) shows the frequency response of a 1.2 m device to frequencies rangingfrom 75 GHz to 105 GHz at V DC = 4.5 V, V RF = 2 V and V DC = 4.5 V, V RF = 3 V.Peaks in efficiency occur at 94 GHz for V RF = 2 V and at about 90 GHz for V RF = 3 V,as would be expected for the slower drift velocity at the higher RF amplitude.Under a DC bias of 5 V at 1.2 m the variation of natural frequency withtemperature is very nearly linear and amounts to about 15 GHz per 100 K change intemperature (see the lower inset in Figure 4). Extrapolating from the DC results, wecan estimate that the optimum device length would need to change by ~ 0.125 m forevery 100 K change in temperature. In order to test this hypothesis, we have examinedthe optimum device length for a device operating at 300 K under an RF bias of V DC =4.5 V, V RF = 2 V comparing it to devices operating at 500 K. Figure 9 compares thesetwo cases and shows a peak efficiency of ~ 7 % occurring at about 1.5 m at 300 Kcompared to a peak, also of ~ 7 %, occurring at 1.2 m at 500 K. The difference in theoptimum device lengths between the two temperatures is therefore about 0.3 m, inreasonably good agreement with the prediction of 0.25 m based purely on the DCresponse.The previous simulations were all conducted with an active layer doping of 2 10 16 cm -3 . It would be advantageous, in terms of the operating temperature (andlifetime) of the device, to reduce this doping as far as possible. To this end weperformed simulations of a 1.2 m device with active region doping levels at 1 10 16cm -3 , 1.5 10 16 cm -3 and 2.0 10 16 cm - . It was found that, at 500 K, the 1 10 16 cm -3device failed to sustain oscillations under a V DC = 5 V bias, but the 1.5 10 16 cm -3device did work, although the domains only had a weak depletion region with muchmore the appearance of an accumulation layer. This was particularly true if V DC waslowered to 3.5 V. Despite this mixed mode, however, the difference in the natural13


frequencies between the 1.5 10 16 cm -3 device and 2.0 10 16 cm -3 device was quitesmall (134 GHz and 125 GHz respectively for V DC = 5 V and 142 GHz and 138 GHzrespectively for V DC = 3.5 V). Reducing the doping level below 2 10 16 cm -3therefore reduces the ability of the device to sustain dipoles and consequentlyincreases the natural frequency a little. The effect of lowering the doping on the RFperformance of the device and the optimum device length is therefore to increase therequired length for given V DC and V RF operating potentials. This change, though, isvery small. Figure 9 shows the efficiency against active region length for the 1.5 10 16 cm 3 device for V DC = 5.5 V and V RF = 2 V. The peak occurs at about 1.2 m (aswith the 2 10 16 cm -3 ) device and we have achieved this agreement by increasing V DC= 4.5 V in the 2 10 16 cm -3 device by 1V.We know of no relevant experimental data on notch devices with which tomake comparison. Our results for the uniform and graded devices are consistent with[2], where a 1.7 m device uniformly doped at ~ 1 x 10 16 cm -3 generated 40 mW (1.6%) at 80 GHz, and with [3], where ~ 1 m devices with doping graded from 7.5 x 10 15cm -3 to 2 x 10 16 cm -3 generated powers ranging from 185 mW at 102 GHz to 60 mW(1.3 %) at 150 GHz. They are also consistent with [1], wherein ~ 1.1 m devicesgenerated in excess of 50 mW (3 %) at 94 GHz, provided we allow for a (slight)grading in the doping. As mentioned in section 2, the attainable drive levels arelimited by restrictions imposed by the thermal resistance and minimum matchableimpedance. Thus the idealised efficiencies indicated above are likely to be reduced inpractice, but the relative trends should be preserved. Figure 11 shows the variation ofoutput power and impedance for a (typical) device cross-section of ~ 50 m diameter.Such impedances are quite practical in terms of circuit matching.4. ConclusionsFor InP Gunn diodes the optimum device response to an RF potential occursas much as 30 GHz below the natural (DC response) frequency. There are alsosubstantial temperature effects on the device natural frequency, approximately 10 to20 GHz per 100 K change in temperature. This variation means that the device length14


must be selected with some care. As discussed above (see also Figure 9), the fullwidth at half maximum of the efficiency versus active region length characteristic iscomparable with the shift of this curve for a temperature change of 100 K. As devicesare usually intended to operate in ambient temperatures ranging from – 40 0 C to + 800 C thought obviously needs to be given to designing the device to operate at thehighest ambient temperature and (possibly) whether to include a heater to maintainthis temperature in cooler environments.Of the three devices investigated, the uniformly doped accumulation layerdevice was the least efficient, with monopoles forming midway along the deviceactive region so that ~ half the device acted as a wasteful resistive dead space.Introducing graded doping was found to cause dipoles to nucleate and these domainsformed closer to the cathode leading to an increased efficiency. The most efficientdevice, however, was the notch device, with domains forming very close to thecathode. As a consequence of this, for a given operating frequency, the requiredactive region length becomes progressively shorter as we go from the uniform designto the graded design to the notch design (see e.g. Figure 9).We conclude by recommending the ‘optimum’ device configurations for InPGunn devices designed to operate at 94 GHz (results elsewhere in the paper provide‘design rules’ for other frequencies). They should consist of n + cladding regions dopedin excess of 2 10 18 cm -3 . For the accumulation layer device, a 1.6 m active regiondoped at 1.7 10 16 cm -3 should yield ~ 5 % efficiency at about 450K. For the gradeddevice, a 1.4 m active region with graded doping changing linearly from 1 10 16 cm -3 at the cathode to 2.25 10 16 cm -3 at the anode should yield an efficiency of about 5.5% at 450 K. For the notch device, a lightly doped 0.2 m notch (~ 2-4 x 10 15 cm -3 ),followed by ~ 1.0 m region doped uniformly at ~ 1.5-2 x 10 16 cm -3 should yield anefficiency of up to 6.5 % at 450 K. Allowing for thermal resistance, impedancematching losses etc., efficiencies of order 4 % and power levels in excess of 200 mWshould be attainable for a 50 m diameter device operating at ~ 450 K. Furtherrefinements such as combining notch doping with grading are possible.15


References1. di Forte-Poisson M. A., Brylinski C., Colomer G., Osselin D., Hersee S.,Duchemin J. P., Azan F., Lechevallier D. and Lacombe J.: “High-power, highefficiencyLP-MOCVD InP Gunn diodes for 94 GHz”, Electron. Lett., 1984, 20,pp. 1061-10622. Kamoua R., Eisle H. and Haddad G. I.: “D-Band (110-170 GHz) InP Gunndevices”, Sol. State Elec., 1993, 36, pp.1547-15553. Eisele H. and Haddad G. I.: “High-performance InP Gunn devices for fundamentalmode operation in D-band (110-170 GHz)”, IEEE Micro. Guided Wave Lett.,1995, 5, pp. 385-3874. Eisele H. and Haddad G. I.: “Efficient power combining with D-band (110-170GHz) InP Gunn devices in fundamental-mode operation”, IEEE. Microw. GuidedWave Lett., 1998, 8, pp. 24-265. Eisele H. and Haddad G. I.: “D-band InP Gunn devices with second-harmonicpower extraction up to 290 GHz”, Electron. Lett., 1994, 30, pp. 1950-19516. Jones S. H., Zybura M. F., Carlstrom J. E. and Obrien T. M.: “A 63-170 GHzsecond-harmonic operation of an InP transferred electron device”, IEEE Trans.Electron. Dev., 1999, 46, pp. 17-237. Eisele H. and Haddad G. I.: “Two-terminal millimeter-wave sources”, IEEE.Trans. Microw. Theory., 1998, 46, pp. 739-7468. Eisele H., Rydberg A. and Haddad G. I.: “Recent advances in the performance ofInP Gunn devices and GaAs TUNNETT diodes for the 100-300 GHz frequencyrange and above”, IEEE. Trans. Microw. Theory., 2000, 48 (Part 2), pp. 626-63116


9. Judaschke R.: “Comparison of modulated impurity-concentration InP transferredelectron devices for power generation at frequencies above 130 GHz”, IEEE.Trans. Microw. Theory., 2000, 48 (Part 2), pp. 719-72410. Jones S. H., Tait G. B. and Shur M.: “Modulation-impurity concentrationtransferred electron devices exhibiting large harmonic frequency content”,Microwave Opt. Tech. Lett., 1992, 5, pp 354-35911. Zybura M. F., Jones S. H., Tait G. and Jones J. R.: “100-300 GHz Gunn oscillatorsimulation through harmonic-balance circuit analysis linked to a hydrodynamicdevice simulator”, IEEE Microw. Guided Wave Lett., 1994, 4, pp. 282-28412. Franklin J., Kuo H. C., Liu J., Vizcarra R., Pao Y. C., Cheng K. Y. and PickrellG.: “Gas source molecular beam epitaxial growth of 77 GHz InP Gunn diodes forautomotive forward looking radar applications”, J. Vac. Sci. Technol. B, 2000, 18,pp. 1645-164913. Friscourt M. R. and Rolland P. A.: “Optimum design of n + nn + InP devices in themillimeter range frequency limitation - RF performances”, IEEE Electron Dev.Lett., 1983, 4, pp.135-13714. Friscourt M. R., Rolland P. A., Cappy A., Constant E. and Salmer G.: “Theoreticalcontribution to the design of millimeter-wave TEOs”, IEEE Trans. Electron. Dev.,1983, 30, pp. 223-22915. Zybura M. F., Jones S. H., Tait G. and Duva J. M.: “Efficient computer aideddesign of GaAs and InP millimeter-wave TED including detailed thermalanalysis”, Sol. State Elec., 1995, 38, pp. 873-87916. Kamoua R.: “Monte-Carlo based harmonic-balance technique for the simulationof high-frequency TED oscillators”, IEEE. Trans. Microw. Theory., 1998, 46, pp.1376-138117


17. Fischetti M. V.: “Monte Carlo simulation of transport in technologicallysignificant semiconductors of the diamond and zinc-blende structures. 1.Homogeneous transport”, IEEE Trans. Electron. Dev., 1991, 38, pp. 634-64918. Hockney R. W. and Eastwood J. W.: "Computer simulations using particles", IoPPublishing Ltd., Bristol, 1988.19. Jacoboni C. and Reggiani L.: "Monte Carlo Method in transport", Rev. Mod.Phys., 1983, 55, pp. 645 - 70520. Dunn G. M., Walker A. B., Jefferson J. and Herbert D.: “Monte Carlo simulationof InP and GaAs MESFETS”, Semicond. Sci. Technol., 1994, 9, pp. 2123-212918


Figure CaptionsFig. 1 A schematic illustration of the simulated devices showing the doping densityprofile in each case.Fig. 2 The variation of the natural frequency of oscillation (monopoles) with activeregion length for the uniformly doped device at 500 K. The points show thefrequency at the indicated DC potentials whilst the line is the approximatebehaviour at a nominal field of ~ 4 10 6 Vm -1 . The upper inset shows thevariation in frequency as a function of applied bias for a 1.4 m device (at 500K) and the lower inset shows the variation in frequency as a function oftemperature for a 1.4 m device under 5 V DC bias.Fig. 3 The variation of the natural frequency of oscillation (dipoles) with activeregion length for the graded device at 500 K. The points show the frequencyat the indicated DC potentials whilst the line is the approximate behaviour at anominal field of ~ 4 10 6 Vm -1 . The upper inset shows the variation infrequency as a function of applied bias for a 1.5 m device (at 500 K) and thelower inset shows the variation in frequency as a function of temperature for a1.5 m device under 6 V DC bias.Fig. 4 The variation of the natural frequency of oscillation (dipoles) with activeregion length for the notch device at 500 K. The points show the frequency atthe indicated DC potentials whilst the line is the approximate behaviour at anominal field of ~ 3.5 10 6 Vm 1 . The upper inset shows the variation infrequency as a function of applied bias for a 1.2 m device (at 500 K) and thelower inset shows the variation in frequency as a function of temperature for a1.2 m device under 5 V DC bias.Fig. 5 A 1.7 m graded (dipole) device, with V DC = 5 V and V RF = 2 V at 94 GHzand 300 K. (a) The imposed potential and current response. (b) The electricfield profiles at three different times. (c) The corresponding electron densities.19


This device is too long and the dipoles do not have sufficient time to traversethe active region; this is reflected in the current response which lags thepotential by only ~ 100 0 .Fig. 6 A 1.5 m graded (dipole) device, with V DC = 5 V and V RF = 2 V at 94 GHzand 300 K. (a) The imposed potential and current response. (b) The electricfield profiles at three different times. (c) The corresponding electron densities.This device is about the correct length and the current lags the potential by ~140 0 . Shortening the device still further causes the current to lag furtherbehind, but the advantage of this is negated by a decrease in current amplitude.Fig. 7 The variation of the efficiency, RF power and phase angle (of the peak currentwith respect to the peak potential) as a function of active region length at 500K(a) Uniform device with V DC = 5 V and V RF = 2 V. (b) Graded device withV DC = 5 V and V RF = 2 V. (c) Notch device with V DC = 4.5 V and V RF = 2 V.Fig. 8 The variation of the efficiency, RF power and phase angle (of the peak currentwith respect to the peak potential) as a function of RF frequency at 500K, withV RF = 2 V (filled circles) and V RF = 3 V (open squares). (a) Uniform device(1.5 m, V DC = 5 V). (b) Graded device (1.4 m, V DC = 6 V). (c) Notch device(1.2 m, V DC = 4.5 V).Fig. 9 The efficiency as a functions of active region length at 94 GHz showing theincrease in the optimum length of each device with decreasing temperature.(a) Uniform device with V DC = 5 V and V RF = 2 V. (b) Graded device withV DC = 5 V and V RF = 2 V. (c) Notch device with V DC = 4.5 V and V RF = 2 V.Fig. 10The efficiency as a function of active region length at 94 GHz and 500 K. (a)Uniform (monopole) device at 2 10 16 cm -3 (circles) with V DC = 5 V and V RF= 2 V, and 1.5 10 16 cm -3 (squares) with V DC = 5 V and V RF = 2 V. (b) Notch(dipole) device at 2 10 16 cm -3 (circles) with V DC = 4.5 V and V RF = 2, and at1.5 10 16 cm -3 (squares) with V DC = 5.5 V and V RF = 2 V.20


Fig. 11The variation of power and impedance for 50 m diameter devices as afunction of RF frequency (V RF = 2 V), at a temperature of 500K. (a) Uniformdevice (1.5 m, V DC = 5 V), (b) graded device (1.4 m, V DC = 6 V), (c) notchdevice (1.2 m, V DC = 4.5 V).21


Uniform doping deviceDoping DensityGraded doping deviceNotch doping deviceCathode Active Region AnodeFigure 122


Frequency (GHz)250.0200.0150.0100.050.0Frequency4V5V6V1901701501.4micronsFrequency130250 350 450 550Temperature K1601501401304V5V6V1.4microns3.5 4.5 5.5 6.5Potential (V)0.9 1.1 1.3 1.5 1.7 1.9Device Length (Microns)6VFigure 223


Frequency (GHz)150.0125.0100.0Frequency1401301201106V1.5micronsFrequency1301251201151101051004V6V8V1.5microns3 4 5 6 7 8 9Potential (V)6V75.0100250 350 450 550Temperature K1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8Device Length (Microns)Figure 324


Frequency (GHz)200.0175.0150.0125.0100.075.050.025.00.0Frequency1601501401306.0V5.0V1.2microns3.5V7.0VFrequency120300 350 400 450 500Temperature K1401351301251201151102.5 3.5 4.5 5.5 6.5 7.55.0V1.2micronsPotential (V)6.0V0.8 1.0 1.2 1.4 1.6 1.8Device Length (Microns)Figure 425


Field (MVm −1 )Potential (V)20.015.010.05.00.0−5.00.0 0.5 1.0 1.5Position (microns)Density (x10 24 m −3 )12 ps15 ps18 ps00.0 0.5 1.0 1.5Position (microns)7.06.0(b)12 ps15 ps18 ps21 ps(c)(a)5.04.03.02.00.0 10.0 20.0 30.0Time (ps)120010008006004002000Current (MA m −2 )Figure 526


Field (MVm −1 )Density (x10 24 m −3 )Potential (V)30.020.010.00.012 ps15 ps18 ps−10.00.0 0.5 1.0 1.5Position (microns)12 ps15 ps18 ps0.00.0 0.5 1.0 1.5Position (microns)7.06.05.04.03.02.00.0 10.0 20.0 30.0Time (ps)120010008006004002000Current (MA m −2 )Figure 627


Power (MWm −2 )Phase oEfficiency %7.06.05.04.03.02.0150.0a1100.0a250.0−100−120−140−160−1801.3 1.5b1b2a3 b3 c3c1c21.1 1.3 1.5 1.0 1.1 1.2 1.3Transit Region (Microns)Figure 728


Power (MWm −2 )Phase oEfficiency %7.06.05.04.03.02.01.00.0150.0100.050.00.0−120−140−160a1a2−18070 90b1b2a3 b3 c3c1c270 90 110 70 90 110Frequency (GHz)Figure 829


6.05.04.03.0Uniformdopingdevice500K300KEfficiency (%)2.06.05.04.03.02.01.00.07.06.05.04.03.0500K500K300K300KNotchdopingdeviceGradeddopingdevice2.01.0 1.2 1.4 1.6 1.8 2.0 2.2Device Length (Microns)Figure 930


6.0Efficiency (%)Efficiency (%)5.04.03.02.01.30 1.40 1.50 1.60 1.70 1.808.06.04.02.0Uniform DeviceDevice Length (Microns)Notch Device0.01.00 1.10 1.20 1.30 1.40Device Length (Microns)Figure 1031


Power (mW)ResistanceΩReactance3503002502001501000−1−2−3−4−5−6−3−4−5−6−7−880 90 100a1 b1 c1a2 b2 c2a3 b3 c380 90 100 110 80 90 100Frequency (GHz)Figure 1132

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