T.e.L.G. SOLLNER, E.R. BROWN, and H.Q. LE

Microwave and MiUimeter-WaveResonant-Tunneling Devices

Resonant-tunneling devices, which may be capable of operation at terahertz frequen­cies, have been developed and tested. Included in these solid state microelectroniccomponents are oscillators, self-oscillating mixers, and hannonic multipliers. A char­acteristic ofthese devices, negative differential resistance (NDR), has been observed atroom temperature. Resonant-tunneling transistors, which promise operation in theterahertz frequency range, are also proposed.

PHYSICS OF RESONANT TUNNELING.,

A resonant-tunneling diode can respond toelectrical impulses in picosecond or sUbpico­second times. Therefore, these devices mayprovide a basis for developing electronic devi­ces that operate at terahertz frequencies.

The essential features of resonant tunnelingare shown in Fig 1. A thin layer of GaAs (2 to 10nm) is sandwiched between two thin layers ofAlxGal-#' The addition ofaluminum to GaAsraises the band-gap above that of GaAs so theAlxGal-xAs regions act as partially transparentmirrors to electrons; the higher energy level ofthesebarriers reflects the electronsbackto theregion of the structure from which they came.Thecharge transportacross the structure takesplace bytunneling through the thin (1 to 5 nm)AlxGal-# barriers.

This structure is the electron analog of aFabry-Perot resonator. As shown schematic­ally at the bottom of Fig. 1, the resonatorexhibits peaks in the electron transmission(current) as the incident electron energy (vol­tage) changes.

The physical implementation of these prin­ciples is summarized in Fig. 2. The layeredmaterial is grown in wafer form by molecularbeam epitaxy. Then the active regions are de­fined with ohmic contacts. These contacts areused as a mask to isolate the region under thecontact, either by etching mesas (as shown inFig. 2), orbyproton implantation, which makesthe surrounding material nonconductive. Be­cause the contact is oniy a few microns indiameter, electrical connection to the ohmiccontact is made with a pointed wire (whisker).

The Lincoln Laboratory Journal, Volume I, Number 1 (1988)

In some cases, the whisker acts as an antenna,couplinghigh-frequencyacfields to the double­barrier diode.

Using the Fabry-Perot analogy, coherence ofthe electron~wavefunction is required acrossthe entire double-barrier region to maintainresonant tunneling. Anyscatteringthat occursin either the well or the barriers will alter thewave function phase randomly, destroying itscoherence and therefore, the conditions re­quired for resonant tunneling. But a differentpicture (see Appendix, "Resonant TunnelingTheory"), one that does not require coherencebetween the parts of the wave function outsideand inside the well, can produce negative resis­tance, the essential characteristic that is ex­ploited in the devices that are described in thisarticle.

In 1973, Tsu and Esaki [1] derived the two­terminal current-voltage (IN) curves for finitemultiple-barrierstructures.This matchingtech­nique hasbeenremarkablysuccessful inexplain­ing experimental results. In 1974, Chang et al[2] were the first to observe resonant tunnelinginamonocrystalline semiconductor. Theyuseda two-barrier structure and ohserved the reso­nances in the currentbymeasuringthe I-Vcurveof the structure. The voltages at the currentpeaks agreed well with Chang's calculations.

A decade later, interest in the field wasrenewed when Sollner etal [3] showed that theintrinsic charge transportmechanism ofa two­barrierdiode could respond to voltage changesin less than 0.1 ps (> 1 THz). More recently,negative differential resistance (NDR), a char­acteristic ofresonant tunneling, has been mea­sured at room temperature [4].

89

SoUDer et al. - Microwave and Millimeter-Wave Resonant-Tunneling Devices

SPEED OF RESPONSE

Two factors indicate that the response timeof a double-barrier resonant-tunneling struc­ture should be as little as 0.1 ps: the resonant­state lifetime of an electron and the time re­quired for a double-barrier structure to reachequilibrium after an electrical impulse. Thispredicted response time is the time requiredfor the device's current to respond to a suddenchange in voltage. The comparison of the mea-

Fig. 1(a) - The energyprofile ofan electron in a double­barrier resonant-tunneling structure is shown here. Thetop illustration, which includes the energy well pro­duced by the twoAlxGal_xAs layers, shows the unbiasedenergy profile. The AlxGal_xAs layers act as partiallytransparent mirrors to the electrons, similar to a Fabry­Perot resonator. (b) In this plot of diode current as afunction of incident electron energy, the large resonantcurrent at pointA corresponds to the energyprofile ofA;the valley in the current-profile at point B corresponds toenergy profile of B. Although the energy of incidentelectrons is higher at B, the absence of resonance low­ers the current.

sured and predicted times not only gives anindication ofthe accuracy ofthe models, it alsoindicates the fundamental limits of operationimposed by the structure of double-barrier de­vices. One ofthe most significant limits ofoper­ation is fmax, the maximum useful frequency atwhich the device exhibits NDR. This frequencyis the point above which NDR is no longerobservable at the terminals of the device.

If the voltage across a double-barrier struc­ture is instantaneously changed, the currentthrough the device changes to a different steady­state value. As in a Fabry-Perot resonator, thesteady-state charge in the well must decreasewhen the currentdecreases, and increase whenthe current increases. The lifetime of any reso­nant state, including the one represented byanelectron initiallyplaced in the well between thetwo barriers ofa resonant-tunneling structure,is given by T =~/LlE, where LlE is the energyhalf-width ofthe transmission probabilityfunc­tion through the resonant state. It takes approx­imatelyone lifetime to fill or emptythe well to anew steady-state value. Since the carrier trans­mission probability is determinedbythe ampli­tude of the wave function inside the well, thecurrent will reach its new steady-state value inapproximately the lifetime of a resonant state.

The lifetime of an electron in between thebarriers has been calculated for three repre­sentative structures by Sollner et al [5) andranges from 4 ps for a 2.5-nm AlAs barrier to0.16 ps for a 3.0-nm Gao.7AlO.3As barrier. InTable 1, this time is found from T = 1I(27TfLlE).

The transit of electrons across the structure'sdepletion region produces an additional delaythat ranges from 0.16 to 0.69 ps. Total delays,the intrinsic response times, therefore rangefrom 0.4 to 5.0 ps.

For signals with periods much shorter thanthe intrinsic response time, the current lagsthe applied voltage and the I-V curve for thehigh-speed signals should deviate markedlyfrom the dc I-V curve. The intrinsic responsetime was first measured experimentally byexamining the difference between the dc I-Vcurve measured and the I-V curve inferred fromhigh-frequency measurements. Because the re­sponse times were in the picosecond range,

~DepletionRegion

Voltage

Voltage

A

-- ...

-c::(1)......::J

U

LargeResonantCurrent

b)

SmallNonresonant

Current

AccumulationRegion

a)

90 The Lincoln Laboratory Journal. Volume I, Number 1 (1988)

SoUDer et aI. - Microwave and Millimeter-Wave Resonant-Tunneling Devices

Whisker

Ohmic Contact

0.5.um ' ' __ ~~..lo..lo..~~~o...lo..lo...lo..lo..:l.1/GaAS,1017_10 18 cm-3 n-Type

1-5 mm ' __ AlxGa1_xAs

2-10 mm ----- GaAs

1-5 mm ::::~-- AlxGa1_xAs

~-------_.............--1-5 .um __....~L. .......

n+ GaAs Substrate, 1018 cm-3 Si

Fig. 2 - This double-barrier diode has 1- to 5-nm barriers and a 2- to 10-nm well.

operation at terahertz frequencies was nec­essary.

The straightforward approach to detenrnn­ing the frequency response of a device is tosweep through the I-V CUIve at increasing speeduntil the measured I-V curve differs from the decurve. Unfortunately, it is difficult to measurecurrent at frequencies above those accessibleto sampling oscilloscopes (100 GHz). There­fore, we used a differential measurement tech­nique. We swept through alarge,low-frequencyvoltage-range and measured the diode currentwith relatively simple conventional techniques.At the same time we superposed a small high­frequency signal across the diode. The low­frequency current revealed changes in curva­ture of the I-V curve that were proportional tothe high-frequency signal. Besides tractabil­i~y, this method of measurement closely re­sembles the actual operating conditions of de­vices which utilize NDR. In practical operation,a device is biased into the negative differentialregion by a large de bias and the superposedvoltage doesn't extend far outside the NDRregion.

The circuit used for applying ac and de fields

The Lincoln Laboratory Journal, Volume 1, Number 1 (1988)

to the double-barrier diode is shown in Fig. 3.The corner-reflector mount was originallydeveloped for Schottky-diode mixers in the farinfrared [6]. Frequencies between de and about20 GHz can be applied through the coaxial con­nector via the whisker that contacts the activearea. The GaAs substrate is soldered to thechip stud, which is at the same ground poten­tial as the comer reflector. For frequencies ofabout 100 GHz to a few terahertz, the longwhisker acts as an antenna, and the conduct­ing surfaces cause images of the whiskerto produce an antenna array. The array will re­ceive energy in a beam that has a frequency­dependent direction, but is approximately 45°from all surfaces of the cube. The full cone­angle of the beam is about 20°.

For the 2.5-THz measurements, for example,the power produced by an optically pumpedmethanol laser (about 100 mW) was matched tothe antenna pattern with a lens, thus couplingabout 50% of the incident power onto theantenna and producing an ac signal across thedouble-barrier structure. The characterizationof the comer-reflector mount at lower frequen­cies (using measurements performed by Fet-

91

Sollner et aI. - Microwave and Millimeter-Wave Resonant-nmneling Devices

terman et all led to an estimate of 50 n for theantenna impedance ZA" This parameter wasused in Eq. (1) to calculate the curves in Fig. 4.

At high frequencies the current responsivity~,which is the change in dc current (t.I), dividedby the change in ac power applied, (t.Pac)' isgiven by

<1I(V) 21"(V)ZA ( 1 )2Rj(V) = <1Pac = (1+ZA/Rs)2 wRsC (1)

In Eq. 1, I" is the second derivative of the I-Vcurve at the ac frequency of interest. Thisexpression gives the I-V curve for current re­sponsivity measured over the voltage range ofinterest. Measurements were made at 1, 138,761, and 2,500 GHz on a double-barrier diodewith 3.0-nmwell and barriers. The results at dc,

1 GHz and 2.5 THz are shown in Fig. 4. Themeasurements for 138 and 761 GHz were essen­tially identical to the I-GHz curve. Since theI-GHz signal's period is long compared withthe expected intrinsic response time, deviationin the I-V curve shouldn't occur until frequen­cies that are orders of magnitude higher arereached. The reason for the change between dcand 1 GHz is not known, but it is probably dueto slow traps in the material.

By 2.5 THz, the diode's I-V curve looks quitedifferent from the dc curve. In one direction,NDR has vanished, but it remains in the otherdirection. Sollner et al [3] take this as evidencethat the intrinsic response time for this deviceis of the order of T = (27Tf)-1 = 6 X 10-14 s. Thisresult agrees approximately with theoretical

Table 1 - Measured and Calculated Parameters forThree Different Wafers of Double-Barrier Diodes

Material ParametersBarrier materialBarrier thickness (nm)Well thickness (nm)Doping outside barriers (cm-3)

Electrical ParametersPeak-to-valley ratio, 300 KPeak current density (Xl04 A cm-2 )

Depletion layer at bias (nm)Capacitance (fF)aMaximum negative conductance (ms)aSeries resistance (.o.)a

Oscillation CharacteristicsDC bias IB, VB (mA, V)

fosc (GHz)b

AlAs2.54.5

1 Xl018

1.7/10.815

1005.010

0.7,0.40

20.7

Wafer

2 3

Gao.7AI0.3As AlAs3.0 1.54.5 4.5

2 XlO17 2 X 1017

1.3/1 3.5/11.2 4.030 7050 208.0 13.015 15

2.7,0.32 3.0,0.95

43.7 201

Maximum Oscillation Frequencyf max (GHz)C

f depl (GHz)d

f':'E (GHz)e

Theoretical

351,000

40

70500

1,000

270230400

92

aTypical values for a circular mesa of 4-J.'m diameter.

bMaximum observed fundamental oscillation frequency.

Cfmax = (21TC)-l{-Gmax/Rs-G~ax)'12

dFrom depletion layer drift time assuming a drift velocity of 107 cm/s.

eFrom calculation of energy width of transmission through double-barrier structure.

The Lincoln Laboratory Journal, Volume 1, Number 1 (1988)

SoUDer et a1. - Microwave and Millimeter-Wave Resonant-Tunneling Devices

12.5-J.LmDiameter Tungsten

IntermediateFrequency OSM

Connector900 Copper

CornerReflector

Tungsten WhiskerAntenna

GaAs Chip

CopperGround Plane

Chip StudLock Screw

CopperGround Plane

Detail of Chip Stud Mounting

Fig. 3 - This corner-reflector mount is used to apply signals to double-barrier diodes. For frequencies between de and20 GHz, the signal is coupled through the OSM connector. Above 100 GHz, the long whisker acts as an antenna,coupling the signals into the chip from a fuJI cone-angle of about 20°.

expectations from Table 1 for 3-nm barriers ofAlO.2SGao.7SAs (ftiE = 1 X lOIS). The asymmetryof both the dc I-V cUlVe and the response mayindicate that the two barriers or the two deple­tion regions are not identical.

The double-barrierdiode's equivalent circuit,shown in Fig. 5, provides a model for furtherunderstanding of this device. Included in theequivalent circuit are the voltage-dependentdynamic conductance G(V), the series resis­tance Rs ' and the parallel capacitor C that isinherent in the device structure. To a goodapproximation, the capacitance is formedacross a combination of the two barriers plusthe depletion region on the anode side of the

The Lincoln Laboratory Journal, Volume I, Number 1 (19881

biased device. The slope of the low-frequencyI-V cUlVe gives the approximate conductance,ie, (dI/dV)-1 =~ + 1/G = 1/G.

RESONANT-TUNNELINGOSCILLATORS

The NOR displayed by the double-barrierdiode is the basis of a fast and simple two­terminal oscillator. Interest in the oscillatorapplication stems from the need for a solidstate oscillation source at frequencies above300 GHz. In this region, few fundamental-modesolid state sources are available, so the double­barrier diode would be useful for applications

93

SoUDer et aI. - Microwave and Millimeter-Wave Resonant-Tunneling Devices

(2)

20 r-------------""T"""II'---.

C

0.24 0.48

J112

- G~ax

oVoltage (V)

_1 [-Gmax

21TC RS

G(V)

-0.48 -0.24

QRS =Pepi A + Rspread + Rc

E 0(1)........::l

U

Fig. 4 - The current-voltage (I-V) curves of a double­barrier diode show the variation with frequency of thedevice's negative differential resistance - it essentiallydisappears at 2.5 THz.

Fig. 5 - Using this equivalent circuit, the double-barrierdiode's maximum frequency of oscillation can be easilycalculated.

that require only modest amounts of power.Furthermore, these oscillations give a directand unmistakable proof of the speed of thesedevices. Of course, inherent circuit elements,particularlythe series resistance and the devicecapacitance shown in Fig. 5, must be consid­ered for circuit applications of these devices.

In the further analysis required for circuitapplications, the conductance, G(Vo), is inde­pendent of frequency but strongly dependenton the voltage amplitude, V0' across the device.The real part of the impedance, ZD' measuredacross the equivalent circuit of Fig. 5 is nega­tive up to a frequency given by the expression

1/2_ 1 (-Gmax 2 )fmax - 21TC ~ - Gmax

where Gmax is the maximum negative value ofdynamic conductance in the NDR region of theI-V curve. For all frequencies above fmax, thereal part ofthe terminal impedance will be posi­tive, making it impossible for oscillations tooccur.

Brown et al [7] found double-barrier diodeoscillators that cover the frequency range of20to 200 GHz (frequencies below fmax). Figure 6shows the experimental results obtained inthis range with diodes from the wafers listed inTable 1. The initial experiments were performedwith a device from Wafer 1 in a coaxial resona­tor, giving an oscillation frequency of 20.7 GHzand an output power well below 1 W. Attemptsto achieve oscillation with this device at fre­quencies near 40 GHz in a WR-22 waveguideresonator were unsuccessful, consistent withthe theoretical fmax of 35 GHz. The firstmillimeter-band results were obtained in thevicinity of 30 GHz and 40 GHz in WR-22 andWR-15 waveguide resonators, respectively,using a device from Wafer 2. This device couldhave achieved higher oscillation frequencies,but because of the relatively low peak-to-valleyratios of devices from Wafer 2, no attempt athigher oscillation frequencies was made. Thewafer's low peak-to-valley ratio indicates thatdevices from this wafer will provide limitedpower output and logic-swing capability.

The voltage range over which NDR exists forthese devices limits the output power of oscil­lators that use them. Kim and Brandli [8) and

94 The Lincoln Laboratory Journal, Volume I, Number 1 (1988)

SoOner et al. - Microwave and Millimeter-Wave Resonant-Tunneling Devices

100 Resonator Wafer

• Coaxial 1

S • WR-22 2::t • WR-15 3... 10

• WR-6 3Q)

~

~• WR-3 3

0

11a..+-'~

Co+-'~

0 I0.1 •0 50 100 150 200 250

Frequency (GHz)

Fig. 6 - The output power versus frequency of reso­nant-tunneling diodes for three different wafers wasmeasured in five different resonators.

Trambarulo [9] have shown that the maximumoutput power, assuming a sinusoidal voltagewaveform, is Pmax =(3/16)LH/tN, where ~I and~V are the current and voltage ranges of thenegative resistance region. For the 4-f.lm­diameter diodes ofWafer 3 in Table 1, this rela­tion gives Pmax = 225 f.lW. Diodes oflarger areacan produce more output power, but Gmaxscales linearly with diode area, making it verydifficult to obtain dc stability in larger devices.All of the 4-f.lm-diameter devices tested to datehave been stabilized with standard 50 f1 coaxi­alloads.

Diodes from Wafer 3 have produced the mostpowerful oscillations and the highest oscilla­tion frequency to date. This wafer extended themaximum observed oscillation frequency ofresonant-tunneling diodes from 56 to 201 GHz.The output power produced at 201 GHz wasabout 0.2 f.lW, although it reached 60 f.lW atlower frequencies. Several of the diodes testeddid not oscillate at all. The difficulty in initiat­ing oscillations near 200 GHz is consistentwith Eq. 2, which predicts that fmax = 270 GHzfor this diode.

The Fig. 5 model is identical to that used forp-njunction tunnel diodes. Indeed, the double­barrier resonant-tunneling diode and the p-njunction tunnel diode are similar, displayingsimilarities in I-V characteristics and in circuit

The Lincoln Laboratory Journal, Volume I, Number 1 (1988)

behavior. The major difference between the twotypes of diodes is in the magnitude of theirparasitics. In the p-n junction tunnel diode,very high doping densities are required on bothsides of the junction (N ~ 1 X 1019 cm-3 ) toachieve a high tunneling current density. Thishigh doping density creates a short depletionlayer and therefore a relatively large specificcapacitance. The double-barrier diode, however,can achieve a high current density with muchlower doping densities on both sides of thestructure (N = 1017 to 1018 cm-3 ).

Agood figure ofmerit for comparing the speedofdifferent diodes is the ratio ofspecific capac­itance to peak current density, y = Cs/Jp • Thisratio is known as the speed index [10]; it is ameasure of the current available for chargingthe device capacitance. For Wafer 3, this quan­tityisy = 1 X lOSpFcm-2/4.0 X 104 Acm-2 = 3.0psN. The fastest p-n junction tunnel diodesever reported [11] were made of GaAs and hady =14 to 16 psN, nearly a factor of five poorerthan the double-barrier devices. Moreover, thep-njunction tunnel diodes [12] achieved a max­imum experimental oscillation frequency ofonly 103 GHz with an output power well below1f.lW.

SELF-oSCILLATING MIXERS

Near the NDR region in an I-V curve, aresonant-tunneling diode's dynamic conduc­tance varies rapidly as a function ofthe appliedsignal voltage. This feature makes the resonanttunneling diode an efficient mixer. The Fourierseries of the diode's dynamic conductance haslarge components at the oscillation frequencyfo and its first few harmonics, particularly theeven harmonics when the I-V curve is antisym­metric about the bias point. The relativestrength of these components will determinethe efficiency of power conversion from thesignal frequency fs to the intermediate fre­quency fl, assuming that fs > fl. In the funda­mental mode of conversion, the signal has fre­quencyfs = fo ± fl, and in the second-harmonicmode, the signal frequency is fs = 2fo ± fl. Themost efficient conversion should be in thesecond-harmonic mode at the dc bias point ofmaximum negative resistance, because this

95

SoOner et aI. - Microwave and Millimeter-Wave Resonant-Tunneling Devices

point has approximate antisymmetry in the I-VCUlVe [ie, I(V) = -I(-V)). However, the fundamen­tal mode should achieve its maximum efficien­cy at bias voltages nearest the regions ofgreat­est cUlVature, where the Fourier series of g(t)has a predominant coefficient at the oscilla­tion frequency.

The resonant-tunneling self-oscillating mixerhas the potential to displace the Schottkydiodein many millimeter-wave applications. To dothis, it must demonstrate a competitive noisefigure, roughly 3 to 6 dB in the microwaveregion and 6 to 10 dB in the millimeter band.Although noise figures have not yet been stud­ied, measurements ofstable resonant-tunnelingdiodes indicate that they have very low intrin­sic noise (13). In fact, the measured noise poweris less than expected from the full shot noise

expression, for reasons that are not fullyunderstood. Nevertheless, this low noise figurewill undoubtedly work to the benefit of theresonant-tunneling-diode-based self-oscillat­ing mixer. And the resonant-tunneling self­oscillating mixer provides the intrinsic capa­bility to achieve conversion gain. Mixers suchas the standard Schottky diode aren't capableof gain and usually show losses of severaldecibels.

Using the fundamental mode of coaxial res­onant tunneling oscillators, we have operatedthem as mixers in the microwave region. Shownin Fig. 7 is the mixing spectrum ofan oscillatorwith an oscillation frequency of 14.2 GHz, asignal frequency of 8.2 GHz, and an intenne­diate frequencyof6.0 GHz. The single-sidebandconversion loss in this case is just under 6 dB,

-40 .-------,-----r---r--,---..----r-----,,..-----'T-----r----,

ow

lJ

Eco2...

CIJ~oa..

-50

-605 10

Frequency (GHz)

15

Fig. 7 - The frequency down-conversion of a signal at frequency 1/ by a double-barrier diode oscillating at thefrequency marked OW produces the difference frequency labeled OW-I/.

96 The Lincoln Laboratory Journal, Volume I, Number 1 (l988)

SoOner et aI. - Microwave and Millimeter-Wave Resonant-Tunneling Devices

-rr -rr/2 0 rr/2 rr

Phase (rad)

Fig. 8 - Voltage and current waveforms for a double­barrier diode reveal that the local maxima in the currentwaveform, if equally spaced in phase, should lead to astrong fifth harmonic component in the current-powerspectrum.

overall antisymmetry of this curve about theorigin.

To demonstrate this odd-harmonic genera­tion, a diode's I-V curve can be modeled with aseventh-order polynomial. Using this model,the diode is assumed to be driven by a sourcethat has an internal impedance less than theminimum negative resistance of the double­barrierdiode. Thus the currentacross the diodeis a single-valued function of the drive voltage.The numerically determined current-waveformof an 0.5 V source is shown in Fig. 8. The localmaxima in this waveform, if equally spaced inphase, should lead to a strong fifth harmoniccomponent in the current-power spectrum.This spectrum, shown in Fig. 9, predicts thatthe available fifth-harmonic powerwill be 0.065times that of the fundamental.

Figure 10 illustrates the power spectrumobtained for a resonant-tunneling diode thatwas mounted in a 50.n coaxial circuit andpumped at 4 GHz. As expected, even harmonicsare absentand the fIfth harmonic predominatesamong the odd harmonics. However, the mea­sured efficiency was only about 0.5%, signifi­cantly less than the theoretical prediction of6.5%. This discrepancy can possibly be attrib­uted to the test circuit, which does not allow

0.2~E

0 .....c::(I)......~

u

-0.4

0.4

>~ Ol---+--------"I~---;CO.::a> -0.2

0.2

which is only about 3 dB higher than the bestresults for room-temperature Schottky-diodemixers in the same frequency region. The exper­iments on the second-harmonic mode havejustbegun, using a waveguide oscillator in the mil­limeterband. The bestconversion loss achievedto date is about 12 dB for an oscillation fre­quency of50 GHz and a signal frequency of100GHz. This performance is comparable to thebest results reported for a pair of Schottkydiodes in the antiparallel configuration [14].

RESISTIVE MULTIPLIERS

Resonant-tunneling devices excel as resis­tive multipliers. A resistive multiplier, which isa form ofharmonic multiplier, generates powerat frequencies that aren't conveniently avail­able from fundamental oscillators. Harmonicmultipliers are often used for radio astronomy.In radio astronomy, heterodyne receivers, oper­ating at frequencies above 100 GHz, use powerfrom a harmonic multiplier as a local oscillatorsource. Harmonic multipliers are also the pri­mary source of power for molecular spectros­copy in the submillimeter wavelength spec­trum.

Currently, resistive multipliers usually useSchottky-barrier diodes, but the advantages ofresonant-tunneling diodes will promote theiruse as resistive multipliers. The absence ofeven harmonics in a resonant-tunnelingdiode'sdynamic conductance simplifies the design ofmultiplier circuits, particularly in the milli­meter-wave region. Also, because of its nega­tive resistance, the maximumtheoretical gener­ation efficiencyofa double-barrier diode can besignificantly higher than an ideal diode's n-2

(where n is the harmonic number) [15].If a resonant-tunneling diode is pumped so

that the peak amplitude of the voltage acrossthe diode occurs above the device's resonant­current peak, at least three local maximain thediode's currentwaveform will be produced overone cycle. (See Fig. 8 for a theoretical curve.)These maxima correspond to third- or higher­order odd-harmonic generation. The ease withwhich these higher-order odd harmonics areobtained is due to the presence of a peak and avalley in the diode's I-V curve, as well as the

The Lincoln Laboratory Journal, Volume I, Number 1 (1988) 97

SoOner et aI. - Microwave and Millimeter-Wave Resonant-Tunneling Devices

Fig. 9 - A power spectrum corresponding to the volt­age-current plot of the Fig. 8.

Fig. 10 - A strong fifth-harmonic component was con­firmed experimentally for a 4.25-GHz input signal.

Exposure

A= 0.85 J.Lm-Unexposed---- Q

······ .. ··10 Q

-'- 100Q

Theory

0.09

0.07Experiment

0.05

:;{0.03

E 0.01

Fig. 11 - Persistent photoconductivity is a characteris­tic of resonant-tunneling diodes. The experimental re­sults were obtained from a diode that was cooled to 20 Kin the dark and then exposed to progressively greaterlevels of light.

independent tuning of the harmonics. Ideally,the fifth harmonic should be tenninated with aresistance greater than the source resistance.But the third harmonic should be tenninatedwith a reactance, which eliminates power dis­sipation and reinforces the fifth-harmonic vol­tage. Combining these features in a one circuitwill allow independent tuning ofthe harmonicsand greater conversion efficiency for the fifthharmonic.

....c::~ -0.01 '. '1'1 r:::J I" ... ..:

U -0.03 (I ..... '. '1 ....1/ . I ~ ..

-0.05 I !i \~/-0.07 .: i

Ii-0.09 L......;....J;.....--L.----L_J......-.....L...---L. L.--...L-....J..--l

20,...--------------,

16

12

8:;{

4E.... 0c::Q)....

-4....::l

U-8

-12

-16

-20-0.4 -0.2 0 0.2 0.4

Voltage (V)

20

7fO5fO

Frequency

3fO

10

Frequency (GHz)

4.25f- GHz

12.75GHz 21.25

f- ....~.. ur v ...

- .J

-

I I-802

20

0

EIn -20't:l

....Q)

3: -4000-

-60

0.1 -

E::l........tlQ)a. 0.01 f-CJ)

....Q)

3:0

0-

0.001 ~

98 The Lincoln Laboratory Journal, Volume I, Number 1 (1988)

SoOner et aI. - Microwave and Millimeter-Wave Resonant-Tunneling Devices

PERSISTENT PHOTOCONDUCTIVITYAND A RESONANT-TUNNELINGTRANSISTOR

Atransistorbasedona double-barrier resonant­tunneling structure could significantlyimproveupon the present state of the art. Persistentphotoconductivity provides clues to the opera­tion ofsuch a transistor. wherein the well regionacts as the device's control electrode.

A resonant-tunneling structure sometimesexhibits persistentphotoconductivity [16], thatis, the structure's I-V curve shifts with succes­sive exposures to light. Figure 11 illustratesthis shift. Photoionization ofDX centers in theAlO.3Gao.7 barriers in the structure causes theshift in the I-V curve. (DX centers are latticevacancies associatedwith a nearbydonor atom.For a detailed discussion of DX centers, seeNelson [17] or Lang et al [18].) This photoioni­zation creates a dipole region with fIxed posi­tive charge in the barriers and free electronsoutside the barriers. Any electrons that resideinitially in the well quickly escape because ofthe higher energy of the confined band edgewithin the well and the short resonant-statelifetime. The dipoles produce the bandbendingshown in Fig. 12. The well is lowered in poten­tial by an amount 111>, and the barriers are alsolowered. The resulting shifted I-V curve shows

r-----,I

+ + +

a peak transmission that has been moved to alower voltage by the lowered well and a highercurrent density caused by the lower effectivebarriers.

Figure 12 shows that DX centers in the barri­ers provide a way ofadjusting the well potentialrelative to the outer contact regions. This effectis analogous to the modulation of the basepotential of a conventional transistor. In thiscase, the structure's potential well serves asthe control electrode.

The transconductance of such a device, Gm•

is related to the change in collector currentdensity, IlJc ' and the change in well potential,111>. by

(3)

where A is the emitterarea The shift in the wellpotential is approximately related to the shiftin the current peak 11Vp by

(4)

This expression is valid only for the specificdiode ofSollner et al [19]. One factor of two onthe right side approximately accounts for thedepletion region on the collector side whenbiased to the current peak. The other factor oftwo arises from the base-to-emitter voltage,

r----..,I

+ + +

----- No Ionized Centers

With Ionized Centers

Fig. 12 - Positive charge in the barriers of a double-barrier diode produces band bending (red line); a device withoutionized centers has no band bending (black line).

The Lincoln Laboratory Journal, Volume I, Number 1 (1988) 99

SolIDer et 81. - Microwave and Millimeter-Wave Resonant-Tunneling Devices

which is, at most, half of that applied betweenthe base and collector. Thus the transconduc­tance becomes

4A~Jc

Gm=~p

(5)

Specific contact resistances of the order of10-7 f1 cm2 are necessary to realize such a highextrinsic transconductance.

The frequency above which the small-signalshort-circuit current gain drops below unity is

where Rb is the base resistance and Cc is thebase-to-collector capacitance. As the base isverythin and lightlydoped, it mightbe expected

where C is the total input capacitance. Using a1-j..tm gate contactand 40-nm n- regions, we findfT = llO GHz.

The maximum frequency of oscillation fmaxwill also depend on the base resistance. Fornegligible emitter resistance,

Symbols

DoPmax

But there is one complication. The leakagecurrent also changes with !:J.cj>, but this changeis probably related to the presence of OX cen­ters in the barriers rather than to the modula­tion of the well potential. To account for thiscontribution, we assume that, atvoltages belowthe current peak, the transistor output imped­ance is large and positive, so we can extrapolatethe excess current at high voltage back to zeroand keep the output impedance positive. Theseextrapolations are shown in Fig. 13. Usingthis figure, an emitter width of 1 j..tm gives anintrinsic transconductance of 4,000 mS/mm.

Units are shown in brackets.

A Cross-sectional area of a device [cm2)

C Capacitance [F)Cc Collector capacitance [F)Cs Capacitance per unit area [F/cm2 )

Ec Fermi energy [J)e Charge on the electron [CIfI Intermediate frequency [Hz)fmax Frequency above which the terminal

conductance is positive for all vol­tages, hence maximum oscillationfrequency [Hz)

to Output frequency [Hz)fs Signal frequency [Hz)fT Frequency above which the small­

signal short-circuit current gain isbelow unity [Hz)

filE Frequency corresponding to resonant­state lifetime [Hz)

Gmax Maximum negative value of voltage­dependent conductance [51

G(V) Voltage-dependent conductance of aresonant-tunneling diode [5]

g(t) Conductance of a diode modulated bya changing voltage (5)

I Current [A)IF Intermediate frequency [Hz)J c Collector current density [A/cm2)

J p Peak current density [A/cm2 )

t:N

'Yw<t>(x)

CfT = 2rrG

m

Carrier concentration [cm-3)

Maximum output power obainablefrom a negative-resistance amplifier[WJBase resistance [D.JCurrent responsivity [AlWJSeries resistance [D.IVoltage [V)Voltage amplitude [VJVoltage at frequency m [V]Antenna impedance [D.JDevice impedance [D.JLoad impedance [D.JEnergy half-width of transmissionfunction [JjCurrent excursion of negative differ­ential resistance region [AJChange of current [AIChange of ac power [WJShift of the voltage of the currentpeak from ionized charges in the bar­riers [VJVoltage excursion of negative dif­ferential resistance region [AjShift in potential of the well fromionized charges in the barriers [eVJDielectric constant [F/cmJSpeed index [slV)Angular frequency [S-l JElectrostatic potential energy leV)

(6)

(7)

100 The Lincoln Laboratory Journal, Volume I, Number 1 (1988)

SoUDer et a1. - Microwave and Millimeter-Wave Resonant-Tunneling Devices

0.800.640.32 0.48

Voltage (V)

0.16

4 ~/1Vp

GM =' 4/11/ /1Vp

~ 3E .....<0

ii.....~c

Q) 2 0l-I-

~::lU ~

"<

that the base resistance would be high. How­ever, the quantum-well geometry reduces theresistance considerably. Electron mobilities inmodulation-doped quantumwells are veryhighat temperatures less than 100 K. Although thisstructure is not a modulation-dopedwell in theusual sense, the base layer near the resonantcurrent peak. acquires charge from the transit­ing carriers without any direct doping [20]. Forpresent samples, the average well-charge den­sity is approximately 1017 cm-3 •

Using a mobility of 5 X 105 cm2(V-s for abase carrier density 2 X 1017 cm-3 (the bestmobility [21] at 50 K), a 1 X 20-,umemitter, anda 4.0-nm well thickness, the base resistance isless than 10 !1. This gives an RbCc product ofabout 0.5 ps, resulting in an fmax of 330 GHz.Any increase in current density increases fTand fmax proportionately. Theoretically pre­dicted currents are several times higher thanpresently observed values.

CONCLUSIONS

Much fertile, yet uncultivated, territory re­mains in the realm of multiple-barrier tunnel­ing. Three-terminal devices are in their infancy,as are devices for digital applications. The pos­sibility of electro-optical effects has receivedsome attention, and several novel devices haveresulted [22]. Most structures to date have con­tained only two barriers, but investigation ofthe interaction of three or more barriers mayyield even more interestinganduseful phenom­ena

An extension of multiple-barrier structuresto the inclusion of many barriers produces asuperlattice. Because of domain formation,superlattices have been impractical electricaldevices in the past. Many variations remainuntested, even unanalyzed. For example, the"CHIRP" superlattice was examined in somedetail [23], but onlyone type ofperiodvariationwas investigated. The domain formation thathas limited this field to date may be overcomewith structures that are yet undeveloped.

All of the devices discussed in this paperhave been small comparedwith their operating

Fig. 13 - These calculated 1- V curves for a resonant­tunneling transistor are based upon the assumption thatthe output impedance of the transistor is large and posi­tive and that the excess current at high voltage can beextrapolated smoothly back to zero.

15

10

~5

E..... 0cQ)l-I-

-5::lu

-10

-15-2 -1 0 2

Voltage (V)

Fig. 14 - The predicted peak-to-valley ratio of a reso­nant-tunneling device's I-V curve is much greater thanthat measured for any experimental devices. Improve­ments in material purity should bring the observed val­ues into closer agreement with the theory.

The Lincoln Laboratory Journal, Volume I, Number 1 (1988) 101

SolIDer et aL - Microwave and Millimeter-Wave Resonant-Tunneling Devices

wavelength. Therefore, they are lumped ele­ments, not transmission media. A bulk mate­rial that could provide large, fast impedancenonlinearities would be useful at high frequen­cies. With two-barrier structures, these nonlin­earities are difficult to create, but some varietyofsuperlattice may provide the material neces­sary for large-scale structures that will findapplication as traveling-wave devices.

The materials growth that makes possiblethe high spatial resolution in heterostructureformation is well advanced and progressingrapidly, but much improvement is still possi­ble. Material of sufficient quality for observingreasonable peak-to-valley ratios at room tem-

102

perature has been available only for two years.Theoretically, as shown in Fig. 14, this peak-to­valley ratio should be much greater. Materialsof greater purity could validate most of theassumptions leading to the calculated curve ofFig. 14.

In short, the future of multiple-barrier tun­neling structures appears bright, especially inview of the high level of interest in the field.Some of the devices that are just beginning todemonstrate feasibility will be commerciallyexploited in the next several years and manyyet undevised structures will reach the samepoint in the years to come.

The Lincoln Laboratory Journal, Volume I, Number 1 (19881

SolIDer et a1. - Microwave and Millimeter-Wave Resonant-Tunneling Devices

Appendix: Resonant Tunneling Theory

Temporal Behavior

calculated in the barrier region using the self­consistent Thomas-Fermi equation (cgs units).

Time evolution of the system has been eliminatedfrom the stationary-state calculation above. But it ispossible to find the lifetime of a transiting electronin the resonant state that it occupies while it isbetween the two barriers. The approach, first derivedfor atomic and nuclear resonances, is applicable toany resonant state and can be applied to resonanttunneling. The lifetime is given by the uncertaintyrelation, T =.fi/ liE; liE is the half-width ofthe peak in

where Ef is the Fermi energy, E is the dielectric con­stant, and no is the average volume-doping density.This expression is solved analytically in the regionswith nonzero net charge and then matched numeri­cally at the boundaries. In practice, a parabola isfitted to the solution in the cathode to limit theband-bending region. The spatial extent of the fittedregion is taken to be about twice the Thomas-Fermiscreening length. A potential profile calculated for adouble-barrier structure with doping carrier densityof 1017 cm-3 in the outer regions is shown in theFigure.

Once the potential has been found, the transmis­sion coefficient ofan electron with a given energy isdetermined by using the transfer-matrix method andmatching boundary conditions. The current is thenfound by integrating over the incident electron dis­tribution and the densityofavailable final states [11.The transfer matrix is numerically calculated for anarbitrary parabolic potential profile. To guaranteerapid convergence, the potential is divided into a few« 10) spatial segments with transfer matrices cal­culated for each partition.

Even though the cathode contains an accumula­tion region, we obtain better agreement between thecalculated and measured transmission coefficientsif we use the equilibrium Fermi distribution of thecathode material and ignore possible tunneling ofthe accumulated electrons. This agreementbetweentheory and experiment may be due to the improba­bility of electrons scattering (inelastically) into theaccumulation region, which makes the lifetime fortunneling out ofthe region shorter than the time forscattering in. However, this means that there ismuch less band bending than has been assumed.

(A-I)4tren 5 [ I )]3/2 ~et>l/lx) = --E-O- ( I - I _ e~ ~

Stationary-State Calculation

The theory of resonant tunneling is still evolving.The full problem is complicated, involving self­consistent solution of Poisson's equation and thetime-dependent Schrodinger equation. The spatialquantization that creates the effects of interest alsorenders inadequate many of the common approxi­mations used in the solution of these equations. Tofurther complicate matters, scattering from impuri­ties, defects, other carriers, and collective excita­tions are almost certainly important, but the inclu­sion ofthese effects in detail is a difficult theoreticalproblem. On the positive side, however, the simplestcalculations seem to explain the general outline ofthe experimental observations.

The first simplification to make in the analysis ofthe resonant-tunneling structure is the eliminationof time-dependence in the solution of the control­ling equations. This stationary-state treatment isbased on the approach first applied to finite super­lattices byTsu and Esaki [1]. The calculation shownhere incorporates some of our own refinements.

For a first-order solution to the problem, weassume that electrons are the only charge carriersand that they interact only with potential discontin­uities in the conduction band. In addition, we usethe simplification of the effective-mass model forthe electrons. The matching of wave-functions athetero-interfaces is based on the conservation ofprobability current, which also accounts for the dif­ferent effective masses in different semiconductors.We use superposition to determine the potentialprofile as an electron makes a transit of the struc­ture; the potential is taken as the sum of the poten­tial due to the conduction-band offsets, the appliedbias, and any localized charges within the structure.A further, and final, simplifying assumption is thatthe regions outside the barriers house an electrongas, the field-screening behavior of which is des­cribed by the Thomas-Fermi approximation.

The first step in the calculation of a resonant­tunneling I-V curve is the determination of the spa­tial variation of the electrical potential experiencedby the electrons as they transit the double-barrierdevice under consideration. In addition to the poten­tial change produced bythe barrier regions, the elec­trostatic potential applied by the external (biasing)field produces accumulation and depletion regionsthat will perturb the potential profile. The spatialdependence of the electrostatic potential, </>(x) , is

The Lincoln Laboratory Journal, Volume I, Number 1 (1988) 103

SolIDer et aI. - Microwave and Millimeter-Wave Resonant-Tunneling Devices

which maintains the coherence ofthe wave functionacross the incoming barrier, the sequential modelattempts to incorporate the effects of scattering byeliminatingthe assumption ofphase coherence. Thismodel is called the sequential model because eachelectron is presumed to enter the structure andtunnel through the first barrier, achieve a resonantstate within the structure's potential well, and thenexit the structure sequentiallybytunneling throughthe remaining barrier. Luryi proposed that all phasecoherence is lost before each electron leaves thestructure's potential well and that the negativeresistance exhibited by the double-barrier deviceresults from the conservation of momentum. Whenthe peak in the density of states in the well (formomentum perpendicular to the well) is below theconduction band edge ofthe cathode, electrons cannot tunnel into the well.

Wei! and Vinter [25] have recently calculated thatthe peak current densities should be the same forboth the ballistic and the sequential models. It maybe, however, that the two models are equivalent asthey are presently defined. In their sequential­tunneling calculations, Wei! andVinteruse the sameboundary conditions as those used for the resonantmodel (see Ref. 8 in their paper); they maintain thecoherence ofthe wave function across the incomingbarrier. The effects of the second barrier enter viathe width of the quasibound state in the well, againwith a calculation that assumes coherence acrossthe barrier. Perhaps it is not surprising that, with noscattering in the well, the calculations of ballisticand sequential tunneling give the same result.

Wei! and Vinter do attempt to include the effects ofscattering in the well, via a broadening of the quasi­bound state. They conclude that, as long as theenergy width of this state is small compared to theenergy width of the incoming carriers (the usualexperimental situation), the lower peak transmis­sion is offset by the additional width. Thus the inte­gral determining the peak current is unaffected.However, the technique of including scattering stillimplicitly assumes the phase coherence discussedabove, even though scatteringwill generallyalter thephase after the scattering event.

This calculation does not appear to be the same asthe one originally suggested byLuryi [24] because itdoes not perturb the phase coherence across thestructure. There are also important scattering pro­cesses, such as scattering in the barriers, that arenot in Luryi's model. Thus the role of scatteringremains one ofseveral important unanswered ques­tions in resonant tunneling.

20 40 60 80 100 120 140

Distance (nm)

-1 .0 '--_'-----''------'_----'_----':=--.1._---'

o

Scattering

the transmission coefficient T(E). Frequencies cor­responding to f~E = (27TTt l are calculated for thethree structures and listed in Table 1.

A time-dependent calculation of the electron dis­tribution has been performed by using the Wignerfunction approach [20). The time required to reachequilibrium after an impulse to the system is com­parable to that estimated by the resonant-state life­time. This calculation. however, offers the advantageof predicting the time evolution of the wave func­tions for all times.

A complete time-dependent solution should takeaccount of charge redistribution from applied elec­tric fields and motion of carriers through the deple­tion and accumulation regions. Scattering plays animportant part in these processes, because scatter­ing in the barriers removes the assumed conditionofconservation oftransverse momentumduring tun­neling, and scattering in the well region or regionsdestroys the coherence of a carrier wave functionover the structure.

According to Luryi [24], scattering may dominatethe charge-transport process through a double­barrier structure. His proposal has led to the devel­opment ofa second, sequential, model ofthe double­barrier structure. In contrast to the ballistic model,

1.0 ,...-------------~

0.5

:;-Q)

>- 0OJ~

Q)C

L.U

-0.5

Calculatedpotential energy ofan electron as it transits adouble-barrier diode.

104 The Lincoln Laboratory Journal, Volume I, Number 1 (1988)

SoDner et aI. - Microwave and Millimeter-Wave Resonant-Tunneling Devices

None of the experimental work described herecould have been accomplished without help fromstaff members skilled in the art of material growthand fabrication. We are especially indebted to W.D.Goodhue for producing excellent quality hetero­structures grown by molecular beam epitaxy, forsuggesting useful structures, and for overseeingmuch of the processing. C.L. Chen has also beenvery helpful in processing, as have G.D. Johnson,K.M. Molvar, W.F. DiNatale, and RF. Murphy. Expertpackaging help has been provided by N. Usiak, D.J.Landers and P.J. Daniels. C.D. Parker has providedconsiderable expertise with the measurements.

We also owe much to the environment of ideas inwhich we work. P.E. Tannenwald, B. Lax, C.O. Bozler,A.R Calawa, B.J. Clifton, M.W. Geis, W.D. Goodhue,MA. Hollis, RA. Murphy and H.J. Zeiger at LincolnLaboratory; F. Capasso and S. Luryi at AT&T BellLaboratories; W.R Frensley, RT. Bate andMA. Reedat Texas Instruments; M. Heiblum and RA. Kiehl atIBM; D.D. Coon at the University of Pittsburgh; H.Fetterman at UCLA; H. Sakaki at the University ofTokyo; and L.F. Eastman at COTIlell have all contrib­uted to useful technical discussions.

This work was sponsored by the US Army Re­search Office and by NASA.

REFERENCES

1. R. Tsu and L. Esaki, "Tunneling in a Finite Superlat­tice," Appl. Phys. Lett. 22. 562 (1973).

2. L.L. Chang, L. Esaki, and R. Tsu, "Resonant Tunnelingin Semiconductor Double Barriers," Appl. Phys. Lett.24. 593 (1974).

3. T.C.L.G. Sollner, W.D. Goodhue, P.E. Tannenwald, C.D.Parker, and D.D. Peck, "Resonant Tunneling ThroughQuantum Wells at Frequencies up to 2.5 THz," Appl.Phys. Lett. 43. 588 (1983).

4. M. Tsuchiya and H. Sakaki, "Room Temperature Oper­ation of High-Performance AlAs/GaAs/AlAs ResonantTunneling Diodes with Atomically Controlled BarrierWidth," IEEE Int. Electron Devices Mtg., 662 (1985).

5. T.C.L.G. Sollner, W.D. Goodhue, and H.Q. Le, "ObselVa­tion of Millimeter-wave Oscillations from ResonantTunneling Diodes and Some Theoretical Considera­tions of Ultimate Frequency Limits," Appl. Phys. Lett.50. 332 (1987).

6. H.R. Fetterman, P.E. Tannenwald, B.J. Clifton, C.D.Parker, W.D. Fitzgerald, andN.R. Erickson,Appl. Phys.Lett. 33. 151 (1978).

7. E.R. Brown, T.C.L.G. Sollner, W.D. Goodhue, and C.D.Parker, "Millimeter-band Oscillations Based on Res­onant Tunneling in a Double-barrier Diode at RoomTemperature," Appl. Phys. Lett. 50. 83 (1987).

8. C.S. Kim and A. Brandli, "High-frequency High-powerOperations ofTunnel Diodes," IRE Trans. Circuit The­ory eT8. 416 (1961).

9. R.F. Trambarulo, Int. Solid-State Circuits Con]., Phila­delphia, PA, 1961.

10. P.E. Davis and G. Gibbons, "Design Principles andConstruction of Planar Ge Esaki Diodes," Solid StateElectron. 10. 461 (1967).

11. D.T. Young, CA. Burrus, and R.C. Shaw, "High Effi­ciency Millimeter-Wave Tunnel-Diode Oscillators,"Proc. IEEE 52. 1260 (1964).

12. CA. Bunus, "GalliumArsenide Esaki Diodes for High­Frequency Applications," J. Appl. Phys. 32. 1031(1961).

13. E.R. Brown, T.C.L.G. Sollner, and W.D. Goodhue, SolidState Research Report, MIT Lincoln Laboratory1986:1. 37 (1986).

14. D. Carlson and M.V. Schneider, "SubharmonicallyPumped Millimeter-Wave Mixers," IEEE Trans. Micro­wave Theory Tech. MTT 26. 706 (1978).

15. C.H. Page, "Harmonic Generation with Ideal Rectifi­ers," Proc. IRE 46. 1738 (1958).

16. E.R. Brown, T.C.L.G. Sollner, W.D. Goodhue, and C.D.Parker, "Fundamental Oscillations up to 200 GHz in aResonant-Tunneling Diode," Device Research Con].,Paper IV A 2 (1987).

17. R.J. Nelson, "Long-lifetime Photoconductivity Effectin n-Type GaAlAs," Appl. Phys. Lett. 31. 351 (1977).

18. D.V. Lang, RA. Logan, and M. Jaros, Phys. Rev. B, 1015(1979).

19.

20.

21.

22.

23.

24.

25.

T.C.L.G. Sollner, H.Q. Le, CA Correa, and W.D. Goodhue,"Persistent Photoconductivity in Resonant TunnelingStructures: Toward a Resonant TunnelingTransistor,"IEEE/Comell Con]. Advanced Concepts in High SpeedSemiconductor Devices and Circuits, p. 252.W. Frensley, "Quantum Transport Simulation of theResonant-Tunneling Diode," IEEE Int. Electron Devi­ces Mtg., Paper 25.5 (1986).A.C. Gossard, "Quantum Well Structures and Super­lattices and Their Applications Potential," Inst. Phys.Corif. Ser. 69, 1 (1984).F. Capasso, "New MUltilayer and Graded Gap Optoelec­tronic and High Speed Devices by Band Gap Engineer­ing," SUlf. Sci. 142. 513 [1984).T. Nakagawa, N.J. Kawai, and K. Ohta, "Design Princi­ples for CHIRPSuperlatticeDevices," SuperlatticesMicro­struct. 1. 187 (1985).S. Luryi, "Frequency Limit ofDouble-barrier Resonant­Tunneling Oscillators," Appl. Phys. Lett. 47.490 (1985).T. Weil and B. Vinter, "EquiValence Between ResonantTunneling and Sequential Tunneling in Double-barrierDiodes," Appl. Phys. Lett. 50. 1281 [1987).

ACKNOWLEDGMENTS

The Lincoln Laboratory Journal, Volume I, Number 1 (1988) 105

{,

SoOner et ale - Microwave and Millimeter-Wave Resonant-Tunneling Devices

T.C.L. GERHARD SOLLNERisa stalImemberintheMiero­electronics Group. Duringhis five years at Lincoln Lab­oratory, he has concentrat­ed on novel approaches tohigh-speed devices. Before

coming to Lincoln Laboratory. Gerry was an assistant pro­fessor at the University of Massachusetts. He received abachelor's degree in physics from the Georgia Institute ofTechnology and a doctorate in physics from the Universityof Colorado. In his spare time, Gerry enjoys windsurfing.cooking. and skiing.

106

HAN QUANG LE is a staffmember in the QuantumElectronics Group. Beforejoining Lincoln Laboratorytwo years ago. he worked forthe National Magnet Labora­tory at MIT. Han received a

PhD in physics from MIT. Han's current research is focusedon optoelectronics. In his free time, he enjoys exploringwilderness areas.

The Lincoln Laboratory Journal, Volume 1, Number 1 (1988)