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Quantum Electronics

Udi Meirav and Mordehai Heiblum

The pursuit of smaller, faster devices for manipulating the flow ofelectrons is riow approaching the whimsical world dominated by wavedYfJamics.

If you have ever used a pocketcaJculator, you probably couldriot help but be amazed howsomething so small can be sosmart-and so fast. In fact, thesmallness is even more impres­sive when looking beyond whatmeets the eye. The actual brainsof these calculators, integratedcircuits, are made of silicon tran-

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sistors too small to be seen withthe naked eye. But try to pro­gram your calculator to performsomewhat more complex calcula­tions and you won't fail to noticea slight delay before the answeris displayed. This perceptible de­lay is the major reason drivingmany scientists to seek new waysto make transistors faster yet.

• Gallium arsenide is the pre­ferred m{1terial for researchingquantum elecfronic i?ehavior oc­curring at the limits of circuitrymlQiaturization. In this scanningtunneling microscop~ image of thesurface of gallium ars'enide; indi­vidual atoms are "visible"(gallium­blue, arsenic-red);

As the tasks expected fromcomputers get more numerousand complex, the number of elec­tronic steps-and consequentlythe time-required to completeeach task increases; The briefpause of the pocket calculator be­comes a significant delay in bigcomputing machines. One of thekeys to quickening the pace ofthese machines is to have eachelement of the electronic circuit-transistors, of which there aremillions-carry out its oWnlittlefunction faster. Faster meanspassing electrons, the carriers ofelectric current, from one end toanother in less time.

Looking at this simply, for agiven electron speed, the smallerthe device, the less time it takesit to perform its' function. Sinceelectrons can easily travel at

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.MESOSCOPICTRANSISTORS

SIMPLE TRANSISTOR

• Top: In a simple transistor, theflow of electrons from the sourceto the drain is regulated by thegate. The basic goal of miniaturiz­ing circuits is to increase transis­tor speed by decreasing the dis­tance from the source to the drain.• Center: Closer examination of

the path of.a single electron re­veals it to be highly irregular be­cause of the marw impurity a tomsin the conducting material.• Bottom: As transistor sizes aredecreased, they eventually be­come so small that each transistorcontains only a few impurityatoms. As a result, each transistorhas unique properties.

tions (impurity atoms), each ofwhich slightly affects the elec­tron motion. Mass-producedtransistors are not truly identi­cal at the atomic level, yet mass­produced electronic circuitsbehave identically. (All pocketcalculators give the same results,after all.) They do so becauseeach device contains a largenumber of defects and impurityatoms whose combined effect issome kind of total or average ef­fect. As long as the average is ofa sufficiently large number of de­fects, statistics guarantee thatwe will always get very similarresults. However, as the devicesare scaled down, the number ofthe defects is no longer so large.In principle that is good, but eachdevice has its own few randomlydistributed defects. This meansthat statistical averaging is nolonger effective, and thus eachdevice will behave unlike any oth­er one.

Another reason has to dowith the very nature of the elec­tron motion as explained by

The breakdown of scaling

Much of the intrigue of mesoscop­ic physics arises because scien­tists ha,:"e discovered that aselectronic devices shrink in sizebeyond certain limits, new andunfamiliar phenomena occur; thesimple rules of size-scaling nolonger work.

Why this breakdown of scal­ing? There are several.differentcauses. The first has to do withstatistics, in a sense. Electronicdevices can be no more perfectthan the materials (such as sili­con) from which they are made.Th.us, the electronic devices inuse today have many random de­fects (imperfections of the micro­scopic structure) and contamina-

speeds of 200,000miles per hour;or :mQre,and a transistor can be10 times smaller than a humanblood cell, a single operation maytake well under a billionth of asecond. Still, for complex com­puter tasks involving trillions ofoperations, these delays rapidlyadd up to precious seconds, min­utes,and hours, leading to the de­sire for even faster device opera­tions and further size reduction.

Underlying this simplisticreasoning is the assumption thatas we,reduce the size of the elec­tronic components, they behavethe same way-only faster. Isthis assumption valid? This ques­tion heralds a new field of re­search sometimes referred to asmesoscopic physics-the realmof very small scale electronics.

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quantum mechanics. At the be­

ginning pi the, century scientistsca.meto r~alize that electrons donot behave like tiny charged solidballs but in many ways are morelike waves of matter and charge.EacJ1electron is spread out overa certain region of spa-ca in awave -like form that depends onhow the electron is moving andhow much energy it has. As longas the device through which theel~ctron moves is large comparedwith the electron's wavelength,the electron does not carehow large the device really is-whether an inch, or a thou­sandth of an inch. However,when the device size is only a fewmillionths of an incJ1, which iscomparable to the electron wave­length, the election cannot fit in­side ariymore. To do so it wouldhave to change its wavelength,which would require additionalenergy. This will profoundly in­fluence the operation of devicesas their dimensions shrink be­yond certain limits.

Elec,t,ro.nic behavior of verysmtim devices

By now we are aware that"small" electronic devices behaverather differently than conven­tional ones. But what is reallysmall? This is determined by theway electrons move through thedense array of atoms that formthe semiconductor device. As aconsequence of their wave na­ture, electrons u8u'allypass rightby the atoms without any colli-

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sions, unless they run into some­thing irregular, which eventuallythey always do. That could be ei­ther a wrong kind of atom (animpurity), a misplaced atom (de­fect), an atom vibrating in a crys­tal lattice (temperature-causedatomic vibrations), or even an­other electron. Thus, a meaning­ful measure for smallness in thecontext of scaling breakdown isthe average distance the electrontravels before it undergoes a col­lision and scatters to another di­rection. This average distancebetween collisions is called themean free path, or MFP.

Collisions between electronsand atoms in crystals are clas­sified into two groups. The firsttype, called elastic, involves col­lisions in which the electronchanges its direction but not itsenergy. Since impurity atoms inelectronic devices are much heav­ier than electrons, electrons col­liding with impurity atomschange only their direction of mo­tion, but not their speed or ener­gy. This is analogous to a ball hit­ting a wall and bouncing off atthe same speed it came in with.Elastic collisions of electronswith impurity atoms are themost prevalent type of collisionthat occurs in devices that havebeen cooled to very low tempera­tures.

In the second type of colli­sion, called inelastic, the electronchanges not only its direction butalso its energy. This type of col­lision gradually becomes moreprevalent as a semiconductor iswarmed. Inelastic collisions oc-

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Crystallinestructure

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CLASSICAL REF~ECTION(A particle phenol11enon.)

The barrier, a thin sandwichedlayer

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Ther~lectron reflects because itsenergy is less than the barrier

. height.

QUANTUM MECHANICAL TUNNELING.. (A wave phenomenon.) .

RESONANT TUNNELING'(Transmission depends on the electron wavelength.)

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cur when the electron collideswith an atom vibrating in a crys­tal lattice or with another elec­tron. This process is analogous toa ball hitting another ball or amoving object, which is very like­ly to change the baB's speed.Thus we distinguish between twotypes of collision, each having itscharacteristic MFP-elastic andinelastic.

Although billiard ball analo­gies are useful imagery, theyare clearly insufficient for visual­izing the wave-like behavior ofelectrons. It is here that the dis­tinction between elastic and ine­lastic collisions proves particu­larly helpfu1. As the electronflows through the material, partsof its wave split off and recom­bine in countless ways in a

. phenomenon called interference.However, partial waves interfere

• Top panel: In classical elec­tronics, a nonconcJuctlng layersandwiched between conduclinglayers presents a totally reflec'liveenergy barrier to all electronswhose energy is less than theenergy required to pass throughthe layer.• Middle: In quantum electronlc's,only most electrons whose energyis less than the barrier height arereflected by the barrier, whlle, in aprocess calledtunneling, Cl smallpercentage of the electrons reachthe other side of the barrier.• Bottom: Even more dlstan t fromour common sense is the quantumphenomenon ofresonant tunnel­lng,!n which elec trons of preciselythe fight energy, and hfmce wave­lengt~, pass through two energybarriers without any loss ofstriingth. As shown, electrons of anon~resonant wavelength are al­most completely blocked by thetwo barriers. (See text on p. 300.)

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Inelastk; collisions occur when the

electron collIdes with an atom vIbrating

Ijl a crY$tal lattk;e or with anotherelectron.

only if they "remember" thatthey originated from the sameelectron, that is, if they remain"in phase." Here lies the specialrole of inelastic collisions: Theyerase quantum mechanical mem­ory or shift the phase of thewaves randomly, eliminating fur­ther interference between thepartial waves that had split offbefore the inelastic event.

So, in devices of today-alllarger than the inelastic MFP-interference effects do not playany major role. However, asshrinking device sizes approachthe mesoscopic level, the devicesmay be shorter than the materi­al's inelastic MFP. Since inelas­tic collisions are rare in thesedevices, interference patterns,which are different for each de­vice, have a strong influence onthe electrical behavior of the de­vices. This is seen in the con­ductance (the inverse of the re­sistance) of mesoscopic devices.In one device it might happenthat the partial waves of eachelectron interfere destructively(cancel each other) at the outputend, causing the output currentand hence the conductance to below. The opposite effect can takeplace in another device, if the in­terference happens to be con-

structive. Very minor differencesin the number and location of im­purities between shnilar devicescan affect the interference pat­tern drastically. It was thus pre­dicted, and has been verified ex­perimentally, that in apparentlyidentiCal deVices-when smallerthan the inelastiC MFP-the con­ductance varies in a characteris­tic but unpredictable way. Thisastonishing quantum phenom­enon is called universal conduct­

ance fluctuations.

Electrical characteristicsof even smaller devices

Further down the line of shrink­ing scales, that same wave­character of electrons that caus­es interference brings about aphenomenon from which quan­tum mechanics derives its name:energy quantization. The con­straint imposed on an electron byentering into a small space dic­tates a choice of a few specificwavelengths that it can fit in"comfortably." Since wavelengthis related to energy, the confinedelectron's energy can only attainseveral specific values, or quan­tized energies. This quantizationeffect is a direct result of the size

and shape of tl:J.edevice iri ques­tion and is thus a.n obvious causefor scaling breakd9wn.

Let's look a.t a few remark­able examples of quantization ef­fects.

Lower dimensionality If a deviceis made small (on the order ofthe electron wavelength) in onedimension (for example, alongthe vertical z-axis) and extensivein the x-y plane, the electron mo­tion is frozen in the z-directionwith a quantized value of energyand wavelength to match. At thesame time, the electron is free tomove in the x-y plane. Suchan environment, called two­dimensional, permits no currentflow in the z-direction, and alsocauses electrical behavior in thex-y plane that is different fromelectrical behavior in the com­mon three-dimensional environ­ments.

Reduction of device size intwo directions (say the z- andy-directions) will cause quantiza­tion of electron motion in thesetwo dimensions and permit cur­rent flow only in one dimension(the x-dimension). Thu.s a one­dimensional electronic environ­ment is created. Furtherquaritization will lead to "zero

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QUANTUM ELECTRONICS

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the barriers were not there! Thisstrange phenomenon, called reso­nant tunneling, is a consequenceof the interference between allthe partial waves of the elec-

~ tron bouncing back and forth be-~ tween the two barriers. It man­~ ifests itself experimentally in~ resonant tunneling devices firstg as an increase, then as a reduc­!tion in the tunneling current~ when the voltage, which deter­~ mines the electron energy, is in­~ creased above the resonant level.~ This is in sharp contrast to all

§ normal conductors where cur­rent always increases propor-'tionally to voltage.dimensions," or to a quantum

box, which behaves like a "big"artificial atom, with electronstrapped inside.

Tunneling This is one of themost amazing consequences ofthe wave nature of electrons.Think for a moment about a ballrolling toward a hill. The onlyway it can get to the other side isif it has enough energy to climbup to the top and then roll downthe other side. With less energy,it will roll up part way and then

• An analogue to the focusing oflight waves has recently beendemonstrated In this lens that fo­cuses a stream of electrons flow­Ing Inside a semiconductor. Thelighter regions are a thin layer ofmetal deposited on the surface ofan underlying semlconductor(dar­kef). By applying voltage to the bi­concave ."Iens" In the center, elec­trons flowing out of opening E canbe focused to pass only throughopening P2 Instead of throughopenings P1,P2, and P3 as they dowhen no voltage Is applied to thelens.

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roll back down. This is not thecase in quantum mechanics foran electron moving toward anelectrical hil1. Even if the elec­tron has less energy than re­quired to surmount the barrier, itstill has some chance to arrive atthe other side-by tunneling. Thethinner the barrier, the greaterthe probability of tunneling. Thisis because the electron waves al­ways penetrate somewhat intothe barrier, but the thicker thebarrier, the smaller the fractionof the electronic waves arrivingon the other side.

Resonant tunneling Now put twothin tunneling barriers one afterthe other with a small space be­tween them. Although the prob­ability of an electron penetratingboth of them is very small, if theelectron energy coincides withthe allowed quantized energy forthe space between the barriers,the electron can go through thetwo barriers unobstructed-as if

Single electrons When a deviceis very small and the electriccurrents are reduced as well, thefact that electrons are separateparticles becomes apparent.Current no longer flows like asmooth fluid but becomes morelike bullets coming out of a ma­chine gun. The situation is fur­ther affected by the fact thatelectrons repel each other. Thiscreates a situation where the ad­dition of a single electron into atightly confined region createselectron overcrowding and cur­rent cannot flow through this re­gion, unless sufficient energy isgiven to the incoming electron.Very small devices of this sorthave been seen to change theirresistance enormously when asingle electron is added to them.Such devices can, in effect, ac­tually count the number of elec­trons inside them-a tantalizingprospect for using a single de-

Wecan envIsion the emergence of anew generation of multiple value logk;electronic devices.

vice as a multivalue variable in­stead of just an on-off switch.

Ballistic electron. devices

Structures with dimerisionssmaller than both the elastic andinelastic MFP allow unimpeded,or ballistic motion of electrons-the equivalent of motion inempty space-but with the im­portant addition. of energy quan­tization. Since in ballistic motionthe electron undergoes no colli­sions, its velocity is maximized,and so is the speed of the device.The velocity can be up to 10timeshigher in this situation than innormal semiconductors.

Electron optics But ballistic mo­tion implies more thfln just plainspeed; in ballistic motion, the elec­tron also maintaiil.s its direction.Here one can.realize a direct anal­ogy between electrons as wavesand light waves, which travel instraight lines. The analogy sug­gests that at mesoscopic levelswithin semiconductors, optical­like behavior is possible with bal­listic electrons. One can envisionreflection, refrllction (bending oflight when it crosses between dif­ferent media), and even focusing

of ballistic electrons. For exam­

ple, by creating a shallow elec­tric voltage-,barrier shaped likea small lens, electrons passiIl,gthrough will slow down-as lightwaves slow in a glass lens-andcQnvergeinto a sharp point on theother side. Changing the voltagewill .change the distance of theconvergence point.

Quantized condudance Anotherunique feature of ballistic elec­tron devices is that their conduct­ance is no longer a continuousfunctior. of their size and shape.RaFher, the c()nductance itself isqmrn.tized;.ahYE-Y.staking VE-iuesthat are iriteger multiples of auniversal value, the inverse of aresistance 12,906 ohms in value.This fact also suggests applica­tions for multivalue digital logic,where any integer can be unam­biguously represented by a spe­cific value of resistance ..

Outlook

While miniaturization of elec­tronic devices is driven bya straightforward objective-speed-it may bring many oth­er unexpected benefits, not theleast of which is a glimpse into

the fascinating worlds of mesos­copic physics. Further down theroad, as the history of science hastaught us time and again, we willbenefit from this new knowledge.We can envision the emergence ofa new generation Of electronicdevices go~ngbeyond the binary,on-offswitching transistors of to­day, into multiple value logic.Thus a single logic device mightdo the job done today by many.The increased density will yield,again, speed. New modes of af­fecting electronic properties,such as controling the phase ofthe electrons, may yield devices~at E-reextremely fast, or ex­~remely sensitive to minute ex­ternal signals. Devices that workn.ow only at temperatures closeto the absolute zero might workat room temperatures using nov­el schemes.

One thing is certain, theworld of electronics of the futurewill be quite different from ourelectronic world today, and inways that can only begin to beimagined now.•

Udi Meirav is at the department of

phllsics at the MassachU$etts Instt'tute ofTechnoloPlI. Mordehaz' Hez'blum zs a re­search sdentzst at the IBM Thomas J.Watson Research Center z'n YorktownHez'phts, New York.

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