properties of planar nb/α-si/nb josephson junctions with various degrees of doping of the α-si...

ISSN 1063�7761, Journal of Experimental and Theoretical Physics, 2012, Vol. 114, No. 5, pp. 818–829. © Pleiades Publishing, Inc., 2012.Original Russian Text © A.L. Gudkov, M.Yu. Kupriyanov, A.N. Samus’, 2012, published in Zhurnal Eksperimental’noi i Teoreticheskoi Fiziki, 2012, Vol. 141, No. 5, pp. 939–952.

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1. INTRODUCTION

The modern stage of developing the elements ofsuperconducting electronics requires new technologi�cal approaches to the formation of Josephson junc�tions. The old solutions [1, 2] based on superconduc�tor (S)–insulator (I)–superconductor (S) tunnelstructures have rather long ceased to meet the require�ments imposed on a number of devices, including fastsingle�quantum logics [3] and programmable voltagestandards [4, 5]. The attempts to replace SIS by SNSor SINIS structures, in which weak coupling waslocalized in the region of a normal (N) layer, alsofailed.

The most complex problem in developing an SNSjunction technology was the problem of choosing anormal conduction material. Such an N metal mustsimultaneously satisfy two mutually conflictingrequirements. On the one hand, it must have longeffective coherence length ξN, i.e., must be low�resis�tance, to ensure high critical�current densities at atechnically reasonable normal layer thickness. On theother hand, its transport properties must be substan�tially lower than those of superconductors to preventsubstantial suppression of superconductivity in S elec�trodes [6]. The available set of materials (e.g., PdAu,TiN alloys [7, 8]) turned out to be very scarce. The val�ues of ξN in such structures did not exceed severalnanometers and were comparable with the character�istic roughness size of junction boundaries.

For SINIS contacts to be applied in practice, it wasimportant to retain an approximately equal transpar�ency of their boundaries during preparation [9]. The

barriers in all materials were formed by the oxidationof aluminum. The substantial difference in the mor�phologies of an Al film on an S electrode and the filmlocated between dielectric layers makes it possible toachieve the required symmetry only in the case of low�transparency barriers [10–14].

The only solution to this problem is to use struc�tures with a resonance character of conductivity in aweak�coupling region. The first structures of this typehave long been prepared [15, 16] and even were used asworking elements in single�junction devices [17].However, the level of developing a technological basisand the foundations of electron transport in resonancestructures at that time made it impossible to pass to theproduction with even a medium level of integration.

The discovery of high�temperature superconduc�tivity substantially stimulated basic research of reso�nance tunneling in Josephson structures with semi�conductor oxide layers from both theoretical andexperimental viewpoints [18–21]. It was also created agood basis for the modern stage of studying the pro�cesses in low�temperature resonance Josephson struc�tures [22].

In the helium temperature range, the first attemptsof fabrication planar SNS junctions with a silicon layerthat were based on a niobium technology were able toachieve practically important values of the mainparameters [15]: normal junction resistance RN washigher than 1 Ω and the characteristic voltage Vc =IcRN was up to 1 mV. This fact served as a ground forthe further development of the process of formingJosephson junctions with a silicon layer and for study�

Properties of Planar Nb/α�Si/Nb Josephson Junctionswith Various Degrees of Doping of the α�Si Layer

A. L. Gudkova, M. Yu. Kupriyanovb, and A. N. Samus’a

a ZAO Kompelst, Lukin Scientific Research Institute of Physical Problems, Zelenograd, Moscow, 124460 Russiae�mail: [email protected]

b Skobeltsyn Institute of Nuclear Physics, Moscow State University, Moscow, 119991 RussiaReceived July 29, 2011

Abstract—The properties of Nb/α�Si/Nb planar Josephson junctions with various degrees of doping of theamorphous silicon layer are experimentally studied. Tungsten is used as a doping impurity. The properties ofthe Josephson junctions are shown to change substantially when the degree of doping of the α�Si layerchanges: a current transport mechanism and the shape of the current–voltage characteristic of the junctionschange. Josephson junctions with SNS�type conduction are formed in the case of a fully degenerate α�Silayer. The properties of such junctions are described by a classical resistive model. Josephson junctions witha resonance mechanism of current transport through impurity centers are formed at a lower degree of dopingof the α�Si layer. The high�frequency properties of such junctions are shown to change. The experimentalresults demonstrate that these junctions are close to SINIS�type Josephson junctions.

DOI: 10.1134/S1063776112030144

ORDER, DISORDER, AND PHASE TRANSITIONIN CONDENSED SYSTEM

JOURNAL OF EXPERIMENTAL AND THEORETICAL PHYSICS Vol. 114 No. 5 2012

PROPERTIES OF PLANAR Nb/α�Si/Nb JOSEPHSON JUNCTIONS 819

ing the current transport mechanisms in such struc�tures. Later, the best characteristics were achieved onramp type Nb/α�Si/Nb Josephson junctions [23, 24].The α�Si layer in these junctions was diffusionallydoped with Nb atoms to achieve full degeneracy of thesemiconductor. The ramp type junctions demon�strated high current densities, up to 105 A/cm2 orhigher. The normal resistance of the Josephson junc�tions was almost temperature independent due to thefull degeneracy of the α�Si layer to metallic conduc�tion. The electrical resistivity of the layer (ρN) wasmuch higher than the electrical resistivity of niobium(ρS). Therefore, the suppression of superconductivityin niobium electrodes was negligibly small, and theorder parameter at the interface with an α�Si layerremained identical to that deep in the niobium elec�trodes. This fact was an advantage of Nb/α�Si/Nbjunctions over other Josephson junction designs,where pure metals or metallic alloys were used as aninterlayer. Ramp type Josephson junctions exhibitedhigh values of Vc, up to 1 mV. The current–voltagecharacteristics (CVCs) of the junctions were one�val�ued, and excess current Iex existed in the high voltageregion. Therefore, Nb/α�Si/Nb junctions were attrib�uted to SNS junctions. The shape of temperaturedependence of the junctions critical current was alsotypical to that of SNS devices.

The prospects of using Josephson structures with adoped silicon layer in superconducting electronics isnow beyond all doubt [25–33]. However, the questionof the physical mechanisms of current transport insuch structures is still open in spite of significantadvantages in solving the technical problems related totheir production.

The purpose of this work is to study these mecha�nisms. We also investigate the electrophysical proper�ties of planar Nb/α�Si/Nb Josephson junctions. As aweak�coupling material, we used amorphous silicondoped with tungsten by cosputtering of materials, incontrast to a layer of niobium�doped amorphous sili�con used in [26–32] and tested in [15, 23]. With thissubstitution, we were able to substantially simplify thecontrol of the technological processes of production ofstructures at all stages and to use the proposed tech�nology to fabricate integrated circuits for a Josephsonvoltage standard with several thousands of active ele�ments per chip.

2. EXPERIMENTAL

Modern technological methods can produce vari�ous Josephson junctions with high basic electricalparameters. However, to fabricate Josephson junctionswith a good reproducibility of the parameters, one hasto meet some technological requirements. Stringentrequirements are imposed on the energetics of techno�logical processes and the reproducibility of the param�eters of individual layers in a superconducting hetero�structure. The purity and energetics of technological

processes must ensure a high purity and atomic sharp�ness of an interface during both the formation of aninitial heterostructure and at the end of the entire cycleof preparing a superconducting integrated circuit.

The reproducibility of the planar junction parame�ters depends on the surface quality of the lower nio�bium electrode. The requirements for the surface mor�phology of the lower electrode are reduced to the sur�face roughness of a niobium film δ. The roughnessmust be much smaller than the α�Si layer thickness(δ � d). We studied the surface morphology of Nbfilms prepared by magnetron sputtering of niobiumused to form a superconducting heterostructure. Fig�ure 1a shows an atomic force microscopy (AFM)image of the Nb film surface. It is seen that the ener�getics of magnetron sputtering makes it possible todeposit Nb films with a surface roughness less than0.5 nm. This means that planar Josephson junctions atd ≥ 5 nm will have a satisfactory reproducibility of theparameters.

Magnetron sputtering is a low�energy thin filmdeposition method. With this method, one can deposit

200

400

600

800

1000

0.2

0200

400600

8001000

(a)

10 nm

(b)

nm

nm

nm

Fig. 1. Structure of an Nb/α�Si/Nb Josephson junctionformed by magnetron sputtering: (a) surface morphologyof the base Nb electrode film and (b) TEM image of thecross section of the Nb/α�Si/Nb structure.

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GUDKOV et al.

almost amorphous films from refractory materials.The purity of amorphous films is rather high underconventional vacuum conditions owing to a high sput�tering rate. Amorphous silicon layers were also formedby magnetron sputtering. An α�Si layer in ramp typejunctions was doped by diffusion of Nb into α�Si, andan α�Si layer is now doped during its formation in thecourse of cosputtering of Si and W from a mosaic tar�get. This method makes it possible to exactly fix the Wconcentration in an α�Si layer. In our experiments, theW concentration was varied in the range 6–11%.

The formation of planar Josephson junctions beganwith the formation of a three�layer Nb/α�Si/Nb struc�ture by magnetron sputtering in one vacuum cycle.Figure 1b shows a transmission electron microscopy(TEM) micrograph of the cross section of an Nb/α�Si/Nb structure. It is clearly visible that the α�Si–Nbelectrode interfaces are atomically sharp. Using pho�tolithography and dry etching, we then formed planarJosephson junctions. Figure 2 shows the cross sectionof one of the planar Josephson junctions prepared inthis work. The lower Nb electrode thickness was200 nm, the α�Si layer thickness was 7–9 nm, the

upper electrode thickness was 100 nm, and the wiringNb layer thickness was 400 nm. A superconductingcontact was formed between the wiring Nb layer andthe upper Nb electrode. A high�quality superconduct�ing contact was provided by choosing conditions ofhigh�frequency Ar cleaning of the surface of the upperNb electrode in insulation windows before depositingthe wiring Nb layer. As insulation, we used Al2O3 layersdeposited by electron�beam evaporation. The insula�tion layer thickness was 350 nm. The formedNb/α�Si/Nb planar Josephson junctions had an areaof 6 × 6 μm2 or 9 × 9 μm2. To study the effect of the Wconcentration on the transport properties of the α�Silayer, we prepared and analyzed a series ofNb/α�Si/Nb structures having the same thickness(d ≈ 8 nm) and differing in the W concentration inα�Si.

3. I–V CHARACTERISTICS OF THE Nb/α�Si/Nb JUNCTIONS

Figures 3–6 show the CVCs of the formed struc�tures that were measured at T = 4.2 K. At relativelyhigh tungsten concentrations (about 11%), the CVC ofthe junctions have the shape typical of Josephsonjunctions with metallic conduction (see Fig. 3). In thelow�voltage range, this characteristic is well describedby a resistive model with the McCumber�Stewartparameter

(1)

where C is the geometrical capacitance of the Joseph�son junction and Ic and RN are its critical current andnormal resistance, respectively. A finite excess currentexists at high voltages, which additionally indicates fulldegeneracy of the α�Si layer in this concentrationrange. Microwave radiation induces Shapiro steps inthe CVC, and the oscillations of their amplitudes as afunction of the microwave signal power are describedby Bessel functions and dependent on the Josephsonjunction voltage in a standard manner. The behavior ofthe CVC segments between current steps has a classi�cal character.

When the degree of doping decreases (below 11%),the properties of the junctions change: the junctioncritical current decreases and the normal resistanceincreases at the same α�Si layer thickness. Figure 4shows an example of a planar junction with β ≥ 1 andVc = 0.036 mV. The CVC is seen to change substan�tially as compared to that of a classical SNS junction.An excess current changes into a deficit current atvoltages higher than the gap voltage, V > Vg. A segmentclose to a horizontal line but having a finite slopeappears between the critical current and the resistivesegment in the CVC. The behavior of CVC changesqualitatively under an external radiation frequency.The first step amplitude exceeds the critical current ofthe junction. The amplitudes of the steps and their

β 2e��⎝ ⎠⎛ ⎞ IcRN

2 C 1,<=

Nb1

α�SiNb2

Nb3

Al2O3

14 3 2

(a)

(b)

Fig. 2. Planar Nb/α�Si/Nb Josephson junction: (a) sche�matic cross section of the junction and (b) micrograph ofthe junction. (1) Lower Nb electrode, (2) Nb/α�Si/NbJosephson junction, (3) superconducting contact region,and (4) wiring of the upper Nb electrode.



behavior weakly depend on the ratio of the character�istic junction frequency to the external action fre�quency.

A further decrease in the W concentration isaccompanied by an increase in parameter β and leadsto the appearance of a small capacitance hysteresis inthe CVC. Figure 5 shows the characteristics of such aJosephson junction with β > 1. This hysteresis is alsoretained in the CVC segments between current stepsunder an external radiation frequency. The characterof the resistive segment in the CVC is identical to thatin the previous case. Figure 5b shows the CVC of ajunction with a larger current scan. However, the CVCshape becomes substantially nonlinear at high volt�ages. This behavior indicates another mechanism ofthe transport of a normal current component throughthe structure, which is caused by inelastic resonancetunneling processes; that is, it differs qualitatively fromthat in SNS structures (see Fig. 3).

At a lower tungsten concentration, the capacitancehysteresis in the CVC increases (Fig. 6). The behaviorof CVC changes strongly under the action of an exter�nal radiation frequency. At a low radiation power(Fig. 6b), a current step at double voltage 2V1, whereV1 corresponds to the radiation frequency, appears inthe CVC. As the radiation power increases further(Fig. 6c), the double step increases and a current stepappears at 2/3V1. The first current step correspondingto voltage V1 does not appear. This behavior indicatesa substantial difference between the current�phasedependence of the Josephson junction Is(ϕ) and asinusoidal law.

Figure 7 shows the family of CVCs that demon�strates the change in CVCs shown in Figs. 4 and 5 withincreasing temperature on the scale sufficient toresolve the critical current (Fig. 7a) and to show non�linear behavior of CVC at high voltages (Fig. 7b).

V, mV

−8

−2

−0.3 −0.2 −0.1 0.30.1 0.20

F = 61 GHz−6

−4

−10

2

8

4

6

0

10

V, mV

−2

−0.3 −0.2 −0.1 0.30.1 0.20

F = 73 GHz−4

−6

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4

0

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−2

−0.3 −0.2 −0.1 0.30.1 0.20

−6

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−10

2

8

4

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0

10

−2

−0.3 −0.2 −0.1 0.30.1 0.20

I, mA

−4

−6

2

4

0

6

(b)(a)

I, mA

Fig. 3. CVCs of planar Nb/α�Si/Nb Josephson junctions with β < 1 and characteristic voltages Vc = (a) 0.3 and (b) 0.12 mV. (bot�

tom panels) CVCs of the junctions under the action of external radiation frequency F. The junction area is 6 × 6 μm2.

822


GUDKOV et al.

To supplement these qualitative changes in theproperties of the Josephson junctions induced by adecrease in the doping impurity concentration withsome quantitative estimates, we will dwell on an anal�ysis of the temperature dependences of the criticalcurrent Ic(T) and the shape of CVC contacts at highvoltages.

4. TEMPERATURE DEPENDENCEOF THE CRITICAL CURRENT

In contrast to traditional Josephson tunnel struc�tures (where characteristic voltage IcRN is a function ofonly the contact temperature), the Josephson junc�tions under study have internal shunting, which iscaused by inelastic tunneling through localized states(LSs). Therefore, to compare the temperature depen�dences of IcRN with the predictions of theoretical

models, we will focus on the shape of Ic(T) curvesrather than on the absolute values of IcRN.

As follows from the Ambegaokar–Baratoff theory[34], the Is(ϕ) dependence for direct tunneling is sinu�soidal and, in the temperature range near the criticaltemperature, obeys the law Ic(T) ∝ (Tc – T) and has anegative curvature.

If resonance tunneling through one LS dominatesduring superconducting current transport, the Is(ϕ)dependence differs from a sinusoid irrespective of therelation between the modulus of the order parameterof the electrodes and the effective width of a resonancelevel. However, Ic(T) at T ≈ Tc is still proportional toTc – T and has a negative curvature [22].

In the absence of mesoscopic effects, the total cur�rent through a junction is determined as the averagingof the supercurrent passing through an LS with a dis�

V, mV

−5

−4 −3 −1 41 30

−10

−15

5

10

0

15

(b)

I, mA

V, mV

−0.2

−0.6 −0.4 −0.2 0.60.2 0.40

F = 76.5 GHz−0.4

−0.6

0.2

0.4

0

0.6

(c)

I, mA

I, mA

0.4

0 2 4 106 8

0.2

0.6

0.8

1.0

(d)

Rd, ΩV, mV

−0.2

−0.6 −0.4 −0.2 0.60.2 0.40

−0.4

−0.6

0.2

0.4

0

0.6

(a)

I, mA

2−2

Fig. 4. CVC of a planar Nb/α�Si/Nb Josephson junction with β ≥ 1 and Vc = 0.036 mV: (a) independent CVC, (b) current�enlarged CVC of the junction, (c) CVC of the junction under the action of an external radiation frequency, and (d) differentialresistance of the junction. The junction area is 9 × 9 μm2.



tribution function δ(ER, x0) over LS energy ER in thevicinity of the Fermi energy and over LS position x0 inthe junction layer. The shape of an Ic(T) curve dependssubstantially on the penetrability form of the LS reso�nance curve D when LSs are uniformly distributed inboth the weak�coupling region and over the position ofenergy level ER in the vicinity of the Fermi level of thesuperconductors. In the general case, this curve isdetermined by a Breit–Wigner–type formula [35] anddepends on the energy width of the resonance level Γand the spatial coordinate of LS x0. If the resonancewidth is large, then D ≈ D(x0) and the averaging overthe LS energy and coordinate [36] results in an Ic(T)dependence that coincides with the dependence thatfollows from the KO�1 theory and holds true for dirtySNS structures [37]. When LSs are localized at thecenter of the layer (so that actually D ≈ D(ER)), theaveraging leads to an Ic(T) dependence that is similarto the dependence derived for the coherent mode of

two�barrier SINIS junctions [38]. In both cases, theIs(ϕ) dependence is not sinusoidal. Note that, in allcases described above, Ic(T) ∝ (Tc – T) when the tem�perature tends to the critical one and the curvature ofthe d2Ic/dT2 curves has a negative sign.

In the general case [20, 39, 40], the averagingresults in Is(ϕ) ∝ sinϕ. The temperature dependencesof the critical current are also linear near Tc. The cur�vature of the Ic(T) curves depends on the relationbetween resonance level width Γ and electrode orderparameter Δ. In the narrow resonance band limit (Γ �Δ), the sign of curvature changes from negative to pos�itive [20, 40].

At a higher LS concentration, supercurrent trans�port can appear along resonance percolation trajecto�ries containing a large number of LSs [41] or impurityclustering can take place with the formation of metal�lic conduction regions inside the junction layer. In theformer case, a narrow metallic conduction subband

V, mV

−0.5

−0.8 −0.4 −0.2 0.80.2 0.40

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1.5

(a)

I, mA

0.6−0.6V, mV

−2

−1.5 −1.0 −0.5 1.50.50

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(b)

I, mA

1.0

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3

V, mV

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−0.8 −0.4 −0.2 0.80.2 0.40

−1.0

−1.5

0.5

1.0

0

1.5

(c)

I, mA

0.6−0.6

F = 71 GHz

Fig. 5. CVC of a planar Nb/α�Si/Nb Josephson junction with β > 1: (a) independent CVC, (b) current�enlarged CVC of the junc�tion, and (c) CVC of the junction under the action of an external radiation frequency. The junction area is 9 × 9 μm2.

824


GUDKOV et al.

forms inside the energy gap of the semiconductorbecause of the overlapping of the wavefunctions ofimpurity electrons, and supercurrent transport alongthis subband is analogous to that in a narrow�bandnormal metal. It is important that the curvature of theIc(T) dependence changes its sign from negative topositive when the distance between the superconduct�ing electrodes L becomes larger than the decay lengthfor superconducting correlations ξN in such a channel.In the latter case, the properties of the junctionsshould be close to two�barrier structures with a lowtransparency of the barriers separating a cluster fromthe electrodes. The CVCs of such structures shouldhave the current deficit at high voltages [43, 44], andthe curvature of the Ic(T) dependence should be posi�tive [9, 38].

Figure 8a shows the experimental Ic(T) depen�dences of Nb/α�Si/Nb Josephson junctions with vari�ous degrees of doping of the layer for β > 1.Figures 8b–8d show these dependences normalized

by the critical current at T = 4.2 K in comparison withthe predictions of theoretical models in [9, 20, 38–42]. It is seen that the experimental Ic(T) curves in thevicinity of Tc are also linear but characterized by a pos�itive curvature.

The dashed curve in Fig. 8b shows the Ic(T) curvecalculated for resonance tunneling through one LS inthe limit of an infinitely small (Γ � Δ) resonance curvehalf�width [20, 40]. The experimental points are seento be below the calculated curve. When Γ increases,the curvature of the temperature dependences rapidlychanges its sign from positive to negative, which indi�cates that this supercurrent transport mechanism doesnot occur in the Josephson junctions under study.

In contrast, the theoretical predictions for SINISjunctions in [9, 38] have a too sharp temperaturedependence: as follows from Fig. 8c, the calculatedcurves have a curvature that substantially exceeds theexperimental curvature.

V, mV

−0.5

−0.8 −0.4 0.80.40

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2.0(a)

I, mA

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−0.8 −0.4 0.80.40

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I, mA

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−0.8 −0.4 0.80.40

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I, mA

−1.5

1.5

F = 75.6 GHz

2/3V1

2V1

F = 75.6 GHz

Fig. 6. CVC of a planar Nb/α�Si/Nb Josephson junction with β > 1: (a) independent CVC and (b), (c) CVC of the junction underthe action of an external radiation frequency. The junction area is 9 × 9 μm2.



Finally, it follows from Fig. 8d that, despite differ�ent tungsten concentrations, the shapes of the Ic(T)curves are almost the same and close to the depen�dence calculated for Josephson SNS junctions withL/ξN ≈ 4–5 [42]. This finding implies that, in this con�centration range (6–10%), a supercurrent passesalong the resonance percolation channels havingformed in the layer. The current�carrying abilityincreases with the ligand concentration via an increasein the number of such channels rather than via achange in their internal structure caused by possibleclustering processes changing ξN. Based on the tem�perature dependences IcRN(T) calculated in [42] andthe critical currents obtained at T = 4.2 K (Fig. 8a), wecan estimate the conductivity of the resonance perco�lation channels, which is σrp ≈ 2, 1.5, 0.7, and 0.3 Ω–1.As will be shown below, these values are comparablewith the experimental conductivities of the structuresunder study.

It should also be noted that the normal conductiv�ity of the resonance percolation channels not alwayscauses the formation of an excess current in the CVCof a junction. Such an excess current does take place[43] if resonance percolation conduction band widthΓ exceeds 2Δ. In the opposite limiting case (which islikely to occur in our structures), the excess current isproportional to Γ and the current deficit is propor�tional to Δ – Γ. Therefore, in the case where Γ � Δ,the competition of the mechanism resulting in thecurrent deficit proportional to Δ – Γ in CVC with theprocesses accompanying the formation of the excesscurrent proportional to Γ eventually leads to a currentdeficit (Fig. 4b) [45]. It is important that the competi�tion of the two mechanisms described above shouldlead to a faster (compared to Δ(T)) decrease of thecurrent deficit with increasing temperature, since(unlike Δ) Γ is not a function of temperature. It is thisbehavior that was observed in our experiments.

5. TRANSPORT OF NORMAL CURRENT

As follows from the curves shown in Figs. 4–7, theshape of CVC changes substantially with the impurityconcentration in the α�Si layer: as the tungsten con�centration decreases, it transforms from the CVC of aclassical SNS junction to the curves typical of two�barrier Josephson structures [9–12, 44]. This changecan only be explained by another current transportmechanism, which dominates over both the mecha�nism of direct current passage through the N layer anddirect electron tunneling through the layer. The differ�ence between the measured and calculated [42] valuesof IcRN by more than an order of magnitude also pointsto the fact that these contributions are not decisive andthat the main transport of normal electrons proceedsvia elastic and inelastic resonance tunneling processes.

In this case, resonance tunneling through one ortwo LSs becomes predominant and the shape of CVCs

at high voltages should be close to the shape followingfrom the Glazman–Matveev theory [46],

(2)

(3)

I G1⟨ ⟩ G2 T 0,( )⟨ ⟩ G2 0 V,( )⟨ ⟩+ +( )V,=

G1 T 0,( )⟨ ⟩ S

α2�� gα3E0( )

2 Lα��–

⎩ ⎭⎨ ⎬⎧ ⎫

,exp∝

G2 T 0,( )⟨ ⟩ SLα�� 2gdα2T( )

2∝

× λep

E0λep

T�� L

α��–

⎩ ⎭⎨ ⎬⎧ ⎫

exp

2/3

,

V, mV

−0.5

−1.5 −0.5 1.50.50

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0.5

1.0

0

2.0

(a)

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−1.5

1.5

−1.0 1.0

12345

6

V, mV−3 −1 310

−5

−10

5

0

10

(b)

I, mA

−2 2

1

2

345

Fig. 7. (a) Family of CVCs of an Nb/α�Si/Nb Josephsonjunction (Fig. 5) recorded at a temperature of (1) 4.2,(2) 5.5, (3) 6.5, (4) 7.5, (5) 8, and (6) 9 K. (b) Family ofCVCs of an Nb/α�Si/Nb Josephson junction (Fig. 4) on alarge current scale recorded at a temperature of (1) 4.2,(2) 6.0, (3) 7.2, (4) 8.3, and (5) 9.0 K.

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GUDKOV et al.

(4)

Here, S is the cross�sectional contact area; g, E0,and α are the density of resonance centers, the posi�tion of the energy level of LS with respect to the Fermienergy, and the LS radius, respectively; λep is a dimen�sionless constant characterizing the electron–phononinteraction; and L is the interelectrode distance.

G2 T 0,( )⟨ ⟩ SLα�� 2gdα2eV( )

2∝

× λep

E0λep

eV�� L

α��–

⎩ ⎭⎨ ⎬⎧ ⎫

exp

2/3

.

Factors S/α2 and S/Lα in Eqs. (3) and (4) specifythe total number of statistically independent channelsof tunneling through one and two LSs, respectively.The existing difference is caused by the fact that, in thecase of two LSs, these centers should not be locatedalong a straight line normal to the structure interfaceplane. In this case, factor (Lα)1/2 determines the effec�tive distance between LSs in the layer volume at whichthe efficiency of a resonance conduction channel isretained. Factors (gα3E0)

2, (2gdα2T)2, and (2gdα2eV)2

set the probability of formation of the correspondingconduction channel. For a channel with one LS, thisprobability is determined by the effective volume ofthe layer space to be used by an electron to perform

Fig. 8. (a) Ic(T) dependences for Nb/α�Si/Nb Josephson junction samples A3, B8, Z7, and Zh7 with various degrees of doping

of the layer at β > 1 corresponding to σrp ≈ 2, 1.5, 0.7, and 0.3 Ω–1, respectively. (b–d) Comparison of these dependences nor�malized by Ic(T = 4.2 K) with those calculated for various ratios of L and ξN: (b) model of a junction with resonance tunnelingthrough one LS (dashed curve L1), (c) model of a two�barrier SINIS junction, and (d) model of a junction with SNS�type con�duction (L3 = L/ξn = 3, L6 = 6). Calculated curves L1, …, L6 are located from right to left.

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Ic, mA

(a)

54 6 7 8 9 10T, K

A3

B8

Z7

Zh7

1.2

1.0

0.8

0.6

0.4

0.2

0

Ic/Ic(4.2 K)

(b)

0.50.4 0.6 0.7 0.8 0.9 1.0T/Tc

A3

B8

Z7

Zh7

L1

1.2

1.0

0.8

0.6

0.4

0.2

0

Ic/Ic(4.2 K)

(c)

0.50.4 0.6 0.7 0.8 0.9 1.0T/Tc

A3B8Z7Zh7

1.2

1.0

0.8

0.6

0.4

0.2

0

Ic/Ic(4.2 K)

(d)

0.50.4 0.6 0.7 0.8 0.9 1.0T/Tc

A3B8Z7Zh7

L6L3L1

L2L3L4L5



resonance tunneling. For channels with two LSs, thisprobability also depends on the layer volume to be usedfor tunneling and on the energy portion (T or eV) thatcan be received or given by an electron during tunnel�ing. The last factors in Eqs. (3) and (4) specify the con�ductivity of the optimal tunneling channel.

Figure 9 shows the resistive segments of the CVCsof several junctions with β > 1 and their approximationby Eqs. (2)–(4). The points represent the experimen�tal data, and the solid lines present the results of calcu�lation by the formula

(5)

with parameters σn ≈ 4, 0.9, 0.55, and 0.53 Ω–1 andβn ≈ 4.55, 1.04, 0.625, and 0.32 Ω–1 V–4/3, whose val�ues are maximal for the left curve and decrease fromleft to right.

It is clear from Eqs. (4) and (5) that, at a fixed layerthickness and a given voltage, the ratio of coefficientsβn is proportional to the squared ratio of the LS con�centrations in the weak�coupling region. In particular,it follows from this fact that the LS concentrationdecreases by a factor of 1.4, 2.7, and 3.8 when goingfrom the left to the adjacent CVC curves, sequentially.

We assume that the main contribution to conduc�tion at low concentrations is made by channels of elas�tic and inelastic resonance tunneling through one LSand estimate the number of such channels. For elasticprocesses, the Larkin–Matveev theory [47] gives

(6)

where ∝ exp{–L/α} is the average penetrabilityand is the total conductivity of the channels ofelastic tunneling through one LS. The electron–phonon interaction during inelastic tunneling throughone LS broadens the resonance curve for the penetra�bility coefficient and simultaneously decreases themaximum of this curve, retaining average transpar�ency almost unchanged in the temperature rangeunder study [48]. This means that Eq. (6) can be usedto estimate the total number of elastic and inelastictunneling channels through one LS when the experi�mental value of conductivity is substituted into

it. We have σn ≈ 0.55 Ω–1 allowing for the fact that ourestimates even for structures with the minimum nor�mal conductivity (σrp ≈ 0.3 Ω–1) demonstrate thatapproximately half this conductivity is attributed toconduction through resonance percolation channels.This substitution for ≈ σn – σrp ≈ 0.25 Ω–1

yields

(7)

I σnV βnV7/3, σn+ G1⟨ ⟩ G2 T 0,( )⟨ ⟩+= =

Nelπ�

e2�� Gel⟨ ⟩ π2 S

α2�� gα3E0( ) D⟨ ⟩ ,= =

D⟨ ⟩Gel⟨ ⟩

D⟨ ⟩

Gtotal⟨ ⟩

Gtotal⟨ ⟩

Ntotalπ�

e2�� Gtotal⟨ ⟩ 3 103

.×≈=

Since the most effective channels correspond to theLSs located in a layer of thickness α near the center ofthe layer, the concentration of W atoms in α�Si is

(8)

where S ≈ 8 × 10–7 cm2 is the cross section of the junc�tion and α ≈ 5 × 10–8 cm is the effective LS radius inamorphous silicon doped with elements that formdeep impurity levels in it [17, 23, 27, 28].

It follows from the relation between coefficients βnthat, for the CVC corresponding to σn ≈ 4 Ω–1, thecontribution to the conductivity from the channels oftunneling through one LSD accounts for about half ofthe total conductivity (3.8 × 0.5 ≈ 2 Ω–1). As followsfrom the estimates given above, the second half is theconductivity along resonance percolation channels.

Using these estimates, we can also estimate theconduction band width of a resonance percolationchannel Γ [49],

(9)

Here, J0exp{–σ–1r2} is the overlap integral, α is thelocalization radius, r1 is the distance between twonearest impurity centers, r2 is the distance between the

gNtotal

αS�� 1 1017

cm3–,×≈=

Γ 2z0J0 α 1– r2–{ },exp=

J0e2

εε0

��α 1– 32�� 1 α 1– r1+( ) 1

6�� α 1– r1( )

2+ ,=

r13

4πg��⎝ ⎠⎛ ⎞

1/3

, r22g��⎝ ⎠⎛ ⎞

1/3

,= =

α 1–�

1– 2mW0( )1/2.=

7

6

5

4

3

2

1

I, mA

0 0.5 1.0 1.5 2.0 2.5 3.0V, mV

Fig. 9. Approximation of the resistive segments of the CVCof Nb/α�Si/Nb Josephson junctions with β > 1 by theGlazman–Matveev formula for the CVC during resonancetunneling through two LSs. for the curves from left to right:σn = 4, 0.9, 0.55, and 0.53 Ω–1; βn = 4.55, 1.04, 0.625, and

0.32 Ω–1 V–4/3.

828


GUDKOV et al.

centers of pairs, z0 is the coordination number, m =0.26me, and W0 is the impurity level energy calculatedfrom the conduction band bottom, For g ≈ 1 ×1017 cm–3, z0 = 2, and α = 0.5 nm, from Eq. (9) we findthat impurity band width is Γ ≈ 0.2 meV, which isabout five times smaller than the energy gap in nio�bium (Δ ≈ 1 meV).

6. CONCLUSIONS

When the W concentration in the α�Si layerincreases, structures with a tunneling type of conduc�tion change into structures with internal shunting,which appears due to the formation of inelastic reso�nance tunneling channels for normal electrons.Simultaneously, superconducting current paths thatare additional to tunneling channels form in the layer.However, in contrast to inelastic processes (where pre�dominant channels are caused by resonance tunnelingthrough one or two LSs), the number of LSs in super�conducting channels turns out to be substantiallylarger, which actually results in the formation of quasi�one�dimensional metallic conduction channels in thelayer. In this case, an increase in the tungsten concen�tration is accompanied by an increase in the number ofsuch channels rather than an increase in the channelconductivity.

Thus, the developed Nb/α�Si/Nb Josephson junc�tions with various degrees of doping of the α�Si layerby a refractory W impurity have advantages over othertypes of Josephson junctions in both their propertiesand manufacturability. We showed that the control ofthe impurity concentration and, thus, a change inparameter β can smoothly change one mechanism ofcurrent transport through a Josephson junction intoanother: current passage through a semiconductordegenerated into metallic conduction can be changedinto resonance current transport through impuritycenters in the semiconductor. Actually, when changingthe impurity concentration in the α�Si layer from 6 to11% and varying the junction area, we can form planarJosephson junctions with the required characteristicsfor any practical applications. Note that, irrespectiveof the type of conduction in the weak�coupling regionin the structures under study, the transport of dissipa�tionless superconducting current in them is caused bythe Andreev reflection of quasiparticles from theboundaries between the weak�coupling region and asuperconductor [22].

We revealed interesting properties of Josephsonjunctions with β ≥ 1. Under the action of an externalfrequency, the step amplitude on the CVCs of suchjunctions can be comparable with or even higher thanthe critical current and is almost independent of theratio of the frequencies, as compared SNS Josephsonjunctions. This property is suitable for a supercon�ducting integrated circuit for a programmable voltagestandard. Moreover, a high value of Rd is thought to

increase the response of such junctions in receiving–converting devices.

By analogy with SNS junctions, it is reasonable tocall these Josephson junctions SDS (superconductor�doped or degenerate semiconductor–superconduc�tor) junctions with allowance for their unique proper�ties, including those revealed earlier and related to thelong de Broglie wavelength of electrons in the α�Silayer, for the fact that they are intermediate betweenSNS and SIS junctions, and for the fact that currenttransport occurs exclusively due to impurities in thesemiconductor layer. The investigation of Nb/α�Si/Nb Josephson junctions to separate the resonancemechanism of current transport in a pure form, with�out shunting by conduction along random impuritychannels in the α�Si layer is the subject of a separateconsideration.

ACKNOWLEDGMENTS

We are grateful to A.I. Kozlov, A.A. Gogin, andA.Yu. Trifonov for their inestimable help in preparingand processing of the experimental samples, and alsoto V.K. Semenov and A.B. Zorin for fruitful discus�sions of the results.

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Translated by K. Shakhlevich

properties of planar nb/α-si/nb josephson junctions with various degrees of doping of the α-si...

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