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International Symposium on Space Terahertz Technology, Moscow, 2014

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Power Load Dependencies of Cold Electron Bolometer Optical Response at 350 GHz
Mikhail A. Tarasov, Valerian S. Edelman, Andrey B. Ermakov, Sumedh Mahashabde, and Leonid S. Kuzmin
Abstract-- Cold electron bolometers integrated with twin-slot antennas have been designed and fabricated. Optical response was measured in 0.06-0.6 K temperature range using black body radiation source at temperature 2-15 K. The responsivity of 0.3*109 V/W was measured at 2.7 K radiation temperature. The estimated ultimate dark responsivity at 100 mK can approach Sv=1010 V/W and reduces down to 1.1*108 V/W at 300 mK for the sample with absorber volume of 5*10-20 m3. At high power load levels and low temperatures the changes of tunneling current, dynamic resistance and voltage response have been explained by non-thermal energy distribution of excited electrons. Distribution of excited electrons in such system is of none-Fermi type, electrons with energies of the order of 1 K tunnel from normal metal absorber to superconductor i nstead of relaxing down to thermal energy kTe. This effect can reduce quantum efficiency of bolometer from hf/kTph in ideal case down to single electron per signal quantum in the high power case. Index Terms--bolometers, nanofabrication, slot antennas, submillimeter wave technology, superconducting devices

I. INTRODUCTION

C

old-electron bolometer with Superconductor-InsulatorNormal metal-Insulator-Superconductor (SINIS) structure has promising predicted performance [1,2]. Under microwave irradiation additional excited electrons with high excess energy provide increase in tunneling current and/or decrease of dc voltage and such response is dependent on applied power and frequency. Usually for theoretical estimations it is assumed that microwave radiation is equivalent to dc heating at the same absorbed power. In such process the electron temperature of absorber is increased over the phonon temperature. However in normal metal for Terahertz radiation at frequency f >>kT/h dominates quantum absorption of photons with energy E=hf>>kT by single electrons [3 -6]. In this case the energy distribution of electrons is determined by a balance
Manuscript received on May 29, 2014. This work was supported in part by the Swedish Space Agency SNSB and Swedish scientific agency Vetenskaps RÅdet. M.A.Tarasov and A.B.Ermakov are with the V.Kotelnikov Institute of Radio Engineering and Electronics of Russian Academy of Sciences, 125009 Moscow, Russia (phone: 7-495-6293418; fax: 7-495-6293678; e-mail: tarasov@hitech.cplire.ru). V.S.Edelman is with the P.Kapitza Institute for Physical Problems of Russian Academy of Sciences, Moscow, Russia. S.Mahashabde and L.S.Kuzmin are with the Chalmers University of Technology, Gothenburg, Sweden.

of processes of photon quantum absorption, electron -electron, electron-phonon, phonon-electron, phonon escape processes, and tunneling of excited electrons in a SIN junction [3,4] . This distribution function is significantly different from equilibrium Fermi distribution. Microscopic calculations of tunneling current in clean limit [3,4] for electron -electron and electron-phonon collision integrals show that increase of response is dependent on multiplication of excited electrons with energies >kT due to electron-electron interactions and reabsorption of nonequillibrium phonons that did not escape from absorber. Multiplication of non-equillibrium electrons leads to increase of current response I(P), in which P ­ absorbed power, and this multiplication leads to increase in current I for voltage bias mode. Thus current response I of SINIS detector can exceed the photon counter limit of e/hf, but still being below the bolometric response limit of e/kT. Studies and optimization of energy relaxation in electron system at low temperatures can help to improve the practical optical response of SINIS detectors. In our earlier experiments [7,8] we observed voltage response V(I)=VI,P=0­VI,P, which shows that there is no thermal equilibrium in electron system. Now we performed detail analysis of new experimental data on IV curves, dynamic resistance, optical response to show absence of equilibrium in electron system and significant tunnel current due to electrons with excess energy. II. EXPERIMENT Bolometers containing 3 serial SINIS structures were integrated in twin-slot antennas. Bottom layer of bolometer was made of normal-metal Al absorber 10 nm thick in which superconductivity was suppressed by underlayer of ferromagnetic film [9]. For microwave signal such bolometers were connected in parallel by means of capacitive connection. Dimensions of elements: area of tunnel junctions 0.25 m2, length, width and thickness of normal metal strip between tunnel junctions 1*0.1*0.01 m3, dc resistance of single absorber ~200 . Parallel connection for microwave signal makes antenna load of 60 . Tunnel junctions parameters were similar to earlier studied in [7,8]. When cooling down to T< 0.1 K the resistance ratio Rd(V=0)/Rn (in which Rd=dV/dI, Rn - asymptotic normal resistance) approached Rd/Rn=15000, and total resistance of array at 0.1 K approached Rd(V=0)=400 M. Samples were measured in dilution cryostat equipped with pulse tube refrigerator [10]. Additional recondensing stage with liquefying of He gas in a 0.12 liter container allows to


International Symposium on Space Terahertz Technology, Moscow, 2014 keep temperature below 0.1 K during 4 -5 hours with compressor shut down. Chip with SINIS receiver was mounted inside copper radiation shield at temperature 0.4 0.45 , in which inner wall was painted with black absorber containing Stycast® 2850FT. Silicon chip 0.35 mm thick was attached to sapphire hyperhemisphere 10 mm in diameter that collect radiation to the planar antenna. Lens itself was glued with Stycast® 1266 in copper holder screwed to the dilution chamber. Measurements with RuO2 thermometer glued to Si plate instead of detector show that its temperature at 0.1 K differs by less than 2-3 mK from mixing chamber temperature measured by LakeShore® thermometer with absolute error below 5 mK. In front of lens in the bottom of radiation shield it was a hole 5 mm in diameter, which was covered with planar bandpass filters [11] for central frequency of 330 GHz and total passband of 50 GHz. Spectral transmission within 10% accuracy is described by product of two Lorentz lines with halfwidth of 70 GHz. Transmission in the maximum was over 90%. Distance from lens to filter is 2 -3 mm, between filters 2 mm, from filter to black body source 2 -3 mm. Radiation source is a black body made of Si wafer covered with NiCr film of square resistance of 300 . Wafer was mounted on heat insulating legs to 1 K pot. Temperature of radiation source was monitored by resistance of a calibrated RuO2 chip-resistor and heating varied by current through this NiCr film in the range of 0.9-15 K. Dissipated power was up to few milliwatts, time constant for heating/cooling of the order of 0.1 s. Power received by antenna was calculated using Planck formula for single mode
Pin
cid en t

2

= df

(1 ) in which TR- radiation source temperature, factors K1 and K2 accounted for transmission of filters and spectral matching of antenna. For twin-slot antenna we take Lorentz line with halfwidth of 100 GHz and maximum at 330 GHz. Influence of K2 was rather small, below 20%. Multiplier K3=0.72 takes into account reflection of sapphire-silicon and sapphire-vacuum interfaces. III. EXPERIMENTAL IV CURVES AND ESTIMATIONS OF
ELECTRON TEMPERATURE

hf K1 K2 K3 hf 1 exp kT R

Equivalent electron temperature in normal metal absorber was deduced from dependencies of dynamic resistance Rd=dV/dI and comparison with dV/dT dependence of ideal SIN junction at some effective electron temperature. In Fig. 1a,b presented IV curves for two electron temperatures and calculation according to simple analytic relation (2). IV curve of ideal SIN junction for voltages below the gap of superconductor V=/e (in which -- energy gap of superconductor), for single junction can be presented as [12]: eV 1 eV (2 ) I V,T = 2kTe eV exp kT sinh kT eRn e e In our case we have 6 junctions connected in series, so measured values of Rn and V are divided by 6 to fit with

model curve. Voltage derivative of current brings dynamic conductivity and inverse value is dynamic resistance. In experimental curves measured voltage corresponds to 6V sin in which VSIN ­ voltage across the single SIN junction. Gap voltage V in (2) according to BCS theory corresponds to eV=(0)=1.76*kT in which T ­ critical temperature. It can be determined from the dependence Rd(T, V=0), which in the temperature range ~ 0.3 ­ 0.5 K has exponential shape. At higher temperatures it should be accounted also the temperature dependence (T), and at temperatures below 0.2 K dynamic resistance Rd approaches constant value that is explained by overheating of electron system by external radiation. Value of equivalent e can be estimated by fitting with equation (2). In our case using =k*2.45 we obtained good correspondence of experimental calculated curves in all figures. Small difference can be observed at V>0.4-0.5 mV, where resistance is higher compared to calculated one due to electron cooling. In our fitting we use value of that corresponds to T c~1.4 K. In measurements at T=1.5 IV curve is linear and at 1.3 nonlinearity is clear visible, so T c is within this range. If electron system is excited b y radiation, then dependence is different from heating of sample, see fig. 1b. There is no more correspondence with simple thermal model. If we take Te for which Rd(V=0) is the same as in model, then at higher bias current the difference in resistance ca n be more than 10 times larger. One can see that power response and temperature response are different at 70 mK and coincide at 340 mK (Fig. 2). Dependencies of responsivity dV/dP on phonon temperature and equivalent electron temperature are presented in Fig. 3a,b for radiation power levels 0.22 pW, 1.35 pW, 2.95 pW, 4.95 pW. When plotted in dependence on electron temperature (b) the shape of dependence is more natural and shows that responsivity is dependent on nonequilibrium electron temperature. When irradiated at 5 pW load the responsivity is reduced by an order of magnitude compared to 0.2 pW power load. When bath is heated to 0.34 K these responsivities become equal for all power loads which means that in this range detector becomes linear, d V/dP is independent on power and is determined by temperature. In this case electron and phonon temperatures are very close, and nearly equal. It means that increase in bath temperature leads to increase of relaxation processes and thermalization of electron system. Losses in bolometer can be roughly estimated from power to current transfer ratio, or current responsivity. Compare a number of incoming quanta IQ=5*108 s-1 for 0.1 pW at frequency 330 GHz and number of excited electrons that tunnel due to irradiation IS=6*108 s-1 (current increase at this power load). Quantum efficiency =IS/IQ=1.2 is close to unity, which means that one quantum produce just one electron, that is a photon counter mode. There is no multiplication of excited electrons number which was predicted in [4] for bolometric mode of operation. If energy did not escape from electron system, then the number of excited electrons with energies in the range ~ (0.2 ­ 1) should be 30 times more.


International Symposium on Space Terahertz Technology, Moscow, 2014

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0,4

Tchip 340 mK

0,04

Tchip 70 mK

Prad = 4.8 pW
0,2

Prad = 4.8 pW
0,02

calculated, Te = 370 mK Te = 345 mK

0,0

0,00

calculated, Te = 235 mK Te = 205 mK

I, nA

Prad <0.01pW Prad <0.01pW
-0,2 -0,02

-0,4

a
-400 -200 0 200 400

I, nA

-0,04

b
-400 -200 0 200 400

V, V

V, V

Fig. 1. IV curves of SINIS bolometer at bath temperature 340 mK (a) and 70 mK (b). Solid lines correspond to experimental data ob tained at two radiation power levels of 4.8 pW and below 10 fW. Stars and circles ­ calculated curves for 370 mK and 345 mK (a), and 235 mK and 205 mK (b).

300

IV. DISCUSSION
V(70mK, <0.01pW )-V(70mK, 4.85pW )

200

V(70mK)-V(170mK)

100

0

V(340mK, <0.01pW )-V(340mK, 4.85pW )
-100

V(340mK)-V(364mK)
-200

-300 -1 0 1 2 3

I, nA

Fig. 2. Voltage response dependencies on dc bias for temperatures 70 mK and 340 mK. Solid lines under 4.85 pW irradiation, dashed - response to equivalent increase in temperature without irradiation .

According to estimations [17] the difference of calculated and experimental curves proves the absence of equilibrium in electron system when energy distribution for electrons with energy above the Fermy energy and holes with energy below it does not correspond to Fermi distribution with equivalent electron temperature. These excited electrons can be viewed in two groups: thermalized and athermal. Impact of thermalized electrons can be estimated assuming that their temperature corresponds to calculated for the case when calculated curve tangenting experimental at V=0, and dynamic resistance of both are equal. In Fig.1b such assumption leads to the electron temperature under irradiation estimation of 235 mK. The impact from athermal electrons can be estima ted as a difference between measured and calculated and can be up to 70% of the total response. When temperature increase the relaxation processes speed-up and at 0.34 K the impact from athermal electrons is much less. At the same time impact from thermalized electrons increase, they prevail in tunneling current. As a result the voltage dependence of response approaching the calculated one.

V, V


International Symposium on Space Terahertz Technology, Moscow, 2014

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250

200

P =0.22 pW

V/P, V/pW

150

1.35 pW
100

2.95 pW

50

4.95 pW
0 0,0 0,1 0,2 0,3 0,4

T,K

250

200

P =0.22 pW

Microscopic model described in [13] assume that as the result of electron-electron interaction primary electron after each inelastic collision will produce three new quasiparticles: two electrons and one hole. Each of them has hf/6 of initial energy. Absorption of one phonon will produce two quasiparticles: one electron and one hole, similar to photon absorption. Spontaneous emission of phonons preserves the number of quasiparticles. Rate of electron-electron collisions that are necessary for multiplication of electrons is an order of magnitude slower compared to electron-phonon relaxation which reduce excitation energy and do not lead to multiplication of quasiparticles. The phonon -electron process can slightly increase bolometer response above the photon counter limit. Model of thermalization in normal metal is also discussed in [16]. According to this model the most probable process for energy relaxation of electron from energy level of E= is down to /4 and emerging of phonon with energy 3 /4. This energy is much higher compared to thermal phonon s and we obtain a nonthermal distribution for both phonons and electrons. First we estimate the diffusion constant for electrons in normal metal:

V/P, V/pW

150

1.35 pW
100

D=

1 e N
2

(3 )

50

2.95 pW
0 0,20

4.95 pW
0,25 0,30 0,35 0,40

Te, K

Fig. 3. Responsivity dependence on bath temperature (top panel) and on equivalent electron temperature (lower panel) for radiation power levels 0.22 pW, 1.35 pW, 2.95 pW, 4.95 pW.

Radiation power is collected in a normal metal absorber with dimensions much less compared to the wavelength, so it can be considered as a lumped element. When absorbing the radiation quantum energy hf/k =16 K, all this energy is transferred to electron, it forms electron -hole pair with energies from 0 to hf above/below the Fermi energy. The average energy of excited electron and hole is 8 K. Excited electrons and holes diffuse towards the area of tunnel junctions with diffusion time diff , after that transfer into superconducting electrode with time constant sin. During this period energy is redistributed due to electron -phonon, phonon-electron, electron-electron, phonon-phonon and phonon escape processes. As a result energy of excited electrons is reduced, their number can increase, some power escape into substrate and superconducting electrodes. Additional tunneling current under irradiation depends on ratio of time constants of these processes. Since all time constants are strongly dependent on excitation energy, the dynamics become very complicated, especially taking into account transition from two-dimensional to three dimensional cases when changing temperature and power. Processes in superconducting electrode will be also ignored; we assume it as a thermal sink.

in which =0.07 *m, N=2.3*1010 m-3eV-1 is electron density at Fermi level, this brings D=0.004 m2/s. Diffusion time for electrons to travel the distance about 1 m from the middle of absorber to tunnel junction area is diff=0.25 ns. Relation of diffusion constant with speed v mean free pa th l is D=lv/3. Taking Fermi velocity vF=2*106 m/s one can get the mean free path in absorber l=6 nm. Thickness of absorber in our samples is 10 nm, which is comparable to mean free path. Diffusion time through the thickness of absorber is 0.025 ps. One more important parameter is a characteristic time for tunneling in SIN junction. Time constant for electrons to escape from normal metal to superconducting electrode is determined by time of many attempts providing close to unity probability to tunnel through the barrier. Transparency of barrier is related to normal resistance of junction. According to [3, 12], if in the bias point differential resistance is close to normal resistance, then tunneling time constant is



sin

= N 0e 2 Rn St

(4 )

in which N is density of states at Fermi level, Rn is normal resistance of junction, S junction area, t film thickness. For aluminum film 10 nm thick, RnS=~1000 *m2, this corresponds to sin~40 ns. As a result sin>> diff and distribution of electrons along the normal metal is uniform. Nonequillibrium condition of system is mainly determined by relation between electron-electron and electron-phonon time constants. The last can be estimated similar to [13, 14] as:

3 I 0 k 6 N (0 ) ep= E4

(5 )

Parameter I0=25, electron-phonon constant =2.3 nW/(m3*6). For average excitation energy of electrons


International Symposium on Space Terahertz Technology, Moscow, 2014 E/k=8 it corresponds to ep= 0.2 ns, that is comparable to diffusion time. The wavelength of such phonons with energy 8 and sound speed in aluminum ~5000 m/s equals to phonon~30 nm and it is larger compared to film thickness. It means that such phonons propagate at small angles to the boundary between Al absorber and Si substrate and probability of their escape to substrate is rather small. The last stage of electron-phonon interaction producing quasi-Fermi distribution happens at phonon temperature 340 mK or 70 mK with corresponding electron temperatures 370 mK and 235 mK for which electron-phonon power flow in absorber is 280 fW and 28 fW. Actually electrons interact with phonons of the entire volume of Al absorber and Al superconducting electrodes that is 10 times as large, this makes corresponding power flow up to 3 pW and 0.3 pW. Opposite process of phonon-electron interaction is rather fast, according to [9,14]:

5

tunneling sin to electron-electron and electron-phonon time constant. Finally, we can pick out two groups of time constants, first is energy independent, it is diffusion time dif=0.25 ns, tunneling time sin=40 ns, phonon escape time esc=2 ps, and phonon-phonon time pp=0.6 ns. Energy dependent time constants are second order dependent 1/E 2 electron-electron time ee and pe, and also a fourth order dependent 1/E4 electron-phonon constant ep. Dependencies are presented in Fig. 4.

1000000

100000

Time constant, ps

10000

tdiff tsin tescape tep tpe tee tpp

In which NA*nd ­ atomic density that is for aluminum 6*10 22 cm-3, D=428 K ­ Debye temperature. If we take the distribution of energy from electron with initial energy 8 to electron and phonon with the ratio 1:3, this corresponds to pe(6 K)=5 ps. The dynamics is quite different for electrons in the region of tunnel junctions. For acoustic waves bo th normal and superconducting electrodes separated by barrier below 2 nm thick is the same material and phonons can escape from normal into superconductor metal in few picoseconds without returning energy to electrons in absorber. Such process is a loss channel for energy that irreversibly escapes to superconductor or substrate. Characteristic time for such escape through the thickness of absorber tabs is escape=tabs/vsound=2 ps. Phonon relaxation time can be estimated in the case of scattering at boundaries by dividing the characteristic length of our sample about labs=3 m by sound speed pp=labs/vsound= 600 ps. Redistribution of energy among electrons is governed mainly by electron-electron interaction. Equation for calculating of such time constant ee for two-dimensional case corresponding to thin normal absorber taken from [12,14]:

234 N A nd k pe = 3 6 D E 2

3

(6 )

1000

100

10

1 1 2 3 4 5 6 7 8

Energy, K

Fig. 4. Time constant dependencies on excitation energy plotted in Kelvins i.e. E/k.

Electron-electron and electron-phonon time constants become equal at energy around 3.7 K, and for lower energies electronphonon interaction get slower, so electron -electron can become dominating. To increase bolometer efficiency the length of absorber should be increased providing diffusion time dif longer compared to ee and ep, value of ep should be increased by using absorber material with lower electronphonon parameter sigma; resistivity, density, and acoustic impedance of absorber material should be increased as well. According to [3] the optimal resistance of SIN junction should be around 10 k. V. VOLTAGE RESPONSE In our experiments at low bias we observe significant maximum that is not presented in conventional model of SINIS bolometer without strong power load. This maximum is increasing with signal power level that contradicts to eventual explanation by Coulomb blockade that should increase with cooling and reducing of power level. In IV curves current increase is observed compared to the dark IV curve. We assume that such additional maximum corresponds to direct detection at nonlinearity of SIN junction. At zero bias there is no detection because of IV symmetry for both half periods of signal and for bias about 50 -100 V there is maximum of rectified signal at maximum of nonlinearity. Contrary to bolometric detection here we have direct detection (rectification) of incoming signal. In Fig.5,6 presented response dependencies measured at black body source temperatures 0.89; 1.8; 2.25; 3.0; 3.6; 4.3; 4.9; 5.5; 6.0; 6.6;

ee =

hE

F

E 2 E 2 ln F E

(7 )

in which EF=11.6 eV ­ is Fermi energy. At electron temperature of 8 this time is ee=1 ns, that exceeds ep = 0.2 ns for the same electron energy. For three -dimensional case ee is dozens times as much compared to two dimensional. Value of ee becomes equal to sin for temperatures in the range (1...1.3) . Value of ep becomes equal to sin for electron temperatures ~2 . From the above revue it is clear that due to complicated combination of electron-electron, electron-phonon, phononelectron interactions which vary with signal frequency and power, the energy distribution of electrons is much different from simple Fermi distribution. Nonequillibrium of system is mainly determined by ratio of escape time for electrons due to


International Symposium on Space Terahertz Technology, Moscow, 2014 7.2; 8.3; 9.8; 11.2; 12.5 K. Voltage response obtained by subtraction of adjacent IV curves.
80 60 40

6

210 110 d rdV35 m

6 6

0 110
6 6

Response, V

20 0 -20 -40
110

210 4 410

0

410

4

Vm Fig. 7. Second derivative of normalized IV curve at 350 mK.
11 10 9 8 7 6 5 4 3

-60 -80 -1000

110

110

-500

0

500

1000

d RdV15 m d RdV21 m d RdV35 m

110 110 110 110 110

Voltage, V

Fig. 5. Voltage response at lower levels of signal in the range 1-4 . Standard bolometric response observed at about half-gap voltage bias, and at lower bias around quarter gap voltage corresponding to higher nonlinearity appears a direct detector response.

110 4 210

110

4

0 Vm

110

4

210

4

200

Fig. 8. Curvature dR/dV in logarithmic scale for temperatures 150, 210, 350 mK.

100

0

-100

-200

-1000

-500

0

500

1000

Voltage, V

Fig. 6. Voltage response in wider radiation temperature range 1 - 15 .

Simple calculation of second derivative of IV curve for SIN junction (Fig.7) shows that maximum curvature is presented at lower bias voltages. For comparison in Fig.8 similar dependencies is presented in logarithmic scale for three temperatures of sample. Curvature is increasing by four orders with cooling from 350 mK to 150 mK

Nonlinearity of SIN junctions was earlier used for heterodyne and direct detection of microwave signals in [18,19], in which were used Pb/Bi/In-oxide-Ag junctions with area of 1.2 m2 and specific capacitance of InOx of 4 F/cm2. Noise temperature comparable to SIS junctions was demonstrated in such junctions when biased near the energy gap. Specific methods of fabrication for lead and niobium SIN junctions of 0.5 m2 area are described in [20,21]. Noise temperatures down to 140 K were obtained at signal frequencies up to 320 GHz [22]. One more similar structure of SINS type is described in [ 23], for which the estimation of noise temperature is at the level of 13 for signal frequency 330 GHz. Direct detectors in mm-wave band with NEP =10-15 W/Hz1/2 [24] working at 4.2 K did not found practical applications, but for temperatures below 300 mK they can be competitive with superconducting bolometers. According to [25] the conventional current response at relatively low frequencies can be presented as (8 ) In nonlinear SIN or SIS junction with responsivity S/2>e/hf this expression should be modified to the relation for quantum assisted tunneling

Response,V

[

( (

) )

() (

( )

)

]

(9 )

Assuming that shot noise is dominating in such detectors in2=2eIB we can estimate the NEP of matched detector as


(10)


International Symposium on Space Terahertz Technology, Moscow, 2014 that can approach in quantum limit maximum value of NEP=hf(2IB/e)1/2 In our case at T=100 mK for bias current 0.01 nA and output band 1 Hz this corresponds to 2*10-18 W/Hz1/2, and comparable to estimations for bolometric response of SINIS structure. In this rough estimations we do not take into account input mismatch
( )

7

REFERENCES
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, in which Rrf is antenna

impedance and Rs is detector impedance. For planar antenna we can take source impedance of 70 . Active part of nonlinear detector impedance in quantum assistant tunneling limit is
( ) ( )

(11)

contrary to dynamic resistance in bias point for classical detector. This value will be partially shunted by SIN junction capacitance with specific value of about 60 fF/m2 that is about 10 at signal frequency of 350 GHz. For comparison we can also mention super-Schottky diodes with superconductor-semiconductor junctions Pb-GaAs that were first proposed in [26]. Shape of IV curve and detector response analytic theory for super -Schottky diodes were developed in [27]. Current response can be presented as
( )

(12)

This value approaches classical limit Rcl=e/2kT for lower frequencies hf<<2kT and quantum limit Rq=e/hf for higher frequencies hf>2kT. For T=100 mK the characteristic frequency separating two cases is only 5 GHz. For our signal at 350 GHz the nonlinearity scale for quantum assisted tunneling corresponds to dV~hf/e=1.3 mV, and energy gap of single Al SIN junction is only 0.2 mV. In this scale we cannot expect quantum detection, but lowfrequency components of black body thermal radiation and external RF interferences like mobile telephones and TV stations will be detected and make impact to current as we can see in Fig. 6. Such detector effect can be assumed as significant for frequencies below 50 GHz for bias close to zero and for frequencies below 100 GHz for bias around the gap voltage. VI. CONCLUSION For SINIS detectors nonequillibrium in electron system plays the main role in optical response performance. Ultimate parameters can be achieved for maximum multiplication of electrons in absorber due to electron-electron interactions and absorption of nonequillibrium phonons. Time of electronelectron collisions is relatively big at the beginning of such process and diminish multiplication. Nonequillibrium of phonon system is determined by freedom of phonon escaping to superconducting electrode that is fabricated from the same aluminum as absorber. The natural way to increase multiplication and response of detector is using material with lower ee, higher ep, and higher acoustic mismatch with aluminum, that can be Hafnium. Inversion of sequence of layers with placing absorber above superconductor can also reduce phonon escape to substrate.