A multi-walled C nanotube ( MWCNT ) was straight grown, straight from a substrate by a home-madecustom microwave plasma-enhanced chemical vapour deposition ( MPECVD ) method, between the accelerator electrodes interconnects. . And, for the intent of interconnects, the temperature dependance of electric resistance theoretical account analysis of this about fixed length and diameter individual MWCNT was carried out to look into the conveyance belongingss and the negatron dispersing mechanism. A theoretical account analysis of the temperature dependance of electric resistance of this fixed length and fixed diameter single MWCNT was carried out to look into the conveyance belongingss and negatron dispersing mechanism of the interconnects. Some theories are quoted given by which we can explicate the unnatural behaviour of the negative temperature coefficient of electric resistance ( TCR ) and in tantrum the our experimental consequences. Harmonizing toTo explain the consequences, the the hopping conduction mechanism theory can be used to depict the behaviour of electric resistance in the high temperature scope, whereas the variable scope skiping conduction theory may predominate at low temperatures.
Meanwhile, Overall, a grain boundary sprinkling theoretical account is besides found provided that can coincidentally suit the full measured curve ( from high to low temperatures ) of of the temperature dependance of electric resistance.
N Fatah Revolutionary Council – are expected to spread out their matter-of-fact public-service corporation in the applications of really big scale devices Nano-Scale electronic devices are expected to go more and more built-in to future high – public presentation integrated circuit devices due to their intrinsic belongingss sing latency and power dissipation. Carbon nanotubes base to play a pivitol function in the fiction of these electronic nano-scale devices due to their belongingss such as for their extensively decrease of power ingestion and transmittal clip. The fmechanical flexibleness, bearable opposition to chemical corrosion, and their high field emanation belongingss. of C nanotubes play a permeant function in manufacturing electronic nano-devices [ 1-3 ] . Besides, Tthe electronic conveyance propertiesy related to the electronic conveyance of C nanotubes particularly causes great attentionattract important involvement.
[ 4-6 ] . To accomplish the high velocity transmittal demands of the bit as the driver for future interconnect development, the potency of C nanotubes as an interrelated stuff has been recognized [ 7 ] . To farther Si integrated circuit ( IC ) engineering, the high velocity transmittal demands of french friess must be taken into history and the fresh belongingss of CNTs show promise to assistance in future IC bit interconnect developments. [ 7 ] .Furthermore, In theory, electronic conveyance in pure, perfect metallic SWCNTs and MWCNTs occurs would happen ballistic ballistically so that negatrons can transport through the tubing axis without any power dissipation due to dispersing [ 8, 9 ] . Therefore, negatrons and phonons would propagate easy along the same tubing axis.In pattern though, there are many factors to see. A.
Naeemi [ 10 ] used the tantamount circuit theoretical accounts to imitate the assorted electron-phonon dispersing mechanisms as a map of temperature every bit good as modelingand provided mold of the temperature coefficient of opposition ( TCR ) for different types and lengths of CNTs. However, the Certain defects ( merely like Stone-Wales defects and the Aharonove-Bohm consequence [ 11, 12 ] ) and every bit good as accelerators staying in the CNTs will really act upon electric resistance due to the excess sprinkling and. Besides, the interface raggedness and. The little grain size of the CNTs besides cause fluctuations inof the electronic conveyance features. [ 7 ].
The Sself-heating besides plays a important function in short length nanotubes transporting current under high-bias. [ 13 ] . .A. Svizahenko [ 14 ] besides reported that, ” big diameter nanotubes are preferred because even the semi-conducting shells can transport current due to little set gaps” , and “the conductance lessening with addition in prejudice was cause by contemplation of incident negatrons at traversing sub-bands due to dispersing with zone boundary phonons.”In this work, we attempt to suit and suit theoretical account thea temperature dependance of the electric resistance theoretical account of MWCNTs harmonizing to the the existent experimental consequences from high to low scope temperature ( 300 ~ 25 K ) consequences ( 300 ~ 25 K ) of from a singlen single MWCNT with a about fixed length and diameter, as shown in Fig. 1. which This MWCNT was fabricated by home-madea usage, microwave plasma enhanced chemical vapour deposition ( MPECVD ) system.
[ 3, 15 ] and with about fixed length and diameter, as shown in Fig. 1. In order to depict explicate the behavior consequence of a negative temperature coefficient of electric resistance ( TCR ) , we take into history the theory theories of the hopping conduction mechanism, the variable scope skiping conduction, strong localisation ( kfl0 ~ 1 ) and grain boundary sprinkling.
( a ) Hopping conduction
If the figure of impuritiesy or defects in the crystalline construction additions, so electron wavefunctionwave map spans merely a few lattices and slices exponentially. Therefore, the conduction is varied due to electron burrowing between localized provinces and the a negative TCR arises from phonon-assisted skiping conductivity. Excitement of negatrons to Ec, which contributes to the conduction by skiping, can be expressed as [ 13 ] due to strongly localised provinces:( 1 )where Ec is the mobility border and EF is the Fermi energy. This signifier of conductivity is usually, ly predominant at relativityelatively at high temperatures or when ( Ec-EF ) is little.
( B ) Variable scope hopping
Thermally activated, variable scope skiping conductivity by negatrons in the provinces near the Fermi energy at low temperatures is described as [ 16 ]( 2 )where R is the skiping distance, ?ph denotes the phonon energy, B is the coefficient related to the denseness of province and vitamin D indicates the dimension.
This status occurs at sufficiently low temperatures.
( degree Celsius ) Grain boundary sprinkling
Mayadas and colleagues were the first researches who theoretically treated explored the boundary sprinkling of negatrons in thin polycrystalline metal movies. However, Hoffmann and colleagues through empirical observation proposed a superior method to take into history to and explicate the boundary sprinkling of negatrons. The conduction of thin polycrystalline movies strongly deviates from the conduction of its matching bulk individual crystalline stuffs. Hoffmann and colleagues stated that the decrease of conduction depends exponentially on the figure of grain boundaries per average free way ( MFP ) and all negatrons reflected by the grain boundaries along one average free way do non lend to the ensuing current. The dc conduction of polycrystalline movies can be assumed as [ 17 ]( 3 )where is the figure of grain boundariesy per mean free way and Tg is the mean chance for an negatron to burrow a individual grain boundary.
Such, such that the effectual average free way can be expressed as( 4 )where is due to the Matthiessen ‘s jurisprudence. Here, lo is the elastic mean free way ensuing from acoustic phonon dispersing while the temperature dependance of inelastic average free way Lin is expressed as, which is about estimated by Bloch-Gruneisen ‘s jurisprudence and so can be assumed as further.. Besides, ifIf the grain size is rG, the crystalline proportion inside the movie can be denoted as. Therefore, the conduction can be revised as( 5 )Furthermore, we can eventually obtain the electric resistance( 6 )The temperature dependance of grain boundary sprinkling can act bring forth a positive or negative temperature coefficient of electric resistance ( TCR ) depending on the pick of transmittal coefficient T and the grain size roentgenium.
Experimental Design Descriptions
In this survey, a MWCNT was fabricated by the MPECVD [ 3, 14 ] method.
for the intent of patterning an analysis of the temperature dependance of electric resistance of aat a existent MWCNT interconnecting, a MWCNT was fabricated by a MPECVD [ 3, 14 ] method. The cCatalyst Ni electrodes were deposited onto a SiO2 bed which was grown on a Si wafer by the traditional thermic oxidization system to forestall current escape from the MWCNT device. The spread between the electrodes is 5 ~ 10 millimeter benefiting from the moisture etching procedure. The MPECVD process was ab initio heated and stabilized at 650 °C and 10-5 millimeter of mercury where the CNTs grew easy by with increasing microwave power.
Then, a mixture gas of methane ( CH4 ) and H ( H2 ) was introduced to the deposition chamber through mass flow accountants. The microstructures of the electrodes and MWCNTs were examined by scanning negatron microscopy ( SEM ) , as shown in Fig. 1 ( a ) and. Fig 1 ( B ) is the a cross subdivision image of another sample at of the same batch. The morphology is strongly depends on the growing conditions, particularly the temperature and input microwave power. It is evidently that the MWCNT grew justly straight between the two electrode tablets and gotwith a about fixed length of 3 ?m and diameter of 100 nanometer ( even though there are some decompression sicknesss therepresent ) . From Fig 1 ( B ) , it is clearly shown that bed by layerthe layered construction and withhas a 2.3 nm/per bed feature.
And, theThe temperature dependance of electric resistance of this individual single MWCNT was measured by the standard four-point-probe method.
Consequences and treatment
Harmonizing to the semi-experimental status ofMooij correlation in broken metals Mooij [ 18 ] , it will expose athere will be a negative TCR when the electric resistance of metals or semiconducting materials is larger than 100 ~150 mW-cm. That impliesy that a the worse ailing conduction conductive of a metal ever behavior behaves as a negative TCR stuff. That ‘s why it was presumed at that place will acquire the propertywould be a of negative TCR phenomenon in this survey.The original measuring informations of TCR of a singlethe single MWCNT, ( with multiple defects formed on the organic structure during the growing procedure ) is shown graphed in 2 ( a ) . It Resistivity would be usually additive with regard to temperature. But, for measures that vary polynomially or logarithmically with temperature, it may be possible to cipher a temperature coefficient that is a utile estimate for a certain scope of temperatures.
Then, inIn order to detect visualise the this behaviour of TCR, Fig. 2 ( B ) is illustrated in logarithmic secret plan ver.of T-1 from Fig. 2 ( a ) .
The, where dashed lines represent the adjustment suiting curves relative to T-1 under different inclines at both high temperature ( left side ) and low temperatures ( right side ) .It There is evidently clearly shown that a a rapid, increasinge tendency with the diminishing lessening in temperature from high to low temperature, , particularly below 50 K, . This clearly presents a negative TCR ( dr/dT & lt ; 0 ) phenomenon clearly and here couldthat can non be explained with semi-classicalsemi-classical theoriesy. Harmonizing to Fig. 2 ( B ) , it seemseems to connote that there will be two suiting theoretical accounts to manage the variable tendencies of TCR and with a transitionent point.There are some similar treatments consequences from old research workers.
P. Sheng [ 19 ] reported in his work that for high-resistivity farinaceous disordered systems, the low-field conduction exp ( -A/T? ) with ? = 1/2 is obeyed over big temperature ranges with possible crossing overs to ? = 1/4 at low temperatures and to ? & gt ; 1/2 at high temperatures. And, theThe temperatures at which the crossing overs occur depend on the distribution of grain size.
A. Naeemi [ 10 ] besides reported that, as shown in Fig. 3, that for single- and few-wall CNTs, it the Temperature Coefficient of opposition ranges 1/ ( T-200K ) for lengths much larger than the negatron MFP ( average free way ) . For MWCNT with big diameter ( & gt ; 20 nanometer ) , TCR varies from -1/T to +0.66/ ( T-200K ) as the length varies from zero to really big values. There exists a “singular point” around 200 K and separate adjustment theoretical accounts into two parts.
They got their consequences by simulations and assumed the organic structure of the object is would be perfect. What will go on in a existent MWCNT interconnectedness line which owns multiple defects?In this our work, the hopping conduction and the variable scope skiping conduction theory are employed to suit the experiment consequences for the two different inclines figures of Fig Fig. 2 ( B ) .In the theory of skiping conduction mechanism, the fluctuation of electric resistance at relativity comparatively high temperatures is relative to the Boltzman factor, exp ( -e/kT ) . The hHopping conduction theory, s=sminexp ( -e/kT ) , is employed where the fitting consequence curve is shown shown in Fig.ure 4 ( a ) . The electric resistance smin derived from the adjustment curve is 38 mW-cm, and the corresponding activation energy vitamin E is 4.46 meV which is rather close to the energy spread.
Therefore, as the temperature increased increases the thermic energy will excite an negatron from the cornice set to the conductivity set which leads to a high conduction.However, the TCR at in the low temperature portion scope can non be explained by the exponential jurisprudence above. But, when from usingthe the strong localisation theory ( kfl0 ~ 1 ) , so variable scope hopping may predominate at low temperatures, as shown in Fig. . 4 ( B ) . The exact variable scope skiping theory describes the low temperature behaviour of the electric resistance in strongly disordered systems where provinces are localized and can be expressed aswhere Rav is the mean hopping distance, N ( eF ) is the denseness of province, vph is the coefficient harmonizing to the phonon spectrum, B is the coefficient related to the denseness of province, and vitamin D indicates the dimension.Uniting these two theoretical accounts, it we can cover the whole ttemperature scope from high to moo ( 300 ~ 25 K ) , and ) and note T there exists a remarkable point about 150 K ( it which is lower 50 K lower K than in the work secret plan of A.
Naeemi [ 10 ] in Fig. 3 ) . This well-matched consequence is shown shown in Fig.ure 4 ( degree Celsius ) and expalained by taking into history the combined equations of skiping conduction theory and variable scope skiping conduction theoriestheory, and. T thhe fitting consequences are shown in Table I.
It comes to a greatis really consistent with Mott ‘s anticipations ( for the conduction of formless stuffs ) .The significance of the remarkable point here was presumed as to be a transeunt passage point of the that governs the conditional changeing from inelastic to elastic hits. It is a step of the temperature above which more manners of phonons in MWCNT ‘s MWCNTs organic structure will be excited. In this work, we named this remarkable point as athe “Lue Point” temperature to depict the this uniqueness belongings of MWCNTs.
For comparing intents, the grain boundary dispersing theoretical account was besides employed to suit for the electric resistance versus temperature of theour individual single MWCNT. The best adjustment consequence is shown in as a solid line in 5, and makes the physical restraints of the combining weight. ( 6 ) with p=1 and Tg & lt ; 1.In general, the value of p depends on the dominant inelastic sprinkling mechanism and is presumed to be fixed in the scope of 0.5 ~ 4 in the temperature scope [ 20 ] .
The parametric quantities obtained by suiting the R-T curves with least square mistakes method are listed in Table II. The parameter term, , indicates that the negatrons are scattered by barriers in one average free way ( lo ) where RG is the interval between grains. Harmonizing to the SEM image shown in 1 the diameter of the MWCNT is about smaller than 100nm with approximately 2.3 nm/per bed, therefore the elastic mean free way obtained by the fitting consequence of grain boundary sprinkling theoretical account is about 3 ~ 4 nanometer.Besides, the The parametric quantity, B, plays a important function to and affects the inclination of the R-T curve, due to the average free way ‘s cubic decimeter ( T ) =lo/ ( 1+bTp ) changing discrepancy with the temperature.
Harmonizing to the Matthiessen ‘s regulation, 1/l ( T ) =1/lo+1/lin, where Lin is the average free way due to the inelastic sprinkling which comes from the part of the optical phonon, we deduce that the interaction between the phonon and negatron at low temperatures is must be little. That is, the inelastic mean free way varied changing with temperature causes the negative TCR feature in our survey. In add-on, the negatron transmittal chance Tg for negatrons to go through a individual grain boundary is about the order of 10-1 as derived from the fitting consequence. is about the order of 10-1.
In this survey, we have performed the growing of the singleproduced an single MWCNT across the electrodes by a method of microwave plasma enhanced chemical vapour deposition ( MPECVD ) and measured the temperature dependance electric resistance of the individual this MWCNT to look into the its electronic propertiesy.For comparing, the consequence of quantum parturiency ( strong localisation ) and grain boundary theories were quoted to explicate the anomalous electric resistance ( a negative TCR ) feature.
In theOn the portion of strong localisation, the fitting consequence can be obtained by uniting skiping conduction theory in the high temperature scope and variable scope skiping conduction theory at the low temperature scope. And, theThe most appropriate adjustment consequence is accomplished by utilizing the grain boundary theory. The remarkable “Lue point” temperature can be successfully described the as a uniqueness belongings of MWCNTs. Besides, The the littleness of thenano- size of the fancied MWCNTs ensures the proof of the grain boundary sprinkling theoretical account. The and the temperature related inelastic average free way dominates the R-T curve doing the negative TCR characterist.
[ 1 ] S.
Iijima, C. Brabec, A. Maiti, and J. Bernholc, J. Chem. Phys. 104 ( 1996 ) 2089.[ 2 ] S.
Y. Chen, H. Y.
Miao, J. T. Lue, and M. S. Ouyang, J. Phys.
Calciferol: Appl. Phys. 37 ( 2004 ) 2 73.[ 3 ] L. W. Chang and J. T. Lue, J.
Nan Science and Nanotechnol. 5 ( 2005 ) 1672.[ 4 ] M.
P. Anantram and F. L e onard, Rep. Prog. Phys. 69 ( 2006 ) 507.[ 5 ] M.
Koentopp, C. Chang, K. Burke, and R. Car, J. Phys. : Condens. Matter 20 ( 2008 ) 083203.[ 6 ] B.
P. Ribaya, J. Leung, P. Brown, M.
Rahman, and C. V. Nguyen, Nanotechnol. 19 ( 2008 ) 185201.[ 7 ] J. Li, Q. Ye, A.
Cassell, H. T. Ng, R. Stevens, J. Han, and M. Meyyappan, Appl. Phys.
Lett. 82 ( 2003 ) 2491.[ 8 ] W. Liang, M. Bockrath, D. Bozovic, J.
H. Hafner, M. Tinkham, and H. Park, Nature 411 ( 2001 ) 665.[ 9 ] S. P.
Frank, P. Poncharal, Z. L.
Wang, and A. de Heer, Science 280 ( 1998 ) 1744.[ 10 ] A.
Naeemi and J. D. Meindl, IEEE Electron Device Lett. 28 ( 2007 ) 135.[ 11 ] T. Ando, H. Matsumura and T.
Nakanishi, Physica B 323 ( 2002 ) 44.[ 12 ] Y. Miyamoto, A. Rubio, S. Berber, M.
Yoon and D. Tomanek, Physical Review B 69 ( 2004 ) , 121413 ( R ) .[ 13 ] E. Pop, D. Mann, J.
Reifenberg, K. Goodson, and H. Dai, IEDM. Tech.
Dig ( 2005 ) 253.[ 14 ] hypertext transfer protocol: //arxiv.org/PS_cache/cond-mat/pdf/0504/0504004v1.pdf[ 15 ] S.
Y. Chen, L. W. Chang, C. W. Peng, H. Y.
Miao, J. T. Lue, J.
Nanosci. Nanotech. 5 ( 2005 ) 1887.[ 16 ] N. F. Mott and E. A.
Davis, Electronic Process in Non-crystalline Materials. Claredon Press, Oxford ( 1979 ) .[ 17 ] J. Vancea, H. Hoffman, and K. Kastener, Thin Solid Films 121 ( 1984 ) 201.[ 1 8 ] A. M.
Jayannavar and N. Kumar, Physical Review B 37 ( 1988 ) 573.[ 19 ] P. Sheng and J. Klafter, Physical Review B 27 ( 1983 ) 2583.[ 20 ] N.
Giordano, Phys. Rev. B 22 ( 1980 ) 5635
[ 1 ] S. Iijima, C. Brabec, A.
Maiti, and J. Bernholc, J. Chem. Phys.
104 ( 1996 ) 2089.[ 2 ] S. Y. Chen, H. Y. Miao, J.
T. Lue, and M. S. Ouyang, J. Phys. Calciferol: Appl. Phys. 37 ( 2004 ) 2 73.
[ 3 ] L. W. Chang and J. T. Lue, J. Nan Science and Nanotechnol. 5 ( 2005 ) 1 67 2.[ 4 ] M.
P. Anantram and F. L e onard, Rep. Prog. Phys. 69 ( 2006 ) 507.
[ 5 ] M. Koentopp, C. Chang, K. Burke, and R. Car, J. Phys. : Condens.
Matter 20 ( 2008 ) 083203.[ 6 ] B. P. Ribaya, J. Leung, P.
Brown, M. Rahman, and C. V. Nguyen, Nanotech n ol. 19 ( 2008 ) 185201.[ 7 ] J.
Li, Q. Ye, A. Cassell, H. T. Ng, R. Stevens, J. Han, and M.
Meyyappan, Appl. Phys. Lett. 82 ( 2003 ) 2491.
[ 8 ] W. Liang, M. Bockrath, D. Bozovic, J. H. Hafner, M. Tinkham, and H.
Park, Nature 411 ( 2001 ) 665.[ 9 ] S. P. Frank, P. Poncharal, Z. L. Wang, and A. de Heer, Science 280 ( 1998 ) 1744.
[ 10 ] A. Naeemi and J. D. Meindl, IEEE Electron Device Lett. 28 ( 2007 ) 135.[ 11 ] T.
Ando, H. Matsumura and T. Nakanishi, Physica B 323 ( 2002 ) 44.[ 12 ] Y. Miyamoto, A. Rubio, S.
Berber, M. Yoon and D. Tomanek, Physical Review B 69 ( 2004 ) , 121413 ( R ) .[ 1 3 ] E.
Pop, D. Mann, J. Reifenberg, K.
Goodson, and H. Dai, IEDM. Tech. Dig ( 2005 ) 253.[ 1 4 ] hypertext transfer protocol: //arxiv.org/PS_cache/cond-mat/pdf/0504/0504004v1.pdf[ 1 5 ] S.
Y. Chen, L. W.
Chang, C. W. Peng, H.
Y. Miao, J. T. Lue, J. Nanosci. Nanotech. 5 ( 2005 ) 1887.[ 1 6 ] N.
F. Mott and E. A. Davis, Electronic Process in Non-crystalline Materials. Claredon Press, Oxford ( 1979 ) .[ 1 7 ] J. Vancea, H. Hoffman, and K.
Kastener, Thin Solid Films 121 ( 1984 ) 201.[ 1 8 ] A. M. Jayannavar and N. Kumar, Physical Review B 37 ( 1988 ) 573.
[ 19 ] P. Sheng and J. Klafter, Physical Review B 27 ( 1983 ) 2583.