Fundamental Forensic Sci
Fundamental Forensic Sci FOR 200
Popular in Course
Popular in Forensic Science
Derek Wyman II
verified elite notetaker
Mr. Efrain Pfannerstill
verified elite notetaker
verified elite notetaker
verified elite notetaker
verified elite notetaker
verified elite notetaker
This 4 page Class Notes was uploaded by Jessica Johns on Tuesday September 8, 2015. The Class Notes belongs to FOR 200 at University of California - Davis taught by Staff in Fall. Since its upload, it has received 16 views. For similar materials see /class/191784/for-200-university-of-california-davis in Forensic Science at University of California - Davis.
Reviews for Fundamental Forensic Sci
Report this Material
What is Karma?
Karma is the currency of StudySoup.
You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!
Date Created: 09/08/15
PHYSICAL REVIEW B VOLUME 58 NUMBER 22 RAPID COMMUNICATIONS 1 DECEMBER 199811 Finite size effects in bismuth nanowires Kai Liu and C L Chien Department of Physics and Astronomy The Johns Hopkins University Baltimore Maryland 21218 P C Searson Department of Materials Science and Engineering The Johns Hopkins University Baltimore Maryland 21218 Received 18 September 1998 Arrays of sernimetallic Bi nanowires fabricated by electrodeposition exhibit strong nitesize effects in transport properties as the carrier meanfree path is limited by the wire dimensions We have observed a resistivity enhancement a very large positive magnetoresistance and a resistance maximum that depends on the strength and orientation of the magnetic eld and the nanowire diameter These results demonstrate electrodeposited Bi nanowires as a new medium for studying the intricate physics in Bi nanostructures 80163182998522461 Magnetic nanostructures such as multilayers eg Co Cu Refs 173 and granular solids eg CoAg Refs 4 and 5 with metallic constituents have attracted a great deal of attention due to the realization of new phenomena such as negative giant magnetoresistance GMR and interlayer coupling6 The effect size of GMR in magnetic nanostruc tures is generally on the order of a few to a few tens of percent except in nearly perfect superlattices which show the largest GMR effect of about 150 at 42 K7 To date the constituent materials in the overwhelming majority of mag netic nanostructures include transition metals alloys and noble metal elements Recently we have successfully fabricated arrays of semi metallic Bi nanowires by electrodeposition in a new at tempt to explore nanostructured semimetals Semimetallic bismuth Bi is a material that exhibits interesting magne toresistance MR characteristics9 and nitesize effects Pure bulk Bi is known to exhibit a large positive MR with a prescribed eld dependence The electronic properties of Bi are fLmdamentally different from those of common metals due to the complex and highly anisotropic Fermi surface The elongated pockets of holes and electrons with small ef fective masses lead to a large Fermi wavelength of about 400 A as opposed to a few A in most metals10 The carrier mean free path in Bi can be as much as a millimeter at 42 K several orders of magnitude larger than those for most metals11 Due to the Lmusual electronic structure Bi has been used to study both classical and quantum nitesize effects for which the characteristic lengths are the carrier meanfree path and Fermi wavelength respectively The pursuit of quantum size effects initiated by the observation of resistiv ity oscillations in Bi thin lms as the thickness is varied12 has continued to attract attention since the 1960s1 3913 15 Most of these studies involve Bi thin lms for which lm thickness is a convenient variable To date the fabrication of high quality Bi thin lms has been limited to molecular beam epitaxy Other traditional deposition techniques such as sputtering have been Lmsuc cessful in preserving the intrinsic Bi properties in thin lms such as the large MR effect due to the inferior lm quality There have also been early studies using the Taylor process 01631829985822l468l41500 PRB E to fabricate micron and submicronsize Bi wires 3917 The electrodeposited Bi nanowires we fabricated offer a new me dium for studying the intricate physics as well as applica tions in Bi nanostructures The Bi nanowires were electrodeposited into nanometer size cylindrical pores in polycarbonate membranes18 They are typically 10 pm in length arranged in a parallel manner Detailed electrodeposition conditions of the Bi nanowires have been published elsewhere8 In this work nanowires with diameter of 2 pm 1 am 400 nm and 200 nm were fabricated with a corresponding wire density of 2X10 2 X105 1 X 106 and 3 X 106 wiresmmz respectively Struc tural characterizations by xray diffraction TEM and elec tron diffraction con rmed a polycrystalline rhombohedral structure Typical Bi grains in the wires are elongated in shape with the width comparable to and the length up to 274 times the wire diameter For transport measurements two Au strip layers were pat terned on the top and bottom surfaces of the membrane in order to make electrical contact to a smaller number of Bi nanowires19 A quasifourprobe geometry was achieved by attaching a voltage lead and a current lead to each Au strip layer The measured resistance is the sum of the Bi nanowire resistance and the contact resistance the latter of which is negligible due to the much larger area in the current path This method allows us to estimate the resistance of a single Bi wire from a group of wires connected in parallel Assuming all the Bi wires in the selected area contribute equally to the total resistance then the resistance of a single Bi nanowire is rather large For the case of 400nm wires the resistance per wire is over 1000 Q in the temperature range of 57300 K This is much larger than the value of about 1007200 I expected using the resistivity of 115 M0 cm for bulk Bi at 300 K or the value of 200 M0 cm for electrode posited 1 umthick polycrystalline Bi lm at 300 K Electron microscopy shows that the vast majority of the nanowires have protruded above the membrane surface and are ex pected to make electrical contact with the Au layer There fore there is an enhancement of 5710 times in the resistivity due to the nanowire geometry Previously similarly large resistivity enhancement has also been reported in multilay R14 681 1998 The American Physical Society RAPID COI II IUNI R14 682 KAI LIU C L CHIEN AND P C SEARSON PRB E 400 nm Bi Nanowires 400 nm Bi Nanowires 10 I I I I I 104 a 39 8 1 02 g 6 H50k0eJwnes 9 100 39 39 A m g a E 098 4 39 H50kOe Wll39eS a 096 2 H0 3 H1 Wires lokoe 0 102 300 H50 kOe b 39 39 I Q 13900 39 50k0e39 HJ wires transverse 2 Ea 200 40k0e39 a g 098 E E 30k0e 100 39 Hlwires longitudinal 096 39 b H Wires 20k0 5 10k0e I I I I I I I I 0 0 20 40 60 0 100 200 300 T K T K FIG 1 Temperature dependence of a resistance and b mag netoresistance of the 400nm Bi nanowires with and Without a magnetic eld of 50 kOe applied perpendicular and parallel to the Wires ered CoCu nanowires19 Since the meanfree paths of Co and Cu are much smaller than the wire dimensions the ad ditional resistance is due mainly to scattean at the numer ous CoCu interfaces and to a lesser extent boundary scat tering at the wire surface In the present case of Bi wires scattering at the wire surface and particularly grain bound aries is expected to be strong since the wire dimensions are much less than the bulk Bi meanfree path which could reach mm scale at low temperatures Therefore the enhance ment of resistivity in Bi nanowires can be ascribed to clas sical nitesize effects as the meanfree path is effectively limited by the wire diameter Further evidence of strong nitesize effect will be illustrated later We next describe the temperature and eld dependence of the transport properties The temperature dependence of the resistance of 400nm Bi nanowires is shown in Fig 1a In zero magnetic eld the resistance increases gradually with decreasing temperature The ratio of resistance at 5 K and 293 K R5 KR293 K is about 15 This negative tem perature coef cient TCR is observed in all the Bi nanowire samples with different diameters The TCR of Bi is deter mined by the relative contributions due to the carrier con centration and mobility which have opposite temperature dependence With increasing temperatures the carrier con centration increases whereas the carrier mobility decreases leading to respectively a negative and a positive TCR When the temperature dependence of the carrier mobility is sup pressed by structural imperfections or nitesize effects that of the carrier concentration dominates the TCR In the present case of Bi nanowires because of the polycrystalline FIG 2 Temperature dependence of resistance normalized to the value at 5 K of the 400nm Bi Wires showing resistance maxi mum at Tmax for various values of a transverse and b longitudi nal magnetic eld nature of the material and the smaller wire diameter in com parison with the meanfree path the TCR is generally nega tive Upon the application of a magnetic eld H the resistance of the Bi wires increases for both eld parallel longitudinal and perpendicular transverse to the wires as shown in Fig 1a for H 50 kOe It is noted that the transverse MR in Bi nanowire is always larger than the longitudinal MR Further more the temperature dependence of the resistance shows a maximum at Tmax at about 40 K The resistance maximum under a magnetic eld observed in Bi wires resembles the resistance maximum in zero magnetic eld in very thin single crystallike Bi lms lt60 rim10 13 In those previous studies the value of Tmax was found to shift to higher tem peratures as the lm thickness was reduced In the Bi nano wires such a maximum does not occur until a suf ciently large magnetic eld is applied The temperature dependence of the MR effect size is shown in Fig 1b Because the resistance R0 at H 0 is weakly temperature dependent the temperature dependence of the MR is essentially that of the resistance in the eld RH also exhibiting a maximum at low temperatures In the case of 400nm wires the trans verse and longitudinal MR are about 70 and 40 at room temperature respectively increasing to about 300 and 150 at around 40 K We have further examined the resistance maximum at low temperatures Figure 2 shows the development of such a re sistance maximum in transverse and longitudinal magnetic elds for the 400nm wires To illustrate this effect more clearly the resistance has been normalized to the value at 5 K In the transverse geometry Fig 2a the maximum is RAPID COl Il IUNI PRB FINITESIZE EFFECTS IN BISMUTH NANOWIRES R14 683 45 39 39 I I I I I I I I I I I I I I I I I O 200nm J 1 0 O 40 I O 200nm O I 35 400nmJ E g D 400nm 00 E 30 i E 3 0 2pm J I 9 BE I I 25 39 E 10 20 39 I I I I I I I I I 15HH39H MINIMUM 40 20 0 20 40 10 20 30 40 50 60 H kOe H kOe FIG 3 The dependence of resistance maximum Tmax on mag netic eld for various wire diameters where solid and open sym bols stand for transverse J and longitudinal ll eld geometry respectively not appreciable until the applied eld is above 20 kOe be yond which Tmax is shifted to higher temperatures A similar trend is observed in the longitudinal geometry Fig 2b except that the threshold of the applied eld is larger about 30 kOe in order to induce a maximum The maximum in the transverse geometry always occurs at a higher temperature than that in the longitudinal case The value of Tmax also depends on the wire diameter When the same magnetic eld is applied in the same geometry the value of Tmax increases with decreasing wire diameter The dependence of Tmax on eld strength eld orientation and wire diameter is summa rized in Fig 3 In very thin Bi lms the appearance of Tmax was attrib uted to the rapid increase of mobility at low temperatures a mechanism originated from the quantum size effect13 The size quantization decreases the number of available states therefore restricts the electronphonon scattering Further more at very low temperatures there are no phonons ca pable of transferan electrons between the sizequantized subbands The suppression of electronphonon scattean ef fectively increased the mobility In the present Bi nanowires the size quantization may have come into play as the small est wire diameter is already comparable to the Fermi wave length It was estimated that for ZOOnm Bi wires the quan tum size effect should take place in Tlt30 40 K17 This effect results in the dependence of Tmax on the wire diameter The fact that no resistance maximum is observed in zero magnetic eld as in the case of thin single crystallike Bi lms10 13 is due to the polycrystalline nature of the nanow ires Application of a strong magnetic eld can introduce magnetic quantization The phonon scattean processes are also impeded in the similar fashion by magnetic quantization at low temperatures9 especially in strong magnetic elds where the energy difference in adjacent magnetically quan tized subbands becomes larger The resultant increase of mobility at low temperatures gives rise to the resistance maximum The dependence of Tmax on eld orientation is essentially a geometrical effect of the Lorentz force when the magnetic eld is applied parallel and perpendicular to the current The positive MR of Bi originates from the ordinary MR FIG 4 Representative magnetic eld dependence of a magne toresistance and b dlVIRdH for 400nm Bi nanowires with the deviation eld HD indicated effect which is the curving of the electron trajectory by a magnetic eld The characteristic quantity is war inversely proportional to the carrier density where we is the cyclotron frequency and 7 is the relaxation time9 The ordinary MR in most metals is usually very small less than a few percent owing to the very small values of war However in semi metallic Bi due to the very low carrier concentration several orders of magnitude smaller than those in most metals the characteristic term wov is much larger leading to a large positive magnetoresistance The fact that Bi is a compen sated metal also enhances the MR because the Hall eld cannot be setup to completely balance out the Lorentz force as in common metals The magnetic eld dependence of the MR is represented in Fig 4 for the 400nm wires At all temperatures the MR is nonhysteretic quadratic at low elds and becomes linear at higher elds The solution of the Boltzmann equation readily gives a H 2 dependence of MR for small elds At higher elds deviation from the H 2 dependence occurs at a certain eld value H D de ned as the deviation eld The location of H D can be demonstrated in the derivative of MR as shown in Fig 4 where the H 2 dependence of the MR at 7HDltHltHD and the H dependence at HgtHD are evi dent It is more insightful to examine the deviation from the H 2 dependence in terms of the intrinsic quantity 006739 which dictates the eld dependence of MR This term can also be expressed as uHclH where u is the carrier mobility and l is the carrier meanfree path When deviation occurs the value of H D may vary from one Bi sample to another How ever the intrinsic quantity uHD clHD is the same for all Bi samples and thus serves as a reference point to gauge the carrier mobility or meanfree path in various Bi sampleslo 20 We have determined the value of H D at different tempera tures for various nanowires as shown in Fig 5 In the 400nm wires H D is 11 kOe at 300 K and decreases to 9 kOe at 200 K and 5 kOe at 40 K The reduction of H D at lower temperature corresponds to an increasing carrier mean free path and mobility Since H D only decreases by a factor of 22 from 300 40 K the carrier mobility increases by the same factor This is consistent with the suppression of the temperature dependence of the mobility discussed earlier At the same temperature narrower wires show a larger H D or RAPID COl Il IUNICr R14 684 25Iquot39Iquotquot I I I 200nm 20 L o 400nm 39 11 lum g 15 I 211m 5 f 10 I 1 I 5 39 39 0 I I I I I I 0 100 200 300 T K FIG 5 Temperature dependence of the deviation eld HD for various wire diameters smaller meanfree path and mobility For example at 300 K H D is 20 kOe in 200nm wires 11 kOe in 400nm wires 73 kOe in 1um wires and 6 kOe in 2um wires In compari son in bulk Bi single crystals deviation from the quadratic eld dependence occurs at a very small eld of only 4 0e at 42 K relating to a very long meanfree path of about a millimeter20 In our Bi nanowires H D is several thousand Oe even at very low temperatures The large values of H D KAI LIU C L CHIEN AND P C SEARSON PRB indicate a reduction of meanfree path by over three orders of magnitude to less than 1 um on the same scale as that of the nanowire diameter As a crude estimate relating a meanfree path of 1 mm to a deviation eld of 4 0e as in bulk Bi one obtains a reduced meanfree path of 200 nm for the 200nm wires 360 nm for the 400nm wires 550 nm for the 1um wires and 670 nm for the 2um wires This estimate agrees very well with the simple argument made earlier of restrict ing the meanfree path to the nanowire diameter It gives further credence to the conclusion that the enhanced resistiv ity in Bi nanowires is indeed due to the nitesize effects In summary we have demonstrated that electrodeposited Bi nanowires provide a means for studying quasione dimensional Bi nanostructures Because of the unusual elec tronic properties of the semimetallic Bi and the nanowire geometry we have observed strong nitesize effects in the transport properties such as the resistivity enhancement the resistance maximum and the speci c eld dependence of the MR Large positive magnetoresistance 300 at low tem peratures and 70 at room temperature have also been ob served The onedimensional nanostructures of sernimetals show promise of a medium for fruitful explorations of inter esting phenomena and technological applications This work was supported by NSF Grant No DMR 9732763 1M N Baibich J M Broto A Fert F Nguyen van Dau F Petroff P Etienne G Creuzet A Friederich and J Chazeles Phys Rev Lett 61 2472 1988 2S S P Parkin R Bhadra and K P Roche Phys Rev Lett 66 2152 1991 3B Dieny V S Speriosu S Metin S S P Parkin B A Gurney P Baumgart and D R Wilhoit J Appl Phys 69 4774 1991 4A E Berkowitz J R Mitchell M J Carey A P Young S Zhang F S Spada F T Parker A Hutten and G Thomas Phys Rev Lett 68 3745 1992 5J Q Xiao J S Jiang and C L Chien Phys Rev Lett 68 3749 1992 6P Grunberg R Schreiber Y Pang M B Brodsky and H Sow ers Phys Rev Lett 57 2442 1986 7E E Fullerton M J Conover J E Mattson C H Sowers and S D Bader Appl Phys Lett 63 1699 1993 Phys Rev B 48 15 755 1993 8Kai Liu C L Chien P C Searson and Kui YuZhang Appl Phys Lett 73 1436 1998 9A B Pippard Magnetoresistance in Metals edited by A M Goldman P V E McClintock and M Springford Press Syn dicate of the University of Cambridge Cambridge 1989 pp 1507153 10N Garcia Y H Kao and M Strongin Phys Rev B 5 2029 1972 11D H Reneker Phys Rev Lett 1 440 1958 w s Boyle and G E Smith Prog Semicond 7 1 1963 12Yu F Ogrin Pis ma Zh Eksp Teor Fiz 3 114 1966 JETP Lett 3 71 1966 13Yu F Komnik E I Bukhshtab Yu V Nikitin and V V An drievskii Zh Eksp Teor Fiz 60 669 1971 Sov Phys JETP 33 364 1971 14C A Hoffmann J R Meyer F J Bartoli A Di Venere X J Yi C L Hou H C Wang J B Ketterson and G K Wong Phys Rev B 48 11 431 1993 15M Lu R J Zieve A van Hulst H M Jaeger T F Rosenbaum and S Radelaar Phys Rev B 53 1609 1996 16D A Glocker and M J Skove Phys Rev B 15 608 1977 17M Gurvitch J Low Temp Phys 38 777 1980 18T M Whitney J S Jiang P C Searson and C L Chien Sci ence 261 1316 1993 19K Liu K Nagodawithana P C Searson and C L Chien Phys Rev B 51 7381 1995 20R N Zitter Phys Rev 127 1471 1962
Are you sure you want to buy this material for
You're already Subscribed!
Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'