Dulta, P K

Kinoshila, J

Yoshihiro, K

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Indian J. Phys. 73A (5), 703-709 (1999) N O T EU P  A- an international journalComparative studies of GaA$>hetero-structure samples for quantum Hall resistance standardP K Dulta* , J Kinoshila, K Yoshihiro, A Iwasha, H Nishinaka and T EndoElectro-Technical Laboratory, Tsukuba SHI, Ibaraki-305, JapanandC K SarkarDepartment of Physics, B E College (D U.), Shibpur, Howrah-711 103, IndiaReceived 13 September 1998, accepted 7 June 1999Abstract : Comparative measurements of quantised Hall resistance (/?// /. / = 2, 4) of GaAs-hetero-structure samples grown under different conditions, have been earned out at sample temperatures of 1 5 K and 0 5 K The measurements have been done under identical conditions with both samples housed together in the same cryostat The inter companson of Hall plateaus with standard reference resistors 4 5  ^R,\2 9 initially Then further scalingdown to I indicates that the values obtained are in belter agrecinem within / ? / / 4  rather than Rff 2 aniong the samples with combined uncertainty better than 2 x 10  ^(I orcstimatc)Keywords ; Quantum Hall effect (integer), GaAs-hetcro-structurc, magnetic field Hall plateaus uncertainty and standardPACS Nos. : 73.40.Hm, 72.20 My, 06.20.FnSince, the discovery of the quantum Hall effect (QHE) in 1980 [ 1], in certain high mobility low-dim ensional sem i-conductor devices, which when placed in a large magnetic field at a very low tem perature o f 1.0 K or below, the device exhibits quantized Hall resistance Thereafter, the Comity Consultatif d ’Eleclricitd (CCE) at its meeting in September of 1988 recom m ended- ^'Present Address ; National Physical Laboratory. New Delhi-110012, IndiaE-mail: pkdutta#csnpl.ren.nic.in 1 ^©  1999 I ACS704 P K  Dutta et a lwhere, /i is a Planck’s constant, e is the electronic charge and i is an integer and R/( = 25812.807 ± 0.005 is the von Klitzing constant, an universal quantity assumed to beequal to the invariant quotient of the fundamental constant which came into effect on January 1990 [2] in order to obtain a world wide uniformity o f resistance standard. Thus, the easy availability and evaluation o f the m etrological quality of d ifferent sam ples (Si-M O SFET and G aA s-hetero-structure) became essential for belter understanding of some of the unexplained phenomenon which are not well understood even lo-dale [3~7]. H ence, the necessity o f further study to test the consistency o f experim ental values previously reported on randomly collected various GaAs>hclero-structurc samples, became necessary.The purpose of the present studies is to compare the QHR (/?//.,) of different GaAs- hetero-struclurc samples fabricated under different conditions. The QHR is measured under identical experimental conditions with two samples al a time housed together in the same sample probe independently connected to the measuring circuit at sample tem peratures of1.5 K and 0.5 K. This also evaluates critically the present GaAs-samples under experimental conditions dedicated to metrological purpose to access non-negligiblc type-B error within uncertainty better than 1.2 x 10‘*. The details of the experim ental apparatus have been briefly described and Hall Plateaus resistance has been compared with reference resistors{^R,\2 9^^ ^R,6 4 5 ^ ) 'Several GaAs-Ga^Alj.^As hetero-structure samples were attempted and compared in a cryostat where two samples can be mounted at a time in the probe arrangement. Here, the two sam ples which were obtained from ETL (Elcctro*Tcchnical Laboratory) and BIPM  (Bureau International des Poids et M easures), are correspondingly m arked as S-1 and S-2 respectively. The samples of BIPM were originally supplied by Laboratories d ’Electronique Philips (LEP), France [8] under BIPM -EUROM ET project.The sample fabricated at LEP sometimes has a protective layer and the typical sample carrier concentration (n) is = 5.1 x 10* ^  m - and the values of carrier mobility (jn) is 25 T“‘. The sample (S-2) was mounted on TO -8 header in ETL. ETL samples (S-1) was configured in its own laboratory. The samples were classical Hall bar shaped geometry, prepared by photolithographic technique. The length and width of the sample are typically 2000 micron and 400/200 micron respectively. The contact terminals were fabricated with diffused AuGcNi contacts o f good quality, ensuring access to 2DEG. These are essential for satisfactory use in precision m easurem ent of the Hall plateau [8]. The sam ples were compared with standard resistors (/?/? 12 y i i  or 2 /f/  ^  ^45Q  and 45 i i )  o f known drift over several years.The experim ental apparatus is sim ilar to the one already described [9] except the superconducting magnet which has been used, is a new magnet of 15 Tesla at 4.2 K and 17 Tesla at 2.2 K. The sample probe has been newly designed with provision to m ount two samples at a time and also to cool down to temperatures 0.5 K from 4.2 K by ^He pumping. Here, the m easurem ent has been done al sample temperatures of 1.5 K and 0.5 K and the tem peratures o f the sample were monitored by vapour pressur'*. thermometry and also withComparative studies ofCaAsdietero-structure samples etc 705a germanium thermometer. The current U sp) through the device has been fed from especially fabricated highly stable Hg battery source and the sample current was maintained at 10 pA in all cases for precision measurement purpose. The electrical leads are well screened FFEF cable with high insulation resistance to keep leakage current minimum and the sample probe and its electrical insulation had ^cen checked and the electrical leads were kept isolated from cryogenic system by mounting on kind of teflon flange to aviod any ground loop current. Besides, the system thermal noise and other system drift such as l / /  noise in the null detector have been taken care of by introducing frequent current reversal and periodic measurement of Hall voltage followed by reference resistors 9 Q or 45 ^  ^od 6 45 ^)*The detailed description of measuring circuit is given in Ref. (91 which also described the relationship in determining the unknown voltage {V x) against the output oi the potentiometer. During comparison of Hall plateaus measurement, two GaAs-samples have been mounted at a time putting one of them up-side down very close to each other. This has uniquely facilitated the comparison of Hall plateaus of two different samples in one cooling cycle at 1.5 K and also 0.5 K. The samples have been interchanged within its own top and bottom position in order to ensure there is no error due to the positioning of the samples, after every set of measurements. The Hall voltage (V,/) and the longitudinal voltage ( V^x) ^re measured and plotted by X-K recorder against the magnetic field (B /)  with ramping up and down as shown in Figure 1 for Isd  -  ^®r typical sample (S-2 ) withoutput'of nanovoltmeter Null detector (N il) . Therefore, once the exact magnetic field (B i)  o f  the Hall plateaus ( i = 2 or 4) is known, the mid-point at the minimum of longitudinal voltage (V^ xx) is identified.The comparison of Hall plateaus value (/ = 2, 4) has been done wiih reference resistor (/?/?). The comparisons of 4 with ^ 45 £} and of B ^  2 ^ R .12 9with modified direct current comparator (DCC) (Guildline Model-9930). The system was coupled to IBM PC-AT computer for data acquisition and also for processing of data. Once the measurement was initiated, initially, the minimum of longitudinal resistivity (pxx)/ = 2 or 4) of each sample was measured and the mid-point of the minimum was chosen and then the computer PC based data acquisition was carried out. The sequence of measurement has been kept in the same manner as it has been practiced in last several years in order to keep combined uncertainty within its limit. There arc in general about 40 sets of readings for each cycle of run for single sample and each set of reading consisted of 16 readings with sequential reversal of polarity of current (Iso)- measurement time was kept at about 4 -i — 5  hours for 40 sets of reading in order to attain type >4-random uncertainty better than1.5 X  10~«. Besides, the comparison of B ^  ^ 45 to B ^joo  and then sequential measurement of scaling down to 112 (B /i) using cryogenic current comparator (CCC) were carried out in subsequent steps of measurement. The details of the cryogenic current comparator (CCC) system  has been published elsewhere [10]. The sensitivity of the comparator (CCC) is 4 x 10“  ^AT/^®, where 0° is the flux quantum. The /^?.6 45 ^^.12.9 reference resistors arecard type YEW Type 2781 (Thomas type resistor) scaled in a metal can filled with silicon706 P K Dutta et alfluid and it .^ioo is a standard resistor. These are placed at a temperature regulated oil bath controlled to ± 3 mK at a nominal temperature of 20.I6°C.Figure 1. The recording of the Hall Voltage iVxy) the longitudinal voltage{Vxx) for sample S-2 as a function of magnetic field for l^p  = 10 pA. The arrows indicate the direction of the magnetic field ramping.The QHR measureinents for ^H.2 and R //,t were done in X - Y recorder as shown in Figure 1. The magnetic field were applied normal to the 2-DEG plane and the measurements were made at /so current of 10 |xA for all precision measurements purpose. The respective quantized Hall plateaus were confirmed to be flat in the level of 0.08 Cl before respective measurements of 2 and R// 4. The temperature independence of Rff,2 checked by measurements made at 1.5 K and 0.5 K of the respectivesamples. The mid-point of the Hall plateaus of the sample S-1 and S-2 are obtained at 12.0 T  and 9.65 T for i = 2 and 5.70 T and 4,60 T for i = 4 respectively at 7* s  1.5 K (Table 1). Also, some test of minimum of pxx  at lower or higher current (Iso) and sample temperature of 0.5 K and 1.5 K were done. In view of large number of readings vrhich were taken by computer PC in the mode of when theyis low enough (typically pxx  is 0.25 mQ) and then and Vg measurements were•SDComparative studies of GoAs-hetero-structure samples etc 707Table 1. Midpoints of Hall plateaus for samples.(Sample temperature 1.5 K and Sample current = 10 pA)Sample mid mid. Bz Vxx(GaAS’hetero) 0  = 4) 0  = 2) (*=4, 2)(Tesla) (Tesla) (ppm)S-l 5.70 ; 12.0 0.008S-2 4.60 9.65 0.022carried out. The superscript (-) or (+) indicate direction of the current (Iso)- The results of the final set of the readings are given belowSample AR (ppm) (/ = 2)(/?^ 2 " ^/f.i2 9)  ^^PA2 9AR (ppm) (/ = 4)^R,b  45)^  ^/?.6 45No S-l No S-2+ 11.4170 + 11.4333+ 18.1984 •I- 18.1856In case of sample no. S-l» (he resistivity p xx  is 0.008 ppm (approx) for / = 2 and / = 4 respectively while p x x  is 0.022 ppm for sample no. S-2 while the sample current is 10 and the sample temperature 1.5 K. The uncertainty budget for the 4 vs 4 (6453.2 Q), a comparison had been estimated accordingly (Table 2). By taking theTable 2. Uncertainty budget in comparison for /?//4 vs Rg (6453 2 Q)Uncertainty for the /?//4  vs R^ (6453 2 Q) compansonSource of uncertainty Uncertainty estimated1 ) Random uncertainty 12 ( X  10'^)2 ) Potentiometera) Linconty 1 3b) Resolution of current comparator 53) Fractional ampere-tum measurements 3(linearity of DVM)4) Variation of mcasunng current55) Leakage resistance 16 ) Drift of 6453.204 016RSSme;«urcd ..lues of * „  Md for cKh of d« respecii.. s«ople .oddown .he .,«»ure.nen.s in s.eps of lOO O, 10 a  1 n  (*..,) CCC ttehmque. Ihe valuesderived for x arc the following :R m C l =(1 -5.6112X i (H) for/ = 2 incase of sample no. S-l.J?, , n  =  ( 1 -  5.6275 X 10-*) for t =  2 in case of sample no. S-2,708 P K Dutta et aland R R ^ '^  = (1 -  5.6245 x 10^) for / = 4 in case of sample no. S-1,R r  \S^ = (1 -  5.6336 X 10"^) for / = 4 in case of sample no. S-2.In order to check consistency of values between y^?,6.45» ^measurements was also carried out subsequently by CCC technique and it was found to be in agreement within uncertainty of 6.75044 x 10'^ ± 0.007 x  10~  ^ (1 a  estimate). The uncertainty budget of comparison of /?/f,6 45 steps to scaling down to 1 is also estimated accordingly. Besides* it is necessary to make small correction for the drift of this 6453.2 Q and 12906.25 resistor during the time lag of QHR measurement and scale down process.In conclusion, the comparison of the sample no. S-1 and S-2 could evidently show that the samples are in excellent agreement with each other within the given relative uncertainty of < 2.0 x 10“®. This also reconfirms the previously reported [8] invariance of QHRs with different sample characteristics. The relatively better agreement of Rf^ 4 as compared to R fj 2 possibly be due to the factor that the short term drift of 9^  relatively larger compared to or effect of high Hall electric field is morepronounced [3]. It may be mentioned here that the sample no. S-2 showed somewhatunusually high deviation (as high as 0.70 ppm) during its first measurement cycle even when we noticed that V x x  was very low. In the light of recent work of Jeckelmann and Jeanneret [11], the measurement may require further careful check (e ,g , in the potential terminal contact resistance, although nothing unusual was obwserved in normal measurement of Hall plateaus) before any deilnite conclusion can be drawn. This deviation however, did not repeat in subsequent measurement sequences after thermal cycling of both the samples to room temperature, which is also reported Jeckelmann e t a l  in his extensive studies of GaAs-samples [12].A cknow ledgem entOne of the authors (PKD) would like to thank INSA-JSPS programme for providing financial grant to carry out the work at ETL, Tsukuba and is also grateful to Prof. S Kawaji of Gakushuin University, Tokyo for providing constant support during the course of this study at ETL, Japan. He is also grateful to the Director, NPL for his interest in the work. The GaAs-samples provided by Laboratories d'Electronique Philips (LEP), France through Dr. Thomas Witt of BIPM (Paris) are gratefully acknowledged.Referencesm  121 [3]K Von Klitztng, G Dorda and M Pepper Phys, Rev. Lett. 45 494 (1980)B N Taylor and T Witt Metrologia 26 47 (1989)S Kawaji, H iizuka. T Kuga and T Okamota Physica B256 56 (1998)[4] L Bliek, G Hein, D Jucknischke, V Kose, J Niemcyer, G Weimann and W Schlapp Surface Sci. 196 156 (1988)[5] S Kawaji. N Nagashima, N Kikuchi, J Wakabayashi, B W Ricketts, K Yoshohiro. J Kinoshita, K Inagaki and C Yainanouchi fEEE Trans, /nstr. Meas. lM-38 270 (1989)[6] A Hartland. K Jones. J M Wiliam, B L Gallagher and T Galloway Phys. Rev. Lett. 6 969 (1991)Comparative studies of GoAs-hetero-structure samples etc(7) K Yoshihiro, C T Van Dcgrift, M E Cage and D Yu n y s .  Rev. 845 14204 (1992)709[8] F Piquemal, C Geneves, F Delahaye, J P Andre, J N Patillon and P Fnjlink IEEE Trans. Instr. Meas. 43 2(1993)|9] J Kinoshita, N Nishinaka, K Segwa, C T Van Dcgnft and T Endo IEEE Trans. Instr. Meas. IM-40 249 (1991)110] J Kinoshita, K Inagaki, C Yamanouchi, K Yoshiliro, S Kawaji, N Nagashima, K Nohuyasu and J Wakabayashi IEEE Trans. Instr. Meas IM>38 290 (1989)[11] B Jeckelinann and B Jeanneret IEEE Trans Instr MeBs. IM-42 (1997)[12] B Jcckclraann, B Jeanneret and D Inglis Phys. Rev B$S 13124 (1997)

Comparative Studies of GaAs-hetero-structure Samples for Quantum Hall Resistance Standard

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Comparative Studies of GaAs-hetero-structure Samples for Quantum Hall Resistance Standard

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