Investigation of Parallel Conduction in

IEEEJOURNAL OF QUANTUMELECTRONICS, VOL. QE-22,NO. 9, SEPTEMBER 1986 1753 Investigation of Parallel Conduction in GaAs/AlxGal- x As Modulation-Dop...
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IEEEJOURNAL

OF QUANTUMELECTRONICS,

VOL. QE-22,NO.

9, SEPTEMBER 1986

1753

Investigation of Parallel Conduction in GaAs/AlxGal- x As Modulation-Doped Structures in the Quantum Limit P. KIRK,

AND

P. S. KOBIELA

The modulation doping technique, while instrumental in achieving high electron mobilities, is also responsible for an effect called persistentphotoconductivity(PPC) [lo]. This effect is characterized by a light-induced conductivity enhancement that persists for longtimes (in some systems, 2 lo8 s) at low temperatures. The PPC has been attributed to the excitation of electrons out of deep donorrelated traps in the AlGaAs, known as DX centers, which suppress recapture due to large lattice relaxation [ 111. In I. INTRODUCTION the GaAs/Al,Ga, -,As system, these excited electrons are UANTIZEDHallresistanceandthesimultaneous able to maintain quasi-equilibrium with the 2DEG layer zerodiagonalresistancestateoftwo-dimensional in the GaAs [ 121, forming a parallel conduction path in carriers is now a well-documented phenomenon in a numthe Al,Gal -,As. ber of systems [1]-[3]. This phenomenon, occurring at ThePPC in GaAs/AlxGal- x As modulation-doped low temperature and.high magnetic field,is characterized structures has been utilized by a number of authors [3], by the experimental fact of the Hall resistance pxy becom[ 131-[ 151 to modulate the carrier density when studying ing quantized in units of h/ie2 where h is Planck’s conquantum transport. Although PPC has been studied in the stant and e is the electronic charge. When pxy takes on GaAs/Al,GaI -,As system by a number of workers [ 161quantized values of h / e 2 , the diagonal resistivity pxr ap[18] none of these studies has explored the effects of PPC 0. The quantum number i proaches zero in the limit T on the behavior of the 2DEG in the quantum limit. Here is anintegerfor integral quantization,whichcanbe we present a detailed study of PPC effects on the quantum understood within the framework of an independent partransport coefficients in high-mobility a GaAs/ ticle picture [4], [5]. The quantum number can also take Al, Gal - x As modulation-doped structure. The measureon fractional values [6], [7], which is believed to arise ments are compared to low field values of the transport fromthecondensationof the 2D carriers into a highly coefficients to derive information concerning density, mocorrelated fluid-like ground state [SI. bility, and the distribution of carriers in the 2DEG and Since the first observation of the integral quantum Hall parallel conduction path. effect in the two-dimensional electron gas (2DEG) of a

Abstract-We present a detailed study of the transport in GaAsi Al,Ga, -,As modulation-doped structures in the low field and high magnetic field quantum limit for varying amounts of parallel conduction in the AlGaAs region. We observe the apparent breakdown of quantum Hall effect behavior due to low mobility carriers in the parallel channel. The onset of conduction through the parallel channel by quantum transport measnrments has been observed, along with a nonlinear dose dependence due to photoexcitation.

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[ 11, thephenomenon has Si-MOSFETinversionlayer been studied in numerous embodiments of 2D carrier systems. The systems that have attracted the most attention arethecompoundheterojunctionepilayerstructures, in particular the GaAs/AlxGal -,As systems [2], due to the lattice match of the constituents. The perfection of these heterojunction systemshasallowedtheachievementof extremely high carrier mobilities by the modulation doping technique [9]. The quantum Hall effect has been seen in numerous 111-V compound systems and recently in a 11-VI system [ 3 ] . Manuscript received December 1, 1985; revised March 10, 1986. M . A. Reed is with the Central Research Laboratories, Texas Instruments, Inc., Dallas, TX 75265. W. P. Kirk and P. S . Kobiela are with the Department of Physics, Texas A&M University, College Station, TX 77843. IEEE Log Number 8609339.

11. THEORY Let us first consider single carrier conduction for two parallel media in the absence of any quantum transport phenomena.Let us also define the media by theindex i( = 1, 2). Under theinfluence of a mutually perpendicular electric field E and magnetic field B , we can express the conductivity tensor for media i as

where ni is the carrier density, e is the electronic charge, mT is the effective mass, w,, is the cyclotron frequency,

0018-9197/86/0900-1753$01.00 O 1986 IEEE

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and ri is the scattering time. For simplicity, we consider a single relaxation time ri for the carriers in media i . Now, the toal conductivity of the two-component system can be expressed as a sum of the individual conductivity tensors:

+

r2

NO. OF QE-22, ELECTRONICS, QUANTUM VOL.

Here, the low-mobility region dominates the resistivity, whereastheHallresistanceissimply the sheetcarrier density. Let us now consider transportin this systemin the

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The measured quantities ofinterest are usually the comTo understandtheobservation of the ponents of the resistivity tensor. These quantities are the quantumlimit. quantum Hall effect in the 2DEG, let us initially set n2 = Hall resistivity p and the magnetoresistance pxx.We can ? 0. In a 2DEG that is void of any imperfections, it can be find these quantities by inverting (2), whereupon

and

To specialize, let us define media 1 as the 2DEG at the GaAs/Al, Gal - x As heterojunction interface, and media 2 as the Al, Gal -,As. For this situation, we shall assume that the mobility of the carriers in the 2DEG, y l , is much greater than the mobility in the parallel conduction path,

shown (by going to the frame of reference cE X BIB2) that ox, = nec/B, which does not exhibit a quantized density. To explain the experimentalobservationsofthe quantum Hall effect requires the existence of localized states in the tailsof each Landau level subband. When the cc2. It is convenient to define the low magnetic field and Fermi level resides in these localized states, which cannot carry any current at T = 0, the remaining extended states high magnetic field limits of these general expressions. of the filled Landau levels automatically adjust to carry At low magnetic field (wcl r 1 and wc2r2 > which is the quantized resistance in units of 25, 813 0. l ) , we have The experimental result is a step structure in the Hall ren1 n2 sistance versus magnetic field or carrierdensity, normally controlled by a gate voltage. An alternative to gate modulation of carrier density is to photoexcite carriers intothe 2DEG from traps. The concurrent effect of this modulaand tion technique is the subject of the present investigation. Let us now consider the presence of a media (Al,Gal -.As) parallel to the 2DEG. Prior to any pho-

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duced strain. Low field values of the mobility and carrier density were measured at T = 1 K, and were found to be p = 10m2/V s and n = 2.8 X lOI5 mP2, respectively. The quantum transport measurements were taken between 20 mK and 7.0 K in a dilution refrigerator using a 7.8 T superconducting solenoid to apply magnetic fields perpendicular to the sample. Temperature measurements weremadeusinga3Hemeltingcurvethermometer. Transport measurements were made by pulsing a dc current source and averaging voltages for positive and negative current polarities to eliminate thermal EMF problems. Excitation current amplitudes ranged from10 nA to 5 pA. The pulse sequence consisted of a 650 ms positive pulse, a 5 ms off period, a 650 ms negative pulse, and a 500 ms settlingperiod.Dependingon .the temperature range, the sequence period ranged from5 to 30 s to avoid any Joule heating of the charge carriers. Light excitation was made by direct illumination from a GaAsP/GaAs red LED. Light dose was controlled by varying the time the LED was activated by a constant (20 mA) current. Dose quantities reported in this paper refer to the calculated number of photons arriving at the sample. For our particular experimental configuration, there wereapproximately 7.8 X 10” photons/s striking the B sample surface. The photon dose wasvaried up to an empirically saturated dose value. No attempt has been made to correct for possible reflection of photons at the sample surface nor for absorption in the sample; thus, absolute where the integer i again takes on the appropriate quanintensity figures mustbeviewedcautiously.However, tized values. These values of the Hall resistivity will derelative dose values reported here were easy to control viate (specificially, decrease) from thewell-defined quanand are thus highly precise. tized values upontheonset of parallel conduction. IV. RESULTS A N D DISCUSSION Similarly, we can see from(7) that the diagonalresistivity will remain vanishingly small in the quantum limit until QuantumHallresistanceplateauscorresponding to carriers populate the parallel conduction band. Thiseffect Landau level filling factors down to i = 2 have been obhas important consequences in the use of quantum Hall 1 showstheHall resisserved in thesestructures.Fig. effect as a resistance standard or as a method for deter- tance pxy and the diagonal magnetoresistance p.rx at T = mining the fine structure constant. A high precision mea- 75 mK for a sample cooled under dark conditions and besurement of p,, simultaneous with the “standard” pxy val- fore anyphotoexcitation by theLEDsource.The Hall ues puts a limit on the number of carriers in the parallel plateausagreewiththetheoreticalquantized values to conduction path, and thus a limit on the deviation of p x y within the resolution (dynamic range) limitations of from the standard values. i = 4plateau, we theapparatus;specifically,forthe Q,whereas p,(theohave p,,(experimental) = 645312 111. EXPERIMENTALPROCEDURES magnetoreretical) = 6453 Q. The minima in the Thesamples studied weremodulation-dopedGaAs/ sistance could be resolved to within k0.05 Q for p,, valAlo,3Gao,7As heterostructures grown in a Riber 2300 MBE ues less than 1 Q . on a Cr-doped GaAs substrate. The epitaxial layers conFig. 2 shows ,oxy as a function of magnetic field as the sisted of a 1 pm nominally undoped GaAs buffer layer photoexcitation dose is varied, and Fig. 3 shows p,, as a followedbya150 Alo,3Gao,7Asspacerlayer and 500 function of magnetic field for the samephoton doses used of Si-doped Alo,3Gao.7As. The samples were thenfab- in Fig. 2. The measurements were taken sufficiently long ricated into Hall bridges using standard photolithographic after excitation and at approximately the same time after techniques.Theminimumchannelwidthused in these photoexcitation to eliminate possible transient and nonexstudies was 150 pm to exclude any localizationeffects due ponential decay effects of the PPC [ 101. The photon doses to short channel effects [20]. The samples were mounted ranged from a minimum of 3.9 X lo9 photons to 2.5 x onto ceramic flatpacks for lead strain relief. l O I 3 photons. There was no temperature cycling or temThe samples were cooled slowly ( - 30 h) from room perature variation between the sets of measurements. We temperature to low temperature in a light-tight container clearly observe the systematic shift of the quantum Hall to eliminate residual PPC and to minimize thermally inplateaus (and the accompanying magnetoresistance min-

toexcitation, we shall assume that the Al,Gal -,As is depleted, although it contains deep level complexes known as DX centers [ 111. Electrons photoexcited from the DX centers remain in the Al, Ga, -,As conduction band for a long time because their recapture by theionized donors is impeded by a microscopic potential barrier. These free electrons transfer to the 2DEG channel (either by tunneling throughtheinterfacebarrier or through the ohmic contacts) and thus add to the 2DEG density [ 161-[18]. However,asthenumber of photoexcitedcarriers increases, the effective doping concentration increases [ 161. As a consequence, the depletion widthsat the surface and at the heterojunction interface, which are inversely proportional to the effective doping concentration, become smaller upon photoexcitation. Preliminary investigations of this effect have been reported [16], [ 191. However, the transition from a depleted to a conducting barrier region has not been investigated in detail. To consider the case of parallel conduction through this barrier region, we will assume that media 2 cannot support a2DEG.Substituting (9) into (8) forthecase of mixed condunction, we have for theHall resistivity in the high field and quantum limit

A

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JOURNAL IEEE

OF ELECTRONICS, QUANTUM

VOL. NO. QE-22,

9, SEPTEMBER 1986

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no light

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Fig. 2. Hall resistance versus magnetic field at T = 75 mK for the sample described in Fig. I after varying amounts of (cumulative) photon dose. The photondosesare: (a) 0, (b) 3.9 X IO9, (c) 7.8 X IO9, (d) 1.2 X IO'', (e) 1.6 x IO", ( f ) 3.1 x IO1', (g) 3.9 x IO", (h) 7.8 x IO", (i) 1.6 X I O i 2 , (k) 3.1 X IO", ( I ) 6.2 X lo",(m) 1.3 X lo", (n) 2.5 X lot3.

ima) toward higher magnetic field as the density of carriers in the 2DEG increases. We observe the full development of some less-developed plateaus that were weak (i = 5 ) or nonexistent (i = 7) at lower magnetic fields. The effect is more apparent for the odd-integer plateaus

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since the spin energy is smaller than the Landau energy at these field values. Upon reaching a critical photon dose ( > 7 . 8 X lo"), quantumtransportapparently breaks down, and the plateaus deviate from the expected values. At the same time, the magnetoresistance minima rise significantly above zero. The density of carriers as a function of light dose was determined in two ways: by the high field values of the (n = B/ep,), either by extrapolating Hallresistance through the apparent Hall plateau centers or choosing the value at a single plateau center, and by the periodicity of the Shubnikov-deHaas (SdH) oscillations in pxx [i.e., n = 2e/hA(l/B)]. This is shown in Fig. 4(a). The departure of these two methods of determining the carrier density becomes apparent at a dose of 1.6 x lo", which is the samedoseatwhichthequantumtransportclearlydeviates. Referring to (S), we see that the high field Hall resistance method gives the combined carrier density in both the 2DEG and the Al,Gal - x A s , whereas the oscillations in pxx are essentially measuring the 2DEG carrier density. If true, the carrier density determined from the low field Hall resistance values as predicted from (6) should agree

REED et al.: PARALLELCONDUCTIONINMODULATION-DOPEDSTRUCTURES 19.0 -

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well with the method using the SdH oscillations in ,ox,. The comparison in Fig. 4(b) shows excellent agreement. It should be noted that magnetic freeze-out effects [21], 6 T , are not evident since both which would occur at the low andthe high field densities are the same [Fig. 4(a) versus Fig. 4(b)] until the onset of parallel conduction. Once we have determined the electron distribution in the two regions, we can also determine the mobility of the electrons in the Al,Gal -,As. Choosing a photon dose of wehave nl (2DEG) = 5.5 X l O I 5 m-2and 2.5 X n2 (Al,Gal-,As) = 7.5 X IOl5 mP2. Using (7) in the quantum limit, we get p 2 = 0.19 m2/V s. It should be noted that the condition w , ~>> 1 is not yet completely satisfied in the Al,Gal -,As since the magnetoresistance background is stillincreasing, so the mobility may be slightly higher than this value. A sensitive test to determine when conduction starts in the Al, Gal -,As region is to observe the deviations of the pxy values from the quantized values, as predicted by (8). Fig. 5(a) shows the values of the i = 4 plateau as a function of photon dose. The onset of parallel conduction is > 7.8 X 10". We can define the again clear for a dose limits of conduction in the Al,Gal -,As by observing the minima in pxx, as shown in Fig. 5(b). Using the value for the mobility in the Al,Gal -,As derived above and our resolution limit of 0.05 Q,the carrier concentration in the Al,Gal -,As region for photon doses up to 7.8 X 10" is found from (7) to be < 4 X 10" mW2.Bridge techniques used by other workers [22] have measured minimum resistances in these regions to be < lop7Q. From this, it is possible to put an upper limit on the number of carriers

number of photons x 10"

Fig. 5. (a) Hall resistance versus photon dose taken at the i = 4 plateau. The inset shows an expanded scale between 0 and 2 X IO" photons. (b) Magnetoresistance versus photon dose taken at the i = 4 minima. The insets shows an expanded scale between 0 and 2 -X 10" photons.

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( < 1 X lo5 mP2) in the Al,Gal -,As region if no deviation is observed (in fact, structure at the edges of theHall plateaus seen in [22], especially pronounced at high photon doses in our present work, could be due to parallel conduction). Using (lo), this would imply a deviation of 1 part in 2 X lo9 on the quantized Hall resistance values due to parallel conduction. An area that deserves further attention in this study is the nonlinear photon dose versus 2DEG carrier density behavior that can be seen in Fig. 2. This is replotted and shown in further detail in Fig. 6. The sharp transition at a dose of 1.6 X lO"\does not appear to have any effect, other than on the carrier density, on the quantum transport coefficients. We can rule out conduction through the next higher conduction subband because of the well-behaved oscillations in ,ox,. We as yet do not have an explanation of for this photoexcitation phenomenon.Thedynamics

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this process clearly deviates from present understandings [3], [ 2 3 ] of the detailed photoexcitation mechanisms, imHowplying a morecomplicatedrateequationmodel. ever, the microscopic model interpretation of DX centers as the responsible traps [ l l ] in the Al,Ga, -,rAs is still consistent with our results. V. SUMMARY We have done a systematic study of the low field and quantumtransport coefficients in a GaAs/Al,Gal -,As modulation-doped heterostmcture. We find that the onset of conduction through a parallel path in the Al, Gal -,As isreadilyobservableviaquantumtransportmeasureallow us todeterminethe ments.Thesemeasurements distribution of carriers in the 2DEG and in a parallel path. We can also use the measurements to put limits on the perturbation of the quantized resistance values due to a parallel conduction path.

ACKNOWLEDGMENT We are indebted to H. D. Shih for growth of the MBE sample, to R . T. Bate, W. R. Frensley, and P. A. Penz for helpful discussions, and toJ . Williams for sample fabrication. REFERENCES [ I ] K. von Klitzing, G. Dorda, and M. Pepper, “New method for highaccuracy determination of the fine-structure constant based on quantized Hall resistance,” Phys. Rev. Lert., vol. 45, pp. 494-497, 1980. [2] D. C. Tsui and A. C. Gossard, “Resistance standard using quantization of the Hall resistanceof GaAs-AI., Ga, ,As heterostructures,” Appl. Phys. Lett., vol. 38, pp. 550-552, 1981. 131 In addition to n-channel Si-MOSFET inversion layers [ l ] and elecheterostructures [2], the integral quantum trons in GaAsiAl., Ga, Hall effect has been observed inelectrons in InGaAsiInP (Y. Guldner, J.P.Hirtz,A. Briggs,J. P. Vieren, M . Voos,andM.Razeghi, “QuantumHalleffectandhoppingconduction in In.,Ga,_,As-InP heterojunctions at low temperature,” Surface Sci., vol. 142, pp. 179181, 1984); electrons in InAsiGaSb (E. E. Mendez, L. L. Chang, C. A. Chang, L. F. Alexander, and L. Esaki, “Quantized Hall effect in single quantum wells of InAs,” Surface Sci., vol. 142, pp. 215-219, 1984); holes in GaAsiAl,Ga, _,As (H. L. Stormer, Z . Schlesinger, A. Chang, D. C. Tsui, A. C. Gossard, and W. Wiegmann, “Energy structure and quantized Hall effect of two-dimensional holes,” Phys. Rev. Left., vol. 51, pp. 126-129, 1983); an electron-hole gas in InAsi GaSb (E. E. Mendez, L. Esaki,and L. L. Chang, “Quantum Hall effect in a two-dimensional electron-hole gas,” Phys. Rev. Lett., vol. 55, pp.2216-2219,1985);andthe n-channelinversion layerof Hg,Cd, -,Te (W. P. Kirk, P. S. Kobiela, R. A. Scheibel, and M. A. Reed, “Investigation of the 2-dimensional electron gas in HgCdTeby J. Vac. Sci. Technol., JulyiAug. quantumHallmeasurements,” 1986). [4] R. E. Prange, “Quantized Hall resistance and the measurement of the fine-structure constant,” Phys. Rev., vol. 23B, pp. 4802-4805, 1981. [5] R. B. Laughlin, “Quantized Hall conductivity in two dimensions,” Phys. Rev., vol. 23B, pp. 5632-5633, 1981. [6] D. C . Tsui,H.L.Stormer,andA.C.Gossard,“Two-dimensional magnetotransport in the extreme quantum limit,” Phys. Rev. Lett., vol. 48, pp. 1559-1561, 1982. [7] V. M. Pudalov and S. G. Semenchinskii, “Fractional quantization of theHallresistivity in siliconmetal-insulator-semiconductorstructures,” Pis’ma Zh. Eksp. Teor. Fiz., vol.39,p.143,1984 (JETP Lett., vol. 39, pp. 170-172, 1984). [SI R. B. Laughlin, “Anomalous quantum Hall effect: An incompressible quantum fluid with fractionally charged excitations,” Phys. Rev. Letr., vol. 50, pp.1395-1398,1983. [9] R. Dingle, H. L. Stormer, A. C. Gossard and W. Weigmann, “Elec~

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tron mobility in modulation-doped semiconductor heterojunction superlattices,” Appl. Phys. Lert., vol. 33, pp. 665-667, 1978. [lo] An excellent review of the subject can be found in M. K. Sheinkman and Y . Ya. Shik, “Persistent photoconductivity in semiconductors,” Fiz. Tekh. Poluprovodn.. vol. 10, pp.209-233,1976 (Sov. Phys. Semicond., vol. 10, pp. 128-143, 1976). 1111 D. V. LandandR. A. Logan, “‘Large lattice relaxation model for Phys. presistentphotoconductivity in compoundsemiconductors,“ Rev. Letr., vol. 39, pp. 635-639, 1977. [12] F. Stem, “Charge transfer in photoexcited Al,Ga, -,As/GaAs heterojunctions,” in Proc. MSS-II, Kyoto, Japan, 1985, to be published. [I31 H. P. Wei, D. C. Tsui, and M.Razeghi,“Persistentphotoconductivity and the quantized Hall effect i n Ino,s,Gao,,7As/InP heterostructures,” Appl. Phys. Lett., vol. 45, pp. 666-668, 1984. photoconduc(141 M. J. Chou, D. C. Tsui, and G. Weimann, “Negative tivity of two-dimensional holes in GaAs/AlGaAs heterojunctions,” Appl. Phys. Left., vol. 47, pp. 609-611. 1985. 1151 R. G. Clark, R. J. Nicholas, A. Usher, C. T. Foxon, and J. J . Harris, “Odd and even fractionally quantized statesin GaAs-GaAIAs heterojunctions,” unpublished. 1161 E. F. Schubert, K. Ploog, H. Dambkes, and K. Heime, “Selectively doped n-A!,Ga, -.As/GaAs heterostructures with high-mobility twodimensionalelectrongas for fieldeffect transistors,” Appl. Phys., V O ~ .33A, pp. 63-76, 1984. [17] H. L. Stormer, A. C. Gossard, W. Wiegmann, and K. Baldwin, “Dependence of electron mobility in modulation-doped GaAs-(AIGa)As heterojunctions: Influence of electron density and A1 concentration,” Appl. Phys. Lefr., vol. 39, pp. 912-914, 1981. [18] A. Katalsky and J. C. M. Hwang, “Illumination stimulated persistent channel depletion at selectively doped AI, ,Ga,,As interface,” Appl. Phys. Lett., vol. 44, pp. 333-335, 1984. [I91 S . Luryi and A. Kastalsky, “Anomolous photomagnetoresistance in modulation-doped AIGaAs/GaAs heterostructures,” Appl. Phys. Lerr., vol. 45, pp. 164-167, 1984. [20]H. 2. Zheng, K. K. Choi,D. C.Tsui, and G. Weimann,“Observation of size effect in the quantum Hall regime,” Phys. Rev. Lett., vol. 55, pp. 1144-1 147, 1985. 1211 E. H. Putley, “Freeze-out effects, hot electron effects, andsubmillimeterphotoconductivityinInSb,” in SemiconductorsandSemimetals, Vol. I : Physics of I l l - V Compounds, R. K . Willardson and A.C.Beer,Eds. NewYork:Academic,1966,pp.289-313. 1221 D. C . Tsui,A.C.Gossard, B. F. Field,M.E.Cage, andR. F. Dziuba. “Determination of the fine-structure constant using GaAsAlGaAs heterostructures,” Phys. REV. Left.,vol. 48, pp. 3-6, 1982. of conductancenear 1231 H.J. Queisser,“Nonexponentialrelaxation semiconductor interfaces,” Phys. Rev. Lett., vol. 54, pp. 234-236, 1985.

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W. P. Kirk was born in Joplin, MO, in 1942. He received the B.A. degree in physics from WashingtonUniversity,St.Louis, MO, in1964, and the M.A. and Ph.D. degrees in physics from the State University of New York at Stony Brook in 1967 and 1970, respectively. From 1970 to 1975 he held Postdoctoral Fellow and Assistant Professor positions at the University of Florida, Gainesville. In 1975 he joined the Physics Faculty of Texas A&M University, College Station, as an Assistant Professor and became an Associate Professor in 1978. Since 1983 he has been a Professor of Physics. He has been Director of the Campus Helium Liquefaction Facility since 1976. Dr. Kirk’s research interests in experimental low-temperature physics include the quantum Hall effect, transport properties of metals and semiconductors, macroscopic quantum effects, and many-body effects. In support of this work Dr. Kirk has developed extensive low-temperature, high-magnetic-field laboratories where transport studies down to 0.0003 K have been made and measurements in applied fields up to 14 T can be made at very low temperatures. He has authored approximately 80 journal articles and conference papers and one book chapter. He has received a Brookhaven National Laboratory Summer Fellowship (1967) and an NSF Postdoctoral Fellowship (1970-1972). He was a Visiting Scientist at M.I.T. Cambridge, during the Summer of 1973. Dr. Kirk is a member of the American Physical Society, the American

1759 Association for the Advancement of Science, Sigma XI, the Texas Academy of Science, the American Vacuum Society, and the Materials Research Society. He is listed in Who’s Who in American Men and Women ofscience and Who’s Who in Technology Today.

P. S. Kobiela wasborn in Krakow, Poland, in 1951. He received theM.S. degree in physics from the Jagiellonian University in 1974. From 1974 to 1981 he was a member of the Low Temperature Laboratory at the Institute of Nuclear Physics, Krakow. Since 1971 he has undertakengraduatestudiesinphysicsatTexas A&M University, College Station, where he currently holds a Research Associate position. His special fields of interest include plastic and liquid crystals,transportinsemiconductors,lowtemperature calorimetry, the absolute low-temperature scale, and applications of cryogenics in medical and veterinary sciences. He holds two patents for cryogenic devices and is co-author of 17 journals and conference reports. Mr. Kobiela is a member of the American Physical Society.

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