s.y. mensah, f.k.a. allotey and n.g. mensah- nonlinear acoustoelectric effect in semiconductor...

8/3/2019 S.Y. Mensah, F.K.A. Allotey and N.G. Mensah- Nonlinear Acoustoelectric Effect in Semiconductor Superlattice

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Available at: littp://www .ietp.trieste.it/~pub-off IC /9 9 /1 4 8

United _\a.t;ions Educational Scientific a,nrl Cultural Organizationan d

International Atomic Energy AgencyTHE ABDUS SALAM INTERNATIONAL C ENT RE FOR THEOR ETICA L PHYSICS

NO NL I NE AR ACO US T O E L E CT RI C E F F E CTI N S E M I CO N DUCT O R S UP E RL AT T ICE

S.Y. Mensah 1Department of Physics. L aser and Fibre Optics Centre. University of Cape Coast,

Cape Coast, Ghanaan d

The Abdu s Salam International Centre for Th eoretical Physics, Trieste, Italy,F.K.A. AUotey

National C entre for Mathematical Sciences, Charm Atomic Energy Comm ission,Kwabe.nya, Accra, Ghana

an dThe Abdus Salam International Centre for Theoretical Physics Trieste, Italy

andN.G. MensahDepartment of Mathematics, University of Gape Coast, Cape Coast, Ghana.

M IRAM ARE - TRIE STEOctober 1999

'Regular Associate of tlie Abtlus Stilani ICTP.


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AbstractAcoustoelectric effect in semiconductor superlatt.ice(SL) has been studied for a hypersound

in llio region ql 3? 1. A nonlinear dependence of the acoustoclociric current j" 'l: on the constantelectric field E is observed. It is note d th at wh en the electric field is neg ative the cu rren t j a crises, reaches a peak and fails off. On th e other h an d, w hen the electric field is positiv e th ecuiTcni decreas es, reaches a peak and ihen rises. A similar observ ation h as been noted for anacoustoelectric interaction in a multilayered structure resulting from the analysis of the Si/SiO^stru ctu re. The do min ant m echanism for such a. behaviour is att rib ute d to the periodicity of theenergy sp ectru m along ih e ST. axis.


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1 IntroductionElectron transport insemiconductor superlat tice(SL) or milltiquantum well structure is usuallygoverned by drift, diffusive and tunneling current flow. A ballistic carrier motion can also beobserved, provided that the size of the system is smaller than the mean-free path, ranging uplo some hundred microns in some pu re materia l. Con cep tually different from those mech anismsare transport phenomena based on energy and momentum transfer from externally propagatingentities to the electron m edium . Such "dragging" experim ents have been stud ied in great detail indouble electron layer systems [1] where internal "Coulomb friction" between the two layers causesthe dragging force, "Ph oton drag" induced trans po rt was observed for inter sub ban d tra nsitio nsof a quasi-two-dimensional electron system (2DE S) [2], In[3] Nagamune et al. observed the effectof a. dc current on the drift of optically generated carriers in a quantum well. Another interestingmechanism based on the transfer of energy and momentum is the interaction of acoustic phononswith carrier charges in semiconductor materials. This mechanism occurs not only during thescattering of quasi-momentum carriers with lat t ice vibrat ions but also when acoustic wavesprop agate th rou gh th e mate rial. Am ong the effects observed are the absorp tion (amplification)of acoustic waves [4-7], aeonstoelectrie effect(AE) [8-13], a.constomagnetoelectric effect(AME)[14-18], aeoustothermal effect [19] and acoustomagnetothermal effect [19],

These phenomena have, however, received very little attention inSL even though they haveimm ense device applica tions. The intera ction between surface acoustic; wave(SAW) and m o-bile charges insemiconductor layered structures has become an important method to study thedynamic conductivi ty of low-dimensional systems inquantum wells. These studies include thequantum Hall effect [20], the fractional qu an t urn H all effect [21]. Ferm i surfaces of compositeFermions around a half-filled La nd au level [22], and c om m ensu rability effects caused by the lat-eral superlattiee induced by SAW [23]. It has also been noted that the transverse acoustoelectricvoltage(TAV) is sensitive to the mobility and to the carrier concentration inthe semiconductor,thus it has been used toprovide a characterization of electric prop erties of semico nductors [24].Interface st ate d ensity [25], jun ctio n depth[2tl], and carrier mobility [27] have been measuredwith this method. Recently TAV has been proposed as aneffective tool in the measurement ofmicrostructures and superlattiee parameters [28-31].

In this paper we shall endeavor to extend [32] to cover the nonlinear relation of the acous-toelectric current with the constant electric held. Acoustoelectric effect is the transfer of mo-mentum from the acoustic waves to the conduction electrons as a result ofwhich may give riseto a. current usually called the acoustoelectric current j'"'- or in the case of an open circuit, aconstant electric field Eac.

The study of this effect is vital because of the complimentary role it may play in the un-ders tanding of the propert ies of the SL which we believe should find an important place in th eacoustoelectronic devices. Experimental evidence of the dependence of the acoustoelectric effect

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on the parameters of SL has been reported in [33], In [31] experimental work on the acousto-electric interaction of SAW in GaAs inGaAs superlattice has been reported. A theoreticalmodel for measuring TAV in mullilayered structure resulting from the analysis of ihc Si/S1O2has also been reported in [34]. In that work analytical results were compared with experiments.

In this work, it will be shown that the presence of the minibands in the SL will result in a,nonlinear dependence of the j a c and the ratio ^- (where P is the absorption coefficient) on thewave number q. Also, in the presence of an applied constant electric field E a threshold valueEo is obtained where the acoustoelectric current changes sign. Finally it will be noted that theacoustoeleetric current rises and reaches a peak then drops in a manner similar to the negativedifferential conductivity observed in SL in the presence of constant electric field.

This paper is organised as follows. Tn section 2 we outline the theory and conditions necessaryto solve the problem. In section 3 we discuss the results and finally in section 4 we draw someconclusions.

2 Theory

Proceeding as in [32] we calculate the acoustoeleetric current in SL, The acoustic wave willbe considered as a hypersound in the region ql 3> 1 (if is the electron mean free path, q isthe acoustic wave number) and then treated as a packet of coherent phonons(monochrornat.icphomms) having a 5 function distribution

^ 0 8 ( k - q ) h = l (1)

where k is the phonon wavevector, Ti is Planck's constant divided by 2TT.


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of the fact that

GP',P Gp, p ( - 0we t:a,n express eqn(3) in the form

r = -. \ 2 [ fG(p,,i)\2[f(ep+q-f(ep)]9) -

where the vector ^;(p). as indicated in [35], is the mean free path l.-i(p).Thus the acoustoelectric current in eqn(5) in the direction of SL axis becomes

\G(p..q)\2[f(eplll)-f(eI>)}-lz(p)]Hr-p-


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f(p) = / -cxp(-t/r)Mp - cEt), (11)Jt i THere

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whererc- s the electron density, T is the tempera ture inenergy units and /n(x) is the modifiedBessel function.

Th e key physical para me ter describing ihe eleclron distribu tion in ihe bands is the dispersionrelation, for superlattkes the dispersion law isgiven by

In cqn(13). p i and p z are the transverse and longitud inal (relative to the superlattiee axis)components of the quasi momentum, respectively. A,, is the half width of th e i/1'1 allowed mini-band ,

are the size-quanti/ed levels in an isolated conduction film, d = d0 +


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(17)

where 0 is ihe Hoavisidc slep function, b =3 R e s u l t s an d d i s c u s s i o nWe shall solve cqn(17) for two par ticula r cases, (i) In the absence of the applied con stant field(E=0), from eqn(17) we obtain

It can be observed from eqn(18) that, when uq 3> 2As in(r/ri/2). j'*c = 0 i.e. there ap pears a,iransparency window. This is a. consequence of ihe conservation law. Under this condition thereis no absorption of acoustic waves hence no acoustoelcctric current [36], The SL can thereforebe used as an acou stic wave filter. It is also observed tha t the dependence of flc on q is stronglynon-linear. The ratio fS where T~ is calculated under the same conditions as in [36], is givenby

= _ 2 cT J

Hence, we observe th at jz/T r, depends on the wave number q, i.e. it has a spatial dispersion.This behaviour is unlike the homogeneous semiconductor (bulk material) which is independentof q.

It is worth noting tha t, at A 3> T. when the SL is behaving as a homogeneous semiconductor,jz/V ~ as given in eqn(19) satisfies the Weinrekh relation

As stated in [35] the change in sign of the acoustoelectric current can be attributed to the factthat the main contribution of the acoustoelcctric current at qd c 2TT is from electrons near thetop of the miiiiband, i.e. by electrons with a negative mass.

(ii) In a weak constant electric field, e.Edr


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From eqn(21) it is observed that at

the acoustoelectric current, changes sign. The value Ey t:a,n be interpreted as a. threshold field.E(] is a function of the SL parameters d and A, and temperature T, frequency tufl and thewavenumber q. For example, at A/T 2Asin(gd/2),i.e. j " c = 0. We attributed the cause to the presence of the conservation laws and suggested theuse of SL a,s a phonon filter. Finally, we noted that there exists a threshold field i'u for whichthe aeoustoelectric current changes sign and that this value increases with a decrease in A andincreases with an increase in toq.


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AcknowledgementsThis work was done within the framework of the Associatcship Scheme of the Abdus Salani

International Centre for Theoretical Physics. Trieste. Italy. Financial support from the SwedishTnlemaiional Development Cooperation Agency is acknowledged.

References

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[25] Davari B, Das P and Bharat R 1983 J. Appl. Plrya. 54 415[26] Davari 13 an d Da.s P 1982 Proc.lEEE Ultramm. Syinp. 479[27] Bcrs A, Cafarclla J H and Burke B E 1973 Appl. Phys. Lett. 22 399[28] Tabib-Azar M and Das P 1987 Appl. Phys. Lett. 5 43fi[29] Palma F and Da,s P 1986 Proc. IEEE Ultraxtm. Symp. 45 7[30] Das P, Tabib-Azar and Evcrson J H 1985 Appl. Surf. Sci. 2 2 / 2 3 7 3 7[31] Vyim V A, Kanter Yu O, Kikkarin S M. Pnev V V, Fedorov A A and Yakovkin I B 1991Solid State Communications 78 823[32] Me nsali S Y. A llotey F K A and Adjep ong S K 1994 J. Coiidcns. Matter 6 6783[:i;j] Vyiin V A, Kanter Yu O, Kikkarin S M, Pne v V V, Fadorov A A and Y akovkin 1988Academy of Science USSR 1 Hli All union Conference on Physics of Semiconduclors(Kishinev,1988) Vol3 (Kishinev Academy) p!18[34] Palma F 1989 J. Appl. Phys. 66 292[35] Kry chk ov S V and M ikheev \ P 1982 Fiz. Tekh. Poluprov. 16 109

Sliiiiclcv G M, Meiisah S Y and Tsurkau G I 1988 J. Condcns, Matter 21 L1073

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" (

Fig. 1. Dependence of J^/J? on ^ A = O.leV; A = 0.09 eV;_ _ A = 0.07eV; A = 0.05eV

II


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-3 -2.S - 2 "1.5 "I -0 .5 (1 0.5 1 1.5 2.5

Fig. 2. Dependence of J^/Ju) , = 7 . 8 x on

eEdr wq = 1.2 xWq = 3.8 x

tu, = 7.9 x

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s.y. mensah, f.k.a. allotey and n.g. mensah- nonlinear acoustoelectric effect in semiconductor...

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