Zadanie pt. Digitalizacja i udostępnienie w Cyfrowym Repozytorium Uniwersytetu Łódzkiego kolekcji czasopism naukowych wydawanych przez Uniwersytet Łódzki nr 885/P-DUN/2014 zostało dofinansowane ze środków MNiSW w ramach działalności upowszechniającej naukę

Wendler, Lutz

English

Repozytorium Uniwersytetu Łódzkiego (University of Lodz Repository)

Acta Physicae Superficierum ■ Vol П • 1990THE ROLE O F INTERFACES IN  P L A SM O N -PH O N O N  C O U PL IN G  IN  SEM IC O N D U C TO R  Q U A N T U M  WELLS A N D  SUPERLATTICESLUTZ WENDLERSektion Physik der Friedrich-Schiller-Universität Jena,Max-Wien-Platz 1, Jena-6900, GermanyM odulation doped microstructures such as heterostructures, quantum wells, wires, dots and superlattices attract much interest because o f their novel fundamental physical properties and the resulting potential device applications. Within these layered structures it is possible to produce a low-dimensional electron gas with an electron number density varying in a large range. The confinement o f the electron m otion perpendicular to the heterointerfaces leads to size quantization in one, two or three directions.Electrons in the conduction band of a polar semiconductor strongly interact with longitudinal (LO) phonons. It is well known that the electron gas of a heavily doped semiconductor can support charge-density oscillations organized by long-range Coulomb fields. The polar of Frohlich-type o f electron-phonon interaction leads to a strong coupling between these charge-density oscillations, the plasmons, and the LO phonons if their frequencies are comparable, forming a polaron gas. In modulation-doped semiconductor microstructures this coupling also occurs. But there are two basic differences between a microstructure, which is a layered system, and an ordinary 3D  bulk crystal, that one must consider:(i) Confinement of the electron motion and, hence, the electrons form a low-dimensional electron gas.(ii) The spectrum o f the optical phonons interacting with the electrons of the low-dimensional electron gas is altered by the interfaces of the system. The ordinary dispersion-free LO phonons are changed to be modes confined in each individual layer. And further new states, interface phonons, occur in the spectrum of the optical phonons with electric fields mainly localized at the interfaces of the system and decaying exponentially from them.For the investigation of the plasmon-phonon coupling in the presence of interfaces we use as an example the simple geometry of a double heterostructure (DHS, interfaces are assumed to be perpendicular to the z-axis). This structureconsists of a smaller-gap-semiconductor in a > z > 0, which is symmetrically embedded by a wider-gap-semiconductor.According to the symmetry of the D H S the electron motion is quasi-free in the x-y  plane with the wave vector component £ |(. Using the simple infinite barrier model potential for the DH S and neglecting band-bending, the energy eigenvalues are« it \ h2ku й2л2 ,**( I ") = ^ + w (K + 1 ) : K = 0 - 1' 2 ......  mThe long-wave length optical phonons in the absence of quasi-free electrons in a D H S are given by M axwell’s equations and matching boundary conditions across the two interfaces. We describe both semiconductors by lattice dielectric functions of the formсо?..-CO2£ v N  =  £ o o v  — T ------------T  ( 2 )ù)fv- c o 2where v =  1 denotes the small-gap-semiconductor and v =  2 the wider-gap one. In a D H S with the dielectric functions according to Eq. (2) LO phonons with coL and interface phonons exist. For the single layer geometry there are two types of interface phonon modes [1 ]:  antisymmetric coA± and symmetric a)s±To calculate the properties o f the Q 2D polaron gas o f a D H S we have derived the longitudinal dynamically screened interaction potential [2^4]. It reads within the electric quantum limitWKK.(&и, со) =  £ {ÔLK — WKL(q ii , со)Xl ](q ц, со) x Wl°K(q^, со). (3)Herein W & i ^ . c o )  is the screened and WKK.(ąn,co) is the bare interaction potential given byЩ:к‘(ЯII >ш) =  Укк'(Qh) +  Jx’x ' I I  > ш) • (4)This interaction potential signifies the scattering of an electron from the subband0 to К  by another electron which becomes scattered from 0 to K ’. VK^ . (q]{) represents the bare electron-eiectron and У £ , ( $ п,ш) the bare electron-phonon interaction potential. It is shown [1 ] that caused by the symmetry properties of the D H S the bare interaction potential has the following properties:^ 1 1 * 0 , Wl 0 =  W ^j=0, W2: # 0 , W20=  W02 9^0 and W21 =  Wi2 =  0. Because of the large energetic separation between the 0-th and the 2-nd subband at the usual layer thicknesses of a D H S the contribution of W20 is very weak. Therefore, it is a good approximation to neglect the off-diagonal elements in (3). This means that intra- and intersubband processes are decoupled. The full RPA expression of the polarization function Х ^Й ц.ш ) of the quasi-two-dimensional electron gas is calculated in [2 ] .The condition for the existence of collective excitations is that self-sustaining collective oscillations occur. This means that the dispersion relation representsa resonance condition which defines the eigenfrequencies co=(Oj(Ą^) o f the collective excitation having an infinite life-time. In the regions of the co_4|| plane with ImXjJ'öii. <u)=0 the dispersion relation of the coupled excitations follows from (3) tow k k  (<Jи. w) -  2**($II ■ ш) =  0 ■ (5)Equation (5) describes: (i) coupled intrasubband plasmon-phonon modes if K = 0  and (ii) coupled intersubband plasmon-phonon modes if K > 0 .  In the regions where Im ц, со) /  0 is valid single-particle intra- and intersubband excitations occur and hence, the collective excitations are Landau-damped [4 ] . Due to the symmetry properties of the D H S the intrasubband plasmons couple only to the LO phonons of the layer and to the symmetric interface phonons but not to the antisymmetric one. For the intersubband plasmons the situation is vice versa.If a strong magnetic field (ha>c> k BT) is applied perpendicularly to the heterointerfaces, the physical situation is quite changed. The magnetic field causes a quantization of the electron motion in the x-y  plane in addition to the size quantization in z-direction. Hence, a completely quantized situation arises. The possible collective excitations of this magnetoplasma are intra- and intersubband principal m agnetoplasm ons and Bernstein m odes. These magnetoplasmons couple to the optical phonons of the system. We found the general result that all modes are free of Landau damping for all wave vectors and temperatures for ha>c $>kv T  because of the loss of the contin uum of extended states.The developed theory of plasmon-phonon coupling can be applied also to other layered structures. For superlattices the electrons form mini-bands representing the dimensionality of such a system between three or two. D ue to the spatial periodicity the optical phonons form Bloch waves with dispersion curves forming two double bands [5 ] . The resulting coupled mode spectrum has a very rich resonance structure. The new development of submicron lithography (selective etching patterns into the top layer of a heterostructure and then deposition of a metal gate in nm dimensions) allows the investigation of one- and zero-dimensional electron systems due to strong electrostatic confinement. With the additional parameter, the gate voltage, it is possible to vary the dimensionality from 2D  to ID  or from 2D  to OD. One of the future directions is to apply the here developed theory of collective excitations to these new microstructures and to investigate their properties in dependence of the dimensionality. Further, it is necessary to look for the effects of a magnetic field in those cases where a hybridization of the Landau levels with the quantum confined states occurs.REFERENCES[1 ]  L. Wendler and R. Pechstedt, phys. stat. sol. (i) 141, 129 (1987).[2 ] L. Wendler and R. Pechstedt, phys. stat. sol. (b) 138, 197 (1986).[3 ] L. Wendlçr *nd R. Pechstedt, Phys. Rev. B35, 5887 (1987).[4 ] L. Wendler, Solid State Commun. 65, 1197 (1988).[5 ]  L. Wendler aąd R. Haupt, phys. stat. so i (b) 143, 487 (1987).

The Role of Interfaces in Plasmon-Phonon Coupling in Semiconductor Quantum Wells and Superlattices

Biblioteka Nauki - repozytorium artykuÅÃ³w

http://dspace.uni.lodz.pl:8080/xmlui/bitstream/11089/15912/1/APS2WENDLER_67_70.pdf

The Role of Interfaces in Plasmon-Phonon Coupling in Semiconductor Quantum Wells and Superlattices

Abstract

Similar works

Full text

Available Versions

Repozytorium Uniwersytetu Łódzkiego (University of Lodz Repository)

Biblioteka Nauki - repozytorium artykuÅÃ³w

The Role of Interfaces in Plasmon-Phonon Coupling in Semiconductor Quantum Wells and Superlattices

Abstract

Similar works

Full text

Available Versions

Repozytorium Uniwersytetu Łódzkiego (University of Lodz Repository)

Biblioteka Nauki - repozytorium artykuÅÃ³w

Biblioteka Nauki - repozytorium artykuÅÃ³w