Semiconductor Superlattices and Interfaces. Proceedings of the International School of Physics “Enrico Fermi”

468 Pages·1993·10.582 MB·English

by  A. Stella and L. Miglio (Eds.)

ITALIAN PHYSICAL SOCIETY
PROCEEDINGS
OF THE
INTERNATIONAL SCHOOL OF PHYSICS
«ENRICO FERMI»
CXVII
COURSE
edited by A. STELLA
Director of the Course
and by
L. MlGLIO
Scientific Secretary
VARENNA ON LAKE COMO
VILLA MONASTERO
25 June - 5 July 1991
Semiconductor Superlattices
and Interfaces
1993
NORTH-HOLLAND
AMSTERDAM - OXFORD - NEW YORK ■ TOKYO
Copyright ©, 1993, by Societä Italiana di Fisica
All rights reserved. No part of this publication may be reproduced, stored in a retrieval
system, or transmitted, in any form or by any means, electronic, mechanical,
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P. PAPALI
Library of Congress Cataloglng-ln-PublIcatlon Data
International School of Physics "Enrico Fermi" (1991 : Varenna,
Italy)
Semiconductor superlattIces and interfaces : Varenna on Lake Como,
V/1 Via Monastero. 25 June-5 July 1991 / edited by A. Stella and by L.
M1g1 lo.
p. cm. — (Proceedings of the International School of Physics
"Enrico Fermi" ; course 117)
At head of title: Italian Physical Society.
ISBN 0-444-81643-7
1. Semiconductors—Surfaces—Congresses. 2. SuperlattIces as
materials—Congresses. 3. Quantum wells—Congresses. I. Stella,
A. (Anglollno) II. Mlgllo, L. III. Socleta Italiana di fisica.
IV. Title. V. Series: International School of Physics "Enrico
Fermi" Proceedings of the International School of Physics. "Enrico
Fermi" ; course 117.
QC611.S9I58 1991
537.6" 22—dc20 93-28288
CIP
Proprietä Letteraria Riservata
Printed in Italy
Preface·
When we started to collect proposals for lessons and seminars concerning
this school, we quickly realized that the number of topics was diverging. Actu-
ally, it is hard to confine a wildly expanding area, such as the one of semicon-
ductor microstructures and interfaces, into a few and well-settled streamlines,
as is usually required in summer schools.
As a matter of fact, it should be noted that the intermixing among theory,
experiments and applications is a typical feature of this field. Furthermore,
many outstanding contributions come not only from the academic side, but also
from industrial laboratories.
So we decided to offer the student a kaleidoscopic view of the subject, by se-
lecting several topics in the fundamental properties of interfaces, superlattices
and quantum wells, to which we added some more on growth techniques and
applications. In spite of the rather «entropic» look of the program, the school
came out quite nicely. The results have been encouraging and the students did
participate very actively, thanks also to the daily homework provided by M.
CARDONA. Along the same lines we also organized the volume of the proceed-
ings, starting (exactly as at the school) with a broad overview on the subject by
L. ESAKI and concluding with the problems suggested by M. CARDONA, who
kindly accepted to solve and comment them for the written presentation, be-
sides giving two appreciated lectures on Raman spectroscopy, which are not in-
cluded in this volume.
We are much indebted to many people who actively contributed to make this
school successful. First of all to the teachers and to the students, who played
the first edition of the «Fermi Games», a very amusing competition of skillful-
ness conceived by the secretarial staff, headed by Mrs. E. MAZZI, who kindly
and professionally took care of the logistic support to our school.
The financial support for scholarships by the Gruppo Nazionale di Struttura
della Materia of CNR and the Italian Physical Society is gratefully acknowl-
edged: we regret that not all of the requests of grants (especially the high num-
ber from eastern Europe) could be satisfied, due to the limited size of our bud-
get. Finally, one of us (L.M.) wishes to thank the Dipartimento Fisica dell'Uni-
versitä di Milano for the partial support and C. MOLTENI for the kind help pro-
vided to the editorial work of this volume.
A. STELLA
Director of the School
L. MlGLlO
Scientific Secretary
DC. Bosio 14) L. Esaki 28) R. Rodrigues 42) J. Sapriel 55) S. Scandolo
2) F. Marabelii 15) G. Guizzetti 29) L. Colombo 43) M. Voos 56) M. F. Righini
3) C. Marabelii 16) L. Miglio 30) Α. Sassella 44) M. Missori 57) A. A. Mura
4) R. Zamboni 17) F. Flores 31) Α. Vinattieri 45) C. Arena 58) F. Romanato
5) Chen Chen-jia 18) V. Capozzi 32) Β. Fraboni 46) M. Gulia 59) G. Ferri
6) C. Presilla ' 19) C. Molteni 33) F. Tassone 47) M. Gurioli 60) J. A. Hernandez
7) M. Toivonen 20) V. Bellani 34) J. Salzman 48) J. Martinez 61) J. Arriaga
8) M. Altarelli 21) G. Mula 35) C. Arcangeli Pastor 62) R. Valente
9) A. Borghesi 22) C. Bungaro 36) M. Guidetti 49) F. Gozzo 63) T. S. Sethi
10) G. Margari- 23) J. Hugi 37) N. Kalkan 50) M. Dahmen 64) N. Pinto
tondo 24) R. Briptti 38) V. Voliotis 51) C. D. Wilkinson 65) A. Terrasi
11) L. Molenkamp 25) R. Redhammer 39) R. Thomas 52) M. Amiotti 66) R. Kucharczyk
12) A. Stella 26) Ε. Mazzi 40) S. Dosanjh 53) L. Carraresi 67) N. Marzari
13) F. Bassani 27) Μ. Sabadini 41) E. Dupont 54) F. Mauri
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The Evolution
of Semiconductor Quantum Structures.
Do-It-Yourself Quantum Mechanics.
L. ESAKI (*)
IBM Thomas J. Watson Research Center - Yorktown Heights, N.Y. 10598
1. - Introduction.
In 1969, research on quantum structures originated from a proposal of an en-
gineered semiconductor superlattice by ESAKI and Tsu[l,2]. In anticipation of
advancement in epitaxy, two types of superlattices were envisioned, with alter-
native deposition of ultrathin layers: doping and compositional, as shown at the
top and bottom of fig. 1, respectively.
This was, perhaps, the first proposal of designed semiconductor quantum
structures. Namely, we asserted that quantum states such as narrow bands or
confined states could be artificially created if potential barriers and wells were
fabricated by means of successive deposition of different semiconductor layers
with thicknesses smaller than the phase-coherent length of electrons. Since the
electronic characteristics of semiconductor structures are mainly governed by
such quantum states, it was predicted that new electronic materials can be de-
signed and engineered to obtain unprecedented transport and optical properties
through tailoring band parameters with the control of the potential profile dur-
ing the layer deposition.
Since the one-dimensional potential is introduced along with the superlattice
(SL) axis (perpendicular to the deposited plane layers), we thought that, if our
attempt was successful, elegantly simple examples in one-dimensional quantum
physics, for instance, resonant electron tunneling [3], Kronig-Penney band
model or Stark localization, which had remained textbook exercises, could, for
the first time, be practiced in a laboratory: Do-it-yourself quantum mechanics
would be possible, since the principles of quantum theory dictate the design of
semiconductor structures or devices.
(*) Present address: University of Tsukuba, Ibaraki, 305, Japan.
1 - Rendiconti S.I.F. - CXVII 1
2 L. ESAKI
Fig. 1. - Spacial variations of the conduction and valence band edges in two types of super-
lattices: doping (top) and compositional (bottom).
At the inception of the SL idea, it was recognized that the long, tailored lat-
tice period provided the unique opportunity to exploit electric-field-induced ef-
fects. Our early analysis of electron dynamics in a modestly high electric field,
along with the SL axis, led to the prediction of the occurrence of a negative dif-
ferential resistance which could be a precursor of the Bloch oscillation. The in-
troduction of the SL, apparently, allows us to explore the regime of electric-
field-induced quantization such as Stark ladders, which is not readily accessible
in natural crystals.
Before reaching the SL concept, we had explored the feasibility of structural
formation by epitaxy of ultra-thin barriers and wells which might exhibit
resonant electron tunneling. It was thought that semiconductors and tech-
nologies developed with them might be suitable for demonstration of the
quantum wave nature of electrons associated with the interference phenome-
na, since their small Fermi energies due to low carrier densities help make
the de Broglie wavelength relatively large. Namely, the Fermi wavelength
THE EVOLUTION OF SEMICONDUCTOR QUANTUM STRUCTURES ETC. 3
macroscopic regime
1 μπι
superlattice
or
quantum wells
100 nm
10 nm
1 nm
interatomic spacing
microscopic regime
0.1 nm l·-
m
crystal quality
(decreasing temperature)
Fig. 2. - Schematic illustration of a «mesoscopic» quantum regime (hatched) with a super-
lattice or quantum wells in the insert.
X = 2n/k , where k is the magnitude of the Fermi wave vector, is given as
F ¥ F
a function of the carrier density n, as follows: X = (8π-/3^)1/3 for a
F
three-dimensional (3D) system, (2π/η)1/2 for a two-dimensional (2D) system,
A/n for a one-dimensional (ID) system.
The idea of the SL occurred to us as a natural extension of double- and multi-
barrier structures: Namely, the SL is a series of quantum wells (QWs) coupled by
resonant tunneling, where quantum effects are expected to prevail. An impor-
tant parameter relevant to the observation of such effects is the phase-co-
herent length or, roughly, the electron inelastic mean free path, which depends
heavily on bulk as well as interface quality of crystals and also on temperatures
and values of the effective mass. As schematically illustrated in fig. 2, if charac-
teristic dimensions such as SL periods and QW widths are reduced to less than
the phase-coherent length, the entire electron system will enter a mesoscopic
4 L. ESAKI
0 U I U ! I I ! I Ü Ü I
0 0.2 0.4 0.6
energy (eV)
Fig. 3. - Comparison of density of states in the three-dimensional (3D) electron system
with those of a superlattice, and the two-dimensional (2D), one-dimensional (ID) and zero-
dimensional (0D) electron systems.
quantum regime of reduced dimensionality, being placed in the scale between
the macroscopic and the microscopic.
It was theoretically shown that the introduction of the SL potential perturbs
the band structure of the host materials, yielding unprecedented electronic
properties of quasi-two-dimensional character [1, 2]. Figure 3 shows the density
of states p(E) for electrons with m * = 0.067m in an SL with a well width of
0
100 Ä and the same barrier width, where the first three subbands are indicated
with dashed curves. The figure also includes, for comparison, a parabolic curve
El/2 for 3D, a steplike density of states for 2D (quantum well), a curve
Σ > (E - E - E )~1/2 for ID (quantum wire), and a delta-function ^W _
m n
- E - E — E ) for 0D system (quantum dot) where the quantum unit is taken to
1 m n
be 100 Ä for all cases and the barrier height is assumed to be infinite in obtain-
ing the quantized energy levels, Ε, E and E . Notice that the ground-state
λ m n
energy increases with decrease in dimensionality if the quantum unit is kept
constant. Each quantized energy level in 2D, ID and 0D is identified with the
one, two and three quantum numbers, respectively. The unit for the density of
states here is normalized to eV_1cm~3 for all the dimensions, although
eV_1cm"2, eV-1cm_1 and eV-1 may be commonly used for 2D, ID and 0D,
respectively.
THE EVOLUTION OF SEMICONDUCTOR QUANTUM STRUCTURES ETC. 5
2. - Epitaxy and superlattice growth.
In the early 1970s, we initiated the seemingly formidable task of engineer-
ing nanostructures in the search for novel quantum phenomena [4]. Heteroepi-
taxy is of fundamental interest for the SL and QW growth. Innovations and im-
provements in growth techniques such as MBE [5], MOCVD (metallo-organic
chemical vapor deposition) [6] and MOMBE (metallo-organic molecular-beam
epitaxy) or CBE (chemical beam epitaxy) during the last decade have made
high-quality heterostructures possible. Such structures possess predesigned
potential profiles and impurity distributions with dimensional control close to
interatomic spacing and with virtually defect-free interfaces, particularly, in a
lattice-matched case such as GaAs-Ga! _ ^AL^As. This great precision has
cleared access to a mesoscopic quantum regime.
The semiconductor SL stuctures have been grown with III-V and II-VI
compounds, as well as elemental semiconductors. For those semiconductors in-
volved, energy gaps at 4.2 K vs. lattice constants are plotted in fig. 4. The intro-
duction of II-VI not only extended the available range of energy gaps in both
the high and low directions, but also facilitated magnetic superlattices with
compounds such as CdMnTe and ZnMnSe.
lattice constant (Ä)
Fig. 4. - Plot of energy gaps at 4.2 K vs. lattice constants.