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Electroluminescence spectra of an STM-tip-inducedquantum dotCroitoru, M.D.; Gladilin, V.N.; Fomin, V.; Devreese, J.T.; Kemerink, M.; Koenraad, P.M.;Sauthoff, K.; Wolter, J.H.Published in:Physical Review B

DOI:10.1103/PhysRevB.68.195307

Published: 01/01/2003

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https://doi.org/10.1103/PhysRevB.68.195307

https://research.tue.nl/en/publications/electroluminescence-spectra-of-an-stmtipinduced-quantum-dot(34a44d78-b242-4363-9568-714cd03a2784).html

PHYSICAL REVIEW B 68, 195307 ~2003!

Electroluminescence spectra of an STM-tip-induced quantum dot

M. D. Croitoru,* V. N. Gladilin,* V. M. Fomin,* ,† and J. T. Devreese†

Theoretische Fysica van de Vaste Stoffen (TFVS), Universiteit Antwerpen, Belgium

M. Kemerink, P. M. Koenraad, K. Sauthoff,‡ and J. H. WolterCOBRA Inter-University Research Institute, Eindhoven University of Technology, The Netherlands

~Received 25 February 2003; revised manuscript received 23 June 2003; published 11 November 2003!

We analyze the electroluminescence spectrum of an STM-tip-induced quantum dot in a GaAs surface layer.A flexible model has been developed that combines analytical and numerical methods and describes the keyfeatures of many-particle states in the STM-tip-induced quantum dot. The dot is characterized by its depth andlateral width, which are experimentally controlled by the bias and current. We find, in agreement with experi-ment, that increasing the voltage on the STM tip results in a redshift of the electroluminescence peaks, whilethe peak positions as a function of electron tunneling current through the STM tip reveal a blueshift.

DOI: 10.1103/PhysRevB.68.195307 PACS number~s!: 73.21.La, 78.60.Fi, 73.21.Ac, 78.20.Bh

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I. INTRODUCTION

Semiconductor quantum dot~QD! systems are of continuing scientific interest due to their three-dimensional carconfinement, resulting in atomlike characteristics1–4 thatmake them valuable for applications. In addition to allowithe study of fundamental physics in a zero-dimensiosemiconductor system, the discrete energy levels in QD’sexpected to result in a number of advantageous propertieoptoelectronics5,6 and memory devices.7–9 Various fabrica-tion technologies of quantum dots have been proposamong them chemical methods, such as metal-orgchemical-vapor deposition~MOCVD! and molecular-beamepitaxy ~MBE!, and electrostatic patterning.

Despite years of intensive research into the optical prerties of quantum dots, there are still several problemsdering device applications of the zero-dimensional properof the dots. These include control of the carrier confinemand energy level separation, areal density and optical quauniformity in size and shape, and ordering of the dots inensemble. The complexity of a system containing ansemble of QD’s, caused by variations in the dot size, shacomposition, and the nearest-neighbor distance, makesdictions of the optical properties problematic. With thismind, a study of the electroluminescence of quantum dwhich have the possibility of tuning their optical characteistics by choosing of parameters like voltage, is of strointerest.

A special and unique type of quantum dot that can onlystudied by using a scanning-tunneling microscope~STM! isthe so-called tip-induced quantum dot.10–13 When a bias isapplied between the metallic STM tip and semiconducsample, the electric field extends into the semiconducstructure and a hole or an electron accumulation layer caformed under the tip. For sufficiently small tip apex radquantization occurs both in the radial direction and alonggrowth axis of the structure. It should be noted that theinduced band bending confines only a single typecarrier—holes in our case. The electrons are repelled fthe region under the tip. Thus the tip forms an antidotelectrons. By putting a barrier just below the surface injec

0163-1829/2003/68~19!/195307~12!/$20.00 68 1953

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electrons can be confined to the surface layer and radiarecombination with holes in the dot becomes possible.analyze the electroluminescence of a quantum dot induby an STM tip in the GaAs surface layer ofGaAs/Al0.25Ga0.75As multilayer structure.13 To describe theenergy spectra of charge carriers the Poisson and Sc¨-dinger equations are solved self-consistently withinframework of the Hartree approximation, by using a finitdifference scheme on a composite grid. The experimentobserved positions of electroluminescence peaks, attribto electron-hole recombination in the quantum dot, are vsensitive to the electron tunneling current, even in the cwhen the current is weak and the effect of electron chargethe electrostatic potential profile in the structure is negligibWe show that this puzzling sensitivity can be linked to vartions of the STM-tip contact area with varying current. Tdeveloped model also allows us to calculate the electrolunescence spectrum as a function of the applied tip voltag

The remaining part of the paper is organized as followin Sec. II, the results of optical spectroscopy measuremeperformed on a STM-tip-induced quantum dot, are psented. In Sec. III, a quantum mechanical description ofsystem of holes and electrons, as well as the numermethod of the self-consistent solution of the Poisson aSchrodinger equations are given. Calculation of the eletroluminescence spectrum is presented in Sec. IV. In Secthe results of the calculations are discussed.

II. EXPERIMENTAL SETUP AND RESULTS

The experiments are performed in a low-temperatSTM setup with light collection facilities.14 The sample thatwas used in the experiments is grown by molecular-beepitaxy. The surface layer is a 17-nm-thick undoped Galayer, the barrier material is Al0.25Ga0.75As. The first dopinglayer is ad layer of beryllium acceptors, placed 200 Å belothe GaAs/Al0.25Ga0.75As interface. The deeper layers of thsample contain, among others, a quantum well and a sulattice, 62 and 107 nm below the surface, respectively. Thcontribution to the optical spectra is discussed in Ref.Prior to mounting, the samples are sulfur passivated, wh

©2003 The American Physical Society07-1

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M. D. CROITORUet al. PHYSICAL REVIEW B 68, 195307 ~2003!

results in a surface that is covered with a thin sulfur layetypically one or a few monolayers thick—and is free of gstates.16 Because of the presence of this insulating top laythe STM tip is in physical contact with the sample surfaunder typical experimental conditions. However, the resing deformation of the tip apex is found to be the totaelastic.

Since the GaAs surface is free of gap states, a surfaceaccumulation layer is formed under the tip at positive sambias. The light that is emitted when the holes in this layrecombine with electrons that are injected from the tipcollected by two large-diameter fibers and projected ocooled Si charge-coupled device~CCD! by a 30-cm mono-chromator. The typical integration time was 30–60 sec.

III. MODEL

In our model we consider the structure sketched in FigThe shape of the STM tip is modeled by a truncated cobecause when the tip made of a soft metal~Pt! is pressed tothe semiconductor layer, its apex becomes flat. The STMand GaAs layer are separated from each other by an insing sulfur passivation layer of thicknessl 1 ~Ref. 13!. Theholes and electrons are confined in the cap layer of widthl 2 .The width of the Al0.25Ga0.75As barrier is l 3 . TheAl0.25Ga0.75As layer borders on the In0.25Ga0.75As quantumwell. The contact area of the STM tip with the multilaystructure is a circle of radiusRtip . Owing to the axial sym-metry of the system, the cylindrical coordinatesr, w, andzare used. Thez axis is directed along the symmetry axisthe tip, which is chosen parallel to the growth axis of t

sv

eunf

ed

19530

r,

t-

olelersa

.e,

ipat-

structure. While the hole motion is confined in all directioby the potential well, the electron motion is confined onalong thez axis.

A. Hole states in the quantum dot

In order to find the energy spectra of holes, trapped inquantum dot, we solve self-consistently the Poisson equa

FIG. 1. Scheme of the tip/insulator/GaAsAl0.25Ga0.75As/quantum well structure. The shown calculated hodensity distribution corresponds to the STM-tip voltage23.1 V andthe radius of the tip, 20 nm.

d the

1

r

]

]r S r]U~r ,z!

]r D1]2U~r ,z!

]z2 52rh~r ,z!

«0« i, ~1!

where rh(r ,z)5enh(r ,z) and « i are the hole charge density and dielectric constant of the material, respectively, anSchrodinger equation, which governs the hole motion,

2\2

2 F 1

mji~z!

1

r

]

]r S r]

]r D11

mji~z!

1

r 2

]2

]w2 1]

]z

1

mj'~z!

]

]zGC j ,s,n,m~r ,w,z!1V~r ,z!C j ,s,n,m~r ,w,z!5Ej ,s,n,mC j ,s,n,m~r ,w,z!,

mji ,'~z!5H mj

i ,'@GaAs# , if zPGaAs layer,

mj

i ,'@Al0.25Ga0.75As# , if zPAl0.25Ga0.75As layer.~2!

ion

f

yer

ap-tion

astn

Here the indexj labels the hole band type:j 51 for a holewhich is heavy for motion along thez axis and light in theplane of the GaAs layer andj 52 for a hole which is light formotion along thez axis and heavy in the plane of the GaAlayer. For the case of a quantum well the light and heaholes exactly decouple atukiu50. Since the lateral size of thdot is much larger than the GaAs unit cell, only states aroukiu50 contribute to the wave functions in the dot. The efect of coupling is very weak in the close vicinity of thcenter of the Brillouin zoneki50 ~see, e.g., Refs. 17 an

y

d-

18!. The indexs labels subbands due to the size quantizatof the hole motion along thez axis. The indexn is the radialquantum number andm is the angular quantum number othe lateral~in the plane of the GaAs layer! motion of thehole. Since the holes are accumulated in a rather thin lanear the surface, the hole motion along thez axis is expectedto be faster than the lateral motion. Hence the adiabaticproach can be used: i.e., it is assumed that the lateral moof a hole takes place in the potential formed by the fmotion along thez axis. Therefore, the hole wave functio

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the

n

ELECTROLUMINESCENCE SPECTRA OF AN STM-TIP- . . . PHYSICAL REVIEW B 68, 195307 ~2003!

can be represented as a product:C j ,s,n,m(r ,w,z)5C j ,s

' (z;r )C j ,s,n,mi (r )eimw, where C j ,s

' (z;r ) andC j ,s,n,m

i (r )eimw are the wave functions of the transver~along the z axis! and lateral motion, respectively. ThSchrodinger equation governing the transverse motion ohole reads

2\2

2

]

]z

1

mj'~z!

]

]zC j ,s

' ~z;r !1V~r ,z!C j ,s' ~z;r !

5Ej ,s~r !C j ,s' ~z;r !, ~3!

where V(r ,z)5eU(r ,z)1Vbarh (z) with U(r ,z) the electro-

static potential.Vbarh (z) describes band offsets for a hole. W

adopt the following rule for the band-gap energy differenbetween GaAs and Al0.25Ga0.75As: DEc /DEg567% andDEv /DEg533% ~Ref. 19!. So

Vbarh ~z!5H 0 meV, if zPGaAs layer,

102 meV, if zPAl0.25Ga0.75As layer,

`, if zPsulfur layer.

~4!

When solving the Schro¨dinger equation~3!, the total poten-tial energy V(r ,z) is modeled by a piecewise lineafunction20

Vp~r ,z!52@Al~r !1al~r !z#, zl 21,z,zl , l 51,...,nz ,~5!

wherezl are the nodes of the partition of the segment@0,L5 l 21 l 3# in nz parts. The functionsAl(r ) andal(r ) are de-termined by

al~r !52V~r ,zl !2V~r ,zl 21!

zl2zl 21,

Al~r !5V~r ,zl !zl 212V~r ,zl 21!zl

zl2zl 21. ~6!

In the interval (zl ,zl 21) and at a fixed value ofr, the equa-tion for the transverse wave functionC j ,s

' (z;r ) transformsinto

]2

]xl2 C j ,s

' ~xl !1xlC j ,s' ~xl !50, ~7!

where

xl52Fz1«1Al

j

alj G ~al

jmj'!1/3,

alj5

2mj'

\2 al , Alj5

2mj'

\2 Al , «52mj

'

\2 E~r !. ~8!

A general solution of this equation is

C j ,s' ~xl !5cl

1Ai ~xl !1cl2Bi~xl !, ~9!

19530

a

e

where Ai(x) and Bi(x) are Airy functions.21 Using the con-dition of continuity of the wave function and of its derivativat the nodes, we obtain a homogeneous set of equationthe coefficientscl

i :

c01Ai „~mj

' l !1/3x01…1c0

2Bi„~mj' l !1/3x0

1…50,

cl1Ai „~mj

' l !1/3xl1…1cl

2Bi„~mj' l !1/3xl

1…

2cl 111 Ai „~mj

' l 11!1/3xl 110

…2cl 112 Bi„~mj

' l 11!1/3xl 110

…

50,

cl1~al

jmj' l !1/3Ai 8„~mj

' l !1/3xl1…1cl

2~aljmj

' l !1/3Bi8„~mj' l !1/3xl

1…

2cl 111 ~al 11

j mj' l 11!1/3Ai 8„~mj

' l 11!1/3xl 110

…

2cl 112 ~al 11

j mj' l 11!1/3Bi8„~mj

' l 11!1/3xl 110

…50,

cn1Ai „~mj

'n!1/3xn0…1c0

2Bi„~mj'n!1/3xn

0…50, ~10!

where xl052@zl 211(«1Al

j )/alj #(al

j )1/3 and xl152@zl1(«

1Alj )/al

j #(alj )1/3. The secular equation corresponding to t

above set of equations yields the spectrum of the subbenergies, characterizing the transverse motion of holes:

Ej ,s~r !5\2

2mj' « j ,s~r !. ~11!

Each of the energiesEj ,s(r ) determines the top of a holsubband in the multilayer structure and plays the role ofadiabatic potential for the lateral motion.

Consequently, the equation, which describes the moalong ther coordinate, is as follows:

2\2

2mji~z!

F1

r

]

]r S r]

]r D2m2

r 2 GC j ,s,n,mi

~r !

1Ej ,s~r !C j ,s,n,mi

~r !5Ej ,s,n,mC j ,s,n,mi

~r !. ~12!

Our numerical approach to solving the Schro¨dinger equation,which governs the lateral motion of the holes, is to modeleffective potentialEj ,s(r ) by a steplike ring function

U j ,sk ~r !5

Ej ,sk 1Ej ,s

k21

2, r k21,r ,r k , k51,...,nr ,

~13!

wherer k are the nodes of the partition of the segment@0,RH#in nr parts andEj ,s

k 5Ej ,s(r k). In the interval (r k21 ,r k) andat a fixed value ofr, the equation for the wave functioC j ,s,n,m

i (r ) takes the form

2\2

2mji~z!

F1

r

]

]r S r]

]r D2m2

r 2 GC j ,s,n,mi

~r !

1Ej ,s

k 1Ej ,sk21

2C j ,s,n,m

i~r !

5Ej ,s,n,mC j ,s,n,mi

~r !, ~14!

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no

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tion

-ntial


where r k21,r ,r k , k51,...,nr . A general solution of thisequation is

C j ,s,n,mi ,k ~r !5bk

1Am~Alkj r !1bk

2Bm~Alkj r !

5H lk1Jm~Alk

j r !1bk2Ym~Alk

j r !, if lk.0,

bk1I m~Alk

j r !1bk2Km~Alk

j r !, if lk,0,

~15!

whereJm(r ) andYm(r ) are Bessel functions of integer ordm, and I m(r ) and Km(r ) are modified Bessel functions ointeger orderm ~Ref. 21!. Here

lkj 5

2mji~z!

\2 S Ej ,s,n,m2Ej ,s

k 1Ej ,sk21

2 D . ~16!

Using the condition of continuity of the wave functioand of its derivative at the nodes, we obtain a homogeneset of equations for the coefficientsbk

i , which reduces to

S bn1

bn2D 5S S11 S12

S21 S22D S b1

1

0 D . ~17!

Here the transmission matrix is defined by

S5 )k5nr

1

W21~r k!W~r k21!, ~18!

where

W~r j !5S Am~Alkj r k! Bm~Alk

j r k!

Alkj

mji Am8 ~Alk

j r k!Alk

j

mji Bm8 ~Alk

j r k!D , ~19!

W21~r j !5S Alkj

mji

Bm8 ~Alkj r k!

Dkj 2

Bm~Alkj r k!

Dkj

2Alk

j

mji

Am8 ~Alkj r k!

Dkj

Am~Alkj r k!

Dkj

D ,

~20!

and

th

d

in

19530

us

Dkj 55

2

mjipr k

, if lkj .0,

21

mjir k

, if lkj ,0.

~21!

The secular equation corresponding to the above set of etions yields the energy spectrum of holes, confined inquantum dot.

Given a particular number of holes in the quantum dwe find the quasi-Fermi levelEF

h for holes from the equation

Nh5 (j 51,2

(s,n,m

f h~ j ,s,n,m,EFh !, ~22!

where f h( j ,s,n,m,EFh) is the probability of occupation by a

hole of the quantum state~j, s, n, m!. Then, within the Har-tree approximation scheme, the hole charge density mawritten as

rh~r ,z!5e (j 51,2

(s,n,m

uC j ,s,n,m~r ,w,z!u2f h~ j ,s,n,m,EFh !.

~23!

This is the basic formula employed to invoke a seconsistent solution to the Schro¨dinger and Poisson equation

The procedure, involved to calculate the hole statesthe corresponding electrostatic potential, is divided into thsteps. At the first step, the electrostatic potentialU(r ,z) inthe whole structure is calculated in the absence of hoThen the obtained potential is used as the initial guess initeration procedure. In order to solve the Poisson equanumerically we choose to work in the domainV5@0, l 11 l 21 l 3#3@0, RH# with the following boundary conditions:

]U~r ,z!

]r Ur 50

50, U~r ,z!ur 5RH50, ~24!

U~r ,0!5Vtip for r P@0,Rtip#, U~r ,l 11 l 21 l 3!50.~25!

The potential at the interface between the Al0.25Ga0.75As bar-rier and In0.25Ga0.75As quantum well, which has a high concentration of charge carriers, is assumed to be equipotewith U50. The mesh on the domainV is defined as follows:

$V i j %5H ~r,z!PVUr i5 (k51

i

hr~k!, zj5 (k51

j

hz~k!, 0< i<nr , 0< j <nzJ . ~26!

as aforit-

ot,imalten-lue,

The distance between nodes along the two axesr, z is takento be variable in order to make the grid more dense indomain of the induced quantum dot.

At the second step, the Schro¨dinger equation, describingthe hole motion along thez axis, is solved. The obtainefunction Ej ,s(r ) is used to calculate ther-dependent wavefunction ~15!, according to Eq.~14!. The wave functions areused to calculate the hole density. At the third step, solv

e

g

the Poisson equation, with the charge density obtainedresult of the previous step, yields a new approximationthe electrostatic potential, which is involved in the nexteration.

At a given number of holes in the induced quantum dthe second and third steps are repeated until the maxabsolute value of the difference between electrostatic potial at consecutive iterations is less than a required va

7-4

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a

nd

le:

o

frsusle

du

Tha

io

osethe

rear-n

s

thethethe

lemary

eis


which establishes the measure of the accuracy. Whencreasing the number of holes in the quantum dot, the etrostatic potential, obtained earlier for a smaller numberholes, is used as an initial guess for calculations.

We introduce the valueNh(0) , which is themaximal num-

ber of holes, trapped in the tip-induced quantum dot, atgiven potential of the STM tip. The valueNh

(0) is the largestinteger number~the ‘‘equilibrium’’ number of holes!, whichsatisfies the following inequality:

E~Nh~0!!<E~Nh

~0!21!1E`~1!, ~27!

where E`(1) is the energy of one nontrapped hole aE(Nh

(0)) is the energy ofNh(0) trapped holes.

B. Electron states in the quantum dot

Given the electrostatic potential formed by the hocharge, we solve the Schro¨dinger equation for the electrons

2\2

2 F 1

mei~z!

1

r

]

]r S r]

]r D11

mei~z!

1

r 2

]2

]w2

1]

]z

1

me'~z!

]

]zGCe,se ,ne ,me~r ,w,z!

1Ve~r ,z!Ce,se ,ne ,me~r ,w,z!

5Ee,se ,ne ,meCe,se ,ne ,me

~r ,w,z!. ~28!

mei ,'~z!5H me

i ,'@GaAs# , if zPGaAs,

me

i ,'@Al0.25Ga0.75As# , if zPAl0.25Ga0.75As.~29!

The indexse labels subbands due to the size quantizationthe electron transverse motion. The indexne is the radialquantum number andme is the angular quantum number othe lateral motion of the electron. The electron transvemotion is faster than the lateral motion; consequently, wethe adiabatic approach similarly to the above case of hoThe electron wave function can be represented in a proform Cse ,ne ,me

e (r ,f,z)5Ce,se

' (z;r )Ce,se ,ne ,me

i (r )eimew,

whereCe,se

' (z;r ) andCe,se ,ne ,me

i (r )eimew are the wave func-

tions of the transverse and lateral motion, respectively.Schrodinger equation governing the transverse motion ofelectron is

2\2

2

]

]z

1

me'~z!

]

]zCe,se

' ~z;r !

1Ve~r ,z!Ce,se

' ~z;r !

5Ee,se~r !Ce,se

' ~z;r !, ~30!

whereV(z,r )52eU(z,r )1Vbare (z). HereVbar

e (z) describesband offsets for an electron. Consequently, the equatwhich describes the motion along ther coordinate, is as fol-lows:

19530

n-c-f

f

ees.ct

en

n,

2\2

2mei~z!

S 1

r

]

]r S r]

]r D11

r 2

]2

]w2DCe,se ,ne ,me

i~r !

1Ee,seCe,se ,ne ,me

i~r !

5Ee,se ,ne ,meCe,se ,ne ,me

i~r !. ~31!

In order to numerically solve the Schro¨dinger equation,which governs the lateral motion of the electrons, we enclthe domain of electron motion, which is much larger thaninduced quantum dot, inside a cylinder of radiusRE andheightl 21 l 3 , on the surface of which the wave functions aforced to vanish. The domain of numerical modeling, chacterized by the radiusRE , is chosen to be much larger thathe radius of the contact area.

To calculate the electron wave functionCe,se ,ne ,me

i (r ),

we express it as

Ce,se ,ne ,me

i~r !5(

lbl ,me

&JmeS m l ,me

r

RED

REJme8 ~m l ,me

!~32!

and finally obtain a set of linear equations forbl ,me:

(l

F S \2

2mei~z!

S m l ,me

RED 2

2Ee,se ,ne ,meD d l ,l 81vse ,me ; l ,l 8Gbl ,me

50, ~33!

where

vse ,me ; l ,l 85E0

REdr

r

RE2

2JmeS m l ,me

r

RED JmeS m l 8,me

r

RED

Jme8 ~m l ,me!Jme

8 ~m l 8,me!

3Ee,se~r !. ~34!

The found set of energiesEe,se ,ne ,meand wave functions

Ce,se ,ne ,me(r ,f,z) together with the set of hole energie

Ej ,s,n,m and wave functionsC j ,s,n,m(r ,f,z) are used for theanalysis of the electron-hole radiative recombination.

Let us estimate the average number of electrons inproximity of the quantum dot. In the absence of currentnumber of electrons in this region can be described byfollowing differential equation:

]Ne~0!

]t5ge

th2Ne

~0!

tdr, ~35!

wheregeth is the rate of thermal excitations of electron-ho

pairs. The timetdr characterizes the electron drift away frothe quantum dot in the absence of current. In a stationsituation we obtain

Ne~0!5ge

thtdr . ~36!

When a currentI tip is turned on, the time evolution of thnumber of electrons in the proximity of the quantum dotgiven by

7-5

eth

-nle

ybe

n

r

s-oiliibol

nsc-

he

sar-a

thergy

tip

sesa

isre-ac-

he

toive

mbbi-

snsi-

ts

ina-

ion

a-


]Ne

]t5ge

th1I tip

e2

Ne

tdr. ~37!

Hence, in a stationary situation, we obtain

DNe5I tiptdr

e, ~38!

whereDNe5Ne2Ne(0) . The characteristictdr appears to be

of the order of 0.5 ps~Ref. 22!. Consequently, the averagnumber of additional electrons due to the current throughSTM tip, I tip'10 nA, is of the order of 1023. Since theexperiments are performed atT54.2 K, also the averagenumber of electrons in the absence of current,Ne

(0) , is small(;1023). It is obvious that the probability to find simultaneously two or more electrons in the proximity of the quatum dot is negligible and many-electron effects play no ro

IV. INTENSITY OF THE ELECTROLUMINESCENCE

The intensity of the electroluminescence at a frequencVin the quantum dot created by the STM tip can be describy the following expression:17

I ~\V!; (j ,s,n,m

(se ,ne ,me

f h~ j ,s,n,m,EFh ! f e~se ,ne ,me!

3P~ j ,s,n,m,se ,neme ,\V!, ~39!

where f e(se ,ne ,me) is the probability of occupation by aelectron of the quantum state (se ,ne ,me). The probability ofelectron-hole recombination,

P~ j ,s,n,m,se ,ne ,me ,\V!;uOj ,s,n,m,se ,ne ,meu2d~Ej ,s,n,m

1Ee,se ,ne ,me1Eg2\V!,

~40!

is proportional to the squared modulus of the overlap integof the electron and hole wave functions:

Oj ,s,n,m,se ,ne ,me[E C j ,s,n,m~r ,w,z!Ce,se ,neme

* ~r ,w,z!

5dm,meE r dr dw C j ,s,n,m

i~r !

3(l e

bl e ,me

&JmeS m l e ,me

r

RED

REJme8 ~m l e ,me

!

3E dzC j ,s' ~z;r !Ce,se

*' ~z;r !. ~41!

For obtaining the stationary distribution functionf h( j ,s,n,m,EF

h) and f e(se ,ne ,me) in the presence of a nonzero tunneling current through the tip, in the case of a rigous consideration, it is necessary to consider a nonequrium situation. However, since the current through the tipweak and the radiative lifetime of holes is expected tomuch longer than the time of relaxation between the h

19530

e

-.

d

al

r-b-see

energy levels, we assume that the distribution functiof h( j ,s,n,m,EF

h) can be described by the Fermi-Dirac funtion with quasi-Fermi level for holesEF

h :

f h~ j ,s,n,m,EFh !5

1

expS Ej ,s,n,m2EFh

kT D 11

. ~42!

The energies of electrons injected from the tip into tGaAs layer are extremely high~;2.5–3.5 eV with respect tothe bottom of the conduction band in the GaAs layer!. On theother hand, our estimations show~see next section! that therecombination probability, Eq.~40!, takes appreciable valueonly for electrons whose energies lie within a relatively nrow interval with a width of;150 meV. We assume that asresult of the energy relaxation of electrons injected fromtip, the occupation probability does not depend on the eneof an electron.

The electrons injected in the GaAs layer from the STMhave zero angular momentumme . After injection the elec-tron can further acquire a nonzero angular momentumme byscattering. However, the scattering probability decreawith increasing the kinetic energy of an electron due toradial accelerating electric field. With strengthening thfield, the radial electron motion approaches the ballisticgime. Therefore, we assume that due to a strong radialcelerating field, the occupation probability for states with tangular quantum numberumeu.0 is negligible as comparedto that forme50:

f e~se ,ne ,me!;dme0 . ~43!

We will also consider the opposite limiting case when duea strong scattering the electron motion is rather diffusthan ballistic so that the decrease off e with increasingumeuis negligible.

Let us analyze how change of the energy of the Coulointeraction between holes due to the electron-hole recomnation ~the electrostatic potential for the remaining hole!affects the electroluminescence spectrum of the dot. Tration energies can be represented in the form

DE5E~Nh,1e!2E~Nh21,0e!, ~44!

whereE(Nh,1e) is the energy of the system, which consisof Nh interacting holes and one electron, andE(Nh21,0e) isthe energy of the system after the electron-hole recombtion. These terms are expressed as follows:

E~Nh,1e!5E~Nh!1Eg1Ee1D, ~45!

whereD describes the Coulomb energy due to the interactbetweenNh holes and one electron,

E~Nh21,0e!5E~Nh21!1EFh~Nh!2Eh , ~46!

whereEFh(Nh) is the quasi-Fermi level ofNh holes andEh is

the energy of the hole, involved in the radiative recombintion. Substituting Eqs.~45! and~46! into Eq.~44!, we obtain

7-6

gtaondod

wan

e-la

y

s is

xi-nde-al-

a-

re-

tite

on-

tiala,

dottherre-ip-d inith

al

e

a


DE5D«1h, ~47!

where

D«5Eh1Eg1Ee ~48!

and

h5E~Nh!2E~Nh21!2EFh~Nh!1D. ~49!

The quantityh describes a correction to the transition enerdue to the recombination-induced change of the electrospotential for the remaining holes. As a result of the electrhole recombination, the total charge in the quantum dotmain does not change and, moreover, the charge densitytribution changes only slightly. Therefore, the quantityh isnegligible as compared to the transition energy.

V. RESULTS AND DISCUSSION

The experimental sample is characterized by the folloing parameters. The thicknesses of the GaAsAl0.25Ga0.75As layers are, respectively,l 2517 nm and l 3546 nm. The dielectric constants of these layers are«2513.2 and«3512.2. In our model we consider two reprsentative sets of parameters, which characterize the insulayer: sulfur case, where the insulator layer widthl 150.25 nm and the dielectric constant«154 @surface of theGaAs cap is covered with one monolayer of Ga-bound~Ref. 16!#, and vacuum case, wherel 150.5 nm,«151 ~sur-face of the GaAs cap is separated from the STM tip bvacuum barrier!. The hole masses are

m1'5

m0

g122g2, m2

'5m0

g112g2, ~50!

FIG. 2. ~a! Calculated profile of the electrostatic potentieU(r ,z) extended into the structure in the vacuum case atVtip523.1 V, Rtip520 nm. ~b! Hole density distribution induced by thSTM tip in the GaAs layer of the same structure atVtip523.1 V,Rtip520 nm.

19530

ytic--is-

-d

tor

S

a

m1i5

m0

g11g2, m2

i5

m0

g12g2, ~51!

with the Luttinger parameters for AlxGa12xAs Ref. 17. Herem0 is the free electron mass. The electron effective mastaken as follows:

me5~0.06710.083x!m0 . ~52!

The work functions of a pure Pt and GaAs are appromately the same within uncertainties due to faceting acontaminations.23 Therefore, we assume the difference btween those work functions to be zero in our numerical cculations.

The calculations were performed with the following prameters of our model: RH5200 nm, RE51000 nm, l51,..., 1000@see Eq.~32!#, nr5800, andnz5200. Whencalculating the electroluminescence spectra, we haveplaced thed function in Eq.~40! by a Lorentzian functionwith the half widthG55 meV. This allows us to smooth ouelectroluminescence intensity oscillations, related to a finsize of the domain of numerical modeling of the electrmotion, characterized byRE . The results of numerical calculations are presented in Figs. 1–8.

Figure 2 illustrates the profile of the electrostatic poteninduced by the STM tip with the radius of the contact areRtip520 nm, at the tip voltageVtip523.1 V. It is clearlyseen that the hole charge accumulated in the quantumdoes not completely screen the electrostatic potential indepth of the GaAs layer. The inset demonstrates the cosponding density of the holes, trapped by the STM-tinduced quantum dot. The charge of holes is concentratea relatively thin layer near the interface insulator/GaAs, w

FIG. 3. ‘‘Equilibrium’’ number of holes in the quantum dot asfunction of the squared radius of the contact area atVtip523.1 V~solid lines! and the absolute value of the applied voltage atRtip

520 nm ~dashed lines!.

7-7

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,

m

aplym

ethct

-ceu

-

t

onec-tr

in

lulehoc

sededoadle

ranc-on

thfo

th

a

ec

u

s-K.

gap-

ku-n


a lateral size that is almost equal to the tip diameter. Tthick solid line shows the potential profile at the interfainsulator/GaAs.

Figure 3 displays the ‘‘equilibrium’’ number of holesNh

(0) , in the quantum dot, calculated using Eq.~27!, as afunction of the squared radius of the contact area~solid lines!and of the voltage applied between the STM tip and seconductor structure~dashed lines!. The ‘‘equilibrium’’ num-ber of holes is approximately proportional to the voltageplied and to the contact area of the STM tip. Qualitativethis result is in agreement with what we would expect frothe classical theory of capacitance~linear increase in chargupon an incremental change of the applied voltage orarea of the contact between the STM tip and semicondustructure!.

In Fig. 4 we present~a! the typical experimentally observed electroluminescence spectrum of the tip-induquantum dot;~b! the electroluminescence spectrum calclated for the voltage on the STM tip,Vtip523.1 V, and theradius of the contact area,Rtip516 nm, in the case of a negligibly weak dependence off e on me ; ~c! the electrolumi-nescence spectrum calculated for the voltage on the STMVtip523.1 V, and the radius of the contact area,Rtip516 nm, in the case of the electron distribution functigiven by Eq.~43!. We see that the electroluminescence sptrum in panel~c! is much closer to the experimentally observed one, which supports our assumption that the elecdistribution function rapidly decreases with increasingme .Therefore we will use the electron distribution functionthe form ~43! in our further calculations.

Figure 5 shows the calculated positions of the electrominescence peaks as a function of the number of hotrapped in the quantum dot. The insets of these figure sthe calculated electroluminescence spectra of the tip-induquantum dot at the voltage on the STM tip,Vtip523.1 V,and the radius of the contact area,Rtip520 nm. The peaks inthese spectra are marked with series of letters. It can bethat positions of the electroluminescence peaks, attributethe electron-hole recombination in the quantum dot, are vsensitive to the number of holes, trapped in the quantumAn increase of the number of holes in the quantum dot leto a greater transition energy between hole and electronels ~blue shift of the electroluminescence peaks!. The reasonfor such behavior is the fact that an increase of the numbeholes in the quantum dot results in a narrowing of the qutum well for holes and in a widening quantum well for eletrons in thez direction. This pushes both hole and electrlevels down. For holes, the potential well in thez direction ismuch narrower than that for electrons. Correspondingly,downward shift of energy levels is more pronouncedholes than for electrons.

An examination of different terms entering Eq.~39!shows that for the structure with the vacuum barrier,lowest hole states (j 51, s51, n51,2,3) and the electronstates in the energy range 850–1000 meV give the mcontribution to the electroluminescence spectrum.

Figure 6 illustrates the position of the peaks in the eltroluminescence spectrum as a function of the voltageVtipapplied between the STM tip and the semiconductor str

19530

e

i-

-,

eor

d-

ip,

-

on

-s,wed

entoryt.sv-

of-

er

e

in

-

c-

FIG. 4. ~a! Typical experimentally observed electroluminecence spectrum of the tip-induced quantum dot, taken at 4.2Note that the luminescence at 1.43 eV is dominated by band-transitions of the In0.25Ga0.75As layer.~b! Electroluminescence spectrum calculated for the voltage on the STM tip,Vtip523.1 V, andthe contact-area radiusRtip516 nm in the case of a negligibly weadecreasing off e with me . ~c! Electroluminescence spectrum calclated forVtip523.1 V andRtip516 nm in the case of the electrodistribution function given by Eq.~43!.

7-8

-n

n

tn--d

ee


FIG. 5. Positions of the electroluminescence peaks as a functioof the number of holes, trapped ithe tip-induced quantum dot atVtip

523.1 V, Rtip520 nm. ~a! Sulfurcase. ~b! Vacuum case. Here thenumber of holes in the quantum dois treated as a free parameter. Isets: calculated electroluminescence spectrum of the tip-inducequantum dot atVtip523.1 V, Rtip

520 nm. The electroluminescencintensity maxima are marked by thseries of the lettersAi andBi .

ly

ea

as

d

ththoth

hoeece-

tling

ne

trthru

rerh

thlollero, fls

sein

duethee-he

the

e to24.thea,of

sof

ee ofs in

thetiple,, totallyin-

rge-can

hiftetrygh

por-

are

s intun-

s a

ture at 4.2 K. Panel~a! corresponds to the experimentalobserved peaks. Panels~b! and ~c! display numerical resultsobtained in the sulfur and vacuum cases, respectivClearly, in agreement with experiment, the peak positionsa function ofVtip reveal a redshift, which can be explainedfollows. An increase of the voltage shifts the bottom~top! ofthe dot~antidot! upwards nearly proportional to the applievoltage. The width of the dot in thez direction is reduced dueto a stronger screening. Hence an increase ofVtip leads to adeepening of the potential well for holes and to a rise ofbarrier for electrons. This, in its turn, raises the energy ofrelevant electron state with respect to the bottom of the cduction band in the absence of applied voltage and shiftshole levels also upwards. This is because the rise of theenergy level due to the shift of the bottom of the dot is largthan its lowering due to the stronger confinement. Indewhen changing the voltage on the STM tip, for instanfrom Vtip521.9 to 23.1 V, the hole and electron levels responsible for peakB2 in Fig. 6~c! shift from 2974 to2530meV and from 593 to 892 meV, respectively. Consequenthe upward shift of the hole energy levels with increasVtip is larger~444 meV, in our example! than that for elec-trons~299 meV, in our example!. Thus these effects result ia redshift in peak positions in the electroluminescence sptrum.

In Fig. 7 we present the peak positions for the specshown in the insets of Fig. 5 as a function of the radius ofcontact area between the STM tip and semiconductor stture. It is seen that an enlargement of the radiusRtip leads toincreasing transition energies~blueshift!. This can be ex-plained by the fact that an enlargement of the contact ashifts the conduction and valence bands upwards. Thissults in a rising potential barrier for electrons and a sligdeeping of the potential well for holes. Consequently,recombining electron has to occupy a higher energy leveorder to have a considerable overlap integral with a hwave function. The upward shift of the hole levels is smalthan the increase of the energy of the recombining electIndeed, when increasing the radius of the contact areainstance, fromRtip516 to 24 nm, the hole and electron leveresponsible for peakB2 in Fig. 7~b! shift from 2588 to2510 meV and from 821 to 927 meV, respectively. Conquently, the upward shift of the hole energy levels withcreasingRtip is smaller~78 meV, in our example! than that

19530

ly.s

een-elerd,,

y,

c-

aec-

ae-teinern.or

--

for electrons~106 meV, in our example!. So a change of thecontact area influences both hole and electron levels, butto the weak confinement for holes in the radial direction,shifts of the electron and hole levels jointly lead to a blushift of the transition energy. Comparing the amplitude of tblueshift from the left-hand panel of Fig. 7~about 120 meV!with that from the right-hand panel~about 30–40 meV!, weconclude that an increase of the effective thickness ofinsulatorl 1 /«1 weakens the effect ofRtip on the electrolumi-nescence peak positions.

We have estimated corrections to the above results duthe exchange effects using the method described in Ref.The calculations are performed for the applied voltage onSTM tip, Vtip523.1 V, and the radius of the contact areRtip516 nm. Under these conditions, when the numberholes is small~approximately 20!, the exchange correctionare expected to be maximal within the considered rangeparameters. As follows from Table I, the inclusion of thexchange effects in our calculations for the analyzed rangvoltages and radii only slightly changes the peak positionthe electroluminescence spectrum.

In the experiment, the STM feedback system increaseselectron tunneling current through the tip by moving theforward.13 Since the tip is already in contact with the sampthis leads to a flattening of the STM tip and, consequentlyan enlargement of the contact area. Hence the experimenobserved blueshift of the electroluminescence peaks withcreasing tunneling current can be attributed to an enlament of the contact area. From the above analysis, weconclude that the applied STM-tip voltage governs the sof the peaks through the confinement along the symmaxis of the tip, while the tunneling current does this throuconfinement along ther coordinate.

In our model, we assume that the contact area is protional to the tunneling current:

I tip5apRtip2 , ~53!

wherea is treated as a fitting parameter. The calculationsperformed fora50.0025 nA/nm2. Figure 8 displays experi-mentally observed and calculated positions of the peakthe electroluminescence spectrum as a function of theneling current.25 From the panel~b! of this plot we can seethat the tendency in the behavior of the peak positions a

7-9

thob

ar

re-f-ofwe

ator

ofro--

au-in-y

ot,luteing

thece

the

ecnsti

e

. 5the

um

The


function of the tunneling current, obtained as a result ofnumerical calculations, agrees with that experimentallyserved. Moreover, also the absolute positions of peakswell as the magnitude of the shift with increasing currentconsistently described by the theory.

FIG. 6. ~a! Peak positions of the experimentally observed eltroluminescence spectrum of the tip-induced quantum dot, take4.2 K, vs biasVtip . Positions of the electroluminescence peaks afunction of the absolute value of the voltage applied to the STMat Rtip520 nm in the sulfur case@panel~b!# and in the vacuum cas@panel~c!#.

19530

e-ase

A number of experimental parameters are unknown pcisely, so it is of interest to consider the stability of the efects, calculated in this work, with respect to variationsthese parameters. For example, from the above analysissee that an increase of the effective thickness of the insull 1 /«1 weakens the effect of tunneling currentI tip on the elec-troluminescence peak positions. Similarly, the influencethe voltageVtip on the peak positions becomes less pnounced with increasingl 1 /«1 . At the same time, the direction of the electroluminescence peak shift with varyingI tip orVtip does not depend on a particular choice ofl 1 /«1 . A num-ber of simulations prompt us to the conclusion that alsoparticular choice of the shape of the STM tip does not inflence this direction. We have to distinguish between the ‘‘trinsic’’ properties~i.e., properties that are not influenced bparameter choices! and ‘‘extrinsic’’ properties~which are in-fluenced by parameter values! of the model. A blueshift ofelectroluminescence peaks with increasingI tip , as well as aredshift of these peaks with increasingVtip , can be consid-ered as intrinsic properties of the tip-induced quantum dwhile the absolute peak positions as well as the absovalues of the electroluminescence-peak shifts with varyI tip or Vtip are extrinsic properties.

VI. CONCLUSIONS

In order to describe the hole states that are confined inquantum dot induced by an STM tip in the GaAs surfalayer of a GaAs/Al0.25Ga0.75As multilayer structure, we havedeveloped a model based on a self-consistent solution of

-atap

FIG. 7. Positions of the electroluminescence peaks from Figas a function of the radius of the contact area at the voltage onSTM tip, Vtip523.1 V, in the sulfur case@panel ~a!# and in thevacuum case@panel~b!#.

TABLE I. Peak positions in the electroluminescence spectrfor the STM-tip-induced quantum dot atVtip523.1 V, Rtip

516 nm calculated with and without the exchange corrections.peaks are labeled as in Fig. 5~b!.

B1 B2 B3 B4 B5 B6

Transition energywithout exchangecorrections~meV!

1390 1406 1425 1453 1465 1493

Transition energywith exchangecorrections~meV!

1390 1410 1428 1453 1464 1494

7-10

-e-

eft

e


FIG. 8. ~a! Peak positions forthe experimentally observed electroluminescence spectrum of thtip-induced quantum dot vs tunneling current.~b! Calculated po-sitions of the electroluminescencpeaks from Fig. 5 as a function othe electron tunneling currenthrough the structure in thevacuum case at the voltage on thSTM tip, Vtip523.1 V.

faoi

ponecaunthceurth

lulingh

eri-ar-ngt.

0,Gn.adeci-

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U-

B

,

.

s

H

o-

c

.

rn,

H.se,

ad,

H.

et-

d

Poisson and Schro¨dinger equations within the framework othe Hartree approximation. The hole states are obtainedfunction of the voltage applied to the STM tip and the gemetric and material parameters of the system under thevestigation. We consider the influence of the electrostatictential formed by the STM tip and the charge distributionthe trapped holes on the electron states. The electrolumicence spectra of the STM-tip-induced quantum dot areculated as a function of the applied voltage and of the tneling current through the tip. We have shown thatapplied STM-tip voltage affects the electroluminescenpeak, positions through confinement along the growth dirtion of the semiconductor structure, while the tunneling crent does this through lateral confinement. An increase ofvoltage on the STM tip results in a redshift of the electrominescence peaks. In contrast, an increase of the tunnecurrent shifts the electroluminescence peaks towards hi

*Permanent address: Department of Theoretical Physics, Stateversity of Moldova, str. A. Mateevici 60, MD-2009 Kishinev, Republic of Moldova.

†Also at Technische Universiteit Eindhoven, P. B. 513, 5600 MEindhoven, The Netherlands.

‡Present address: Physikalisches Institut, Universita¨t Gottingen,Bunsenstraße 13, D-37073 Go¨ttingen, Germany.1J. Y. Marzin, J. M. Ge´rard, A. Izrael, D. Barrier, and G. Bastard

Phys. Rev. Lett.73, 716 ~1994!.2M. Grundmann, J. Christen, N. N. Ledentsov, J. Bo¨hrer, D. Bim-

berg, S. S. Ruvimov, P. Werner, U. Ritcher, U. Go¨sele, J. Hey-denreich, V. M. Ustinov, A. Yu. Egorov, A. E. Zhukov, P. SKop’ev, and Zh. I. Alferov, Phys. Rev. Lett.74, 4043~1995!.

3Y. Toda, S. Shinomori, K. Suzuki, and Y. Arakawa, Appl. PhyLett. 73, 517 ~1998!.

4A. Chavez-Pirson, J. Temmyo, K. Kamada, H. Gotoh, andAndo, Appl. Phys. Lett.72, 3494~1998!.

5A. Passaseo, G. Maruccio, M. De Vittorio, R. Rinaldi, R. Cinglani, and M. Lomascolo, Appl. Phys. Lett.78, 1382~2001!.

6D. Bimberg, M. Grundmann, and N. N. Ledentsov,Quantum DotHeterostructures~Wiley, New York, 1999!, and referencestherein.

7T. Lundstrom, W. Schoenfeld, H. Lee, and P. M. Petroff, Scien286, 2312~1999!.

19530

s a-n-o-fs-l--

eec--e

-g-er

energies. Both these results are in agreement with expment, demonstrating vast possibilities of tuning optical chacteristics of the STM-tip-induced quantum dot by varyiparameters like the applied voltage and tunneling curren

ACKNOWLEDGMENTS

This work has been supported by GOA BOF UA 200IUAP, FWO-V projects Nos. G.0274.01N, G.0435.03, WOWO.025.99N ~Belgium!, and the European CommissioGROWTH Program, NANOMAT project, Contract NoG5RD-CT-2001-00545. The research of M.K. has been mpossible by the Royal Netherlands Academy of Arts and Sences. One of the authors~K.S.! would like to acknowledgefinancial support by the Deutsche ForschungsgemeinscGrant No.~SFB 345!.

ni-

.

.

e

8Y. Alhassid, Rev. Mod. Phys.72, 895 ~2000!.9L. Zhuang, L. Guo, and S. Y. Chou, Appl. Phys. Lett.72, 1205

~1998!.10M. Wenderoth, M. A. Rosentreter, K. J. Engel, A. J. Heinrich, M

A. Schneider, and R. G. Ulbrich, Europhys. Lett.45, 579~1999!.11R. Dombrowski, C. Steinebach, C. Wittneven, M. Morgenste

and R. Wiesendanger, Phys. Rev. B59, 8043~1999!.12M. Yamauchi, T. Inoshita, and H. Sakaki, Appl. Phys. Lett.74,

1582 ~1999!.13M. Kemerink, K. Sauthoff, P. M. Koenraad, J. W. Gerritsen,

van Kempen, V. M. Fomin, J. H. Wolter, and J. T. DevreeAppl. Phys. A: Mater. Sci. Process.72, S239~2001!.

14M. Kemerink, J. W. Gerritsen, J. G. H. Hermsen, P. M. KoenraH. van Kempen, and J. H. Wolter, Rev. Sci. Instrum.72, 132~2001!.

15M. Kemerink, K. Sauthoff, J. W. Gerritsen, P. M. Koenraad,van Kempen, and J. H. Wolter, Phys. Rev. Lett.86, 2404~2001!.

16G. Hirsch, P. Kru¨ger, and J. Pollmann, Surf. Sci.778, 402~1998!.17G. A. Bastard,Wave Mechanics Applied to Semiconductor H

erostructures~Les Editions de Physique, Paris, 1988!.18M. Kemerink, P. M. Koenraad, and J. H. Wolter, Phys. Rev. B54,

10 644~1996!.19P. Harrison,Quantum Wells, Wires and Dots: Theoretical an

Computational Physics~Wiley, Chichester, 2000!.

7-11

.ol

leial

H.

P

c

nsnsns.rge

ure,ateTheoletheinakse

ibu-d—hift


20E. P. Pokatilov, V. M. Fomin, S. N. Balaban, V. N. Gladilin, S. NKlimin, J. T. Devreese, W. Magnus, W. Schoenmaker, N. Claert, M. Van Rossum, and K. De Meyer, J. Appl. Phys.85, 9~1999!.

21Handbook of Mathematical Functions, Natl. Bur. Stand. Appl.Math. Ser. No. 55, edited by M. Abramowitz and I. Stegun~U.S.GPO, Washington, D.C., 1965!.

22From a consideration of the classical electron drift in the acceating electric field~in the center of the quantum dot the potentenergy of an electron is of order of 800 meV! we obtain thattdr

is of the order of 0.5 ps.23M. Kemerink, K. Sauthoff, P. M. Koenraad, J. W. Gerritsen,

van Kempen, and J. H. Wolter, Phys. Rev. Lett.86, 2404~2001!.24P. A. Bobbert, H. Wieldraaijer, R. van der Weide, M. Kemerink,

M. Koenraad, and J. H. Wolter, Phys. Rev. B56, 3664~1996!.25As has been mentioned above, the energies of electrons inje

19530

-

r-

.

ted

from the tip are high. In order to recombine with holes, electrohave to relax to the energy interval, where their wave functiohave considerable overlap integration with hole wave functioIn the course of nonradiative relaxation, electrons create a lanumber of phonons and heat up the domain of the structwhere the quantum dot is formed. It is of interest to investigthe effect of this heating on the electroluminescence peaks.numerical simulation has shown that rising the effective htemperature from 4.2 K until 77 K leads to an increase inhole numberNh

(0) trapped in the quantum dot. This increaseits turn leads to the blueshift of the electroluminescence pe~;4–5 meV!. This result implies that if we take into account theffect of heating, caused by the electron current, on the distrtion of holes in the quantum dot, these—more advancecalculations would give a somewhat more pronounced bluesof the electroluminescence peaks with increasing current.

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electroluminescence spectra of an stm-tip-induced … · electroluminescence spectra of an...

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