University of Warwick institutional repository: http://go.warwick.ac.uk/wrap. A Thesis Submitted for the Degree of PhD at the University of Warwick.
University of Warwick institutional repository: http://go.warwick.ac.uk/wrap A Thesis Submitted for the Degree of PhD at the University of Warwick http://go.warwick.ac.uk/wrap/4007 This thesis is made available online and is protected by original copyright. Please scroll down to view the document itself. Please refer to the repository record for this item for information to help you to cite it. Our policy information is available from the repository home page.
ON THE ELECTRICAL AND STRUCTURAL
PROPERTIES
OF
BORON DELTA LAYERS IN SILICON
Nevil Lee Mattey
Thesis submitted for the degree of Doctor of Philosophy. University of Warwick, Department of Physics.
September 1991.
CONTENTS
I-
Introduction
1
2. Previous Work
4.
2.1 b Doping in 111-V Semiconductors
4.
2.2 b Doping in Silicon
6.
2.3 Transport in b Layers
9.
3. The Growth and Structural Characterisation of 14.
Boron 6 Layers 3.1 Growth by MBE
14.
3.2 Structural
17.
and compositional characterisation
Secondary ion mass spectrometry a)
17.
b) Cross-sectional transmission electron microscopy
19.
b) X-ray diffraction
19.
21.
4. Electrical Measurements
21.
4.1 C-V profiling Sample preparation a)
21.
b) C-V measurement
21.
Automation c)
C-V profiling of
24.
Measurements
25.
a) Sample preparation
25.
b) Cryogenics
30.
4.2 Transport
Thermometry c)
30.
d) Transport measurement
33.
e) Computer control
36.
5. Theory
37.
5.1 The 6 layer as a 2D system
37.
5.2 Capacitance- voltage profiling
41.
5.3 Transport
44.
in 2D systems
a) Strong localisation and the metal-insulator transition
44.
b) Scaling theory and weak localisation
47.
c) Electron-electron
54.
interactions
d) Corrections due to weak localisation and electron- electron interactions
6. Results and Discussion
55.
57.
6.1 Structural characterisation
57.
SIMS analysis a)
58.
b) XTEM
61.
XRD c)
63.
6.2 Electrical properties C-V measurements a)
65.
b) Transport measurements
71.
7. Conclusions and Further work References
65.
99. 102.
Figures and Tables
2.1 Schematic diagram of the WET
13.
2.2 Band diagram of the sawtooth doping superlattice
13.
4.2 Equivalent circuit for C-V measurement
22.
4.3 SIMS profiles of as grown and annealled B6 layers
29.
4.4 Circuit used to measure resistivity, Hall effect
and magnetoresistance
34.
5.1 "V" shaped quantum well due to 6 layer
40.
5.2 Scaling behaviour of the conductivity
53.
5.3 Electron diffusing round a closed path of elastic
53.
scattering centres 6.1 Densitometer plot from bevel and stain of aB6
layer
57.
6.2 SIMS profile of B6 layer and reconstucted profile
59.
6.3 Extrapolation of up and down slopes and FWHM
60.
6.4 Extrapolation
60.
depth of apparent and peak conc.
6.5 XTEM micrograph of aB6 layer
62.
6.6 XRD rocking curve
64.
6.7 Structure used for C-V measurements
67.
6.8 Typical IN characteristic for Al Schottky barrier
67.
6.9 C-V for Al Schottky barrier
68.
6.10 N-d for Al Scottky barrier
68.
6.11 C-V for Ti barrier
69.
6.12 N-d for Ti barrier
69.
6.13 SIMS profile of C-V structure
70.
6.14 Resistance and Hall coefficient between 0.3K and 30K for a sample of sheet density
7.6xI013CM-2
76.
6.15 As above for a sample of sheet density 2.2xjOI3Cff2 6.16 As above for a sample of sheet density
1.8xjOI3CM-2
77. 78.
6.17 Calculated subband structure for Si: B 6 layers
79.
6.18 Magnetoresistance of sample 3 in a magnetic field
83.
6.19 Change in resistance versus B/T for sample 3.84. 6.20 Plot of LnR versus B"' for sample 3
89.
6.21 Plot of Ln R versus T'12 for sample 3 with B= 12 Tesla
90.
6.22 Plot of Ln R versus B"' for sample 2
91.
6.23 Plot of Ln R versus B
112
92.
for sample 1
97.
6.24 Log-log plot of resistance versus sheet density 6.25 Temperature
dependence of the conductivity
of aB6
layer of sheet density 9xlO"cm-'
98.
Table 1
75.
Table 11
82.
Table 111
88.
Table IV
94.
Acknowledgments
I should like to acknowIdge the contributions of the following without whom this work would not have been possible: Richard Kubiak and Richard Houghton for growing the layers, Mark Dowsett and Bob Barlow for SIMS analysis, Peter Augustus for TEM and Adrian Powell for the X-ray diffraction. Thanks also to the remainder of the ASR group for their input, especially Robin Biswas, Pete Phillips and Dave Smith. Finally I wish to acknowledge the contributions
of Mike Kearney and my
for help Whall, the transport Terry the theory their of results. with supervisor,
DECLARATION
The work described in this thesis was carried out either by or at the instigation of the author. It is presented according to the guidelines laid down in the regulations of the University
Warwick by Phys/PG3(1988). of as prescribed
Some of the work described herein has been, or is in the process of being,
published: Mattey N L, Hopkinson M, Houghton R F, Dowsett M G, McPhail D S, Whall T E, Parker EHC,
Booker G R, Whitehurst J, 1990, Thin Solid Films, 184,15.
Mattey N L, Dowsett M G, Parker EHC,
Whall T E, Taylor S, Zhang J F,
1990, Appl. Phys. Lett. 57 (16), 1648. Powell A R, Mattey N L, Kubiak RAA,
Parker EHC,
Whall T E, Bowen D
K, 1991, Semicond. Sci Technol. 6,227. Mattey
N L, Whall,
T E, Kubiak
RAA,
Kearney M, to be submitted to
Semicond. Sci. Technol. Mattey
N L, Whall
T E, Biswas R G, Kubiak
Mag. Phil. to submitted
RAA,
Kearney M, to be
SUMMARY
This thesis describes the first successful growth of boron 6 layers using
silicon MBE. SIMS has been used to demonstrate that the layer widths are 2nm has been as confirmed -
by TEM. This is probably an overestimate, an
average value of (0.3+0.5)nm
being obtained from XRD, suggesting that these
are the thinnest 6 layers produced to date. Hall and XRD measurements indicate that the boron dopant is fully activated up to sheet coverages of 1/2monolayer, i. e. - 3.5xlO"cm-'. The CV profile obtained for aBb FWHM
layer of sheet density
2.5xIO12CM-2
has
3nm, is be 6 in doping to the a result shown which consisitent with -
light of recent theoretical work. Resistivity, magnetoresistance and the Hall effect have been measured at temperatures
down to 0.3K using magnetic fields of up to 12T on samples of 12
8x 4xlO density in to the cm-1) sheet range
1013CM-2
2D weak localisation and .
in interaction have been observed samples of effects associated electron-electron These 1.8xlO"cm-' density of spin-orbit scattering. evidence with above sheet insulator" to undergo a" metalsamples are shown
transition
in high magnetic
fields with variable range hopping at 12 T. Samples of sheet densitY < IxIO"cmI, show activated transport
from which it is concluded that the critical acceptor
insu lator for transition the metalseparation
in this system is significantly
less
Si: is B. It doped, that this in found bulk, the may than suggested uniformly value be due to the splitting confinement.
due band degeneracy to the quantum of valence
Chapter 1.
INTRODUCTION
The semiconductor integrated
circuits
industry
is constantly
of greater functional
striving
complexity
towards producing
and increased speed of
operation with an associated demand for reduced power consumption. This has led to a continuous scaling down of device geometry. This study is concerned with the properties of the so called "b" doped down scale of the dimensions in one
system which represents the ultimate
direction - ideally to one atomic plane. Following
the development of growth
techniques such as molecular beam epitaxy (MBE) where the growth mechanism is essentially
two-dimensional,
the realisation
of such structures
becomes
practicable. Classical descriptions
of the transport
properties
invalid, quantum mechanical effects become the limiting provide means of producing the behaviour
of such systems are factors and may also
A device complete understanding of actions. novel
from is thus these a scientific essential, not only systems of
but technological one. a also viewpoint, This thesis describes the first study of the properties of the boron 6 doping layer in silicon. A review of related work in the III-V semiconductor systems and antimony,
is in Chapter in 6 two. layers given silicon arsenic and gallium 1
Chapter three describes the growth procedure used to produce the first successful boron delta layers in silicon along with the techniques used to characterise the structural and compositional properties of the as grown layers. The techniques developed for the electrical assessmentof the layers are discussed in Chapter four along with details of the modified MOS process developed to fabricate test structures and devices. Chapter rive gives the theoretical background to the results presented and
discussed in Chapter six. Analysis of data from secondary ion mass spectrometry (SIMS) carried out using a range of impact energies suggests that the as grown FWHM
of the 6 layers is - 2nm, as is supported by transmission
microscopy (TEM). More recent work on the interpretation from X ray diffraction implying
of
of rocking curves
suggests a width of < Inm (Powell et al, 1991a), b)),
that these layers are the thinnest produced to date. Results obtained
from capacitance-voltage profiling 2xjOI2CM-2
electron
give a FWHM of - 3mn for a sheet density
is be to shown consistent a quantum mechanical description. which
The subband structure of the p-type 6 layer in silicon has been calculated using a simple algorithm
developed from the model of Schubert et al (1985)
free into the takes carriers. effect of account which The results from measurements of the transport properties of 6 layers of 4xlO"'cm-' 0.3K down 4xlO"cm-' in temperatures to density to the at range sheet
2D localisation in discussed terms and associated electron-electron of weak are interaction effects for sheet densities > 1.8x
1013CM-2
localisation. is shown to occur at a sheet density of the critical impurity
.A _
for the metal-insulator separation
2
transition to strong
IXIO13CM-2
transition
suggesting that is significantly
lower in the 6 doped system than for bulk Si: B. It is suggestedthat this may be due to the splitting of the valence band degeneracy by the quantum confmiement. Magnetoresistance measurements on the weakly localised samples using fields of up to 12T are interpreted in terms of a magnetic field induced metalinsulator transition due to the shrinkage of the wavefunction. It is concluded that measurements at low fields are required to further separate the weak localisation and interaction terms and that the present description of the magnetoresistance results requires a more detailed comparison with alternative
theories of hopping transport.
3
CHAPTER 2.
PREVIOUS WORK,
2.16 Doping in HIN
Semiconductors.
The concept of introducing
dopants: in one atomic plane was origonafly
improve doping to the proposed profile control of Ge in GaAs grown by NME
(Wood et al, 1980). Previously Bass (1979) had reported sharp dopant spikes resulting from the absorption of Si onto a growth interrupted
GaAs surface.
Zrenner et. al (1985) reported the observation of the 2D subband structure due to the V shaped quantum well and coined the term "b" layer since the donor
distribution was described by the Dirac 6 function. The confinement of the Si donors to one atomic plane was inferred from the agreement between calculated first The direct demonstration donor the of and measured subband energies.
distribution was provided by Schubert et al (1988) who showed that the width of the layers was comparable to the lattice constant for growth temperatures 5500C. :5 The work on Si 6 layers in GaAs has been applied to produce P type discussed III-V Be, to layers using semiconductor systems as a number of other CVD. techniques (1990a) Schubert to by as in the review such other growth and
The development of 6 doping techniques has advanced the understanding fundamental of
the of effect especially segregation, surface as such processes
Si diffusion Also 1990a). (Schubert, the and coefficients of Fenni level pinning
4
Be in GaAs and AIxGal-,,As and C in GaAs have been determined for the first time using rapid thermal annealing of 6 doped samples followed by C-V prordi g (Schubert 1990a). 6 doping has also found a number of device applications in GaAs, including the WET where a6 layer is used as channel in MESFET a structure
as shown in figure 2.1. Provided the channel is at the optimum depth of - 30nm, the WET has been shown to have advantages over depletion mode MESFETs and HEMTs, at least for short gate lengths (Schubert et al, 1986, Schubert and Ploog, 1985). These include higher transconductance due to the proximity of the channel to the surface and the increased carrier density, higher breakdown voltage due to the lower electric field between the gate and channel and good high frequency linearity due to the linear dependence of the gate-source capacitance on the gate voltage. Non-alloYed ohmic source and drain contacts have been produced using 6 layers near the surface (Ploog et al, 1987). 6 layers have also been used as a source of carriers
in modulation
doped heterostructures
as discussed in the
Ploog (1987) Schubert (1990a). et al and reviews of Sawtooth doping superlattices, consisting of a series of alternating N and P type 6 layers in an undoped background with a period in the range 10-200nm, features doping to common superlattices. As shown in figure show a number of 2.2, these include spatial separation of electrons and holes resulting enhanced recombination hole ground property
in an
lifetime and a reduced energy gap between electron and
host to the semiconductor. states compared
is the tunability
of this gap by the injection
A third
important
of carriers
which
in ionized impurity thus the the charge potential wells compensating accumulate
5
and increasing the effective energy gap. This leads to a number of interesting optical properties (Schubert, 1990a) and has important applications in the area of semiconductor lasers, offering the prospect of operation at shorter wavelengths combined with frequency modulation. Both current injection and optically pumped superlattice lasers using 6 doped GaAs have been demonstrated.
2.2 6 Doping in Silicon Historically,
developments in Si MBE have followed those in the M-V
first The systems. reported growth of 6 layers in Si was by Zeindl et al (1987) 6 doping achieved who using Sb, the favoured N type dopant for Si MBE. The
dopant profile was deduced from a combination of SIMS and TEM
which
layer 2nm. The existance of the V shaped quantum well suggested a width of was demonstrated by tunneling spectroscopy where structure in the differential current-voltage characteristic of a Schottky barrier was attributed to the subband 6 layer. To enable accurate determination of the surface coverage the structure of of Sb during the growth
interrupt
it was necessary to reduce the substrate
temperature to about room temperature,
where the sticking coefficient of Sb is
Sb Sb In to the the surface segregation overcome of well-known order unity. layer was buried by a thin amorphous Si cap of thickness - 3nm deposited at room temperature
"solid 700T using which was subsequently recrystallized at
difficulties these An alternative method of overcoming phase epitaxy".
is to use
dopant ion beam few hundred this technique (ie. low a source, as eV) a energy a
6 layers 1989) (Denhoff As 1989) Sb (Li been to has et al, and et al, used produce in Si.
6
Eisele (1989) reported the growth of Sb 6 layers in Si with a range of sheet densities from
_
1012CM-2
to
5xjOI4CM-2
>
precipitates at doping levels -
5xjOI4CM-2
and, from TEM analysis, noted -
The degree of activation was
investigated using Hall measurements carried out at 4.2K to freeze out parallel conduction paths. A maximum sheet density > lo"'cm-' was obtained. The Hall mobility for the degenerate samples was almost independent of sheet density with a maxiiinum value of - 100cm'V-'s-'. A more thorough
investigation into Sb 6
layers was carried out by Van Gorkum et al (1989) where more accurate surface coverages were obtained by saturation
Sb followed by partial coverage of
desorption at a substrate temperature of 750'C. Hatl measurements were used to determine a saturation sheet density of
8xjOl3CM-2
.
Rutherford
back-scattering
was used to confirm that a large fraction of the Sb was not on lattice sites for a Sb layer. The carrier distribution saturated
investigated was using C-V profiling
which yielded extremely sharp carrier profiles which were modelled classically (Van Gorkum
Yamaguchi, and
1990) in contrast to the quantum mechanical
GaAs developed for in (Schubert 1987,1990b). The model et al, profiles obtained range of applicability
Chapter in 5. is discussed these of models
The growth of the first reported P type 6 layers in Si (Mattey et al, 1988)
is fully described in Chapter 3. Other attempts at producing B6 layers using a compound
B source (HBO, ) were hampered
by surface segregation effects
from temperatures the to substrate use necessity resulting incorporation oxygen
> 7000C to prevent
(Tatsumi et al, 1988). The use of Ga in combination with
(Zeindl been Sb 6 has for layers developed technique et al, the reported also 1990), however Ga has the disadvantage of being a relatively deep acceptor and
7
is incompletely activated even at room temperature, although the degree of activation increases at high doping levels (> 1019cm-3)due to the formation of an
impurity band. Device applications for 6 layers in Si have also centred around FET structures.
Zeindl et al (1989) reported the fabrication
of a MESFET
with a
degenerate conducting channel, similar to that shown in figure 1.1. However, this device prototype was produced by crude in-house processing techniques resulting in gate dimensions of 2mm. x 5mm and had to be operated at low temperature (in practice 4K) to freeze out parallel conduction paths. The high doping level meant that the channel could not be fully depleted before breakdown
of the
Schottky gate and thus the device could not be turned off. More satisfactory structures Shiraki,
were produced
following
computer
simulations
(Yamaguchi
and
1988) which also suggested that a6 layer of opposite type incorporated
below the 6 layer channel would act as a punch-through applications.
Depletion
mode MOSFETs
in stopper short gate
2jxrn have been length with gate
have 1988) (Yamaguchi designs these shown complete and et al, produced using
(also MOSFETs drain to the conventional current as compared pinch-off of depletion mode) of the same geometry which could not be pinched off. from Si in 6 for layers The possibility of optoelectronic applications arises the intersubband
infra-red in the direct transitions spacing allowing
(IR). Park
intersubband hole using have (1990) the absorption of observation reported et al Fourier
transform
infra-red
B ten spectroscopy with a structure consisting of
30nm by layers of nominally separated quasi-b absorption
degree The Si. of undoped
for four larger that factor than found be to reported of about a was
8
GaAs/Al. Gal-. As quantum wells, although the resonance peaks were somewhat broader which was attributed to the non-parabolicity of the hole bands. The wavelength of the absorption peaks was also shown to be tunable by varying the doping sheet density. Tempel et al (1990) reported an IR detector based on a tunnel structure consisting an Sb b layer 20nm below a Schottky contact. The fashioned into a waveguide with the ends polished at an angle of structure was 45' so that the IR beam made multiple passes through the 6 layer. The device 4.2K to was cooled and illuminated
IR with where it was found that the tunnel
current was modulated by the ER signal.
2.3. Transport in 6 Layers Dohler (1978) pointed out the advantages of a 2D system consisting of a thin doping spike buried in an opposite type background as compared to the Si inversion
MOSFET transport
layer which has had a major
in invesigation the role of
in 2D, as discussed in the review by Pepper (1985). These advantages
in 2D location homogeneous the the the carrier gas a of relatively centre around background
rather
than at the Si/SiO2 interface
where there are problems
is deviate from interface likely interface to the structure charge, associated with ideal and where the differing
dielectric constants on each side of the interface
lead to image potentials. The doping spike also represents a well defined random impurity
distribution
insulator transitions
for the this study of metalsuitable system makes which in 2D.
In contrast to the GaAs/AkGal-, As modulation doped heterojunction which Hall fractional integer in the the quantum and has been extensively used study of
9
for (see Harris ballistic OD 11), transport effect along with example, and et al, 1989), the 6 doping system is highly disordered, having carrier mobilities of below 100 cmV-'s-' as compared to 10'-10'cmV-'s-' in the heterojunction. Another area of interest in 2D systems arises from the work of Abrahams
et al (1979) which suggestedthat there was an abscenceof extended states in 2D ie. all states are localised and there is no such thing as a truly metallic 2D "weak localisation" This system. Boltzmann conductivity.
appears as a logarithmic
correction
to the
It was subsequently found that a logarithmic correction
interactions from in disordered electron-electron a also arises system (Alshuler 1980,1981, al, et
Fukuyama, 1980). The logarithmic correction was first
Osheroff, films (Dolan 1979) in Si inversion in thin and metal and observed layers (Bishop et al, 1980). Uren et al (1980) were able to separate the weak localisation. and interaction
effects in a Si inversion layer using a magnetic field.
These effects have also been observed in GaAs/AkGa, As heterostructures (Poole -,, Si, length, increased to 1981) the as compared electron screening where et al, interaction to gives rise
field. Weak localisation and effects at zero magnetic
in Chapter fully 5. discussed interaction more effects are electron-electron 6 little in 2D layers, for transport the Despite the potential using study of in this been has area: reported work In the III-V
been to have Haas de Schubnikov used oscillations systems
Cheng 1988, (Gilh-nann al, et et al, the occupations and energies subband study
1988) (Gillmann been has Hall along et al, observed 1989), the quantum effect 1988). (Zrenner transition induced al, field et metal-insulator the magnetic with (1989,1990) Ye by investigated been have using et al Strong localisation effects 10
a system of 20 Si 6 layers in GaAs where variable range hopping with a value of 1/3 for the exponent in Mott's law Oe. a =exp (VTO)") was reported, however this
value is open to question
(Koch,
1990). The anisotropy
of the
magnetoresistance was taken as evidence for the 2D nature of the system with the expected shrinkage of the donor Bohr radius with increasing magnetic field giving rise to a positive high field magnetoresistance which was larger for perpendicular
than
for
parallel
fields.
At
low
magnetoresistance was observed which was attributed
fields,
< 1T,
a negative
to quantum interference
between different hopping paths between initial and final states. For 6 layers in Si the work carried out by Zeindl et al. (1988) and Van
Gorkum et al (1989) identified a metal-insulator transition at a sheet density of _
IX1013CM-2
for Sb layers, a similar value being obtained for As (Denhoff et al,
1989) and for B (Mattey et al, 1991) 6 layers in Si. These values of critical sheet density are significantly impurity average
in excess of what would be expected based on the
for the transition separation
observed in 3D (Mattey et al,
1990). Hui-Min et al (1989) observed strong freeze-out for Sb b layers of sheet density :!ý 2.6xlO"cm-' and note that even this sheet density is greater than would be expected for bulk Sb doped Si, their data suggests a critical sheet density of 5xlO"cm-, -
low limited temperature measurements were of a number although
undertaken. Van Gorkum et al (1989) analysed the behaviour of the resistivity and Hall hopping in transport terms with of activated coefficient of a non-metallic sample however low dominant being temperatures, no comment was made at conduction for density the the metal-insulator sheet critical elevated on
11
transition.
Denhoff
et al (1989) asserted, from unpublished magnetoresistance data, that the metalinsulator transition in As 6 layers is driven by the opening of the Coulomb gap caused by the 2D electron-electron
interaction.
The angular dependence of the magnetoresistance of an Sb 6 layer in Si has been used to confirm the 2D nature of the system (Van Gorkum et al, 1989), whereby a cosine dependance was found between the magnetoresistance and the angle of the magnetic field with respect to the 6 layer in a plane perpendicular to the current
flow.
Thus the magnetoresistance
depended only upon the
field component of magnetic normal to the plane of the 6 layer which suggested that the conduction is limited to a layer much thinner than the cyclotron radius (- 30nm at 1T). The maximum value of the magnetoresistance amounted to - 3% field a with
of IT
magnetoresistance
at a temperature
4K, the observation of a negative of
"interesting" was noted as
but could not be explained. It is
from the the that arises supression of weak magnetoresistance negative possible localisation by the magnetic field (see Chapter 5. ). Denhoff et al (1989) report that magnetoresistance measurements on an As 6 layer revealed weak localisation. interaction and elect ron-electro n
best however, to the of the author's effects,
knowledge, these results remain unpublished. This thesis describes the first major study of the transport properties of b layers.
12
IL
Figure 2.1 Schematic diagram of the 5MESFET.
Fl
L-e ý,- --,e
------ ---------------------------
------------------------
-----------
----
------------
------------------------------
--------------------------------------------
-----------------------------
------------
--------------------------------------------
-----------------------------
7 ----------
--------------------------
--------------------------------------------------- -----------------------..........
Figure 2.2 Band diagram of the sawtooth doping superlattice showing the effective bandgap Eg
13
CHAPTER 3.
THE GROWTH CHARACTERISATION
AND STRUCTURAL 'D Q OF BORON 6 LAYEvo.
3.1 Growth by Molecular Beam Epitaxy ME).
The confinement of impurity
atoms to a few monolayers (ideally one) to
6 layers places very high demands on the MBE growth technique. produce A full description of silicon MBE is given elsewhere (eg Parker, 1985). The (single involves epitaxial crystal) growth process
Si of on a heated Si substrate.
An electron beam evaporator is used as a source of Si and dopant fluxes are To high by the thermal purity cells. ensure process effusion shuttered provided is carried
in an ultra-high out
dimensionally
vacuum environment.
Growth
occurs two-
doping the of prorde. prospect of monolayer resolution offering
However, thermal
diffusion
for dopants to segregate at the tendency the and
li-inits incorporated the being than achievable on place growth surface rather for be the had to Thus the of production optimised conditions growth resolution. 6 layers. Initially
layers were grown in a modifed VG Semicon V80 MBE system
Standard back-damaged 1990). (Houghton, boron fitted with an elemental source desorb the flux the to Following oxide, native clean (100) substrates were used. a temperature, substrate
0.3/im Si doped at
T.,, was lowered to 7000C and the interface buried by
1X1016CM-3
followed 0.5 boron nms-' grown at a rate of with 14
by OAAm of Sb doping at
IXIO16CM-3
T, was lowered to 400'C and growth .
interrupted whilst the layer was exposed to aB flux of 5xlO"cm-'s-' for between 40s and 240s to give surface coverages in the range
2xI012CM-2
to
IXIO13CM-29
since
B has a unity sticking coefficient. The reduction in T, serves to limit diffusion of
the B layer, any further reduction being undesirable due to the incorporation of hydrocarbons at temperatures below about 350T. Finally T, was returned to 700T and a 100mm cap grown at a rate of 0.65nins-1. This stage being intended to provide complete activation of the 6 layer along with good crystallinity
in the
layer. capping This was the first reported successful growth of Bb layers (Mattey et al, 1988), a previous attempt
having produced smeared profiles and onlY 70%
1988) due (Tatsumi, to the necessityof using growth tempertures above activation 7000C to prevent incorporation
0 from HB02 the source along with possible of
to compound sources. also common effects clustering The majority
in in layers this a new generation study were grown of used
VG Semicon V90S MBE system high uniformity, extremely
for low is growth rates and optimised which
SiGe Wafer for the structures. growth of as required
have be diameter to 75mm 150nun, be to used diameters can wafers although up Edinburgh the where processing at
Microfabrication
Facility is required.
be had V80 in to the modified since the The growth method used system temperature V90S in of the changes rapid time heater response system precludes due to its physical size.
had low doping temperatures B advanced. Also the understanding of at identified have 1991a) Parry 1990, Kibble, (Jorke et al, and A number of authors 15
transitions from equilibrium to kinetically limited incorporation enabling doping above the bulk solid solubility
limits at low temperatures, the transition
temperature being dependent on growth rate. Any B flux above the incorporation limit
under given conditions accumulates on the surface and will smear the
profile as it incorporates after tennination
of the B flux. It has also been
Si(100) that the established surface can accomodate a maximum of - 0.5 (one monolayer is equivalent to a sheet density of 6.8xjOI4Cnf2)of B monolayers and remain 100% electrically active (Headrick et al, 1990). In this case the (2xl) reconstruction and an ordered layer may be preserved surface undergoes a by low temperature
(at 3000C). This effect is not observed
epitaxial overgrowth
interrupt, a growth without
a saturation coverage of - 0.25 monolayers has been
(Parry 1991b). for growth et al, continuous reported The general conclusion is that for high B doping levels and high resolution low growth a
temperature
high growth and a
rate are required
given the
1991). Parry, (Kubiak and constraint of achieving good material quality With regard to these factors the b layers were grown as follows:
After a flux clean at 8500C the Si buffer layer was grown, doped as Si The 4800C. T, to 0.1 source reduced was whilst nms-' of rate at a required, 10"cm-'s-' flux between layer to the and of aB exposed and shuttered was in the 10 to range for to coverages surface achieve minutes up s-'
R
1014CM-2
1012CM-
IOIICM-2
to
long being between being enough The exposure time a compromise .
lead to long to as to ensure that accurate coverages are obtained and not so excessive unintentional
impurity incorporation.
T, remaining and the cap grown with
Finally, the Si shutter was opened
480T, at
16
found this it that was since
produced complete activation up to 3 .
5X1014CM-2
the level maximum attainable ,
(see Chapter 6).
3.2. Structural and Compostional Characterisation.
Having grown the layers it is necessary to confirm that they are 6 doped,
ie no excessive broadening has occurred during growth, and that the sheet density is as intended. Initially bevel and stain technique. background
a quick check was provided using the well-known A sample containing
aB6
layer in an N-type
was bevelled at an angle of - 0.1' using a proprietry
solution
(Syton). A conu-nercial stain which delineates P-N junctions was applied and the illuminated. sample Three main, more quantitative,
techniques have been used during the
course of this study:
3.2(a). Secondary Ion Mass Spectroscopy (SIMS).
SIMS can provide information species within
depth distribution the on
full A description a sample.
of an impurity
SIMS is given in a number of of
involves Clegg, basic directing (eg 1990). The beam process a of primary reviews ions, in this case02', from
the surface.
in being the results sample which material sputtered at The resulting
secondary
ions are directed
to a mass
interest. Thus tuned to the time species of a plot of counts versus spectrometer 17
is obtained which may be converted to concentration using a suitable calibration (general-ly an ion implanted standard) and to depth by measuring the final depth of the crater and assuming a constant erosion rate.
However the interaction of the ion beam with the sample leads to recoil in SIMS differing the effects which result and atomic mixing proffle
implantation
from the true impurity total impurity
distribution,
integrated the although profile will give the
dose. These effects are dependent upon the primary
decreasing the primary generally
ion energy,
ion energy improves the depth resolution.
However it is necessary to maintain a sufficient count rate which in turn depends beam the current on 450 eV/0' of energy instrument
using02+
In decreases practice a primary energy. with which
ion
(a EVA2000 the quadrupole minimum attainable using was ions at normal incidence). A further
complication arises
from the assumption of constant erosion rate. At the start of a profile there is a finite time before equilibrium with primary
is established. During this time, which increases
ion energy, an "altered layer" (in this caseS'02) is established at
"differential is the The the 1988). (Dowsett shift" effect net the surface et al, ion increasing decreases feature energy depth primary with a given of apparent
(Wittmaack and Wach, 1981). 6 SIMS the profiles of In order to assess the impact of these effects on density layer of nominal sheet layers a range of profiles were taken through aB6 IXIO13CM-2
6.1. Chapter in These results are presented .
18
3.2(b). Cross-sectional Transmission Electron Microscopy (XTEM).
To provide confirmation of the results of the SIMS analysis XTEM was also undertaken. The technique has been developed for strained systems (Baxter, 1988). Mass contrast has been successfully used to image Sb 6 layers in Si (Zeindl et al, 1987), the 6 layer being seen as a dark line of width - 2nm in a bright field
image of a (110) oriented cross-section. This contrast mechanism cannot be applied to the lighter B atoms. However the Bb layer should lead to a degree of
lattice strain which it should be possible to image. Samples of sheet density
IX1013CM-2
and
3.5xjOI4CM-2
(the maximum
attainable) were examined, the results are discussed in Chapter 6.1.
3.2(c). X-Ray Diffraction
X-ray diffraction
(XRD).
techniques, having the advantages of ease of sample
being non-destructive, preparation and epitaxial
have been applied extensively to strained
layers (Dineen and Sherwood,
1989).
The differences
in lattice
in lead to between the system changes components of a mismatched parameter the Bragg angle for a given reflection. encountered
Due to the small degree of lattice
double crystal XRD techniques are almost
mismatch
generally
invariably
hampered by being the angular techniques necessary, single crystal
19
Since divergance. beam highly B doped 6 due the the to width of a reflection layer should produce an appreciable degree of lattice strain, it was though likely that XRD would have a role in characterising
these layers.
Double crystal XRD was undertaken using a Bede 150 diffractometer with (004) four beam conditioner used to enhance the bounce a monolithic channel-cut fringe contrast in the region close to the Si (004) substrate reflection (Powell, Mattey,
Whall,
Parker
incidence reflections
Bowen, and
1991). Both
(004) and (113) glancing
it found were used since was necessary to consider two
degree the to of strain present. obtain unambiguously reflections In order to achieve maximum density attainable (3.5xIO"cm-')
strain a sample of the maximum sheet
To determine the structure of the B was used.
layer the rocking curves were simulated, using dynamical diffraction various strain
profiles
theory, for
(Powell et al, 1991a, b). The results are presented in
Chapter 6.1.
20
Chapter 4.
ELECTRICAL
MEASUREMENTS
4.1 Capacitance-voltage profiling
4.1a) Sample preparation
For C-V measurements an ohmic contact to the substrate and a Schottky contact, of well defined area, to the epilayer surface are required. Samples about 1cm square were taken from a wafer. The ohmic contact to the heavily doped substrate was made by sputtering aluminium
in an Iontec
Nlicrovac 350 sputter coating system with a base pressure of 5x 10-' torr and an operating pressure of about 3 militorr The Schottky barrier
of high purity argon.
proved much more problematic,
as discussed in
Chapter 6.
4.1b) C-V Measurement
Prior
to C-V
profiling
the sample was mounted
on a Wentworth
Laboratories MPIOOOW probe station and the I-V characteristic determined using Providing I-V 4145B the Packard Hewlett characteristic parameter analyser. a was saisfactory,
the diode was connected to a Hewlett
impedance analyser. 21
Packard 4192A LF
To measure the depletion capacitance of the diode as a function of applied bias, a small AC voltage, v, is added to a steady state biasq Vb and a phaseL 900 in the detector to of current, component measure advance sensitive used function" This the a required capacitance as of vce gives inVb. to the steps compared
Vbprovided vc is smaU
This assumes, however, that the diode can be
in rigure RC 4.1a). network as shown simple parallel as a adequetely modelled If there is a significant series resistance, R., as shown in figure 4.1b), the measured C increasi "true" from differ the C. the g error capacitance, wifl capacitance,
frequency. with 0
f
-fl
ER3 S
'3) Figure 4.1 for: resistance. parallel a) Equivalent circuits resistances. parallel and series
22
A number of authors have considered this problem (Blood, 1986, HumerHager, 1988) and have shown that, CM
C
1
[l+
]2+
(RsIRP)
«Ä)RsC)
2
is RP the parallel resistance and w is the angular frequency. where The initial work on C-V profiling
had to be carried out on non-optunised
structures grown on low doped substrates (Mattey et al, 1990) where the ohmic 6 layer. Thus, as the layer is depleted an increasing to the contact was made is presented. The problem was initially series resistance low operating frequency
solved by the use of a
(300 Hz), however errors can then result from the
(Blood, deep 1986). It has been states shown that the value of K, RP presence of from C be determined measurements of admittance at two frequencies and may (Humer-Hager, 1988). For the equivalent circuit of figure 4.1b) with admittance Y and x=Rp(. oC,
+R =R -1ySp
I-IRP
1
X
11.
(4.2)
+X2)
+X2)
Splitting Y into real and imaginary components and eliminating RP then gives, im (Re
Y
y_ 1y12R, )
23
(4.3)
W-i th
WC=XIRP
1 y12 Rp Im Y= and
[XI
(1+X2)
x
wc=
IM
Y1
(4.4)
].
I
(1 +X2)
(4.5)
If RPC is assumed to be independent of frequency, then an expression for 11,is given from the measured capacitances Cj, conductances Gj, and admittances Yj at frequencies coi(i = 1,2) can be obtained from equation (4.4). After
determining
R,,, C is determined
(4.4) (given that Rp=x/wC). equation
using equation (4.5) and Rp from
The corrected capacitance value is then
used to calculate the apparent carrier concentration, N and depth, d.
4.1c) The automation of C-V measurements The impedance analyser was interfaced to a BBC Master microcomputer Software IEEE bus. the via was written
to automate the C-V measurement.
Values of start and stop bias, bias step, oscillator level and frequency were input. One or two frequency measurements could be employed. The data was collected G, C disc to the corrected necessary, and where versusVb9 output and values of for future analysis. The carrier
depth from then profile versus was produced
dC/dVbbeing determined by differentiating (4.2), (4.1) the value of and equations a polynomial
fit to the data.
24
4.2 Transport Measurements. 4.2a) Sample Preparation Whilst
arbitrary
it is possible to make resistivity
measurements on samples of
1957), bridge Pauw, (Van der a shaped specimen enables the shape
separation of the tensor components of the resistivity and allows compliance with
international standards for the measurement of resistivity and Hall coefficient (ASTM F 76-73,1978). It is possible to fabricate Greek cross structures (the for Van der Pauw (Wieder, 1979)) by "painting" the technique geometry preferred the cross onto the epilayer surface with wax dissolved in xylene, allowing the wax to harden, and removing the remaining epilayer using a CNA
etch. Contact is
then made to the 6 layer by smearing Ga-In eutectic over the ends of the cross. This, of course, also makes contact to the substrate however, if the substrate is doped below - 1011cm-' it will be highly resistive compared to a "metallic" layer at low temperature.
6
This method is limited to highly doped samples and is
4.2K. to spot measurements at only really suited In view of the previous success of the group in modifying standard MOS
it 1988), (Smith from MBE devices was et al, to material grown produce processes for transport Hall bar to follow structures this route decided to produce FET fabrication for the At of time the made was provision same measurements. A 1989). Gorkum (Van set was layer mask al, et channel as structures using a6 MOSFETs MESFETs bars, Hall along with and designed to produce a range of 3nun 3mm out carried processing with chip x a number of other structures on a by the Edinburgh
Microfabrication
Facility.
degradation to In order prevent excessive 25
due 6 layer to the profile of
thermal diffusion it is necessaryto modify a number of the conventional process for several steps. Thermal oxidation cannot be used, temperatures of IOOOOC hours are required.
Experiments
attempting
to reduce this temperature
to
NOT 5nm were producing only of poor quality oxide after 24 unsuccessful, hours. For routine passivation an oxide deposited at 4350C, generally used as a masking layer, has been employed. This is known to be of insufficient quality for (Smith 1990). CVD a gate oxide et al, oxidation was used to produce a gate oxide in the rwst N-channel devices (Van Gorkum et al 1989), but was unavailable at Edinburgh.
However
a room-temperature
plasma-grown
oxide of a quality
had been developed at Liverpool University thermal approaching 1987), therefore with
the
it was decided to attempt to utilise this oxide in combination
remaining
processing
due to contamination unsuccessful and Liverpool,
(Taylor et al,
at
Edinburgh.
Initial
experiments
were
in between Edinburgh the transit of wafers
this was solved by use of a full RCA clean prior to oxidation.
The other main problem is in implant activation. Ion implanted contact form to regions are used
6 layer since the depth and the to ohmic contact
hence be to dopant avoiding contact controlled can accurately concentration of is implanted in the that However, to species the substrate. ensure order electrically
high temperature the to region, a amorphised anneal activated and
anneal at
1000'C -
for
several minutes
is usually
employed.
Previously,
furnace into inserting by the been had a wafers obtained activation satisfactory
installation Following the 1988). (Smith 15s of rapid for 1000'C al, et at thermal
(RTP) process
facilities
Edinburgh at
a more repeatable,
better
found down to 6s for 10s 9500C and was ramp up with at anneal characterised 26
provide complete activation (DeLima, 1990) and was employed for the later layers.
The implant activation has, by far, the most significant impact on the "thermal budget", the remaining processing using a maximum temperature of 435'C for 30 minutes. Analysis of x-ray rocking curves on a number of anneal-led has demonstrated samples no significant temperatures of O
with the hole energy E. The de Broglie wavelength is then matched to the well
width:
'XdB
=h
(5.3) (2m * E)1ý2 2e
(n+')'XdB
reo E 2D
(5.4)
2N
a
With n=0,1,2....
Thus the subband energies amount to,
2D
2
En
2-1/3
4EF
2/3
(n+1)
«213
(5.5)
hN, ' e
(m *) 112 r'O
and the real space extent of the subbands to,
h (n+ 1) 2 (2m *,Eý)1/2
/3
(5.6)
This approach gives similar values for the subband energies to calculations based on the WKB approximation,
however, since it ignores the effect of free
higher the subband energies are significantly carriers,
overestimated.
A more accurate solution was obtained by following
the approach of
Schubert et al (1986) who propose a simple polygonal model to give an analytic 38
description of the effect of free carriers. The triangular well is retained with the band bending due to the free carriers assumedto occur at the points N.where the i'6 subband intersects the potential well, as shown in figure 5.1b. The subband separation is then given by:
Ei - Ei-, =e2N 2c
2D 1: A _ j=O
reo
(5.7)
njl(xi-xi_1)
where the values of xi are obtained from matching the de Broglie wavelength (equation 5.3) to the well width as above. The carrier
density, rk., in the 0
subband may be obtained as a function of the Fermi energy EFusing the density
of states,
ni=
m*I(EF-E)
(5.8)
ý2 TU,
A computer program was written to calculate the subband structure for a given carrier
sheet density using equations 5.7 and 5.8. Initially
the bare
from 5.5 Fermi is the are obtained energies equation and energy the set subband to the bottom of the lowest subband. The Fermi energy is then incremented in
1meV steps and the subband energies recalculated for the given subband is (the The the terminated term subband occupation when program occupation. is density. in 5.7 to the the equal acceptor sheet equation sununation sign under
39
_Jac
----------
"V" a) shapedquantum well formed by 6 layer.
detta
-- - ---
Figure 5.1
- ----
b) Polygonal well. 40
5.2 C-V Proriling Conventionally, the doping profile of a semiconductor may be obtained from the dependence of the depletion capacitance per unit area, C, of Schottky a contact on the applied reverse bias, V. Within the depletion approximation,
the
doping concentration, n(x), is given by the well-known equation: 3 ( dC -1 -C n(x)= dV) ee reO
(5.9)
With e equal to the electronic charge, the semiconductor relative permitivity
Er
and the dielectric constant co. The depth, x, of the depletion edge is determined
from C, e
(5.10)
reO c
As was first pointed out by Kennedy et al (1968), n(x) is not, in general, the doping profile, but is the profile of majority is constant with depth, then the majority
If the doping concentration carriers. carrier profile will be identical to the
doping profile assuming complete activation and the absence of significant trap states. However,
for changes in doping profile the carrier profile will change
for The length decay diffusion. due the to characteristic scale carrier more slowly is Debye-Hfickel in doping the concentration of carrier concentration at a change by, LD, length, given screening
F'reokT e2N doping is N the concentration. where
112
(5.11)
Thus near an abrupt change in doping
41
0
conce ration at xO(Blood, 1986)9 1/2
( 2)
2LD
n(x) -e In the case of degenerate doping the appropriate
length scale is the Thomas-
Fermi screening length, Lm, given by, 1/2 LTF =2e
3
reo(EF-EC) e2N
(5.13)
Given that LDis - 4nm in Si at 300K with a doping concentration of IxIO"cml, it is clear tha the C-V profile
from
a6
layer is likely to be significantly
broadened as compared to the doping profile, typically of FWM1
>1
theory in
(Lee and Ramakrishnan, 1985) to give,
a(L) =a_e2 B
it
2ý
Ln
Boltzmann is the conductivity classical where uB 2
B=
ne
Ll 1
(5.27)
by, given
Ir
(5.28)
Physically this weak localisation correction to the classical conductivity
Aronov by Altsuler first interference from and elucidated effects quantum arises (1985). Figure 5.4 shows an electron diffusing round a closed path of elastic scatterers.
If the probability
amplitude
of the electron traversing
the path
is*2, the traversing T, the is that anticlockwise path electron of and clockwise the probability,
W, of the electron returning
49
to the origin is given by,
.2
(5.29)
ie.
12+ 1*2 ]2+[*
**21+1*1*; 12
]
Since phase is maintained during elastic scattering, T, and*2are referrig
coherent each
to the same path but traversed in opposite directions. Hence
W=
(5.30)
4[*12
Which is equal to twice the classical probability localisation
will
be reduced by any inelastic
(2[fl').
This tendency to
process. If -r, is the inelastic
free is time the the time conductivity and mean scattering r
is given by (from
5.27, equation
Ln
GBe
(5.31)
2Tc 2!ý
TP, the depends T temperature independent is temperature If r as on and r, of conductivity
is then, 'I
peB
Application
2Tc 2!h
Ln T
(5.32)
the destroys time field the of symmetry reversal of a magnetic
hence interference the destruction negative a the and leading to of wavefunctions; defined be de-phasing time a phase A where can -r., magnetic magnetoresistance. field, B, by is induced the magnetic radian one change of
50
(5.33)
4eBD Provided Tm< -r, r, should replace -r, in equation 5.31, leading to,
A cr(B)
for the approximate
e2 2Tc 2th
eD-rB
Ln
change in conductivity
field. magnetic with
The electron spin is neglected in the above argument, presence of spin-orbit
(5.34)
however in the
coupling the spin no longer a good quantum number and
direction during The dependent term scattering. spin may undergo a change of consists of two parts - the triplet
state where the two electron wavefunctions
1) (magnetic the + and m= singlet state quantum number spins parallel carry -1,0, Following Alshuler the spins. antiparallel and electron wavefunctions carry where Aranov (1985) representing the singlet state by *00 and the triplet states by *j., the interference term I is given by, tm=+i
21
The spin-orbit its momentum.
(5.35)
[*IM]2_[*oj2
between the is dependent the electron spin and angle on coupling Since the two wavefunctions
are equivalent
to the electron
is directions, in approached each scattering centre traversing the path opposite term types the two thus hence (and of spin momenta), velocities opposite with
differently. be affected will In the case of the singlet state with
the spin-orbit spins, opposite
the two will waves have and the wavefunction each on effect same interaction will
51
be in phase at the onigin.
In the case of parallel spins, the spin direction will be changed by equal, but opposite, amounts at a scattering centre. Thus after a time 7,. (the spin-orbit scattering time), the spins wil-I be randomized and the wavefunctions will tend to cancel each other out at the origin. If T,. > -r, the constructive interference of the [jrOj2 be destroyed, interference 2 triplet state will the term becomes _/1
(see
5.35), equation and the correction to the classical conductivity becomesnegativeweak antilocalistion.
The magnetoresistance will therefore be positive, at least for
low fields, at high fields the magnetic de-phasing time, r. will become less than TSO and the spin-orbit
interaction
does not have time to occur, thus the
becomes This has been used to determine 7.0 negative. effect magnetoresistance experimentally
(Bergmann,
1985).
It should be noted that in the weak localisation regime the temperature dependence of the Hall (Fukuyama,
mobility
is the same as that
of the conductance
1980) thus AR,, /R,, =0 (where R,, is the Hall coefricient).
52
flfg) d=
0
Ing
Figure 5.2
Scaling behaviour of conductance(after Kramer et al, 1985).
Figure 5.3 (after Dugdal( influence diffusing the scattering elastic Closed path of an electrom of under 1987)
53
5.3c) Electron-Electron Interactions The above picture ignores electron-electron interactions. Shortly after the logarithmic correction to the Boltzmann conductivity due to weak localisation was discovered, Alshuler et al (1980,1981) and Fukuyama (1980) showed, using diagrammatic perturbation
theory, a similar correction could arise from electron-
interactions in a disordered system. electron Bergmann (1987) provided a physical description of the process by which the electron-electron
interaction
may be enhanced in the presence of disorder.
The process involves the interference of two electrons, if the energy difference is of the order of kT, the thermal coherence time, rT may be written as,
t kT Provided
ýý' TO9 'rT
(5.36)
the elastic scattering time, it is possible that an electron
in Chapter 5.3b may interfere with elasically scatterred round a closed path as 'electron for (1987) hologram' Bergmann the the coined phrase another electron. (since it is such a path a record of the closed charge pattern established round is It that the traversing the second path). possible with associated phase change it in have the the traverse suffered change phase same path and electron will traversing
the path exactly compensated by the electron hologram.
electron-electron holographic
interaction
can enhance one electron wavefunction
Thus the by such
processes.
Alternatively
one may consider the electron-electron
interaction
to be
in the together the presence of closer spatially remain electrons since enhanced 54
such elastic scattering process than would plane wave states.
The net effect of the interaction is to produce a Coulomb gap in the density of states at the Fermi energy. Fukuyama (1980) described the interaction in terms of coupling constants i=1 gi where and 2 describe the exchange terms ie. those with parallel spin which Coulomb interaction the reduces
(due to the Pauli principle)
4 i=3 and and
describe the Hartree terms which include the Coulomb interaction but ignore The conductivity spin effects.
for a single valley amounts to: correction
8cr
=a i
XgLn B
4nkT-r I
(5.37)
ýh
depend the is disorder the X(= h/4rEFT) nature of on gi parameter and a where the interactions.
According to Fukuyama (1981) g, =1 andg2=93=94=F/2
Coulomb interaction screened
for a
is F a screening parameter. where
The magnetoresistance due to interactions arises from orbital and Zeeman
fields low the At 1985). Ramakrishnan, oribtal (Lee and spin-splitting effects contibution
dominates. Spin-splitting
important, become effects
due the to suppression of anti-parallel magnetoresistance the Zeeman spin-splitting
giving a positive
interactions once spin
becomes comparable to kT.
localisation due electron-electron to and Corrections 5.3d) weak interactions. be likely to interactions are localisation electron-electron Both weak and by is the D, weak diffusion affected The constant, in system. real any present N(4) Fermi the energy, density at the states of localisation and
55
is affected by the
electron-electron
interactions.
Since these two are related to the conductivity
by
2 DN(EF), the net effect is additive, or=e AG
AD
AN(EF)
(5.38)
N(EF)
Although both have a logarithmic
temperature dependence (in 2D), it is possible
to separate the two effects by considering the behaviour of both R and RI, (Uren
1980). al, et
56
Chapter 6.
RESULTS AND DISCUSSION 6.1 Structural Characterisation
Figure 6.1 shows a microdensitometer plot obtained from a bevelled and stained B6 layer which is delineated as a dark line the width of which suggests 2nm. Although it is layer a6 not clear exactly what this line represents width it is interesting to note that such a crude technique can be applied to such high More from SIMS, TEM results quantitative were obtained resolution structures. XRD analysis. and
ENO
2nm
B C DEPTH
Figure 6.1. optical density plotted versus depth along a bevel of angle 0.130 of a 5. The 6 layer is B 2nm. the apparent of width stained -
57
6.1a) SIEMSAnalysis Figure 6.2 shows a SIMS depth profile
density
1XI013CM-2
of a sample of nominal sheet
taken using extremely low energy primary ions (450 eV/O').
The measured areal dopant density is 1xIO" in cm-', good agreement with the growth schedule and the FWHM
is 3.6mm.
Also plotted on figure 6.2 is the
reconstructed profile at zero impact energy which has FWHM of 2.7nm and was
obtained as follows: A series of SIMS profiles of the 6 layer taken with primary ion energy, Ep, in the range 450 eV/O+ to 1.7 keV/O+ showed increasing asymmetry and broadening of the 6 profile due to atomic mixing and beam incorporation
along
with the differential shift (see Chapter 3.2a). Figures 6.3 and 6.4 show the dependence of the leading and trailing slopes, FWHM,
peak concentration and position on Ep. If the broadening and
processes are all linearly
shifting
extrapolated obtained.
to EP =0 However,
dependent on energy, these data may be
and the reconstructed this
reconstruction
in figure 6.2 shown
profile
constrains
the profile
shape to
exponential up and down slopes meeting at a cusp. It is impossible to determine how close this is to the true prorile.
It is likely that density renormalisation
(Collins intrinsically 1985), effects not et al,
dependent on EP, give rise to residual
broadening which makes the reconstruction a worst case. To investigate this further a series of profiles of a shallow (5 keV) boron implant in Si was taken over the same energy range as the delta. Assuming that incorporation by b limited the decay the mixing and profile was entirely slope on decay the to the slope of correct slope values at each energy were used effects,
58
the implant profile and extract its true magnitude. This process was found to give an implant
Ep, 450 independent that, of showing even at profile eV/O+ , the 6
prorde was entirely due the SIMS process. Hence the true width of the 6 layer is narrower than that obtained from the profile at EP = 450eV by an unknown factor 2, least by a of amount, probably i. e. the true width is < 2nm. at Subsequently
6 layers have played an important
elucidate the mass transport
role in attempting
to
inherent in SIMS the technique and it is processes
thought that they could offer advantages as calibration
standards compared to
ion implants (Dowsett et al, 1991). 1
20
FWHM 2-7nm
lo"
1ý8 V) 9 ru 17 10
16 10
5 101
0
-08
-04
-lz
wlb
Depth (microns)
Figure 6.2.
ions 450eV/0' layer at normal SIMS profile of aB5 obtained using impact incidence (full line) and the reconstructed profile at zero line). (broken energy 59
7 6 m u CLI 10
s
Ns E
4
ca. 0 V)
3 2
00
I 'IV
-I
olýl
Impact Enerqy (keV/O+)
Figure 6.3
Extrapolation of SIMS data to EP=O.
-115 _r_4C2. (V
':ýl 13 4
-111
0
0-5
1-5
1-0
2-2 0 m E L.1
LJ
0 UJ
r' 1-4 a
1-0 1 0
0-5
1.5 1.0 Impact Eneray(keV/C')
Figure 6.4
60
6.1b) XTEM To provide further was used. Preliminary 1XI013
-2nm
CM-2
information
on the 6 layer width cross-sectional TEM
analysis was performed on aB6
layer of areal density
(Mattey et al, 1990a). The 6 layer was seen as a dark line of width
in a bright field two-beam g=400 image. However some structure was
evident, possibly due to precipitation complete activation). uncertainty
(although Hall measurements suggested
The contrast mechanism was also the subject of some
(Whitehurst,
1989). Figure 6.5 shows the micrograph
a sample of the maximum
sheet density
(3.8xjOI4CM-2
from obtained
) examined in the (110)
direction using a many-beam overfocus condition to obtain sufficient contrast. The surface texture contrast is due to the ion beam milling used in the sample preparation.
The apparent width of the b layer is 2nm, however it is thought that
this is greater than the true width due to lack of contrast, stress in the film and Fresnel effects (Powell, Mattey, Kubiak, Parker, Whall and Bowen, 1991). There
is no evidence of any preciptates nor of any defects nucleating at the b layer density. dislocation lWcm-' limit the on of which places an upper
61
:
f.
.'. "T""
Is,,.
4.:
.
kl,
.1ý4
I
A.
IV
I
I
5 Layer
Figure 6.5. 3.5xlO"crn-'. density layer sheet of image a5 of TEM 62
6.1c) Double Crystal XRD More recently double crystal XRD was undertaken on a sample of sheet
density 3.8xlO"cm-' (Powell, Mattey, Kubiak, Parker, Whall and Bowen, 1991). Figure 6.6 shows the rocking curve obtained in the (113) direction,
the (004)
rocking curve was also obtained to enable the unambiguous determination of the degree of strain. The five peaks result from interference between the diffracted beams from the b layer and cap and the diffracted beam from the underlying Si. The sharpness of the peaks is indicative of good crystalline quality which suggests that the B layer is pseudomorphic direction
ie. tetragonally
in the growth contracted
(100). The depth of the b layer was determined
from the fringe
the in 2nm, found be 51 growth schedule to + with agreement good separation and 6.6 is in Figure the Also TEM. SIMS from shown and and the values obtained simulated
for the structure rocking curve
from inset, this in the and shown
1nm the limit of it is width on to further simulation of an upper place possible The date. to 6 layer is the thinnest reported the 6 layer, suggesting that this
0.002mm 0.031 be + found to which, direction lattice contraction in the (100) was for 0.7xlOF'3cm3 5.6 + the of density, a value of the calculation enables sheet given that in is This obtained B with agreement lattice value the contraction per atom. fully is 6 layer the that activated. B for activated suggesting
63
r
COUNT RATE (SEC'l) 70 -1
CONCENTRATION
60 1
50 40
DEPTH
30 201 Experimental 10
Simulation
-1000
ANGLE
0
(ARCSEC)
1000
Figure 6.6 XRD Rocking curve for aB6 layer of sheet density 3.5xlO"cm-'.
64
6.2 Electrical Properties
6.2a) C-V Measurements
To investigate further the structure of the 6 layer C-V measurements were undertaken. The sample configuration
in figure 6.7 shown was used to minimise
the effects of series resistance as the 6 layer is depleted (Van Gorkum, 1986). The two frequency technique (Chapter 4) was used to determine the true capacitance in the presence of any effects due to residual series and parallel resistances. Measurements were carried out at numerous frequencies of up to 5MHz to check the validity of this approach and to justify the assumption that the effect of deep states could be ignored. Initially
sputtered
Al was used as a Schottky barrier
with no post-
deposition anneal. Figure 6.8. shows a typical I-V characteristic,
C plots of
for d N V the a sample of nominal sheet versus versus and resulting values of density 2xlO"cm-'
is It that 6.10 6.9. in figures clear respectively. and are shown
hole due the to bias, is depleted of 6 layer presence the presumably at zero trapping structure
states at the metal/semiconductor it was necessary to drive
interface. In order to profile this
the junction
into forward
bias, with
Al The subject also were contacts conductance. consequent increase in parallel Si, into Al the diffusion the or viceof to ageing, possibly due to field enhanced the reducing whilst Any 1981). anealling, (Sze, post-depostion at attempt versa
increase the to interface tended ageing effects. due to depletion charge,
65
Despite the extensive literature on the subject (eg. Rhoderick, 1978) great difficulty
Schottky in barriers reliable producing was experienced on MBE-Si.
Sputtered Mo, Pt and evaporated Al and Au: Sb were investigated in combination with a number of pre-deposition cleans with little success. Sputtered titanium was found to exhibit
the same behaviour
as Al with no post-depostion anneal,
however a stable Schottky barrier was obtained following a ten second anneal at 550'C, presumably due to the formation of a titanium silicide. Figures 6.11. and 6.12. show the C-V characteristic nominal
-
2x1 density sheet
1-5xjOl2CM-2
012CM-1
and the resulting
for a sample of profile
The areal density of the C-V .
profile
of
FWHM The density. intended favourably the sheet compares with
description this 2.4nm is in the system of quantum mechanical of agreement with FWHM which predicts a
of - 3nm
by the 8nm to predicted as opposed -
it that interest is This (Wood). description expected since was of result classical (classical) larger the to predicted width. the observed profile would correspond The apparent discrepancy between the intended depth of 50rum and the due be to is to thought C-V from 32mn the depth profile observed of apparent
barrier. Schottky formation the in the silicide of the consumption of silicon Figure 6.13 shows a SIMS profile taken through the test structure and confinus that this is the case.
66
'Onm De-t
ý-0
+
nm
: uOETflTe
Ohmic
Figure
::, -nTGcT
6.7
Structure
used
for
C-V
measurements
3.
0
-10
-20
-30
40
-I
voýts Figure I-V
(V)
6.8 characteristic
for
S Al Ilchottlll -y barrier.
6.7
I. U
0.8
0.6 0
0
0.4 Ce 0
0.2
0.0 11111 0.0 -0.5 Figure 6.9.
0.5
1.0
2.0
1.5
2.5
3.0
Volts(V)
C-V characteristic using Al Schottky barrier. n19 II ki
10
18
1017
4-1
16 1n
0.00
0.05
Figure 6.10.
0.10 Depth
0.15
0.20
4 m)
Carrier profile obtained from figure 6.9.
68
0.25
U.
15U
vs Voltage
Capacitance
3
UC
U C C U C 0 0 (3
011ý,,
-0.5
I.
0.0
ýý.
11
0.5
1.0
Volts
Figure 6.11.
,ý.
,
2.5
3.0
ýV)
C-V characteristic using Ti Schottky barrier.
co 1-4 C z 0 P-ý E-
I . S
z z C
5-,
\
S S S S . -. --- S
el __Z I
0L
30
20
40
DEPTH(nm) Figure 6.12. Carrier profile obtained from figure 6.11.
69
50
10
23
I
CA
:2
10
22
10
21
is
CD 1--4 Z CD S. -4
to 10
20
10
19
17
Z Z
18 10
0.00
16 10
0.02
0.04
0.06
0.08
0.10
0.12
DEPTH (MICRONS) 12 2xlO
-2 Boron delta 20/7 with Ti cap. Sheet concentration cm FW'HM 8.5 mn. EVA 2000 SIMS primary ions 5 keV, 200 nA
+ 2
Figure 6.13. SIMS profile of sample used for C-V measurements showing relative depth of 6 layer.
70
6.2b) Transport Properties The degree of activation
of the B6
layers was investigated using Hall
measurements carried out at 4.2K (to freeze out parallel conduction paths) on inhouse processed Greek cross structures. It was found that complete activation was obtained interpretation
sheet densities
up to
(3.5+0.4)xlO"'cm-'.
However,
of the Hall measurements is complicated by the multi-subband although Eisele (1989) has argued that the measurement leads to a
conduction, minimum
for
value. The problem of the multi-subband
is discussed in conduction
more detail below. For a more thorough investigation of the transport properties Hall bars
of size 30,gm x 310/4m were fabricated from structures containing p' 6 layers in a p-
(1016Cm-)
background.
To ensure that the measured properties were due to
the 6 layer and not to any other effect, for example a surface inversion layer, test structures
containing
two 6 layers and with no 6 layer were measured. All
lVm-'. field less than of measurements were carried out with an electric -
Figures 6.14,6.15 for B6 T plotted verus 7.6xjO13CM-2
.
Hall 6.16 the coefficient show resistance and and layers of sheet density in the range 1.8xlO"cm-' to
The logarithmic
dependence between - 0.5K and - 20K is
(see localised 2D hole behaviour the carriers gas of weakly of a consistent with 0
Chapter 4. ). The behaviour above 20K is thought to be primarily due to the occurence of parallel conduction paths. According to theory (see Chapter 4), R7 is sensitive to both localisation interaction RHis to the mechanism. interaction only sensitive whilst effects and 71
For a single subband (the these expressions to multi-subband of relevance conduction is discussed below), ((1_3
bRo Ro
= -RD
14F*) - ap) e2 2!h 27c
In
kTc ýh
where F* is a renormalised screening parameter, r is the elastic scattering time, is p the temperature expononent of the phase breaking rate (ie. -r,,proportional to TP) and czis a phenomenological factor depending on the spin-orbit scattering rate. oz=l for no spin-orbit
scattering, oz=-1/2 for strong spin-orbit
scattering
(Altshuler et al, 1981). The Hall coefficient is given by, 6RH RH
e2 2RO
(1
27r2: h
_3
14F
*) In
-
kT-c
gli
BB
_F*G 2U 1)
G is due to the Zeeman spin splitting the term where containing
(6.2)
in the finite
magnetic field necessary to measure the Hall coefficient. The function G(X) >0 has two limits of interest (Burdis and Dean, 1988):
The Zeeman contribution
G(X)-0.091 X2 aS Xýo
(6.3)
x G(X) - ln as X-oo 1.3
(6.4)
is normally
ignored, but the present results were
be its 0.5T, hence field high effect should of magnetic obtained using a relatively 0.16)mo/2, (0.5 to + Taking corresponding a mediaii effective mass of considered. light hole heavy the effective massesq g/'BB/k and the mean of
72
2K and -
neglecting the Zeeman contribution results in an error of < 5% in r. Values of R.,
the measured sheet density, N, (= I/eRH) 9g
and the
extracted parameters F* and up at a temperature of 4K are presented in Table 1. Since it is expected that p-ý! (Fukuyama and Abrahams, 1983, Altshuler -l et al, 1982), the fact that up < 0.34 suggeststhe presence of spin-orbit scattering in these samples. As up decreases and becomes negative as Ns increases it seems that the spin-orbit
scattering is associated with the boron concentration in the 6
layer. The saturation of REj may be due to the dominance of spin-orbit scattering low temperatures, at
however this mechanism probably cannot account for the
saturation
of R,, which is associated with interaction effects. Furthermore,
behaviour
interaction (equation 6.2) be due Zeeman R,, to the term of cannot
the
in be is This terms of the explicable phenomenon may which of wrong sign. electron
heating
temperatures
due to a long
elect ron-ph onon scattering
time
low at
(Bishop et al, 1982).
The value of F* - 0.9 is not inconsistent with typically measured values is and approximately predictions
independent
is The (1981). Fukayama qualitatively present system of
from that of Kichigin
different
in (1984), a where very strong spin-orbit scattering et al
InSb/GaAs heterojunction -
in density the agreement with of sheet
led to a value of up=-0.5
V and a negative value of
fundamentally be this that may parameter suggesting -0.48,
altered by the
presence of strong spin-orbit scattering. It is not expected that the multi-subband
73
6 layers the will affect nature of
the argument, as it has been shown (Kearney and Butcher, 1988, lwabuchi and Nagaoka, 1989) that multi-subband systems can be treated through an effective renormalisation of the diffusion constant and the magnitude (but not the sign) of the prefactor
is incidentally, A reached, conclusion similar (x.
for multi-valley
systems, where this time g, oz(g, is the valley degeneracy) varies with the
intervalley scattering rate, 11,T, but always remains greater than unity. However, idea an of the subband structure,
including the
wavefunction widths
may be
obtained from the polygonal model discussed in Chapter 5.1. There is some uncertainty
as to the appropriate effective masses and band non-parabolicities in
the confining potential of the 6 layer, the situation being further complicated by the presence of strain. Nevertheless, taking the bulk effective masses at 4K as 0.531,0.234 I
0.153 for the heavy, spin-orbit and
light hole split and subband
Fermi lying below (EMIS, 1989), the those energy minima subband respectively 6.17. Hence in figure density the function doping values of sheet are shown as a of effective
diffusion
in Table I (Rcýe2N(EF))` D= were calculated shown constant
is I Fermi the is (kF (4, kF': the and wavevector estimated and values of rm*D)/h -": free path). elastic mean (Lee interaction localisation The conventional theories of weak effects and Ramakrishnan, and
1985) are derived under the assumption that
kFl
ý> >L
for be useful Morgan et al (1985) have argued that the predictions should also lower values somewhat
kFl
I,
however in the present case
Hall kFl the resistance and low values of conduction
kFl
Despite these -1.
data are indicative
transport the be activated contrasted with and should
below.
74
of metallic discussed
Table 1. Ru-]/kll
Ns/CM-2
(4K)
(4K)
(4K)
3.69
7.6x1()13
22
0.96
-0.14
1.2x10-"
41
0.85
0.01
7.5x10-5
0.69
3.4
38
0.88
0.34
6.6x10-5
0.61
3.8
6.76 9.4
2.3x10 1.8x
£/CM2V-1
13
1013
s-'
F*
75
up
D/M-2S-'
kFl
Width/nm
1.11
2.8
1.2
5.5 --1
111
5.0
1.0
4.5
er
C\2
0.9
4.0
0.8
3.5
,e v14r, 0.7
3.0 0R0
vRH
0.6 1 0.1
.5
10
T/K
Figure 6.14. Resistance, of sheet the
R density
temperture
and
Hall 13
1.8x1O range
coefficient,
cm
-2
plotted
0.3K to 30K.
76
R
of a sample H'
versus
Log T in
7.5
4.0
Ißep. lel% 0 7.0
3.5
F]
VVIVVVV v
C\2
vw V4
6.5
V
4m
3.0
vir
v v vvv
V V,f v
vv v- IV v
6.0
2.5
0
VRH
2.0
5.5 L 0.1
10
1
T/K
Figure 6.15. Resistance, of sheet the
R density
temperature
and 2.3xlO range
Hall
coefficient,
13
cm
-2
plotted
0.3K to 30K.
77
R
sample a of H'
versus
Log T in
9.0
3.88
3.84
VVV $V IF vv
Q)
8.5
Y) C\2
3.76
0 co
VV v
8.0
3.72 ,
68
7.5
El
3.64 ,
RH
7.0
10
0.1 T/K Figure 6.16 Resistance,
of
the
sheet
R
density
temperature
and F-] I
8xIO
range
Hall 13
cm
coefficient, -2
plotted
0.3K to 30 K.
78
RH'
versus
of
a sample
Log T in
EF 0 -2o -40 -60 -80
-100
-120
-140
-160
-180 Heavy
-200
Light -220
-240
Hole Hole
Spin-orbit
56
234
10
2D
13 cm
-2
FI_C'Ure 6.17. CaICLIlated function as c-A
subband
energies
of sheet
densitv. 79
for
B6
layers
Figures 6.18,6.19
and 6.20 show the magnet oresistance of the three
samples above at temperatures perpendicular formulae
of 1.3K, 2K and 4K with the magnetic field
and parallel to the b layer. It seems reasonble to use 2D transport
provided
the cyclotron
Lc=(h/2-xeB)"'
radius
confinement width, w of the 6 layer. From table Iwbehaviour
should
occur
for
B< 70T.
According
is greater than the
3nm and thus 2D
to theory,
the
parallel
magnetoresistance is soley due to a Zeeman spin-splitting effect in the interaction correction given by (Lee and Ramakrishnan,
-e
2 47r th
F*G
AR(B)
with
RE: 3(0)
This term should be proportional
1985),
(6.5) kT
(B) A -Rr-,
(6.6)
to B' at low magnetic fields and InB at high
fields, crossing over at Bc- kT/gAB (see equations 6.3 and 6.4). For g=2 and m* =0.33mo
B, amounts to 0.35T.
Calculated
values are compared to the
experimental values in table H with B=12 T and assuming F*=0.9.
The
theoretical values are too small by factors of between 1.6 and 2.1. Similar discrepancies were observed by Bishop et al (1982) for the 2DEG in the Si inversion layer. Putting g=3, as reported by Englert et al (1980) and using a but is this stretching smaller value of m*=0.16mo gives satisfactory agreement, the analysis. More significantly,
AR 11is not a universal function of B/T as shown
in rigure 6.21. The theory also predicts that the magnetoresistance will be anisotropic by interaction in An localisation terms the contributions. and orbital virtue of 80
estimate of the phase relaxation
time T. is required
,
taking
the result of
Fukuyama (1984),
FkT
(6.7)
4E F ln
The values shown in Table 11 are obtained and are in reasonable agreement with experunenta
values ofT,, quoted in the literature
(Uren et al, 1981) despite the
low values of EFr/h. The orbital terms are given by (Fukuyama, 1981, Isawa and
Fukuyama, 1984, Altshuler et al, 1980),
Aa (B)
e2a rl- 941 -+ 2th 2Tc
interaction the where orbital
factor94
+ -2i 4eDBT. 10
ln
4eDBr,,
(6.8)
0.1, is digamma function. D the and Ik -
and ozare obtained from Table I assuming p=1. Equation 6.8 should be valid for B< (h/8weDr) ie < 80T in the present case. Finally, AR-, (B)/R[j(0) is taken as the sum of the three terms. The calculated values predict considerable anisotropy,
However in by Table H, is an error experhnent. as shown which not supported in the calculated value of -r,,, which is certainly plausible, is sufficient to explain the difference between theory and experiment.
In summary, the above analysis gives order of magnitude agreement with the experimental magnetoresistance data. However it fails in important to account for the details of the parallel magnetoresistance,
temperature dependence.
81
respects
particularly
its
Table 11. Fractional
in field 12T increase temperature for in of at a an change resistance
of 1.3K.
Theory
Experimental Sample I
RE] (1.3K)
3.72 k f)
Interaction
(Zeeman)
0.078
Interaction
(Orbital)
2.5 10-3 x -
Localization
(Orbital)
0.025 0.10
0.12
AR ii /Rr7 (0)
0.078
0.12
TO s
9x
AR
I
/Rm(O)
10-12
Sample 2 7.4 kil
R ý] (1.3 K) Interaction
(Zeeman)
0.193 (_L) 0.194 (11)
Interaction
(Orbital)
4x 10-4
Localization
(Orbital)
3.6 10-3 x + 0.19
0.39
AR /Rr--
0.194
0.40
Ts
12 8x 10
/Rr-i
AR
Sample 3 11.7 k0
(1.3 K)
R
Interaction
(Zeeman)
0.33
Interaction
(Orbital)
0.025
Localization /Rr-, (0)
AR
AR /R, -- (0) s
(Orbital)
J 0.36 (11)
0.21 0.145
0.51
0.36
0.60
8x 10-12
82
3
Sample 1.9 Filled
1.8
symbols
Open symbols
B Perp. F7 B Parallel.
T- 1.3K
F7
T=2. OK
1.7
1.6
1.5
F-1 1.4 C-ý It CD
7
1.3
,19
D v
1
T=4. OK
ý
-" (-) 0 77
1.0
71 -ýý
y
/7
77
0.9
1iiIII 018
S"
'10
B/Tesla
Figure
6.. 18
Magrietoresistance
the of
83
sample
Figure of
6.14
11
12
SAMPLE 2. B Parallel 10.0
0 V
0
9.6 17 0
9.2
7D 17 0
8.4
8.0 07 F-I
0
T= 1.4K
'7
T=2. OK
11 T=4. OK
Ll -7
6 ,.
(1-7 El VEJ U--30/
B/T
Tesla
ICI
Figure 6.19. Parallel versus
ma.,anetoresistance B/T.
84
for sample
2. plotted
A more promising
explanation
of the magnetoresistance
results would
appear to be found in the concept of wavefunction shrinkage (Shklovsku and Efros, 1984). It is believed that field induced metal-insulator a magnetic transition to a strongly (ie. exponentially) localised state has occurred. Transport at the highest fields is then by 2D variable range hopping,
for which Usov,
Ulinich and Grebenschikov (1982) write,
(6.9)
ao exp _(To) T
with
eB To = N(EF)kh 0
where N(EF) is the density of states at the Fermi level. The resistance in a field parallel to the 2DHG is plotted versus B"' in figure 6.20.
Linear behaviour is
observed for high fields, the gradient increasing as the temperature is lowered. This is explained by noting that the condition for applicability
of equations (6.9)
and (6.10) is L2
(6.11)
a
85
where R is the hopping distance Lc is the cyclotron radius and a is the radius of
the wavefunction in zero field. Following Mott's original analysis (1968) for variable range hopping gives,
kT (Ef) nN
(h)
B>
(6.12)
4
2a
v-1 M-2. From the slope of the plot at 1.3K - figure 6.20 N(EF) -= 4x eFigure 6.21 shows In R plotted versus T"' between 0.5K and 4K from which N(EF) - 4.5 x 10'0 eV-1 m-2 is obtained, in satisfactory agreement with the 1020
analysis of the magnetoresistance isotherm. A possible explanation of this result is as follows: Presuming
impurity
Hubbard bands at B=0.
band conduction
is occuring,
shrinkage which splits the bands and gives rise to hopping. 14
is both Mott and Anderson localisation.
Hubbard bands, N(EF) -
4neN,, le
between
this
constant
is expected
dielectric
value
2
catastrophe
ýhIVSýffo
concentration
for the large discrepancy
large near a metal-insulator Obtaining
1991).
and
12 for Si N(EF)
1983). With Er
fact is that the one
and the experimental
(Mott,
In other words there
is the absolute permittivitY where E 9
A possible explaination
to be very
g
For a relatively small splitting of the the
N. is the acceptor sheet density (Schklovskii, is 4x 1018 eV-' CM-2 obtained. -
overlappi
of a magnetic field leads to wavefunction
Application
1/2
with
a
from
the dielectric transition
the
--the
expression
in low boron the ionization 45 EO the of energy meV, = with
it is found N(EF) that limit and using the experimental valve of
for B> be (6-10) applicable should equation
to obtain a sensible result. are needed
93T! ie. much larger values of a
This is quite consistent with what has
86
been stated above. In the by be localisation replaced a present picture a should length Z which tends to infinity as the transition from an insulator to a metal approaches (Mott and Kaveh, 19859write a/t = const (Ec-E)' as E --oEc from below with s-
1).
Similar analyses may be carried
for 1 2 out samples and as shown in
figures 6.22 and 6.23, but the critical field Bc for onset of this behaviour seems to be higher in sample 1 (table 111) as expected from equation (6.10).
The
decrease decreases, 1.3K RE] be this gradients at as attributed to the greater may increases. Hubbard bands Ns overlap of as
0
87
Table III
Slopes and Critical
Fields of LnRO versus B" plots
Sample No
Slope/T-'
Bc/T
Temp/K
1
0.056
7.8
1.34
2
0.16
4.8
1.4
3 11
0.24
4.8
1.3
1
88
1
1
0.65
T= 1.3 K 0.60
B Parallel
0.55 0.50 0.45 T=2. OK
0.40 F7 C:
0.35 0.30
El
0.25 0.20
T=4. OK
F-1 0
0.15
.
0.10 0.05
.
/ .
0.00
v
V
n n,5
0.0
0.5
1.0
2.0
1.5
(B/Tesla)
2.5
3.5
3.0
1/2
Figure 6.20.
Ln R density the
versus
plotted F-I 1.8xIO
magnetic
13
cm
-2
B R
1/2
F-I
field.
89
for
is the
the
sample
resistance
of sheet and
B is
SAMPLE 3.
D.9
1.8
17
9.6
-
J. .
D.3
0.2
0,
-
tz
1.0
(T
Figure
6.2-1. -I/I:
Ln R versus 13
1.8x10
KI)
cm
T'
)
B= at
-2
90
122T for
the
sample
of sheet
density
Sample
2.
2.35 T= IAK
2.30 T=2. OK 2.75
2.20 T=4. OK C
2.15 I
2.10 a.
05 2.
.
1
00
5 ', -9 0.0
0.5
1.0
10
1.5 (B/Tesla)l
3.0
of sheet
density
/2
6.22'
Figure ýn
Ln R versus 13
2.3xlO
2.5
T
for
the
-2
cm
.
91
sample
3.5
Sample
1.
1.45 B Perpendicular
T- 1AK
T-2K
1.40
T=4K
0 17
1.35 '7 0
77
i -ýn
0.0
0. -lý
2.5
1.5 .12.0
11.0
(B/Tesla)
3.0
1/2
FIgure 1/2
Ln R versus 13
8-KIO
cm
B
for
-2
92
the
sample
of sheet
density
3.5
Figure 6.24 shows a log-log plot of the sheet resistance REDof 6 layers having sheet carrier densities in the range 4x 1012 to 3.5xlOI3 CM-2 The rapid rise . in R. for sheet densities below transition with Nc -
IX1013CM-2
1013 CM-2
provides evidence for a metal-insulator
The electrical properties .
of ab layer of sheet
density 9x1011CM-2 are thus of particular interest. In this case the background doping is n-
(_
1015CM-3)
The measured Hall mobility .
temperature of 300K is 30 +5
in the layer at a
cm' V-s-', which is somewhat lower than the
figure of 53cm 2 V-1s-1(Kubiak et al, 1987) obtained in uniformly
of the equivalent doping concentration (ie. WO" structure
CM-3)
(Figure 6.17) suggests that the confinement
doped MIBE Si: B
The calculated subband . splits the valence band
degeneracy and lowers the energy of the ground state heavy hole subband with respect to that of the light holes. A shnilar result was reported by Bangert, et al (1974) for a p-type Si inversion layer. It is therefore possible that transport in , heavy-hole states dominates, with a consequent increase in effective mass and in scattering as compared to bulk. Figure 6.25 shows the variation temperature.
of the conductivity
Assuming the conductivity
layer this of with
is due to a series of exponential terms
fitted data factors to, the were ai, with activation energies Ejand pre-exponential -ei
3
ae
The resulting values are given in table IV:
93
kT
(6.13)
Table IV Pre-exponential factors and activation energies obtained from fitting the data of
Figure 6.25 to equation 6.13 ori/10-1
fl-I
23.1+0.40
iEi/meV 20+0.3
2
1.80+0.10
0.76+0.02
3
1.79+0.09
0.58+0.03
94
At the highest temperatures E, is indicative of the excitation of holes into the valence band, from which it is concluded that EF lies in impurity states. For temperatures
below - 70K impurity
conduction
is dominant.
The activation
energy 'E2is taken as evidence for transport in an upper Hubbard (A') band is whilst 'E3 thought to be associated with nearest neighbour hopping in the lower Hubbard (A) band. The observation of conduction in the A' band together with the low values of activation energy suggests that the impurity
separation in this
sample is close to, but above, the critical value for the metal-insulator
transition
(Mott and Davies, 1979). In uniformly
doped Si: B the onset of metallic behaviour occurs at an
impurity average
separation of 3.5nm (Chroboczek et al, 1984), whereas the
average impurity
in the 6 layer is 2.2 + O.Imn, as deduced from the separation
peak concentration .
of the SIMS profile
(2.2 x 10'9 cm-'), itself an underestimate.
This discrepancy cannot be explained by broadening of the 6 layer during Hall bar
fabrication.
primary
Resolut ion- limited
SIMS
ions) showed, to within experimental
measurements
(using 2.2keV/0'
in the profile change error, no
is broadened it is layer Thus, deduced to a maximum that the after annealing. FWHM
of = 5um
implying
Gaussian impurity assuming a
impurity in increase the average an profile,
separation,
to = 2.9nm which is still significantly
below the predicted critical value.
Similar behaviour has been observed in Sb (Van Gorkum. et al, 1989) and does the In transition 1989). the Si (Denhoff at in occur b As layers contrast et al,
1989). (Qui-Yi GaAs in Si b-layers for impurity al, et separation predicted Theoretical work on the Mott transition
95
(Krieger and Nightinggale,
1971,
Martino et al, 1973) has shown that the critical separation R, depends on carrier by the charge carriers. effective mass and on the number of valleys populated
It is therefore Possible that the observed decrease in R, in b doped Si: B is due to due degeneracy to the the carrier confinement, which splitting of valence-band is also suggested by the low value of the room temperature Hall mobility.
0
96
9
8
7
6
0
4
-?
.
ýj-,) Loglo
Figure Log-Log density
14
N. S/cm
15
-2
6.24 plot for
of' resistance Si: B 6 layers.
97
8K versus at
sheet
carrier
10
-IE 13
b
4
2 so
100
150
200
T/ K
Figure 6.25. 6 layer Si: B dependence of Temperature of the conductivity of an 9xlO"cm-'. density sheet
98
250
Chapter 7.
CONCLUSIONS
AND FURTHER WORK
MBE has been used to produce the first reported B6 layers in Si. From the analysis of SIMS data taken over a range of primary concluded that the FWHM
ion energies it is
of as grown Si: B 6 layers is
