Bulk growth of GaAs An overview

Abstract

The III–V compound GaAs is of rising importance for opto- and microelectronics, especially, for LEDs and LDs and for high-frequency devices like HBTs, HEMTs and MMICs, respectively. The device performance and degradation mechanisms are critically influenced by bulk properties. Hence, considerable efforts are aimed at a reduction of crystal imperfections and improvement of the uniformity of physical properties connected with the need to increase the crystal diameter. This goal is not easy to attain because of the well-known proportionality between crystal diameter and dislocation density. The efforts focused on a reduction of the dislocation density (below 104 cm−3 at least) by reducing the non-linearities of the thermal field in LEC growth have led to the development of fully encapsulated and vapour pressure controlled Czochralski method (FEC and VCZ, respectively). A second line to the same objective has been the improvement of the vertical Bridgman (VB) and vertical gradient freezing (VGF) methods to commercial maturity. The state of art, pros and cons, and the developments of the growth methods to be expected in future are summarized in the present paper. Some fundamental problems of heat transfer, dislocation dynamics (polygonization) and non-stoichiometry related growth phenomena are discussed more in detail.

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*Corresponding author. Fax: #49 30 6392 3003; e-mail:
pr@ikz-berlin.de.
Journal of Crystal Growth 198/199 (1999) 325—335
Bulk growth of GaAs An overview
P. Rudolph*, M. Jurisch
Institute of Crystal Growth, Rudower Chaussee 6, D-12489 Berlin, Germany
Freiberger Compound Materials GmbH, Am Junger Lo(we Schacht, D-09599 Freiberg, Germany
Abstract
The III—V compound GaAs is of rising importance for opto- and microelectronics, especially, for LEDs and LDs and
for high-frequency devices like HBTs, HEMTs and MMICs, respectively. The device performance and degradation
mechanisms are critically influenced by bulk properties. Hence, considerable efforts are aimed at a reduction of crystal
imperfections and improvement of the uniformity of physical properties connected with the need to increase the crystal
diameter. This goal is not easy to attain because of the well-known proportionality between crystal diameter and
dislocation density. The efforts focused on a reduction of the dislocation density (below 10cm\ at least) by reducing the
non-linearities of the thermal field in LEC growth have led to the development of fully encapsulated and vapour pressure
controlled Czochralski method (FEC and VCZ, respectively). A second line to the same objective has been the
improvement of the vertical Bridgman (VB) and vertical gradient freezing (VGF) methods to commercial maturity. The
state of art, pros and cons, and the developments of the growth methods to be expected in future are summarized in the
present paper. Some fundamental problems of heat transfer, dislocation dynamics (polygonization) and non-
stoichiometry related growth phenomena are discussed more in detail. 1999 Elsevier Science B.V. All rights reserved.
PACS: 81.81.05.Ea; 81.10.Fq
Keywords: GaAs; Crystal growth methods; Temperature field; Defects
1. Introduction
There are two key application branches of
GaAs —high-frequency microelectronics and opto-
electronics. The growth technologies for single
crystals to meet the needs of these two application
fields have diverged. Whereas microwave devices
require high-purity quasi-undoped (EL2 and car-
bon controlled) semi-insulating (SI) wafers, op-
toelectronic devices require n>(usually, Si-doped),
i.e. semiconducting (SC) substrates. In the first case
the growth from an As-rich melt is required, main-
ly, by using the well-established inert gas pressur-
ized liquid encapsulated Czochralski (LEC)
method constituting nearly 92% of all industrial
supplied SI GaAs substrates (nowadays, the re-
maining 8% are produced by vertical Bridgman
(VB) or vertical gradient freeze (VGF) methods).
0022-0248/99/$ —see front matter 1999 Elsevier Science B.V. All rights reserved.
PII: S 0 0 2 2 - 0 2 4 8 ( 9 8 ) 0 1 2 0 8 - 1

On the contrary, optoelectronic material is usually
grown from uncovered near-stoichiometric melts
under ca 0.1 MPa controlled As pressure by the
old-established horizontal (HB) or vertical
Bridgman (VB) techniques. Due to the rapidly
rising interest in SI GaAs wafers for important
global electronic applications, the present paper
deals as a priority with the crystal growth issue in
this area.
The market share of low-voltage GaAs ICs is
expected to increase from 2% in 1996 to 5% in
2001 in comparison to silicon [1]. It is accom-
panied by the demand for lower specific costs per
die in device manufacturing which requires from
the point of view of a crystal grower, optimization
of presently used crystal growth and wafer produc-
tion technologies as well as the transition to
150 mm (6) SI GaAs crystals with new equipment
and technologies. It has to be noted that, similarly,
the forecast of the optoelectronic market shows
a doubling of LED and LD production until 2001
requiring a marked increase of productivity of SC
GaAs wafers too. At the same time, except for costs,
the requirements of the users concerning device
relevant wafer properties will increase additionally.
Obviously, these requirements depend on device
physics and manufacturing technology.
Considering SI GaAs it should be mentioned
that presently about 66% [1] of the total semi-
insulating wafer area is processed using ion im-
plantation for FETs-fabrication, the remainder by
different epitaxial techniques for heterostructure
devices like HBTs with MBE and MOCVD hold-
ing the lead. The central parameter of an FET is the
turn-on threshold voltage (») the fluctuations of
which across a wafer must be minimal for ensuring
high yield of devices. » is proportional to the
channel carrier concentration given by the differ-
ence between the concentration of the implanted,
electrically active donor and that of the net shallow
acceptor which on its part is related to the electrical
resistivity of the SI substrate. The implantation
efficiency is known to be determined by the concen-
tration of boron and the mid-gap donor EL2.
Moreover, an influence of As precipitates on thre-
shold voltage seems to exist. Accordingly, high uni-
formity of EL2, carbon and background impurities
and by this way of electrical resistivity across a cell,
the wafer and along the crystal and a high repro-
ducibility of the specification among the boules
are of crucial importance. Because of a tight
connection between cellular structure and
local uniformity this implies a homogeneous dislo-
cation density and cellular structure as well as
a control of arsenic precipitates across the wafer
and along the boule. Presently, average dislocation
densities (10cm\ are accepted for this class of
devices.
Compared with this, the requirements on wafer
homogenity for epitaxy-based devices are believed
to be lower. This is related to the commonly used,
manyfold proved practice to suppress influences of
substrates on yield and performance of epilayer
devices by buffer layer structures. Nevertheless, it
was shown that serious wafer-induced imperfec-
tions like threading dislocations are generated in
epilayers responsible for a degradation of devices
produced. Therefore, a low and homogeneously
distributed dislocation density is increasingly im-
portant for these devices too. Moreover, it is a pre-
requisite of epitaxial technologies that wafers have
to be produced with a well-conditioned epi-ready
surface. As for ion implantation, a high thermal
stability of the structural defects, low level of resid-
ual strain and high mechanical strength have to be
ensured to reduce breakage possible on handling in
the device production line.
In the case of SI material the efforts are aimed
first of all at perfection of the LEC technique to
guarantee, at least, that the 4crystal qualities are
transferred to the 6production. But also modified
Czochralski techniques, like VCZ (Section 3.2), are
of increasing interest in order to reduce the as-
grown thermoelastical stresses and parameter in-
homogeneities. A second line to the same objective
has been the improvement of VB and VGF
methods to commercial maturity.
2. Bulk growth methods-pros and cons
2.1. Liquid encapsulated Czochralski (¸EC)growth
Adapted to GaAs by Mullin et al. [2] the LEC
method is nowadays the most widely used growth
method for SI GaAs crystals. Comprehensive
326 P. Rudolph, M. Jurisch /Journal of Crystal Growth 198/199 (1999) 325–335

reviews of the method are contained in Refs. [2,3].
The method has matured to grow huge single
crystals up to 6in diameter from melts up to about
28 kg [4] using multi-heater growth furnaces in-
cluding after heater for controlled cooling down of
the crystals. Crucibles from high-purity pyrolytic
boron nitride (pBN) which are (multiply) reusable
[5] are applied without exception. The growth is
performed mainly in an argon atmosphere at about
2 MPa. But low- and medium-pressure versions are
used, too. Recently, some structural improvements
were demonstrated by using pressures below
1 MPa [6]. To define the electrical resisitivity of the
material and to compensate for macrosegregation,
crystals are grown under carbon- and (limited)
EL2-control. This implies the establishment of re-
producible initial conditions for growth by opti-
mized evacuation and purging procedure of the
growth chamber, heating up, melting and hom-
ogenization of the charge. The carbon content is
controlled by the (initial) water content of the
boron oxide and a proper CO fugacity of the
growth atmosphere in the course of the growth
process [7]. The EL2 is mainly defined by ingot
annealing.
The advantages are (i) a free growth without
container contact, (ii) circular cross section, (iii) use
of the gettering ability of boron oxide to influence
background impurities, (iv) “conditioning”of the
melt by its defined overheating before dipping,
(v) carbon control. The problems arising are (i)
stoichiometry control due to uncontrolled gallium
and arsenic losses through the boron oxide encap-
sulant, (ii) selective As evaporation of the crystal
surface emerging from the encapsulant resulting in
Ga droplets or trails which reduce yield, (iii) high-
temperature non-linearities (typically, temperature
gradients as a rough measure for non-linearities in
the temperature field are 100—150 K/cm) in the
growing crystal near the solid—liquid-phase bound-
ary and at the emerging region resulting in a rather
high and inhomogeneously distributed dislocation
density in the range (0.5—1);10cm\, (iv) un-
steady and forced convection in the melt and
turbulence in the gas phase causing dopant
inhomomogeneities and fluctuating temperature
and stress fields in the growing crystal, (v) high
investment and process costs, and (vi) necessity of
a post-growth multi-step heat treatment in order to
improve the residual stress level and homogeneity
of the electrical properties.
2.2. Vapour pressure controlled Czochralski
(VCZ) method
A powerful method to realize more homogene-
ous temperature fields with low-temperature gradi-
ents in the range 15—35 K/cm in a Czochralski
growth system for 4—6diameters is the VCZ
method. The main constructive feature is the pres-
ence of an inner chamber leading to the shielding of
the growing crystal and hot gas from the water
cooled walls of the outer high-pressure vessel and,
therefore, to the promising precondition of mark-
edly reduced temperature gradients in axial and
radial directions. In order to avoid the decomposi-
tion of the very hot crystal surface by arsenic dis-
sociation and formation of Ga trails as the crystal
emerges through the top of the BOlayer a tem-
perature controlled As pressure within the inner
chamber is maintained during the whole growth.
The inert gas pressure and boron oxide encapsulant
are still employed allowing a quite accurate
stoichiometry control by use of slightly As-rich
presynthesized GaAs starting charge. VCZ has
been developed and introduced into industrial
practice (for InP) in Japan [8,9,57]. Concerning
GaAs, 3—6SI crystals have been successfully
grown at the R&D stage too. A review of VCZ
development and results are given in Ref. [10]. The
main advantages are: (i) reduced thermal stresses
leading to a reduced dislocation density
()10cm\), a more homogeneous distribution
and a larger cell size across the crystal, (ii) mirror-
like surface of the crystal indicating a
near-stoichiometric composition and leading to
increased yield, (iii) low level of residual strains.
Disadvantages are: (i) difficulty of visual process
control, (ii) control of carbon content, (iii) relatively
high complexity of the equipment and therefore
increased investment costs, (iv) enlarged process
time and high operational costs.
Nevertheless, VCZ is one of the most promising
techniques for a constraint-free crystal growth of
GaAs with large diameters in a “tailored”temper-
ature field to ensure minimal thermally induced
P. Rudolph, M. Jurisch /Journal of Crystal Growth 198/199 (1999) 325–335 327

stresses that is of interest for HBT production, for
example.
2.3. Fully encapsulated Czochralski (FEC) growth
Aimed at a reduction of stress level during
growth, especially at the contact boundary between
the crystal and BOsurfaces, and avoidance of
selective As evaporation from the free crystal sur-
face, the full encapsulation of the growing crystal
by boron oxide was used to grow SI GaAs single
crystals by Nakanishi [11,58] for the first time in
1984. Newer results are described by Elliot et al.
[12]. A significant lower dislocation density could
be demonstrated. Encouraging electrical properties
were observed. Main problems, however, concern
limitations in length and diameter of the crystals as
well as the control of the carbon content. Therefore,
this method did not prevail in large-scale industrial
production.
2.4. Hot wall Czochralski (HWC) technique
Early in the history of GaAs crystal growth
HWC systems were used by Gremmelmaier [13],
Steinemann and Zimmerli [14], since they are ca-
pable of a reversible in situ control of stoichiometry
via the total As pressure in the growth chamber
neglecting the low Ga pressure at melting temper-
ature. A gas-tight growth chamber with hot walls
requiring additional heating above the As source
temperature, an arsenic source the temperature of
which must be carefully controlled at about 620°C
and feed through mechanisms for translation and
rotation of seed and crucible are the most impor-
tant ones of the complex ingredients of a HWC
system. An advanced electromagnetic levitation
system has been used [14] for seed and crucible
motion without any mechanical leads. Due to the
much lower-temperature gradients inherent to the
hot wall system low dislocation GaAs crystals have
been grown as demonstrated by Tomizawa et al.
[15] and Nishizawa [16]. Even dislocation-free
samples with diameter (15 mm were reported
[14]. But there are serious technical and scientific
disadvantages of the method preventing its applica-
tion in industrial production until now: (i) complex,
difficult to solve system requirements, (ii) pressure
control inside and outside the growth chamber,
(iii) difficulties to control stoichiometry due to tem-
perature gradients across the free GaAs melt sur-
face, (iv) control of carbon content and suppression
of background impurities, (v) high investment and
operating costs.
2.5. Horizontal Bridgman (HB) technique
The HB method has been established decades
ago, for GaAs single crystal growth by Folberth
and Weiss [17] in 1955. Pretreated (sand blasting
or etched) quartz boats as well as pBN boats are
used today in order to decrease the interaction
between melt and container, i.e. dislocation density.
More details are given in review [18], for example.
The major advantages are: (i) no encapsulant not
only avoiding thermal stresses, but also allowing
for a precise control of stoichiometry, (ii) free
growth of upper region and (iii) relatively low-
temperature gradients in the solid adjacent to the
solid—liquid interface which result in a low disloca-
tion density of about 10cm\. The HB is still
today the most applied production method for
Si-doped SC material for optoelectronics. Main
disadvantages are: (i) the non-circular (D-shaped)
cross-section making adaptation to device manu-
facturing difficult and leading to significant techno-
logical waste when circular wafers are produced
and (ii) the limited width of the shoulder which
amounts to about 75 mm allowing up to 2
wafers
at maximum in regular production. This diameter
is insufficient for the production of laser arrays.
2.6. Vertical Bridgman (VB) and vertical gradient
freezing (VGF)
Although first attempts to grow GaAs crystals by
the VB method were published already in the 1960s
this technique has been rediscovered for the prep-
aration of low dislocation III—V materials in the
late 1980s initiated by the publication of Gault et
al. [19]. In the meantime it has prevailed in indus-
trial crystal growth of SI GaAs. The growth of 3to
6crystals has been reported [20,21,41,59]. The
dislocation density is in the range from 500 to
5000 cm\. The dislocations are likewise arranged
in a more or less distinct cellular structure, but the
328 P. Rudolph, M. Jurisch /Journal of Crystal Growth 198/199 (1999) 325–335

Table 1
Comparison of industrially applied bulk growth methods for GaAs
LEC VCZ HB VB/VGF
Scientific/technical features
Capability for low
dislocation density
Poor Good Very good Very good
Uniformity of
dislocation distribution
Moderate Good Good Good
Cell, cell size Small Large Very Large Very large
C-Control Very good Not solved Poor Not solved
Stoichiometry/EL2
control
Good Good Poor (?) Very good
Crystal length Very good Limited Good Good
Crystal diameter Very good Very good Limited Very good
Background impurities Low Low Low Low
Technical realization Good Possible Good Good
Commercial features
Investment cost High Very high Low Low
Operational cost High High Medium Low
Process maturity Very high Low High High
Productivity High Medium Medium Low
Fields of application le-devices/implantation le-devices/implantation,
LEDs
LEDs, LDs le-devices/expitaxy,
LED, LDs
cell size is significantly larger. Equivalent to
LEC material supersaturated As in as-grown
crystals is mainly precipitated at dislocations
with a larger particle size due to much fewer nuclea-
tion sites. Without an additional heat treatment the
EL2 concentration is lower as compared to LEC
GaAs. The homogeneity of the electrical properties
of VB/VGF crystals seems to be comparable
to LEC-material, at least after annealing, but
no details about the annealing procedure are
available yet.
Earlier problems with reduced single crystalline
yield and crystal quality which were mainly at-
tributed to the melt-crucible contact and the re-
lated mechanical stresses due to adhering parasitic
nucleation have been successfully solved by the
application of pBN crucibles. The crucibles are
either heat treated to form a protecting skin of
boron oxide or the melt-crucible contact is sup-
pressed by boron oxide encapsulant.
Advantages of the VB/VGF method are: (i) pro-
duction of almost cylindrically shaped crystals up
to 6at the moment, (ii) low thermal gradients
resulting in low residual strains and low dislocation
density, (iii) approximately uniaxial heat and mass
flow, (iv) optional control of stoichiometry by
a separately heated As source, (v) possibility of
a post-growth heat treatment in the growth equip-
ment, (vi) compared to LEC lower investment costs
even if multi-heater systems are involved. Problems
are caused by (i) no visual control of growth, (ii)
difficulty of carbon doping and carbon control, (iii)
increase of crystal length, and, maybe, (iv) purity.
Supported by the existing literature it can be
concluded that VB/VGF is one of the most promis-
ing methods for semi-insulating and semiconduct-
ing GaAs crystal growth in future.
Table 1 summarizes the main features of the bulk
crystal growth methods for GaAs mentioned
above. According to the authors opinion LEC will
remain the leading method for mass production of
SI GaAs wafers, especially for ion-implantation-
based device technologies, but the share of SI GaAs
wafers with reduced residual stresses and disloca-
tion density produced by VCZ or/and VB/VGF is
expected to increase continuously.
P. Rudolph, M. Jurisch /Journal of Crystal Growth 198/199 (1999) 325–335 329

3. Selected fundamental problems to be solved in
future GaAs bulk growth
3.1. Heat transfer and thermomechanical stress
It is experimentally (e.g. Ref. [22]) and theoret-
ically (e.g. Ref. [23]) well established that indepen-
dent of the growth method used the density and
distribution of dislocations in melt grown crystals
are due to a thermoplastic relaxation of thermally
and, to a much lower extent, constitutionally in-
duced stress during growth. But the extent of relax-
ation depends on the growth method used: the
longer the resting time at high temperatures
(VCZ/VB/VGF) the lower the residual strain level
(as an example, typical strain levels are: 6LEC:
1;10\,6VCZ: 5;10\,4VB: 3;10\ [8,57]).
Therefore, the content of dislocations is deter-
mined by the (time and space dependent) stress level
during growth and the thermophysical and mechan-
ical properties of the solid. The level of thermal stress
(and its local and temporal fluctuations) is unam-
biguously related to the temperature field (including
its fluctuations) in the crystal during growth and
cooling-down procedure. Hence, the knowledge
and control of the temperature field at all process
stages are of essential significance. Due to the diffi-
culties of experimental determination the numer-
ical simulation is of increasing importance for heat
flow analysis and “tailoring”. Today, it is a power-
ful tool supporting efforts to reduce stress in a given
growth system if verified numerical models are
available. Two approaches have been used so far:
1. Calculation of thermoelastic stress field (linear
theory, isotropic and anisotropic analysis) of crys-
tal for a given temperature field using available
computer packages and comparison (of the re-
solved shear stress in the glide systems or the von
Mises invariant) with the critical resolved shear
stress (CRSS) taking into account its temperature
dependence known from high-temperature creep
experiments (p!011 [kPa]"22.72 exp(4334.0/¹)
[24]). The (local) dislocation density can then be
concluded from a dislocation density parameter
p [25] given by p"
"pC
G"where
pC
G""p01G"!p!011 for "p01G"'p!011,
0 for "p01G")p!011,(1)
i.e. maximum stress at any time of the growth
determines the local dislocation density. Examples
of this approach for LEC and VB/VGF growth can
be found in Refs. [26,27].
2. Estimation of the local dislocation density
from the constitutive law linking the plastic
shear rate and dislocation density with the applied
stress in the course of the cooling down procedure
of the crystal. The constitutive law for SI GaAs
reads [28]
de/dt"ob»(q!D(o)Kexp!Q
k¹, (2)
where ois the density of moving dislocations, bthe
Brugers vector (0.4 nm), »a preexponential factor
(1.8;10\ mK>N\Ks\), mis a material con-
stant (1.7), Qthe Peierls potential (1.5 eV), Da para-
meter relating oand q(3.13 N/m) and q is the
applied stress. Details of this approach can be
found in Refs. [29—31], for a profound review see
Ref. [32].
The temperature field in the crystal during
growth necessary for a stress analysis can be experi-
mentally determined or calculated from local or
global models of the growth system as reviewed in
detail by Dupret and van den Bogart for Czoch-
ralski and Bridgman growth [33].
In LEC growth of GaAs at medium and high gas
pressures convection in the gas phase apart from
conduction and radiation is known to influence the
heat balance significantly and must be included in
the model. But due to the large geometrical dimen-
sions and high-temperature gradients in an indus-
trial LEC system resulting in very large Rayleigh
numbers ('10for the gas phase) this convection
is turbulent and therefore difficult to model. Turbu-
lent convection in the gas phase has been included
only recently [34,35] for a 2-D system by using the
approach of effective turbulent viscosity and ther-
mal conductivity in the corresponding con-
servation. The so-called k—emodel was used as a
turbulence model [36,37]. Convection in the melt is
assumed to be laminar. In fact, it has been demon-
strated that models neglecting gas convection
cannot predict accurately the thermal field in the
growth system. The calculated power consumption
of a LEC system was shown to be in reasonable
330 P. Rudolph, M. Jurisch /Journal of Crystal Growth 198/199 (1999) 325–335

agreement with experimental data which justifies
the model and enables to do at least trend analysis
if geometry, etc., is changed [35]. But much work
has been left to improve the physical model and its
numerical realization.
As in LEC models which involve radiation and
(effective) heat conduction in the gas phase only,
a (absolute) maximum of stress is found in the near
surface region of the crystal where it emerges from
the boron oxide encapsulant (e.g. Ref. [23]) as well
as from the crucible [37], i.e. in regions of discon-
tinuities of radiative heat flow. The stress peak at
the boron oxide decreases when the crystal grows
which is due to the decrease of the melt height and
a reduced radiative heat transfer to the surround-
ings. The thicker the boron oxide layer the lower
the stress level at emergence. Stresses are minimal
in a circular region around R/2, (R—radius) of the
crystal and slightly increase in the center which
results in an W-shaped distribution. In Ref. [37], it
was shown that the stress maximum in the centre of
the crystal increases relative to the near-surface
maximum with increasing length of the crystal.
Generally, the total stress level increases with in-
creasing diameter of the crystal. If, as usual, the
solid—liquid interface is convexly curved indicating
radial temperature gradients, a second maximum of
stresses is observed at the interface near the periph-
ery [23,38]. A concave part of the interface was
shown to enhance considerably the stress level
[39]. As concavity of the interface increases with
growth rate there is an influence of growth rate on
stress level at the interface, too.
As a result of this type of analysis it became
obvious that the LEC method is characterized by
a higher stress level as compared to the other
methods. As radial gradients are inevitably neces-
sary in unconstrained meniscus controlled methods
like LEC and VCZ to attain a responsive diameter
control there exists some kind of lower stress level
and a corresponding dislocation density which can-
not further be reduced.
By contrast, in VB/VGF growth, the crucible
confines the crystal which assures diameter control
and permits to reduce temperature gradients and
non-linearities of the thermal field by more than an
order of magnitude as compared to LEC growth
without the limitations mentioned above. But as
VB/VGF is usually realized by imposing small
axial temperature gradients on the cylindrical
boundary of the crucible, by the furnace system
there exist radial gradients, too, manifesting them-
selves by a curved solid—liquid interface and ther-
mal stresses in the solidified crystal. As
demonstrated, e.g. in Ref. [40] using the “static”
thermoelastic approach mentioned above the cal-
culated dislocation density parameter is maximal at
the periphery of the crystal and its distribution
corresponds rather well with measured etch pit
density across a 3wafer. The stress level strongly
depends on the prescribed axial temperature gradi-
ent and increases monotonically with increasing
diameter of the crystal. To give an example,
p"20 MPa has been obtained at the periphery
of a 3VGF GaAs crystal grown at —5 K/cm in the
solid which is comparable to the peak stress found
for LEC growth [37]. But if the prescribed gradient
is reduced to 2 K/cm p"0 is found in the central
part and the boule there becomes almost disloca-
tion-free illustrating the potential of VB/VGF
growth. Even fully dislocation-free crystals seem to
be possible in the future if a still better approxima-
tion of the required uniaxial temperature can be
realized. An interesting approach in this direction is
the heating system published in Ref. [41]. It should
be noted, however, that like in dislocation-free
silicon the absence of dislocations acting as
sinks/sources of point defects would lead to
a supersaturation of intrinsic point defects and the
generation of different kinds of defect clusters.
3.2. Dislocations and substructure
Elementary mechanisms of thermoplasticity are
conservative glide and stress-induced diffusional
climb motion of dislocations, multiplication of dis-
locations by interaction and their rearrangement.
Dislocations are introduced from the dislocated
seed crystal, initiated at outer surfaces or internal
phase boundaries and generated at different kinds
of dislocation sources. Homogeneous nucleation of
dislocations is insignificant.
Generally, the as-grown density of dislocations
and their distribution cannot be significantly re-
duced or changed by post-growth heat treatment.
Hence, measures to reduce dislocation density and
P. Rudolph, M. Jurisch /Journal of Crystal Growth 198/199 (1999) 325–335 331

Fig. 1. Radial EPD distribution across LEC (1), VCZ (2) and
VGF (3) wafers, grown at IKZ Berlin (1,2) and at Forschun-
gszentrum Ju¨ lich (3).
to influence their distribution have to be taken in
the growth process directly.
To compare the growth methods of commercial
importance for SI GaAs typical average dislocation
densities measured according to ASTM F1404
are given for 4crystals: LEC: (5—8);10cm\
[42], VCZ: )1;10cm\ [43,60], VB/VGF:
)5;10cm\ [41]. Their characteristic distribu-
tions across a wafer is represented in Fig. 1. As can
be seen, the VCZ wafer shows a more U-like than
LEC typical W-like distribution which was also
found for HWC wafers [15]. However, from the
VB/VGF wafer it follows that at markedly more
reduced average dislocation density the distribu-
tion is increasingly inhomogenous. Completely
dislocation-free areas or cross-like dislocation
arrangements on a dislocation-free “background”
are found.
Typical for GaAs, dislocations form a cellular
structure which is most evident for LEC grown
crystals. Cells have a globular shape except for
regions between the centre and periphery of the
crystal where cells elongated in the 11102-direc-
tion are observed. The cell size decreases with in-
creasing crystal diameter. With decreasing average
dislocation density the cell walls disintegrate into
fragments and the cell size increases. Typically,
(500 lm for LEC, '1 mm for VCZ and
'1—2 mm for VB/VGF has been observed for 4
SI GaAs crystals. The cellular structure is due to
static and dynamical, i.e. stress assisted polygoniz-
ation of dislocations [44] and, hence, influenced by
the temperature field and cooling process in the
crystal region behind the interface. Constitutional
supercooling and the associated with it loss of stab-
ility and cellular breakdown of the interface shape
as a reason for the cellular structure can be ex-
cluded as shown by Wenzl et al. [45,48].
Apart from isolated and arranged in cell walls
dislocations occasionally slip lines, localized dislo-
cation clusters, subgrain boundaries and lineages
have been observed in melt grown crystals indepen-
dent of the growth method used which deteriorate
yield.
Slip lines are due to crystallographic glide and
therefore indicate still significant thermal stress at
lower temperatures where diffusional creep is un-
important. As the backstress is proportional to the
actual dislocation density (see constitutive law as
given by Eq. (2)) slip lines are more evident where
the dislocation density is low and have to be avoid-
ed by a proper adjustment of the temperature field.
According to Tower et al. [46] and Shibata et al.
[47] the appearance of dislocation clusters is re-
lated to concavely curved regions of the
solid—liquid interface exhibiting local maxima of
thermal stress. As growth proceeds the local dislo-
cation density increases, subgrain boundaries are
formed and finally transition to polycrystalline
growth takes place. Consequently, localized dislo-
cation clusters density can be suppressed by estab-
lishing a slightly convex shape over the whole
interface in the course of growth.
As already mentioned the averaged stress field in
a growing crystal is superposed by fluctuating stres-
ses due to unsteady convection in the gas phase and
in the melt especially for LEC- and, maybe, VCZ-
growth. The influence of these unsteady thermal
stresses on dislocation generation and rearrange-
ment has not been studied in detail until now and
requires a careful analysis in the future.
Lineages and subgrain boundaries typically
propagating along the crystal axis for rather long
332 P. Rudolph, M. Jurisch /Journal of Crystal Growth 198/199 (1999) 325–335

distances seem to be related to the solid—liquid
interface. But details of their formation and the
knowledge about influencing technological and
technical parameters on it are still insufficient too.
Single dislocations as well as the dislocation cell
walls are known to influence the local thermodyn-
amical potential of the different components in-
cluding intrinsic defects due to a mechanical (stress
field) or electrical interaction. This results in equi-
librium segregation to/from dislocations/cell walls,
i.e. an enhancement or depletion of components in
the sourroundings of dislocations/cell walls com-
monly called the gettering of dislocations. It follows
that the more favourable distribution of defects
across cells can be influenced by heat treatment and
a corresponding freezing-in procedure at cooling-
down resulting in a homogenization of physical
properties.
3.3. Stoichiometry related growth problems
According to a the rather well-established phase
diagram of Ga—As [48] the compound GaAs is
characterized by a congruent melting point slightly
deviated from stoichiometric concentration to-
wards As-rich side and a temperature-dependent
homogenity range including the stoichiometric
compound and retrograde solid solubilities at both
sides. Consequently, to grow a GaAs single crystal
of stoichiometric composition the solidification of
a Ga-rich melt (ca 3 at% excess) is required. This is
of special interest because the dislocation density of
GaAs single crystals exhibits a slight minimum at
stoichometric composition which was ascertained
by Parsey et al. [49] and proved by others [50] for
HB as well as for HWC growth [15] and is ex-
plained by Nishizawa et al. [51] as a result of
lowest intrinsic point defect concentration taking
part in the propagation of dislocations. But this
finding is not used in commmercial Czochralski
crystal growth. One of the reasons is the risk of
a constitutional supercooling and loss of mor-
phological stability. Furthermore, the precondition
for semi-insulating behaviour of GaAs is an As
excess above a critical content. Therefore, SI GaAs
is almost exclusively obtained from an As-rich melt
resulting in crystals with off-stoichiometric, ar-
senic-rich composition favouring the As-antisite
defect known as the double donor EL2 which is of
crucial importance for compensation. A profound
review of the complex intrinsic defect chemistry
representing the basis for heat treatment of GaAs
can be found in Ref. [48].
As mentioned above, the EL2-concentration of
as-grown GaAs single crystals depends on the
growth concentration and cooling conditions,
i.e. the growth method used. It amounts to
(1.2—1.5);10 cm\ for LEC-crystals with an
obvious influence of the melt composition and inert
gas pressure, but is mostly significantly lower for
VCZ [52,53] and VB/VGF [21] crystals yielding
here (5—8);10 cm\. On the other hand, the
EL2-content of as-grown VB/VGF GaAs can be
increased by a post-growth annealing at about
850°C to values typical for LEC GaAs. At first sight
such behavior can be qualitatively explained by
a heuristic TTT diagram discussed in Ref. [54] but
more detailed investigations are recommended.
Due to the retrograde solid solubility, an As-
supersaturation results at cooling-down leading to
the precipitation of As-particles in the solid GaAs.
The (probably liquid) As-precipitates are first nu-
cleated at dislocations where heterogeneous nu-
cleation takes place leading to a precipitation-free
region around dislocations and cell walls. Depend-
ing on the cooling procedure much smaller matrix
precipitates are observed in the interior of the cells.
As precipitates may influence device manufacturing
a control of their concentration and size distribu-
tion is necessary. This can be done by a (mass-
preserving) ingot annealing (e.g. Refs. [55,56]) fol-
lowed by a freezing-in the supersaturated solid
solution or by a wafer annealing under defined As
overpressure resulting in an extraction of arsenic
(e.g. Refs. [55,56]).
4. Conclusions and outlook
GaAs is of rising importance for opto- and
microelectronics, especially, for high-frequency de-
vices like HBTs, HEMTs and MMICs. To meet the
rapidly increasing demand, efforts are directed to-
wards growing high-quality semi-insulating crys-
tals with an enlarged diameter of 150 mm. The
careful consideration of methodical pros and cons
P. Rudolph, M. Jurisch /Journal of Crystal Growth 198/199 (1999) 325–335 333

shows that the well-established LEC technique will
remain the leading technique for mass production
of SI wafers. But a certain share of such wafers with
reduced residual stress and dislocation density,
being of interest for some special devices like HBTs,
will be produced by VCZ and/or VB/VGF
methods.
For perfection of the growth methods, i.e. reduc-
tion of thermomechanical stress in the growing
crystal, the knowledge and “tailoring”of the tem-
perature field at all process stages are of essential
significance. For that, powerful numerical simula-
tion programs including gas convection and based
on an improved physical model have to be com-
pleted. The optimization of the temperature field
and cooling program is of highest importance to
control the density and rearrangement of disloca-
tions. At the same time the correlation between
unsteady thermal stress and dislocation generation
and clustering has to be studied more carefully.
Further, due to the correlation between the dislo-
cation structure and physical properties including
their mesoscopic and macroscopic homogeneity,
a more detailed knowledge about the interaction of
dislocations with extrinsic and intrinsic defects and
their relation to the stoichiometry is required.
Acknowledgements
The authors wish to thank Dr. T. Flade and
Dr. B. Weinert from Freiberger Compound
Materials GmbH for critical reading of the manu-
script and helpful remarks. They are indebted
to Dr. K. Sonnenberg from Forschungszentrum
Ju¨ lich for providing of the VB/VGF crystal results
and Dr. M. Neubert from IKZ Berlin for cowork-
ing and for discussions in the field of VCZ growth.
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