Growth of semi-insulating GaAs crystals in low temperature gradients by using the Vapour Pressure Controlled Czochralski Method (VCz)

Progress in Crystal Growth

PERGAMON

Progress in Crystal Growth and Characterization of Materials (2001) 119-185

and Characterization of Materials

http://www.elsevier.com/locate/pcrysgrow

GROWTH OF SEMI-INSULATING GaAs CRYSTALS IN LOW TEMPERATURE GRADIENTS BY USING THE VAPOUR PRESSURE CONTROLLED CZOCHRALSKI METHOD (VCz) M. Neubert * and P. Rudolph Institut fiir Kristallztichtung, Max-Born-Str. 2, 12489 Berlin, Germany " coresponding author: phone 049+30 63923030, fax 049+63923003 e-maih [email protected]

ABSTRACT The present paper gives a review on fundamentals, modelling, growth, structural and electrical properties of semi-insulating GaAs single crystals, grown in low temperature gradients by the Vapour Pressure Controlled Czochralski Method (VCz), with diameters from 75 up to 150 ram. Special attention is drawn to the investigation of the temperature-fields inside the growing crystals (and thus thermoelastic stress). Additionally, the influence of convective transport of heat within melt and inert gas is investigated by both experiment and modelling. Thermodynamic aspects of arsenic pressure control within the inner VCz chamber as well as the special experimental and technological challenges are discussed. High quality 100 mm (4inch) crystals with EPD < 104 cm 2 and low as-grown residual strain are presented. Very low carbon concentrations of ~1014 cm 3 were obtained for the first time in VCz crystals. This material, as one of the challengers to conventional LEC material, is able to meet similar electrical specifications whilst showing improved structural quality and better parameter homogeneity even in the as-grown state. Initial studies of a VCz crystal grown without boric oxide encapsulant is presented. KEYWORDS GaAs, Liquid Encapsulated Czochralski (LEC), Vapour Pressure Controlled Czochralski (VCz), heat transfer, interface, thermomechanical stress, dislocations, electrical properties PACS: 81.05 D, 81.10, 44.05, 68.45, 65.70, 61.72 F 0960-8974/01/$ - see front matter © 2001 Elsevier Science Ltd. All rights reserved. PII: S0960-8974(01)00005-5

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1 INTRODUCTION The world marked of GaAs has been rapidly growing within the last decade; it is expected to increase further and is currently showing growth rates of more than 20% p.a. It divides into two key application branches: the long-established optoelectronics and the rapidly developing high-frequency microelectronics. Whereas optoelectronic devices (LEDs, LDs) require n+ (usually, Si-doped) semiconducting (SC) substrates, microwave devices require high purity quasi-un-doped (EL2 and carbon controlled) semi-insulating (SI) wafers. The respective growth technologies for these two application fields have diverged. Optoelectronic material is usually grown from uncovered near stoichiometric melts by the old-established horizontal Bridgman iHB) or vertical Bridgman (VB) techniques. In the second case the crystals are grown by the conventional high-pressure liquid encapsulated Czochralski (LEC) method. More than 90% of all industry supplied SI GaAs substrates are produced by this method. In the nineties VB SI material was also launched to the market [1, 2]. The present paper focuses on semi-insulating GaAs, grown by VCz only. Today, about two thirds of this material is used for FETs-fabrication by ion implantation, the other third for production of hetero-structure devices, like HBTs, by epitaxial techniques (MBE, MOCVD). However, the latest market forecasts predict that this ratio will be displaced in favour of epitaxial production within the next years. One of the crucial parameters of FETs is their turn-on threshold voltage (Vth). It is proportional to the Channel carrier concentration and therefore connected with the electrical resistivity of the SI substrate. To ensure a high yield of devices a homogeneous distribution of the resistivity in axial and radial directions of the crystals is absolutely necessary. Due to their interaction with imperfections and native point defects dislocations contribute noticeably to the resistivity distribution. Thus, both parameters are closely connected to each other mad even a homogeneous dislocation density distribution is of high interest. At present, absolute dislocation densities of< 10s cm 2 are accepted for this class of devices. In the case of epitaxial-based devices, however, lower dislocation densities are of increasing importance. Despite the application of buffer layer structures serious wafer induced imperfections such as threading dislocations are propagated into epilayers and are responsible for device degradation [2]. HBT (Heterojunction Bipolar Transistor) and related bi-polar devices which are the newest of the GaAs-technologies being utilised by mainstream industry. Compared to MESFET-IC's (Metal Semiconductor Field Effect Transistor-Integrated Circuit) the advantages are: better linearity, higher efficiency, simplicity, higher power density, smaller die, lower noise and even lower overall costs despite a higher cost differential due to the use of epitaxial instead of blank wafers. The reliability of these minority-type device structures especially at high temperatures is believed to be determined by the same degradation mechanisms [3] as for laser and luminescence diodes: non-radiative recombination and defect generation at lattice defects like dislocations and vacancies (so-called dark point defects) accelerated by residual strain in the active layer, high dopant concentrations and precipitates. With

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this reasoning an increasing demand is observed for semi-insulating and semi-conducting substrates with a low dislocation density. For laser applications low-EPD substrates are an indisputable requirement. 4 inch (100mm) is the standard wafer diameter used for device production today, but is currently being replaced by 150 mm (6-inch) [4]. This process is enforced by i) the demand for cost reduction in device production and ii) the possibility for use on free 150-mm wafer silicon processing equipment. The first suppliers have recently matured 6-inch GaAs crystal production (see e.g. [5]). However, with increasing diameter the thermal induced stress inside the growing crystal also increases and, thus, the dislocation density. Whereas typical 4-inch LEC crystals show average dislocation densities of (5 - 8) x 104 cm 2 those with 6-inch diameter exhibit roughly double that density (1 - 1.5) x 105 cm 2. Hence, the main efforts are aimed at maintaining the 4-inch crystal qualities on transfer to the 6-inch production line. This specification is scarcely possible by the conventional LEC technique because of its typical thermal requirements. However, much effort has been made to modify this method in order to match the particular requirements as follows. The thermally induced stress within the growing crystal as being the most important parameter with respect to the dislocation density can be reduced by linearising its internal temperature field. To a first order approximation this can be done by lowering the temperature gradients in axial and radial directions [6]. This is quite easy to realise by simply changing the thermal insulation inside the puller in contrast to that usually used in conventional LEC. However, growth in low axial temperature gradients causes high crystal surface temperatures. Depending on temperature and composition, the arsenic partial pressure of the solid phase can reach several bars. If the crystal emerges from the protective boron oxide melt at temperatures markedly above 1000°C incongruent evaporation takes place, resulting in re-melting of the solid GaAs phase. To suppress the decomposition of the solid phase, new LEC-modes for low temperature gradient growth were developed like HWC (Hot Wall Czochralski) [7, 8, 9], FEC (Fully Encapsulated Czochralski) [10] and VCz (Vapour pressure controlled Czochralski) [11,12]. The latter is characterised by growing the crystal within an additional gas-tight inner chamber and applying a source of solid arsenic to produce a certain arsenic partial pressure (Fig. 1). This keeps the crystal in a two-phase solid-gas equilibrium (the existence region of the solid phase GaAs). It is important to note that the boric oxide encapsulant is still employed in the VCz case, in contrast to HWC which was primarily developed for in-situ control of melt stoichiometry. Another way to grow GaAs with low internal stress is the VB technique [12]. However, this method is not the subject of the present paper and was compared with VCz more in detail in reference [2]. A review of activities to grow crystals under low thermal stress conditions (among them VCz) is given in reference [11]. The key points driving the today's industrial and industry-related investigations on GaAs bulk crystal growth are i) the increase of the crystal dimensions (diameter and length) to lower the wafer costs, ii) assessment and control of certain material properties like e.g. resistivity and iii) homogeneous distribution of these parameters throughout the whole crystal increasing the yield. It will be shown that the VCz method is capable of meeting these requirements. After a brief introduction to the historical background an overview

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122

sure vessel )urce Iding tmber er stal ter apsulant

It ,'ible

Fig. 1 Schematic drawing of the VCz set-up used in the IKZ labs.

on the fundamentals and methodical features will be given. Global numerical simulation plays an important role in VCz developments. Structural and electrical qualities of VCz crystals, grown at the Institute of Crystal Growth (IKZ) in Berlin, will be presented and compared with work in the literature. A short introduction to the first VCz growth experiments without boric oxide encapsulant, i.e. a newer hot-wall approach, is given at the end.

2 HISTORICAL BACKGROUND The VCz growth mode of LEC was created in Japan. The first description is a patent publication of Furukawa Electric Co. in 1983 (Fig. 2) [13]. An additional quartz cover with a liquid (B203) sealing of the pulling rod is brought into the high pressure vessel and contacts the melt nera the crucible. The arsenic atmosphere inside this cover is controlled by the temperature of the upper part of the cover where solid arsenic condenses, initially added to the GaAs starting charge. One year later Sumitomo Electric Industries Ltd. published a patent with a stationary vessel covering the whole crucible requiring a second seal around the crucible rod [14]. From this time onwards, Sumitomo Electric Industries Ltd., one of the today's leading VCz producers world wide, started the development of dislocation-reduced GaAs and InP by applying this technique [ 14, 15]. Numerous patent modifications were published at the end of the eighties and beginning of the nineties including constmctions for better control of the As pressure by mounting the source outside the VCz chamber (see e.g. [16]). Meanwhile excellent 4-inch and 6-inch SI GaAs crystals with very low residual stress and etch pits density (EPD) below 104 cm "2 have been reported [12, 17]. Even semi-conducting 3-inch Si-doped GaAs crystals with

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dislocation densities of some hundreds per centimetre squared in the core region were grown successfully by

VCz [18]. A further important producer of VCz crystals is Japan Energy Co. (former Nippon Mining Co.). Since the first patent publication in 1987 [19] continuous work was carried out resulting in the production of lowdislocation 3-inch Fe-doped InP single crystals [20, 21]. Their efforts were directed to the application of solid seals and a two-piece inner chamber construction with upper quartz and a lower graphite part [22]. A summary of Japan Energy's VCz InP activities is given in [23]. Also Toshiba Co. published some fundamental investigations on GaAs growth by the so-called arsenic ambient LEC technique, a similar version to the VCz method. An X-ray shadowprojection system was used to control the crystal diameter during growth within the inner chamber made of quartz (or pBN) [24]. It is interesting to know that such an arrangement was already in application in 1986 the time the first original VCz paper was published by the same producer [25]. Studying

22

the

literature

more carefully, one can also find some hints about VCz growth of oxide crystals. High Z

.:1

quality BGO was grown in a gas-tight inner chamber by

Fig. 2 The first original patent sketch of Funflcawa Electric Co. [13] with 16 - inner quartz chamber, 21 - condensate of As, 4 - main heater, 4 a, b auxiliary heaters, 20 - liquid sealing bath.

applying

a

low

axial

temperature gradient [26]. In reference [27] a growth arrangement is described to

control the stoichiometry of PbMoO4 by using a MoO3 evaporation source thus improving the optical transmission of the crystals.

124

M. Neubert, B Rudolph/Prog. Crystal Growthand Charact. 43 (2001) 119-185 At IKZ the VCz activities were started in 1995.3-inch and 4-inch SI GaAs crystals with EPD < 104 cm 2

have been obtained, quite comparable with Japanese results [11, 28, 29]. In contrast to many of the former VCz approaches solid sealing was generally applied because of better handling [30]. For the first time special attention was drawn to the optimisation of the temperature field within the growing crystal as a function of the inner constructions by global computer modelling [31, 32]. Another important need was to reduce the carbon concentration within VCz crystals down to values of < 1014 cm 3 as firstly reported in reference [33]. Meanwhile, a large number of VCz experiments have been carried out representing the basis for the following description of VCz growth of SI GaAs.

3 FUNDAMENTALS 3.1 The control of the semi-insulating behaviour of GaAs crystals The SI behaviour of GaAs is closely connected with the arsenic antisite defect Asoa acting as a deep level donor [34]. When discovered during spectroscopic measurements, the structure of this defect was not known and it was simply called EL2, an electron trap [35]. Nowadays, state of the art SI GaAs is intentionally carbon-doped. The carbon (CA0 acts as a shallow accepter and is used to generate n-type semiinsulating behaviour by fully compensating the residual shallow donors leaving partially ionising EL2. The net-concentration of free electrons is thermally generated from the native point defect EL2. Martin et al. [36] have shown that the compensation mechanism can be described by the equation:

NeL2 ( EeL2 -n=4"7xlO'7lNsA-Nso t exp ~- - - kT J -

(1)

for a narrow range where the boundary conditions

Nerz > Nc-lNsA - Nsol>O

(2)

are satisfied. The symbols in Eqns. (1) and (2) denote n, NELZ, NSA, NSD, Nc - concentrations of free electrons, EL2, shallow acceptors, shallow donors and carbon, respectively; EEm - formation energy of the EL2 defect and kT - thermal energy with k - Boltzmann constant. The EL2 concentration in as-grown crystals depends on the melt composition and increases with increasing arsenic atom fraction xAs if it exceeds approximately 0.475 [37]. Usually, the crystals are grown from slightly As-rich melts to achieve EL2 concentrations of about 1016 cm 3. Precise EL2 values can be set by post-growth bulk annealing [5]. To grow the crystals with the desired electrical resistivity the incorporation of the concentration of compensating carbon into the growing crystal is controlled by the chemical potentials of oxygen and carbon. This controls the CO fugacity within the growth ambient [38]. Additionally, the carbon incorporation is also influenced by the water content of the boric oxide and the nitrogen partial

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pressure as it is well known. Today, these technological problems are well mastered for the conventional LEC process. As it will be shown later, setting a desired EL2 concentration is also not difficult in the VCz mode. However achieving precise control of carbon incorporation is of much greater complexity due to the presence of an inner chamber with a separate gas volume and dense arsenic atmosphere. Hence, the production maturity of a VCz arrangement for the growth of semi-insulating material can be reached only after this issue has been mastered.

3.2 Plastic deformation in crystals: generation and motion of dislocations In single crystals plastic deformation is realised by generation and motion of dislocations, resulting in an increase of the dislocation density inside the plastically deformed volume. Generation of dislocations is possible by various mechanisms. Among others some important sources are i) condensation of native interstitials or vacancies forming dislocation loops during cooling-down processes due to supersaturation (e.g. [39]), ii) nucleation at indentations of the surface appearing e.g. at micro diameter fluctuations, evaporation roughening and / or kinetically stepped (vicinal) surface regions [40, 41] and iii) spontaneous generation under the influence of internal induced thermomechanical and mechanical forces [2,6]. The first one, requiting the lowest nucleation energy, has been surprisingly very seldom found in GaAs [42]. The much higher formation energy in the second case is reduced by energy gain due to notch effects [40]. The third one is the least likely one because bonds have to be tom up inside the crystal without any energy gain requiring very large stresses in the range of 10.2 to 10~ G (shear modulus) [43]. Thus, homogeneous nucleation of dislocations is unlikely for the stress values being observed in the present study. Second phase inclusions, however, may induce dislocations by lattice mismatch. Finally, the motion of dislocations already present (like those being introduced from the seed crystal) leads to an increase of the dislocation density expressed as the dislocation line length per unit volume (cm/cm 3 or: cm-2). This mechanism requires low activation energies and is the most important one with respect to dislocation density. In some materials dislocations move close together forming dislocation networks to minimise their free enthalpy [44]. Such processes result in a mosaic structure with sub-grain boundaries (cell walls), being typical for GaAs, see Sect. 5.2.2.6. This effect is called polygonisation of dislocations [45]. Newer approaches, however, treating the dynamic interaction between moving dislocations as a non-equilibrium process in an open thermodynamic system consider two modes of generation of the mosaic structure i) elementary shifts of dislocations forming the conventional treated polygonisation network in a microscopic sense and ii) a self-organised overstructure with mesoscopic dimensions [46, 47]. The latter can be believed to be the cell structure with dimensions of some hundreds of microns up to some millimetres. Case i) may be the dislocation arrangement within the cell walls showing smaller dimensions in the range of some microns (see also Sect. 5.2.2.6).

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Dislocations can move by two fundamental mechanisms - slip and climb. Both show different thermal activation energies. Slip of dislocations only requires the switching of inter-atomic bonds between neighbouring atoms. The atoms themselves are only moved a little bit around their equilibrium positions. Slipping is only possible in planes being spread out by Burgers- and line-vector of the dislocations. The slip process does not need high thermal activation. Thus, it occurs down to even low temperatures, approximately 0,5 Tm (melting point). In fact, the slip line generation in (001) GaAs wafers was observed down to temperatures in the range of 400 to 750 °C [48]. Climb of dislocations is associated with emission or capture of native point defects. Thus it is a diffusion-limited process because point defects have to be transported to or away from the dislocation core via self-diffusion. Climb occurs in any direction and usually needs higher thermal activation than slip. As a role of thumb it occurs down to 0.8 Tin. For the zinc-blende structure the Petroff-Kimeding mechanism [49, 50] is discussed. The dislocation climbs a unit step by capturing an arsenic interstitial Asi leaving a gallium vacancy behind: Asi ° + Gac~ = GaAs unitclimb+ VGa°. These Vc~° can be occupied statistically by further Asi ° forming the well known antisites AsGa (EL2). That is why the EL2 defect is closely related to the dislocation structure in GaAs (see Sect. 5.3.4). The driving force for dislocation motion or its spontaneous generation is the internal stress, resulting in a strained lattice. In the case of GaAs melt growth the temperature distribution inside the crystal is of fundamental importance. It is well known that a free expanding body is completely stress-free if i) it has a uniform temperature or ii) the temperature field inside is exactly linear. Any deviation from linearity (i.e. occurrence of second order derivatives of the spatial temperature field distribution) generates thermo-elastic stress [51, 52]. There are two general ways to treat thermo plasticity i) the static consideration comparing the acting stress with a certain stress threshold (critical resolved shear stress, CRSS) exceeding which starts motion of dislocations and ii) the dynamical consideration after e.g. Alexander and Haasen [53] as follows below. Reducing the three dimensional problem to the linear case the thermal stress cr can be estimated after [51] to be creatE

L2 ( 0 2 T / ~ x 2 ) z a r

E gT m=

(3)

with a r - thermal expansion coefficient, E - Young's modulus, L - characteristic length (for a cylindrical crystal about 1/5 of its diameter), T- temperature, x - respective coordinate and b7" ~ - the maximum deviation of the isotherm from the linear course with respect to this characteristic length. The c c ~ s can be determined by investigating the threshold of the beginning of plastic deformation experimentally. It is again a function of temperature and can be found from the GaAs literature [54] to be:

CrcRss=22.72kPa

('4334K'~ exp ~ )

(4)

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127

Near the melting point o f GaAs Eqn. (4) has a value o f approximately 0.5 MPa. Applying the constants aT = 8

X 10 "6 K "1 and

E = 7.5 x 104 MPa for GaAs in the right term o f Eqn.(3) one can see that e.g. a deflec-

tion o f the phase boundary o f only 67" m~x~ 1 K is large enough to reach or exceed the critical resolved shear stress. For a 4-inch crystal growing in an axial temperature gradient o f approximately 20 K/cm this is a deflection o f 0.5 nun or 0.5% normalised to the crystal diameter. This is a nearly unattainable value even for VCz crystal growth and thus, dislocations are generally able to move. On the other hand, new dislocations nucleated from aperfect lattice need stress values exceeding the CRSS by a factor o f 103 -

104 [55]

and con-

sequently, this process does usually not occur. However, the motion o f dislocations does not start abruptly. The more precise way to study dislocation motion is to consider the dynamic approach. As stated above, Alexander and Haasen [53] first pointed out in a quantitative treatment o f the plastic deformation 6 o f a crystal involving the motion o f dislocations that:

d-f=~bdt

N Bo e x p ( ~ -ET ) ( r - A~tN) m

(5)

where the number o f mobile dislocations N changes with time t after

dt - K N B

oexp

(6)

with ff - geometrical factor, b - Burgers vector, Bo - pre-exponential factor ta be fitted experimentally, E activation energy, T - absolute temperature, r - applied stress, A - strain hardening factor, K - multiplication constant, m - stress exponent. Usually, all constants and parameters have to be determined from deformation experiments at several temperatures up to Tm (more details are given in [56]). Looking at Eqn. (6), the velocity o f dislocation density change has three main proportionalities: i) the starting dislocation density N itself (number o f sources), ii) thermal activation exp(-E/kT), and iii) effective shear stress ( r - A~rN ) indicating that the total amount o f stress r is reduced by a term proportional to ~/N, i.e. the larger the number o f dislocations the more rigid the material becomes. In other words, the total stress is shielded by the stress field surrounding the dislocation cores itself. Generally speaking, the effective shear stress increases with decreasing dislocation density and vice versa. This effect was shown by Tsai [57] who modelled the dislocation multiplication in cylindrical [001]oriented GaAs crystals. He assumed an initial dislocation density along the solid-liquid interface on each slip system to be 1 cm 2. Solving Eqn. (6) for undoped GaAs the following parameters were used: K = 3.1 x 10 .4 m N "l, m = 1.7, Bo = 1.8 x 10 -8 m2m+lN'ms"l, E = 1.5 eV, A = 3.13 N m "l [57, 58]. It could be shown that within the first 2 millimetres behind the interface an enormous increase o f N from 1 to some 102 cm 2 occurs while N increases from 102 to 104 cm "2 within the following 30 ram. In other words, the lower the absolute dislocation density, the faster the multiplication o f dislocations under comparable stress conditions. This

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~ Neubert, P Rudolph/Prog. C~stal Growth and Charact. 43 (2001) 1 1 ~ 1 8 5

result is very important to know for analysing the experimental results o f VCz crystal growth. It will be shown in Sect. 5.2.2.7, that the tendency for slipping is dramatically increased in a cooling VCz crystals with dislocation densities around 5 x 103 cm -2 compared to those showing densities o f one order o f magnitude above.

3.3 Global simulation o f the thermal and stress fields within the growing crystal Global computer simulations are a powerful tool for optimising the temperature field inside the furnace and the growing crystal as a function o f structural elements and the outer insulation. It is generally used at IKZ Berlin for the development o f new crystal growth furnaces and has been reported for the first time in the literature for the VCz method in [31, 32]. The simulations were carried out with the two software programs CrysVUN++ [59] and STHAMAS [60] for 3- and 4-inch VCz assemblies. Both programs consider axisymmetric geometries (2D). CrysVUN++ is a finite volume code with an unstructured grid comprising heat transfer by conduction and radiation and the release o f the latent heat. STHAMAS is also a finite volume code, but it works with structured grids and can additionally simulate the heat and momentum transfer in fluid phases by convection. In both programs the melt temperature at the tri-junction (crystal, melt and boric oxide) is established by fitting the heating power. The thermal boundary conditions at the outer highpressure vessel are set at a constant temperature o f 300 K. The calculated temperature fields within the crystals are used to calculate the thermo-elastie stress distributions in terms o f the scalar yon Mises stress (crvM). It is used to analyse the influence o f the thermal field on the structural quality o f the growing crystals. In cylindrical coordinates it becomes

I

(¢rrr-Crzz)

CrvM =

+ (cr~b - Crrr) 2 + (o~b - O-zz) 2 + 60-rz 2 2

( 7 )

with ~ , (i = r, z, (b) - normal stresses and ~r,~ - shear stress. From Eqn. (7) it follows that Crvgis a positive scalar i.e. tensile or compressive components o f the stress field are not more recognisable. The programs deliver graphical outputs o f the temperature field within the whole fumace, stream lines within the fluid phases and isolines o f the von Mises stress field inside the crystal. A compilation o f the applied material parameters is given in [32]. To evaluate the melt convection in more detail, a special strategy has been developed at IKZ by additionally involving the finite element code FIDAP. At first, the global temperature field was simulated for the whole furnace by CrysVUN++. Then, the CrysVUN++ results were used as boundary conditions to calculate the melt convection within the crucible of the VCz assembly using FIDAP [61, 62]. The special feature o f this method is the use o f temperatures a n d heat fluxes through the boundary areas separating crystal, melt, gas etc. as boundary conditions for the partial differential equations.

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The results o f VCz simulations are presented and discussed in Sect. 5.2.1.

3.4 Thermodynamics and arsenic pressure control As mentioned above, VCz is a modified LEC technique (compare Fig. 1), i.e. the boric oxide melt is still used as an encapsulant. However, caused by the low temperature gradients the crystal surface is very hot when it emerges from the protective boric oxide melt. Looking at Fig. 3 it can be seen that e.g. for a temperature o f about 1200 °C the total arsenic pressure is at least 0.5 bar (5 x 10 -2 MPa); comparison with Fig. 4 shows that the gallium partial pressure can be neglected. This high arsenic partial pressure causes arsenic evaporation from the solid phase which has to be avoided.

102

LAs~(~

PAs(otm)2

2~ I S G o A I ,

L*6

,

%,

--

~

'

~%%u 1.6

Ii-

I O $ o K -I T

Fig. 3 p~-l/T projection of the existence region of GaAs after [63] considering the total arsenic partial pressure. From the diagram one can read hat GaAs is still in equilibrium with its gas phase, e.g. for a temperature of T o ~ = 1200°C, while the arsenic partial pressures may vary from approx. 0.3 to 3 atm (1 atm = 0.1 MPa)

Because o f the B203 encapsulant the liquid phase o f GaAs is strongly hindered to communicate directly with the gas phase (of course they can, but only very little via diffusion, being neglected here). Therefore, equilibrium considerations have to be carried out only for solid and gas phase in order to prevent arsenic evaporation from the growing crystal. Applying Gibbs' phase rule the number o f freedom F o f a closed thermodynamic system can be determined as F = C - P + 2, with C - number o f independent components, and P - number o f phases in a three-dimensional phase space (temperature-pressure-composition). In the present case C = 2 (Ga and As) and P = 2 (solid and gas) and thus, F equals 2. Fixing one o f them, e.g. the temperature, there is still one degree o f freedom left - the partial pressure. Fixing a second parameter, e.g.

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M. Neubert, 17Rudolph/Prog. Crystal Growth and Charact. 43 (2001) 119-185

the composition of the solid phase makes the system 2

~ --

I

I

I

I

I

I

I

invariant. To determine the actual equilibrium condi-

AS 4

tions between solid and gas phase the pAs - 1 / T phase diagrams like those shown in Fig. 3 'and Fig. 4 -

AS~

"

have to be used. As can be seen, for a fixed temperature, the arsenic partial pressure over solid GaAs

X-

varies strongly within the phase limits. This range is

0.-4

smaller near the congruent melting point (left edge of the phase field) and broadens to more than two orders of magnitude for lower temperatures. Consequently, if only the solid phase (GaAs crystal) has to be stabilised one can choose the arsenic partial pressure over a wide range (Fig. 3). With the partial pres-~O 0.6~

I 0,70

I I 0,7.~1 0"60

I I \~t \ I 04m~) O. I;KI 0.111~) 1.,O0

I Ito~

sure, of course, the deviation from stoiehiometry of I*10

the solid phase changes. However, because of the

10~/T*K

diffusion limitation this only results in a skin of nonFig. 4 p-1/T projection of the existence region of solid GaAs after [64], considering the partial pressures of the individual species Ga, As, As2 and As4 (1 atm = 0.1 MPa).

defined composition of less than one millimetre in thickness and can be neglected compared to the boule diameter. If the boric oxide melt is removed from the

system the situation changes completely. Here, the number of phases increases to 3 (the melt is now in contact with the gas phase) and the number of degrees of freedom decreases to 1. Fixing the temperature (solidification temperature) the system becomes invariant. In that case the crystal grows under conditions almost identical with those of the Hot-Wall-Czochralski (HWC) regime [7, 8, 9] and the control of the melt composition becomes possible (and necessary!). The only difference between HWC and VCz is the application of static and dynamic equilibria, respectively. First experimental results on this mode of VCz are given in Sect. 6.1. The above equilibrium considerations (in both cases) are also valid, if the system is semi-open, i.e. if a little outflow of arsenic takes place. It has only to be guaranteed that the stock of arsenic in the source can always compensate the arsenic loss throughout the whole growth run and that the net flow from the arsenic source into the growth chamber is always equal to that through the leaks of the chamber. The diffusive loss through the leak-openings of the VCz chamber can be estimated from a static solution of FICK's first law [65]

NA~ =DAMP dRT

ln/P~[ kP-PA~J

(8)

M. Neubert, P. Rudolph/Prog. Crystal Growth and Charact. 43 (2001) 119-185

131

with Na~ - arsenic flux in units of [mol m 2 sl], DA~ - arsenic diffusion coefficient in the leak-opening, d - gap width o f the leakage split, R - universal gas constant, T - absolute temperature, p - total gas pressure andpA, partial arsenic pressure inside the chamber with p > PAs- Eqn. (8) clearly shows that generally the lowest possible arsenic pressures have to be chosen and the difference between p and p ~ should b e large to minimise the arsenic loss out of the chamber.

3.5 Crystallisation velocity The maximum possible crystallisation velocity is an important parameter and is determined by i) the balance of heat fluxes and ii) the criterion for the avoidance of constitutional supercooling. The first criterion enables one to estimate whether it is possible to conduct the latent heat from the growing interface. Assuming a nearly uni-axial heat flow from the melt into the cylindrical crystal, this thermal balance is given if the growth velocity vc is roughly

<___L_l(k rc_k ar, V c - p c A H t ~ " c dz

' dz)

(9)

with Pc - crystal density (5.3 g cm3), AH~ - latent heat of fusion (726 W s g-l), kc.j - thermal conductivities of crystal (7.12 x 10 -2 W cm "1 K "I) and liquid phase (I 7.8 x 10 .2 W cm "l K "1), dTc,t/dz - temperature gradients in crystal and liquid phase respectively (the GaAs-specific values are given in parenthesises). For a cylindrical VCz crystal the critical growth rate can be estimated using the above values together with typical temperature gradients of 25 K cm 1 and 5 K cm l in crystal and melt respectively. Eqn. (9) yields ~ 8.3 mm h q and thus, in the VCz-case the growth velocity should be approximately the half of that usually applied for conventional LEC growth [l, 5]. A second limiting factor for choosing the crystallisation rate is the avoidance of constitutional supercooling as discussed in detail for undoped GaAs in [64]. Similar to the well known Tiller criterion [66] the consideration is based on the idea that the real slope of temperature .with composition near the phase boundary has to be larger than the slope of the liquidus. A critical growth velocity Vc can be derived fulfilling the condition

< (
vc-

(0.5-y)

'

~dyJ

(10)

with dT¢/dz - temperature gradient at the interface, Dt - diffusion coefficient of the excess component in the melt, y - mole fraction of the melt and dT/dy - slope of the liquidus in the T-y phase diagram. Obviously, vc can be chosen to be very large close to the congruent melting point (dT/dy=O). The question that needs to be resolved is, what is the maximum excess of gallium or arsenic that is permitted to avoid constitutional supercooling using vc like calculated from Eqn. (9). For the VCz ease assuming dTc/dz = 25 K cm -1, Dl ~ 105

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M. Neubert, 17 Rudolph/Prog. Crystal Growth and Charact. 43 (2001) 119-185

cm 2 s1 and using the data given in [64] to estimate the slope of the liquidus, the compositional range between 0.49 _-. y < 0.51 can be safely used whilst avoiding constitutional supercooling. This, in fact, is the necessary range in which VCz is usually carded out. Summarising the above results, the growth velocity is mainly limited by the thermal balance of the system (Eqn.(9)) and not by constitutional supercooling (Eqn. (10)), see also Sect 5.2.1.1. Additionally, estimating the influence of the dopant carbon with maximum melt concentrations in the range of 1016cm "3 (10-4 at%) the Tiller criterion yields no critical limitations for the growth velocity. In general, these estimations are in good agreement with our own experimental results and those taken from literature. Tatsumi et al. [12, 17] used maximum growth rates of 6 and 3 mm h "1 for 4-inch and 6-inch VCz GaAs crystals respectively, grown in axial temperature gradients of about 20 K cm 1. A value of 5 mm h -1 was used by Ozawa et al. [25]. Usuda and Fujii [24] reported a pulling rate of 5 mm h 1 at a temperature gradient within the B203 encapsulant of 35 K cm -t . The same average value (4 - 8 mm h l ) has been described in former authors papers [28, 29] and even for heavily Si-doped 3-inch crystals recently grown by Hashio et al. [ 18].

4 EXPERIMENTAL

4.1 The VCz technique, methodical aspects 4.1.1 Construction of the inner chamber, general growth conditions Fig. 1 shows the schematic drawing of the VCz arrangement used at IKZ for 3-inch and 4-inch SI GaAs growth. As already mentioned in Sect. 3.4 the main difference compared to the conventional LEC technique is the presence of an inner chamber shielding the growing crystal and the hot gases from the water cooled walls of the outer high pressure vessel. It is precondition for growing the crystals in a markedly reduced axial and radial temperature gradient environment compared to the conventional LEC technique. In order to prevent the arsenic evaporation and thus dissociation of the very hot crystal surface an arsenic partial pressure is established within this chamber by a temperature controlled source of pure arsenic. Two industry-scale pullers LPA Mark 3 and CI 358 were modified and equipped with VCz specific inner assemblies for both 3-inch and 4-inch growth, respectively. All crystals were grown in [001] directions with growth rates between 3 and 5 mm/h. The inert gas pressure (Ar or N2) was varied in the range from 0.4 to 2.0 MPa. The arsenic partial pressure was set according to the thermal requirements between some tenth and one atmosphere, see Sect 3.4. To construct a sufficiently gas-tight inner chamber satisfying the basic technological requirements two essential problems had to be considered: i) the chamber material, and ii) the sealing principle. It is known from literature and patent descriptions that quartz [25], graphite-quartz combinations [20], coated graphite

M. Neubert, P Rudolph/Prog. Crystal Growth and Charact. 43 (2001) 119-185

133

[67, 68] and pBN or Mo [68] were applied as chamber materials. Some of these materials were also studied in the author's laboratory and, additionally, aluminium oxide ceramics. These materials differ in several properties like porosity (tightness), machineability, mechanical strength, thermal strength, thermal conductivity and -expansion, electrical resistivity, chemical inertness against the aggressive gas atmosphere and others. At IKZ high-density coated graphite has been used successfully [33]. Concerning the second problem, there are two different methods to reduce the shaft feedthroughs (rotation and translation) and the openings of the chamber with liquid or solid sealing. Liquid is to be preferred if the sealing should be hermetically tight (e.g. B203). However, from a technological (i.e. handling) aspect in the author's laboratory solid sealing was preferred [30] whilst accepting a small diffusive loss of arsenic through the seals which was compensated by the arsenic source.

4.1.2 Thermal insulation The traditional thermal insulation technique applied in LEC pullers with a co-axial sandwich-structure comprising graphite radiation shields separated by graphite felt was completely changed. To improve the handling the complete insulation was replaced by CBCF (carbon bonded carbon fibres). CBCF can be easily handled and show much better insulating properties than a graphite sandwich structure of the same thickness. Additionally, with the help of this new material it became possible to construct insulation completely wrapping the whole system of heaters and inner assemblies like that shown schematically in Fig.1 and in

more detail in Fig. 12. This is highly advantageous from two points of view i) the power consumption of the furnace can be reduced dramatically (in the case of the CI358 puller below 6 kW to grow 4-inch crystals) and just as much the supply of cooling water and ii) the complete inner assembly becomes nearly thermally independent from the outer machine. The second point became essential for the VCz development at IKZ because it enables one to develop the inner VCz assemblies independently from the respective machine and to transfer the ready solutions into any machine of interest.

4.1.3 Temperature control Industry-scale LEC pullers are usually equipped with two different thermocouples to control the main heater temperature. One is positioned beside the heater, the other at the crucible bottom. Because it is not possible to insert a thermocouple into the melt near to the growing phase boundary, the most authentic information about the crystallisation process can be obtained from the crucible bottom thermocouple. However, the "thermal" distance between the tulip shaped main heater and this thermocouple is very large. The problem, again, gets worse in low-temperature gradient systems like VCz. Thus, simply controlling the main heater using the crucible bottom thermocouple in a single loop yields an unacceptable precision of + 2 K. Considering the typical temperature change rates for VCz growth which are in the range of 1K/h and below,

134

M. Neubert, B Rudolph/Prog. Crystal Growth and Charact. 43 (2001) 119-185

Z Jl

Y

heater

I x

T,,~t.,.~ hr,,~,- i

"slave" ~N~-J ~..itSa,2.... I "master" ~ 1

w

Td esired,crucible

Fig. 5 Scheme of the applied cascade controller

this could not be accepted. The much better solution proved to be a cascade controller. Its principle is illustrated in the right part of Fig. 5. The main-controller (master) compares the desired and the actual temperature at the crucible bottom thermocouple and generates a desired temperature for the heater thermocouple. The latter temperature is compared with the actual heater temperature by the second controller (slave) generating the desired power instruction for the main heater. With the help of this cascade controller the precision could be increased by a factor of about 20 up to + 0.1 K being sufficient for the VCz requirements. The disadvantage of a cascade controller is, of course, its sluggishness compared to a single loop controller. However, considering the very low crystal growth rates this is of minor importance.

4.1.4 Diameter control The control of the crystal diameter is not trivial in the LEC case and the problem, again, becomes worse in the VCz case because of the much lower temperature gradients. From our experimental investigations we know that the VCz system shows a non-linear behaviour with a strong time delay. From steprespond experiments the time delay was determined to be in the range of 20 to 50 minutes (depending on the respective machine). A simple PID controller is not suitable to robustly control the crystal diameter with sufficiently good precision because it is not quite good adapted for the properties of such a system. Consideration was given to alternative procedures for diameter control in Czochralski (and especially LEC) crystal growth that can be found in references [69], [70], [71] and [72]. They are the basis for current investigations at IKZ labs to refine the diameter control [73]. Although the situation again turns worse for low temperature gradient systems like VCz, the following is also valid for conventional LEC. To be able to control the crystal diameter at all, a simple PID controller is applied in connection with the conventional crystal weighing technique, see e.g. [74]. The general form of a PID controller is

M. Neubert. 1~Rudolph/Prog. Crystal Growth and Charact. 43 (2001) 119-185 Ay=K,

IAxdt+K~

~x+Ko

135

(ii)

~

0

with Ay arid Ax - control

input and control deviation respectively,

K, Kp KD - the control parameters and time

t. To grow a cylindrical crystal, usually the first time derivative of the mass deviation is used as control deviation: Ax = d/dt Am = A~n, because constant A~n is synonymous with a constant crystal radius. The control input Ay then is defined as the first time derivative of the heater temperature (or power). With this, Eqn. (11) becomes:

]'= K , Am + K p z~n + K o ~ n

(12)

.

Unfortunately, Am does not linearly change with the crystal radius. Thus, problems arise within the conical parts of the crystal (head and tail). This can nearly be neglected growing tall crystals with small diameters but becomes more and more significant with increasing diameters. Usually this disadvantage is compensated by correspondingly fitting the control parameters, however this does not reflect the true properties of the system. Thus, it is better to re-calculate the crystal radius numerically from the mass signal by directly using AR as the control deviation. In this case Eqn. (11) becomes:

180 ,.--,

E

16o

140 ,,....a

t,.. 120 (~

E °

~ ~

~ ~

lOO

8o 60 4O 2O

I

0

,

I

20

,

I

40

,

I

60

,

I

80

,

I

100

,

i

120

,

I

140

,

I

160

,

I

180

,

I

200

,

I

220

,

I

,

240

crystal lenght [ram] Pig. 6 Behaviour of the diameter control in the VCz case. Change of the.proportional and integral part of the PID controller. To avoid the danger of an oscillating system the controller was adjusted to take account of a "creeping behaviour" (6-inch experiment, see Sect. 6.2.).

3~ Neubert, t? Rudolph/Prog. Crystal Growth and Charact. 43 (2001) 119-185 n

136

(13) o

To adapt the controller to the thermal system the control parameters were fitted very carefully whilst taking account of a "creeping behaviour". This is necessary because otherwise the system tends to oscillate because of the strong delay times. On the other hand such a "creeping behaviour" results in a very slowly or never reducing control deviation like shown in Fig. 6. Thus, the transient time of the controller becomes equal to the growth time of the crystal! Additionally, in such a case problems arise with step-like changes of the crystal geometry (e.g. change of slope of the desired radius when switching from the conical to the cylindrical part). Here the system tends to oscillate again. This problem can only be overcome with an external n

change of the term SAR dt by hand. However, there were good experienced at IKZ labs to "help" the

con-

0

troller this way. Doing so, fairly good diameter control can be achieved at least in the cylindrical part of the crystal. However, this procedure has nothing to do with a robust diameter control! Summarising the above, it becomes very clearly that a PID controller is not the satisfactory solution for controling the crystal radius as already stated.

4.1.5 Viewing conditions One of the main problems to be solved for VCz growth was to establish and guarantee good viewing conditions into the inner chamber throughout the whole run. This is essential with respect to single crystalline seeding and twinning. Both, the tendencies for polycrystalline growth and twinning increase when lowering the temperature gradients [88]. Mostly, even before the growth run was started (during melting of the GaAs), the viewing windows became opaque due to the formation of crystalline deposits at the windows. With the help of semi-quantitative EDX measurements these coatings were identified to consist of Ga, As and O. Surprisingly this process could not be suppressed by raising the window temperature up to approximately 1100°C. Investigating this phenomenon, it is clear that direct transport of GaAs by evaporation from the melt could be excluded because of the very low partial pressure of gallium (Fig. 4). Rather, the following succession of chemical reactions derived from thermo-chemical calculations have been found to explain the coating process at the viewing windows (and certainly at any other "colder" part of the inner chamber i.e. the pulling rod, chamber lid etc.). It has to be noted that "colder" means temperatures still above 900°C. Free gallium is extracted from the melt due to reaction with boric oxide forming the gallium suboxide Ga20 by the reaction 6 Ga + B203 4:~ 2 B + 3 Ga20. Ga20 dissolves in the boric oxide, exhibiting a noticeable vapour pressure greater than those of gallium, arsenic and arsenic oxides [75]. Thus, Ga20 evaporates

3,L Neubert. P Rudolph/Prog. Crystal Growth and Charact. 43 (2001) 119-185

137

and condenses at the "colder" windows by the disproportion reaction 3 Ga20 ¢0 4 Ga + Gae03, releasing free gallium which immediately reacts with the arsenic of the gas phase according to 2 Ga + As2 ~ 2 GaAs. Finally, GaAs crystallites are formed in a matrix of gallium oxide which causes scattering of both the visible as well as the IR light. Moreover, if fused silica is used as a window material Ga203 can initiate a recrystallisation involving tridymit formation. Finally, this serious problem could be satisfactorily solved. Fig. 7 shows a TV snapshot of the top view towards a growing VCz crystal under optimised optical condii]ons.

Fig. 7 View through the optics into a VCz chamber. In the beginning stage of growth the crystals grow with a squared shape (left); edge length in this picture is approx. 15 mm. Later, the comers of the crystals begin to round off (right). The image was copied from video tape and thus, has limited quality.

4.2 Crystal characterisation Mainly well-established standard techniques were used for the analytical investigation of the SI GaAs VCz crystals. To analyse the radial distribution of the relevant parameters thin slices, 1 - 5 mm in thickness, were cut perpendicular to the (100) growth axis at different values of the solidified fraction g of the boule. For longitudinal analysis (e.g. striation analysis [76]) slices were cut parallel to the growth axis, also with (100) orientation. Two different etching techniques were used. Striations were resolved using the so-called diluted Sirtl with light (DSL) [77]. For the measurement of the etch pit density (EPD) and their distribution the wafers were polished and subsequently etched using standard KOH melt at 370°C. Additionally, an optical EPD mapping technique, developed at IKZ Berlin [78], was used to analyse the lateral distribution. The qualitative investigation of dislocations and their distribution can also be made using DSL [79]

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M. Neubert, B Rudolph/Prog. Crystal Growth and Charact. 43 (2001) 119-185

The residual stress at room temperature was evaluated by photoelastic analysis (stress-induced birefringence) using a searming infrared polariscope, see e.g. [80]. The distribution of arsenic precipitates was studied by IR laser scattering tomography (LST - formerly known as 'ultra microscopy') first used for GaAs by Ogawa et al. [81]. An advanced version of LST was developed at IKZ Berlin [82, 83]. It is well-known that sub-microscopic arsenic precipitates are found mostly to decorate dislocations already existing at high temperatures. Thus, the dislocation line becomes indirectly visible by a chain-like array of precipitates scattering the IR light [84]. Because of this LST is a powerful and non-destructive tool to study dislocation patterns in GaAs. Additionally, the spatial dislocation distribution can be resolved by i) video sequences moving a light plane into the volume of the crystal, ii) superposing the data of successively imaged light planes (layer-by-layer) obtaining images similar to X-ray transmission topography, iii) using data to compute a 3D image or iv) making stereo photographs. Additionally, some investigations on precipitates were also carried out by DSL [79]. The concentrations of residual impurities were detected by glow discharge mass spectrometry (GDMS). The concentrations of important system-inherent elements like C, O, B and H were investigated by local vibrational mode (LVM) IR-absorption at liquid nitrogen temperature [85]. For the determination of the content of the substitutional carbon atoms (CAs) the calibration factor137K = 9.2 x 1015 cm"1 [86] has been used. The EL2 concentration was ascertained by near IR absorption measurements. The electrical resistivity, free carrier concentration and mobility were obtained from Hall- and conductivity measurements. In order to test the electrical homogeneity a resistivity mapping by the point contact (PC) technique [87] was carded out.

5 RESULTS AND DISCUSSION 5.1 Vapour pressure control The appearance of VCz crystals is a sure proof for the thermodynamic conditions during growth. Mirror-like surfaces indicate that the crystal was held in a true two-phase thermodynamic equilibrium. Otherwise, rough surfaces give evidence of insufficient arsenic counter pressure or an exhausted arsenic source. In this case arsenic sublimes from the crystal surface and its composition adjusts to a phase condition outside the limits of the solid-gas coexistence region. As a consequence, little droplets of Ga-rich melt are formed at the crystal surface. These droplets can grow by coalescence or through further As evaporation. Becoming big enough, they slide tear-like down at the crystal surface, unfavourably affecting crystal growth as it has been described for LEC growth in reduced temperature gradients, see e.g. [88]. Additionally, smaller droplets penetrate into the crystal volume by a travelling solvent mechanism (TSM) [89] as explained schematically in the left part of Fig. 8. Exposing the droplets to a radial temperature gradient the GaAs matrix is par-

M. Neubert, P. Rudolph/Prog. Crystal Growth and Charact. 43 (2001) 119-185

139

T,

:-_c,\ '._'_'_'_D

TIj-/-

local

coor'dinmle

i

GaAs

Fig. 8 TSM [90] mechanism in VCz GaAs after formation of Ga-rich droplets due to incorrect adjusted arsenic pressure control. Scheme of the driving force for droplet motion (left). Traces of Ga-rich droplets near the edge of a VCz crystal grown at arsenic underpressure (right). The droplet itself and the traces are decorated by bundles of dislocations (light micrograph after standard KOH etch).

tially dissolved at the droplets hotter surface (enhanced solubility) while GaAs crystallises at the opposite cold site (supersaturation). As a result the droplet moves parallel to the vector of the steepest temperature increase. Usually, the droplets are able to penetrate into the crystal a distance of approximately 1 - 3 mm, not more. This is due to the magnitude and the changing direction of the vector of the temperature gradient (Fig. 13) during growth. The droplet movement leaves traces of dislocations behind and after the final crystallisation of the just immobile droplet numerous dislocations are generated around its periphery (Fig. 8), see also [90]). Hence, this process has to be avoided in any case by correctly adjusting the arsenic partial pressure. Beside fixing a sufficiently large arsenic partial pressure one has to ensure a leakage rate being small enough to guarantee equilibrium conditions like already discussed in Sect. 3.4. In the author's laboratory a total arsenic loss through the solid seals was determined from experiments to be in the range of 1-2 g h ~. With the help of Eqn. (8) it is possible to estimate the ,,effective leakage slit width" of the inner chamber. Assuming a (realistic) total slit length of 100 cm, an average slit depth of 5 mm, an average temperature of 1000 K, a gas consisting on average of As3 (As2 and As4) species with a diffusion constant ofDas ,~ 0.1 cm 2 s -1 where the total pressure i s p = 5 x 105 Pa and the arsenic partial pressurepAs = 5 x 104 Pa, then the effective slit width can be estimated to be between 70 and 150 microns. This is quite a reasonable result. Fig. 10 and Fig. 9 show typical VCz crystals grown under those optimised conditions. Their surfaces show a perfect mirror-like lustre indicating that the crystals grew under conditions of two-phase equilibria, i.e. inside the existence region of the phase relationp~-l/T according to Fig. 3.

140

M. Neubert, P. Rudolph/Prog. Crystal Growth and Charoct. 43 (2001) 119-185

Fig. 10 3-inch SI GaAs crystal grown by the VCz-technique in a LPA Mark 3 puller.

Fig. 9 4-inch VCz crystals, grown in a CI 358 puller.

5.2 Structural quality 5.2.1 How to influence dislocation density and distribution As discussed in Sect. 3.2 the dislocation density is mainly associated with thermo-mechanic stress generated from non-linearities of the temperature field within the growing (or cooling) crystal (Eqn.(3)). Deviations from linearity can result from various causes the most important of them are i) direction and distribution of heat flux inside the crystal, ii) mode of heat exchange at the crystal surface, i.e. radiation and gas convection, iii) melt convection affecting the shape of the growing interface, iv) boric oxide height, and v) geometrical features of the crystal like shoulder shape and constancy of the crystal diameter. All of these factors were carefully investigated experimentally, assisted by numerical simulations and will be discussed 1 the following sections.

Neubert, P. Rudolph/Prog. Crystal Growth and Charact. 43 (2001) 119-185

Fig. 11 Global temperature field inside a VCz puller, calculated with CrysVUN++, half cut of the 2D symmetry.

141

Fig. 12 Global temperature field of a VCz arrangement, calculated with CrysVUN++, reproduces as a mirror image (2D symmetry). The figure shows a grey-scale image of the calculated temperature field with additional isotherms drawn (AT=100K). The present picture is a transformation of a red-blue graph. Thus, the heater appeares darker then its surrounding but, is the hottest part. Obviously, the heat flux is highly co-axial within the crystal.

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M. Neubert, t? Rudolph/Prog. Crystal Growth and Charact. 43 (2001) 119-185

5.2.1.1 Heat flux

The temperature field is usually visualised in terms of isotherms. The heat flux q is proportional to the temperature gradient and determined by the FOURIER's law q = - k grad T (k - thermal conductivity). It is directed normal to the isothermal line and (ifk is constant) proportional to the isotherm spacing. This means that to achieve zero thermal stress inside the cylindrical crystal, in the ideal case, the heat flux through it has to be completely co-axial and constant. In other words the isotherms should be equidistant flat planes normal to the crystal axis. Such conditions, of course, can only be approached. Especially at the cylinder jacket of the crystal the heat exchange can not be completely suppressed and thus, the isotherms will be partially curved in that region.

2.4

\1.2 MPa ~

= 0.25 M Pa

Fig. 13 Calculated temperature field (right) inside a growing 4-inch GaAs VCz crystal with resulting von-Mises stress field (left). The most important factor for establishing a nearly axial heat flow within the crystal have proved to be the thermal insulation surrounding heater system and the inner VCz chamber and the boron oxide encapsulant. Fig. 11 and Fig. 12 visualise the results of respective nufiaerical simulations. The two VCz arrangements differ in the fashioning of the top insulation (above the lid of the inner chamber). Whilst the top is not insulated in Fig. 11 (open lid), it is strongly insulated in Fig. 12. The latter case is promising for reduceing the power input and the axial temperature gradient to a minimum, however, crystal growth becomes more and more difficult. Thus, a compromise between both variants has to be found. Fig. 13 shows an elongated detail of Fig. 11. and illustrates that nearly equidistant isotherms can be reached within the growing crystal (right) resulting in a very low stressed crystal volume (left). Additionally, of course, a careful adjustment of the crucible position according to the main heater is also required. The main flux of heat has to be coupled into the melt, flowing axially i) down to the bottom and ii) upwards through the crystal. With sufficient

143

lt& Neubert, t? Rudolph/Prog, Crystal Growth and Charact. 43 (2001) 119-185

cooling the crystal top extracts the heat after a nearly co-axial passage. As a rule o f thumb one can say that the hot spot o f the heater has to be situated axially in the proximity o f the line segment between centre o f the melt and crucible bottom holder. Both measures together (insulation and crucible position) lead to favourable results concerning stress reduction in the growing crystal.

5.2.1.2 Gas convection

In order to study the impact o f gas convection on the temperature distribution the VCz set-ups were simulated additionally using the STHAMAS code (see Sect. 3.3). Comparing Fig. 14 a and b the temperature field in the gas within the VCz chamber is altered considerably compared to the CrysVUN++ simulation, although nearly the same heater powers were calculated. Fig. 15 shows a line scan o f the temperature distribution along the axis o f the apparatus for both cases (with and without gas convection). Surprisingly, apart from small absolute temperature differences, nearly identical temperature gradients o f about 37 K/cm are calculated within the growing crystal. This is an important result because in the conventional LEC case calculations with and without gas convection differ markedly from each other [60]. The main reason for this

P= 11.8 kW

P= 11.4 k W

P= 11.5 k W a

b

c

Fig. 14 Calculated global temperature fields of a VCz arrangement inside the puller LPA Mark 3 carried out with the codes CrysVUN++ (a) and STHAMAS (b), in both cases without consideration of convective transport and with STHAMAS (c) including gas convection of argon gas at 0.9 MPa. The calculated stream field is added on the left side of (c). P indicates the calculated heater powers, the measured power consumption was 12.5 kW. The distances of the isotherms are 50 K in all three cases.

144

M. Neubert, P Rudolph/Prog. Crystal Growth and Charact. 43 (2001) 119-185

result is the dimension of the gas-filled volume surrounding the growing crystal. As it is well known, the Grashof number (Gr) scales with the 3rd power of the dimension of the vessel being large in the LEC case (whole recipient) and small in the VCz case (inner chamber). Additionally, Gr scales with the 1st power of the temperature differences. However, the temperature differences of both methods also differ significantly. They are in the range of 1200 - 1300 K under LEC conditions, 400 - 500 K for the 3-inch VCz set-up (Fig. 14) and 350 K for the 4-inch VCz case (Fig. 11 and Fig. 12). All in all, the convective contribution to the internal transport of heat is very different for LEC and VCz. The observed small contribution in the VCz case is the major argument for carrying out the optimisation of the thermal field using mainly the CrysVUN++ code.

•.

." with without gas c o n v e c t i o n

0.7

E

19.7 K/cm

0.6

7

.9 19.3 K/cm

O

o O

0.5 g------- 37.1 K/cm

-i:i ii [/ I

0.4

21 K/cm

[

~ '

[:~:~ii::-,":~

0.3 O O

O O

O O

O O

O O

t e m p e r a t u r e [K] Fig. 15 Calculated axial temperature distribution (left) taken from Fig. 14 b and c. Values of the local temperature gradients are added. The corresponding temperature field and the interior of the VCz arrangement is drawn at the right for comparison. The isotherms are separated by 25 K.

M. Neubert, P. Rudolph/Prog. Crystal Growth and Charact. 43 (2001) 119-185

145

5.2.1.3 Melt convection

The shape of the phase boundary is important with respect to two well-known problems i) thermal stress, growing with increasing curvature (see also Sect. 5.2.2.4), and ii) dislocation bunching, taking place if concave or convex-concave shapes of the interface appear [91 ]. In the case of non-facetted growth the phase boundary is an isothermal plane, i.e. it reflects the local directions of the heat flux from the liquid to the solid phase. Consequently, minimum stress and no dislocation bunching will be reached with a nearly flat, slightly convex interface (regarded from crystal to melt). For that reason the study of melt convection is of great importance because the interface morphology is clearly influenced by the convective transport of heat within the melt.

[v~[,n,x= 13.5 mm/s (GaAs) Iv~l..~= 0.006 mm/s (B20~)

Iv~.l~ = 5.6 mm/s (GaAs) ]v~l,L, = 0.0033 mm/s (B~O0

[v~l, ~ = 1.76 mm/s (GaAs) Iv~.lm~x= 0.069 mm/s (B20.0

Fig. 16 Simulated influence of the melt convection on the interface shape (CrysVUN++ / FIDAP). The calculations were made for iso-rotation of crystal and crucible, respectively, applying three different rotation rates. Each figure compiles the temperature distribution in the melt (left) and stream lines (right) while below a comparison of several interface shapes is shown. Rotation rates: a) 0 rpm, b) 5 rpm, c) 21 rpm. Interface shapes: a) buoyancy driven convection only (convex-concave) versus transport of heat by radiation / conduction only (slightly convex), b) 5 rpm (upper) versus 0 rpm (lower), c) radiative / conductive transport only (upper), 21 rpm (middle) and 5 rpm (lower).

The melt convection was simulated in two ways i) a combination of CrysVUN++ and FIDAP, ([62], already shown in Sect. 3.3), and ii) STHAMAS [32]. Both methods lead to similar results and thus, the resuits obtained by CrysVUN++ / FIDAP will be shown here. Fig. 16 compiles the simulation results. Both, crystal and crucible were rotated at equal rates and the results of increasing the rotation rates from zero (a) to 21 rpm (c) are shown. It can be seen very clearly that the initially highly deflected concave-convex phase boundary becomes more and more fiat with increasing rotation rate. Finally, the interface shape approaches that obtained by CrysVUN++ calculations neglecting melt convection. The buoyancy driven convection in case (a) can be nearly suppressed with high iso-rotation rates (c). Tho convective roll is dramatically slowed down (compare the inset of maximum melt convection velocity in each picture) and moved outwards away

146

Neubert, 17Rudolph/Prog. Crystal Growth and Charact. 43 (2001) 119-185

radial stress distribution LEC vs. VCz

"~ ~i [-..~~ dT/dz=120 K/. . dT/dz=60K/enl 2

"..,

.

.

oxide melt. Finally, the heat transport

.

.'"

typical 3" LEC

within the melt is dominated by thermal

°.

conduction. As practice shows, in any

~= 10~

6

~

from the crystal interface below the boron

case it is possible to find conditions for

2

the given growth arrangements where the

/:

N 10 0 5

melt flow plays only a minor role for heat 4 VCZ IKZlabs

J 0

10

20 30 radius [ram]

40

,50

Fig. 17 Comparison of calculated radial stress distributions near the growing interface for typical 3-inch LEC crystals after [6] and4-inchVCzcrystals [32].

transfer inside the melt. The latter is a precondition to get nearly fiat and monotonous convex shaped interface boundaries and thus, low dislocation densities. Fig. 13, again shows such an optimised case for an interface shape in a 4

inch VCz growth system. As expected, the nearly uni-axial heat flow (nearly equidistant and flat isotherms) through the crystal guarantees relatively low values of the von Mises stress as demonstrated at the left-hand side. The main part of the interface area and the core region of the growing crystal are exposed to very low stress, often below the critical resolved shear stress CrCRSS(Eqn. (4) (approximately 0.5 MPa near the melting point of GaAs). However, near the crystal edge stress peaks of 1.8 and 3.7 MPa appear. They are mainly caused by the discontinuities of the material properties like thermal conductivity and emissivity (solid and liquid GaAs, boric oxide). This is well-known from the conventional LEC process [6] where the absolute stress values are, however, higher by about one order of magnitude than in VCz crystals (Fig. 17). Fig. 18 shows an example of striation analysis within a VCz crystal grown under similar conditions like those used for the calculations in and Fig. 13. As can be seen, the experimentally obtained interface shapes are close to the simulated ones. Additionally, it is no problem to grow VCz crystals with nearly flat interfaces (compare also Fig. 26) and

/

........

¢'

"--2--

again this dramatically reduces thermal stress. However, it will be shown in Sect. 5.2.2.4 that a fiat interface (no radial temperature gradient) is disadvantageous for single crystalline yield and the avoidance of twin generation etc. Thus, a slightly convex interface shape should be preferred.

Fig. 18 Striation analysis of a longitudinal cut of a 4-inch GaAs VCz crystal grown under nearly optimised conditions. There are nearly flat interfaces. Obviously, fiat interface shapes increase the difficulties with diameter control.

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147

5.2.1.4 Boric oxide height For conventional LEC growth one can usually find in the literature that the dislocation density increases with decreasing boric oxide height (see e.g. [56]). Investigating this relation, surprisingly the opposite behaviour was found for the VCz case. The dislocation density and its radial distribution inhomogeneity decreased with decreasing boric oxide height. Similar results were described for VCz growth of Si-doped GaAs crystals by Hashio et al. [18] attributing this phenomenon to the decreased radial temperature difference due to the hotter crystal surface if a smaller amount of encapsulating boric oxide is used.

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r [cm]

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6

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Fig. 19 a) calculated stress fields in 4-inch VCz crystals as a function of the boric oxide height; b) line scans taken from a) of the axial and radial distributions of the yon Mises stress. To explain these inverse effects of LEC and VCz regimes in more detail, the problem was simulated numerically as shown in Fig. 19. In agreement with the experimental results, in both directions (radial and axial) the total stress decreases markedly with decreasing B2Oa height. The reason for that may be illustrated as follows. Obviously, in the LEC ease with higher temperature gradients and a relatively cold gas ambient the boric oxide mainly acts as an insulating material, shielding the growing crystal from the cold environment. Consequently, the higher the bode oxide the smoother the temperature field inside the crystal becomes. In the VCz-case, however, low temperature gradients and a hot ambient gas temperature are already

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present and thus, the temperature field is much more homogeneous. Hence, a higher boric oxide acts as a disturbing medium (discontinuities of thermal properties) with respect to heat transfer and the stress inside the crystal increases with increasing height. Additionally, the deflection of the phase boundary increases with increasing boric oxide height and thus, the stress (Fig. 19 a). This was confirmed by both numerical simulations and experiments and is discussed in more detail in Sect. 5.2.2.4.

5.2.1.5 Crystal shoulder shape and diameter uniformity As it was shown in Sect. 5.2.1.1 the heat flux has to be arranged to pass through the crystal mainly coaxially, i.e. entering via the solid-liquid phase boundary and exiting via the crystal top. Because of the extreme small seed cross-section compared to that of the final crystal cylinder the majority of the heat will leave the crystal by radiation via the shoulder region (and a smaller amount by convective cooling). Considering the typical shoulder shapes this cannot happen strictly coaxially. As a consequence, remarkable thermal stress appears in this region, see Fig. 20 a. However, contrary to the facts discussed in Sects.5.2.2.2 and 5.2.2.7, this effect is localised to a small limited crystal volume which moves away from the dangerous hot region during growth, and is thus a minor problem. To reduce its influence on dislocation multiplication in the initial stage of growth the application of an after heater is recommended. Surprisingly, until today, no shoulder shape has been proved to be ideal for the VCz case. Both steep and fiat sloped crystals were obtained from the same producers (see e.g. [12, 18, 23]).

i

30MPa k "]/ ,-,-" ,--" --

3,3 ~

[5.9.~,ii

2

Fig. 20 Calculated stress fields of a crystal with exact cylyndrical shape (left) and curved shape (middle) grown underidentical thermal situations. The picture of an etched slice, taken from the edge region of a real crystal with marked diameter uniformities, is added (right).

A more dangerous factor with respect to dislocation multiplication is a strongly fluctuating crystal diameter. This is an acute problem for VCz because of the drastically reduced radial temperature gradients causing problems with diameter control. As simulations show the thermal stress increases considerably

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149

compared to a flat cylinder grown in the same ambience if large diameter fluctuations occur, especially in those regions where the diameter decreases (compare Fig. 20 a and b). In fact, larger densities of dislocations and slip lines have been observed in crystals with diameter fluctuations (Fig. 20 c). Additionally, the phase boundary tends to be concave when the diameter decreases (Fig. 20 b), being responsible for dislocation bunching (Sect. 5.2.1.3). Therefore, a well-defined diameter control is of the highest importance for VCz growth, but difficult to achieve (Sect. 4.1.4). Fig. 9, Fig. 10 and Fig. 26 b show 3- and 4-inch VCz crystals, grown in the author's laboratory, exhibiting sufficiently good diameter uniformities, although they are far from ideal.

5.2.2 Dislocation density and distribution - experimental results 5.2.2.1 Seed induced dislocations

Usually, the seed crystal is not dislocation-free. Thus, a significant fraction of these dislocations continues to grow into the new crystal. Surprisingly, the dislocation density decreases abruptly by one or two orders of magnitude compared to that of the seed crystal (Fig. 21). This behaviour was reproducibly observed in VCz crystals. The same phenomenon appeares in GaP and has also been reported e.g. for InP LEC crystals [92]. In [92] this behaviour was attributed to the formation of sessile dislocations when the seed contacts an overheated melt. Similar effects are also well known from low temperature processes like THM and LPE [89]. Here looping processes of immobile dislocations were discussed like those shown in the inset in Fig. 21. However, it is highly questionable if the seeding of a melt at very high temperatures can be compared with such low-temperature processes. It can only be speculated that the process may be connected with the partial re-melting of the seed and the reaching of temperatures near to the melting point where dislocations again become highly mobile. All in all the effect is not yet understood. After seeding when the diameter of the growing crystal increases the thermal stress increases too and dislocations begin to multiply. The resulting dislocation density becomes a function of the thermal field again.

Fig. 21 Etched axial cut of a VCz crystal. After seeding the dislocation density is dramatically reduced by more than one order of magnitude. The sketch on the left side illustrates the dislocation looping process at the phase boundary.

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5.2.2.2 Radial EPD distribution

Working out the rules given in Sects. 5.2.1.1, 5.2.1.3 and 5.2.1.4 the dislocation density could be successively decreased. As demonstrated in Fig. 22 the EPD was reduced from an average value o f 5 x 104 cm 2 in former conventional 3-inch LEC crystals passing 104 cm 2 and reaching lowest values o f about 5x103 cm -2 4-inch VCz crystals. Finally, it was possible to grow 4-inch crystals with EPD's reproducibly lying at and below 104 cm 2 across the main areas o f the slices. Fig. 22 shows a typical EPD distribution for 4-inch VCz crystals, grown at IKZ labs.

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30

40

,

50

[mm]

Fig. 22 Radial EPD evolution in VCz SI GaAs crystals grown between 1995 and 1997 at IKZ in Berlin. For comparison the EPD in a conventional 3-inch LEC crystal, grown in the same laboratory, is added.

Similar results were reported by Tatsumi et al. [12, 15, 17]. These authors showed that even in 6-inch VCz crystals the mean dislocation density can be reduced down to approximately 5 x 103 cm "2. Not only the absolute EPD could be decreased compared to LEC, but also the overall distribution inhomogeneity. Generally, VCz wafers show a more U-like distribution than the LEC-typical W-like distribution [2]. In the best crystals the EPD scatter lies at a factor o f 3 throughout the whole wafer (see e.g. lowest curve in Fig. 23). Fig. 24 shows an optical EPD mapping o f a 4-inch VCz half-wafer. The dislocation density is distributed very homogeneous over the wafer. This is attributed to the nearly plane interface and the resulting homogeneous and low stressed volume behind it (for comparison see Fig. 13, Fig. 19 and Sect. 5.2.2.4). Near the edge, however, the dislocation density strongly increases caused by the steep increase o f stress near the boric oxide surface as shown in terms o f the calculated von Mises stress e.g. in Fig. 13 and

~L Neubert, 1~Rudolph/Prog. Crystal Growth and Charact. 43 (2001) 119-185

151

Fig. 20 a. Unfortunately, the whole crystal passes this stress maximum, covering the crystal with a "skin" o f increased dislocation density.

o ! 13. H.I

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~ 0

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i 20

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Fig. 23 Current stage of 4-inch VCz growth of SI GaAs at IKZ Berlin. The average EPDs in the main parts of the wafers are below 104 cm-~.

Generally speaking it is possible to achieve very homogeneous radial EPD distributions at and around 104 cm 2 (lowest curve in Fig. 23). In the case o f optimised thermal conditions the dislocation density again decreases in the bulk but is "pinned" at the stress maximum near the boron oxide surface. Thus, the wafers typically show a "flan case" - like EPD relief (Fig. 24).

Fig. 24 Optical EPD-mapping [78]. The EPD is drawn in arbitrary units and corresponds to one of the lines in Fig. 23.

5.2.2.3 Axial EPD distribution The as-grown low dislocation density can only be preserved if the crystal is carefully cooled down to room temperature. If the cooling rate is chosen too high the EPD continuously increases along the crystal axis. The corresponding experimental data, lower and upper curve respectively, can be seen in Fig. 25. This

2k£ Neubert, P Rudolph/Prog. Crystal Growth and Charact. 43 (2001) 119-185

152

behaviour can be understood as follows. For the initial temperature drop of some hundreds of degrees the crystal top cools down within the temperature field of the heater assembly during growth. The cooling rate is given by the product of axial temperature gradient and pulling speed. For VCz this is in the range of approximately 10-20 K/h. In contrast to that the crystal tail cools down just after solidification in accordance with a specific cooling-down regime. Application of a larger cooling-down rate after growth that is experienced by the crystal top during growth generates additional thermal stress within the tail part of the crystal. Consequently, the dislocation density is increased compared to the as-grown value. The latter does not

80000

occur in the top part because this region of the crystal already temperatures where dislocation already stays stays at at temperatures where the the dislocation

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motion is nearly frozen-in. A homogeneous axial EPD

40000

distribution can actually be obtained by carefully ad-

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justing the cooling-down program (lower curve in Fig. 25).

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axial position

The effect of dislocation generation or multiplication during the cooling-down process is of more significance in VCz than in LEC crystals because of the lower as-grown dislocation densities increasing the

60

70

80

[mm]

Fig. 25 Axial EPD distributions in 4-inch VCz crystals depending on the cooling-down rate after finishing growth. The data points are mean values of < 110> traces along one sample diameter. Upper curve _>150 K/h, lower curve _<50 K/h

effective shear stress (last term in Eqn.(6)). As a rule of thumb it can be stated that the cooling-down rate has to be in the same order of magnitude as the coolingdown rate during growth. Higher cooling-down rates may be achieved by adjusting the heat flow out of the crystal strongly in an axial direction (similar conditions apply as in the growth of the crystal, see Sect. 5.2.1.1).

5.2.2.4 Interface shape Several VCz test series have been carried out showing that the favoured monotonous slightly convex interface shape can only be achieved by isorotation of crystal and crucible respectively (compare Sect. 5.2.1.3). Using isorotation the deflection of the phase boundary can be chosen in a wide range by adjusting the ratio of crystal to crucible rotation rates (of course with respect to the current crucible position and growth velocity). Surprisingly, the crystals can be roughly divided into two groups with respect to their dislocation densities. Growing the crystals with nearly plane interfaces results in dislocation densities at and below 5xl03 cm 2. Increasing the deflection by only some percent (ratio of diameter and deflection depth in the centre of the crystal) causes a steep increase of the dislocation density up to 104 cm ~2and above (Fig. 26). Simulations made for the estimation of the maximum possible growth speed may be used to illustrate this.

M. Neubert, P. Rudolph/Prog. Crystal Growth and Charact. 43 (2001) 119-185

153

Fig. 38 shows that the phase boundary shape influences the thermal stress within the crystal mainly in the region nearest to the vicinity of the interface itself. Nevertheless, the average dislocation density alters by a factor of three to five. This is a clear hint that the most dislocation multiplication occurs mainly in the vicinity of the phase boundary and thus, at temperatures near to the melting point. Although the nearly plane interface is advantageous with respect to the dislocation density it causes other problems like i) difficulties with diameter control (no radial temperature gradient), ii) problems with twin generation, both can be seen from Fig. 26 a, and iii) the risk of slightly concave phase boundary shapes with the above mentioned disadvantages. Thus, a plane interface is usually avoided and crystals are grown with slightly convex interfaces, accepting dislocations densities of about 104 cm 2.

A

al

20 rata

b) Fig. 26 4-inch VCz crystals grown a) with nearly plane interface, typical EPD 5xl03cm -2 and b) with slightly convex interface, typical EPD 2 x 104cm-2. Obviously the diameter control is much more difficult in case a) and the tendency for twin formation is increased (right crystal in a).

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5.2.2.5 Residual strain

During cooling-down the dislocation mobility is frozen-in at a certain temperature, i.e. the applied stress falls below the temperature dependent CRSS (Eqn. (4)). Consequently, the strained lattice cannot any more relax by plastic deformation and the crystal lattice remains elastically strained. This residual strain can be measured at room temperature with the help o f the photoelastic effect [80]. Residual strain is an important parameter for the final wafer geometry (flatness, bow etc.).

Fig. 27 Residual strain obtained from photoelastic measurements in as-grown 4-inch VCz (100) wafers prepared from the top (left) and body (right) region of the crystal. Dark regions: [St - St] - 1 x 10-6 (approx. 0.5 MPa); white: - 1 x 10-5(approx. 5 MPa).

Fig. 27 presents characteristic photoelastic strain maps o f two as-grown 4-inch VCz (100) wafers taken from the crystal top (left) and tail (right). The body wafer shows a very low residual strain o f I Sr - St I < 2 x 10 .6 (approx. 1 MPa) for 99% o f the wafer area. This is about one order o f magnitude lower than in as-grown LEC crystals and comparable to bulk-annealed LEC wafers. Similar results for 4-inch VCz wafers were presented by Tatsumi and Fujita [12] with average values o f I Sr - St l = 2.8 x 10 "6. Considering further results in the literature [14, 15] it can be concluded that, in general, as-grown VCz wafers have a lower strain than as-grown LEC wafers which are almost comparable to bulk-annealed LEC material.

5.2.2.6 Cell structure and its origination

A typical and unique property o f GaAs among other compound semiconductors is its cellular structure. Because o f the decoration o f the dislocation cores with arsenic precipitates the cell structure can comfortably be investigated by the LST technique (see Sect. 4.2).

M. Neubert, P. Rudolph/Prog. Crystal Growth and Charact. 43 (2001) 119-185

155

Fig. 28 LST images of SI VCz GaAs (negative image), a) image taken from only one light plane (integration depth is approx. 15 lam). The typical cell structure becomes visible and the result is comparable to EPD measurements, b) and c) integration over 10 successive light planes i.e. projection of a larger volume element (150 lam); the result is similar to Xray transmission topography, b) (100) projection showing a dislocation network similar to a), while c) is a (110) projection showing dislocations in {111} slip planes. The lower edges of the pictures indicate a length of approximately 2 mm.

Fig. 28 a shows a LST image taken from one incident light plane with a thickness o f approximately 15 microns. The result reminds one o f the typical EPD etch analysis (compare Fig. 33). Fig. 28 b and c, however, were made using the layer-by-layer technique (i.e. superposition o f several images) better illustrating the dislocation network. Finally, Fig. 29 shows a 3D reconstruction o f the spatial arrangement o f precipitates made with LST data. There are still two conflicting opinions about the origin o f the GaAs cellular structure. On the one side it is believed to be formed by constitutional supercooling,

z z

see e.g. [93]. If the cells are due to constitutional supercooling a columnar structure o f these cells should be expected, i.e. a clear texture parallel to the growth di-

~

\

rection [1, 94]. However, studying the LST images it becomes very clear that the dislocation cells show a globular or isotropic shape [95,97]. Additionally, con-

stitutional supercooling results in corrugations on the exterior o f [001] GaAs crystals [96] like that shown in Fig. 30; also these are not found. Fig. 31 shows morphological instabilities intentionally forced by a very high growth rate. The phase boundary is highly facetted with a columnar structure.

Fig. 29 Computer animated 3D image of arsenic precipitates decorating dislocations in a VCz crystal. With the help of the computer the cube can be viewed from any direction to study the spatial arrangement of the dislocation lines.

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M. Neubert, B Rudolph/Prog. Crystal Growth and Charact. 43 (2001) 119-185

If the cell structure would be due to such constitutional supercooling the same had to be found in the shapes of the interfaces revealed by the striation analysis. This is obviously not the case (see Fig. 18 and Fig. 26). Rather, the discussion in Sect.3.5 gives evidence that constitutional supercooling is not to be expected for the compositional interval used in VCz growth. Finally, to our ~i~:i~

' ~ ~: ~

~ . .... ~

knowledge, there is not a single mention of cell structures in InP, or other III-V compound semiconductors, although they are always grown under similar LEC or VCz conditions like GaAs.

Fig. 30 Morphological instabilities at the crystal surface due to constitutional supercooling occuring due to markedly enhanced growth velocity (sharp diameter increase) near the end of the crystal (see also Sect. 3.5).

Fig. 31 Morphological instabilities at the phase boundary of a VCz GaAs crystal due to constitutional supercooling. The phase boundary is broken into facetted, columnar growth. Pictures were taken after pulling the crystal off from the melt.

Rather, the globular shape of the dislocation cells is expected to be the result of stress-induced dislocation multiplication and rearrangement by dynamical polygonisation after growth. This hypothesis is confirmed by various experimental results e.g. described in Sect. 5.2.2.3. There it was shown that the initial dislocation density increased axially (and thus, the cell dimensions decreased) when choosing too high cooling-down rates. This effect could be avoided by choosing lower cooling rates. Experimental data show that the cell dimensions depend on the average dislocation density and the growth conditions applied. This is illustrated in Fig. 33. Typical cell diameters in LEC crystals lie between 100 - 300 Ixm while in VCz crystals at about 1 mm and above. The formation of closed cell structures can be observed in VCz wafers down to average dislocation densities of approximately 5 x 103 - 1 x 104 cm -2. If the EPD decreases (locally) below these values the cell structure begins to dissolve and the dislocations become nearly statistically distributed (Fig. 32). At those low dislocation densities the single dislocations are separated too far from each other to interact i.e. their mean path width (as a function of temperature, time and stress field) becomes smaller than the average dislocation separation. These conditions can vary for different growth techniques (e.g. growth velocity). Thus, contrary to VCz, in VGF crystals the formation of dislocation cells is observed down to average dislocation densities of about 103 cm "2 (Fig. 34, left picture).

M. Neubert, P Rudolph/Prog. Crystal Growth and Charact. 43 (2001) 119-185

157

Fig. 32 KOH-etched VCz sample of a local area with an average dislocation density of about 2 x l03 cm-2, the distribution is nearly statistical.

To proof whether the cell structure is generated in the solid phase experimentally, low-EPD 4-inch SI GaAs single crystals with <100> orientation were bulk annealed and cooled-down much faster than after growth. Neighbouring wafers taken before and after the annealing were KOH-etched to reveal the dislocation structure. The respective wafers are shown in Fig. 33. A partially fragmented cellular structure with a

Fig. 33 Optical micrographs of KOH-etched GaAs wafers grown at the IKZ labs. Comparison of typical cell dimensions in (a) LEC and (b) VCz crystals.

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M. Neubert, P. Rudolph/Prog. C~stal Growth and Charact. 43 (200D 119-185

Fig. 34 Adjacent VGF wafers taken from the as-grown part (left) and the bulk-annealed part (right). Obviously, the cell dimensions have changed from left to fight (courtesy of FCM).

cell size well above 1 mm is obvious for the as-grown material (Fig. 34, left). The average EPD is approximately 1600 cm 2 in this case. After annealing and fast cooling-down the adjacent part the EPD was enhanced to 2400 cm -2. Dislocations are again arranged mainly in a cellular structure, however, the average size o f which is significantly lowered (Fig. 33). Consequently, the cell structure has been changed in the solid state and thus, has nothing to do with constitutional supercooling.

Fig. 35 LST images from the cell structure (left) and a cell wall (right) ofa VCz crystal (see also [97])•

Of special interest is the presence o f a dislocation substructure within the cell walls (Fig. 35). To our knowledge this is the first time it has been revealed by LST [97]. The most surprising fact is that even this shows the features o f polygonised networks in a classical manner resembling honeycomb pattern. Based on

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this observation the dynamic relaxation process seems to be a two-stage one. There is a macroscopic one, where subnetworks in the cell walls are formed. Probably, the use of the newer concepts of dynamic interaction between dislocations in ensembles [98, 99] will help to understand this phenomenon more clearly. Following reference [98], a deformed crystal is an open system in thermodynamic sense, far from equilibrium which is capable of self-organisation in the form of self-sustaining waves of plastic flow. As a result the rearrangement of the as-polygonised dislocations in a "dissipative" superstructure made of globular-like cells is imaginable. Of course, at present such a hypothesis is still speculative and requires more detailed investigations.

5.2.2.7 Slip lines

Fig. 28 c shows a layer-by-layer LST image of dislocation slip systems in (110) projection. The appearance of decorated slip systems gives rise for the conclusion that slip occurs parallel to dislocation climb at temperatures near the melting point. In contrast, if they were not decorated they had to be generated at lower temperatures (below the temperature of maximum arsenic solubility, see Sect. 5.3.1.). Thus, it is possible to estimate the temperature range for the initiation of slip lines (or slip systems) like that demonstrated in reference [101]. The simultaneous occurrence of decorated slip systems and a decorated dislocation network (Fig. 28 b and c) shows that both can be considered as high-temperature processes. However, near the edge region of the crystals we can find slip line patterns which are definitely not decorated with arsenic precipitates as LST investigations showed. These slip lines can only be resolved by KOH etch (Fig. 36). Consequently, they had to be generated at much lower temperatures than those imaged in Fig. 28 c. Such slip lines were investigated by Kuma and Otoki [101]. The authors concluded that such slip occurs generally at low temperatures because the slip lines observed by them were not decorated. Although they were right in their conclusion we now know that things are different. Slip generally takes place from low to very high temperatures being characterised by the transition from single to secondary (cross) slip and, additionally, more and more disturbed by climb processes near to the melting point temperature. Fig. 36 4-inch SI GaAs VCz wafer with high density of slip lines in the edge region. The average dislocation density is slightly below 104 cm-2.

160

34. Neubert, t~ Rudolph/Prog Crystal Growth and Charact. 43 (2001) 119-185

5

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..................... no slip lines ........ medium density high d e n ~ b /

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i

=

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.

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.

i

..........

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i

,

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i

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.

13 Nipping

.

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|

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16

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17

.

i

18

,

i

19

[arb. units]

Fig. 37 Gaussian plots of the fi'equency distribution of the occurrence of slip lines for the three categories as indicated in the text. The location of the curve peaks, i.e. the average risk factor, is indicated with numbers.

The low temperature slip (also investigated in wafers subjected to inhomogeneous lateral temperature fields [100]) seems to be a typical problem of the VCz technique because of its low absolute dislocation density. Looking at Eqn.(6) in Sect. 3.2 the effective shear stress increases with decreasing dislocation density. Thus, in VCz crystals there is less resistance against slipping dislocations being introduced at the crystal surface moving towards the centre. Compared to that, in LEC crystals slip motion is more effectively blocked due to the higher initial dislocation density. For more details on this issue see [97]. Another probable reason for the initiation of low-temperature slip lines seems to be the stress induced by large crystal diameter fluctuations. As it was shown in Sect. 5.2.1.5 (Fig. 20) large diameter fluctuations generate higher stress in the edge regions of the crystal compared to an ideal cylindrical crystal. This stress may additionally be responsible for the increased tendency to generate low-temperature slip lines. In summary, the following three important "risk factors" may be supposed to promote the slip line generation: i) low dislocation densities (less than 104 cm2), ii) large crystal diameter fluctuations, and iii) high coolingdown rates after growth (compare Sect. 5.2.2.3). In order to estimate the probability for slip line generation in VCz crystals the three risk factors were judged arbitrarily each in three categories (high, medium and low) and attributed to small numbers between 1 and 10. This approach is, of course, somewhat subjective but some rough tendencies can be estimated from experimental data. The experimental results were ordered in three categories too (high, medium and no slip line density) and then compared with the risk factors. The

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resulting Gaussian distribution curves for each category o f slip line density are compiled in Fig. 37. As can be seen the peaks o f the Gaussian curves for the three categories are clearly separated. Thus, the combination o f the three risk factors makes sense because the category "high slip line density" shows the largest average risk factor. As a consequence the three factors have to be optimised carefully to omit slip line generation.

5.2.3 Other parameters affecting the structural crystal quality It is not easy to pull cylindrical crystals in very low axial and radial temperature gradients. Low axial temperature gradients reduce the effectiveness o f heat axially transported through the crystal. This is especially true o f the latent heat produced at the phase boundary where it cannot be efficiently removed [88]. The rough estimation made in Sect. 3.5., o f course, can also be proved more precisely by numerical simulation.

5.8 MPa

I ,.0 MPa

6 lnln

__..,•

;.I MPa ;.0 MPa

i[7 MPa " t.2 MPa

5.9 MPa ,3 MPa

4 mm 1 1.3 MPa

tl,8 MPa

5,8 MPa

L7 MPa L6 MPa

2.5 1313MPa

0.7 MPa

Fig. 38 Modelling of three 4-inch crystals grown under identical thermal conditions with different growth velocities of 5 mm/h (left), 7mm/h (middle) and 10 mm/h (right). It can clearly be seen that the phase boundary tends to become nearly planar with increasing pulling speed due to the release of the latent heat. The calculated yon Mises stresses are also shown. Obviously, the stress is mainly influenced near the phase boundary i.e. due to the phase boundary deflection.

Fig. 38 shows 4-inch crystals grown with different velocities. Obviously, with respect to the current thermal conditions theses calculations indicate that it should not be possible to grow 4-inch crystals at more than 10 mm/h if one is to reduce the amount o f latent heat being released at the phase boundary effectively. Otherwise the phase boundary would become partially or completely concave. This, again, unfortunately affects the monocrystalline growth, starting with dislocation bunching and often continuing to polycrystalline growth. In practice it was found that 4-inch crystals can be grown at growth velocities between 3 and 5 mm/h. The most critical point with respect to monocrystallinity is the radial temperature gradient. Without any gradient the shape o f the crystal can not be controlled. Especially in the initial part o f the cone (after seeding) the lateral growth can give rise to polycrystalline or dendritic growth. An example o f dendritc growth is given in Fig. 39.

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In very low radial gradients the smallest temperature fluctuations or oscillation of the growth velocity can cause re-melting on a macroscopic scale. This, again, is very dangerous for twin formation [88]. Twins are often formed in VCz crystals, their frequency increases with decreasing temperature gradients. Twins almost always originate in the cone part of the crystal like shown in Fig. 40 while they

Fig. 39 4-inch crystal, grown with a large dendrite

hardly ever occur in the cylindrical part. This gives rise to the conclusion that re-melting effects are the dominant cause of twin generation in VCz crystal growth. Thus, the growth of VCz GaAs crystals becomes a special kind of art due to the lower temperature gradients, but there is a strict limit on the extent of useful temperature gradient reduction. Summarising experience at IKZ labs demonstrates that it is not sensible to grow VCz crystals in axial temperature gradiFig. 40 Top view of a 4-inch VCz GaAs crystal showing a twin originated just after seeding.

ents markedly below 20 K/cm because the monocrystalline yield reduces dramatically.

5.3 Parameters affecting the electrical quality of VCz crystals 5.3.1 Arsenic precipitation For different reasons (among them EL2 concentration), GaAs crystals are grown from a slightly Asrich melt. The solidus of GaAs shows a retrograde slope below the temperature of the maximum arsenic solubility. Therefore, cooling the crystal down below this critical temperature the arsenic in solution in the lattice becomes supersaturated, resulting in precipitation. Fig. 41 shows the T-x projection of the GaAs phase diagram with the enlarged existence region of solid GaAs. Unfortunately, this is only one proposal among a lot of others. Until today, the correct shape of the existence region just as the location of the solubility maximum is not exactly known. The data vary between e.g. 810°C [101], roughly 1100°C [64] and

M. Neubert, P. Rudolph/Prog. Crystal Growth and Charact. 43 (2001) 119-185

163

P(B )/atm D:

I

0,01 0.1

1600

1.ooz-o6

T/OC

1400

1 2 5 10 274060

1400 i l l ~ ~ / ~

1200 1000

1200 8O0 1000 Li

T//K

600

80O s

L i

~os

400

600 200

400

I

0.2

0.4 1_5 p 3"10

0,0

f 0

0.6 0.8 i =-5 -3"10

1.0 y S=1-2x

Fig. 41 T-x phase diagram of GaAs after [64].

1180°C [34]. From bulk annealing it can be assumed that the solubility maximum lies at relatively low temperatures of about 1000°C and this will be used as a convention for the present paper. Investigations by LST and etching techniques (DSL) have shown that one can mainly find arsenic precipitates decorating dislocation lines in as-grown VCz GaAs. This is why the low cooling-down rates of VCz crystals result in large mean free paths of the diffusing arsenic atoms compared to the mean separation of the dislocations and thus, the arsenic precipitates are nucleated heterogeneously at the dislocation cores (decoration precipitates). On the other hand at fast cooling-down (e.g. quenching after bulk annealing) or very low dislocation density the arsenic is nucleated within the crystal matrix (short mean free paths compared to dislocation separation) forming matrix precipitates. Thus, the diffusion kinetics controls the size and density of the precipitates. Decorated precipitates have a low density and large size while matrix precipitates are extremely small with high density. A quantitative estimation of the precipitate density of as-grown 4-inch VCz crystal result in (1 - 2) x 10s cm 3. This density is smaller than in as-grown LEC crystals by approximately a factor of 3 to 5, The same was reported by Tatsumi and Fujita [12]. The authors have attributed this fact to the lower total dislo-

164

M. Neubert, P. Rudolph/Prog. Crystal Growth and Charact. 43 (2001) 119-185

cation density, i.e. reduced nucleation centre& Additionally they reported larger sizes for the VCz precipitates. This can be understood with both, the reduced density of nucleation centres and the low cooling-down rates (longer mean free paths) compared to LEC crystals. Arsenic precipitates may affect the device manufacturing and the properties of the epi-ready surface because they can form pits or hillocks after to ehemo-mechanieal polishing. Thus, their size and concentration has to be controlled. This can be done by post growth ingot annealing (see e.g. [5, 75, 102]). In contrast to wafer annealing where the excess arsenic can be completely removed from the crystal lattice, see e.g. [75, 102, 103], bulk-annealing can only re-distribute the precipitates. However, for most purposes bulk annealing yields satisfactory results and is preferred from the economical point of view.

5.3.2 Residual impurities IKZ VCz development is routinely accompanied with impurity analyses using GDMS (Glow Discharge Mass Spectrometry). Fig. 42 shows the GDMS analysis of a 4-inch VCz crystal. The crystal was grown using argon as inert gas during the beginning stage of the VCz investigations at IKZ. The test pieces were taken from the fresh synthesised starting material and top and tail parts of the as-grown boule, i.e. from locations where segregation plays a minor or major role and the length of stay in the molten stage is short or long, respectively. As can be seen from Fig. 42 the concentration of most residual impurities is lower than 1014 cm -3. Si, P, Cl, Ca, Zn and Se were found to be in the 1015 cm -3 range. Relatively large amounts of the

106

.

-

'

4

1

IIIIII n.II

[

lib

top. ofthe crystal I

g lo

'it 10o

B C

N Na AI P CI Ti Mn Co Cu Se Cd Sn 0 Mg Si S Ca Cr Fe Ni Zn Mo In

kind of residual impurity Fig. 42 Impurity analysis of the starting material, top and tail part of the SI GaAs VCz crystal grown from this material. In the cases where the tree bars are identical indicates that concentrations lie below the detection limit of the respective element.

M. Neubert, P Rudolph/Prog. Crystal Growth and Charact. 43 (2001) 119-185

165

iso-electrical elements B (0.8-2 x 1017 cm "3) and N (2-4 x 1016 cm "3) were found (BN crucible, B203 encapsulant). The high nitrogen concentration can be roughly explained by thermo-chemical modelling [38] and seems to be an equilibrium concentration with respect to the complex chemical system inside the puller. While B increases during the growth run, C, O and Si are reduced by 1 to 2 orders of magnitude and N remains nearly constant. The S is assumed to be a companion of the arsenic in the source and thus, its concentration increases with time. Zn is obviously introduced due to the handling procedure. Both Zn and S could later be reduced in concentration by appropriate measures. The relatively high concentration of boron may be somewhat problematical because the implantation efficiency in implanted devices is known to be influenced by the boron concentration. Additionally, as reported in [104] above a concentration of 1017 c m "3 3 - 4% of the incorporated boron atoms substitute on arsenic sites as acceptors. However, these high values of incorporated boron are not typical for VCz crystals. Usually, the values lie in the range of < 2 x 1016 cm 3. LVM IR-absorption measurements, detecting directly the IBex] defect, roughly confirm the GDMS measurements. The results show that the inner growth chamber only marginally affects the crystal purity. Also the carbon incorporation is not affected by the graphite inner chamber (see the following section). However, the reaction equilibria are generally shifted compared to LEC growth because of the much higher temperatures inside the VCz chamber and thus, in detail, we have found slightly different concentrations of impurities for VCz from LEC.

5.3~3 Carbon concentration and distribution It has been shown in the authors labs that the carbon concentrations in VCz crystals can be adjusted in the range of _< 1014 to > 1016 cm 3 [33]. This is the first presentation of carbon concentrations below the mainly reported lower limit of about (2 - 3) x 1015 em 3 [12, 15, 17] in VCz crystals. It can be stated here that the fundamental mechanism of carbon incorporation in the melt and the growing VCz crystal are not different from those of LEC. Generally, the inner VCz chamber, made of graphite, does not affect the total carbon content. Nearly the same carbon concentrations have been found in conventional LEC crystals grown previously in the same puller under comparable conditions [ 105]. This is additionally confirmed by thermo-chemical simulations. It does not matter whether there are milligrams or kilograms of graphite present in the system. For instance, in VCz crystals, grown from a fresh synthesised starting charge under stationary argon pressure of 10 bars and a boric oxide water content of 200 ppmw in both cases nearly the same carbon concentrations in the range of (1 - 4) x 1015 cm 3 were found in the crystal. This is because of the dominance of the oxygen potential within

the system compared to the presence of elementary carbon [38, 106].

M. Neubert, 17 Rudolph/Prog. Crystal Growth and Charact. 43 (2001) 119-185

166

2

!

T ......... I

;

o

g

-~

~

c

~ 1014' 8 a

0.0

0.2

0.4

0.6

0.8

1.0

solidified fraction g

Fig. 43 Axial carbon distribution in a VCz GaAs crystal grown from repeatedly used material with added Ga203 (upper) and under flowing nitrogen working gas (below). The water content of the boric oxide was 200 ppmw. In both cases the nitrogen working gas pressure was about 4 bars. Varying the water content o f the boric oxide from 200 to 1000 ppmw similar to conventional LEC the carbon concentration in VCz crystals could be decreased down to 1 - 2 x 1015 cm -3. Also the type o f the working gas has an influence. As already described for LEC [38, 107] the experiments with VCz crystals showed that the carbon concentration is about half that using nitrogen instead o f argon gas. This behaviour can be explained with the higher oxygen potential enforced by the decomposition o f the boric oxide and the formation o f BN, resulting in a carbon extraction from the melt [108]. Further experiments were carried out placing titanium getters inside the VCz growth chamber. Titanium cracks carbon monoxide [109], i.e. minimises the CO concentration and thus, limits the carbon incorporation to the melt. Using the titanium getter the carbon concentration could be reduced down to 8 x 10 z4 cm "3 in the conical part o f a VCz crystal. Un3

Jrepeatedly used I 5

;

~

.--~

~

T

~ llr "T:~"e"~T"--- e

¢o

1015 0

=

i

[

i

i

i

i

t

10

20

30

40

50

60

70

80

90

distance from edge [mm] Fig. 44 Radial dist~bution of the built-in carbon concentration m Vcz GaAs

crystals. The qualitative shape of the distributions changes with absolute carbon concentration as explained in the text.

M. Neubert, P Rudolph/Prog. Crystal Growth and Chamct. 43 (2001) 119-185

167

fortunately, the carbon content was again increasing along the crystal axis up to 1,3 x 10 is cm 3. Probably, the titanium surface was self-passivating by the formation o f oxide and carbide layers. It was proved by LVM IR-measurements that no titanium was incorporated in the crystal during the whole run. However, titanium seems not to be the best way to influence the oxygen potential inside the chamber.

•- ~

~, I0 E O

16.

c O

•

m

m

mm

m

m

m

•

•

•

•

1.U"

m

E O

g O to

]015 •

#

•

•

•

v

d~l.,

O

-50

-25

0

25

50

distance from center [mm] Fig. 45 Radial distribution of the carbon concentrations of crystals grown with nearly fiat phase boundaries a) 3-inch and b) 4-inch in diameter.

Fig. 43 shows the axial carbon distribution curve o f a crystal grown with Ga203 added to the boron oxide melt. A roughly constant carbon concentration o f ~ 1 x 1015 cm 3 was measured between g = 0.2 - 0.8. Opposite to other crystals with similar low carbon concentrations, the carbon concentration decreases slightly along the crystal axis. The axial carbon distribution can be classified into two general categories i) crystals grown from starting charges with carbon concentrations below 2 x 1015 cm 3 showing an axial increase o f their carbon content (carbon incorporation from the gas phase via CO gas) and ii) crystals grown from starting charges with a carbon concentration above 5 x 10 ~5 cm 3 showing an axial decrease o f the carbon comem (segregation coefficient k~ = 1.44 [110]; = 2 [111]). Adding Ga203 to the boric oxide, the reaction 3 CO + 2 Ga. <-->3 C + Ga203 is shifted towards the CO / Ga side. Thus, C is extracted from the melt forming CO and the segregation effect becomes dominant, explaining the non-representative behaviour in Fig. 43. Considering the results discussed above stationary (self-contained) regimes are not sufficient for the reduction o f the carbon concentration in VCz crystals markedly below 1015 cm-3. Rather, in order to maintain

168

ll~ Neubert, P Rudolph/Prog. Crystal Growth and Charact. 43 (2001) 119-185

a definite CO concentration and hence fugacity within the growth atmosphere a dynamic regime of flowing gas has to be applied. In fact, growing the crystals under a flowing nitrogen atmosphere the carbon concentration could be markedly decreased down to 8 x 1013 cm 3 near the seed and 1,9 x 10 TM cm 3 near the tail end (Fig. 43, below). Obviously, a flowing inert gas extracts CO effectively from the system and stops its incorporation into the melt. At present, it is not yet possible to control precisely a given CO fugacity in the VCz system but this is under development [33]. Fig. 44 presents several radial carbon distributions in 3-inch VCz crystals (LPA Mark III). Those curves with higher absolute carbon concentration show radially decreasing carbon content while those with lower concentration behave vice versa. This phenomenon can be explained with the interface shape. In the case of a convex phase boundary, the central part of a (later cut) wafer was grown earlier than the edge part. For low initial carbon concentrations the axial distribution follows the carbon incorporation and for high initial concentrations the segregation is as mentioned above. Thus, because of the different times of solidification for low absolute carbon contents the carbon concentration increases from the centre to the edge and vice versa. This behaviour vanishes with a nearly planar interface. Then the solidification occurs simultaneously resulting in a radial equipartition. This is just the case for typical, good quality VCz crystals (Fig. 45).

5.3.4 EL2 concentration and distribution The electrical properties of SI GaAs are closely connected to the dislocation density and their distribution [112, 113]. This is caused by the dislocation motion mechanism (multiplication) which is mainly driven by climb of dislocations. Generally, climb is only possible by interaction of the dislocation with native point defects. As pointed out in Sect. 3.2, climb in GaAs works via the Petroff-Kimerling mechanism producing EL2 defects. Thus, the EL2 concentration directly reflects the dislocation distribution, especially the wellknown cell structure. The EL2 concentration of as-grown crystals is markedly increased near the dislocation cell wails while, it is lower in the cell interior. That is why as-grown GaAs crystals show a mesoscopic inhomogeneous distribution of the electrical resistivity [75, 102] (besides, of course, the gettering of residual impurities in the dislocation cores). This mesoscopic distribution can only be homogenised by post growth annealing, a well-established procedure within the matured technology of SI GaAs large-scale production [5, 75,]. Generally, as-grown VCz crystals are characterised by lower EL2 concentrations (5 - 10) x 1015 cm "3) compared to LEC crystals. This implies that there may be a correlation to the average EPD. Fig. 46 compiles local data of EPD and EL2 concentrations. Obviously, it is not possible to find an unambiguous functional dependence between both parameters. However, as can be seen from Fig. 46, the scatter of the EL2 concentrations decreases remarkably with increasing EPD. The straight line indicates the minimum EL2 concentration that can be reached for a certain dislocation density. Possibly, there are additional factors influencing the EL2 concentration. Beside the dislocation density this can be the cooling-down rate (precipitation of ar-

169

M. Neubert, t?. Rudolph/Prog. Crystal Growth and Charact. 43 (2001) 119-185

senic) and the deviation from stoichiometry grown-in during solidification from the melt. In our VCz crystals the EL2 concentration slightly decreases from top to tail (Fig. 47). This could, possibly, be explained by segregation if one knows that the most of the VCz crystals were grown from repeatedly used material and thus, from gallium-rich melts, i.e. on the left side of the congruent melting point. However, to investigate all factors influencing the final as-grown EL2 concentration requires a separate test program.

5.0

*

4°t

/

.op 0.2

Z 0.4

0.6

Y.

t1

*

.':-'.

0.8

1.0

EL2 °

[1016cm -3]

1.2

1.4

t 1.6

1.8

Fig. 46 Quantitative correlation between local as-grown EPD and EL2 concentrations in different VCz-wafers. The local data were taken from areas of some mm 2.

18

oE

16

1.2

"E

10

8 8

178

W

06 0.4

top

tail axial position

Fig. 47 EL2 concentration of as-grown VCz GaAs crystals measured at top and tail grown in both pullers LPA Mark 3 and C1358.

M. Neubert, P Rudolph I Prog. Crystal Growth and Charact. 43 (2001) 119-185

170

5.3.5 Resulting electrical properties The qualitative correlation between dislocation density, EL2, cartier and carbon concentrations with the electrical resistivity can be clearly demonstrated in Fig. 48 showing a sample with pronounced radial EPD distribution. As can be seen, the EPD curve is slightly W-shaped which is not typical for VCz crystals but very helpful for these considerations. The EL2 distribution shows qualitatively the same distribution as the EPD (although it was shown above that there is nor clear quantitative correlation!). Together with the equipartition of the compensating carbon concentration the cartier concentration shows just the same behaviour. Consequently, the distribution of the carrier concentration finds its expression in the inverse Wshape of the resistivity distribution. Summarising this, the macroscopic resistivity distribution is roughly a function of the EPD distribution as long as the carbon concentration is nearly uniform. Thus, not only the reduction of the absolute dislocation density is of key interest for the VCz investigations but just as much its homogeneous distribution over the whole wafer to level the resistivity distribution.

-• -,,-

10 2

resistivity [10 7 O h m cm] carrier conc. [10 6 cm-3] EL2 ° [ 1 0 1 5 c m -3] -.-e- carbonconc. [ 2 x 1 0 1 5 c m -EL2 ° / carbon conc,

' '

-3]

4

~

3

'

2

~ cr

101 4 a

i

0

~

i

L

10 20

i

i

i

i

30

40

50

i

i

i

r

60

70

80

distance from edge

J

i

90 100

[mm]

Fig. 48 Radial correlation of EPD-, carbon- and EL2-distribution with resulting electrical properties.

M. Neubert, P. Rudolph/Prog. Crystal Growth and Charact. 43 (2001) 119-185

10a

111111 •

C~

171

n

u

=

"

•

•

u

n

n

"

u

n

u

10a

C i t

' ~ 10;'

-

~ f~

~

-n9

~

n

10 e -50

-25

0

50

25

distance from center [mm]

80OO

[11o] " "

~" 7000

" ' "

6000 5000

n

n

i

m

•

•

I

iii

•

•

4000 -50

-25

0

25

50

distance from center [ram]

Fig. 49 Radial distribution of electrical resistivity (a) and cartier mobility (b) in as-grown VCz crystals showing nearly fiat interfaces.

Fig. 49 a and b show radial distributions of the electrical resistivity and cartier mobility being typical for the present stage of as-grown VCz crystals. For instance maximum electron mobilities in the range of 7000 cmZ/Vs were found in as-grown crystals, which correlate well with the maximum of the mobility versus resistivity curve of SI GaAs at = 2 x 107 ~) cm [5]. However, a nearly uniform macroscopic resistivity distribution is difficult to achieve in as-grown crystals. The residual inhomogeneities of the EL2 distribution and thus, the resistivity distribution ([32]) can only be homogenised by subsequent bulk annealing. In the mesoscopic range the same behaviour can be observed as in the macroscopic range. Fig. 50 shows two resistivity maps, taken from different radial positions of a wafer by measuring the point contact current I~ [87]. In the mesoscopic range the resistivity reflects the well known cell structure of GaAs. The explanation is the same as that given above - the resistivity (and thus carder and EL2 concentration) is closely connected to the dislocation density. The point contact current is inversely proportional to the resistivity being high in the cell walls and low in the centres of the cells. The higher current within the walls is determined by both the higher cartier concentration (EL2) and residual impurities which are usually gettered to the dislocation cores. The resistivity difference between cell wall and centre often exceeds one order of magnitude in LEC crystals [75]. Fig. 50 a, was taken from the centre of the wafer with relatively large cells being typical for VCz. Fig. 50 b shows an Ip¢ measurement near the crystal edge. The smaller cell dimensions are a consequence of the increased dislocation density in this position.

172

M. Neubert, t~ Rudolph/Prog. Crystal Growth and Charact. 43 (2001) 119-185

'rmra

lmm

Fig. 50 Mapping of the point contact current I~ of an as-grown VCz-wafer (the Ipc is inversely proportional to the resistivity and, thus, the figures can be regarded as resistivity maps). The pictures of 5 x 5 mm2 were taken from R/2 (a) and near the edge (b). a - large cells (low average dislocation density) with large scatter of resistivity, i.e. EL2; b - small cells (high dislocation density) with smaller scatter of resistivity, i.e. EL2.

The high mesoscopic scatter o f the resistivity can be removed b y post-growth bulk-annealing as already mentioned. The homogenisation effect is achieved by the redistribution o f the EL2 defects. This is demonstrated in Fig. 51 for a typical VCz crystal by radial EL2 line-scans over adjacent wafers from an asgrown (lower curve) and a bulk annealed (upper curve) part o f the crystal. The as-grown EL2 scatter could be dramatically homogenised and the absolute EL2 concentration was fixed to the desired value o f 2 x 1016 cm 3 with a residual scatter o f only 2.5 %. Concluding this section one can state that VCz material is able to meet similar electrical specifications as with LEC material. 1.4

1.2 E ~ 1.0 o .,.-

~, 0.8 uJ

0.6 0.4

....... annealed; std. dev.: 2.5 % -as town; std. dev.: 16.3 %

0

10

20

30

40

radius [mm]

Fig. 51 Radial EL2 distribution along [110] in a wafer taken from an annealed VCz-grown bulk section compared to a VCz wafer from an adjacent as-grown section of the same crystal.

M. Neubert, P Rudolph/Prog. Crystal Growth and Charact. 43 (200D 119-185

173

6 NEWER ACHIEVEMENTS

6.1 Growth without B203 encapsulant - a new hot-wall approach Initially, when the melt growth activities on GaAs were started within the fifties, the application of boric oxide was the stop gap to be able to grow GaAs at all. However, nowadays, it plays an important role not only to prevent the arsenic evaporation from the melt, but also with respect to the complex chemistry and the thermal conditions during growth - see the foregoing paragraphs. On the other side replacing the boric oxide encapsulant may have some advantages like e.g. i) direct control of the melt composition (stoichiometry deviation), ii) growing semiconducting crystals using silicon as dopant and iii) the removal of the stress maximum near the boric oxide surface as described in Sect. 5.2.2.2. In the past there were several attempts to do this by the hot-wall technique [7, 8, 9, 115]. However, from a commercial point of view the hot-wall technique is not suitable for the mass production of GaAs wafers because of its high investment and operating costs [2]. Possibly, the VCz technique is capable to close this serious gap between thermodynamic requirements and technological feasibility. The only difference between hot-wall and VCz is the construction of the inner chamber surrounding the growing crystal. Whereas it is hermetically closed in the hot wall case, it is semi-open in the VCz case. Without any question there is no difference from a thermodynamic point of view whether one grows a crystal in a static equilibrium (hot wall) or in a dynamic equilibrium (VCz). In the latter case one has only to guarantee that i) the compensating arsenic flow from the source into the chamber has to be equal to the outflow of arsenic through the solid seals and ii) that the source of arsenic is not exhausting during the whole growth run. However, analysing the first experiments, it seems to be very difficult to grow crystals without boric oxide in a thermally optimised low temperature gradient system like VCz. The crystals show a very high tendency to develop polycrystalline growth. The main reason for this is the changed thermal field. In the thermally optimised VCz case the boric oxide encapsulant remains as the very last measure to produce a sufficiently high radial temperature gradient and to guarantee the strictly axial flow of heat. Removing this encapsulant the radial gradient reduces dramatically again and the tendency for polycrystalline (or

Fig. 52 DSL-etched sample of the core

region of a n-type SI GaAs VCz crystal grown withoutboric oxide. The unevenand deeper areas are clearly separated and eorrespondto gallium- and arsenic-richmaterial, respectively( see [114]).

dendrite) growth increases. Thus, for growth without boric oxide the temperature field within the whole apparatus has to be rearranged completely compared to conventional VCz. The second probable reason is thermodynamic in nature. Generally, the surface of the melt varies in temperature. It is, e.g., nearly at the melting point temperature in the vicinity of the growing phase boundary

174

M. Neubert, P Rudolph/Prog. Crystal Growth and Charact. 43 (2001) 119-185

whilst it is at a much higher temperature near the crucible wall (close to the heater). As it was already explained in Sect. 3.4, the thermodynamic system is invariant with direct contact between gas phase and the melt. Consequently, each local element of the melt surface corresponds to a particular equilibrium composition with respect to its actual temperature. This, however, may lead to compositional fluctuations at the growing interface when the melt is transported due to convection. In fact, Fig. 52 shows an DSL etched sample of a crystal grown without boric oxide. As shown in this figure, the whole crystal shows a patchwork of areas being either gallium-rich or arsenic rich. Such behaviour has never been observed so markedly before and thus it may possibly be attributed to the described compositional fluctuations. If those fluctuations actually occur, the tendency for constitutional supercooling is increased and can additionally explain the high tendency for polyerystalline growth of this VCz hot-wall growth mode compared to conventional VCz. Nevertheless, the IKZ proudly presents the first GaAs single crystal grown in such a VCz apparatus (Fig. 53). It looks similar to a typical VCz crystal, i.e. the thermodynamics controls as expected. To our knowledge it is the first presentation of a GaAs crystal grown without boric oxide by the VCz technique so far published. Uptil now it has not been possible to grow single crystals with diameters of more than 40 mm due to the above discussed difficulties. However, herewith the confidence shall be expressed that it will be possible to grow crystals by this technique up to diameters of 100 mm in future.

Fig. 53 Side (left) and top (right) view of the first single crystal grown without boric oxide encapsulant using the VCz technique. The diameter is about 40mm.

M. Neubert, t? Rudolph/Prog. Crystal Growth and Charact. 43 (2001) 119-185

175

6.2 First results of6-inch VCz-GaAs single crystals Recently, the growth of 6 inch (150 mm) SI GaAs VCz crystals has been started successfully in IKZ laboratories. Fig. 54 shows two typical crystals, 200mm in length with a weight of approximately 18 kg. Obviously, the outer shape can be controlled much more precisely as it was formerly possible for the 3- and 4-inch crystals. This is caused by the experiences / adaptations described in See. 4.1.4. The crystals were grown with counter rotation. The growth rate of 5 mm h -I is rather high for these diameters and consequently, the phase boundary is correspondingly fiat (Fig. 55).

Fig. 54 6-inch VCz crystals with length of about 200 mm grown at the IKZ Berlin

Fig, 55 Phase boundary shape in the shoulder of a 6 inch VCz crystal revealed by striaton technique.

176

M. Neubert, P Rudolph/Prog. Crystal Growth and Charact. 43 (2001) 119-185

The EPD's o f the first crystals lie in

50000

the range o f roughly 1 to 5 x 104 cm -2 and

40000

are, thus, markedly below those o f typical LEC material. Fig. 56 shows the EPD

cylinderto~..o- EPD[100]1

30000 o 13_ 20000 LU

results o f tree parts o f a 120 mm long

10000

cylinder. As it can be seen the EPD lies at

0

0

10

and below 2 x 104 cm 2 in the top part

20

30

40

50

distance from edge

60

70

80

[mm]

being a consequence o f the very fiat inter50000

face shape (Fig. 55). Then the EPD conN-'

tinuously increases towards the end o f the cylinder. Only the centre o f the slices remains at a dislocation density o f about

cylinl~ ~'k ,k derc~nte 2 EPD[100]1

40000 30000

o 0_ uJ

20000 10000

104 cm "2. This can be explained by the not

0L yet optimised interface because it con-

0

10

20

30

40

50

distance from edge

60

70

80

[ram]

tinuously changes to a concave shape

6oo00 ~ \\

towards the end o f the cylinder. Addition-

This process is not yet optimised.

x. ",~

40000

slice is caused by dislocations moving backwards while growing the tail cone.

cylinderend

50000

ally, the high edge slips density in the end

I÷

EPOtl00jl

30000 w

20000 10000 0

0

10

20

30

40

50

60

70

distance from edge [ram]

Fig. 56 EPD distribution in one of the first as-grown 6 inch VCz crystal.

7 S U M M A R Y AND O U T L O O K To reduce the costs for device production there is an accelerated increase o f the crystal diameter in GaAs wafer production similar to that experienced in silicon production one decade ago. Today's challenge is to produce crystals with larger dimensions whilst maintaining the usual crystal qualities. This is scarcely possible by the conventional LEC technique because o f the necessary high temperature gradients and thus, non-linearities within the growing crystal. The VCz method as a modified LEC technique is one among several approaches to overcome these problems and to meet the above requirements. As shown in the present paper, the thermal induced stress is the main factor influencing the structural crystal quality during growth. All measures to minimise this stress are aimed to linearise the internal temperature field. To a first order approach this can be done by lowering the axial temperature gradient. To

M. Neubert, P. Rudolph/Prog. Crystal Growth and Charact. 43 (2001) 119-185

177

protect the very hot crystal surface from decomposition an additional gas-tight inner chamber is applied together with a temperature controlled source of pure arsenic establishing the necessary arsenic partial pressure inside. There are four crucial points among less important ones for the successful VCz development at IKZ labs i) growing the crystals in dynamic equilibria (Sects. 3.4 and 4.1.1) and ii) use of the high-tech insulation material CBCF, simplifying the technological handling, especially the second point being the pre-conditinn for iii) the thermal seclusion of the inner assemblies (Sect. 4.1.2) reducing the expenditure for the adaptation to different growth systems and iv) consequently establishing a nearly axial flow of heat through the crystal as the most important measure to reduce the thermal induced stress. Beside this the following important resuits were obtained in detail. Refining the inner constructions the arsenic loss out of the growth chamber could be reduced down to 1-2 g h 1. This value is small enrugh to enable growth runs with a duration of several days. If the arsenic pressure is chosen correctly, the crystals show mirror-like surfaces as it would be expected from the phase relations. Combining experimental investigations with numerical simulations a large field of parameters was scanned to find out the best conditions to grow 4-inch crystals with dislocation densities < 104 cm 2 being homogeneously distributed over the main area of the wafers. The most important parameter to achieve this goal has already been mentioned - the co-axial flux of heat through the crystal. Regarding dislocation density and distribution the interface shape should be nearly planar, however, because of the problems with monocrystalline growth and diameter uniformity of the crystals, a slightly convex shape is preferred. At least for the VCz case, iso-rotation of crystal and crucible is a crucial parameter for obtaining nearly fiat solid liquid interfaces with monotonous curvature. The interface shape can be carefully adjusted by setting appropriate rotation rates. Opposite to conventional LEC, it was additionally found that the dislocation density can be reduced and its distribution be homogenised by lowering the height of the boric oxide. To maintain the dislocation density set at high temperatures the cooling-down process has to be carefully adjusted. As a rule of thumb the cooling-down rates have to be in the same range like those the crystal is exposed to during growth. Further characteristic properties of VCz crystals are i) their radial dislocation density distribution being more U-shaped compared to the typically W-shaped of LEC material, ii) slip line generation proceeding from the crystal surface to the centre due to the larger effective shear stress because of the lower absolute dislocation densities and iii) the very low residual strain comparable to that of as-grown LEC wafers. A typical cell structure is also observed in VCz crystals. However the average cell dimensions are larger than those in LEC material reaching several millimetres. Obviously, the cell dimensions depend on the average dislocation density, or in other words, the mean separation of the dislocations with respect to the

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thermal history of the crystal. Falling below densities of approximately 5 x 10j cm -z the cell structure begins to dissolve and the dislocations become nearly statistically distributed in the VCz case. Several arguments are presented to explain the real origination of the cell structure. From our point of view it arises from multiplication and polygonisation of only those dislocations formed after solidification and definitely not due to constitutional supercooling. The electrical parameters of VCz material are comparable with those of conventional LEC material. However, their spatial distribution is more homogeneous in particular cases even in the as-grown state. A remarkable difference compared to LEC crystals shows the EL2 concentration. It is significantly lower in asgrown VCz crystals with respect to the lower dislocation density. A subsequent bulk-annealing is able to redistribute the EL2 defects and to set its concentration to the desired values just like in LEC wafers. Arsenic precipitates are generated during cooling-down similar to the situation with LEC. In VCz crystals almost always decoration precipitates were found aligned at the dislocation cores with lower density and larger size than in LEC. Carbon as the compensating acceptor in GaAs was found to be incorporated on arsenic lattice sites CAs with concentrations ranging from 1016 cm "3 down to below 1014 cm "3, the lower value being firstly reported for VCz crystals. For the first time a single crystal has been presented grown in a VCz apparatus omitting the boric oxide encapsulant. From the thermodynamic point of view the system works similar to a hot-wall regime with the only restriction that the crystals grew in a dynamic equilibrium. With this technique it may finally be possible to grow GaAs crystals with controlled stoichiometry on an industrial scale. However, until today, it is not possible to grow large single crystals under the present VCz conditions in low temperature gradients. Further experiments are required. First 6 inch (150mm in diameter) SI GaAs crystals are presented with showing reasonable structural qualities. In contrast to former investigations on 3- and 4-inch crystals the diameter control could be improved. Summarising this paper, the VCz technique is not easy to master. Because of the low temperature gradients many additional problems arise in comparison to LEC growth of GaAs. Among them the difficulties with temperature and crystal diameter control have to be mentioned as described in detail in Sect. 4. Finally, it has to be noted, again, that the tendency for polyerystalline or dendritic growth and for twinning is markedly increased growing VCz crystals. This has to be mastered by lots of additional measures. However, optimising the VCz process carefully, the technological requirements are roughly the same as those in LEC growth. Thus, the VCz technique is capable of being transferred from the laboratory to an industrial scale.

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ACKNOWLEDGMENTS The authors are grateful to M. Pietsch, M; Czupalla and K. Boumot for growing the crystals, B. Lux for sample preparation, S. Bergmaun, U. Juda and H.Baumtiller for carrying out different etching techniques, J. Donecker and M. Naumann for optical EPD mapping and laser scattering tomography, respectively, J. Kluge for near-band IR absorption (EL2 analysis), W. Ulrici (PDI Berlin) and K. Jacob for LVM IR absorption measurements, N. Abrosimov for residual strain analysis, K. Irmscher for Hail measurements, W. Siegel ( T U B A Freiberg) for point contact measurements, Ch. Frank, W. Miller, U. Rehse, K. Brttcher, J. Fainberg (Univ. Erlangen), G. Miiller (Univ. Erlangen) and S. Eichler (FCM) for numerical calculations. T. Flade, B. Weinert, A. Krhler and A. Seidl from "Freiberger Compound Materials (FCM)" for collaboration and special discussions. Especially, the authors have to thank M. Jurisch (FCM) for his valuable contributions to the present work in form of helpful discussions and for critically reading and revising the manuscript. This work was supported by the German Federal Ministry of Education, Science, Research & Technology under contract No. 01 BM 501/0 and 01 BM 501 A/0.

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Michael Neubert Dr. Michael Neubert was born at August 25 th, 1960 in Jena (Germany) and is currently employed at Institute of Crystal Growth (IKZ) in Berlin, Germany. At present he is the head of the group "Czochralski Semiconductors". M. Neubert was studying Crystallography at the Humboldt University in Berlin. After finishing his studies he joined a Semiconductor Company (WF Berlin) from 1987 - 1989. 1989 to 1994 he went back to Humboldt University as Assistant at the Institute of Crystallography. He focused on native point defect equilibria (stoichiometry related problems) in CdTe and HgCdTe. His PhD thesis "Contributions to equilibrium thermodynamics and diffusive behaviour of native point defects in HgCdTe" was completed in 1994. In spring 1994 he changed to IKZ, beginning his work on low temperature gradient Czochralski growth of GaAs. M. Neubert got the Young Scientist Award of the German Association of Crystal Growth (DGKK) in 2000. He has approximately 20 original publications and owns 3 patent publications.

l!K Neubert, P Rudolph/Prog. Crystal Growth and Charact. 43 (2001) 119-185

Peter Rudolph Peter Rudolph, Professor Dr. habil, Dr. Ing. was born at July 1st, 1945 in Gera (Germany). Since 1994 he is employed at the Institute of Crystal Growth in Berlin and deals with growth and characterisation of III-V compounds, i.e. GaAs, by modified Czochralski method. He received the Diploma of Electronic Technology at the Technical University of Lvov (Ukraina) in 1969. The PhD (Dr. Engineer) of Solid State Physics and Technology (on crystallisation of CdSb layers) he obtainted at the same university in 1972. From 1973 to 1993 he was employed at the Institute of Crystallography and Material Science of the Humboldt University in Berlin as lecturer of Kinetics of Phase Transitions, Crystal Growth and Technical Crystallography. In 1979 he obtained the DSc (Dr. habil) of Crystallography at the Humboldt University. Since 1980 he led the Laboratory of Crystal Growth of IV-VI (PbTe) and II-VI materials (CdTe) and cared the industrial growth of LiNbO3 and PbMoO3. In 1978 and 1992 space crystal growth experiments were carried out. From 1991 to 1993 he was member of the expert group of the ESA on melt growth experiments. From 1993 to 1994 and in 1998 he was employed as Guest Professor at the Crystal Growth Laboratory of Prof. T. Fukuda of the Tohoku University in Sendai (Japan). During these periods he held lectures on Fundamentals of Crystal Growth and dealed with the Bridgrnan growth of CdTe, ZnSe, InP and oxide fiber crystals. He co-laborated with numerous Japanese Companies. During several guest residences he held lectures on Crystal Growth at the Ulan Bator University (1980), Complutense University of Madrid (1987), University of Monastir in Tunesia (1996), Hebrew University of Jerusalem (1996) and ETH Lausanne in Switzerland (1997). He acted as lecturer of several International Schools on Crystal Growth of the IUCr and IOCG in Madras (1995), Rimini (1998), Beatenberg (1998), Campinas (1999), Zao (2000) and Trieste (2001). Since 1996 he is member of the 1UCr Commission on Crystal Growth and Characterization of Materials. His publication work comprises 11 monograph contributions, 3 editions, 134 original publications and 17 patent publications.

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