Germanium Single Crystals, Growth of

Germanium Single Crystals, Growth of

Germanium Single Crystals, Growth of In 1871 Mendeleyev postulated the existence of an unknown element, to be placed between silicon and tin in the pe...

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Germanium Single Crystals, Growth of In 1871 Mendeleyev postulated the existence of an unknown element, to be placed between silicon and tin in the periodic table and which, according to his prediction, had to resemble silicon in its properties; he suggested the name eka-silicon. Mendeleyev’s predictions for the properties of the element with atomic number 32 were remarkably close to reality, as determined after the discovery of germanium in the mineral argyrodite (4Ag .GeS ) by Winkler in 1886. # the #bonding in germanium Belonging to group IV, crystals is covalent. In general, covalent cohesion is characterized by high hardness and electrical insulator or semiconductor behavior. The crystal structure is of the diamond type. A unit cell contains eight atoms, each surrounded by four nearest neighbors in a tetrahedral configuration. For a summary of the physical properties of germanium, see article Germanium. In 1947, Bardeen, Brattain, and Shockley from Bell Labs invented a device which they called a transistor. The transistor could amplify electric current like a valve, but its power consumption was very low. The transistor was made of germanium! Figure 1 shows a picture of this first germanium device, the first indus-

Figure 1 The first point-contact transistor, invented at Bell Labs: made of germanium (courtesy of Bell Laboratories).

trial application of the element germanium. It was only in 1954 that the first silicon transistor was introduced; silicon was cheaper than germanium and available in large quantities, and became the platform for the electronics industry. Nowadays, germanium and some derived chemicals (GeO and GeCl ) are key materials for a wide variety # % of applications (see later). Union Minie' re has been active since the early 1950s in the extraction, refining, and transformation of germanium and is the worldhs largest producer of the element. The total worldwide consumption of germanium is estimated to be about 92–96 t (Table 1). Table 2 focuses on the most important applications of germanium crystals.

1. The Germanium Production Process Germanium is found in low concentrations in certain metallic ores and minerals, where it is always associated with another metal such as zinc, lead, or copper. It is often extracted from the leach residues coming from electrolytic zinc plants. Germanium is in some cases also recovered from coal ash from electric power plants. The zinc leach residue typically contains 0.5% germanium. The potential availability from zinc flow sheets outstrips by far the germanium demand. Tight raw material supply would typically result from the lead-time needed to upscale extraction and refining capacities. Union Minie' re expects a healthy balance between supply and demand until at least 2005. Net demand will only rise slowly due to increased recycling in the industry. A simplified production flow sheet starting from a zinc leach residue is shown in Fig. 2. After leaching the zinc leach residue in sulfuric acid, and solvent extraction, a 50% germanium concentrate is obtained. Chlorination and fractional distillation yield ultrapure GeCl . Hydrolysis of GeCl , filtration, and appro% priate% drying yield various grades of GeO . Electronic grade GeO is reduced in a# hydrogen atmosphere. Care has to# be taken to minimize the synthesis of the intermediate volatile reaction product GeO. After complete reduction the germanium is molten, and a polycrystalline ingot is then solidified. The purity of the germanium at this stage is 10 ppb. The purification process in elemental germanium is principally based on segregation of impurities at the liquid–solid interface. Most impurities in germanium (see Table 3) have a distribution coefficient significantly different from 1, so by controlled directional solidification of the molten phase the material can be purified. The polycrystalline ingots are therefore further purified through zone refining. In this process, a molten section (zone) of the ingot is travelled along the ingot, and the impurities are dragged with it and concentrated at the extremities of the ingot. Yield 1

Germanium Single Crystals, Growth of Table 1 Annual global consumption of germanium (1999). Application Infrared optics Optical fibers PET catalysis Medicine Luminescence Germanate glasses BGO Gamma ray detectors Electronics and optoelectronics

Germanium form\quality

Consumption

Optical grade germanium Ultra-pure GeCl % GeO GeO# GeO# GeO# # Low-chlorine BGO grade GeO # High-purity germanium Electronic grade crystals and wafers

10 50 26 1 3 1 1 1 3

Total (metric tons of Ge)

96

Table 2 The most important applications of germanium crystals. Application

Benefits of Ge

Crystal specifications

Infrared optics (lenses and windows)

transparent in wavelength range 2–15 µm high refractive index (n l 4) low chromatic dispersion high mechanical strength

resistivity 5–40 Ω cm, n-type single crystal (preferentially) low residual stresses

Gamma-ray detectors

high density and atom nr. crystals can be purified to 10"! cm−$ electrically active impurities high carrier mobility

single crystal doping level 10"" cm−$ to 10"! cm−$, depending on detector dimensions deep level density 10) cm−$ low dislocation density

Substrates for GaAs based opto-electronic devices (solar cells, LEDs, diode lasers)

sufficient lattice match with GaAs high mechanical strength lower wafer cost (comp. to GaAs)

single crystal low dislocation density low microdefect density

optimization is achieved by adjusting the cross section of the ingot, the travel speed of the molten zone, length of the molten zone, and length of the ingot (Pfann 1958). The purity of the center part of the ingot is of the order of 1 ppb. These zone-refined ingots can be used as charge material for the growth of electronic- and opticalgrade crystals, but prior to the crystal growth of γ-ray detector-grade germanium, an additional zone refining process is applied, in which the molten zone is started in contact with a single-crystal seed. In this way a complete single crystal ingot is obtained, out of which residual impurities from grain boundaries are eliminated. Impurity concentration in these ingots is of the order of 0.01 ppb, or 10"" cm−$. The Czochralski crystal growth process is then applied to obtain crystals which are subsequently ground, sliced, and shaped for three main application fields: infrared thermal imaging, γ-ray detectors, and opto-electronic substrates.

2. Crystal Growth of Germanium: General Features Single crystals of germanium can be grown by the Czochralski pulling technique, or by horizontal or 2

vertical Bridgman systems. The horizontal zone melting process for germanium has been extensively treated by Cressell and Powell (1957). The melt properties of germanium are given in Table 4. Polycrystalline material of usable, infrared, optical-grade quality can also be obtained by other directional solidification systems, e.g., by the Stockbarger method or the heat exchange technique. Single crystals of germanium cannot practically be grown by the floating zone technique which has been so successfully applied to silicon, because the ratio of the melt surface tension to the density is too small to support a floating zone of more than 1 cm diameter. In this review we will concentrate on the Czochralski method. Germanium was the material on which the Czochralski pulling method was first pioneered by Teal and Little at Bell Laboratories in the 1950s (Teal and Little 1950). Whereas the production scale of silicon crystals by this technology is nowadays much bigger than that of germanium, germanium has always been the favorite material in basic studies of semiconductor crystal pulling. The reasons for this are its relatively low melting point (937 mC), its negligibly low vapor pressure at the melting temperature, its low toxicity, its only-moderate reactivity with graphite and quartz crucible materials, and last but not least the fact that, due to the early high interest in its use for

Germanium Single Crystals, Growth of

Figure 2 Flowsheet of the production of germanium.

semiconductor devices, its physical properties have been very thoroughly documented. Thus it was used to verify the Burton, Prim and Slichter (BPS) theory on the effect of crystal rotation on the effective distribution coefficient (Burton et al. 1953), and to study the phenomenon of microsegregation and cellular

structure due to the effect of constitutional supercooling (Bardsley et al. 1974); it was also the prototype material for the investigation of the dynamics of Czochralski growth (Hurle et al. 1986) and the development of automatic diameter-control systems based on the weight sensor principle (which is now used commonly in silicon growth) (Bardsley et al. 1972, 1977). The general design features of a Czochralski puller for germanium growth are close to those for silicon. Automatic diameter control can be achieved by means of a weight-sensing system, or by camera monitoring of the meniscus (even though the meniscus ring is less bright than in the silicon case, because of the much lower melting temperature of germanium and its low liquid emissivity (0.2) compared to the solid (0.55)). The latter method is only applicable, however, when the crystal shape is round enough to enable the proper video control of the meniscus ring, i.e., in those cases of crystal orientation and growth parameters which minimize the width of the side facets (ridges) on the crystal periphery (see Sect. 5). For the pulling, a shaft, a chain, or a wire can be used. The disadvantages of a shaft system are the elevated height of the puller, and sealing issues. A chain or wire system is more prone to vibrations, and orbiting of the crystal in the melt. The pulling ambient can be any inert gas, or hydrogen, or a vacuum. Pulling under vacuum is not suitable for large-diameter crystals, given the large amount of latent heat of fusion to be removed (0.0025 J kg−" for germanium) and the relatively low thermal conduction in the solid germanium (only 25.14 W m−" K−", compared to 147 W m K−" for silicon). Typically two pressure ranges can be applied, the first slightly above atmospheric pressure and the second from 10 to 30 mbar. Crucibles can generally be made of graphite (isostatic pressed quality). For certain material-quality grades, however, other crucible materials are required (see later). Heating is generally done with a graphite, picket-fence-type resistor heater, using 3-phase alternating current or direct current. For the growth of ultrapure germanium, which requires RF induction heating, a quartz tube can be used for thermal shielding and a high-purity graphite element as RF susceptor. The starting materials for germanium crystal growth have to be of high purity, particularly with respect to electrically active impurities (other impurities can also be important: see Sect. 7). For the growth of infrared-grade and electronic-grade germanium single crystals, the concentrations of electrically active impurities in the starting materials must not exceed 10"$ cm−$. Polycrystalline zone-refined bars and scraps from single crystals can be used for this purpose. For the growth of ultrapure crystals for γ-ray detector applications, the starting material has to be of impurity content less than 10"" cm−$, which is achieved by zone 3

Germanium Single Crystals, Growth of

Figure 3 View of the growing crystal inside the furnace – one can discern the relatively bright (yellow) meniscus ring at the lower end of the crystal cylinder.

refining with single-crystal seeding. Prior to insertion into the crucible, the material is etch-cleaned, rinsed, and dried thoroughly in clean-room conditions. Dopants can be added to the starting material in elemental form or in solid solution in germanium (the latter option is favored if low doping levels are required, e.g., for detector crystals). After loading the crucible, the furnace is evacuated and purged with nitrogen, after which a suitable flow of inert gas or hydrogen is constantly applied downwards through the pulling chamber during the crystal growth, to prevent excessive contamination of the melt by particles and\or evaporating materials. Typical charge size ranges from 10 kg for detector crystals, to over 35 kg for electronic grade crystals, and up to 300 kg for infrared optical-grade crystals. Shortly before the germanium is completely molten, the heater power is reduced to the regime power needed for stabilized crystal growth, in order to limit overshooting of the melt temperature resulting from the high temperature difference between heater and 4

crucible which is applied to enhance a fast meltdown of the charge. A melt stabilization time is then applied, during which temperature distributions in the entire furnace are allowed to attain their definitive constant values. The heating can be controlled by measuring the temperature at some suitable point next to the heater, using a thermocouple or a pyrometer. The right growth temperature can be checked by observing the melting behavior of the seed dipped in the melt. The seed is usually a small cylinder cut from a single crystal of germanium, the cylinder axis being along the crystallographic direction of the crystal to be pulled. The seed is etched before use to remove any surface damage or contamination. The seed is lowered down close to the melt surface, and allowed to come into thermal equilibrium with the melt while it is already rotating. The seed is then dipped into the melt, and if necessary the temperature is lowered slightly until a meniscus can be supported by the seed crystal. The continuation of the growth technology depends strongly on the specified quality (regarding both crystallographic structure and impurity content) of the germanium crystal to be grown, which in turn depends on the application for which the crystal is intended. The facetting of crystals is associated with anisotropy of the surface free energy, the minima of which are in the directions coinciding with the most densely packed faces (Voronkov 1974). The (111) faces are below the roughening temperature at the melting point of germanium and form facets on the crystal\melt interface, tangential to the melting point isotherm. These facets are characterized by the minimum specific surface free energy. The free energy of the germanium (111) face is 0.85–1.10 J m−#, while it is 1.30–1.35 J m−# for the (110) face. For other faces the free energy is considerably higher (Smirnov and Kolesnikov 1994). When a f111g crystal is pulled, a central horizontal facet forms in a convex-to-the-melt interface, or a peripheral ring facet on a slightly concave interface; whilst on a f100g crystal four peripheral outward-sloping facets are formed. At these four peripheral facets on a f100g crystal, the meniscus is locally lifted higher, causing upwardly- curved ridges on the side flats. When the angle of the initial cone reaches approximately 46m for a f100g crystal, and 19m for a f111g crystal, extended (111) mirror faces are formed on the cone. A similar effect is observed on the end cone of the crystal, where for a f111g crystal the mirror faces are shifted over 60m in azimuthal position with respect to the mirror faces on the seed cone. Due to the crystal rotation during growth, the crosssection of the germanium crystal is almost circular, but under certain circumstances it can deviate strongly from a circular shape. Growth is fast along the densely packed (111) planes, but slow perpendicularly, leading to the appearance of terminal (111) facets and the above-mentioned flats on the crystals. Thermodynamically the crystal habit tends to be bordered by

Germanium Single Crystals, Growth of Table 3 Overview of doping elements in germanium.

Sb P As Li Bi Te

n n n n n n

10 13 14 10 13 93

1.2i10"* cm−$ ! 800 mC 2.0i10#! cm−$ ! 850 mC 7.0i10"* cm−$ ! 850 mC 7.5i10") cm−$ ! 825 mC 6.0i10"' cm−$ ! 910 mC 7.0i10") cm−$ ! 850 mC

Equilibrium segregation coefficient, k ! 0.003 0.08 0.02–0.04 0.002–0.01 4.10−& 1.10−'

Ga B Al In Tl Cr Cd

p p p p p p p

11 11 11 12 13 12 16

5.0i10#! cm−$ ! 650 mC 1.0i10") cm−$ 4.3i10#! cm−$ ! 700 mC 4.0i10") cm−$ ! 800 mC 9.0i10") cm−$ ! 910 mC ? 2.5i10") cm−$ ! 825 mC

0.087 17 0.073 10−$ 4.10−& ?  10−&

Element

Type

Ea (meV)

Solubility (solid)

Table 4 Melt properties of germanium. Melting point (mC) Density (g cm−$) Emissivity Thermal conductivity (W cm−" K−") Expansion coefficient (K−") Kinematic viscosity (cm# s−") Specific heat (J g−" K−") Surface tension (N m−") Heat diffusivity (cm−# s−") Prandtl number

936 5.55 0.2 0.71 1.1i10−% 0.00135 0.418 0.62 0.175 0.008

Source: Glasov et al. (1969), Smithells (1983).

(111) flats and\or facets, so a f100g crystal tends to be square and a f111g crystal triangular. Radial thermal gradients in the growth system, however, favor a circular cross section. An angular cross section is enhanced by a high pulling rate, by a low radial temperature gradient in the melt (Pethkov and Redkin 1993), and by melt vibrations (mechanical perturbations at the growth interface driving the crystal to its thermodynamically stable state). When at a certain instant during growth melt vibrations are introduced, the width of the lateral side flats increases readily. To maximize material yield upon grinding the crystal prior to wafer slicing, the cross section should be as near circular as possible. Twin formation is not a frequently observed phenomenon in germanium crystal growth. It can occur, however, especially during crown growth, on the o111q facets at the three-phase boundary in conditions of high temperature and growth-rate fluctuations. 3. Germanium Crystals for Infrared Optics Germanium crystals are widely used as lens or window material in infrared optical systems. Germanium has a transmission range from 1.85 µm to 15 µm, and is

therefore suitable for use in the 8–12 µm wavelength band. Although germanium is practically transparent between 2 and 15 µm, it still experiences free carrier absorption. In order to minimize free carrier absorption, the crystal must be doped n-type with a concentration between 4i10"$ cm−$ and 1i10"& cm−$, resulting in a resistivity of 5 to 40 Ω cm. For monocrystalline germanium this results in an absorption coefficient below 0.02 cm−" at room temperature. Optical-grade germanium must also be optically uniform and isotropic, i.e., the homogeneity of the refractive index must be very low (typically ∆ n 10−%) and the birefringence must be minimized ( 1 µm cm−"). Both high transparency and optical uniformity and isotropy require the minimization of mosaicity and low-angle grain boundaries (Van Goethem et al. 1986). The optically detrimental effect of low-angle grain boundaries is least for crystals grown in the f111g direction. Furthermore, to ensure low birefringence, the residual stresses in the crystal must be minimized (Depuydt et al. 1997). Residual stresses are the result of the plastic strain (through the formation, movement, and multiplication of dislocations) which relieves the thermal stresses exceeding the critical shear stress during cooling down of the crystal above the crystal\melt interface ( Vo$ lkl 1994). To minimize these thermal stresses, this interface should be kept as flat as possible during the growth, corresponding with an almost vanishing radial temperature gradient. These conditions can be accomplished by the use of appropriate heat shields and\or afterheaters above the melt surface. Finite element computer modeling has been performed to calculate stress distributions in the growing crystal. The visco-plastic approach based on the Alexander–Haasen model, in which residual stresses and dislocation densities are calculated using a model including stress relaxation and strain hardening—and for which a numerical technique resulted in good 5

Germanium Single Crystals, Growth of minimize material waste, the diameter increase from seed to crystal body is made abruptly by combining a steep ramp-down of the heater temperature with a decrease of pulling rate, followed by the reverse actions just before the final diameter is reached. Care must be taken to minimize the convexity of the growth interface at this stage, because decrease of the pulling rate implies a decrease of effective segregation coefficient (see Sect. 6), and hence a radial doping gradient, if the interface is not flat. The final diameter is then monitored and kept constant by temperature and pulling rate control loops. To keep the thermal conditions during pulling as constant as possible, the vertical position of the melt surface with regard to the heater is kept constant by lifting the crucible appropriately. Before the melt is exhausted, the crystal is withdrawn from the melt. Single crystals of up to 35 cm diameter are grown in this way. Figure 4 shows a large diameter f111g single crystal. Figure 4 IR-optical grade germanium single crystal (top view). At the front on the table is a 30 cm ruler. The o111q facets on the crown in a 6-fold symmetry can be easily seen. The remainder of the seed is in the center of the crown.

results for the case of GaAs growth (Dupret and Van den Bogaert 1994)—has failed until now to give quantitative results for the case of germanium growth, because the high value of the material parameter characterizing the dislocation mobility gives numerical convergence problems. Qualitatively, however, the obtained results for the residual stresses in the crystal are in good agreement with the residual stresses determined by means of interferometrical characterization of stress birefringence (Depuydt et al. 1997): $ The maximal built-up thermoelastic stresses, which can be considered as an upper limit for the residual stresses caused by partially relieving the thermal stresses, correspond qualitatively with the stress distribution calculated from the stress birefringence, the highest stresses being compressive and occurring at the periphery of the crystal (order of magnitude MPa). $ The stresses depend strongly on the shape of the growth interface: the flatter the interface, the lower the stresses in the crystal. Modeling results, as well as growth experiments, show that in the early stage of crystal growth—during crown growth—the interface shape is convex to the melt, while when the axial distance from the initial cone is more than the crystal diameter, the interface becomes concave, with a nearly flat situation somewhere in between. This was confirmed by birefringence measurements: the residual stresses are the lowest in blanks cut transversally from the second quarter (counting from the seed) of the crystal mass of diameter 25 cm and length 50 cm. To maximize the length of the usable crystal and to 6

4. Ultrapure Germanium Crystals for Radiation Detection Germanium crystals for γ-ray detection must have an electrically active impurity concentration of only 10* to 2i10"! cm−$ (depending on detector size). Therefore a fused silica crucible must be used. Crystals grown in a vacuum were found to contain copper (which introduces detrimental carrier-trapping centers), so a high-purity gas is needed to shield the growing crystal. Crystals grown from silica in an inert gas were found to contain SiO precipitates, so the # shield gas must be hydrogen. Dislocation-free, highpurity germanium grown in a hydrogen ambient has turned out to be unsuitable for detector fabrication, because of a deep level at EVj0.072 eV with a concentration of about 10"" cm−$ (Hall and Soltys 1971, Hansen and Haller 1972). This center has been identified as a divacancy-hydrogen complex (V H) (Haller et al. 1977). Experience has shown that if #the crystal contains at least 100 uniformly distributed dislocations per cm#, the V H trap concentration is too # low to deteriorate the detector performance. It has further been shown that if the local density of dislocations exceeds 10% cm−#, the dislocations themselves begin to act as charge-trapping centers (Glasow and Haller 1976). Meeting the requirement that the dislocation density must be everywhere between 100 and 10% cm−#, over volumes that can exceed 500 cm$, has been a great challenge in crystal growth. To initiate the growth, a low-dislocation-density seed is necked down by fast pulling until only a few dislocations remain. The diameter is then increased under conditions of moderate thermal stress to obtain a proper number of dislocations. An approximately flat interface shape is maintained throughout the body of the crystal. The proper control of dislocation density and distribution is also sensitive to the crystal-

Germanium Single Crystals, Growth of lographic growth direction. Growth along f111g stabilizes a horizontal (111) facet at the interface, which extends into a non-isothermal region, and in which the thermal stresses are frozen in. For any other growth axis, the stresses due to the interface curvature are relieved plastically by the multiplication of dislocations. Pure edge dislocations in f100g crystals tend to line up with the growth axis by moving along at least two of the four different sets of (111) glide planes, and they can often be followed through the entire length of the crystal. This means of propagation makes dislocation counting by etch pit detection on the (100) cross section surface very straightforward, because dislocations are preferentially etched more when intersecting the surface perpendicularly.

5. Dislocation-free Growth Germanium wafers, 4-inch diameter, for GaAs photovoltaic cells for space applications, must have an etch pit density lower than 500 cm−#. The easiest way to obtain this is by the growth of dislocation-free crystals. Growth of dislocation-free germanium crystals of 11 cm diameter is state-of-the-art technology. The largest dislocation-free germanium crystal grown to date has an 8-inch diameter (Fig. 5) Dislocation generation is thermodynamically not favorable because of the increase of Gibbs free energy in the crystal. Therefore, there exists no equilibrium number of dislocations, and so it is physically possible to grow dislocation-free crystals. When the seed crystal is dipped into the melt, dislocations are generated because of the high thermal stresses induced by the temperature shock. Normally these dislocations are propagated into the growing crystal, particularly in the case of a large crystal diameter. The stress which occurs as a result of different cooling rates between the inner and outer regions of the crystal is probably the main reason for the dislocation movement in the case of large crystals. Due to the high stress and temperature in the crystal, the dislocations are not confined to their glide planes, but receive enough energy to spread into adjacent glide planes by cross slip, climb, and multiplication processes. Dislocations in diamond-structure crystals propagate preferably in (111) planes, which are the main glide planes. When a silicon or germanium crystal is pulled in a f100g or f111g direction, all sets of (111) planes are oblique to the pull axis. Therefore, all the dislocations with Burgers vector (a\2) [101]-type will glide out and terminate at the crystal surface— provided that the crystal size is reduced to a very small size, so that the small remaining stress may not be able to move dislocations or to generate new ones, and provided that no new dislocations are formed at the

Figure 5 The largest dislocation-free germanium crystal to date: 8inch maximum diameter. The axial direction is f100g. One of the four side facets can be seen on top.

interface. This principle was originally reported by Dash (1959) who was the first to report the growth of dislocation-free silicon and germanium ingots. From Dash, the procedure to grow dislocation-free silicon and germanium crystals still has the following steps: (i) Neck-in the seed, i.e., reduce the crystal diameter to about 2–4 mm. After a few centimeters the crystal becomes dislocation-free. (ii) The diameter of the crystal is enlarged by decreasing the heater power or by decreasing the pulling speed. Shortly before the desired final diameter is reached, the heater power and\or the pulling speed is raised again to the value at which this diameter can be kept constant. (iii) At the end of the pulling process, when the crystal has to be withdrawn from the residual melt, the thermal shock at this separation can lead to stressgenerated dislocations running back up into the solid all over the still plastic temperature range (above 500 mC), and consequently to yield losses. To avoid this, the end of the crystal is grown tapered down to a very small diameter and then detached from the melt. Dislocation-free growth is relatively stable even for crystal diameters up to 15 cm, in spite of the high thermal stresses. The reason for this is the high energy required to generate a first dislocation in the crystal. If the shear stresses along the principal glide planes do not at any point exceed the critical value σcr for the nucleation of dislocations or for the growth of very 7

Germanium Single Crystals, Growth of small dislocation loops, the crystal will remain macroscopically dislocation-free. Possible causes for the generation of the critical first dislocation during crystal growth are: $ Too high a thermal cooling stress. For example if the crystal\melt interface is highly concave towards the melt, then the inner region solidifies while the periphery is already solid, which causes high stresses due to the 5% volume expansion upon solidification of germanium. $ Too high thermal gradients along peripheral (111) facets (in the case of a convex to the melt interface). $ Thermal shocks. $ Melt vibrations and mechanical shocks. $ Microsegregation of an impurity (e.g., due to constitutional supercooling). $ The inclusion of solid particles at the crystal\melt interface (stresses near foreign inclusions in the crystal may exceed the large-scale thermal stresses significantly). $ Gas bubbles trapped at a highly concave crystal\ melt interface. Once a first dislocation is generated, the thermal stresses cause the multiplication and upwards spreading of dislocations in the formerly dislocation-free part of the crystal. Since the cooling stress reaches its maximum in the crystal periphery, the plastic lattice deformation occurs preferentially near the crystal surface. The plastic deformation terminates when the total energy of the thermoelastic stresses and dislocations reaches a minimum. The height of the upwards extension of the plastic flow above the onset of dislocated growth decreases with increasing axial temperature gradient in the crystal—for normal growth conditions, a height of approximately 1.5 times the crystal diameter becomes dislocated. In the part of the crystal grown after (below) the onset of dislocated growth, the dislocations which are grown-in, or which originated from multiplication processes, move by glide and climb processes and therefore form an irregular network. In the presence of a low temperature gradient, the climb processes can result in a polygonized etch pit structure which corresponds to a configuration of minimum energy for the dislocations. The onset of dislocations can be readily seen by an interruption of the peripheral axial side flats or ridges in the azimuthal positions corresponding to the (111) edge facets (disposed at 90m on f100g crystals, in f110g directions, and 120m on f111g crystals, in f211g directions) (Fig. 6). The ridges consist of alternating inward- and outward-sloping (111) faces, the energetic stability of which is decreased by a dislocated structure. When a crystal becomes dislocated, it can be melted back up to the neck, and the growth can be started again. It must be emphasized that this possibility is a major advantage of the Czochralski growth technology. 8

Figure 6 Peripheral facet ridges on a dislocation-free germanium f100g crystal.

6. Doping Issues Germanium crystals for the different applications mentioned in Table 2 require doping with a specific element to give the desired electrical carrier concentration. An element from group III of the periodic table is used to give p-type conduction, and from group V to give n-type. Dopant concentrations ranging from 10* (ultra-high purity crystals for radiation detection) to 10") dopant atoms per cm$ are used to meet the needs of various applications. A pure dopant element can be directly added into the germanium melt for producing a heavily doped crystal. However, an impurity-germanium alloy or highly doped germanium crystal material is preferred when a low-level doped crystal is needed. The amount of an impurity which can be added is limited by its solubility. Table 3 lists the various n- and p-type dopants in germanium. Antimony is the most practical n-type dopant for moderately and heavily doped crystals, because of its low vapor pressure at the germanium crystal growth temperature. However, its solubility is about one order of magnitude lower than that of phosphorus and arsenic.

Germanium Single Crystals, Growth of Since all n-type dopants in germanium have a segregation coefficient of less than one, during n-type crystal growth a solute-rich boundary layer is formed ahead of the crystal\melt interface. Under conditions of a fast growth rate and a low temperature gradient in the melt, the temperature in this layer can be below its thermodynamic equilibrium liquidus temperature: this is the condition of so-called constitutional supercooling. The supercooling is the result of the higher diffusivity of heat than of solute in germanium (expressed by Pr Sc, with Pr and Sc the Prandtl and Schmidt numbers, respectively). In a region of constitutional supercooling, slight flatness deviations of the crystal\melt interface can result in growth instabilities, leading to the formation of a cellular structure in the crystal, in which regions of relatively low doping concentration are separated by longitudinal trails of segregated dopant element (for a detailed description of constitutional supercooling and microsegregation, see Hurle and Cockayne 1994). In such a structure there exist severe lattice stresses, which lead to high dislocation densities, and in some cases to polycrystalline growth. The effective segregation coefficient, according to Burton et al. (1953) is given by k l k \k j ! (1kk )e−rd/D, with k the equilibrium segregation! coef! ! ficient, r the growth rate, d the solute boundary layer thickness, and D the diffusivity of the solute in germanium. For dopant solutes in liquid germanium, D is of the order of magnitude 10−& cm# s−". For realistic values of d, according to the Cochran formula d l 1.61 (ν\ωs)"/# Sc−"/$ (with ν the kinematic viscosity of germanium, ωs the crystal rotation rate, and Sc the Schmidt number l ν\D), k can be several times k for ! dopants with k 1. ! At UM–Electro-Optic Materials, using antimony as n-type dopant (k l 0.003), a cellular structure was observed at solid! dopant concentrations exceeding 7i10"( cm−$. By lowering the growth rate by a factor of two, the effect of constitutional supercooling could be reduced (due to a thinner solute-rich boundary layer), and dislocation-free crystals with an n-type doping concentration of 10") cm−$ ( ρ l 7i10−$ Ω cm) were grown in this way. For p-type doping, gallium can be used, which has k l 0.09. Dislocation-free, gallium-doped crystals ! were grown with doping concentration ranging from 5i10"' to 7i10") cm−$ ( ρ l 100k3i10−$ Ω cm). Microsegregation of dopant was observed at solid dopant concentrations exceeding 10") cm−$ (this is at higher concentrations than with antimony doping, probably due to the higher segregation coefficient of gallium). A remarkable effect of high gallium-doping concentration is the decrease of the width of the f111g side facets. This can be related to the relative lower incorporation of gallium at facets than in rough surface regions, in contrast to most other solute elements (Dikhoff 1960). Lattice hardening by impurities has been observed

in gallium-doped crystals: dislocation multiplication (in dislocated crystals) was shown to be suppressed for gallium concentrations above 10") cm−$ (Patel 1961). Qualitatively, for all impurities (including the electrically neutral ones), an identical effect has been reported: they increase the critical stress of dislocation generation, and decrease the intensity of multiplication of dislocations (Milhvidsky et al. 1981).

7. Non-doping Impurities 7.1 Carbon The solubility of carbon in the germanium lattice is low (10)–10"! cm−$). Such small concentrations cannot be detected by infrared spectroscopy; the localized vibrational mode of substitutional carbon (531 cm−") can be detected only upon implantation of carbon. In germanium crystals grown from a melt contained in a graphite crucible, there are probably carbon clusters present. The total carbon concentration in such crystals was determined by coating a quartz crucible with "%C. Radiation detectors made from these crystals measured the beta decay of the "%C atoms themselves with an efficiency of nearly 100%. From these measurements, a mean total carbon concentration ("%Cj"#C) of 10"% cm−$ was calculated. Also from the internal radioactive decay measurements, clusters of about 10( atoms of "%C could be identified, superposed on a homogeneous background of "%C (Haller et al. 1982, Hoffman et al. 1997).

7.2 Oxygen Germanium crystals normally contain moderate concentrations of oxygen, much lower than typical Czochralski-grown silicon in which oxygen is a dominant impurity. There are a number of reasons for this difference: the lower melting point of germanium (resulting in less interaction with the crucible), the lower oxygen affinity of germanium, the incorporation of oxygen in SiO inclusions, and the formation of # oxide. High oxygen concenvolatile germanium trations in the range 10"'–10") atoms cm−$ are only obtained when the germanium is deliberately doped with oxygen, for instance by growing the crystal in an oxygen-rich atmosphere (Bloem et al. 1959). Oxygen concentrations of the order 10"$ atoms cm−$ or lower are realized in high-purity germanium crystals for γray detector fabrication, by growing them in a reducing atmosphere and avoiding contact between the melt and silica components. Compared with silicon, where oxygen defects have been the subject of numerous papers, oxygen defects in germanium have been less studied. Investigations during the 1980s and 1990s have, however, partly reduced the gap and it turns out that for major defects such as oxygen 9

Germanium Single Crystals, Growth of interstitials and thermal donors, many similarities in properties and behavior are observed between the two semiconductors. The results indicate that unified models for these defects may be applicable (Clauws 1996).

7.3 Nitrogen Nitrogen is most probably not electrically active in the germanium lattice. The reasons for this are the high dissociation energy of the N molecule, the fact that this molecule can penetrate #into the tetrahedral interstitial sites in the germanium lattice, and the fact that a nitride phase is formed when molten germanium cools down in a N atmosphere. a-Ge −xNx, however, has an absorption #band at ca. 700 cm"−" (the in-plane asymmetrical stretching vibration) (Ciszek et al. 1996, Zanatta and Chambouleyron 1993). See also: Germanium; Silicon–Germanium; Crystal Growth from the Melt; Growth of Shaped Crystals from the Melt; SixGe −x Bulk Crystals; Czochralski " Silicon; Silicon Grown by the Floating Zone Technique

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