The use of magnetic fields in semiconductor crystal growth

Journal of Crystal Growth 113(1991) 305 328 North- Holland

305

Review paper

The use of magnetic fields in semiconductor crystal growth R.W. Series and D.T.J. Hurle DRA Electronics D,i’,s,on, RSRE Ma/cern, St Andrew~Road, Great Ma/cern, Worci. WRI4 ~PS, UK Received 23 April 1991

The application of a magnetic field to semiconductor crystal growth melts in order to control melt flow and thereby dopant distribution on both macro and micro-scales is reviewed. Most emphasis is given to Czochralski and LFC growth and the generation of transverse, axial and configured fields is described. Theories predicting flow and segregation in the presence of a magnetic field are outlined and compared with a wide range of published experimental data relating principally to silicon, gallium arsenide and indium phosphide The technically-important case of oxygen concentration control in Czochralski silicon is considered in detail, including some previously unpublished data. Finally, the published literature on the use of a magnetic field in non Czochralski growth configurations is reviewed.

1. Introduction

oxygen content of the crystal. Subsequent work has concentrated on the application of static fields

It has been ieeognised fur many years that temperature gradients present in the melt during crystal growth give rise to strong buoyancy-driven convection and also, where there is a free surface, to surface tension-driven flows. For all but the smallest laboratory scale apparatus and for materials with relatively low melting points, this convective flow is at least partially turbulent and gives rise to a fluctuating rate of crystal growth which, in turn, produces a microscopically nonuniform distribution of dopant in the crystal. The concept of the use of a magnetic field to damp out this turbulence and thereby improve the microscopic homogeneity of the crystal, was introduced in 1966 independently by Flemings and coworkers [1,2] and by Hurle and coworkers [3,4]. However, sufficient motivation to explore the possibilities did not arise until the late 1970s, when workers with large silicon pullers noted systematic anomalies in the oxygen content of crystals grown on apparently similar pullers. In 1980. a group at NTT reported [40] that the sense of the rotation of the magnetic field due to the three-phase heater with respect to the crucible rotation exerted a significant influence on the 0022 0248 91 503.50

1991

with a variety of configurations to a number of systems including III V compound semiconductors. While control of oxygen and striae in large diameter silicon crystals is probably the most important commercial application of magnetic Czochralski growth, this is by no means the only active research area, In section 2 we outline the basic principles associated with the interaction of a magnetic field with a convecting metallic melt. The common semiconductors are metallic in their molten state. In section 3 we describe the technology for generating fields having different configurations and in section 4 outline the theory of segregation of dopants in the presence of a magnetic field. Application of the techniques to the growth of semiconductors is reviewed in section 5.

2. Basic principles The basic mechanism for the interaction between a magnetic field and a molten semiconductor involves the electrical currents induced in a conductor moving in a magnetic field. These flow

Elsevier Science Publishers B.V. (North-Holland)

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(1)

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5 la\er flow to a much greater degree. The effect will he sensiti~eto the conduc ti~ity of the rigid boundary. In many respects the ability of electric currents to transport energy over larger distances in the melt than siscous mecha nisms is similar to a change in the ~iscosity of the liquid. This has given rise to the term magnetic ~iscosit~ which is often found in the magnetohy . drodynarnic literature. An example of this is dis cussed more fully in section 42.1.

(2)

3. Technolog~ For some simple geometries analytic solutions are possible. However, a detailed calculation of the effect of the magnetic field on the motion of the melt generally requires extensive finite element or finite difference computations. Some generalised statenients can he made, howe~er. First, as B appears in both the expression for the induced current and the damping force, most of the interactions will scale with the square of the field. Since the melt acts as a highly amplifying medium some effects may be more pronounced than this, A second point to note is that the induced EMF is the vector product of magnetic field and fluid velocity. This implies that there is no direct damping of flows parallel to the field lines. It must, however, he noted that, as all the melt is constrained in the crucible, and is essentially in compressible, most flows will at some point he damped and exert back-pressure on the undamped regions. An obvious exception is solid body rotation with a magnetic field parallel to the rotation axis. In addition to an overall damping of the flow field, this leads to an alignment of the convective cells parallel to the flux lines and changes in the cell aspect ratio. Finally it should be noted that, for most semiconductor melts, electric currents can transport energy over much greater distances than viscous mechanisms. This is particularly evident in shear layers close to rigid boundaries with streamlines normal to the field. For example. under an axial field, crystal rotation stirs the melt to a much greater depth than in the non-magnetic case, while under a transverse field the crucible wall acts to

3.1. Generation o/ the field Production of an appropriate magnetic field for the damping of flows is not always straightfor ward. Typicall~. detectable interaction starts at around 500 (3 and some workers are now exanlin ing the effects of fields of up to 30.000 (3 ~6]. lo produce these fields in the melt requires that the niagnet be designed with a bore large enough to contain the crucible, heater and necessary heat shields. This may require the magnetic field to he produced over a volume with a diameter of 0.5 to I ni. Such fields can he produced either by resisti~eor superconducting magnets. For resistive designs the resistivity of the windings is a key parameter in determining the dissipation and the maximum field attainable. This is the reason that it is not possible to use the heater to generate a significant field. Although anodised aluminium strip can he used to fabricate large low-field magnets, the higher conductivity of copper is desirable with high-field designs. Typically power dissipation by the magnet exceeds the heater power. Advantages of resistive magnets are simpler operation, easier fabrication and modification. By contrast, superconducting designs require more maintenance and are less amenable to modification. For both superconducting and resis tive designs there is considerable energy stored in the field and large stresses on the winduiigs. Cost is a sensitive function of specification: for a tvpical resistive system the cost is approximately pro portional to the fourth power of the bore and to the square of the field.

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Use of magnetic fields in semiconductor crystal growth

Problems encountered when marrying a magnet to a puller include saturation of motor and transformer cores as well as stresses on the heater. The latter factor dictates the use of DC heater current

supplies which can range from simple bridge-rectified phase angle controlled AC, 3 phase star/delta motorised Variac systems with 12 pulse rectification to elaborate solid-state regulated systems.

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f. 2. Field configurations Several different geometries have been reported in the literature. Early papers described work with the melt placed between the pole pieces of a magnet giving a transverse field. Later papers have been concerned with axial fields which do not destroy the symmetry of the system. Most recently there have been reports of fields which are deliberately shaped to produce a non-uniform environment in the melt. We consider each of these in turn, 3.2.1. Axtal field With an axial field the magnet takes the form of a solenoid or coil with axis vertical (fig. 1). The melt is placed in the centre. In some systems. such as that reported by Kim and Smetana [71,more than one coil is used to allow trimming of the field uniformity. Pole pieces and soft iron cores are generally of limited value as gains in the field intensity are generally offset by concentration of the field near the outside of the bore and reduction in the field in the central regions.

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3.2.2. Transcerve held The transverse geometry was the earliest geometry to he studied [5.81. In its simplest form the melt is placed between the pole pieces of a magnet so that the field lies at right angles to the growth axis (fig. 2). With simple transverse systems the field in the melt is generally highly non-uniform. To help improve field uniformity it is desirable to work with air-cored coils. Often these will require supercon ducting designs so as to keep power consumption within reasonable hounds. There may also he con siderable stray fields. One engineering point to note is that the forces on a simple “picket fence” heater are generally higher than with an axial field, as in the latter case the majority of the conductor length lies parallel to the field. 3.2.3. C’onftguredjield The object of a configured field is to match the shape of the magnetic field to the flows in the melt so as to damp harmful flows and retain beneficial flow patterns. There are various reports in the patent literature of a wide variety of designs.

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Use of magnetic fields in semiconductor crystal grostth

although it is far from clear which designs have actually been tested. Distinction can be made between static designs in which the field remains fixed with respect to the laboratory and dynamic designs where the magnet is rotated, often in synchronization with either the crystal or the crucible rotation. Equally, a distinction can be made between fields which retain the rotational symmetry of the Czochralski process and those which do not. One of the principal problems in working with configured fields is that it is generally rather difficult to design coils or pole pieces to be located close to the melt. ~Ihe types of strategy which spring to mind for small systems might include manufacture of the crucible support shaft (and

possibly the crucible support) from ferromagnetic materials or suspending a coil around the crystal. The one configured field which has received serious experimental study is the cusped field (fig. 3) formed with a pair of Heimholtz coils operated in opposed current mode. This work is reported in section 5.1.2.3.

4. Theory of flow and segregation in the presence

of a magnetic field 4.1. Flow and temperature fields

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forced and natural convective components. Forced flows arise from differential rotation of crystal and crucible with buoyancy-driven flows given by imposed temperature gradients and potentially, also. solutal convection driven by dopant segrega tion and non—congruency of multi component melts. Additionally. Marangoni convection can occur at the free-melt surface. Thin shear layers develop at the crystal melt and crucible melt in terfaces and also a detached shear layer forms a Taylor Proudman column beneath the crystal. The diversity of length scales and multitude of driving forces makes computer modelling difficult and expensiv e Because the application of a magnetic field damps the flows and thickens the shear layers. the magneto-hydrodynamic computation is actually more readily performed than the pureR hydrodynaniic one. Most numerical models to date make several gross assumptions about the flow field. First, it is generally assumed to he rotationally symmetric. Analogue models, such as those studied by Jones [71]. suggest that this is frequently not the case. Second. many of the parameters required in the simulation are not known with any degree of confidence. It is often found that the overall flow pattern is sensitive to quite small changes in the parameters. This arises partly as the flow’ fields have an amplifying action and a small change in one area of the melt can drive the overall flow pattern into another mode. A third difficulty lies in the complexity of the numerical model. All existing mesh-based models require the user to specify the mesh to be used. This can have a large impact on the final results and cause some important aspects of the flow field to be missed. Despite these problems many of the existing numerical models give results which intuitively seem reasonable. The magneto-hydrodynamic equations to be solved are considerably simplified by the fact that the magnetic Prandtl number (P 51 o~sp.(,v,where j.tj.t,5 is the magnetic permeability, n the electrical conductivity and the kinematic viscosity) is very small. The induced magnetic field can, therefore, he neglected compared to the imposed field. Langlois and Lee showed that Joule heating effects can also be neglected [91. Digital simulation of a Czochralski melt in the

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presence of an axial magnetic field has been car ned out by Langlois and I cc [9] and also by Mihel~u.~ and Wingerath (10]. The latter authors showed that a magnetic field of 2000 (3 was suffi cient to damp both the temperature and flow oscillations in the melt. (‘artw right et al. 11 corn pared order of magnitude estimates with an asymptotic analysis to deduce the propei scaling laws and concluded that the principal value of the magnetic field was to damp tLirhulence and that the optimunl field was the minimum field which achieved this objective. Very recently Mtunakata and Tanasaw’a [78] have demonstrated in model experiments and numerical simulation a macro scopic oscillation of the flow in a Czochralski melt which they ascribe as the cause of non-rotational growth striations. the oscillatory flow is caused by an interaction between the buoyancy driven flow’ and the forced convection due to the rotating crucible. They further modelled conditions in a gallium arsenide melt in the presence of an axial magnetic field and demonstrated by numerical simulation that the field was effective in suppress ing the oscillatory flow. Considerable insight into the effect of ~in axial field on the flow has been provided by Hjellming and Walker (12 15] who used asyniptotic analysis to deduce the nature of the boundary layers formed. They showed that the finite (i.e. non zero) conductivity of the semiconducting crystal pro foundly affected the azimuthal motion and this us confirmed in numerical simulations by Langlois et al. [16]. Some insight into the effects of crucible and crystal rotation can he obtained in a qualitative manner. In the absence of a crystal, crucible rota tion will set up a radial pressure gradient in the melt. If the melt is rotating as a solid body the radial pressure gradient will he the same at all heights and so there will he no driven flow If we now consider the effect of advected liquid using up the crucible wall and flowing inwards, then the liquid will carry excess angular momentum and so start to increase in angular velocity as it moves inwards. This will in turn increase the radial pressure gradient at the top which will oppose the advected flow. It may he seen therefore that vi the alssene of a c’ri’rtal. crucible rotation decreases

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Use of magnetic fields in semiconductor crystal growth

convection. If we now consider the effect of a crystal only weakly coupled to the system (as appropriate to the case of silicon in zero field) crystal rotation will have little effect. If, however, the crystal influences the flow field to a significant depth there will be an imbalance between the radial pressure gradient in the top and bottom of the melt leading to strong forced convection. It is found experimentally [42] and also both in analytical [17,20] and numerical models [37] that an axial magnetic field leads to an increased coupling between the crystal and the melt. We may conelude, therefore, that one important effect of a magnetic field will be to increase the importance of crucible and crystal rotation in promoting flows in the bulk of the melt. Note also that it is the magnitude of the square of the angular velocity which determines the radial pressure gradient. It would be expected that for non-zero counter-rotation of the crucible and crystal, effects will not increase monotonically with increasing rotation rate, but rather go through some local minima at the point where the radial pressure gradient under the crystal matches that at the bottom of the crucible, An understanding of the bulk flow as outlined above is necessary for consideration of the thermal stability of the system and for understanding non-conservative doping behaviour where there are sources and/or sinks for dopant in the system. The most important example of this is the uptake of oxygen in Czochralski silicon (see section 5.1.2 below). However, in most cases, the doping is conservative and as a result, in a well mixed melt, the dopant concentration is uniform in the bulk melt and varies only adjacent to the crystal melt interface which acts Inas this a differential for dopant and solvent. event only sink the flow field adjacent to the crystal melt interface is of importance, and an analytical approach using rotating disc theory is rewarding. Hydro-magnetic flow at a disc rotating in an infinite fluid embedded in a uniform axial-magnetic field has been analysed by Kakutani [19] and an equivalent analysis has been developed by Kobayashi [26]. The basic assumptions of the theory are that the crystal has infinite diameter and rotates with angular velocity ~ in a semi-infinite melt. In some

311

models the melt at infinity is rotated so as to simulate the effect of crucible rotation. The liquid is drawn towards the crystal melt interface, both as a result of the suction due to the growth of the crystal and under the influence of the centrifugal pumping action of the crystal rotation. The melt, which has an electrical conductivity a, is situated in a uniform axial magnetic field of intensity B 0. The magnetic field induces electric currents in the melt which flow and produce a self-force on the melt which opposes the motion. The crystal is assumed to be electrically insulating. It is possible, by means of a similarity transformation, to solve the Navier Stokes equation to determine the flow field in the melt. In the high field limit the expression for the axial component of flow has a reasonably compact form characterised by a single dimensionless parameter N, the magnetic interaction parameter. In the zero field case the expression for the flow field is more complex and it is not possible to write the flow field at all points as a single equation. In an analysis of the effect of an axial field on dopant segregation at the interface, Hurle and Series [20] recognised that the overall form of the flow field at small values of N is qualitatively similar to the high field expression with some small positive value for N. Accordingly a simple expression for the flow field ahead of the rotating crystal can be written. The axial component of flow h(z) then takes the form (in the simple case of zero far-field rotation): 1 h(z) , , [‘1 2 exp( z~/~)1, (3) 3N Vi~ where N’

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and where h and z are expressed in dimensionless form (scaled by the Ekman layer thickness The form of this equation is in keeping with the concept of a magnetic viscosity discussed in seetion 2. The constant 0.427 prevents N’ from becoming zero as B 0 falls to zero and represents the effect of the kinematic viscosity of the melt. The assumptions in this analysis have been vindicated

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in a more detailed study by Organ and Riley [22] and Hicks and Riley [23]. Similar expressions with extra terms can he written when the fluid at infinity is rotating (C’artw’night et al. [24]). 4.2. Segregation 4.2.1. A vial Jteld Segregation under an axial field is most con v’eniently divided into two parts: that which oc curs close to the crystal melt interface, and that which results from effects within the hulk of the melt. As the former is better understood, this will he discussed first. The effect of an axial field on segregation has been analysed on the basis of an infinite disk rotating in a semi-infinite melt by’ Hurle and Series [20] and independently by Kobayashi [26]. Cartwright et al. [24] have extended the theory to include the effect of rotation of the melt at infin ity, while Hicks and Riley [231 have analysed the effect of finite crystal size. Hjellming and Walker [12] have discussed the effect of finite electrical conductivity of the crystal. We discuss here the analysis of the segregation ahead of a semi infinite insulating crystal and compare the analysis to the familiar Burton. Prim and Slichter (BPS) [21] theory. The starting point for the analysis is a know Iedge of the flow’ field ahead of the crystal. The BPS theory is based on the power series expansion due to Cochran [271. Only the first term is taken and hence the axial flow is assumed to he paraholic. For many melts this is adequate: however, numerical analysis shows that while at low fields a modification to the power series solution is possihle, at quite modest fields (typically greater than 500 (3) the diffusion profile extends into regions of the melt for which the power series expansion breaks down. Hence it is necessary to use a more complex model of the flow field such as eq. (3). Availability of a reasonably simple expression for the flow field allows the diffusion problem to he solved. The boundary conditions to the diffusion solution assume that the solid and liquid composi tions at the interface are related by the equilibriun1 distribution coefficient K() and also that the far-field liquid composition has some uniform

value. Solution of the diffusion equation then allows a relationship between the crystal composition and the far-field liquid composition to he derived. Fxpressing the ratio of solid composition to far—field liquid composition as A~ giv es: I K,, A 1 A (_i)

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c I and where l~is the crystal growth rate and 1) the dopant diffusion constant. A plot of I as a function of q and 0 is shown in fig. 4. Analytic limiting forms under zero and high field condi tions together with plots of the variation of J with tj and 0 are given in ref. [20]. Additional plots can he found in the paper by Cartwnight et al. [241. which also discusses various limiting forms as well as the ef’fect of rotation of the liquid at infinity. Experimental validation of the theory has been obtained from experimental studies of the axial distribution of phosphorus and carbon in silicon by Series et al. [41] and of the axial segregation of gallium in silicon by Ravishankar et al. [28]. The parameter I corresponds to the normalised extent of the diffusion profile. A small value for J indicates that the diffusion profile is confined close to the crystal and most of the diffusion profile falls in the region of the melt controlled by the rotating crystal melt interface. As I ap proaches unity the diffusion profile extends into the region of the melt where the flow is influenced by the far-field behaviour. The boundary layer theory discussed above is based on a similarity transformation which reduces the problem to a one-dimensional analysis. As a result, provided the far field dopant distrihu-

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tion is uniform, the analysis predicts a radially uniform distribution of dopant in the crystal. Experimentally crystals grown under axial fields are notorious for their poor radial uniformity. This may be due to two causes. First, under some conditions the diffusion boundary layer ahead of the crystal can become perturbed radially. Second, the bulk liquid composition at the edge of the boundary layer can be non-uniform due to the formation of non-mixing cells in the bulk of the melt. Ideally some form of perturbation analysis should be carried out to determine under what conditions poor uniformity might be expected. For the case of perturbations of the boundary layer, Riley and co-workers [22,23] have analysed the effect of vortices caused by crystal rotation on the boundary layer in an attempt to model the effect of finite crystal radius. Studies of the be-

haviour of the bulk of the melt are very much more difficult. Numerical modelling of the buildup of dopant in non-mixing cells is computationally very expensive because of the long time constants involved. In section 5.1.2.1 some indirect experimental evidence is discussed. We now discuss what insight can be gained into the conditions under which non-uniformities of the boundary layer are important, based on a simple dimensional analysis developed in ref. [42]. During growth there exists ahead of the crystal a diffusion boundary layer, within which the solute composition varies rapidly, and a momentum boundary layer inside which the fluid flow is essentially under the control of the crystal rotation and outside which it is heavily influenced by the bulk melt convection. The relative extent of the two boundary layers can be varied by varying

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growth conditions. Wilson [29] has demonstrated that for an arbitrary fluid flow’ the extent of the diffusion profile, L, 1. is given by:

convection in the hulk of the melt. Ihis will sen ouslv perturb the flow field solutions at distances

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where I is as defined in eq. ~ lo study the likely perturbations of the momentum boundary layer, it is profitable to note that during the derivation of the flow field [I 9] the full solution is split into two parts. termed the inner and outer solutions. The inner solutions are determined by the boundary conditions at the crystal melt interface while the outer solutions are determined by the limiting form at infinity. The transition from the inner to the outer solu lions takes place at a distance proportional to the characteristic length of the momentum boundary’ layer L,1~ Under an axial magnetic field L,11 is given by: I In cc (II)

which L~is greater than L we can expect signifi cant radial compositional variations Fxpressed mathematically, the condition for good radial uni forrnitv is then:

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Schmidt number. This is marked on the graph for the case of silicon. (The actual value will not vary much between semiconductor systems). Only

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R. W. Series, I), Ti Hurle

Use of magnetic fields in semiconductor crystal growth

315

growth in the unshaded region is expected to yield crystals with acceptable uniformity. To translate this graph into physical units it is necessary to specify either a growth rate or a rotation rate. As it is generally possible to vary crystal rotation over a much greater range than the growth rate we plot the graph in practical units assuming a growth rate of I mm/mm which is fairly typical for silicon. We can now plot on the graph contours of constant field (fig. 6). It can be seen that, for zero field, growth will always occur in a regime of good radial uniformity. However, the application of quite a modest field of only 500 G will require a crystal rotation rate in excess of 30 rpm to achieve acceptable radial uniformity. To achieve acceptable uniformity with a 2000 G field would require a crystal rotation rate in excess of 700 rpm, which would present a formidable engineering challenge. Similar graphs can be constructed from the more complex model with far-field melt rotation [24] but the effect is to reduce the size of the regime in which acceptable crystals can be grown.

[26] has demonstrated that a similarity solution to the flow field is still possible. In his solution, he demonstrates that the Cochran flow due to the rotating disk (the classic solution utilised in the Burton, Prim and Slichter theory) is not affected by a transverse magnetic field provided that the electrical conductivity of the rotating crystal is much smaller than that of the melt. The analysis is more sensitive to this latter assumption than is the axial field case. The transverse field affects only the pressure distribution in the melt. A more rigorous analysis, taking account of the finite size of the crucible and the 3D effects this introduces, has been carried out by Williams et al. [73]. Hence the segregation of conservative dopants should not be affected by such a field. In practice, transverse fields have a large effect on the thermal symmetry of the system, which can lead to pronounced rotational striae in the crystal as well as affecting the flow of hot melt at the crucible walls.

4.2.2. Transverse field Despite the fact that a transverse field destroys the rotational symmetry of the system, Kobyashi

verse magnetic fields have serious limitations. Whilst both achieved the desired result of damping out the turbulence in the melt, they have

4.2.3. Cusped field We have seen above that both axial and trans-

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different, and frequently’ undesirable, effects on the solute segregation. The breaking of the geo metrical symmetry of the Czochralski process. which results from the application of a transverse magnetic field, accentuates dopant striations caused by that asymmetry. On the other hand, as we hav’e seen, the use of an axial field inherently degrades the radial uniformity. A solution to this problem was devised mdcpendentlv by Series [32] and by Hirata and Hoshikaw a [33]. These workers proposed the use of a field configured so that, in the plane of the crystal melt interface, it was purely radial whereas deep in the hulk of the melt it was predominantl~ axial. Thus the rotational symmetry of the system is preserved while close to the crystal melt inter face there is no axial component of field. Such a field configuration was achieved by the use of ci pair of Helmholt, coils operated in the opposed curi ent mode. {he diameter and separation of the coils can he chosen to maximise the component of field normal to the crucible walls which, as is shown in section 5.1.2.3. has additional desirable effects for (‘zochralski silicon growth. With this configuration a large fraction of the melt volume is suhiect to magnetic damping so that there is a reduction in turbulence and concomitantly in the doping striations. Riley and coworkers [34.35] have ii rimerical ly simulated cony ection and oxygen ti ansport in the presence of a cusped field. 4 s’. ()‘s i’gen Iranspoil field

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.\s discussed in section 5.1.2. incorporation of oxygen into silicon crystals differs fundamentally from other systems and so has received special attention. The first digital simulation of oxygen transfer and segregation was performed by Lee et al. [36] for the ease of an axial magnetic field of strength either 1000 or 2000 (3 A somewhat more sophisticated simulation was sLibsequently carried out by Organ and Riley [17]. I hese authors took account of the temperature-dcpendence of the erosion rate at the crucible wall and sols cci for the temperature field over the crucible wall surface, assuming a constant heat flux through that surface. They concluded that the

gnc’tu fields

iii

sc’oiii ondus till s Fl sial gi oh i/i

inhibiting effect of the field upon the radial mo— tion should alw av s lead to a reduction in the proportion of the available oxygen that is incorporated. A greater proportion of oxygen is expected to he assimilated when forced convective effects, due to crystal rotation, dominate than when free convective effects, due to heat input, prevail. I he study complements the earlier work of I cc et al. [36]. who concentrated on the effects of the rela— tive rotation of crystal and crucible. (,, ommon to both studies is the recognition that a flow pattern which exhibits a two cell meridional circulation can he expected to ~ield a proportionately lower concentration of oxygen in the .rystal than the corresponding one cell circulation. Hicks et al. [34] subsequently extended their analysis to the case of a cusped field. The iesult.s of the simulation are compared with experimental results in the next section. The combined effect of an axial magnetic field and periodic growth rate fluctuations on segregation has been analysed by (‘artwright and Wheeler [25].

S Applications ~,

I. (‘..ochnal,ski gross’ili

I. / Inirodw fbi: As mentioned earlier. motiv ation behind ie search into magnetic crystal growth goes beyond the initial promise of i niproved crystal urn formitv Details of the use and the effect of the field vary and so it is appropriate to discuss the effect (SI the field separately for the different semiconductor materials. ‘s~

1.2 .Silicon Silicon is grown from a reactive crucible (silica) which gives rise to oxygen as the dominant inipur i tv in the crystals. The hehavioLi r (sf cis’s gen in silicon is highly complex and is used to advantage during modern integrated circuit fiihrication. ‘The response of the silicon to processing is highly dependant on the exact oxygen concentration and it is believed that substantial benefits arise if oxygen incorporation into the growing cr~staIcan he controlled to better than ~~‘iboth in absolute ~.

R. W. Series, I) Ti Hurle

Use of magnetic fields in semiconductor ens sial growth

terms and on micro- and macroscopic scales. Control of the incorporation of oxygen into the growtng crystal is one of the prime motivations behind research into magnetic Czochralski growth. Before discussing the effect of a magnetic field, it is appropriate to review very briefly the mechanism of oxygen incorporation into the growing crystal and a few other salient facts about silicon growth. The oxygen originates from reaction of the molten silicon with the silica crucible. The reaction is temperature sensitive [38,59]. It is generally believed that the erosion rate of the silica is determined primarily by the rate of transport of oxygen by diffusion through a crucible melt boundary layer. The oxygen is lost from the melt by two mechanisms: incorporation into the growing crystal and evaporation from the melt free surface as silicon monoxide. The latter loss mechanism accounts for approximately 98% of the total flux. The magnitude of the fluxes through the system dictates that large composition gradients exist within the melt. It therefore follows that, unlike conservative dopants, the oxygen content of the crystal is highly influenced by the conveLtive flows in the bulk of the melt and by boundary layers at the crucible melt interface and the meltfree surface. Flows in the free surface are known to be strongly influenced by Marangoni flow. Here, too, silicon can be expected to differ from other semiconductors since, as well as high temperature gradients in the surface, there will be considerable solutal Marangoni convection driven by the evaporation of oxygen as silicon monoxide from the free surface. For a review’ of the effects of oxygen and other impurities on the surface energy of silicon, see Keene [39]. Our state of knowledge about the more mundane aspects of oxygen incorporation is rather less clear. There continues to be considerable debate about the value of the segregation coefficient of oxygen in silicon. Reviews on this subject have been published by Jaccodine and Pearce [80] and also Barraclough [81]. For the present we note only that all experimental results obtained in our laboratories can be explained assuming that the distribution coefficient is close to unity. In addition to problems associated with oxygen, there are other significant differences between the

317

Czochralski growth of silicon and that of many other semiconductors. The crystal is mechanically strong and is generally grown with a high temperature gradient in the solid. To permit as high a growth rate as possible the temperature gradient in the melt is generally maintained as low as is consistent with the needs of the diameter control system. This generally operates with a fast-acting control loop which modulates the crystal lift rate and a longer term loop which acts on the heater power. The nett effect is that the microscale growth rate of the crystal is heavily influenced by the diameter control system and, in contrast to GaAs, the effects of thermal fluctuations in the melt (for normal growth conditions) are less of a problem. The effects of a magnetic field on oxygen incorporation in silicon were first noted by Hoshikawa et al. [401 who reported differences in oxygen content caused by rotation of the melt under the action of the three-phase heater. More recent work has studied the effects of axial, transverse and cusped fields. These are reviewed below.

5.1.2.1. Axial field results. There are a number of published studies of the effect of an axial field on silicon growth. Hoshikawa [49] reported reduction in solute striae in crystals grown from 3.5 kg melts with a field of 1000 G. In a later paper, Hirata and Inoue [75] report on the effect of vertical fields on thermal symmetry in silicon melts. Fields of 2500 G led to a significant reduction in thermal fluctuations in the melt; however, the effects of crucible rotation and the presence of a silicon crystal were not reported. A more detailed study of the effects of an axial field was reported by Hoshikawa et al. [76]. They describe the effects of axial fields of up to 1000 G on the phosphorus and oxygen distributions in silicon crystals grown from 3.5 kg melts. Results showed an increase in axial oxygen content and reduced uniformity of radial resistivity when compared with crystals grown in zero field. Uniformity of axial resistivity was increased. For crystals grown under other rotation conditions significant variations in radial uniformity of oxygen and phosphorus were reported. Some increase in rotational striae was observed at the periphery of crystals grown under

1 IS

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axial field, although at the centre, striae were reduced. A brief overview’ of an extensive in house programme on 25 kg melts by Ohwa et al. [77] reported generally high oxygen content under axial field. More detailed studies have been reported by Series [42]. who investigated the effects of fields of up to 2000 (3 on three-inch diameter crystals grown from 6 kg melts, and by Ravishankar et al. [28]. who made a comparative study of the effects of axial fields of up to 5000 (3 and transverse fields of up to 1500 (3 on four inch diameter crystals grown from 18 kg melts, Series [42] reported a general trend of high oxygen and poor radial uniformity of both conservative dopant and oxygen upt~~n application of the field. The poor radial uniformities of oxygen and of conservative dopants were attributed to different causes. For conservative dopants it was concluded that the prime cause was a change in the relative thicknesses of the dopant and momentum boundary layers (as outlined in sec tion 4 2.1). For oxygen the situation is rather different. Ilere, comparison with the numerical studies of Organ and Riley [37] suggests that the melt is composed of a number of poorly—mixed cells of differing oxygen content. Cells with easy access to the free surface of the melt are generally low in oxygen, whilst those in contact with the crucible, hut isolated from the free surface. have a high oxygen content. Under conditions of high crystal rotation, or of high field, the crystal-driven flow dominates and the crystal grow’s from liquid drawn from deep in the melt, which has had less contact with the free surface. This tends to lead to high oxygen concentrations. especially near the centre of the crystal and near the end of the growth run. Similar experimental results are re ported by Ravishankar et al. [28]. who attributed the changes in oxygen content in part to changes in crucible wall temperature. brought about by changes in heat transport through the melt. It was also noted that it was not possible to grow disloca tion-free material with oxygen content greater than 25 ppma. which was attributed to oxygen precipitation during growth. Both studies reported that. under an axial field, the effect of crystal rotation on oxygen incorporation was strengthened whilst crucible rotation had a much smaller effect. Series

folds

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noted that the ratio of crucible to crystal rotation primarily affected the radial uniformity of oxygen. Quantitative comparisons of the effect of an axial field on the effective distribution coefficient of conservative dopants (outlined in section 4 2.1) were reported for carbon and phosphorus by Series [42] and for gallium by Thomas et al. [18,31] and also Ravishankar et al. [28]. Results show gener ally good agreement with theory, as can he seen in fig 7. The last paper also makes comparison with the numerical studies of Kim and Langlois [43]. A problem which arises when attempting to make comparison with theory is the very poor radial uniformity.

Satisfactory interpretation of experimental data often poses a considerable problem. A large amount of analytical work is required to build up a comprehensive picture of the distribution of impurities throughout the volume of a crystal. without which anomalous behaviour may not he recognised. In addition, detailed interpretation of results frequently requires considerable judgement and collateral inputs from nui’nerical simulation. We illustrate this with reference to figs. X and Q I

0.2

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R W Series, D Ti. Hurle

Use of magnetic fields in semiconductor crs’stal gnosjth

319

go

grid at eleven positions along the length of the

El ~ 601

ensure that the results were rotationally symmetri-

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cal. Five regions can be observed. First, the axial distributions at 15, 20, 25, 30 and 35 mm from the crystal. Additional measurements were made to centre of the crystal (which represents about 80~ by volume) grew from a well-mixed region of the melt. Results for the central core of the crystal (i.e.

(0 50. o 70 I 0 40. ~30’ 2C,

0, 5 and 10 mm from the centre) show a very different picture. For fraction solid (g) less than

0 1C

0

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00

01

02

03

04

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06

07

Fraction Solid Fig. S Axial variation of carbon concentration measured at different radial positions in silicon crvsiais grown with an axial field of 2 kG. Numerical values assigned to each curve represent distance from the crystal axis. The crystal was rotated ai 22 rpm with the crucible counter-rotated at 3 rpm.

In fig. 8 we show the macroscopic carbon distribution throughout the volume of an 82 mm diameter crystal grown under an axial field of 2000 G. (The data are additional to that reported in ref. [42]. fig. 3.) The figure shows analyses on a radial 5 mm -~

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Fig. 9 Numerical simulation of flow in a melt with an axial magnetic field of strength corresponding to Is o. Contours are projected streamlines in a meridional plane. The broken line is the contour of zero stream function (“1’ 0). ‘1’> 0 corresponds to counterclockwise circulation (from Organ and

l3~l)

trapped cell, or else a larger but essentially stagnant cell. To differentiate between these two cases it would be necessary to examine the shape of the transient region. Between g 0.3 and g 0.55 the central pattern appears to fit the distribution found in the outer regions, suggesting that the full diameter of the crystal is now growing in contact with a single cell. Finally, in the region of g> 0.55, the central core again becomes anomalous. This time the composition is lower than in the outer regions, which suggests that the crystal centre is now growing from a cell isolated from the larger outer-circulation pattern. Fig. 9. taken from Organ and Riley [37], shows computed flow fields for a crystal grown under an axial field with a similar value of the magnetic interaction parameter N. This shows an essentially three-cell structure to the melt, cornprising a large outer cell driven by convection up the crucible wall, a smaller cell under the crystal driven by crystal rotation, and a third axiallyelongated cell anchored to the crucible bottom. Although results are not given for a range of melt

-___

Riley

0.1 a very steep transient is seen. For 0.1 < g <0.3 an approximately uniform (but high) carbon concentration is seen, indicating that the central part of the crystal is growing from either a very small

aspect ratios, the gross structure of the melt is entirely consistent with our experimental observations. In general, application of an axial field leads to reduced mixing in the bulk of the melt with poor solute distributions and high oxygen concentration. An additional factor potentially affecting oxygen content is change in heat transport through the melt, brought about by magnetic damping of the flow. The resultant change in the crucible wall temperature will undoubtedly affect the rate of uptake of oxygen hut this is believed to have only

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a second order effect on the overall oxygen distrihution in the crystal. Changes in heat transfer can also change the crystal melt interface shape and, if the servo control of crystal diameter is made quate. lead to changes in crystal radius which, in turn, has an indirect hut major impact on oxygen incorporation.

Flila/

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rotational striae. 1 his is probably brought about by loss of thermal svmnietry in the melt caused by the transverse field. Most workers agree that, in contrast to axial field growth. It iS the crucible rotation which has the dominant effect on oxygen incorporation in the presence of a transv erse field. ~.

1.2.2. Tran,v:ersc field results SuLuki and co workers [5] were the first to report on silicon crystal growth under art applied transverse magnetic field. They used a conventional resistively’ heated puller and grew dislocation-free boron doped crystals 5 cm in diameter on a (lUU) axis using a field of 4000 G. They den’ionstrated that application of the field damped the temperature fluctuations in the melt down to an amplitude of 0.2°C’, whereas in the absence of the field, fluctuations of the order of 2°C amplitude were seen and the melt surface became agitated. The’s also showed that the boron growth striations were eliminated and that the oxygen concentration was significantly lower (4 x 1017 as against I X lO~ cm ~) when the magnetic field w’as applied. This paper generated the subsequent widespread inter est in the application of static magnetic fields, More detailed studies on crystals grown from large melts have been reported by Hoshi et al, [82]. The main result to emerge is that transverse fields lead to low’ oxygen and reduced contamination by impurities present in the crucible. Reasons for this are discussed in the following section on cusped fields. Ehe picture is less clear with regard to the effect of a transverse field on conservative dopant uniformity. Informal discussions with workers in the field suggest that field uniformity is a key issue. The theoretical analysis by Kobayashi [26] shows that a pure transverse field should have rio direct effect on conservative impurity incorporation. However, generation of a pure transverse field over the large diameter required for commer cial crystal growth is very difficult, and even small design errors will give rise to significant axial components at the interface which will degrade radial dopant uniformity. Ravishankar et al. [28] report a reduction in striae caused by thermal convection. However, they admit to an increase in

lot

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field retails

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attempt to resolve some of the problems brought about h’s application of simple axial or transverse fields Series [32] and Ilirata et al. [33] independently developed the cusped field concept. In this a pan of axially symmetric coils are placed c’oaxiallv above and below’ the crystal melt interface, The current through the coils flows in opposite directions. With appropriate design it is possible to achieve a field which is approximately normal to the crucible wall over most of the crucible melt interface and which has no axial component cit the crystal melt interface. Both workers report low oxygen contents and good radial uniforniit’s. F oi a wide range of growth conditions, radial unil’ormit’s of conservative dopants is as good as. or possibly better than, that achieved under zero field condi lions. Comparison of these results with the numerical study of Hicks et al. 34] shows that the model correctly predicts the reduction in the overall oxygen content, the magnitude of the reducticsn being in reasonable accord with the experimental value. Both model and experiment show the most rapid rate of reduction of oxygen concentration at low magnetic- field. fhe desirable properties of this con figu rat ions may’ he attributed to a number of factors. First. the crystal grows in a region of zero ,ixi1il field. Thus none of the problems arising from mnterac tions with the boundary layer are found Second, the melt close to the crystal is in a region of low magnetic field strength and so can become well mixed. Third. the hulk of the melt is in ~i region (if high magnetic field and so turbulent convection is damped. In addition, since the field is normal to the vertical wall of the crucible, the boundary layer adjacent to the wall is thickened, an effect which has been analysed by Kerr and Wheeler [30]. As a result, erosion of the crucible is reduced, leading to low’ oxygen incorporation into the hulk of the melt. 1ii’i

R. W. Series, D. Ti. Hurle

Use of magnetic fields in semiconductor crystal growth

In later work Hirata and Hoshikawa [44] explored the effect of moving the neutral plane of the field away from the plane of the crystal melt interface. They reasoned that by doing so, i.e. by applying a vertical component of the field in the plane of the free surface of the melt and a radial component of field at the vertical crystal wall, they could independently control the rate of cr0sion of the crucible (i.e. the uptake of oxygen) and the rate of evaporation of oxygen (as silicon monoxide) at the melt surface. In reducing the rate of evaporation of silicon monoxide by providing a vertical component of field at the melt-free surface (of magnitude 550 G) they were able to increase the oxygen concentration in the crystal (as well as achieving near constancy in the axial direction) to a value of 1.41 X 1018 cm ~, which is some 35% higher than that obtained with zero magnetic field. Although it is hard to make totally general statements about the effects of crucible and crystal rotation, it is found that, for axial field growth, crystal rotation is the dominant parameter, while for transverse and cusped fields it is crucible rotation. This fits the general principles outlined in section 2 which showed that a field normal to a rigid (non-conducting) boundary strengthen the coupling between the rigid boundary and the melt flow, 5.1.3. Gallium arsenide

Terashima and Fukuda and their co-workers [45,72] were the first to apply a magnetic field to the liquid encapsulation Czochralski (LEC) growth of gallium arsenide single crystals. They applied a transverse magnetic field, generated by a pair of superconducting magnets, to a Cambridge Instruments MSR6RA puller, generating a field of up to 3000 (3. They showed that the temperature fluctuations in the molten gallium arsenide were markedly reduced from around 18°C to only about 0.1°C as the field was increased from 0 to around 1250 G. They successfully grew 2 inch diameter gallium arsenide single crystals in the apparatus but found that the effect of applying a field of 1300 G was to change the material from semi-insulating (with resistivity approximately io~ f2 cm) to semiconducting (10 ~7cm). From a study

321

of the concentration of the native defect deep level (EL2) which controls the electrical behaviour, they inferred that this loss of semi-insulating behaviour was a result of a decrease in the concentration of EL2. They tentatively ascribed this to the marked reduction in the fluctuation of the interface velocity as a result of damping of the turbulent convection. Subsequently this group also developed a superconducting axial magnetic field configuration [46 48] whilst a group at NTT, led by Hoshikawa [74], utilised a conventional solenoid capable of generating a field of 2000 G. Terashima and coworkers [46] made a detailed study of’ the EL2 distribution in the presence of an axial field of 1000 G. The temperature fluctuations were suppressed to an amplitude of <0.3°C. In the presence of the field the EL2 concentration varied very strongly with the composition of the melt with values well below I x 1015 cm for a melt with 45 at% arsenic, rising to the very high value of 1 X 1017 cm in a melt with 51% arsenic. This variation with melt composition is very much stronger than that observed in conventional LEC growth. Terashima et al. ascribed this to the damping of the temperature fluctuations, which damp the velocity fluctuation of the interface. However, a more likely explanation is to be found from a consideration of the variation of the melt composition at the crystal melt interface. In genera! the melt composition will deviate from the congruent composition so that, as growth proceeds, a boundary layer of the excess component (gallium or arsenic) will form at the crystal melt interface. The EL2 concentration, which is controlled by the grown-in concentration of gallium vacancies (Hurle [50]) will depend on this interface concentration. Thus the EL2 concentration rises as the arsenic content in the melt rises. This effect will be much amplified in the presence of an axial magnetic field since this field, by damping the flow, will increase the magnitude of the boundary layer of the excess component. Only for growth from the congruent composition, which has to be very near the equi-atomic composition, will the magnetic field produce no effect. Thus the EL2 concentration should be at its expected value of around 2 x 1016 cm at this composition. For

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arsenic rich melts the magnetic field should procluce an enhancement over that seen in conven— tional LF-C. whereas for gallium—rich melts it should produce ci decrease. This is precisely what I erashima et al. observed. I his interpretation is given weight in subse quent work by’ Kirnura et al. 48]. who used ci superconducting magnet to generate an axial field of rip to 3000 Ci. The’s made careful measurenients of the F [2 distribution down the crystals and showed that increasing the field strength from I ~00 to 3000 Ci reduced the hL2 concentration for melts to the gallium—rich side of congruency hut increased it ‘or arsenic—rich melts. For a melt of 31r no change was obcirsenic composition 50. served as the field was increased, suggesting that this coniposition is near to congruenc’s . The ho

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mogeneit’s of the hL2 distribution was niuch nilproved by application of the field: it showed ci sniooth ‘‘normal freeie’’—Iike variation in the pres— ence of the field hut a quite random axial v aria— tion in the absence of the field. I low’ever. from what has been written in section 4. we would expect the radial uniformity of tlìe F [2 concentration to he significantly impaired in the presence of clii axial magnetic field. This is indeed observed, as is shown in fig. 10 taken from w ork h’s I erashima et al. [47] for the case of growth from a slightly’ gallium rich melt. These authors grew ci gallium rich crystal in which part of the cry stal was grown with seed rotation only. pail with counter rotation of seed and crucible cn’icl. finally, with co—rotation of seed and crucible, In the counter rotation region. the EL2 concentra tioii vvas around I x 100 cm ~. On changing to iso—rotation, the FL2 concentration fell to around 2 x 101 cm ‘. Since the crystal was being grown from a gallium—rich melt the excess gallium houndar’s layer is predicted to increase in height for the iso—rotation case (see (‘artw right ci al.

decrease in the amplitude of the temperature fluctuations ctildl is perhaps due to a reduction in the spatially—averaged segregation coefficient with reduction in amplitude of oscillation of the cry s— tallisation velocity. ct5 described h’s I lurle and .Jakeman [51]. C onsistent with cifi expected in crease of carbon segregation coefficient toss ards unity in the presence of the strong field. tfìe as.icil distribution of carbon became much more uni form in the presence of a field in excess of about 1300 Ci. They also attempted to correlate crystal stoichiometry. measured coulometricalls with nm— tial melt composition when grovvth took place ni the presence of a strong transverse field 521 hut reservations have been expressed about the accuracy of the stoichiornetry measurenient [79] In a stud’s of indium—doped gallium cirsenide grown by the LEC technique with an ciXicil ii’ilg

24]). This increased gallium richness at the inter face generates the observed reduction in F L2 con centration. I erashima and co—s’s orkers [52] also ins estm gated the distribution of the main residual impuri ties in gallium arsenide, namely carbon and boron. Both of these decreased on application of a transverse magnetic field. 4 his decrease correlated with

netic field. Kimura et al. [48] measured a segrega tion coefficient for carbon of 3.0 in .‘ero field which decreased with increasing field until it was near unity at a field of 1000 Ci. Taken with data of I erashima et a!. 1471. this s’s ould imply that the segregation coefficient of carbon is less thai’i Unit’s in otherwise undoped gallium arsenide, hut greater than unity in indium doped material. Alterna—

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R. W. Series. D, Ti Hurle

Use of magnetic fields in semiconductor crs c.ta/ growth

tively. it may be that, with respect to carbon, the system is non-conservative and the mechanisms by which carbon is steadily introduced into, or removed from, the melt may be perturbed by the presence of a magnetic field. Hoshikawa and co-workers [53], using an axial field, found a marked reduction in temperature fluctuations for fields in excess of 800 G. This contrasts with Terashima’s results for the transverse magnetic field where the amplitude of the fluctuations first diminished to a minimum at a field strength of 1500 (3, to fall again to a low value for fields in excess of 3000 G. Hoshikawa et al. were able to grow striation-free semi-insulating crystals with their technique. They also noted that the controllability of the crystal growth process was enhanced by the application of the axial field, This was attributed to the formation of a convex growth interface in the presence of the field. They noted that the diameter of the crystal could be controlled by varying the field. The semi-insulating behaviour was ascribed to compensation of residual carbon acceptors by EL2 and they attributed the difference between their results and those of Terashima (cited above) where the latter obtained lower resistivity in the presence of a field as being due to differences in melt composition and the concentrations of residual impurities, More recently Hoshikawa’s group have cxtended the technique to grow fully encapsulated Czochralski crystals in the presence of a vertical field [54]. In combination with indium doping, they were able to grow completely dislocationand striation-free semi-insulating crystals of 50 mm diameter. Indium doping was used to harden the lattice a recipe known to aid considerably in dislocation reduction, The magnetic field had the additional effect (that is, additional to striation removal) of providing a near-uniform distribution of indium down the crystal. The radial variation of the indium concentration was not reported but we would anticipate that this would be rather non-uniform, 5.1,4, Indium phosphide

Miyairi and co-workers [55] and Satoh et al. [56] have grown 50 mm diameter indium phos-

‘323

phide single crystals in an axial magnetic field applied to. respectively, a Cambridge Instruments Melbourn puller and a locally-designed puller. Miyairi et al. noted that the temperature fluctuations in the melt decreased from an amplitude of around 9°C in zero field to <0.3°C for fields in excess of 1000 (3. Crystals grown in a field of this strength did not show the irregular striations characteristie of crystals grown in zero field but only striations associated with the crystal rotation. This was found true for both crystals which were not intentionally doped and for tin, sulphur and galhum + antimony + sulphur doped crystals. Dislocation clusters known as grappes’~were not found in the crystals and there was a marginal reduction in the average dislocation density. This was ascribed to the avoidance of the dislocation clusters. Satoh et al noted that the dislocation density in K100) semi-insulating iron-doped crystals was reduced from an average level of 8 x i0~ to 3 x i0~ cm ~ when a field of 1500 (3 was applied. Resistivity fluctuations down the crystal were also markedly reduced. MUller and co-workers [58] have grown 3 inch diameter indium phosphide single crystals using the high pressure LEC technique with and without an applied axial field. Their crystals were made semi-insulating by iron doping and a study was made both of the temperature fluctuations in the melt and of the macro- and micro-distribution of the iron. Temperature measurements in the melt showed chaotic fluctuations in zero field which were transformed into near-periodic oscillations of period approximately 0,1 Hz when the field was applied. Irregular striations were seen in the crystal grown in zero field. These were replaced by much weaker, equidistant striations, corresponding to the temporal frequency of 0.1 Hz, in the crystal grown in the axial field. The segregation coefficient of iron in indium phosphide is approximately 10 so that there is a strong macro-segregation down a grown crystal. By applying a large magnetic field during the initial stages of growth and by stepwise reducing this field as growth proceeded, Ozawa et al, [57] and, independently, Hofmann et al. [58] were able to obtain a crystal with a near-constant iron distribution up to fraction solidified approaching g

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0.7 (fig. 11). This technique could usefully he applied to indium-doped gallium arsenide hut, to the authors’ knowledge. this has not ‘set been reported. However, with a purely axial field, prob lems of radial uniformity can he anticipated. Kohayashi and Muguruma [60] have shown theoretically how the magnetic field should he varied as a function of the fraction of melt solidified in order to rnaximise the yield of crystal within sonic hound on the doping concentration. 1..’s. Comparison 01 dijferent field eonJiguralion.s At first sight the lack of radial symmetry which results from imposing a transverse magnetic fieldi might he thought to rule out this approach. How ever, it has been shown to give loss oxygen con centrations in silicon and a much better radial uniformity than is obtainable with an axial mag netic field, however, tile distortion of the thermal field! of the melt accentuates rotational striations. ‘s.

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I he reason for the improved radial dmiformity is evident from Kohayashi’s analysis [26]. where he shows that, to first order, the transverse field has no effect on the boundary layer flow adjacent to the crystal melt interlace. Tile low levels of oxygen attained with ci transverse field are probably the result of the damping of the centrifugal pumping produced h’s’ the crystal rotation and thickennig of the boundary layer at the crucible wall. ‘\n axial field is most effective in reducing stricitions. h’s damping turbulence whilst maintain ing axial symmetry, hut gives very poor radial uniformity. ‘I he relative effects of crucible and crystal rotation are very different for the two magnetic field configurations. Thus, with ciii axial magnetic field the centrifugal pumpmng due to crystal rotatmon gives an enhanced oxygen Coil centration which is, ~ifuncti()m~ of that cry stal rota— tion rate. [‘he crucible rotation under these condi tions has very little effect. B’s contrast. with a transverse magnetic field!, changes nl crystal rotation have little effect: it is crucible rotation which now has the key role ni controlling the oxygen concentration ni sihcctn crystals. I lie separate advantages of the two techniques are largely comhn’3ed in the concept of the cusped magnetic field. The ability to move the neutral plane vs mth respect to the melt surface pro’s idles an additional control variable to enable the oxygen concentration to he optimised (although simulta neous optimisation of ox’5 gemi and conservative clopant distribution still poses a problem). ‘s.2. Othe,’

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I 1

-d fra tori u

1mg ii t se ssl step ssise reduciion in axial magnetic field to minimise m,ierc) segregation in Fe dcped lnP (a) Applied field a function of I radilon of melt solidified. (h) measurect oncco iraiion of iron normal ised io i ni toil mcii conceit ira tiOo I ) The curses ,ire the theoretical segregation curves fssr a sciluie hasing s,ilues of the segregation coefficmenm A shdl~n Fromia Hot mann

ci

,il ~

Whilst the mani interest in the use of magnetic fieldis has been in the area of the commercial growth h’s the Czochralski hum arsenide amid indium been some studies on the field on float zone growth horizontal and vertical other materials. These experinlents of t tech studied the horizontal luriuni—doped nidmum °~ a

process of silicon, galphosphide. there have effects of a magnetic of silicon and on the

Bridgman growth of some dlate hack to the original and Fleniings Ill. w ho Bridgmami growth of tel

amitimonide

ni the presence

transverse amid vertical magnetic field. I hey showed that the effect of the field was to damiip the

R. W Series, D Ti Hur/e

Use of magnetic fields in semiconducior crmsial grossth

thermal fluctuations in the melt and that when this occurred the dopant striations were also eliminated. They performed similar experiments with a dilute aluminium copper alloy [2] and showed that solute banding could be eliminated in this alloy by applying the magnetic field also, Chedzey and Hurle [3] performed similar horizontal Bridgman experiments on indium antimonide but with the transverse magnetic field applied along a horizontal axis. Both configurations of field appeared to be equally efficacious in removing the solute striations. Chedzey and Hurle were able to correlate the waveform of the temperature fluctuations with the spacing of the solute striations. Hurle and Hunt [61] reported on the horizontal directional solidification of the indium antimonide-nickel antimonide eutectic. This is a rod eutectic system and, in the absence of a magnetic field, turbulence in the melt produces a banded form of eutectic in which the rods are repeatedly terminated by the temperature fluctuations. By applying a transverse magnetic field this banding is eliminated and very long uniform eutectic microstructures are obtained. Similar experiments were performed on the eutectic system bismuth/ manganese by Dc Carlo and Pinch [62] with similar results, Robertson and O’Connor [63 65] have studied the effect of both transverse and axial fields on the float zone melting of gallium-doped silicon crystals grown on a (100) axis. Crystals were grown from feed stock of 25 mm diameter. Transverse magnetic fields up to 5500 G were shown to have pronounced effects on the shape of the interface and, for non-rotating crystals, on the cross-seetional shape of the crystal which assumed an elliptical form with a major axis aligned with the field direction, Interestingly, under these conditions. pronounced dopant concentration striations were found in the crystal, spaced in time by roughly a 30 s period. The effective segregation coefficient of the gallium was found to increase in the presence of a magnetic field. A marked reduction in dopant concentration fluctuations is observed for field strengths greater than 3000 (3. However, in the presence of a large axial field, control of the crystal shape became extremely

325

difficult, particularly with low rotation rates. This improved uniformity was confined to a central core region extending to about 1/3rd of the crystal diameter. Vertical Bridgman growth in the presence of a transverse horizontal magnetic field has been used by Kim [66] to grow indium antimonide and by Sen et al. [671 to grow indium gallium antimonide, Kim showed that striation-free crystal growth was obtained above some critical value of the field corresponding to the damping of convective oscillations. Sen et al. studied a concentrated alloy growing under conditions of constitutional supercooling. Using a transverse field of 4000 (3 they showed that the field produced a dramatic reduction in the density of grain boundaries and of twin boundaries. They suggested that a sudden increase in freezing rate caused by turbulence in the presence of a magnetic field could first nucleate twins at the interface before a cellular structure had time to develop. Such twinning would be absent when the fluctuations were removed. Matthiesen et al. [61 grew 1.5 cm diameter germanium crystals in a vertical Bridgman configuration in the presence of an applied axial magnetic field of 30000 G. The solute distribution in the crystal was characteristic of that in diffusioncontrolled growth, showing that the field had cifectively suppressed the convective motion. Very recently Motakef [68] has analysed the scaling laws which apply to segregation in vertical magnetically-controlled Bridgman growth and applied his analysis to Matthiesen et al’s data.

6. Concluding remarks We have seen that the most universal effect of an applied magnetic field is the damping of the convective turbulence in the melt and that, by so doing, it gives an improvement in the micro-homogeneity of dopant distribution. However, it can have more profound effects on dopant distribution. Thus the segregation coefficient is driven strongly towards unity in Czochralski growth in the presence of an axial field. Non-conservative dopants such as oxygen in silicon are influenced by the magnetic field in very complex ways, re-

7 “Is

/d iS

Sc mii’s, /) / .1 1/urIc

I

sc

is!

,/lcIc,’nc’lic Icc/ifs iii 5001/c Si/U/Ui (or 1/1 5 tal i_a oit 1/i

lated to the processes of uptake of oxygen into the melt by erosion of the crucible and evaporative loss from the melt free surface as silicon mono ‘side. These processes have been brought under considerable control with the recently’ pioneered! cusped magnetic field. Whether or not this vviIl find application in the commercial production of large silicon single crystals for VLSI Ii LSI appli cations is less clear since considerations of cost and yield are crucial in commercial operations. l’quall’s. in the case of gallium arsenide, the applicatiom’i of a field might he expected to improve the micro—uniformity of the native defect EL2 w hicli controls the electrical properties of semi-insulating material, The fact is. though. that in present day material the non—uniformity in as—grow’mi crystals is doi’ninated by the polygonmsed dislocation struc ture which results from the thermal stress in the cooling crystal. In any event, such micro-inhorno geneitv can he removed h’s carrying out an anneal ing schedule on the as-grown ingot [69]. The use of a magnetic field might well become of commercial significance in gallium arsenide, once opto-electronmc integrated circuits (OEIC5) have come to maturity since one can anticipate that once (in-chip lasers are required, the demand for lower disloca tion density will become very pressing. To meet this it may he necessary to revert to hardening the crystal lattice by indium doping, a practice tried several years ago and now discontinued. In (irder to achieve uniform doping axially. radially and microscopically, the use of a cusped magnetic field miiay prove attractive. An alternative miiethod for removing melt turbulence and the concomitant solute striations is tci grow the crystals in a gravity-free environment, This has been demonstrated in a number of space experiments. It is therefore appropriate to conipare the merits and demerits of magnetic field damping as against gravity reduction, Aside from the technological aspects of generating the separate environments, lies the difference that magnetic field damping depends on the action of the Lorenz force which is proportional to the vector product of the l’low velocity and the field strength. It therefore has a decreasing influence with decreasing flow’ velocity and so is ill-fitted to the further damping of very weak flow’s. By contrast, a

reduction in gras it’s represents a reduction in the driving hod’s force for convectiomi. However, the space env’iromimemit does riot pro’s ide zero gravity and the residual levels of microgravity ciiicludimig so-called ,g-jmtter) set a lower hound on the ef fectiveness of gravit’s reductiomi. The best results could he anticipated from the combined use of mliicrogravmtv and a magnetic field, wherein the microgravitv would reduce the slow stead’s con‘sectiv’e flows to a minimum with the magnetic field daniping an’s’ ,g-jitter fluctuation. This has been discussed by Baumgartl amid co-workers [70]. Finally. vve wish to miote that this me’s mew has been concerned with the damping of tdirhulence h’s seeking to damp the natural cdiii’s ccii’s c flow which drives it, A major outcomlic of research in the area over the past decade has been the recognition that while turbulent convection is oltemi detrimental, stead’s state comivection lies at the heart of the production of uniform crystals. An altermiative approach to damping convectise flows which would appear to (iffer sonic advantage is to impose a forced flow w’hich dominates over the natural convective flow, Magnetic fields can con tribute here by using them to deliberately stir the melt. This idea has been in use in the steel industr’s for the electro—smelting of some grades of steel for a bug timiie. It nivolves passing an electric current from an external source through the melt so as to cause the melt to “ motor”, The actual magnitude of the current required is quite small. A total current for a typical commercial silicon melt might he only of the (irder of a few amperes Suppose, for example, it was desired to enhance the centrifugal pumping action ni the miielt ahead of a crystal hemmig grown in a transverse magnetic field, If a current is passed through the crystal, the force exerted on the melt by the current will he normal to both the field and the axis of the crystal and 50 will drive the melt adjacent to the crystal in a circular path and increase the cemitrifugal pump ing in the melt, In practice it may he difficult to pass sufficient current through the crystal and a better plan may he to rely on electrodes placed in the melt. C onsider for example the actmomi of two electrodes placed diametrically opposite each other at mid radius, Current is passed from one to the other. The system is (iperated in an axial magnetic

R. W. Series, D T.i Hurle

Use of magneto fcc/d.c in vemcconduc’ior cr1 sta/ grosmth

field, The current flow will create two circular eddies centred around each electrode. The eddies will bring a continual supply of fresh liquid under the crystal and so remove the dopant being rejected by the growing crystal. This will thin the diffusion boundary layer such that the effective segregation coefficient will tend to its equilibrium value. Although such a flow pattern will destroy the rotational symmetry of the system it should be possible to grow a crystal with an acceptable radial uniformity.

Acknowledgments

[161 W E.

327

Langloms. L.N. Hjeilmmng and iS. Walker. J. Cr’sstal

Growth 83 (1987) 51. [171 R.A Cartwrmght, N. El Kaddah and J. Szekely, J AppI. Maih, iS (1Q85) 175 [181 R.N Thomas. H M 1-tohgood, P.S. Ravishankar and T.T. Braggmns. J Crystal Growth 99 (1990) 643

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(1985)

[21] iA. Burton, R C Prim and W.P Slic’hier, J Chem, Phvs 21(1953)1987. [22] AL. Organ and N Riley, J AppI. Math. 36 (1986) 1)7.

1231

T.W. Hicks and N Rule’s, J. Crystal Growth 96 (1989) 957. [24] R A. Cariwrighi. D.T.J. Hurle, R.W. Series and J Szekel’s. J. Crystal Growth 82 (1987) 327. [25] R.A. Cartwrmghi and A A. Wheeler, J Crystal Growth 87

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We are grateful for valuable discussions with Keith Barraclough, Norman Riley, Adam Wheeler and John Wilkes, One of us (R.W.S.) received

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[28] P.S. Ravmshankar. T.T Braggmns and R N. Thomas, J Crystal Growth 104 (1990) 617

[30] OS. Kerr and A.A. Wheeler. J. Fluid Mech. 199 (1989)

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