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Two-component systems (i)

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Two-component systems (ii)

• The surface of a crystal is a cross discontinuity a nd has a free energy associated with it. • The value of this free energy depends on the orient ation of the face and on the other phase in contact (vacuum, liquid).• A first approximation of the surface free energy

selected materials arecompiled in Table 2.2

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Two-component systems (iii)

• The equilibrium shape of a crystal consists of a se t of singular faces by using the principle of surface potential minimizati on (Wulff construction)

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Two-component systems (iv)

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Nearly ideal solid solutions (i)

• Mixed crystals like Ge 1-xSix, In1-xGaxAs , Al 1-xGaxN ⇒⇒⇒⇒ increasing importance

• Monocrystals with high compositional homogeneity (x uniformity) ⇒⇒⇒⇒ required

• From the phase diagram: growth conditions- growth te chnique, T, P and concentration can be determined

• An ideal solution ⇒⇒⇒⇒ a system with complete miscibility in both the liquid and solid phase for the whole compositional range 0<x<1.

• In the low pressure T-x projection ⇒⇒⇒⇒ three fields: liquid, liquid + solid, and solid, separated by two boundaries ⇒⇒⇒⇒ liquidus L and solidus S (fig. 2.6).

• The liquidus and solidus lines can be calculated the oretically.

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Nearly ideal solid solutions (ii)• With respect to the component i=B, the equilibrium between solid and liquid phases is given by

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Nearly ideal solid solutions (iii)

• Fig. 2.6 shows the T-x projection of the Ge-Si phas e diagram.

• Since the experimental and theoretical curves agree well ⇒⇒⇒⇒ one can say that the system exhibits nearly ideal mixin g behavior.

• This is also reflected in the near linear variation of the lattice constant with composition ⇒⇒⇒⇒ Vegard’s rule.

• An important characteristic of the system can be de termined from the phase diagram ⇒⇒⇒⇒ Ko (thermodynamic) equilibrium distribution coefficient of component B.

XBs – concentration of B in solid, X Bl – concentration of B in liquid, ∆hB

o – standard enthalpy and T mB melting temperature of the pure component B, R-constant.

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Systems with compound formation• The tendency to form intermediate phases arises fro m the strong attractive forces between unlike atoms.• In such phases the bonds have much stronger ionic o r covalent character compared to metallic ordered solutions ⇒⇒⇒⇒ the free energies , i.e. entropy and enthalpy are typically low leading to their hig h stability.• The following chemical reaction takes place: mA(s) + nB(s) = AmBn(s)

In this case m=n=1

• Due to the relatively narrow stability region the compound is shown as a single vertical line of exact stoichiometry ⇒⇒⇒⇒ small deviations determine a region called range of existence or range of homogeneity. • In this region the material is still stoichiometric and contains a certain number of intrinsic defects (equilibrium).

• Semiconductor compounds:Width of existence 10-5 -10-2 mole fractionFormation enthalpy of point defects 1- 4eV

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Phase diagram Si-C

Rositza Yakimova SIMC-XIII-2004, Beijing, 20-25 Sept. 2004

� No liquid phase

� sublimation from 1800°C

� solubility of carbon in liquid Si

0,026 at% at 1700°C

0 20 40 60 80 100

Si CAt % C

Graphite+

SiC

V+graphite

V

L

V+L

L+SiC

V+SiC

SiC

Si+SiC

T°C

2830

1402

Growth is a high temperature

process

P = 1 atm

Issues: crucible material,

heating, tightness, purity, etc.

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• The melt growth processes are characterized by relatively low driving forces ⇒ ∆H/Tm usually falls within the range of 10 to 100Jmol-1; ∆T is typically 1-5K

⇒ ∆µ l→→→→s is about 10-100Jmol -1.

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• Because in melt growth and LPE the crystals and layers are grown in near equilibrium conditions ⇒ the actual equilibrium states as described by the phase diagrams can be used as good approximation.• At high deviation from equilibrium ⇒the equilibrium phase diagrams are a rough tool only

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