Amorphous semiconductors KUGLER Sándor. S. Kugler: Lectures on Amorphous Semiconductors 2...

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Amorphous Amorphous semiconductorssemiconductors

KUGLER SKUGLER Sáándorndor

S. Kugler: Lectures on Amorphous SemicoS. Kugler: Lectures on Amorphous Semiconductorsnductors

IntroductionIntroduction

Amorphous materials: NOT NEW!Amorphous materials: NOT NEW!

Iron reach siliceous glassy materials Iron reach siliceous glassy materials recovered from the Moon! (Apollo recovered from the Moon! (Apollo mission) Billion years old!mission) Billion years old!

People has been preparing glassy People has been preparing glassy materials (i.e. SiOmaterials (i.e. SiO22) for thousand of ) for thousand of years.years.

Historical NotesHistorical Notes

Scientific investigations started Scientific investigations started about 70 years earlier. about 70 years earlier. Zachariasen (1932) proposed Zachariasen (1932) proposed that SiOthat SiO22 structure can be structure can be described by a Continuous described by a Continuous Random Network (CRN). Random Network (CRN).

(8 – N) rule(8 – N) ruleN.F. Mott 1969N.F. Mott 1969

In a glass any atom is built in such a way that In a glass any atom is built in such a way that it retains its natural coordination (no dangling it retains its natural coordination (no dangling bonds). Z, the number of covalent bonds bonds). Z, the number of covalent bonds Z = 8 – N, where N is the number of Z = 8 – N, where N is the number of valence electrons. (Original version, where valence electrons. (Original version, where we consider elements only in IV-VI. columns we consider elements only in IV-VI. columns at the periodic table.)at the periodic table.)

Z = N, if N<4. (additional rule)Z = N, if N<4. (additional rule)

The consequence: The consequence: glasses can NOT be glasses can NOT be

doped!doped!

Chittick and coworkers at the Chittick and coworkers at the Telecommunications Lab. in Harlow, Telecommunications Lab. in Harlow, England (1968-70) proposed first England (1968-70) proposed first doping effect in glow discharge doping effect in glow discharge prepared amorphous silicon.prepared amorphous silicon.

Mott’s (8-N) rule was strong enough Mott’s (8-N) rule was strong enough to ignore this effect.to ignore this effect.

Six years later W.E. Spear and P.G. Six years later W.E. Spear and P.G. LeComber (Dundee group) could LeComber (Dundee group) could easily dope their film and it was easily dope their film and it was thermally stable.thermally stable.

DefinitionsDefinitions

Non-crystalline? Non-crystalline? Amorphous?Amorphous?Glassy?Glassy?Randomness?Randomness?Disorder?Disorder?Liquid?Liquid?Crystalline?Crystalline?

A A perfect crystalperfect crystal is that in which is that in which the atoms are arranged in a pattern the atoms are arranged in a pattern that repeats periodically in three that repeats periodically in three dimensions to an infinite extent.dimensions to an infinite extent.

AnAn imperfect crystal imperfect crystal is that in is that in which the atoms are arranged in a which the atoms are arranged in a pattern that repeats periodically in pattern that repeats periodically in three dimensions to a finite extent.three dimensions to a finite extent.

Real crystal: Real crystal: imperfect crystal imperfect crystal having defects like vacancy, having defects like vacancy, interstitial (foreign) atoms, interstitial (foreign) atoms, dislocations, impurities, etc.dislocations, impurities, etc.

Solid phase? -Liquid phase?Solid phase? -Liquid phase?

How to distinguish between How to distinguish between condensed phase and liquid phase? condensed phase and liquid phase?

How to distinguish between How to distinguish between amorphous amorphous materials and materials and liquidsliquids? ? They have very similar diffraction They have very similar diffraction pattern. No long range order.pattern. No long range order.

Glasses – usually said – are liquid Glasses – usually said – are liquid having the atoms frozen the spatial having the atoms frozen the spatial positions.positions.

Solid to liquid “phase Solid to liquid “phase transition”transition”

A solid is a phase whose A solid is a phase whose shear shear viscosityviscosity exceeds exceeds 101013.613.6 Ns/m Ns/m22..

Example: during a day a force of 100 Example: during a day a force of 100 N applied to 1 cmN applied to 1 cm33 of material having of material having such shear viscosity yields a such shear viscosity yields a deformation of 0.02 mm.deformation of 0.02 mm.

Common liquids at room temperature Common liquids at room temperature are of the order of 10are of the order of 10-3-3 Ns/m Ns/m22..

What is amorphous? What is amorphous? What is glassy?What is glassy?

1.1. Definition: Amorphous Definition: Amorphous materials are in condensed materials are in condensed phase and do not possess the phase and do not possess the long range translational order long range translational order (periodicity) of atomic sites.(periodicity) of atomic sites.

2.2. A glass is an amorphous solid A glass is an amorphous solid which exhibits a glass which exhibits a glass transition (see later).transition (see later).

Atomic Scale OrderingAtomic Scale Ordering

Usually we are speaking about three Usually we are speaking about three different orders (simplest definition):different orders (simplest definition):

Short range orderShort range order means the order means the order within the range of 0-10 within the range of 0-10 ÅÅ (local (local order).order).

Medium range orderMedium range order is the order is the order within the range of 10-100 within the range of 10-100 ÅÅ..

Long range orderLong range order means order over means order over 100 100 ÅÅ. .

Classification of amorphous Classification of amorphous semiconductors.semiconductors.

1. Tetrahedrally bonded amorphous 1. Tetrahedrally bonded amorphous semiconductors: a-Si, a-Ge, a-C(?) and semiconductors: a-Si, a-Ge, a-C(?) and their alloys like a-SiC, etc. (tathogen)their alloys like a-SiC, etc. (tathogen)

2. Chalcogenide glasses: 2. Chalcogenide glasses: aa. a-S, a-Se, . a-S, a-Se, a-Te, a-S a-Te, a-SxxSeSe1-x 1-x (pure chalcogenide) (pure chalcogenide)

bb. a-As. a-As22SeSe33,, a-Asa-As22SS33,, a-Pa-P22SeSe3 3 , etc. , etc. (pnictogen-chalcogen (V-VI))(pnictogen-chalcogen (V-VI))

cc. a-GeSe. a-GeSe22,, a-SiSa-SiS22,, a-SiSea-SiSe2, 2, etc.etc.

(tetragen-chalcogen (IV-VI))(tetragen-chalcogen (IV-VI))

Glass formationGlass formation

Glass forming ability has been Glass forming ability has been discussed by Phillips (1979) in term discussed by Phillips (1979) in term of a constraint model. Most inorganic of a constraint model. Most inorganic covalently bonded glasses have low covalently bonded glasses have low values of atomic coordination values of atomic coordination number. An atom which has all number. An atom which has all covalent bonds satisfied, obeys the covalent bonds satisfied, obeys the (8-N) rule i.e. Se has N(8-N) rule i.e. Se has Ncc=2, Ar has =2, Ar has NNcc=3, Si has N=3, Si has Ncc=4, etc. =4, etc.

For a binary alloy AFor a binary alloy AxxBB1-x1-x, the average , the average coordination (m):coordination (m):

m = x Nm = x Ncc(A) + (1-x) N(A) + (1-x) Ncc(B)(B)

Phillips theoryPhillips theory: the glass-forming : the glass-forming tendency is maximized when the tendency is maximized when the number of constraints is equal to the number of constraints is equal to the number of degrees of freedom, Nnumber of degrees of freedom, Ndd. . (usually N(usually Ndd =3, 3D) =3, 3D)

ConstraintsConstraints::

Bond stretching: m/2Bond stretching: m/2Bond bending: m(m-1)/2, but only Bond bending: m(m-1)/2, but only

(2m–3) are linearly-independent (2m–3) are linearly-independent bond angles. bond angles. NNcc=m/2 + (2m – 3)=m/2 + (2m – 3)

NNd d == NNcc

SolutionSolution: : m = 2.4m = 2.4

(m is the average coordination number (m is the average coordination number per atom)per atom)

If m>2.4, network is overconstrained If m>2.4, network is overconstrained (rigid) materials (a-Si,…) opposite (rigid) materials (a-Si,…) opposite

cases m<2.4 underconstrained cases m<2.4 underconstrained (floppy) materials.(floppy) materials.

ExamplesExamples: :

1. 1. IV-VI systemsIV-VI systems such as g-GeS, g- such as g-GeS, g-GeSe, g-SiS, g-SiTe, etc. IV elements GeSe, g-SiS, g-SiTe, etc. IV elements have 4 neighbours, VI elements have have 4 neighbours, VI elements have 2 neighbours. g-Ge2 neighbours. g-GexxSS(1-x)(1-x)

4x+2(1-x)=2.4 => x=0.24x+2(1-x)=2.4 => x=0.2

g-GeSg-GeS44, g-GeSe, g-GeSe44, g-SiS, g-SiS44, g-SiSe, g-SiSe44, g-SiTe, g-SiTe44

are the optimum composition, are the optimum composition, mechanically most stable. Do not forget mechanically most stable. Do not forget that GeSthat GeS22 is the chemically stable is the chemically stable composition. composition.

2. 2. V-VI systemsV-VI systems such as g-AsS, g-AsTe, etc. such as g-AsS, g-AsTe, etc.

V elements have 3 neighbours. a-AsV elements have 3 neighbours. a-AsxxSS(1-x)(1-x)

3x + 2(1-x) = 2.4 => x=0.43x + 2(1-x) = 2.4 => x=0.4

g-Asg-As22SS33, g-As, g-As22SeSe33, etc. are the optimum , etc. are the optimum composition.composition.

Exception: SiO systemException: SiO systemThorpe (1983)Thorpe (1983)

Si-O-Si bond angle distribution is Si-O-Si bond angle distribution is rather wide! The constraint rather wide! The constraint associated with oxygen bond angles associated with oxygen bond angles should be regarded as rather weak should be regarded as rather weak and should be neglected from and should be neglected from consideration.consideration.

Exception: SiO systemException: SiO systemThorpe (1983)Thorpe (1983)

Let’s consider SiLet’s consider SixxOO(1-x).(1-x). In 3=m/2+(2m– In 3=m/2+(2m–3)3)

equation the (2m–3) term associated equation the (2m–3) term associated with bond angles must be modified.with bond angles must be modified.

No bond angle constraint for in oxigen No bond angle constraint for in oxigen case:case:

x(2mx(2mSiSi-3) + (1-x)0 = x(2*4-3) = 5x ;-3) + (1-x)0 = x(2*4-3) = 5x ;

We must solve the following equations:We must solve the following equations:

3 = m/2 + 5x, where 3 = m/2 + 5x, where

m = 4x + 2(1 –x). => x=1/3.m = 4x + 2(1 –x). => x=1/3.

SiOSiO22

is the good glass-forming is the good glass-forming composition.composition.

Other exceptionsOther exceptions

Some a-Ch materials show other Some a-Ch materials show other property; m = 2.67. The reason is the property; m = 2.67. The reason is the following: the constraint for an atom following: the constraint for an atom is 2D plane is define asis 2D plane is define as

NNcc=m/2 + (m – 1), =m/2 + (m – 1), planar structure.planar structure.

NNd d == NNc c = 3 = 3 seesee:: Keiji Tanaka’s Keiji Tanaka’s (Sapporo, Japan) (Sapporo, Japan)

worksworks

Nanocrystalline? Nanocrystalline? Microcrystalline? Microcrystalline? Polycrystalline?Polycrystalline?

Nanocrystalline siliconNanocrystalline silicon ( (nc-Sinc-Si) ) - an allotropic form of silicon - is - an allotropic form of silicon - is similar to amorphous silicon (a-similar to amorphous silicon (a-Si), in that it has an amorphous Si), in that it has an amorphous phase. Where they differ, phase. Where they differ, however, is that nc-Si has however, is that nc-Si has nmnm sizesize grains of crystalline silicon grains of crystalline silicon within the amorphous phase. within the amorphous phase.

MicrocrystallineMicrocrystalline silicon silicon is is similar containing similar containing µµm m size size grains.grains.

Nanocrystalline silicon is in Nanocrystalline silicon is in contrast to contrast to polycrystalline polycrystalline siliconsilicon (or (or polysilicon,polysilicon, poly- poly-Si; Greek words: Si; Greek words: polyspolys meaning meaning manymany) which ) which consists solely of crystalline consists solely of crystalline silicon grains, silicon grains, separated by separated by grain boundariesgrain boundaries. .

Amorphous semiconductors KUGLER Sándor. S. Kugler: Lectures on Amorphous Semiconductors 2...

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