anisotropic etching contents - fritz haber institute of the max...

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Case: anisotropic wet etching

Risto Nieminen

COMP/Engineering Physics, Helsinki University of Technology

Simulation of the evolution of complex surfaces:from atoms to devices

Modern Concepts for Creating and Analysing Surfaces and Nanoscale MaterialsSant Feliu de Guixols, 12-16 May, 2008

Acknowledgments

• Di Cheng, Yan Xing, Prem Pal, Kazuo Sato, Makio Uwaha (Nagoya University, Japan)

• Adam Foster,Teemu Hynninen, Petteri Kilpinen, Eero Haimi, Veikko Lindroos (Helsinki Univ. Tech., Finland)

• Duy Nguyen, Miko Elwenspoek (Univ. Twente, Holland)

• Coventor Inc. (US), IntelliSense Ltd. (Japan)

Dr. Miguel A. Gosalvez

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Anisotropic etching

• Atomististic simulation of etching

๏ Crystallography and data storage

๏ Physical models for the process rates

๏ KMC and CA methods for the time evolution

• Remaining challenges (implementation & physics)

Contents

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Goals and achievements• Surface morphology of (110)

๏ Zigzags structures

๏ Trapezoidal hillocks

๏ Relation to (100)

• Role of metal impurities

• Role of etchant cations

• Role of surfactants

• Activation energy

bunching no bunching •Treat interface as a collection of atoms

•Fundamental assumption: each atom removal occurs with a different rate, depending on the neighborhood

•There are four important aspects for the realization of successful atomistic simulations of etching:

๏ Crystallography

๏ Data storage

๏ Process rates

๏ Time evolution

Atomistic simulations

1. Crystallography 2. Process rates 3. Time evolution2. Data storage

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๏ Lattice

๏ Unit cell

๏ Basis

๏ Rotation to get {hkl} substrate

๏๏ Orthorhombic unit cellsOrthorhombic unit cells

๏ Atom coordinates (n1,n2,n3,m)

๏ Change unit cell for different materials

Crystalline structure

small {755} crystal{100}{hkl} plane

basis

{755} unit cell


unit celllattice

๏ Needed because rates depend on neighborhood

๏ Only necessary for the atoms in the basis

๏ Finding neighbors limited to reading from this list

List of first neighbors

(n1,n2,n3,1)→(0,0,0,2)(-1,-1,0,4)(0,-1,-1,6)(-1,0,-1,8)

(n1,n2,n3,2)→(0,0,0,1)(0,0,0,3)(0,0,0,5)(0,0,0,7)

(n1,n2,n3,3)→

(n1,n2,n3,8)→�

��

List of neighbors

๏ Essential for periodic boundary conditions

Similar for any orthorhombic unit cell

If n1 or n2 are out of range, cycle them at opposite end

↓


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๏ 3D array: lots of empty regions (bulk and etchant)

๏ Octree: Storage where needed, gradual refinement of grid

• Use less memory!

Data storage


To hold 8 points (cyan):41 vs 4096 (=32x32x32)


0 2 4 6 8 10

x 106

0

0.5

1

1.5

2

2.5

3x 10

5 Comparision of Memory Space

Atom Removals

Mem

ory

Spa

ce (K

byt

es)

Dynamicway

Octree withmask

Octree only

0 2 4 6 8 10

x 106

0

0.5

1

1.5

2

2.5

3x 10

5 Comparision of Memory Space

Atom Removals

Mem

ory

Spa

ce (K

byt

es)

Dynamicway

Octree withmask

Octree only

80% less memory

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• Octree’s additional benefits:

๏ Organized data structure

๏ Fast addressability

• Calculation of storage path is possible

• Fast searching inside it

๏ Flexible visualization

๏ Usable in KMC and CA

Data storage


3D

2D

Orthogonal list:smallest memory

but slow addressability

• Removal rates depend on the state of the neighborhood

๏ p(n1,n2) = Removal Probability Function

๏ p(n1,n2d,n2i) or p(n1s,n1b,n2s,n2b) = Removal Probability Table

• Manual fitting by comparison to experiment (KMC), based on

• morphology

• etched profile

• Semi-automatic fit (CCA)

Physical models for the process rates


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• More complex models using ab-initio:

๏ back-bond weakening, steric interaction between H/OH

• E = Ebonds+ETAH/OH+EFNH/OH

• p(n1,n2) = p0e-(E-Et)/KT

๏ Etchant / Temperature gradients• p depends on step density• peff(n1,n2) = p(n1,n2) (1+aρ)• Step bunching - zigzags on (110)๏ Si etching + Cu ads/des• p depends on adsorbed Cu


Physical models for the process rates

Time-dependent process rates

I. Anisotropy of etching: Back-bond weakening by OH and steric interactions (OH-OH and OH-H)

II. Surface morphology: Adsorption of metal impurities as micro-masks (Cu,Pb,...)

How has ab-initio contributed to the understanding of wet etching?

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(I) Chemistry / Electrochemistry• Electrochemistry involved (currents measured when applying potentials)• Etching is a sequential process alternating oxidation and etching• Two oxidation routes: chemical and electrochemical• (Different OH replacement of H-termination)• Oxidation is rate limiting (explains H-termination in experiments)• After OH-termination, fast etching due to OH weakening of backbonds

•Backbondweakeningstudied with

first principles

•Different OH terminations

•ADF•Gradient corrected BLYP functional•Slater-type basis functions•Si-H, Si-OH and Si-O vibr. freq.s agreed with exp

Removal rates depend on termination stateDozens of situations for each site typeSituation changes with time

Ab-initio:

Step dihydrideH terminationPartial OH termination

Full OH termination

Steric interaction: OH-OH Multiple steric interactions: OH-H

• Backbond weakening:

•Also: Steric interactions between terminating species

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Backbond weakening + Steric interactions

backbond weakening

backbond weakening

stericinteractions+

experiment simulations

using SIESTA(A. Foster, T. Hynninen)

(II) Adsorption of metal impurities (Cu, Mg, Pb,...)

Trapezoidal hillocksTrapezoidal hillocks

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• Adsorbs strongly on H-Si and OH-Si

• Adsorption energy depends on local bonding

• (selective adsorption)• Sites with many H’s are

preferred• (dihydrides, kinks)• OH increases

adsorption, decreasing energy spread across sites

• Strong interaction with O makes adsorption more homogeneous

(II) Adsorption of metal impurities: Cu

•Project the Hs and OHs on slightly tilted horizontal plane•Triangulate the resulting 2D point cloud (Delaunay)•Identify each triangle with a Cu adsorption site

• Interaction Enhanced Adsorption (IEA)• Height Enhanced Adsorption (HEA)• Activity Enhanced Adsorption (AEA)

•Hybrid KMC (KLS for Si etching and Cu adsorption/desorption)•First consistent description of the trapezoidal hillocks

(II) Adsorption of metal impurities: Cu

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Conclusions

•Anisotropic etching can be simulated realisticallySurface morphologyEngineering applications

•Ab-initio has clarifiedBack-bond weakeningSteric interactions (OH-OH, OH-H)Adsorption of Cu

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• Kinetic Monte Carlo (KMC)

๏ Monte Carlo (MC) = use of random numbers (stochastic evolution)

๏ Kinetic MC = time is faithfully measured

•non-equilibrium, transients, steady-state

๏ Thermodynamic MC = time is irrelevant

•equilibrium properties / averages

• Cellular Automata (CA)

๏ Deterministic evolution

๏ Time is faithfully measured

• KMC is sequential (never simultaneous processes)

• CA is parallel (many processes simultaneously)

Time evolution


Time evolution


• Atoms are visited one by one• Neighborhood is inspected• Removal rate (or probability) is determined• Decide if atom is removed or remains attached• CA:CA:First pass determines which atoms will be removedSecond pass removes them simultaneously.Two loops to complete a time stepProvides a mean-field like evolution (parallel)• KMC:KMC:Atom is removed as soon as removal is decidedOnly one loop (faster method)Generates purely atomistic propagation (sequential)

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• KMC methods:๏ Constant Time Stepping (CTS):• Metropolis acceptance / rejection๏ Variable Time Stepping (VTS):

• BKL (Bortz-Kalos-Lebowitz) and • KLS (K-Level Search, including: binning, LS, BS, QS,OS,...)

• Completely sequential๏ Simulations can be very fast (5-10μs/event)

๏ Best for surface morphologies๏ Less suitable for engineering applications๏ Difficult to parallelize


Time evolution: KMCConstant Time Step (CTS) vs Variable Time Step (VTS)

• Etching is essentially astep flow process

• Due to stability of (111)• Active steps, inert terraces

Time evolution: KMC


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VTS

Choose process randomly according to reaction ratesAlways accept∆t = 1/R (var.)

CTS

Choose process randomly according to surface fractionsChoose random number eAccept if e ≤ r∆t = 1/N (cons.)

Time evolution: KMC


Time evolution: KMC


Alternative VTS method:BKL (Bortz, Kalos, Lebowitz)

random pick-up

linear search

random numberrandom number

The processes are grouped according to their rates (M different values). Identical processes are listed as many times as they are present. The order of appearance inside a group is irrelevant.

O(M) i.e. independent of N

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Summary: Constant Time Step (CTS) vs Variable Time Step (VTS)

Time evolution: KMC


• VTS requires book keeping, CTS does not.

• VTS: BKL useful only for systems with a few distinct rates

KLS valid for many different rates, also time-dependent

• if the interface is dominated by slow processes:

๏ CTS rejects the processes most of the time (slow simul)

๏ VTS is orders of magnitude faster, especially when using a tree search method

• if the interface is dominated by fast processes:

๏ CTS is fastest and easiest

Large

Low

Large

Large

Large

Medium

Very large

O(KN1/K)

O(N)

O(2log2N)

O(4log4N)

O(8log8N)

O(2log2N1/2)

O(M)

K-level search

Linear

Binary

Quadtree

Octree

Maksym

M-fold grouping

KLS

LS

BS

QS

OS

Binning

BKL

VTS

NoneO(N)Ac c e p t / r e je c tMetropolisCTS

BookkeepingComputationcost

MethodAcronymType

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• Cellular Automata (CA) methods:

๏ Basic CA (BCA)

๏ Continuous CA (CCA):

‣ Exact Time Stepping

‣ Approximate Time Stepping

• Constant Time Step (CTS)

• Standard Time Compensation (STC)

• Backward Time Compensation (BTC)

• Completely parallel

๏ Simulations are slower than using KMC (50 μs/event)

๏ Best for engineering applications

๏ Less suitable for surface morphologies

๏ Trivial parallelization

Time evolution: CA


Basic CA


• Atom is removed if it has:• Two neighbors, i.e. (100), or• Three neighbors, with at least one in the etch front, i.e. (110)• Atom is not removed if it has three bulk neighbors, i.e. (111)• Other atoms are removed.

• Combine these rules with experimentally measured etch rate for (100). Etch rate anisotropy is purely a geometrical effect.

micro-needles

suspended micro-channels

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(755)

R(755) = f(hM,hL(M), rMR-T,rLR-T,rT,rETM,rL(M),rM)

R(755) = f(hETM,hL(ETM), rLR-T,rMR-T,rT,rETM,rL(ETM),rLR-

M)

if rM > rETM

if rETM > rM

Propagation of a crystallographic plane is described as a gradual removal of the atomsCCA

KMC

CCAeach plane

Continuous CA

NextPrevious

Time Stepping in CCAExact Time Stepping = Variable Time Stepping

๏ First loop over surface:• Determine minimum ∆t to remove an atom (or a group with the same ∆t) ๏ Second loop:• Remove only those atoms with this minimum value


Approximate Time Stepping = Constant Time Stepping• First loop over surface:

Determine atoms that need to be removed• Second loop:

Remove only those atoms simultaneously

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Time Stepping in CCA


CCA vs Experiment

exp, 34 wt% KOHsim, 30 wt% KOHsim, 40 wt% KOH

sim, 30 wt% KOHSi(110) wafer

etched hemispehere

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VisualTAPAS - Main technologies

I. Octree data representation (less memory, faster KMC)II. K-Level Search (KLS) for fast Kinetic Monte Carlo (KMC)

simulations (fine-tuned as Octree Search)III. Novel Continuous Cellular Automaton (CCA) simulations using

exact equations for calibrationIV. User-oriented interface providing complex functionalitiesV. Strong links to Density Functional Theory (DFT)

http://www.fyslab.hut.fi/~mag/VisualTAPAS/Home.html

approx. time stepping(std time

compensation)

ExperimentExperiment

fitted + tuned

fitted + tuned

30-35 wt% KOH70-80 deg C

fitted

fitted + tuned

exact

JMM 10 (2001) 88-97

CCA vs Experiment

Simulation

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30-35 wt% KOH70-80 deg C

Simulation

Experiment

fitted + tuned (std time compensation)

CCA vs Experiment CCA vs Experiment

JMM 10 (2001) 88-97Experiment

Simulationfitted + tuned (std time compensation)

30-35 wt% KOH 70-80 deg C

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Animations

Added value for teaching, understanding and developing new processes

Future features in VisualTAPAS

•More concentrations, more temperatures•Activation energies for atom removal rates•Etching other materials (quartz, GaAs,...)•More realistic Deep Reactive Ion Etching (DRIE)•Implementation of growth simulations•Visualization with cross-sections / cuts•A generic KMC / CCA solver?

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On-going and remaining issues• Understanding of Pb as an etchant impurity (ab-initio + KMC)• [Affects etch rate but not the morphology]• Atomistic understanding of the surfactants’ effects (ab-initio?)• [More experiments needed]• ALD growth (3D, conformal, inverse problem to etching)

Surfactants: long molecules, head (hydrophobic), tail (hydrophilic)

Impurity cages

Site-specific adsorption of head; probably at step kinks

hydration shells around tails may locally change the concentration of the etchant

References

M. A. Gosalvez et al.

J. Micromech.Microeng. 18, 055029 (2008) (review); 17, S1 (200); 17, S27 (2007)

New J. Phys. 5, 100 (2003); 8, 1 (2006); 10, 013033 (2008)

Appl. Surf.Sci. 178, 7 (2001); 202, 160 (2002)

Phys. Rev. B 76, 075315 (2007)

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Thank you for your attention!

anisotropic etching contents - fritz haber institute of the max...

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