Charge and Energy Interactions between Nanoparticles and Low Pressure Plasmas A DISSERTATION SUBMITTED TO THE FACULTY OF THE GRADUATE SCHOOL OF THE UNIVERSITY OF MINNESOTA BY Federico Galli IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY Prof. Uwe R. Kortshagen, Adviser May 2010 © Federico Galli May 2010 Acknowledgments I would like to thank my adviser, Professor Uwe Kortshagen, for his guidance and mentoring during the years of my graduate career. To my colleagues and friends in the HTPL group and at the University of Minnesota: thank you for five years of intellectual and personal enrichment. To all the friends and people that I had the opportunity to meet here in Minnesota: you made me feel like at home. Last but first in my heart: thank you family, for everything. i Abstract In this work, the interactions between low-pressure plasmas and nanoparticles are studied with numerical models aimed at understanding the phenomena that affect the nanoparticles charge, charge distribution, heating, and crystallization dinamycs. At the same time other phenomena that affect the plasma properties resulting from the presence of nanoparticles are also studied: they include the power-coupling to the plasmas, the ion energy distribution and the electron energy distribution. An analytical model predicting the nano-particle charge and temperature distribu- tions in a low pressure plasma is developed. The model includes the effect of collisions between ions and neutrals in proximity of the particles. In agreement with experi- mental evidence for pressures of a few Torr a charge distribution that is less negative than the prediction from the collisionless orbital motion limited theory is obtained. Under similar plasma conditions an enhanced ion current to the particle is found. Ion-electron recombination at the particle surface, together with other particle heat- ing and cooling mechanisms typical of silane-argon plasmas, is included in a particle heating model which predicts the nano-particle temperature. The effect of plasma parameters on the nano-particle temperature distribution is discussed and the predic- tive power of the model is demonstrated against experimental evidence of temperature induced crystallization of silicon nano-particles. The power coupled to the plasma is measured together with the impedance nature ii of the plasma, in the case of a pristine and dusty plasma. Nanoparticles are shown to strongly affect the electrical properties of the plasma, resulting in a much more resistive discharge. A study of the ion energy distribution of ions impinging the sruface of nanoparticles is carried out and shows that ion-neutral collisions in proximity of the surface of the nanoparticle not only affects the particle charge but also the average energy of ions bombarding the particle surface. Finally the presence of nanaparticle in the plasma and their ability to selectively in- teract with electrons in a specific energy range is studied to the extent of investigating the effects of the presence of particles on the electron energy distribution of electrons. iii Contents Acknowledgments................................ i Abstract..................................... ii ListofFigures.................................. vii ListofTables .................................. xiii Chapter 1 Introduction 1 1.1 Plasma................................... 1 1.2 DustyPlasmas .............................. 3 1.3 Plasma synthesis of nanoparticles . .. 4 1.4 Application of plasma-produced nanocrystals . ...... 6 1.5 Motivation................................. 9 1.6 Structureofthethesis .......................... 10 Chapter 2 Background 12 2.1 Backgroundonparticlecharging. 12 2.2 Particle Charging accounting for ion-neutral charge-exchange and mo- mentumtransfercollisions . 18 2.2.1 Electronchargingfrequency . 18 2.2.2 Ionchargingfrequency . 19 iv 2.2.3 Chargingmodelsolution . 23 2.3 Background on Power Measurements . 23 2.4 Background on Ion Energy Distributions . .. 25 2.5 Background on Electron Energy Distributions . .... 26 Chapter 3 Charging, heating, and coagulation plasma model 28 3.1 Introduction................................ 28 3.2 Model ................................... 30 3.2.1 Charging.............................. 30 3.2.2 Chargedistribution. 34 3.2.3 Otherresultsofthechargingmodel . 37 3.2.4 Coagulation ............................ 39 3.2.5 Particle heating in a low-pressure argon-silane plasma..... 45 3.2.5.1 Ion-electron recombination on the particle . 49 3.2.5.2 Atomic hydrogen interactions with the particle . 50 3.2.5.3 H diffusion frequency on H-terminated surface . 51 3.2.5.4 H-H recombination on H-terminated surface . 52 3.2.5.5 H-coveragebalance . 52 3.3 ResultsandDiscussion .......................... 53 3.4 Conclusion................................. 58 Chapter 4 Particle Crystallization 59 4.1 Introduction................................ 59 4.2 Two-stepscrystallization . 59 4.3 Squarewavemodulatedplasma . 62 v 4.3.1 Experimentdetails . .. .. 64 4.3.2 Discussion............................. 64 4.4 Conclusions ................................ 65 Chapter 5 The energy distribution function of ions impinging on nanoparticles in a collisional low-pressure plasma 69 5.1 Introduction................................ 69 5.2 Background ................................ 70 5.3 Descriptionofthesimulation. 74 5.4 Results................................... 78 5.5 Conclusions ................................ 86 Chapter 6 Power Measurement 87 6.1 Introduction................................ 87 6.2 Experimentalapparatus . 89 6.3 Equivalent electric circuit and model . ... 91 6.4 Results................................... 94 6.4.1 Powermeasurement. 96 6.4.2 Voltageamplitude ........................ 96 6.4.3 Currentamplitude ........................ 96 6.4.4 Impedance amplitude and phase . 102 6.5 Conclusions ................................ 106 Chapter 7 Self-consistent model for particle charging and evolution of EEDF in a nano-dusty plasma 108 7.1 Introduction................................ 109 vi 7.2 NumericalModel ............................. 111 7.3 NumericalResults............................. 116 7.3.1 Effect of nanoparticles on EEDF in argon low-pressure plasmas 116 7.3.2 Effect of nanoparticles concentration . 116 7.3.3 Effect of neutral pressure on the EEDF of nanoparticles .... 118 7.3.4 EffectofparticlesizeontheEEDF . 119 7.3.5 Self-consistent effect of nanoparticle density . ..... 124 7.4 Conclusions ................................ 129 Chapter 8 Conclusion 130 8.1 Conclusions ................................ 130 Bibliography .................................. 132 vii List of Figures 1.1 “Plasma lamp, illustrating some of the more complex phenomena of a plasma, including filamentation. The colors are a result of relax- ation of electrons in excited states to lower energy states after they have recombined with ions. These processes emit light in a spectrum characteristic of the gas being excited.” (Source: Wikipedia [1]) . 3 1.2 Silicon nanocrystals formed in a non-thermal flow-through plasma re- actorwitharesidencetimeof6ms. [2] . 6 1.3 Silicon nanoparticles can exhibit wavelength-tunable optical lumines- cence as a function of their size and can often be fabricated with narrow linewidths [3]. The luminescence is available only when the nanoparti- cle are crystalline. Crystallization in the plasma is a direct indication that particle experience intense heating mechanism while in the low- pressureplasmas. ............................. 9 3.1 Crystallization temperature dependence on the size of Si nanoparticles synthesized by pulsed laser ablation was studied using Raman scat- tering spectroscopy. The crystallization temperature values for 10, 8, 6 and 4 nm particles were 1273, 1173, 1073, and 773 K, while bulk meltingtemperatureis1683K. 30 3.2 Probability of an ion to undergo none, one or many collisions within the capture radius, defined as in the insert. 31 3.3 Charge carried by a 40 nm diameter particle against pressure in an Argon plasma, T = 400 K, n = 1 1016 m−3, n = 1 1014 m−3; i i × p × Te = 3 eV when not self-consistently evaluated. 33 viii 3.4 Charge carried by a 1 µm diameter particle against pressure in an Argon plasma, T = 300 K, n = 1 1016 m−3, n = 1 1014 m−3; i i × p × Te = 3 eV when not self-consistently evaluated. 34 3.5 Charge distribution against pressure, Argon plasma, Te = 3 eV, Ti = 300 K, n = n = 1 1016 m−3, R =20nm ............ 36 e i × p 3.6 Particle charge distribution for a 10 nm diameter particle, in an Argon plasma, T = 400 K, n = 1 1016 m−3, n = 1 1014 m−3,p=1 i i × p × Torr; Te = 3 eV when not self-consistently evaluated. 37 3.7 Particle charge distribution for a 40 nm diameter particle, in an Argon plasma, T = 400 K, n = 1 1016 m−3, n = 1 1014 m−3,p=1 i i × p × Torr; Te = 3 eV when not self-consistently evaluated. 38 3.8 Particle charge distribution for a 1 µm diameter particle, in an Argon plasma, T = 400 K, n = 1 1016 m−3, n = 1 1014 m−3,p=1 i i × p × Torr; Te = 3 eV when not self-consistently evaluated. 39 3.9 Charge against particle diameter for model and OML, Argon plasma, T = 3 eV, T = 300 K, n = n = 1 1016 m−3,p=1Torr.... 40 e i e i × 3.10 Charge against electron temperature for model and OML, Argon plasma, T = 300 K, n = n = 1 1016 m−3, p = 1 Torr, R =20nm. .. 41 i e i × p 3.11 Charge against ion temperature for model and OML, Argon plasma, T = 3 eV, n = n = 1 1016 m−3, p = 1 Torr, R =20nm. ... 42 e e i × p 3.12 Particle size distribution generated from coagulation of 1 1015m−3, × monodisperse (1 nm diameter) particle source in Argon plasma, Te = 3eV , T = 400K, n =1 1015m−3 in 100 s, with the method in [4]. 44 i i × 3.13 Parametric study of the effects of ion density and hydrogen radical density on the temperature of a 10 nm particle (diameter) in argon plasma, Te= 3 eV, room temperature (300 K) at 200 Pa of pressure. (n =1 1015 1 1015m−3 and n =1 1013 1 1021m−3)... 54 i × − × H × − × 3.14 Parametric study of the effects of ion density and hydrogen radical density on the hydrogen coverage of a 10 nm particle (diameter) in argon plasma, Te= 3 eV, room temperature (300 K) at 200 Pa of pressure. (n =1 1015 1 1015m−3 and n =1 1013 1 1021m−3) 55 i × − × H × − × ix 3.15 Temperature vs.