Dr. Lawrence H. Friedman Profile

Dr. Lawrence H. Friedman

Assistant Professor at Pennsylvania State Univ

SPIE Involvement:

Author

Publications (3)

This will count as one of your downloads.

You will have access to both the presentation and article (if available).

DOWNLOAD NOW

This content is available for download via your institution's subscription. To access this item, please sign in to your personal account.

Email or Username Forgot your username?

Password Forgot your password?

Show

Keep me signed in

No SPIE account? Create an account

Proceedings Article | 14 February 2009 Paper

Surface energy effects on the self-assembly of epitaxial quantum dots

Lawrence Friedman

Proceedings Volume 7224, 722405 (2009) https://doi.org/10.1117/12.809796

KEYWORDS: Crystals, Monte Carlo methods, Silicon, Germanium, Thermal modeling, Quantum dots, Statistical modeling, Error analysis, Mechanics, Chemical analysis

Read Abstract +

Epitaxial self-assembled quantum dots (SAQDs) result from Stranski-Krastanow growth whereby epitaxial 3D islands form spontaneously on a planar thin film. Common systems are Ge_xSi_1-x/Si and In_xGa_1-xAs/GaAs. SAQDs are typically grown on a (001) surface. The formation and evolution of SAQDs is governed in large part by the interaction of surface energy and elastic strain; however, the surface energy density is quite complicated and not well understood. Many growth processes take place at high temperature where stress and entropy effects can have a profound effect on the surface free energy. There are three competing theories of the nature of the planar (001) surface: I. It is a stable crystal facet. II. It is a stable non-faceted surface. III. It is an unstable crystal antifacet. Each leads to a different theory of the SAQD formation process. The first theory appears most often in modeling literature, but the second two theories take explicit account of the discrete nature of a crystal surface. Existing observational and theoretical evidence in support of and against these theories is reviewed. Then a simple statistical mechanics model is presented that yields a phase-diagram depicting when each of the three theories is valid. Finally, the Solid-on-Solid model of crystal surfaces is used to validate the proposed phase diagram and to calculate the orientation and height dependence of the surface free energy that is expressed as a wetting chemical potential, a wetting modulus and surface tilt moduli.

Proceedings Article | 10 September 2008 Paper

Stochastic continuum modeling self-assembled epitaxial quantum dot formation

Lawrence Friedman

Proceedings Volume 7041, 704103 (2008) https://doi.org/10.1117/12.795615

KEYWORDS: Stochastic processes, Diffusion, Anisotropy, Video, Quantum dots, Thermal modeling, Computer simulations, Crystals, 3D modeling, Germanium

Read Abstract +

Semiconductor epitaxial self-assembled quantum dots (SAQDs) have potential for electronic and optoelectronic applications such as high density logic, quantum computing architectures, laser diodes, and other optoelectronic devices. SAQDs form during heteroepitaxy of lattice-mismatched films where surface diffusion is driven by an interplay of strain energy and surface energy. Common systems are Ge_xSi_1-x/Si and In_xGa_1-xAs/GaAs. SAQDs are typically grown on a (001) crystal surface. Self-assembled nanostructures form due to both random and deterministic effects. As a consequence, order and controllability of SAQD formation is a technological challenge. Theoretical and numerical models of SAQD formation can contribute both fundamental understanding and become quantitative design tools for improved SAQD fabrication if they can accurately capture the competition between deterministic and random effects. In this research, a stochastic model of SAQD formation is presented. This model adapts previous surface diffusion models to include thermal fluctuations in surface diffusion, randomness in material deposition and the effects of anisotropic elasticity, anisotropic surface energy and anisotropic diffusion, all of which are needed to model average SAQD morphology and order. This model is applied to Ge/Si SAQDs which are group IV semiconductor dots and InAs/GaAs SAQDs which are III-V semiconductor dots.

SPIE Journal Paper | 1 June 2007

Order of Epitaxial Self-Assembled Quantum Dots: Linear Analysis

Lawrence Friedman

JNP, Vol. 1, Issue 01, 013513, (June 2007) https://doi.org/10.1117/12.10.1117/1.2753144

KEYWORDS: Correlation function, Diffusion, Anisotropy, Stochastic processes, Fourier transforms, Quantum dots, Silicon, Statistical analysis, Germanium, 3D modeling

Read Abstract +

Abstract Epitaxial self-assembled quantum dots (SAQDs) are of interest for nanostructured optoelectronic and electronic devices such as lasers, photodetectors and nanoscale logic. Spatial order and size order of SAQDs are important to the development of usable devices. It is likely that these two types of order are strongly linked; thus, a study of spatial order will also have strong implications for size order. Here a study of spatial order is undertaken using a linear analysis of a commonly used model of SAQD formation based on surface diffusion. Analytic formulas for film-height correlation functions are found that characterize quantum dot spatial order and corresponding correlation lengths that quantify order. Initial atomic-scale random fluctuations result in relatively small correlation lengths (about two dots) when the effect of a wetting potential is negligible; however, the correlation lengths diverge when SAQDs are allowed to form at a near-critical film height. The present work reinforces previous findings about anisotropy and SAQD order and presents as explicit and transparent mechanism for ordering with corresponding analytic equations. In addition, SAQD formation is by its nature a stochastic process, and various mathematical aspects regarding statistical analysis of SAQD formation and order are presented.

My Library

You currently do not have any folders to save your paper to! Create a new folder below.

Folder Name

Folder Description

View contact details

UPDATE YOUR PROFILE

Is this your profile? Update it now.

Sign into your SPIE.org account

Don’t have a profile and want one?

Create an account on SPIE.org

Access to the requested content is limited to institutions that have purchased or subscribe to SPIE eBooks. You are receiving this notice because your organization may not have SPIE eBooks access.*

*Shibboleth/Open Athens users─please sign in to access your institution's subscriptions.

To obtain this item, you may purchase the complete book in print or electronic format on SPIE.org.

ORGANIZATIONAL
Sign in with credentials provided by your organization.

Organizational Username

Organizational Password

Show/Hide Password

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available

Members:

Non-members: ADD TO CART

Keywords/Phrases

Search In:

Publication Years