Chapter 1
Thermodynamics of Homogeneous and Heterogeneous Semiconductor Systems

1.1 Introduction

Elemental and compound semiconductors represent a vast family of materials of strategic interest for a variety of mature and advanced applications in micro- and opto-electronics, solid state lighting (SSL), solid state physical and chemical sensors, high efficiency solar cells and nanodevices. The materials themselves have always been technology enablers and their role today is even more significant in view of the increasing demand for sustainable development applications and high temperature, high pressure technologies.

The semiconductors family includes elemental solids such as silicon, the material of choice for the microelectronic and photovoltaic industry, binary alloys such as the Si-Ge alloys used for their elevated carrier mobilities, and compound semiconductors, of which SiC is used for high power, high frequency devices and phosphides, arsenides and nitrides for the most advanced optoelectronic applications.

Their preparation under defined limits of stoichiometry (in the case of compounds) and purity requires a deep knowledge of the chemistry and physics of liquid-, solid-, vapour- and plasma-growth and post-growth processes.

Semiconductors, like other inorganic and organic solids, may be stable in different structural configurations, depending on the composition, temperature, hydrostatic pressure and strain. Their chemical, physical and mechanical properties under different environmental conditions (temperature, pressure, strain) depend on their elemental composition, stoichiometry, impurity contamination, and also on their point- and extended-defects content. In fact, although solids are a typical class of materials characterized by microscopic order, most of their electronic and optoelectronic properties depend on or are influenced by impurities and point and extended defects.

Knowledge of their macroscopic features, such as their structural, thermodynamic, chemical, electrical and mechanical properties over a broad range of temperatures and pressures, is critical for their practical use. These properties, when not already available, should be experimentally or computationally determined.

This objective, addressed at metals, metal alloys and non-metallic solids, has been in the last few decades the traditional goal of physical metallurgy and physical chemistry. It is also the subject of several excellent textbooks and monographs [1-4], where emphasis is mainly given to structure-property relationships, solution- and defect-theories and nonstoichiometry of non-metallic solids [5], devoting, until very recently [6], only limited attention to elemental and compound semiconductors.

The aim of this chapter, and of the entire book, is to fill this gap and present in the most concise and critical manner possible the application of thermodynamics and physical chemistry to elemental and compound semiconductors, assuming knowledge of the fundamental laws of thermodynamics [7] and the basic principles of solid state and semiconductor physics [8, 9].

The intent is also to show that physical chemistry applied to semiconductors has been, and still is, of unique value for the practical and theoretical understanding of their environmental compliance and for the optimization of their growth and post-growth processes, all having a strong impact on the final properties of the material.

As impurities have a significant role in the optical and electronic properties of semiconductors, their thermodynamic behaviour will be considered in terms of their solubility and distribution among neighbouring phases as well as in terms of formation of complex species with other impurities and point defects.

For elemental semiconductors the main interest will be devoted to Group IV and VI elements (carbon, germanium, silicon, selenium and tellurium), the first of which being characterized by a number of stable phases, some of these of extreme scientific and technological interest, as is the case for diamond and graphene. For compound semiconductors we will consider the II-VI and the III-V compounds, such as the arsenides, phosphides, selenides, sulfides, tellurides and nitrides, all of which are of crucial interest for optoelectronic applications, SSL and radiation detection.

The most up to date physical and structural data of the different systems will be used: the reader interested in thermodynamic databases and phase diagram computation is referred to the Scientific Group Thermodata Europe (SGTE) Solution database, NSM Archive, www.ioffe.rssi.ru/SVA/NSM/Semicond/ and to Gibbs [10].

1.2 Basic Principles

A semiconductor is a thermodynamic system for which one has to define the equilibrium state and the nature of the transformations which occur when it is subjected to external thermal, mechanical, chemical, magnetic or electromagnetic forces during its preparation and further processing.

This system may consist of a homogeneous elemental or multicomponent phase or a heterogeneous mixture of several phases, depending on the temperature, pressure and composition.

A phase is conventionally defined as a portion of matter, having the property of being chemically and physically homogeneous at the microscopic level and of being confined within a surface which embeds it entirely.

The surface itself may be an external surface if it separates a phase from vacuum or from a gaseous environment. It is an internal surface, or an interface, when it separates a phase from another identical or different phase. According to Gibbs, the surface itself may be considered a phase of reduced (2D) dimensionality.

When one is concerned with microscopic or nanoscopic phases, such as nanodots, nanowires and nanotubes, the surface area to volume ratio, increases considerably, as does the ratio of the number of atoms at the surface to those in the bulk (see Table 1.1), with reduction in size of the crystallite phase. This has a significant impact on the physical and chemical properties of the phase itself and of its surface, enhancing in particular its chemical reactivity, but also other properties of relevant importance in semiconductor physics, such as the distribution and electrical activity of dopant impurities.

Table 1.1 Cell size dependence of the surface to volume ratio (As/V) and of the ratio R of atoms sitting at the surface vs those sitting in the volume, for a cubic crystal having an atomic density of 1021 cm-3

For Ge and Si the actual values of atomic densities are and .

A phase may be gaseous, liquid or solid. In extreme conditions it could be stable in a plasma configuration, consisting of a mixture of electrons and ionized atoms/molecules. A phase is condensed when its aggregation state is that of a liquid or a solid material.

The thermodynamic state of a system is defined by specifying the minimum set of measurable properties needed for all the remaining properties to be fully determined. Properties which do not depend on mass (e.g. ) are called intensive. Those depending on mass (i.e. on composition) are called extensive.

A critical thermodynamic state of a system is its equilibrium state. It represents the condition where the system sits in a state of minimum energy and there are no spontaneous changes in any of its properties.

For a system consisting of a single, homogeneous multicomponent phase it is possible to define its thermodynamic state using thermodynamic functions (e.g. the internal energy , the Helmholtz free energy , the Gibbs free energy , the entropy and the chemical potential ), whose values depend on macroscopic parameters, such as the hydrostatic pressure , the absolute temperature and the composition, this last given conventionally in terms of the atomic fraction of the components , being the number of atoms of .

A system is said to be in mechanical equilibrium when there are no unbalanced mechanical forces within the system and between the system and its surrounding. The system is also said to be in mechanical equilibrium when the pressure throughout the system and between the system and the environment is the same. This condition is typical of the liquid state but not of the solid state unless internal mechanical stresses are fully relaxed.

Two systems are said to be in mechanical equilibrium with each other when their pressures are the same.

A system is said to be in chemical equilibrium when there are no chemical reactions going on within the system or they are fully balanced, such that there is no transfer of matter from one part of the system to another due to a composition gradient. Two systems are said to be in chemical equilibrium with each other when the chemical potentials of their components are the same. A definition of the chemical potential will be given below.

When the temperature of the system...