Книги+1 / 2013 [Chandan_Kumar_Sarkar]_Technology_CAD

108.S.K. Saha, Modeling process variability in scaled CMOS technology, IEEE Design & Test of Computers, vol. 27, no. 2, pp. 8–16, March–April 2010.

109.S.K. Saha, Drain profile engineering for MOSFET devices with channel lengths below 100 nm, in Proc. SPIE Conference on Microelectronic Device Technology, vol. 3881, pp. 195–204, September 1999.

110.M. J. van Dort, P. H. Woerlee, and A. J. Walker, A simple model for quantisation effects in heavily-doped silicon MOSFETs at inversion conditions, Solid-State Electron., vol. 37, no. 3, pp. 411–414, March 1994.

111.TMA MEDICI, Version 1998.4, Avant! Corporation, Fremont, California, 1998.

112.S.K. Saha, Non-linear coupling voltage of split-gate flash memory cells with additional top coupling gate, IET Circuits, Devices & Systems, vol. 6, no. 3, pp. 204–210, May 2012.

113.S.K. Saha, Design considerations for sub-90 nm split-gate Flash memory cells, IEEE Trans. Electron. Devices, vol. 54, no. 11, pp. 3049–3055, November 2007.

114.S.K. Saha, Scaling considerations for sub-90 nm split-gate Flash memory cells, IET Circuits, Devices & Systems, vol. 2, no. 1, pp. 144–150, February 2008.

2.1  Introduction

The invention of the transistor in 1947 started the exponential growth of an industry that is now, some decades later, a several hundred billion dollar industry. The first bipolar transistor was announced in December 1947 by William Shockley, John Bardeen, and Walter Brattain at Bell Labs. The first metal-oxide-semiconductor (MOS) transistor and the first integrated circuits were demonstrated in the early 1960s. From that time on the development in the field of microelectronics was impressive. The integration density grew exponentially. Not only has the integration density been steadily growing, but pressure on the industry to deliver in short time-to-market has also been increasing, leaving minimal research and development times for new technology nodes. This has led to intense efforts in the field of numerical simulation of the semiconductor manufacturing process and the resulting device structure, called technology computer aided design (TCAD). TCAD can reduce the number of test cycles with real semiconductor devices and drastically increase the possibilities to vary process parameters as doping concentrations, device geometries, materials, and their composition to a minimum. Here, TCAD gives the opportunity to analyze the effect of process variation within hours instead of weeks for real processing.

The fundamentals of semiconductors are typically found in textbooks discussing quantum mechanics, electro-magnetics, solid-state physics, and statistical thermodynamics. The purpose of this chapter is to review the physical concepts, which are needed to understand the fundamentals of semiconductor devices. We start from the concepts of energy bands, energy band gaps, and the density of states in an energy band. We then discuss the important concept of effective mass. The analysis of most semiconductor devices requires some knowledge of Gauss’s law and Poisson’s equation, which are explained briefly. We then look at transport in semiconductors through the semi-classical Boltzmann transport equation (BTE). Two carrier transport mechanisms—the drift of carriers in an electric field and the diffusion of carriers due to a carrier density gradient—will be discussed. Recombination mechanisms and the continuity equations are then combined into the diffusion equation. We then present the drift-diffusion model, which combines all the essential elements discussed in this chapter. The rapid developments in semiconductor technology over the past 20 years have caused huge interest

in device modeling. The need to understand the detailed operation of very large scale integrated (VLSI) devices and compound semiconductor devices has meant that device modeling now plays a crucial role in modern technology. The main focus is on the phonon transition or Shockley-Read-Hall mechanism. It is of special interest for modeling the carrier generation and recombination at silicon/dielectric interface traps that are caused by negative bias temperature instability. Mobility modeling is also discussed in brief. The operation and types of the MOSFET (metal-oxide-semiconductor fieldeffect transistor) or MOS transistor are discussed in detail. The steady downscaling of MOS transistor dimensions over the past two decades obeying Moore’s law is discussed along with the short-channel effects in detail.

2.2  Band Formation Theory of Semiconductor

The concept of electronic energy bands provides the basis for the classification of solids as good conductors, insulators, or semiconductors. Quantum physics describes the state of electrons in an atom according to the four-fold scheme of quantum numbers. The quantum number system describes the allowable states the electrons may assume in an atom. Individual electrons may be described by the combination of quantum numbers they possess. Electrons may change their status, given the presence of available spaces for them to fit, and available energy. Because shell level is closely related to the amount of energy that an electron possesses, “leaps” between shell (and even subshell) levels require the transfer of energy. If an electron is to move into a higher-order shell, it requires that an additional energy be given to the electron from an external source. Conversely, an electron “leaping” into a lower shell gives up some of its energy, the expended energy manifesting as heat and sound released upon impact.

Leaps between different shells require a substantial exchange of energy, while leaps between subshells or between orbitals require lesser exchanges. When atoms combine to form substances, the outermost shells, subshells, and orbitals merge, providing a greater number of available energy levels for electrons to assume. When large numbers of atoms exist in close proximity to each other, these available energy levels form a nearly continuous band wherein electrons may transit.

The width of these bands and their proximity to existing electrons determine how mobile those electrons will be when exposed to an electric field. In metallic substances, as in Figure 2.1, empty bands overlap with bands containing electrons, meaning that electrons may move to what would normally be a higherlevel state with little or no additional energy imparted. Thus, the outer electrons are said to be “free,” and ready to move at the beckoning of an electric field [1].

bound, and these electrons are involved in chemical reactions [6]. They determine the chemical and electrical properties of Silicon (i.e., 14 electrons can be distributed in 18 states—two 1s, two 2s, six 2p, two 3s, and six 3p states). If we consider N atoms, there will be 2N, 2N, 6N, 2N, and 6N states of type 1s, 2s, 2p, 3s, and 3p, respectively. Figure 2.5(b) shows the band splitting of the silicon. Because the first two shells are completely filled and tightly bound to the nucleus, we have to consider n = 3 level for valence electron. The 3s states corresponding to n = 3 and l = 0 contain two quantum states per atom. This state will contain two electrons at T = 0 K. The 3p states corresponding to n = 3 and l = 1 contain six quantum states per atom. This state will contain two remaining electrons of the individual Si atom (i.e., the band of ‘3s-3p’ levels contain 8N available states). When the inter-atomic spacing decreases, these energy levels split into bands, beginning with the outer (n = 3) shell. The 3s and 3p bands merge into a single band composed of a mixture of energy levels. At the equilibrium inter-atomic distance, the bands again split, having four quantum states in the lower band and four quantum states in the upper band. At T = 0 K electrons will reside at the lowest energy state, thus the lower band (valence band will be full) and the energy states in the upper band (conduction band) will be empty. The band-gap energy Eg is the width of the energy between the top of the valance band and the bottom of the conduction band.

In other words, for inter-atomic spacing, this band splits into two bands separated by an energy gap Eg. The upper band (the conduction band) contains 4N states, as does the lower band (the valence band). The energy gap contains no allowed energy levels for electrons to occupy, thus it is called forbidden band, Eg. The lower bands (1s, 2s, 2p) are fully occupied. But 4N electrons originally in n = 3 shells (2N in 3s and 2N in 3p states) must occupy states in the valence band or the conduction band in the crystal. At 0 K the electrons will occupy the lowest energy states available to them. In the case of Si crystal, there are exactly 4N states in the valence band available to the 4N electrons. Thus at 0 K every state in the valence band is totally filled, while the conduction band is empty.

2.2.2  Band Structure in Compound Semiconductor

A particularly interesting and useful feature of the III–IV compounds is the ability to vary the mixture of elements. For example, in the ternary compound AlGaAs, it is possible to vary the composition of the ternary alloy by choosing the fraction of Al or Ga atoms. It is common to represent the composition by assigning subscripts to the various elements. For example

AlxGa1–xAs refers to a ternary alloy in which a fraction of X of Al atoms and (1 – X) of Ga atoms are present. X can vary from 0 to 1, thus varying the

optical and electronic properties. The composition Al0.3Ga0.7As has 30% of aluminum and 70% Ga atoms [7]. GaAs is a direct band-gap semiconductor