1. Norhayati Soin 06 KEEE 4426 WEEK 3/1 9/01/2006 KEEE 4426 VLSI WEEK 3 CHAPTER 1 MOS Capacitors (PART 1) CHAPTER 1

2. Norhayati Soin 06 KEEE 4426 WEEK 3/1 9/01/2006 CONTENTS 1.1Introduction 1.2Structure and principle of operation 1.2.1Flatband diagram 1.2.2Accumulation 1.2.3Depletion 1.2.4Inversion 1.3MOS analysis 1.3.1Flatband voltage calculation 1.3.2Inversion layer charge 1.3.3Full depletion analysis 1.3.4MOS capacitance Part 1 Part 2

3. Norhayati Soin 06 KEEE 4426 WEEK 3/1 9/01/2006 1.1 INTRODUCTION The primary reason to study the Metal-Oxide-Silicon (MOS) capacitor is to understand the principle of operation as well as the detailed analysis of the Metal- Oxide-Silicon Field Effect Transistor (MOSFET). In this chapter, we introduce the MOS structure and its four different modes of operation, namely accumulation, flatband, depletion and inversion. We then consider the flatband voltage in more detail and present the MOS analysis based on the full depletion approximation. Finally, we analyze and discuss the MOS capacitance.

4. Norhayati Soin 06 KEEE 4426 WEEK 3/1 9/01/2006 1.2STRUCTURE AND PRINCIPLE OF OPERATION

5. Norhayati Soin 06 KEEE 4426 WEEK 3/1 9/01/2006 STRUCTURE Metal-Oxide-Semiconductor structure semiconductor substrate with a thin oxide layer and a top metal contact, referred to as the gate. second metal layer forms an Ohmic contact to the back of the semiconductor and is called the bulk contact. The structure shown has a p-type substrate. We will refer to this as an n-type MOS or nMOS capacitor since the inversion layer contains electrons. Fig. 1.2.1 MOS capacitor structure

6. Norhayati Soin 06 KEEE 4426 WEEK 3/1 9/01/2006 PRINCIPLE OF OPERATION(1) To understand the different bias modes of an MOS capacitor we now consider three different bias voltages: below the flatband voltage, V G < V FB between the flatband voltage and the threshold voltage, V FB <V G < V T larger than the threshold voltage V G >V T Fig. 1.2.2 Charges in an n-type Metal-Oxide-Semiconductor structure (p-type substrate) under accumulation, depletion and inversion conditions

7. Norhayati Soin 06 KEEE 4426 WEEK 3/1 9/01/2006 Accumulation occurs typically for negative voltages where the negative charge on the gate attracts holes from the substrate to the oxide- semiconductor interface

8. Norhayati Soin 06 KEEE 4426 WEEK 3/1 9/01/2006 Depletion Positive voltages. Positive charge on the gate pushes the mobile holes into the substrate. Therefore, the semiconductor is depleted of mobile carriers at the interface and a negative charge, due to the ionized acceptor ions, is left in the space charge region. The voltage separating the accumulation and depletion regime is referred to as the flatband voltage, V FB.

9. Norhayati Soin 06 KEEE 4426 WEEK 3/1 9/01/2006 Inversion(1) Exists a negatively charged inversion layer at the oxide-semiconductor interface in addition to the depletion- layer. This inversion layer is due to the minority carriers that are attracted to the interface by the positive gate voltage.

10. Norhayati Soin 06 KEEE 4426 WEEK 3/1 9/01/2006 Inversion(2) Fig. 1.2.3 Energy band diagram of an MOS structure biased in inversion The oxide is modeled as a semiconductor with a very large bandgap and blocks any flow of carriers between the semiconductor and the gate metal. The band bending in the semiconductor is consistent with the presence of a depletion layer. At the semiconductor-oxide interface, the Fermi energy is close to the conduction band edge as expected when a high density of electrons is present. The semiconductor remains in thermal equilibrium even when a voltage is applied to the gate. The presence of an electric field does not automatically lead to a non-equilibrium condition, as was also the case for a p-n diode with zero bias.

11. Norhayati Soin 06 KEEE 4426 WEEK 3/1 9/01/2006 1.2.1 Flat band Diagram

12. Norhayati Soin 06 KEEE 4426 WEEK 3/1 9/01/2006 Flat band diagram(1) Flatband conditions exist when no charge is present in the semiconductor so that the silicon energy band is flat. Initially we will assume that this occurs at zero gate bias. Later we will consider the actual flatband voltage in more detail. Surface depletion occurs when the holes in the substrate are pushed away by a positive gate voltage. A more positive voltage also attracts electrons (the minority carriers) to the surface, which form the so-called inversion layer. Under negative gate bias, one attracts holes from the p-type substrate to the surface, yielding accumulation.

13. Norhayati Soin 06 KEEE 4426 WEEK 3/1 9/01/2006 Flat band diagram(2) Fig. 1.2.4 Flatband energy diagram of a metal-oxide- semiconductor (MOS) structure consisting of an aluminum metal, silicon dioxide and silicon. The flatband diagram is by far the easiest energy band diagram. The term flatband refers to fact that the energy band diagram of the semiconductor is flat, which implies that no charge exists in the semiconductor. Note that a voltage, V FB, must be applied to obtain this flat band diagram. Indicated on the figure is also the work function of the aluminum gate, F M, the electron affinity of the oxide, c oxide, and that of silicon, c, as well as the bandgap energy of silicon, E g.

14. Norhayati Soin 06 KEEE 4426 WEEK 3/1 9/01/2006 Flat band diagram(3) Fig. 1.2.4 Flatband energy diagram of a metal-oxide- semiconductor (MOS) structure consisting of an aluminum metal, silicon dioxide and silicon. The bandgap energy of the oxide is quoted in the literature to be between 8 and 9 electron volt. The flatband voltage is obtained when the applied gate voltage equals the workfunction difference between the gate metal and the semiconductor. If there is a fixed charge in the oxide and/or at the oxide-silicon interface, the expression for the flatband voltage must be modified accordingly.

15. Norhayati Soin 06 KEEE 4426 WEEK 3/1 9/01/2006 Accumulation band diagram With a negative voltage applied to the metal (gate electrode), holes are attracted to the semiconductor surface underneath oxide and the metal contact. This causes an upward bending of the bands at the semiconductor-oxide interface. This condition, called accumulation, corresponds to the accumulation of holes

16. Norhayati Soin 06 KEEE 4426 WEEK 3/1 9/01/2006 Depletion band diagram As a more positive voltage than the flatband voltage is applied, a negative charge builds up in the semiconductor causing the energy bands to bend downward at the semiconductor- oxide interface. Initially this charge is due to the depletion of the semiconductor starting from the oxide-semiconductor interface. The depletion layer width further increases with increasing gate voltage.

17. Norhayati Soin 06 KEEE 4426 WEEK 3/1 9/01/2006 Inversion band diagram As the potential across the semiconductor increases beyond twice the bulk potential, another type of negative charge emerges at the oxide- semiconductor interface: this charge is due to minority carriers, which form a so-called inversion layer. As one further increases the gate voltage, the depletion layer width barely increases further since the charge in the inversion layer increases exponentially with the surface potential.