# Materials Science and Engineering/Doctoral review questions/Information Suggested to Memorize
### Mobilities of materials classes

| Material | Mobility |
| Metals | $~10^{8}S/m$ |
| Semiconductors (doped) | $~10^{3}S/m$ |
| Semiconductors (undoped) | $10^{-2}S/m\;$ |
| Insulators | $~10^{-14}S/m$ |
| Holes in Si | $~0.05m^{2}/(Vs)$ |
| Electrons in Si | $~0.15m^{2}/(Vs)$ |

### Young's Modulus of materials classes

| Material | Modulus |
| Metals | $~100GPa$ |
| Rubbers | $~10MPa$ |

### Band gap of materials

| Material | Modulus |
| Si | $1.12eV$ |
| GaAs | $1.42eV$ |
| Ge | $0.7eV$ |
| Visible light | $1.77-3.10eV$ |

### Structures of materials

* III-V compounds
* Wurtzite (combination HCP)
* Zinc blende (combination of FCC)

### High-k materials

The term high-κ dielectric refers to a material with a high dielectric constant (κ) (as compared to silicon dioxide) used in semiconductor manufacturing processes which replaces the silicon dioxide gate dielectric. The implementation of high-κ gate dielectrics is one of several strategies developed to allow further miniaturization of microelectronic components, colloquially referred to as extending Moore's Law.

#### Why are high k-materials needed?

Silicon dioxide has been used as a gate oxide material for decades. As transistors have decreased in size, the thickness of the silicon dioxide gate dielectric has steadily decreased to increase the gate capacitance and thereby drive current and device performance. As the thickness scales below 2 nm, leakage currents due to tunneling increase drastically, leading to unwieldy power consumption and reduced device reliability. Replacing the silicon dioxide gate dielectric with a high-κ material allows increased gate capacitance without the concomitant leakage effects.
The gate oxide in a MOSFET can be modeled as a parallel plate capacitor. Ignoring quantum mechanical and depletion effects from the Si substrate and gate, the capacitance C of this parallel plate capacitor is given by
    $C={\frac {\kappa \varepsilon _{0}A}{t}}$
Where
* $\,A$ is the capacitor area
* $\,\kappa$ is the relative dielectric constant of the material (3.9 for silicon dioxide)
* $\,\varepsilon _{0}$ is the permittivity of free space
* $\,t$ is the thickness of the capacitor oxide insulator
Since leakage limitation constrains further reduction of $\,t$, an alternative method to increase gate capacitance is alter $\,\kappa$ by replacing silicon dioxide with a high-$\,\kappa$ material. In such a scenario, a thicker gate layer might be used which can reduce the leakage current flowing through the structure as well as improving the gate dielectric reliability.

#### Choice of Materials

Replacing the silicon dioxide gate dielectric with another material adds complexity to the manufacturing process. Silicon dioxide can be formed by oxidizing the underlying silicon, ensuring a uniform, conformal oxide and high interface quality. As a consequence, development efforts have focused on finding a material with a requisitely high dielectric constant that can be easily integrated into a manufacturing process. Other key considerations include band alignment to silicon (which may alter leakage current), film morphology, thermal stability, maintenance of a high mobility of charge carriers in the channel and minimization of electrical defects in the film/interface. Materials which have received considerable attention are hafnium and zirconium silicates and oxides, typically deposited using atomic layer deposition.
It is expected that defect states in the high-k dielectric can influence its electrical properties. Defect states can be measured for example by using zero-bias thermally stimulated current, zero-temperature-gradient zero-bias thermally stimulated current spectroscopy, or Inelastic electron tunneling spectroscopy (IETS).

#### Fabrication of high k materials
### Moore's Law

Moore's Law describes an important trend in the history of computer hardware: that the number of transistors that can be inexpensively placed on an integrated circuit is increasing exponentially, doubling approximately every two years. The observation was first made by Intel co-founder Gordon E. Moore in a 1965 paper. The trend has continued for more than half a century and is not expected to stop for a decade at least and perhaps much longer.
Almost every measure of the capabilities of digital electronic devices is linked to Moore's Law: processing speed, memory capacity, even the resolution of digital cameras. All of these are improving at (roughly) exponential rates as well. This has dramatically changed the usefulness of digital electronics in nearly every segment of the world economy. Moore's Law describes this driving force of technological and social change in the late 20th and early 21st centuries.
Moore's original statement that transistor counts had doubled every year can be found in his publication "Cramming more components onto integrated circuits", Electronics Magazine 19 April 1965:
"The complexity for minimum component costs has increased at a rate of roughly a factor of two per year ... Certainly over the short term this rate can be expected to continue, if not to increase. Over the longer term, the rate of increase is a bit more uncertain, although there is no reason to believe it will not remain nearly constant for at least 10 years. That means by 1975, the number of components per integrated circuit for minimum cost will be 65,000. I believe that such a large circuit can be built on a single wafer."
* Resource: paper by Megan and George

### Most significant problems of the silicon industry

* Resistance of interconnects
** Channel mobility will be very good

### Modern channel width

* 45 nm gate: channel length
* 7 nm oxide thickness
** Reduce tunneling effects

### BJT

* Draw structure
* How to improve upon the device?
* Significance of heterojunctions