Based on the analysis of the three-dimensional Schrödinger equation, the effects of quantum coupling between the transverse and the longitudinal components of channel electron motion on the performance of ballistic MOSFETs have been theoretically investigated by self-consistently solving the coupled Schrödinger–Poisson equations with the finite-difference method. The results show that the quantum coupling between the transverse and the longitudinal components of the electron motion can largely affect device performance. It suggests that the quantum coupling effect should be considered for the performance of a ballistic MOSFET due to the high injection velocity of the channel electron.

The comparison of the inversion electron density between a nanometer metal-oxidesemiconductor (MOS) device with high-𝐾 gate dielectric and a SiO₂ MOS device with the same equivalent oxide thickness has been discussed. A fully self-consistent solution of the coupled Schrödinger–Poisson equations demonstrates that a larger dielectric-constant mismatch between the gate dielectric and silicon substrate can reduce electron density in the channel of a MOS device under inversion bias. Such a reduction in inversion electron density of the channel will increase with increase in gate voltage. A reduction in the charge density implies a reduction in the inversion electron density in the channel of a MOS device. It also implies that a larger dielectric constant of the gate dielectric might result in a reduction in the source–drain current and the gate leakage current.

The quantum capacitance, an important parameter in the design of nanoscale devices, is derived for armchair-edge single-layer graphene nanoribbon with semiconducting property. The quantum capacitance oscillations are found and these capacitance oscillations originate from the lateral quantum confinement in graphene nanoribbon. Detailed studies of the capacitance oscillations demonstrate that the local channel electrostatic potential at the capacitance peak, the height and the number of the capacitance peak strongly depend on the width, especially a few nanometres, of the armchair-edge graphene nanoribbon. It implies that the capacitance oscillations observed in the experiments can be utilized to measure the width of graphene nanoribbon. The results also show that the capacitance oscillations are not seen when the width is larger than 30 nm.

Based on the energy and momentum balance equations and three-dimensional Schrödinger equations, a physical model of the quantum coupling and electrothermal effects on the electron transport in GaN transistors is proposed. Quantum coupling and electrothermal effects in GaN transistors cause a reduction in the barrier height, changes in the quantised energy levels of the two-dimensional electron gas, and a decrease in the electron densityand source–drain current. This model predicts that the current collapse in GaN transistors can occur under channel electrons with large transverse energy and it can be alleviated by optimising the physical device parameters. The gate length-dependent resistance predicted by the proposed model agrees well with the experimental data reported in the literature. Not only the physical mechanism but also the possibility to improve the reliability of high-electron mobility (HEMT) GaN transistors by optimising its physical parameters has been given in this model due to its analytic nature.

After the carrier drift velocity at the semiconductor/metal interface is considered, current transport in Schottky diodes under a forward electric field is physically modelled. This model reveals that the ideality factor can be physically originated from the drift velocity and the drift velocity can also reduce the effective Schottky barrier height. This proposed model predicts that both the ideality factor and the Schottky barrier height depend on temperature, voltage and doping density, which agree well with the experimental results reported in the literature. The proposed diode current model also predicts a linear dependent relation between the reciprocal of the ideality factor and the effective Schottky barrier height, which is validated by experimental results. Such a model is useful to better understand the thermionic emission current physically in semiconductor/metal contact. It is also useful to characterise the material properties by using the ideality factor.

There is a large difference between the intervalley energy difference of GaN predicted by first-principles calculations and that measured by experiments. The results of full-band MonteCarlo simulation prove that intervalley transitions can occur at a high electric field when the intervalley energy difference measured by experiments is used. When the electric field is lower than $1\times 10^7$ V/m and the intervalley energy difference is higher than 1.2 eV, intervalley transitions hardly ever happen. Because there are almost no electrons in the high-energy valleys inequilibrium states, the electrons in the $\Gamma_2$ valley should be regarded as excess carriers. The occupation probability of electrons in the $\Gamma_2$ valley rapidly increases with the decreased intervalley energy difference between the $\Gamma_1$ and the $\Gamma_2$ valleys. Similarly, it rapidly decreases with the increasing effective electron mass in $\Gamma_1$ valley. When electrons in GaN get more kinetic energy from light or surface electric field, such an increase in the electron energy can be equivalent to a reduction in the intervalley energy difference. By using the concept of effective intervalley energy difference, we can explain why the increase in the source–drain current depends on the gate voltage, light, the sweep mode of source–drain voltage and different types of traps can be explained. In all calculations, there areno electrons in the L-M valleys of GaN.