Germanene on single-layer ZnSe substrate: novel electronic and optical properties

In this work, the structural, electronic and optical properties of germanene and ZnSe substrate nanocomposites have been investigated using first-principles calculations. We found that the large direct-gap ZnSe semiconductors and zero-gap germanene form a typical orbital hybridization heterostructure with a strong binding energy, which shows a moderate direct band gap of 0.503 eV in the most stable pattern. Furthermore, the heterostructure undergoes semiconductor-to-metal band gap transition when subjected to external out-of-plane electric field. We also found that applying external strain and compressing the interlayer distance are two simple ways of tuning the electronic structure. An unexpected indirect-direct band gap transition is also observed in the AAII pattern via adjusting the interlayer distance. Quite interestingly, the calculated results exhibit that the germanene/ZnSe heterobilayer structure has perfect optical absorption in the solar spectrum as well as the infrared and UV light zones, which is superior to that of the individual ZnSe substrate and germanene. The staggered interfacial gap and tunability of the energy band structure via interlayer distance and external electric field and strain thus make the germanene/ZnSe heterostructure a promising candidate for field effect transistors (FETs) and nanoelectronic applications.

Estimation of number of subjects required for comparison of drug versus control in adaptive designs

INTRODUCTION

Adaptive designs have often been proposed as a way of using accruing data to affect future allocation scheme in clinical trials. The goal is to assign more patients to the better treatment. To implement clinical trials efficiently, sample size must be estimated in advance. In adaptive design, it is difficult to calculate the required sample size, because the allocation probabilities keep changing during the course of the trials.

METHODS

We focus on the sample size of two-arm (drug versus control) clinical trials. Based on its asymptotic properties, a formula of calculating sample size is derived for the randomised play-the-winner rule. We also compare sample size and power between the randomised play-the-winner rule and equal allocation. Some simulation studies illustrate the operating characteristics of the designs.

RESULTS AND DISCUSSION

The required sample size of the randomised play-the-winner rule is slightly larger than that of the equal allocation design in most cases. The randomised play-the-winner rule is recommended for ethical reasons.