CHAPTER THREE
INTRODUCTION
In the past two decades, self-organized InAs/GaAs quantum dots (QDs) grown by Stranski- Krastanow (S-K) method have been intensively investigated1 , not only due to their unique properties of “artificial atomsâ€, but due to their possible device applications as well. Although InAs/GaAs QDs are often inserted into Schottky diodes to study their electronic structure2,3, electron resonant tunneling through the QDs in these Schottky diodes is very rarely focused on4-
6. Usually, quantum-dot resonant tunneling signals in current-voltage (I-V) characteristics can only be obtained at extremely low temperature (typically ≤4.2K), either in Schottky resonant tunneling diodes4 (RTDs) or in double barrier RTDs with two-side Ohmic contacts7,8. The main reason is, however, the signals are obscured by thermal current. By virtue of electron beam lithography technique, resonant tunneling via an individual QD in Schottky RTD can be observed at ~130K5 . When very small mesas are fabricated (0.5μm square in Ref. 5), their peripheral regions are not active but depleted and that can to some extent increase the ratio of resonant tunneling current to hot current. Li and Wang’s6 experiments are executed at 77K, but they have not clarified why the detected resonant tunneling peaks do not originate from bound states of Al0.3Ga0.7As/GaAs superlattice structures in their devices. To the best of our knowledge, one can observe electron resonant tunneling through QD Schottky RTDs only in one voltage direction4-6. In the present work, we will exhibit resonant tunneling semaphores under both forward and reverse biased conditions at relatively
high temperature of 77K through reducing the thermal current in In As/GaAs quantum-dot Schottky RTDs by inserting a thin AlAs barrier layer. Our theoretical calculations coincide with experimental results very well.
THEORY
The conduction band profile of our Schottky RTDs can be calculated analytically. Since there are intrinsic layers between metal and n-type semiconductors, the case is more complicated than standard Schottky junction illustrated in semiconductor physics textbooks. Fig. 2 shows the energy band diagram of the RTD in thermal equilibrium, where xd is the depletion layer width, and –V0, -Φ, Φn are electric potentials at x=-a, x=0 and x>xd, respectively (V0, Φ, Φn>0). The origin of the coordinates, x=0, is selected at the interface between 2nm undoped GaAs and n+ GaAs buffer layer. E0 is the differential value between the binding energy state in InAs QD and the conduction band edge of GaAs.
APPLICATION OF HAMILTONIAN ON RESONANT TUNNELING QUANTUM DOT ARRAYS
Considering the Hamiltonian of a one-dimensional (1D) array of N coupled dots, indexed from left to right as 1−N
The Hamiltonian equation above is a representation of Quantum dot array i.e 1- Darray of N coupled dots index from left to right as 1- N. looking at the energy of a quantum dot confined dots (20 energy states been treated as a single quantum system
From the equation
εka is the energy levels in leads
εia is the ith dot of the energy
Ui is the ith inter- dot repulsion and the inter-dot coupling between the ith dot and its right neighbor (the (i+1)th dot)
V L and V R are the tunnels matrix element connecting thedot 1 (dot N) to the left and right lead.
