Effects of Shape and Strain Distribution of Quantum Dots on Optical Transition in the Quantum Dot Infrared Photodetectors
© to the authors 2008
Received: 24 July 2008
Accepted: 11 September 2008
Published: 21 October 2008
We present a systemic theoretical study of the electronic properties of the quantum dots inserted in quantum dot infrared photodetectors (QDIPs). The strain distribution of three different shaped quantum dots (QDs) with a same ratio of the base to the vertical aspect is calculated by using the short-range valence-force-field (VFF) approach. The calculated results show that the hydrostatic strain ɛHvaries little with change of the shape, while the biaxial strain ɛBchanges a lot for different shapes of QDs. The recursion method is used to calculate the energy levels of the bound states in QDs. Compared with the strain, the shape plays a key role in the difference of electronic bound energy levels. The numerical results show that the deference of bound energy levels of lenslike InAs QD matches well with the experimental results. Moreover, the pyramid-shaped QD has the greatest difference from the measured experimental data.
Due to three-dimensional confinement for electrons in the quantum-dot structure, quantum-dot infrared photodetectors (QDIPs) have attracted much attention for theoretical and experimental studies in recent years [1–3]. One important characteristic for QDIPs is the sensitivity to normal-incidence infrared radiation which is advantage to focal plane arrays. The longer lifetime of excited electrons inspirited by the greatly suppressed electron–phonon interaction makes the QDIPs have another advantages of displaying low dark current, large detectivity, and better response . The introduction of strain may provide a facile way to fabricate various wavelength from mid-wavelength to long-wavelength multicolor infrared (IR) detectors via InAs or InGaAs quantum dot (QD) capped by GaAs, InGaAs, InP, or GaInP. Meanwhile, the geometry shape of QDs always results in quite different responding wavelength for QDIPs . Nowadays, more complicated nanostructures, such as QD molecules are investigated for the potential use of photoelectric devices . It is well known that the much sensitivity of QD’s bound energy levels to the shape, size, and strain provides the detector greater potential to obtain the ideal responding wavelength for the application of medical or molecular application. So the study of the shape, size, and strain of QD system has been an interesting subject for the development and precious controlling of the QDIPs structure.
Much theoretical and experimental work has been done to explore the effect of the shape, size, or strain of QDs on the bound energy levels or the possible optical transition. The bound energy levels in fat lenslike QD basing on the quantum-well approximate theoretical results have a bigger difference by comparing to the experimental results. In wojs’ work, the energy levels of lenslike In0.5Ga0.5As/GaAs QD were studied as a function of the dot’s size, and found that the parabolic confining potential and its corresponding energy spectrum were shown to be and excellent approximation . Here, we calculate the strain energy of self-assembled QDs with the short-range valence-force-field (VFF) approach to describe inter-atomic forces by using bond stretching and bending. The role of strain (for three different shapes) in determining the bound levels is analyzed in detail. Considering three different shape QDs with the same ratio of the base to the vertical aspect 3:1, the bound energy levels are calculated by the recursion method . The theoretical results show that the difference of bound energy levels of lenslike InAs QD matches with the experimental results. While the bound energy levels of pyramid-shaped QD have the biggest difference from the measured experimental data. Though the bound-to-continuum transition of the truncated pyramid QD is mostly acceptable because the behavior is much similar to the structure of the well-studied quantum-well infrared photodetectors (QWIPs), the bound ground states of electrons and holes are very far from the experimental results.
The paper is organized as following, in the section “Sample Preparations and Experimental Results,” the investigated experimental device and experimental results such as AFM/TEM images, the photoluminescence (PL), and photocurrent (PC) spectrums are described. In the section “Theoretical Results and Discussions,” the exact strain distributions of pyramid, truncated pyramid, and lenslike-shaped InAs/GaAs QD are calculated by the short-range VFF approach, and the energy levels of the bound states are calculated by the recursion method. The final section discusses the summary.
Sample Preparations and Experimental Results
Theoretical Results and Discussions
Strain and Confinement Profile
Values of C’s  and K’s (at 100 K) of zincblende InAs and GaAs bulk materials
K r (GPaÅ)
K rr (GPaÅ)
V HH and V LH are the heavy-hole and light-hole bands, a c a v and b are the deformation potentials, and E CB/VB are the unstrained band edge energies. Notice that the sheer-strain-induced HH–LH coupling and split-off contributions are ignored. In our calculation we adopt the parameters from Ref. .
The Calculation and Analysis of the Energy Level
The recursion method is used to calculate the energy levels of three different shaped QDs . For the experimental data, the broadening (FWHM) of the PC spectrum and the first peak of the PL spectrum are 34.01 and 29.34 meV, respectively. The broadening is 131.42 meV for the second peak. The much greater difference in the FWHM implies the possibility that the second peak comes from wetting layer, but not from the bound levels of QDs. So for the simplicity of comparing with the experimental results, we only calculate all the energy levels of electron and the bound ground energy level of hole with the corresponding results shown in Fig. 6 (dotted line).
with d PL and d PC being the difference of calculated and measured PL and PC spectrum, respectively. In our calculation, σ is 34.86%, 15.82%, and 5.92% for pyramid, truncated-pyramid, and lens-shaped QD, respectively. For the lens-shaped QD, σ has the least value, which means the QDIP structure is constructed by the lens-shaped QD. The lens-shaped InAs/GaAs QD is observed by many researchers, and in this way our calculation can get a good agreement with the measured data. Also the PL, PC spectrum, and σ provide us a way to find out the most suitable shape and size of QD which makes σ the minimum. The different shape of QDs can have different response wavelength as described in our calculation. The results mean that one can obtain the ideal response wavelength of QDIP structure by controlling the growth condition to change the shape of QDs.
In summary, we have studied the strain distribution of self-assembled QD by the short-range VFF approach to describe inter-atomic forces in terms of bond stretching and bending. The strain-driven self-assembled process of QD based on lattice mismatch has been clearly demonstrated. The recursion method is used to calculate the bound energy levels of QD for three different shapes but at the same ratio 3:1 for the base to the vertical aspect. For the three different shaped QD, the hydrostatic strain ɛHhas a little change. The results indicate that the difference of bound energy is mainly controlled by the shape. The biaxial strain ɛBchanges a lot with the shape. Moreover, the strain and the shape both play key role in determining the ground state of hole. The results show that the difference of bound-to-bound energy levels of lenslike InAs QD matches well with the experimental data, while the pyramid-shaped QD has the biggest difference from the measured data. Though the bound-to-continuum transition for truncated pyramid QD is mostly acceptable because the behavior is much like the well-studied QWIP structure, the bound ground states between electron and hole value is rather far from the experimental results. Also the biggest difference of 48.88% makes the pyramid an impossible shape for our investigated QD. Our theoretical investigation provides a feasible method for finding the most seemly geometry and size of QDIP structure by adjusting the shape/size of QD and the comparing theoretical and experimental results. It is useful in designing the ideal QDIPs device.
The project is partially supported by the National Natural Science Foundation of China (Grant No:10474020), CNKBRSF 2006CB13921507, and Knowledge Innovation Program of CAS.
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