Probing the quasi-localized states in GaNAs
Materials Theory Group > Transport and Atomic Structure in Semiconductor Alloys > Dilute Nitrides > Probing the quasi-localized states in GaNAs
The drastic reduction in mobility observed when a small fraction of the As atoms in GaAs are replaced with N has been attributed to the interaction of conduction band carriers with quasi-localized states associated with clusters of N atoms . These quasi-localized states have been determined from tight-binding calculations  to lie close to the conduction band edge, leading to a strong scattering of carriers whose energy is near-resonant with these states and hence a drastically reduced mobility. As the mobility is so low, fluctuations in mobility are difficult to measure. This has meant that direct experimental verification of the existence of these states has been elusive.
We have proposed a method of probing these quasi-localized N states using mobility measurements in a proposed gated double-well heterostructure . The structure consists of AlGaAs/InGaAs/GaNAs/AlGaAs layers with a front and buried back gate, shown in Fig. 1. The carriers are largely contained in the InGaAs layer, so that their electronic wave function has only a small overlap with N states in the dilute nitride layer. By varying the back-gate field and the In content in the InGaAs layer, the Fermi level can be swept through a portion of the spectrum of localized N levels in the dilute nitride layer, with large reductions in carrier mobility predicted when the Fermi level is resonant with a localized level. To maximise the resolution of the device, the mobility measurements are at low temperature (T=4 K).
The carrier envelopes have been determined using a modified Poisson-Schrödinger approach. The mobility is calculated through solution of the Boltzmann equation in the relaxation-time approximation, with a modified version of the resonance scattering approach used in  adopted to determine the N alloy scattering rate. Phonon scattering and In alloy scattering have also been incorporated in the model.
When in operation, the device will in general have two conducting channels switched on: one in the InGaAs layer and one in the dilute nitride layer. By varying the back gate field it is possible to vary the energy of the sub-band in the dilute nitride layer with respect to the energy of the sub-band in the InGaAs layer. This is illustrated in Fig. 2, which shows the calculated transverse wave functions as a function of depth z in the heterostructure (transport occurs perpendicular to the plane of the figure). As the back gate field is increased from -104 Vcm-1 to +104 Vcm-1, the sub-bands grow closer in energy, hybridize strongly, then swap so that the lower energy sub-band swaps from the dilute nitride layer (75≤ z≤ 78 nm) to the InGaAs layer (50≤ z≤ 70 nm). By further increasing the back gate field it is possible to increase the energy of the sub-band in the dilute nitride layer with respect to the Fermi level so that it is no longer occupied by carriers. When this occurs, the conducting channel in the dilute nitride layer switches off, and the carriers only occupy the sub-band in the InGaAs layer. This is the condition required in order to probe the N states in the dilute nitride layer.
In Fig. 3 variation in carrier mobility as a function of applied back gate field for a heterostructure with an 18 nm InGaAs layer, a 5 nm GaAs layer, a 3 nm dilute nitride layer, In content of 3%, N content of 0.36%, at temperature T=4 K is shown. The front gate field is held constant at 3.7× 105 Vcm-1. When the back gate field rises above -3800 Vcm-1, the conducting channel in the dilute nitride layer switches off and there is a corresponding sudden increase in mobility. Large variations in mobility occur as the Fermi level becomes resonant with states associated with clusters of N atoms that are highly localized in energy.
Figure 1 shows a schematic of the heterostructure device, including front and back gates. The back gate geometry shown here is an example of how back-gating may be acheived in real devices, the details of the actual structure of the back gate do not affect our calculations. The AlGaAs layers have Al content 40% and the doped layer has a Si concentration of 10<sup>18</sup> cm<sup>-3</sup>. Layer thicknesses, In content in the InGaAs layer and N content in the dilute nitride layer, and front and back gate fields are variable in our calculations.
Figure 2 shows the sub-band weights |ψi(z)|2 for i=1 (red line), i=2 (green line) and 1D heterostructure potential V(z) (black line) as a function of depth z in the heterostructure, with z=0 at the top of the device. The Fermi level, EF, is indicated by the blue line. The localized N states |Nj> are located in the dilute nitride layer, at an energy 0.18 eV above the CBE, and are indicated by the thick brown line. The |ψi(z)|2 are plotted (with normalized units) at their sub-band energies Ei. The GaAs VBM is used as the zero of energy. Results are for a 20 nm InGaAs layer (In content 3%), 5 nm GaAs layer, and 3 nm dilute nitride layer (N content 1.2%) in the channel and a constant front gate field of 3.4 × 105 Vcm-1. AlGaAs/InGaAs interface at the top of the channel is at z=50 nm and the GaAs/AlGaAs interface at the bottom of the channel is at z=79 nm. Temperature, T=4 K.
Figure 3 shows the variation in carrier mobility as a function of applied gate field, for a heterostructure with an 18 nm InGaAs layer, a 5 nm GaAs layer, a 3 nm dilute nitride layer, In content of 3%, N content of 0.36%, at temperature T=4 K and constant front gate field of 3.7× 105 Vcm-1.
- John Buckeridge
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 J. Buckeridge, PhD thesis (2010)