AlGaN/GaN High Electron Mobility Transistor Structure Design and Effects on Electrical Properties
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EXPERIMENTAL For an AlxGa1-xN:Si layer pseudomorphically strained on a relaxed AlxGa1-xN layer, the strain, ε⊥, is given by,
a ( Al )GaN − 1, ε⊥ = 2 xAl a ( Al )GaN:Si
(1)
where a(Al)GaN is the a-axis lattice constant for AlN content in the range of 0 – 100%. Vegard’s Law of linear interpolation is assumed. a(Al)GaN:Si is the corresponding a-axis lattice constant at a given Si doping concentration. Table 1 summarizes the lattice constants as a function of Si-doping for GaN:Si and AlN:Si determined by substituting the atomic percent Si associated with the doping level for Ga and/or Al on the column III lattice site of the wurtzite unit cell. 100% activation of the Si dopant was assumed. The undoped GaN and AlN a-axis lattice constants were taken to be 3.1892 and 3.112A, respectively.4 Additional calculations were performed to determine the strain associated with AlGaN on a relaxed GaN layer. The equation for strain, in this case, would be,
aGaN ε⊥ = 2 xAl − 1 ≅ 0.0495 xAl , aAlN
(2)
where aGaN and aAlN are the a-axis lattice constants that were defined earlier and x is the AlN mole fraction which ranges from 0 – 1. No relaxation of the AlGaN or AlGaN:Si was assumed. This would be the case for AlGaN layers below the critical thickness for relaxation. RESULTS Figure 1 illustrates the strain associated with doping AlxGa1-xN with Si for doping concentrations of 5E18, 1E19, and 5E19cm-3 and as a function of the Al content (0≤x≤1). As would be expected, the strain is a strong function of the Si-doping concentration and increases with increasing doping. It should be noted that this strain is tensile since the Sidopant creates a smaller unit cell compared to the equivalent Al mole fraction AlxGa1-xN Table 1. Lattice constants (a-axis) determined for GaN and AlN at Si-doping concentrations of 5E18, 1E19, and 5E19cm-3. Si-doping conc. GaN:Si AlN:Si (cm-3) 5E18 3.1891 3.1119 1E19 3.1890 3.1117 5E19 3.1882 3.1111
F99W4.4
Tensile Strain (%)
1.0E-01
5E19cm-3
1E19cm-3 1.0E-02
5E18cm-3
1.0E-03 0
20
40
60
80
100
AlN% in AlGaN (%)
Figure 1. Si-doping induced strain as a function of mole fraction AlN in AlGaN. Si doping levels are as noted on the graph. undoped unit cell. (This strain is similar in nature to adding additional Al to an undoped AlGaN in, for instance, an AlGaN/GaN HEMT structure.) Figure 1 also indicates a slight decrease in the strain as the AlN mole fraction increases. This is a result of the AlN unit cell being smaller than the GaN unit cell and, thus, the Si substitutional impurity has less of an effect on the AlN lattice compared to the GaN lattice. The Si-doping strain increases with: 1. Increasing Si concentration and 2. Reducing AlN content of the AlGaN. The strain associated with doping GaN with 5E19cm-3 Si is 0.066% and is tensile. DISCUSSION Of greater interest to HEMT structure design is how this effect manifests itself in a strained AlGaN / relaxed GaN system. Figure 2 is a graph of the strain associated with pseudomorphically strained AlGaN on relaxed GaN. If the A
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