ANÁLISIS E INTERPRETACIÓN DE RESULTADOS

The position of the surface Fermi level as a function of alloy composition was inves- tigated using valence band XPS measurements, shown in Fig. 7.3. For the undoped

7.3. InGaN Alloys 122 0.0 0.2 0.4 0.6 0.8 1.0 -1 0 1 2

x (In

Ga

N)

B

a

rr

ie

r

h

e

ig

h

t,

(

e

V

)

GaN

InN

Figure 7.4: Barrier height, ΦB, for undoped and Mg-doped

InxGa1−xN samples. The bar-

rier height, represented schemat- ically inset, is taken as negative if the Fermi level is above the CBM at the surface and posi- tive if the Fermi level is below the CBM at the surface. A band gap bowing parameter of b = 1.4 eV [266] has been used to de- termine the barrier height from the VB-XPS measurements.

InxGa1−xN samples, an increase in VBM to surface Fermi level separation is ob-

served with increasing Ga-fraction, although no such monotonic trend is observed for the Mg-doped alloys. However, it is also necessary to consider the effects of the increasing band gap upon moving from In-rich to Ga-rich alloys. This is achieved by determining the barrier height, ΦB (analogous to the n-type Schottky barrier

height of a semiconductor-metal junction), defined as the conduction band mini- mum (CBM) to surface Fermi level separation, shown in Fig. 7.4. A clear trend in barrier height is evident across the composition range for both undoped and Mg- doped alloys, with the Mg-doped alloys exhibiting higher values of ΦB compared

to the undoped alloys for all alloy compositions, with the largest differences for Ga-rich alloys. This difference in barrier height provides initial evidence that Mg- doping is acting to induce a bulk p-type conductivity across the entire InGaN alloy composition range.

The bulk carrier density in the undoped samples was measured by the single- field Hall effect, and these values were used to determine (via non-parabolic carrier statistics calculations) the position of the bulk Fermi level. The surface and bulk Fermi level positions relative to the semiconductor band edges and the CNL are shown in Fig. 7.5.

For the most In-rich alloys, the surface Fermi level position is pinned well above the bulk Fermi level, indicating an extreme electron accumulation as for

7.3. InGaN Alloys 123 0.0 0.2 0.4 0.6 0.8 1.0 -2 -1 0 1 E CNL E C E mid E V E F (surf) E F (bulk ) GaN InN E n e r g y ( e V ) x (In x Ga 1-x N)

Figure 7.5: Surface (filled circles) and bulk (open squares) Fermi level (EF) for undoped

InxGa1−xN alloys relative to the CNL (ECN L), and InGaN band edges (EC, EV) and mid-gap

position (Emid). The CNL is located 1.83 eV above the VBM in InN (Section 5.3). The variation

in valence band edge is assumed to be linear after M¨onch [21], with the measured valence band offset of 0.58 eV (Section 7.1.1) and a band gap bowing parameter of 1.4 eV [266] (entirely in the conduction band due to the linear variation of the valence band edge) used to define the band edges relative to the CNL.

InN. In contrast, for the Ga-rich alloys, the surface Fermi level is pinned below the bulk Fermi level, indicating an upward band bending and electron depletion at the surface, as known for GaN [189]. For alloys closer to the middle of the composition range, the surface and bulk Fermi level positions move closer together, leading to a reduction in the degree of space-charge characteristics towards flat-band conditions. This is illustrated by Poisson-MTFA calculations, shown in Fig. 7.6, which show a pronounced electron accumulation for InN, virtually no electron accumulation for In0.5Ga0.5N and a large electron depletion layer for GaN.

The surface Fermi level positions determined from the XPS measurements for the Mg-doped alloys, along with those for the undoped alloys, are shown in Fig. 7.7. The pinning position of the surface Fermi level for the Mg-doped and undoped material diverges with increasing Ga-content, as seen from the barrier heights discussed above. Accurate determination of the bulk carrier density is not possible due to the inversion layers for In-rich alloys. However, assuming that Mg- doping causes bulk p-type conductivity, the bulk Fermi level will be located close to the VBM. Consequently, the surface Fermi level is located above the bulk Fermi

7.3. InGaN Alloys 124 -3 -2 -1 0 E F CBM VBM 0 1 2 3 4 InN 0 100 200 300 -3 -2 -1 0 E n e r g y ( e V ) 0 100 200 300 0 1 2 3 4 n ( z ) ( 1 0 1 9 c m - 3 ) In 0.5 Ga 0.5 N 0 1000 2000 3000 -3 -2 -1 0 Depth, z (Å) 0 1000 2000 3000 0 2 4 6 8 n ( z ) ( 1 0 1 6 c m - 3 ) GaN

Figure 7.6: Band bending and car- rier concentration profiles as a func- tion of depth from Poisson-MTFA calculations for InN, In0.5Ga0.5N, and

GaN. 0.0 0.2 0.4 0.6 0.8 1.0 -2 -1 0 1 E CNL E C E mid E V Undoped E F (surf) Mg-doped E F (surf) GaN InN E n e r g y ( e V ) x (In x Ga 1-x N) E C E V E F n ( z) n ( z) n ( z) , p ( z) n(z) p(z) Depth (z) p ( z)

Figure 7.7: Surface Fermi level (EF) for undoped (circles) and Mg-doped (triangles) InxGa1−xN

alloys relative to the CNL (ECN L), and InGaN band edges (EC, EV) and mid-gap position (Emid).

The band edges are constructed as in Fig. 7.5. A schematic representation of the space-charge characteristics of each of the end points is also shown.

7.3. InGaN Alloys 125

level across the composition range, indicating that downward band bending occurs for all alloy compositions. For the Ga-rich alloys, this leads to a hole depletion layer occurring at the surface, as shown schematically in Fig. 7.7. However, for the In- rich alloys, the surface Fermi level is pinned above the mid-gap position; electrons are the dominant carrier species at the surface, creating an inversion layer where the p-type bulk is separated from an n-type surface region by a depletion layer, as represented schematically in Fig. 7.7.