Electrostatic Mechanism of Emission Enhancement in Hybrid Metal-semiconductor Light-emitting Heterostructures Page: 46

(cl +i)(
j+1j

j = 0..9

1
2
1
M9 -
2

(1 -a+ fj+ -z,j+1dj+1
( j+1) j j+1 j
(1 - j,j+) flj,j+ (1 + j,j

(1- j,j+l)j,j+le-1zj+ldj+1
(1 + +j,j+l)fj,j+lezj+ldj+1 )

(4.3.14)

+ 1)flj,j+i
+7) ljj4

qz, jEz, j (W) X L, j+1( )
j,j+l = +l+l(j+ =
The dispersion relation can then be found by relating the j=O coefficients to the j=10O
coefficients. Doing so yields:

C
C)
O
O
0-

91.0-
90.8-
90.6
90.4-
90.2

10 15

0 5 10 15
q1d

20

20

Figure 4.3 Plots of the dispersion relations for the upper and lower branches of
the I-LO phonon modes for the heterostructure pictured in Fig 4.2. The 10
modes arise from zone-folding of the phonons at the super-lattice interfaces.
Black (red) lines represent the (anti-)symmetric phonon modes.

46

. z
1 --
1 -
x-