Chemistry Reference
In-Depth Information
lasers and amplifiers (Adams and O'Reilly 1992; Adams, O'Reilly and
Silver 1998).
To understand the effects of strain on the band structure, we need to
return to the band structure of fig. 5.14(a). The LH and HH bands are only
degenerate because of the cubic symmetry of the lattice and they are split
apart by strain. This splitting arises because the
z
-like valence state now
sees a different environment to the
x
- and
y
-like states due to the change
in unit cell dimensions. In addition, the resulting band structure is highly
anisotropic (fig. 5.14(b) and (c)), with the band which is heavy along the
strain axis,
k
⊥
, being comparatively light perpendicular to that direction,
k
, and vice-versa. This anisotropy can be understood from the
k
p
theory
introduced in Chapter 4, where we saw that the interaction between the
conduction band and a
z
-like state gives rise to a valence band with a low
effective mass along the
z
-direction, and heavy mass perpendicular to that
direction.
When the layer is grown in compressive strain, the bandwith lower hole
mass in the quantum well plane moves to the valence band maximum, as
shown in the LHS of fig. 5.14(b). There is nowamuch better match between
the carrier effective masses in the conduction and valence bands and the
threshold current and carrier density are reduced.
The band splitting is reversed in layers under tensile strain (LHS of
fig. 5.14(c)). A marked reduction in threshold current has also been
observed in tensile-strained lasers. Adifferentmechanismmust be invoked
to explain these improvements. We have already mentioned how the holes
in a bulk laser are distributed equally between states that would produce
light polarised in the
x
,
y
,or
z
directions, so that only one in three holes
contribute to the lasing mode. However, the reduced symmetry in the
tensile-strained layer shifts the
z
-like valence states up in energy compared
to the
x
- and
y
-like states; for sufficient tensile strain, most of the holes then
have
z
-like character and are in the right polarisation state to contribute to
the lasing mode, which is indeed found to have its electric field polarised
along the growth (TM) direction.
Figure 5.17 shows a compilation by Thijs
et al
. (1994) of the measured
straindependence of threshold current density perwell in longwavelength
(
·
InGaAs(P) quantum well lasers. The reduction in threshold cur-
rent with both tensile (LHS) and compressive strain (RHS) is clearly seen.
The maximum threshold current occurs in layers with a small tensile mis-
match, rather than in lattice-matched, unstrained quantum wells. This
occurs because strain and quantum confinement each split the HH and
LH states at the valence band maximum. The splittings add to each other
for compressive strain but are in opposite directions for tensile strain: the
largest threshold current density is then found about the point where the
strain- and confinement-induced splittings are equal and opposite, leaving
the HH and LH bands degenerate.
1.5
m
)
µ
