  InAs quantum wells (QWs) grown on InP substrates are interesting for their
applications in devices with high spin-orbit coupling (SOC) and their potential
role in creating topologically nontrivial hybrid heterostructures. The highest
mobility QWs are limited by interfacial roughness scattering and alloy disorder
scattering in the cladding and buffer layers. Increasing QW thickness has been
shown to reduce the effect of both of these scattering mechanisms. However, for
current state-of-the-art devices with As-based cladding and barrier layers, the
critical thickness is limited to $\leq7$ nm. In this report, we demonstrate the
use of strain compensation techniques in the InGaAs cladding layers to extend
the critical thickness well beyond this limit. We induce tensile strain in the
InGaAs cladding layers by reducing the In concentration from
In$_{0.81}$Ga$_{0.19}$As to In$_{0.70}$Ga$_{0.30}$As and we observe changes in
both the critical thickness of the well and the maximum achievable mobility.
The peak electron mobility at 2 K is $1.16\times10^6$ cm$^2/$Vs, with a carrier
density of $4.2\times10^{11}$ /cm$^2$. Additionally, we study the quantum
lifetime and Rashba spin splitting in the highest mobility device as these
parameters are critical to determine if these structures can be used in
topologically nontrivial devices.
