We perform capacitance-voltage and admittance spectroscopy to investigate the effect of incorporating an InAlAs layer before an InGaAs cap layer on electron emission in self-assembled InAs quantum dots (QDs). We show that this incorporation of a high potential barrier increases the emission time of the electrons thermally activated from the QD ground to the first excited state. The energy separation between the ground and first excited states in the conduction band increases from 57.2 to 79.1, to 89.2, and to 95.6 meV with increasing the thickness of the InAlAs layer from 0 to 10, to 14, and to 20 Å. Combining with photoluminescence (PL) data, the ratios of the energy separation between the ground and first excited states in the conduction band and valence band are determined to be 7.3:2.7 and 7.8:2.2 for 0 and 10 Å InAlAs, respectively. In addition, this incorporation is shown to blueshift the PL first excited state much larger than the ground state.