Determination of the valence band offset of MOVPE-grown ${\mathrm{In}}_{0.48}{\mathrm{Ga}}_{0.52}\mathrm{P}∕\mathrm{Ga}\mathrm{As}$ multiple quantum wells by admittance spectroscopy

The valence band discontinuity of the lattice matched ${\mathrm{In}}_{0.48}{\mathrm{Ga}}_{0.52}\mathrm{P}∕\mathrm{Ga}\mathrm{As}$ heterostructure was determined through a careful analysis of the temperature and frequency dependence of the admittance of $p^{+}∕\mathrm{MQW}∕n^{+}$ structures, formed by a nominally undoped $\mathrm{In}\mathrm{Ga}\mathrm{P}∕\mathrm{Ga}\mathrm{As}$ multiple quantum well region, interposed between $p^{+}$ and $n^{+}$ GaAs layers. The heterostructures were grown through metal organic vapor phase epitaxy by using tertiary butyl arsine and tertiary butyl phosphine as alternative precursors for the V-group elements. The growth conditions were optimized for obtaining sharp interfaces and negligible ordering effects in the cation sublattice. Accounting for the temperature dependence of the Fermi energy and the calculated confining energy $\left(10\mathrm{meV}\right)$ of the heavy holes in the wells, a valence band offset $\Delta E_V=(356\pm 5)\mathrm{meV}$ was derived from the temperature variation of the resonance frequency at which the isothermal conductance over frequency $G\left(\omega \right)∕\omega$ curves show a maximum. The experimental uncertainty of this result is significantly low if compared with the wide range $(240–400\mathrm{meV})$ of the previously reported $\Delta E_V$ values. By considering the band gap difference between InGaP and GaAs, a conduction band offset $\Delta E_C=119\mathrm{meV}$ was estimated. The accuracy of the experimental procedure and the reliability of the main assumptions of the admittance spectroscopy measurements were accurately checked. The obtained results were discussed in light of the large and growing amount of literature data by taking into account the influence of the growth conditions on the physical properties of the $\mathrm{In}\mathrm{Ga}\mathrm{P}∕\mathrm{Ga}\mathrm{As}$ quantum wells.

Figure 1

Sketch of the $n^{+}\mathrm{Ga}\mathrm{As}\parallel \mathrm{In}\mathrm{Ga}\mathrm{P}∕\mathrm{Ga}\mathrm{As}\left(\mathrm{MQW}\right)\parallel p^{+}\mathrm{Ga}\mathrm{As}$ structures.

Figure 2

Equilibrium band bending diagram of the $p^{+}∕\mathrm{MQW}∕n^{+}$ structure together with the equivalent electrical circuit.

Figure 3

Typical experimental $C\left(\omega \right)$ (full symbols) and $G\left(\omega \right)∕\omega$ (empty symbols) curves taken at different temperatures in a $p^{+}∕\mathrm{MQW}∕n^{+}$ structure.

Figure 4

Comparison of direct current-voltage curves measured at $T=300\mathrm{K}$ in a $p^{+}∕\mathrm{MQW}∕n^{+}$ junction (○) and in the corresponding $p^{+}∕\mathrm{In}\mathrm{Ga}\mathrm{P}∕n^{+}$ reference sample (●). In the latter case, the series resistance is about 2 orders of magnitude lower.

Figure 5

(a) $C\left(\omega \right)$ (full symbols) and $G\left(\omega \right)∕\omega$ (empty symbols) curves taken at the same temperature of $340\mathrm{K}$ but with different reverse biases $V_R$. (b) Resonance frequency $\varpi$ as derived by curves of Fig. 5a plotted vs the function $F\{C\left(0\right),C\left(\infty \right)\}$, given by Eq. (4). Here, $C\left(0\right)$ and $C\left(\infty \right)$ are the experimental capacitances of (a).

Figure 6

Carrier profiles obtained by $C\left(0\right)$ vs $V_R$ measurements in the $p^{+}∕\mathrm{MQW}∕n^{+}$ samples with 40 and 25 MQWs.

Figure 7

Energy levels and valence band profile for a QW in the undepleted $p$-type MQW region. $E_F$ is the Fermi energy. $E_{VW}$ and $E_{VB}$ are the valence band top in the GaAs well and in the InGaP barrier, respectively. $E_1^{hh}$ is the deeper energy level for the confined holes.

Figure 8

$Y\left(T\right)$ function vs ${\left(K_{B}T\right)}^{-1}$. Open circles and full dots are data taken in the samples with 40 and 25 MQWs, respectively. The slope gives $(E_1^{hh}-E_{VB})=346\pm 5\mathrm{meV}$.

Figure 9

Temperature dependence of $(E_F-E_1^{hh})$ by considering (a) the occupancy of the first four hole subbands with the Fermi-Dirac statistics (○) or Bolzmann statistics (+) and (b) the occupancy of only the $E_1^{hh}$ subband with Bolzmann statistics. The calculations are performed for $p_s=1.27\times {10}^{11}{\mathrm{cm}}^{-2}$.