在15 nm GaAs/5 nm AlAs单量子阱的GaAs阱层中间，分别进行不同浓度剂量的铍受主的δ-掺杂。铍受主在量子阱层中的扩散浓度分布，由扩散方程数值解出。高温下扩散在GaAs阱层中的Be受主将发生电离，成为带负电荷的受主离子，同时也向量子阱价带的子带中引入空穴。带负电荷的扩散受主离子和价带子带中的空穴，它们都是带电粒子在GaAs阱层中按库伦定律激发电场。相比较而言，对于无掺杂同结构量子阱，在空穴的薛定谔中增加了一个额外的微扰势，从而使无掺杂的量子阱价带的子带有所改变。在有效质量和包络函数近似下，通过循环迭代方法,数值求解了既满足薛定谔方程又满足泊松方程的空穴波函数，找出了自洽、收敛的空穴子带的能量本征值。计算发现考虑到这种额外微扰势，重空穴基态子带hh的能量有一个电子伏特变化，并且随着掺杂受主剂量的增加，重空穴基态子带hh向着价带顶红移，计算结果与实验测量符合得很好。

A GaAs/AlAs quantum well, with a 15 nm-thick GaAs well surrounded by a 5 nm-thick AlAs barrier, is δ-doped with Be acceptors of various doping levels at the well center. The ionized acceptor diffused profiles within the quantum well are solved by the diffusion equation. The additional potential, due to both the ionized acceptor diffused profile and hole distribution in valence-band subbands, is incorporated into the quantum well potential. The self-consistent solution and converged hole energy eigenvalue for the Schrdinger′s and Poisson′s equations are looked for by an iterative method. It is found through calculations that the energy of the heavy-hole ground state hh has changed by about 1 meV, while it is red-shifted towards the valence-band top with increasing Be acceptor doping concentrations. The calculated results are in a good agreement with experimental results.