A variety of effects can lead to short-range attachment barriers in thin-film growth. While it has been predicted that the exponent $\chi$ which describes the dependence of the island density $N$ on deposition rate $F$ in the submonolayer regime (where $N\sim F^{\chi }$) crosses over from the diffusion-limited value $i/(i+2)$ (where $i$ is the critical island size) in the absence of an attachment barrier to the attachment-limited value $2i/(i+3)$ for a strong attachment barrier, this prediction has not been confirmed. Furthermore, the dependence of the effective value of $\chi$ on the barrier strength and ratio $R=D/F$ (where $D$ is the monomer hopping rate) has not been studied. Here we consider the effects of attachment barriers in irreversible growth ($i=1$) for both the case of a barrier to island nucleation and attachment as well as that of an island attachment barrier but no nucleation barrier. Our results indicate that in both cases the effective value of $\chi$ increases with increasing R to a maximum value ${\chi }_{\max }\left(R_{\max }\right)$ which depends on barrier strength before decreasing very slowly toward the diffusion-limited value. In addition, both ${\chi }_{\max }$ and $R_{\max }$ increase as the barrier strength increases. The results of self-consistent rate-equation calculations are also presented and good agreement is found with our simulations. We also present a scaling analysis for the dependence of $R_{\max }$ on the barrier strength for arbitrary critical island-size $i$ and good agreement is found with our simulation results for the case in which there is both a nucleation barrier and a barrier to island attachment.

多种影响会导致薄膜生长中的短程附着障碍。虽然已经预测指数$\chi$ 它描述了岛屿密度的依赖性 $N$ 沉积速率 $F$ 在亚单层状态（其中 $N～F^{\chi }$) 从扩散极限值交叉 $\mathrm{一世}/(\mathrm{一世}+2)$ （在哪里 $\mathrm{一世}$ 是临界岛大小）在没有附着限制值的附着障碍的情况下 $2\mathrm{一世}/(\mathrm{一世}+3)$对于强大的依恋障碍，这一预测尚未得到证实。此外，有效值的依赖性$\chi$ 关于阻隔强度和比例 $\mathrm{电阻}=D/F$ （在哪里 $D$是单体跳跃率）尚未研究。在这里，我们考虑了依恋障碍对不可逆增长的影响（$\mathrm{一世}=1$) 对于岛形核和附着壁垒的情况以及岛附着壁垒但没有成核壁垒的情况。我们的结果表明，在这两种情况下，有效值$\chi$ 随着 R 增加到最大值 ${\chi }_{\mathrm{最大限度}}\left({\mathrm{电阻}}_{\mathrm{最大限度}}\right)$这取决于势垒强度，然后非常缓慢地向扩散极限值下降。此外，两者${\chi }_{\mathrm{最大限度}}$ 和 ${\mathrm{电阻}}_{\mathrm{最大限度}}$随着屏障强度的增加而增加。还给出了自洽率方程计算的结果，并且发现与我们的模拟非常吻合。我们还提供了对依赖关系的缩放分析${\mathrm{电阻}}_{\mathrm{最大限度}}$ 关于任意临界岛尺寸的势垒强度 $\mathrm{一世}$ 并且在同时存在成核障碍和岛附着障碍的情况下，与我们的模拟结果非常吻合。