Universal fluctuations in the growth of semiconductor thin films

Abstract

Scaling of surface fluctuations of polycrystalline CdTe/Si(100) films grown by hot wall epitaxy are studied. The growth exponent of surface roughness and the dynamic exponent of the auto-correlation function in the mound growth regime agree with the values of the Kardar-Parisi-Zhang (KPZ) class. The scaled distributions of heights, local roughness, and extremal heights show remarkable collapse with those of the KPZ class, giving the first experimental observation of KPZ distributions in $2+1$ dimensions. Deviations from KPZ values in the long-time estimates of dynamic and roughness exponents are explained by spurious effects of multi-peaked coalescing mounds and by effects of grain shapes. Thus, this scheme for investigating universality classes of growing films advances over the simple comparison of scaling exponents.Comment: 5 pages, 3 figure

A KPZ Cocktail-Shaken, not Stirred...

“…With an ensemble average over snapshots in the experimental system, the task is to aggregate the statistics of ω = (w 2 − w 2 )/σ 2 w 2 , which is the centered, rescaled, dimensionless order-one fluctuating statistical variable at the core of the universal roughness distribution-P RD (ω). Recently, this metric was applied in 2+1 KPZ Class vapor deposition experiments involving organic [88] and semiconductor [90] thin films. In the former instance, Halpin-Healy and Palasantzas compared experimental data directly to their numerical 2+1 KPZ Euler RD, using WBC "box"-sizes ξ KP Z , for which the statistics were stationary, yielding nearly constant quantities.…”

“…Nevertheless, there has been recent progress on 2+1 KPZ Class extremal-height numerics, where explicit comparison has been made with MRH patchPDFs obtained from thin-film stochastic growth experiments [88,90]. An interesting question there then concerns the higher-dimensional analog of the 1+1 KPZ Class gaussian F-Airy tail; at first glance, the 2+1 KPZ Euler MRHD [88] with (s, k)=(0.884,1.20), though surely different, bears some familial resemblance to the Majumdar-Comtet distribution.…”

“…Importantly, the present KPZ Renaissance has inspired a renewed interest in the 2+1 KPZ problem, as well as other dimension-dependent issues, such as the existence of a finite UCD, and using Wilsonian renormalization group methods, hopes of elucidating the full KPZ phase diagram [83]. Universality of the 2+1 KPZ Class and its associated limit distributions (i.e., higher-dimensional analogs of TW-GUE, TW-GOE and BR-F 0 ) have been well-characterized [84,85,86,87], along with universal spatial and temporal correlators [88,89], supplemented by secondary KPZ "patch" PDFs [88,90]. On the mathematical side, the transmission has shifted into hyperdrive; a rapidly accelerating moveable feast-e.g., [91,92,93,94,95,96,97,98,99,100].…”

Scaling of local roughness distributions

“…This feature led Paiva and Reis [20] to propose the calculation of LRDs in the KPZ growth regime in 2 + 1 dimensions. Recently, improved estimates of this KPZ LRD were shown to match those of semiconductor [21,22] and organic [23] films grown by different methods. Moreover, simulation of the KPZ equation in 1 + 1 dimensions showed agreement with accurate experimental data from turbulent liquid-crystal in five orders of magnitude [24].…”

“…[20] suggested a universal LRD for several KPZ models in 32 ≤ r ≤ 128 (measured in lattice units) after growth times 4000 ≤ t ≤ 8000 (measured in number of deposition trials). These values partly guided the choice of box size in the study of semiconductor films [21,22]. On the other hand, Halpin-Healy and Palasantzas argued that universal LRDs should be measured under the condition r ≪ ξ, where ξ is the lateral correlation length [23].…”