Dear Dr. Almafraji: Surface roughness increases  the efficiency of the heat to electricity  conversion factor in nanometric thin film.  Efficiency of the thermoelectric materials is characterized by ZT the figure of merit, which is given by  ZT=   sig S2T/L. Where  sig  and   La  are the electric and thermal conductivities , respectively.  S  is the Seebeck coefficient. The electronic parts of these conductivities are linearly connected. Therefore only the phonon part of the thermal conductivity can be manipulated almost independently without effecting very much on the electrical counter part.  In thin films,  the phonon scattering cross section of  the rough surfaces dominates  all other bulk scattering agents (point defects, dislocation, grain boundaries etc) due to the fact that it has higher weight factor in the sum of surface and bulk contributions.  . Therefore,    ZT  may show enhancement if one has rough surfaces in nano-size thin films: Further more  this enhancement  increases inversely  with the  expectation value of  (mean wave length)  the surface roughness index. 

In my opinion, the increase in roughness in general should lead to an increase in the effective length of the sample and hence to increase the heat capacity and the resistance of the film.

Dear Dr.Skvortsov;  Thermal [W/ (m.K) and electrical [1/ (ohm.m)] conductivities are specific quantities, their values are independent from the dimensions and the shape of the material under questions. Phonon part of the surface thermal resistivity increases (conductivity La decreases) with the surface roughness. According to the formula I have cited  previously ZT  which is  inversely proportional with the thermal conductivity, therefore it  increases with the surface roughness!!!  

Dear Dr. Oğurtani!

Firstly, in my answer, I'm not talking about the specific values of the parameters that I have mentioned. Secondly, I'm not talking about the thermal conductivity. I speak about a sample thermal capacity which depends on its linear dimensions.

For the case under discussion is important for us not the specific heat, and the heat capacity of the sample (film). Measured and the effect on the parameters of the device it was she! The question is posed is clear: there are two equal-sized substrates made of the same material but with different surface finishes. Will the same heat capacity of sputtered films on them?

Dear Dr. Skvortsov, I think you  and I have missed few article published in Nature related to the affects of surface roughness on ZT. Dear Dr. Skvortsov, going around the Google I have found few experimental results, which confirm my argument why and how the surface roughness effects on the ZT. But no one has made any attemp like us  to give plausible arguments to justfy their findings.

1)Enhanced thermoelectric performance of rough silicon nanowires,

Allon I. Hochbaum1,5, Renkun Chen2,5, Raul Diaz Delgado1, Wenjie Liang1, Erik C. Garnett1, Mark Najarian3, Arun Majumdar2,3,4 & Peidong Yang1

1) Nature 451, 163-167 (10 January 2008) | doi:10.1038/nature06381; Received 7 June 2007; Accepted 9 October 2007

2)Surface Roughness Effects on Phonon Transport in Silicon Nanowires,

Jongwoo Lim †∥, Kedar Hippalgaonkar §∥, Sean C. Andrews †‡∥, Arun Majumdar §∥, and Peidong Yang *†‡∥

Nano Lett., 2012, 12 (5), pp 2475–2482

DOI: 10.1021/nl3005868

Publication Date (Web): April 23, 2012

Abstract ''Although it has been qualitatively demonstrated that surface roughness can reduce the thermal conductivity of crystalline Si nanowires (SiNWs), the underlying reasons remain unknown and warrant quantitative studies and analysis. These results suggest a new realm of phonon scattering from rough interfaces, which restricts phonon transport below the Casimir limit. Insights gained from this study can help develop a more concrete theoretical'' understanding of phonon–surface roughness interactions as well as aid the design of next generation thermoelectric devices.

The surface/interface roughness has been shown to influence strongly the electrical conductivity of semiconducting and metallic thin film.. The thermal conductivity KT(h) of thin films is also less than its bulk value due to heat carrier surface and grain boundary scattering, which was confirmed also by experiment. Finally, it has been shown that surface/interface roughness causes an increase of the film thermal capacitance kCl depending on specific roughness details . The surface roughness contribution is the dominant one leading to a reduction of the thermal capacitance with increasing film thickness

Dear Dr. Tarik and Dr. Leonid , thank you very much for your dissuasion that I need to discuss my results . In my research using of working gass pressure in variation lead to multi surface roughness that I was examine it by AFM. SO I WANT  TO  join this results with each other . Your both answer is wander full , also the researches you suggest is help full but my next equation is way many researchers looking for smooth surface. 

Dear Dr. Almafraji, We have published two comprehensive  papers on the surface  instability, and the healing effects of electrostatic field (electromigration)in thin films exposed to uni- and/or biaxial stresses. They may be helpful for your problem. Best regards.

The computer experiments, which are presented in above mentioned publications, clearly show that only the applied elastic compressive stresses are primary agents responsible for the morphological instability of the surface undulations through the elastic dipole tensor interactions (EDTI) but not the uniaxial tension loading in thin solid films.  Therefore any surface under the uniaxial or/and biaxial tension  may show rather smooth surface morphology  if the temperature is high enough to activate  the surface drift diffusion enhancement  by EDTI. In additional application of the electrostatic field also helps to smooth out the surface roughness and ripples through the surface electromigration in thin film.