Kuntjoro Pinardi

Stresses and strains in lattice-mismatched stripes, quantum wires, quantum dots, and substrates in Si technology

We discuss recent advances made in the theory and measurements of stresses and strains in Si‐based heterostructures containing submicron‐ and micron‐size features. Several reports on theoretical as well as experimental studies of stresses in the substrates with local oxidation of silicon structures on the surface have been published recently. With the advent of GeXSi1−X strained layers and stripes extensive studies of both the stripe and the substrate stresses have also been made. Unlike the previous calculations and analytical models, recent finite element (FE) calculations take into account the coupling between the film–substrate stresses without making the approximation that the interface is rigid or that there is no variation of stresses in the stripes in a direction perpendicular to the interface. The results of these calculations have been compared with the analytical models and limitations of the analytical models have been pointed out. Micro‐Raman measurements of the stresses in the stripes, quant...

Critical thickness and strain relaxation in lattice mismatched II–VI semiconductor layers

Critical thickness hc has been calculated for capped and uncapped lattice mismatched II–VI semiconductor epilayers. Both the old equilibrium theory and the improved theory have been used. The calculated values are compared with the experimental data on epilayers of several II–VI semiconductors and alloys. The observed values of hc are larger than the calculated values, a result similar to that observed with GeSi and InGaAs strained layers. The discrepancy is attributed to the difficulty in nucleating the dislocations. Strain relaxation in layers with thickness h>hc is also calculated. Observed strain relaxation in ZnSe layers grown on (100) GaAs shows good agreement with the equilibrium theory. In other cases, the observed relaxation is sluggish and the residual strain is larger than the calculated value. Many authors have observed that strain near the surface of the II–VI epilayers is small and increases as the depth increases. We describe an improved model to explain this observation. The agreement betw...

Stresses in strained GeSi stripes and quantum structures: calculation using the finite element method and determination using micro-Raman and othermeasurements

Stresses in heterostructures containing lattice mismatched GeSi stripes (of half-width l and thickness h) deposited on Si substrates are calculated using the finite element (FE) method. It is shown that the stress distribution is a unique function of l/h, it does not depend on l and h separately or on the substrate dimensions if the substrate dimensions are sufficiently large. Ratio EE= E1/E3 of the Youngs moduli (E1 is the Youngs modulus of the stripe and Es is the Youngs modulus of the substrate) changes from 0.78 for Ge/Si to nearly 1 when the Ge fraction in the layer is small. The effect of this change on the stress distribution is calculated and is found to be small but not negligible. Stress distribution in the surface layer of the stripe is a weak function of RE. Therefore values of stresses given in this paper can also be used for GaAs-based heterostructures. Analytical models are not capable of giving accurate values of the stresses in these structures. These values show that as h increases and l is kept constant, stress at a constant height zin the stripe decreases and at a constant depth z in the substrate increases, first rapidly and then slowly. It saturates and becomes practically constant for l/h < 0.5. Finite element calculations of circular mesas (quantum dots) are also reported. Experimental values of stresses in stripes, quantum wires and quantum dots are found to be in good agreement with the values calculated by the FE method.

A method to interpret micro-Raman experiments made to measure nonuniform stresses: Application to local oxidation of silicon structures

A method is described to calculate the Raman spectrum from a nonuniformly strained sample taking into account the effects that arise due to finite depth of penetration and diameter of the laser beam. Both the parallel and the focused beams are considered. The case of stress in a Si substrate decaying monotonically with depth z (rapidly near the interface and slowly at larger depths) is considered in detail. The predicted Raman shifts are found to be sensitive to both the distribution of stress and to the absorption coefficient α for the laser light wavelength used. It is found that light scattered from distances much larger than 1/α still contribute significantly to the observed Raman spectrum. The observed shift in the peak of the spectrum does not correspond to the stress close to the interface. If the stress decays more rapidly than the light intensity, the Raman line that originates from the unstrained lower part of the substrate dominates. For transparent material (α=0) and unfocused beam the Raman spectrum consists of only the unstrained Si line; the contribution to Raman line from the strained interface region is completely masked. For measurements of stresses near the interface short wavelength light with an absorption depth of 5–10 nm is recommended. The calculated and observed Raman shifts in a local oxidation of silicon (a processing technique for isolation) with polysilicon buffer between the nitride stripe and the Si substrate are compared. The agreement between the calculated and the observed Raman shifts is very good. The salient points of our approach which enabled us to obtain this agreement are: We took into account the effects of laser beam width, penetration depth, and focusing; we included the stresses in the polysilicon layer and near the polysilicon/silicon interface, and we included contributions from large depths.A method is described to calculate the Raman spectrum from a nonuniformly strained sample taking into account the effects that arise due to finite depth of penetration and diameter of the laser beam. Both the parallel and the focused beams are considered. The case of stress in a Si substrate decaying monotonically with depth z (rapidly near the interface and slowly at larger depths) is considered in detail. The predicted Raman shifts are found to be sensitive to both the distribution of stress and to the absorption coefficient α for the laser light wavelength used. It is found that light scattered from distances much larger than 1/α still contribute significantly to the observed Raman spectrum. The observed shift in the peak of the spectrum does not correspond to the stress close to the interface. If the stress decays more rapidly than the light intensity, the Raman line that originates from the unstrained lower part of the substrate dominates. For transparent material (α=0) and unfocused beam the Raman s...

Raman spectra of strained quantum wires

We have calculated the Raman spectrum of strained wires sandwiched between Si layers. Because of the relatively large width and penetration depth of the laser beam the volume sampled by the beam is large. Using the strain components calculated by the finite element method, the strain induced Raman shifts and Raman spectra were calculated at each point in the volume sampled. The final spectrum obtained by superposing these spectra shows excellent agreement with the observed spectrum. The strain induced shift measured by micro Raman in nonuniformly strained solids does not give strain values in a straightforward manner.

Effect of elastic constants on the stresses in stripes and substrates: a 2D FE calculation

We report results of the finite element (FE) calculations of strains and stresses in stripe-substrate (S-S) heterostructures for several values of Youngs moduli ( for the stripe and for the substrate), stripe halfwidth l and its thickness h. The normalized stress ( is the stress in the large area layer where effect of edge induced relaxation is absent) in both the stripe and the substrate depends only on the ratio and not on the individual values of and . Numerical values of are calculated by the FE method for nine values of and five values of . It is found that has only a weak influence on the stress distribution. in both the stripes and the substrates decreases monotonically and approximately linearly as increases. The values reported in this paper can be used for other values of , l and h by interpolation without the need of making fresh FE calculations for each case. Experimental values of the stresses determined from the luminescence and the micro-Raman data support strongly the conclusion that the dependence of stress on is weak.

A REVIEW OF RECENT WORK ON STRESSES AND STRAINS IN SEMICONDUCTOR HETEROSTRUCTURES

We first discuss the work on strain and critical thickness of large area lattice mismatched epilayers of GeSi, InGaAs and II-VI semiconductors. A summary of Finite Element (FE) calculations of stresses in stripe-substrate heterostructures is then given. Calculated stresses for novel stripe designs are also given. The results are then applied to interpret experiments. Raman and luminescence experiments on stripes of GaAs/Si, GeSi/Si and InGaAs/GaAs, Raman experiments on LOCOS structures and on GeSi quantum wires and quantum dots and luminescence experiments on InGaAs quantum wires are included in the discussion.

Measurement of nonuniform stresses in semiconductors by the micro-Raman method

Micro-Raman measurements are performed with a focused laser beam. Because of its finite diameter ({approximately}1 {micro}m) and penetration depth, the laser beam samples a large volume of the sample. In a nonuniformly strained sample, spectra originating from different points are different. Therefore the observed spectrum depends on both the strain distribution in the sample and the adsorption coefficient of the laser light. The authors describe a method to calculate the Raman spectra taking these factors into account. The calculated spectra show excellent agreement with the experimental results.

Measurement of Residual Stress in Thin Films Using the Optical Microprobe

The laser optical microprobe is a powerful tool for studying the spatial variation of residual stress exploiting the sensitivity of Raman and luminescence spectra to the local stress. Here, using two different examples, we consider some issues determining the depth and lateral resolution of these techniques and their use in stress mapping in thin films. The first example involves Raman microprobe studies of a strained GeSi alloy quantum wire structure. The second example involves stress mapping using chromium ion luminescence in alumina films grown by high temperature thermal oxidation of NiAl single crystals.