Crater depth

In non-highly focussed laser desorption ionisation, employing spot sizes in the range of 50-200 pm in diameter, the surface is deformed by an ablation volume of about 1 pm3 per pixel per laser pulse. But this ablated volume is spread over a large desorption area leading to ablation depths of the order of a few nanometres. In laser microprobing, the same ablation volume leads to ablation crater depths in the micrometer range. 

The value of S will be a complex function of the sample composition, and of the incident ions and their energy, mass and angle of incidence. If the crater depth can be measured independently, the above equation can be used to obtain the value of S. 

Depth scale calibration of an SIMS depth profile requires the determination of the sputter rate used for the analysis from the crater depth measurement. An analytical technique for depth scale calibration of SIMS depth profiles via an online crater depth measurement was developed by De Chambost and co-workers.103 The authors proposed an in situ crater depth measurement system based on a heterodyne laser interferometer mounted onto the CAMECA IMS Wf instrument. It was demonstrated that crater depths can be measured from the nm to p,m range with accuracy better than 5 % in different matrices whereas the reproducibility was determined as 1 %.103 SIMS depth profiling of CdTe based solar cells (with the CdTe/CdS/TCO structure) is utilized for growing studies of several matrix elements and impurities (Br, F, Na, Si, Sn, In, O, Cl, S and ) on sapphire substrates.104 The Sn02 layer was found to play an important role in preventing the diffusion of indium from the indium containing TCO layer. 

Solving Eq. (29.5) for crater radius with this HOB correction yields a radius of only 0.65 ft. Following a rough rule of thumb that crater depth is about one-half the radius, this crater would be only about 4 in. deep. 

The final stage of the SIMS analysis was to quantify the profiles obtained in the initial trial. For this a standard was prepared by implanting a known dose (atoms cm ) of Li ions into the target. This was analysed by SIMS, tracking both Li and matrix ion species, and the crater depth measured by profilometry. This allows calculation of a relative sensitivity factor (RSF) which converts the Li-to-matrix ion intensity ratio into a Li concentration in atoms cm as a function of depth. When the unknown was measured, with Li and the same matrix ion signals recorded, then the RSF was applied to the signal ratio to give the Li level in the unknown. 

The sudden increase in crater depth observed during high irradiance (> 10 W/cm ) laser ablation of silicon [17], which has been ascribed to phase explosion, can be used to establish a new threshold the threshold irradiance for phase explosion. This threshold depends on two laser parameters, viz. beam spot size and wavelength. The larger the beam size and the longer the incident wavelength are, the higher is the laser irradiance required to cause phase explosion. 

The rapid increase in crater depth above the threshold irradiance for phase explosion correlates with a significant increase in signal intensity. The ratio of crater volume to signal intensity, which represents the entrainment efficiency, remains the lowest at laser irradiances slightly above the phase explosion threshold. Such a ratio, however, increases at irradiances well above the threshold (> 10" W/cm ). 

The depth of crater formed at one location increases at a decreasing rate with successive drops. If crater depth is plotted vertically against number of drops plotted horizontally, the curve joining the points eventually will become asymptotic to the horizontal axis. These data can be used to determine when drops at one location become economically ineffective. 

In the SIMS technique, an oxygen or cesium ion beam incident on the sample, sputters atoms from the surface. Either negatively or positively charged ions are mass analyzed and their density displayed as a function of sputter time. By using calibration standards, the density is calibrated as concentration/cm, and by measuring the sputter crater depth/ the time axis is converted to a distance axis, giving a dopant concentration vs. depth plot. 

The procedure of the Fth evaluation according to Eq. 6 is restricted to bulk samples. For deep cavities, the measurement of the absolute crater depth with the help of an optical microscope is difficult. Additionally, w0 has to be determined, e.g., by means of the moving edge method and F0 has to be calculated employing Eq. 5. This technique requires a substitution of the sample by a razor blade, which might lead to experimental uncertainties. 

Also, the method how the ablation parameters are acquired can have a pronounced influence on the results. The ablation rate can be defined either as the depth of the ablation crater after one pulse at a given fluence, or as the slope of a linear fit of a plot of the ablation depth versus the pulse number for a given fluence. Very different ablation rates can result from the two different measurement methods. This is especially the case for materials where ablation does not start with the first pulse, but after multiple pulses, or if the ablation crater depth after one pulse is too small to be measured. The process that occurs if ablation does not start with the first laser pulse is called incubation. It is related to physical or chemical modifications of the material by the first few laser pulses, which often results in an increase of the absorption at the irradiation wavelength [32,33], for example, the formation of double bonds in poly (methylmethacrylate) (PMMA). Incubation is normally observed only for polymers with low absorption coefficients at the irradiation wavelength. 

These models describe a sharp ablation threshold and a logarithmic increase of the ablation crater depth with the number of laser pulses, but the Arrhenius tail is not accounted for [3,5,30,45,46]. A linear dependence can be described with models that consider the motion of the ablation front, but ignore the screen effects caused by the plasma plume. 

SIMS is used for quantitative depth profile determinations of trace elements in solids. These traces can be impurities or deliberately added elements, such as dopants in semiconductors. Accurate depth prohles require uniform bombardment of the analyzed area and the sputter rate in the material must be determined. The sputter rate is usually determined by physical measurement of the crater depth for multilayered materials, each layer may have a unique sputter rate that must be determined. Depth prohle standards are required. Government standards agencies like NIST have such standard reference materials available for a limited number of applications. For example, SRM depth profile standards of phosphorus in silicon, boron in silicon, and arsenic in silicon are available from NIST for calibration of SIMS instmments. P, As, and B are common dopants in the semiconductor industry and their accurate determination is critical to semiconductor manufacture and quality control. 

Engel OG. (1966) Crater depths in fluid impacts. J. Appl. Phys., 37(4) 1798-1808. 

Impact strength of the ferrocement is essential for such applications as boat hulls, container walls and ballistic panels. It was tested by several authors, e.g. Grabowski (1985), with drop hammers, Charpy hammers and air gun projectiles. The results of comparative tests are expressed in crater depth or perforation characteristics and failure energy. The failure energy increases linearly with the wall depth and specific surface of the reinforcement. In Figure 3.4 tensile strength and Charpy impact strength are compared as functions of the specific surface of reinforcement. 

The dependence of crater radius and crater depth upon the depth of burst for a 1 kilo ton explosion in dry soil is shown in Fig. 9.5. Also shown are the range of... dimensions possible from a surface burst to the approximate maximum for an... 

Fig. 4.17 SEM micrographs of poly crystal nickel with (a) an unsputtered polished surface and with sputtered crater bottoms using (b) O2 to a crater depth of 1.5-2.2 pm, (c) O2 with 1 X 10 Torr oxygen backfill to a depth of 1.5-1.8 pm and (d) Cs to a depth of 1.9-2.5 pm. Single crystal Ni is sputtered with O2 to depths of (e) 2.9 pm and (f) 4 pm...

As the name suggests, this method records the crater depth by scanning a stylus over the surface of the substrate analyzed, i.e. in much the same way that contact mode AFM is carried out (AFM is covered in Appendix A. 11.4). Stylus profilometry is applied in contact mode after the removal of the sample from the SIMS instrument. Although stylus profilometry only provides a line scan, it is capable of a depth resolution precision approaching 1 nm. An example of a typical stylus profilometry scan output is portrayed along with a top-down image of the three craters measured in Figure 5.24. Note Only one crater would typically be measured at a time. 

The sputter rate (in units of A/nA.s or nm/nA.s) is then defined by dividing the crater depth (in units A or nanometer), by the sum of the sputter time (in units of seconds) and the primary ion current used in forming the respective crater (in units of nanoampere). This definition assumes a uniform sputter rate over the region (depth) sputtered, hence is only applicable to a specific matrix type. Such measurements should be carried out for each crater to ensure utmost in precision (averaging procedures are often employed to reduce statistical scatter). In the case of multilayered structures, surface profilometry measurements should be carried out once each subsequent layer is sputtered, such that sputter rates pertaining to each of the different layers can be de-convoluted (recall from Section 3.2.2 that sputter rates are dependent on many parameters including those defining the matrix). 

Interferometric methods operate by splitting a monochromatic coherent beam (all waves in phase) of hght into two parts. One part is directed at the surface from which it then reflects and the other part directed at some reference (optically smooth mirror) from which it reflects. When the two parts are recombined, their waves will either interfere in a constractive manner (waves in phase) or destructive manner (waves out of phase). As constructive interference enhances the amplitude of the combined beam, whereas destructive interference suppresses the amplitude, an interference pattern will be prodnced that is dependent on the crater depth. This interference pattern can also be nsed to derive the surface topography of the sputtered crater in both of the spatial dimensions, with the result being an AFM-like three-dimensional topographic image. 

The crater depth value is included with Relation 5.5 as aerial dose values are used, i.e. this allows for the conversion of atoms/cm to atoms/cm. Of note is the fact that a constant sputtering rate is assumed during the course of the depth profile. As any variation in the sputter rate will result in the introduction of errors, implants should remain within a particular film, i.e. should not cross any interface and should not exist within the surface transient region (discussed within Section 3.3.2.2). If a multilayered substrate is to be examined, matrix-matched reference samples for each layer must be examined, with the associated RSF derived. In highly simplified... 

The most efficient method is to measure the crater depth co after sputtering time to, (e.g., by optical interferometry, laser measurements 37] or stylus pro-filometry), so as to derive directly r = Zo/ro- If a multilayer system is studied, the sputtering rate in each layer must be determined. The usual method included in most software, consisting of the conversion of the sputtering time into equivalent TaiOs thickness, is not suitable. 

---