**4.2. Rectangular focal spot arranged along the target radius**

**4.1. Ways of increasing the target utilization efficiency**

to the laser beam, (c) rectangular focal spot along the radius of the target.

improvement in the utilization efficiency.

target utilization.

There are several known solutions to the problem for improving the target utilization efficiency in PLD of thin films. The targets employed for deposition may have polished surfaces. In this case, up to 75% of the target material may be lost [5]. There are cardinal approaches, which, however, substantially complicate the deposition installation suggesting the computer‐ controlled scanning of the large target surface by a laser beam (**Figure 12a**) or moving the target in two perpendicular directions relative to the fixed laser beam (**Figure 12b**). In this case, the material ablation occurs from 90% of the target surface providing in this way a noticeable

160 Applications of Laser Ablation - Thin Film Deposition, Nanomaterial Synthesis and Surface Modification

**Figure 12.** Geometry of the PLD method with: (a) laser beam screening the surface of target; (b) target motion relative

The suggestion in [6] is simple to realize: it is assumed that the laser beam is split into four parts, each of them performing material ablation from a certain area of the rotating target. Thus, a wider plasma jet of the evaporated material is formed (which facilitates the uniformity of the film thickness) and ablation occurs from a larger surface of the target. From the viewpoint of enhancing the target utilization efficiency, this approach is simply an increase in the focal spot dimensions. However, the grooves on the rotating target will still be produced with the following negative consequences. A more reasonable suggestion was patented [7, 8]. The authors complicated the mechanism of target rotation in such a way that the target rotates around two parallel axes. In this case, the laser beam circumscribes a cycloid rather than a circle over the target surface, which will increase the target utilization efficiency. Unfortunately, this approach has also a serious disadvantage (see below), which hinders obtaining high values of

A most simple solution is, evidently, a uniform distribution of laser radiation over the entire surface of a fixed target. Such a distribution can be obtained, for example, with raster‐focusing systems [9]. Nevertheless, as mentioned above, such a scheme cannot be used for depositing multicomponent compounds, because overheating of the target will affect the composition of the latter. Thus, the known methods of enhancing a PLD process aimed at increasing the target utilization efficiency either noticeably complicate the installation or do not solve the problem completely. In the present work, we suggest a simple solution to the problem for attaining a

One possible solution to the problem for increasing the target utilization efficiency is a rectangular spot of the laser beam arranged along the radius of the rotating target, where the focal spot of width *L* has the length of at least the target radius (**Figure 12c**). The center of one focal spot side coincides with the target rotation center O, and the axis of symmetry coincides with the target radius (**Figure 13**). At a first glance, it may appear that it is a simple and effective solution, because ablation of the target material will occur from the entire surface. But the quantity of the substance evaporated from a unit area is proportional to the energy passed on it. The sites of focal spot closer to the target center will affect (per single round) a smaller area than those residing far from the center. Consequently, the target material at its center will be consumed faster than at periphery.

Let a laser beam fall onto the rotating target, which has the form of a disk with radius *R* and thickness *h*0, forming the rectangular focal spot of width *L* arranged along the target radius. In time *t*0, the target executes *N* revolutions and the laser burns a hole at the center of the target. How much of target volume is ablated in this case?

According to **Figure 13**, one should consider two domains of the target surface: inside the circle of radius *L*/2 and outside it [10]. When the target rotates at a constant angular velocity *ω*, all the points inside the circle of radius OA = *L*/2 are exposed to laser radiation during half the process duration (*t*0/2), because for these points the focal laser spot is a semicircle. In other words, inside the rectangular focal spot of width *L* the trajectory of any point residing closer than *L*/2 to the center of rotation (point O) is a semicircle. For example, point D on the target surface is subjected to laser radiation as long as it follows semicircle DF (**Figure 13**). Point B residing at a distance longer than *L*/2 is subjected to laser radiation until it reaches point C having passed the arced path BC.

**Figure 13.** Scheme of the rectangular focal spot directed along the radius of the rotating target [10].

By denoting the rate of target evaporation *σ* (the thickness evaporated per unit time), from the condition of burning the target to a throughout hole, we may write

$$h\_0 = \sigma t\_0 / \,\, \mathcal{D}, \sigma = \mathcal{D}h\_0 / t\_0 \tag{1}$$

The points of the target surface outside the circle of radius *L*/2 at a distance *r* from the center are exposed to laser radiation during the time interval Δ*t* (a single revolution of target) so that after *N* revolutions the target thickness reduces by the value ,

$$h = \sigma \Delta t \\ N = \sigma N \left| \overline{B} \overline{C} \right| / v = \sigma N \left| \overline{B} \overline{C} \right| / (\alpha r), \tag{2}$$

where *v* is the linear speed of point B, ˘ = 2 = 2 × arc sin /2 is the length of arc BC, and = 2 0.

Then at *r* ≥ *L*/2, the reduction of the target thickness will be

$$h = \frac{2h\_0 \text{arc}\sin\left(L/2r\right)}{\pi} \tag{3}$$

Dependences of *h*(*r*) for various *L* are given in **Figure 14**. For the points 0 *< r* ≤ *L*/2, we obtain *h* = *h*0. The volume of the ablated target material is determined by the rotation of curve *h*(*r*) around axis *h*:

**Figure 14.** Target thickness *h* versus radius *r* under PLD in the rectangular focal spot geometry [10].

$$V = \pi h\_1 R^2 + \pi \int\_{h\_1}^{h\_2} \left[ \frac{L}{2 \sin \left( \pi h / \sqrt{2} h\_0 \right)} \right]^2 \,\mathrm{d}h,\tag{4}$$

where ℎ1 <sup>=</sup> 2ℎ0arc sin/2 / and *h*2 = *h*0. This entails

By denoting the rate of target evaporation *σ* (the thickness evaporated per unit time), from the

The points of the target surface outside the circle of radius *L*/2 at a distance *r* from the center are exposed to laser radiation during the time interval Δ*t* (a single revolution of target) so that

where *v* is the linear speed of point B, ˘ = 2 = 2 × arc sin /2 is the length of arc BC,

Dependences of *h*(*r*) for various *L* are given in **Figure 14**. For the points 0 *< r* ≤ *L*/2, we obtain *h* = *h*0. The volume of the ablated target material is determined by the rotation of curve *h*(*r*)

*h* (3)

/ 2, 2 / (1)

(2)

0 0 00 *h t ht* = =

 s

condition of burning the target to a throughout hole, we may write

after *N* revolutions the target thickness reduces by the value ,

Then at *r* ≥ *L*/2, the reduction of the target thickness will be

2 arc sin / 2 <sup>0</sup> ( ) p<sup>=</sup> *h Lr*

**Figure 14.** Target thickness *h* versus radius *r* under PLD in the rectangular focal spot geometry [10].

2

*h*

= + ê ú

*<sup>L</sup> V hR <sup>h</sup>*

2 1

 p

p

1

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( )

p

ê ú ë û ò

é ù

0 d , 2sin / 2

2

*h h* (4)

and = 2

around axis *h*:

0.

s

162 Applications of Laser Ablation - Thin Film Deposition, Nanomaterial Synthesis and Surface Modification

$$V = 2h\_0 R^2 \text{arc } \sin\left(\frac{L}{2R}\right) + h\_0 L R \left(1 - \frac{L^2}{4R^2}\right)^{1/2}.\tag{5}$$

One can see that the volume depends on three parameters: the target height *h*0, the target radius *R*, and the width of the laser beam *L*. Because the value of the target material utilization efficiency is *η* = *V*/*V*0, where *V*0 = π*h*0*R*<sup>2</sup> is the target volume prior to ablation, in view of Eq. (5), we obtain

$$\eta = \left[ 2 \text{arc } \sin\left(\frac{L}{2R}\right) + LR^{-1} \left(1 - \frac{L^2}{4R^2}\right)^{1/2} \right] \pi^{-1}. \tag{6}$$

The value of *η* depends only on two parameters *L* and *R*. Dependences of *η*(*R*) for various values of *L* are shown in **Figure 15**. One can see that at a fixed parameter *R,* the volume of the ablated part of the target is greater at longer *L*.

**Figure 15.** Target utilization efficiency versus target radius at various laser beam spot widths [10].

The expression for the target material utilization efficiency may be simplified. By introducing the parameter *k* = *L*/*R,* we may write Eq. (6) in the form

$$\eta = \left[ 2 \text{arc} \sin \left( k \,/ \, \text{2} \right) + k \left( 1 - k^2 \,/ \, 4 \right)^{1/2} \right] \pi^{-1} \tag{7}$$

Recall that the calculations are performed for the case *R* ≥ *L*/2. At 0 *< R < L*/2, the equality *η* = 1. **Figure 16** presents the dependence *η*(*k*).

**Figure 16.** Target utilization efficiency *η* versus *k*. The dashed line refers to approximation [10].

One can see that at *k <* 1, it is well approximated by the straight line according to the formula

$$
\eta = 0.004 + 0.617k \approx 0.6k \tag{8}
$$

Thus, we have the simple expression for target utilization efficiency with a sufficiently good approximation. Obviously, for experimentally actual values of *L* and *R* where k < 1, the value of *η* will not be greater than 0.5.

Note that the method suggested in patents [10, 11] has a similar drawback. The cycloidal trajectory described by the focal laser spot on the surface of the target arising due to the rotation around two parallel axes will also result in more intense material evaporation from the central part of the target and reduced utilization efficiency.

### **4.3. Focal spot in the form of a sector**

The consideration of the problem stated above suggests its cardinal solution. In the range 0 *< R < L*/2 where the focal spot is a semicircle, the equality *η* = 1 holds. But a semicircle is the particular case of a sector with the angle of 180°. The scheme of the modified PLD method is shown in **Figure 17**, which simply and cardinally solves the problem on the maximal utilization of the target material. The laser deposition installation is suggested, which differs from ordinary devices by a simple optical system placed outside the deposition chamber. It comprises two lenses and a diaphragm and provides the focal spot in the form of a sector on the target surface.

If such a focal spot coincides with a sector‐shape area on the target surface and the density of energy is uniform over the focal spot, then the surface of the uniformly rotating target will be uniformly irradiated, which will provide a uniform material ablation from the surface.

The device suggested was employed for depositing CuO and YBa2Cu3O7–δ films from the targets 10 mm in diameter by the pulses of second harmonic radiation of the Nd3+:YAG laser with the repetition rate of 20 Hz. The optical system provided the focal spot of laser radiation on the target in the form of the sector with an angle of 60° and the energy density of 4 J cm–2. Variations in the target thickness were within *±*2% both before deposition and after five deposition cycles lasting for 45 min. One may assert that the device suggested enhances the target material utilization efficiency up to *η* = 1.

**Figure 17.** Geometry of the PLD method with the focal spot in the form of a sector: (1) laser, (2) optical system, (3) diaphragm with a hole, (4) deposition chamber, (5) target, and (6) laser focal spot in the form of the sector coinciding with the sector of the rotating target surface [10].
