## 3 Results and Discussion  
### Contact-Based Transfer Mechanism  
Since the polyimide is the main driver of the contact-based material deposition within the cLIFT, a characterization of the observed expansion behavior has to be proposed to predict the material deposition (e.g., deposited spot volume \(V_{T}\) and width \(d_{T}\)). In addition to the process separation (Figure 1), we further observed that the polyimide expansion rate decreases under continuous laser irradiation until a maximum and stable blister/structure is reached. Consequently, the occurring structure implies that the polyimide accumulates energy over time \(E(t)\) (stored energy) until a final equilibrium is reached that cannot be surpassed (Equation (1)). This behavior strongly resembles the mechanistic analogue of a charging capacitor. For simplicity, the equilibrium energy is only considered to depend on the laser irradiance and lasing duration. Other potential influencing parameters, such as heat transfer and thermal expansion of the polyimide, are not explicitly characterized, since they should implicitly influence the accumulation of stored energy. Furthermore, the distance between irradiated locations is experimentally determined to be large enough to neglect the effect of residual heat. \[E(t\geq t_{\text{eq}})=E_{\text{eq}} \tag{1}\]  
The stored energy at \(t+\tilde{t}\) is approximated up to the first order by Equation (2), which leads to Equation (3) after evaluating \(\tilde{t}\) at \(t_{\text{eq}}\). Within this equation, a material (polyimide) dependent parameter \(k\) is introduced, which specifies the ability of the material to accumulate energy per unit time. This parameter indicates the proportion of storable energy \(E_{\text{eq}}-E(t)\) that the material can accumulate over a distinct time frame (i.e., increase in stored energy \(E(t)\) over time). This captures the observed effect of continuously decreasing polyimide expansion toward the maximum achievable expansion. Utilizing the initial temporal boundary condition \(E(t=0)=0\), which captures the initial zero-expansion, Equation (3) can be solved to obtain Equation (4) for the progression of the stored energy. Thus, the expansion of the polyimide can be described by the (inverse of the) exponential decay function. \[E(t+\tilde{t})=E(t)+\frac{\text{d}E(t)}{\text{d}t}\tilde{t} \tag{2}\]  
\[\frac{\text{d}E(t)}{\text{d}t}=k(E_{\text{eq}}-E(t))\quad\text{with }k\in\mathbb{R} \tag{3}\]  
\[E(t)=E_{\text{eq}}(1-e^{-k\tilde{t}}) \tag{4}\]  
The expansion of the polyimide volume \(V_{P}\) is a result of the mechanical work induced by this stored energy (\(E(t)\propto V_{P}(t)\)). Furthermore, as an increasing polyimide expansion (increasing \(V_{P}\)) induces an increasing material deposition, the expanded and transferred volumes can be assumed to be proportional \(V_{P}(t)\propto V_{T}(t)\) to each other (neglecting higher order and non-linear terms, such as donor coating thickness, phase change, and gas expansion). To obtain a relationship for the spot width \(d_{T}\), which is another observable quantity of interest, the deposited bell-shaped volume over a circular area \(A_{T,c}\) is approximated by a characteristic height \(h_{T,c}\). For simplicity, the deposition is assumed to expand isotropically, and therefore, the characteristic height relates to the spot width via a constant, which yields Equations (5)-(7). \[V_{T}(t)\propto A_{T,c}h_{T,c}\Rightarrow V_{T}(t)\propto d_{T}^{3}\quad \text{with }A_{T,c}\approx\frac{\pi}{4}d_{T}^{2}\text{ and }h_{T,c}\propto d_{T} \tag{5}\]  
\[V_{T}(t)=\alpha E_{\text{eq}}(1-e^{-k\tilde{t}})\quad\text{with }\alpha\in \mathbb{R} \tag{6}\]  
\[d_{T}(t)=\beta(E_{\text{eq}})^{\frac{1}{3}}(1-e^{-k\tilde{t}})^{\frac{1}{3}} \quad\text{with }\beta\in\mathbb{R} \tag{7}\]  
Next to the polyimide expansion, a proportionality between the laser beam diameter and maximum contact area was observed [31], which is represented by Equations (8) and (9), assuming a circular contact and deposition area.