**2.2 (F)LIMM method**

The (Focused) Laser Intensity Modulation Method or (F)LIMM is a thermal wave method dedicated to the space charge analysis of thin dielectric films (with a thickness from 5 to 50 μm) [21, 22]. This method is originally proposed by Lang [23] in the 1980s, and the characterization of space charge distribution had been performed under volt-off after external DC voltage application. Recent development has been reported that LIMM measurement is carried out under volt-on [24]. The LIMM is much suitable to clarify the space charge characteristics in a polymer film with only several micrometer thickness, which is a typical thickness of passivation layer on a semiconductor chip. **Figure 4** shows the schematic diagram of online LIMM. A DC potential (*Vht*) is applied to the top electrode of the measuring cell through a low-pass filter. (F)LIMM currents are recorded after preamplification and extracted from noise by a lock-in amplifier. To protect a damage from an eventual breakdown of the sample, an electrical protection device was introduced at the output of the measuring cell.

The thermal gradient created by the laser beam induces periodical and local expansions that lead to relative charge displacement regarding to the electrodes within the irradiated volume. Varying the laser beam modulation frequency, one can control the depth of thermal diffusion and then calculate its effect on the total current signal. Finally, a mathematical treatment allows charge density profile reconstruction in the direction of the sample thickness. A modulated laser beam of a frequency *f* heating a surface *S* of a top electrode sputtered on a dielectric nonpolar sample of thickness *L*, to which an additional DC voltage *Vht* is applied, the fundamental (F)LIMM equation for the complex current *I*(*f*) can be expressed by [24]:

$$I(f) = -j\frac{2\pi f}{L}(a\_x - a\_c)eS\left[\int\_0^L E(z)T(z,f)dz + \frac{V\_{ht}}{L}\int\_0^L T(z,f)dz\right] \tag{1}$$

where *z* is the direction normal to the sample, *α<sup>z</sup>* is the coefficient of thermal expansion (K�<sup>1</sup> ), αε is the coefficient of thermal dependence of the dielectric permittivity (K�<sup>1</sup> ), *ε* is the permittivity, *Ei*(*z*) is the internal electric field along *z*axis (V.m�<sup>1</sup> ), and *T*(*z*,*f*) is the simulated spatial variation of the temperature versus frequency.

**Figure 4.** *Schematic diagram of (F)LIMM [24].*

*Behavior of Space Charge in Polyimide and the Influence on Power Semiconductor Device… DOI: http://dx.doi.org/10.5772/intechopen.92165*
