Geometrical Layout Effect on Light Intensity Distribution in SSI-LED
Authors: Shukla Abhinav , Kuo Yue 
Published: July 2021

Like the light emission phenomenon in an incandescent light bulb, Kuo’s group have reported a broad-band white light emission from a new type of solid-state incandescent light emitting device (SSI-LED) (1-4). The device is a simple metal-oxide-semiconductor (MOS) capacitor with a high-k gate dielectric deposited over a p-type Si wafer (1-4). On hard breakdown of the dielectric, nano-sized conductive paths (or, nano-resistors) are formed in the high-k stack. Large passage of current through these conductive paths results in light emission due to the thermal excitation. SSI-LEDs have been shown to have very high color rendering index (CRI) of up to 97.9 (4). This indicates that the light emission process from the conductive paths is close to black body radiation phenomenon. This fact along with temperature estimates made for nano-resistors using simple energy balance-based calculations has been previously utilized to perform light intensity distribution calculations over SSI-LED. (5) In this paper, the authors adapt a similar approach and study the effect of geometrical layout of nano-resistors on the emitted light intensity distribution from SSI-LED at higher magnifications.
Stefan-Boltzmann law quantitates the total energy radiated per unit surface area of a black body across all wavelengths per unit time j^* and is directly proportional to the fourth power of the black body's temperature T. If a black body of surface area A is radiating energy to the surroundings at temperature Tc, the net power radiated can be accounted as given in equation
P=Aeσ(T4-Tc4) (1)
where e is the emissivity of the object and σ is the Stefan–Boltzmann constant. Under the assumption that the nano-resistors formed in the dielectric act as point light sources, emitted light intensity at certain distance from the nano-resistors can be calculated by following inverse-square law. The resultant intensity from all the nano-resistors at any given point in space is simply the scalar addition of radiation intensity from each of the individual nano-resistors, i.e., if I1, I2...., IN are the radiation intensities due to N nano-resistors at a point in space then resultant intensity,
Iresultant = I1+ I2+I3.........+ IN

Reasonable assumptions are made for various physical parameters while performing radiation intensity distribution calculations. For example, nano-resistors with circular cross-sections were assumed to form in the high-k dielectric. Three different diameter sizes of nano-resistors are considered – 20 nm, 50 nm and 100 nm. Four different layout configurations (linear, triangular, square, and face-centered square) of nano-resistors are studied for localized light intensity distribution calculations based on the two-dimensional Bravais lattice symmetries. Intensity calculations are done for two cases. In the first case, nano-resistors of same sizes are considered in all the different geometrical layout configurations. In the second case, larger sized nano-resistors of diameter 100 nm are formed in the vicinity of smaller sized nano-resistor keeping the geometrical layout to be same. The light absorption by ITO gate in the SSI-LED is accounted using Beer-Lambert’s law.
The geometrical layout of the nano-resistors formed in the SSI-LED affected the local light intensity distribution at higher magnifications and will be presented and discussed in detail. The simulated distribution could be correlated to the experimentally observed light dot patterns formed in SSI-LED at higher magnifications, as shown in figure 1 (6).
1. Y. Kuo and C.-C. Lin, Appl. Phys. Lett., 102, 031117 (2013).
2. Y. Kuo and C.-C. Lin, ECS Solid-State Lett., 2, Q59 (2013).
3. Y. Kuo and C.-C. Lin, Solid-State Electron., 89, 120 (2013).
4. C.-C. Lin and Y. Kuo, Appl. Phys. Lett., 106, 121107 (2015).
5. A. Shukla and Y. Kuo, Prime 2020, Abstract #H04-1965 (2020)
6. C.-C. Lin, PhD. Thesis, Texas A&M University, College Station, Texas (2014).

Figure 1