Influence of Vertical and Radial Distances of Nano-Resistors in SSI-LEDs on Light Intensity Distributions
Authors: Shukla Abhinav , Kuo Yue 
Published: December 2020

Broad-band white light emission phenomena from a novel type of solid-state incandescent light emitting device (SSI-LED) was reported by Kuo's group [1-4]. The device is made from the dielectric breakdown of a metal-oxide-semiconductor (MOS) capacitor with a high-k gate dielectric deposited over a p-type Si wafer [1-4]. The device emits light from the thermal excitation of the nano-sized conductive paths in the high-k stack upon the passage of a large current. This blackbody radiation phenomenon is similar to that of the incandescent light bulb [4]. In this paper, the light intensity distributions from nano-resistors with various vertical and radial distances are investigated by simulation.
Equation 1, also known as Stefan-Boltzmann law [5, 6], quantifies the total energy radiated per unit surface area of a black body across all wavelengths per unit time j* that is directly proportional to the fourth power of the black body's thermodynamic temperature T, i.e.,

j* = eσT4
(1)
where e is the emissivity of the object (e = 1 for perfect black body) and σ is the Stefan–Boltzmann constant. Therefore, the total power P radiated from an object of surface area A can be given by the following equation

P = Aj* = eσT4
(2)
Assuming that the nano-resistors formed in the high-k stack behave as point light sources, we can calculate the intensity at a given vertical distance from the nano-resistors. The following equation, i.e., the intensity of light emitted from a point source I is inversely proportional to the square of the distance r, is used in the calculation

I = P/ 4πr2
(3)
The resultant intensity due to all the nano-resistors at any given vertical distance can then be simply obtained by scalar addition of intensity from each of the individual nano-resistors. In order to simulate the light intensity distribution from the SSI-LED, authors made some assumptions based on experimental observations. For instance, nano-resistors with cylindrical geometry are assumed to be formed and distributed randomly across the high-k gate stack [1]. Further it is assumed that all nano-resistors in a SSI-LED are of the same diameter, i.e., 100 nm. In actual, nano-resistors formed on the same device are of different sizes, i.e., the number decreases with the increase of the diameter size [4]. Previously, it has been reported that light emitted from the SSI-LED is similar to that from the conductive paths at the temperature of 4,000 K [7]. The same temperature of 4,000 K was used to calculate the total radiated power P in equation 1. Although it was reported earlier that the temperature across the cross-section of a nano-resistor could vary with its diameter size [7], here we assume it to be constant. Moreover, the effect of thin film ITO gate on intensity of emitted light is neglected for simplifying current calculations. The Beer-Lambert Law could be used to account for the transmittance of light across ITO thin film to further improve the intensity distribution estimation.
Figure 1(a) shows the light intensity distributions of two 100 nm diameter nano-resistor sources observed at varying distance above the nano-resistor/ITO gate interface. Figure 1(b) shows the low and high magnification images of a SSI-LED with the ZrHfO gate dielectric. It can be clearly seen that at the low magnification, the whole SSI-LED appears as a single light dot, i.e., individual nano-resistors are unresolvable [1]. At the high magnification, which is similar to the short distance case, peaks of the two light dots are observable. This study will be extended in 3-D to better understand the light distribution. The result will be discussed in detail. Moreover, the effect of the radial separation distance of the nano-resistors on the light intensity distribution will also be presented and discussed.
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[7] A. Shukla and Y. Kuo, ECS Trans., Submitted, April 2020.

Figure 1