The Nature of Light - Part 5 (Wave Packet and Semiconductors)

The last concept that I want to talk about is the wave-packet. The wave-packet is a superposition of waves. This concept brings the particle and wave properties of light together. A wave-packet consisting of a plane wave in one dimension is:

The Gaussian wave-packet and its Fourier transform. (Goldin, 82)

The G(k) function is Gaussian distribution function. The smaller gets the more F(x) spreads out along x axis. When becomes a delta function, F(x) becomes a sinusoidal function, in which it will comply with the classic light wave laws. F(x) and G(k) are Fourier transform pairs.

So far we have just reviewed a very brief history of optics from Newton to Einstein. In the next part I like to review some materials on MOSFET devices technology and design.

Photoelectric Effect in Semiconductors

There are two major types of semiconductors that use and work with the photoelectric effect, diodes and photocells. The transistor with the GaAs substances will do very well with the photoelectric effect. These types of transistors are called direct transistors because in their recombination process photon emits as result of electrons moved to a less energy level.

The photon emitted in recombination process in a direct semiconductor. (Pierret, 109)

As soon as monochromatic light strike the surface of the semiconductor some of it reflects and the rest of it has intensity of I₀. This intensity decays as far the photon penetrates the semiconductor.

The intensity of light at the distance x from the surface is I. After a photon transfer its energy to the semiconductor, pairs of electron-hole will be created. The rate of photogeneration / is , which is the essence of created current in the material and is function of depth of light penetration and the frequency of the light.

If n and p are number of generated minority carrier, holes in the sea of electrons then:

;

is the rate of photogeneration/ at the surface of semiconductor where the light strikes first.

Therefore if there is not any other effect than light on the semiconductor the generated current is directly proportional to the photogeneration rate. For example in a N-type semiconductor if the minority carrier is p and Dp is the exceeded minority carriers as a result of light then:

is the minority lifetime in from generation to recombination process. As a result of quantitative solution and boundary conditions to the photogeneration problem we can formulate the following equation for the excess minority carriers, in here holes.

The current that is produced as a result of photogeneration process can be calculated as follows:

A is the area, L is the length and q is the charge as a result of generated electron-hole pairs. Also: