Sspd_chapter1_modern physics-foundation of solid state physics_part  (Page 5/5)

Gordon Moore had predicted at the inception of Integrated Circuit Technology that the packing density of CMOS devices will double every 18 months i.e. every one and a half year . That precisely has been followed till date.

Integrated Circuit technology was simultaneously invented by Jack Kilby [Appendix XII ] of Texas Instrument and Robert Noyce [Apendix XIII ] of Fairchild in 1959. Eventually Jack Kilby was awarded Nobel Prize in 2000 for the same. I. C. Technology [50 years Journey of IC Technology-Prologue ] started its journey in 1961 when the first RTL logic was commercially marketed. At that time there were only twenty transistors on the Chip. Today in 2005 there are 1 billion transistors on Pentium “Extreme Edition” 840 Dual Core Chip with a clock rate 3.2GHz.

This hectic pace of microminiaturization has been maintained solely due to commensurate development in Solid State Device Technology [Apendix I, Table I.1, of 50 years I.C. Journey ] .

The development in Solid State Device Technology is the result of the theoretical understanding of Solid State of Matter. And the theoretical understanding has been made possible due to Quantum Mechanics.

So it is imperative that we start our text on Solid State Physics and Devices with a good qualitative and quantitative understanding of Quantum Mechanics.

1.1. MAX PLANCK AND QUANTUM THEORY.

In 1860 Maxwell [Appendix XIV] propounded the four classical equations describing Electro-Magnetic Waves namely:

1. Divergence of Electric Flux Density= Charge Density,
2. Curl of Magnetic Field Intensity= Electric Current Surface Density + Displacement Current Density;
3. Curl of Electric Field Intensity = -Rate of change of Magnetic Flux Density;
4. Divergence of Magnetic Field Intensity = 0;

Almost simultaneously Heinrich Hertz [ibid] generated Electromagnetic Waves and detected the same through a loop antenna. This particular experiment paved the way for the invention of Radio for which both Marconi [Appendix XV] and J.C.Bose [Appendix X]] are credited.

The theoretical explanation of Black Body Radiation kept eluding the Scientists at the close of 19 ^th Century. Rayleigh-Jean formulation could explain the longer wavelength spectral density distribution but on the shorter wavelength side it led to Ultra-Violet catastrophe. On the other hand Wien Formulation could explain the shorter wavelength spectral density distribution but failed to fit the remaining portion of the distribution curve. The Black Body radiation curve is described in Figure (1.1).

Fig.1.1. The Spectral Density Distribution of Black Body Radiation at different Temperatures: T 1 >T 2

At this time of hopelessness, a simple assumption by Max Planck enabled him to arrive at the correct theoretical understanding of Black Body Radiation Distribution. His assumption was that matter is composed of oscillators. Every oscillator has a characteristic frequency ν ₀ and that oscillator will absorb or radiate energy packets of hν ₀ , 2 hν ₀ ,3 hν ₀ ,…… only. Here h is the Planck’s Constant=6.62×10 ^-34 J-seconds. The essence of this assumption is the quantum nature of Electromagnetic Waves which was the basic proposition of Newton also who talked about the corpuscular nature of light which is also Electromagnetic Waves. According to this quantum nature , Electromagnetic Waves of frequency ν always contains an energy packet of hν Joules. Therefore if a monochromatic light source of frequency ν is emitting energy at the rate of P watts then P/( hν) number of energy packets are being emitted per second. More appropriately P/( hν) number of quanta or photons are being emitted by the source per second. If the power of this source is increased then the number of photons per second will increase but the energy packet per photon will remain constant.

Thus quite unwittingly Max Planck gave birth to the Quantum Theory of Electromagnetic Waves..

Einstein used this Quantum Theory to explain Photo-Electric Effect.

Wien’s Displacement Law[Appendix XVI] states :

λ m (wavelength of maximum intensity)= Ω/T ;

Classical Physics has no analytical value of Ω but Quantum Physics correctly predicts it to be : Ω= ch/(4.9651k)= 3×10 -3 mK ;

Substituting this constant in Wien’s Displacement Law: λ _m = (3×10 ^-3 /T) m;

At 3 K, λ _m = 0.1 cm. The Cosmic Microwave Background Radiation(CBR), which we will deal with in Section 1.13 , has exactly this 3K blackbody radiation characteristics.

Stefan Boltzman’s Law[ibid] states:

R(Watt per m 2 ) = e.σ.T ^4 ;

σ = Stefan’s Constant;

e= emissivity ( depends on the nature of the radiating surface);

e=1 means a black body radiator. A black body is a perfect absorber. It is a perfect radiator also.

e= 0 means a perfect reflector. It does not absorb and hence does not radiate.

This law is also known as Fourth Power Law. T is the absolute temperature of the cavity walls.

From Quantum Theory of Black-Body Radiation:

u(total energy density of the radiation in a cavity) = a.T ^4

Classical Physics has no analytical value of σ but Quantum Mechanics gives the value as:

a(Universal Constant) = 8π ⁵ k ⁴ /(15c ² h ³ ). This value conforms to the experimental values.

e (emissivity) = 0 to 1.

σ (Stefan’s Constant) = ac/4 = 5.670×10 ^-8 W/(m.K ⁴ );

end of part1