User:Onthenet/Semiconductors

Semiconductors
In 1947, Bardeen, Brattain, Shockley, built the first semiconductor device. It was a germanium transister with a characteristic length of 20 micron. In this discussion the mathematics and physics associated with semiconductors is developed as time allows.

Schrodinger Equation
The Schrodinger Equation was introduced by Schrodinger in a paper published in 1926. It was motivated by by Bohr's discreption of matter in terms of waves. The Schrodinger equation describes the probability of a observing a particles physical properties such as position, momementum and energy.



\frac{ \partial^2{\psi} }{ \partial^2{x} } = - \frac{h }{2\pi i} \frac{\partial{\psi}}{\partial{t}} $$

Photo Electric Effect
The photoelectric effect was described by Einstein in 1905.



E = h\nu = \frac{hc}{\lambda} $$

Fermi Dirac Statistics
The probability distribution of electrons over all possible ranges of energy is given by the Ferm-Dirac distrubtion. This distribtion can be derived from quantum mechanical principals and holds for all half integer spin particles known as fermions. In the classical limit the distribution approaches the Maxwel-Boltzmann distribution.



\frac{1}{ 1 + exp ( \frac{ E-E_f }{ kT } ) } $$

Beer's Law
The attnuation of light is observed to be some fraction of the arriving number of photons for a given thickness, of a given material. In the limit as the thickness, $$ \Delta x = x - x_o $$, becomes small, a differential relation arises:



\frac{dS}{dx} = k c $$

Which has the solution,



S = S_o \exp{ k c x} $$

Taking the natural log of both sides, the absorbance, $$ A $$, can be defined,



A = \log{\frac{S}{S_o}} = k c x $$

Fick's Law
The gradient field of a some concentration, is referred to as the flux density, $$ J $$

J = - k \nabla c $$

Fick's law is observed in a number of situations. For example the transfer of heat density is given to be proportional to the negative of the gradient of temperatures. In this context, as temperature can be expressed as the derivative of energy with respect to energy, $$ \tau = \frac{ \partial U} {\partial S} $$, the analogy between concentrations, which are differentials with respec to volume, and temperature which are differentials of quantity with respect to entropy,

Fick's law in the context of particle transfer in conjuntion with the Continuity equation leads naturally to the diffusion equation.

Continuity Equation
The divergence of the gradient concentration field, is equal to the time rate of change of the concentration.

In differential form the rate of change of the conserved quantity with respect to time, with respect to some point, is negatively proportional to the diveregence of the flux, $$ J $$



\nabla J = -K  \frac{ \partial c} { dt } $$

The continuity is found in many settings, and is observed to be a conservation law. The conserved quantity may be heat, energy, charge, and so on.

Diffusion Equation
The diffusion equation captures both spatial and temporal change of a quantity, in which both the Continuity equation and Fick's law hold. The flux is determined by the gradient of the concentration. Whereas, the gradient of the flux is determined by the temporal rate of change of the concentration.

It is readily observed that substitution of Fick's law into the Continuity equation, in conjection with the requisit vector calculus identity, and the equilibrium contraint that the concenctration is constant with respect to time, gives the diffusion equation follows,



\nabla^2 c = k \frac{ \partial c }{ \partial t }

$$



\frac{\partial^2 c}{\partial^2 x} = k \frac{ \partial c }{ \partial t }

$$

When the quantity c is temperature, it is observed to be the heat equation.

PN-Junction
A pn-junction is semiconductor configuration whose behavior is characterized by the distribution of minority carriers. The minority carriers themselves seen to be goverend by the continuity equation, and solutions of the diffusion equation under time equilibrium. The diffusion equation itself being observed to be derivable from consideration of the continuity equation and Fick's Law. The simplest equation governing the pn-junction is the so called diode equation,

The excess minority carriers.

I = I_0( exp( \frac{q V }{ kT } ) - 1 ) $$

Inversion


Q_n = C_{ox}(V_G-V_T) $$

Digital Cameras
In digital cameras film is replaced with a photosensitive chip. There are two kinds of photosensitive sensitive chips. One kind is called a CCD image chip, and the other kind is called a CMOS image chip. Both kinds of chips allow for the conversion of light into electrons. In both cases this conversion is achieved by allowing light to be incident upon a silicon pn-junction. However, CMOS and CCD sensors do differ on how these collection regions relate to the rest of the analogue chain.

A CCD sensor chip has an analogue chain which transports collected photo-electrons to an amplifier, via a series of charge coupled capacitors. A CMOS sensor on the hand will typically have an amplifier at each pixel, and not required to transport the delicate electron signal to the required amplifier some greater distance away, as in the case of a CCD sensor chip.

Quantum Efficiency
Photons incident

Modulation Transfer Function
The modulation transfer function is the response to a sinusodial pattern.

Microelectronic Devices

 * 1) TK7874.Y36 1988 1e ISBN 0-07-072238-2 E.S. Yang

Semiconductor Integrated Circuit Processing Technology

 * 1) TK7874.R86 1990 1e ISBN 0-201-10831-3 W.R. RUNYAN AND K.E. BEAN

Analysis and Design of Analog Integrated Circuits

 * 1) TK7874.G688 2001 4e ISBN 0471321680   Paul R. Gray, Paul J. Hurst, Stephen H. Lewis, Robert G. Meyer
 * 2) TK7874.G688 1993 3e ISBN 0-471-57495-3 Gray and Meyer
 * 3) TK7874.G688 1984 2e
 * 4) TK7874.G688 1977 1e

Physics Of Semiconductor Devices

 * 1) TK 7871.85.S988 1981 2e ISBN 0471056618 Sze, S. M., 1936-
 * 2) QC 612.S4 S95  1969 1e

Broad

 * 1) caltech
 * 2) c linga reddy
 * 3) ukentucky
 * 4) http://www.rh.edu/~ernesto/ernesto/Courses/C_F90/mmp/Course_Outline rh.edu]

Title: Semiconductor characterization : present status and future needs / Related Names: Bullis, W. Murray, 1930- Seiler, David G. Diebold, A. C. (Alain C.) Publisher: Woodbury, NY : American Institute of Physics, 1996. Description: xix, 729 p. : ill. ; 29 cm. Subject(s): Semiconductors--Characterization--Congresses. Semiconductors--Design and construction--Congresses.

LOCATION: UW Davis. Book Stacks. Main Floor Status: In Library Call Number: TK7871.85.S4457 1996 Number of Items: 1


 * Noise in semiconductor devices : modeling and simulation /

Author: Bonani, Fabrizio, 1967- Related Names: Ghione, Giovanni, 1956- Publisher: New York : Springer, c2001. Description: xxxi, 213 p. : ill. ; 24 cm. Subject(s): Electronic noise--Mathematical models. Integrated circuits--Simulation methods. Semiconductors--Mathematical models. Series: Springer series in advanced microelectronics, 7

LOCATION: UW Davis. Book Stacks. Main Floor Status: On Loan - Due on 09/14/2005 Call Number: TK7867.5 .B65 2001 Number of Items: 1

Title: Noise and fluctuations control in electronic devices / Related Names: Balandin, Alexander A. Publisher: Stevenson Ranch, Calif. : American Scientific Publishers, c2002. Description: xxi, 390 p. : ill. ; 29 cm. Subject(s): Electronic noise.

LOCATION: UW Davis. Book Stacks. Main Floor Status: In Library Call Number: TK7867.5 .N645x 2002 Number of Items: 1

Title: Noise theory and application to physics : from fluctuations to information / Author: Réfrégier, Philippe. Publisher: New York : Springer, c2004. Description: xiii, 288 p. : ill. ; 24 cm. Subject(s): Fluctuations (Physics) Entropy (Information theory) Series: Advanced texts in physics

LOCATION: Guelph McLaughlin Book Stacks Status: On Loan - Due on 09/14/2005 copy1 Call Number: QC6.4.F58 R44 Number of Items: 1

LOCATION: UW Davis. Book Stacks. Main Floor Status: In Library Call Number: QC6.4.F58 R44 2004 Number of Items: 1

Title: Charge-coupled devices / edited by D. F. Barbe ; with contributions by W. D. Baker ... [et al.]. - Series: Topics in applied physics ; v. 38 Related Names: Barbe, D. F. (David F.), 1939- Baker, W. D. (Wilford Dean), 1942- Publisher: Berlin ;New York : Springer-Verlag, 1980 Type of Material: Book Format: Printed Material Description: ix, 180 p. : ill. ; 24 cm. - Subject(s): Charge coupled devices. ISBN/ISSN: 0387098321 Notes: Includes bibliographical references and index.

LOCATION: WLU Book Shelves Status: In Library Call Number: TK7871.99 .C45C44 Number of Items: 1

Title: A charge-coupled device with resistive polysilicon gate. Author: McGregor, Joel Montgomery. Publisher: [Waterloo, Ont. : University of Waterloo], c1989. Description: x, 113 p. : ill.

LOCATION: UW Davis. Microform Area. Main Floor Status: In Library Call Number: CA2ONUW 12089C31 Number of Items: 1

LOCATION: Annex(off-site) For delivery use "request item from TRELLIS" Status: In Library Call Number: CA2ONUW 12089C31 Number of Items: 1

Title: MODULATION TRANSFER FUNCTION OF FRONT ILLUMINATED CHARGE COUPLED IMAGING SYSTEMS. Author: HARPER, D.H. Description: : book

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Relevance: Title: NOISE MEASUREMENTS OF CHARGE COUPLED DEVICES AT LOW TEMPERATURES. Author: HALL, E.A. Description: : pamphlet

LOCATION: Annex(off-site) For delivery use "request item from TRELLIS" Status: In Library Call Number: CA2ONUW 12076N65 Number of Items: 1