CMOS/BiCMOS ULSI: Low Voltage, Low Power (Prentice Hall by Kiat-Seng Yeo

By Kiat-Seng Yeo

CMOS/BICMOS ULSI offers cutting-edge BiCMOS low-voltage, low-power layout concepts for ULSI and giga-scale integration engineering, protecting method integration, gadget modeling, and characterization. detect the most recent MOS and bipolar types; breakthroughs in copper metallization, isolation, and deep submicron procedures; and new methods to designing good judgment gates, latches, and flip-flops.

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85) k‘ ,q +[g(q) -k lIf(k’)[l - f(k)]6kf,k+q6[E(k’)- E(k) - b ( S ) ] - d q ) f ( k ) [ l - f(k‘)lbkl,k+qb[E(k’)- E(k) - fiw(q)] -[g(q) -k lIf(k)[l - f(k’)16kk‘,k-q6[E(k‘) - E(k) -k b ( q ) l ) , skipping the indices v and y for simplicity. Obviously, the expression s(q)g(q)f (k) - f (k’)16kt,k+q6LE(k‘) - E(k) - fiw(q)l gives the rate of collisions scattering electrons of the state k to state k’ by absorbing a phonon of the state q. 86) s(q)g(q) k,k‘ x f ( k ) [ l - f(k’)]6k’,k+q6[E(k’)- E(k) - b ( q ) l , when including an additional factor 2 for the electron spin degeneracy.

Due to the enhanced functional integration of such modern electron devices, the traditional drift diffusion models [Markowich et al. (1990)I fail in describing the occurring high-field and sub-micron phenomena. Therefore, the semi-classical Boltzmann transport equations must be applied for dealing with phenomena of hot electrons [Ferry (1991)]. Moreover, nonequilibrium longitudinal-optical phonons have been found to strongly affect the electron distribution function (hot phonon phenomena) in polar semiconductors [Vaissiere et al.

R, Y = 1,2,. . ,S with the boundary values x 1 / 2 = -1, x s + 1 / 2 = 1, q 1 p = 0 and qR+1/2 = qmax. Here, qmax is chosen so that g(qmax)can be considered undisturbed by the POP interaction with electrons. 26) x=l y=l demanding 42 E I," = (qX-l/2,qx+1/2) and x y E Iy" = ( X y - l / 2 , X y + 1 / 2 ) . 10). 27) The R x S evolution equations for the coefficients rXyare found by the following strategy. The phonon BTE is integrated over the cell D x y . 25), we obtain an evolution equation for the function G .

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