中原大學九十一學年度碩士班入學招生考試─電子系固態組，基本電磁學

中原大學九十一學年度碩士班入學招生考試

91年 4月12日　9:00 ~10:30　　電子系固態組	誠實是我們珍視的美德，我們喜愛「拒絕作弊，堅守正直」的你！
科目：基本電磁學

Four-point probe measurement as shown in Fig.(1) is frequently used to determine the sheet resistance

of the thin semiconductor layer. The probes are generally arranged in-line with equal probe spacing, S1=S2=S3=S. Two outer probes 1 and 4 carry DC-current I, and regard it as the sheet (or surface) current

flowing between two terminals of the thin layer. However, other two inner probes 2 and 3 are connected to a voltmeter for measuring the voltage drops ΔV across them. To derive is the sheet resistance

of samples:

=4,532．ΔV/I ; where π/ln2=4,532 (15%)

Hall measurement is extremely useful in practice in the determination of type and doping concentration of semiconductors. Consider a rectangular n-type semiconductor bar of length L, width w and thickness d as shown in Fig.(2). The sample is vertically subjected to the magnetic induction

Bo and applied to voltage Vo that causes a steady current Io to flow in the x direction.

(a) Indicate the direction of the Hall electric field Ey and its value in terms of current density Jx. (5%)

(b) Determine the electron (or donor) concentration Ne in relation to Io, Bo and the measured Hall-voltage VH. (10%)

(a)	Prove the steady current that satisfies the Laplace's equation V=0 (5%)
(b)	An infinitely long coaxial cable, as shown in Fig.(3b), the lossy dielectrics of permittivity ε and conductivity σ is filled inthe space (a≦r≦b)between inner and outer radii of a and b, respectively. Use the Laplace's equation to solve the product of resistance R and unit length l, i.e. =R．l=ln(b/a)/σ (15%)
(c)	Determine the capacitance per unit length . (5%)
(d)	If the coaxial line is shown in Fig.(3d) with radii-ratio of b=3a. Two dielectric layers of different permittivities ε1=4ε0 and ε2 =2ε0 , but having the same dielectric strength Em are filled in the region of a≦r≦b . The safety factor of 25% is considered due to the voltage surges or environmental accidents.
	(i)	To design is the thickness of two layers, i.e. determination of c-value. (5%)
	(ii)	Find the rating voltage(maximum operating voltage) Vmax. (10%)

Consider the parallel-plate transmission line with perfectly conducting plates of large extent, separated by a distance of d meters.As shown in Fig.(4), an alternating surface current density

in the z direction flows on the conductor surface:

(z, t)=

Jo．cos﹝ω(t-z/c)﹞ ; ﹝A/m﹞

(a) Find an expression for the electric field, and determine the voltage between the plates, for d=0.1m and Jo=1 A/m (8%)

(b) Use the continuity equation to find an expression for the surface charge density

(z,t) (7%)

The electric field of a transverse electromagnetic wave(TEM-wave) guided within a lossless coaxial transmission line along the z axis is expressed in cylindrical coordinate as

;

where β=ω

; μ and ε are, respectively the permeability and permittivity of dielectric material, and a and b are the inner and outer radii of the coaxial line.

(a) Find the corresponding

in phasor form. (7%)

(b) Write the time-domain expression for

(r,z,t) and

(r,z,t) (8%)

--- END---