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6.10 for 2 pn-diodes with abrupt junction, one of which is made of Si and the

another is made of GaAs, with NA =1017cm- 3 and ND = 2 10

14cm- 3 in both cases:

a) Find the barrier voltage

b) Find the maximun electric field and the space charge region width.

c) Plot the space charge, potential, and electric field distribution along the

diode axis

Solution:

a) The barrier voltage in both cases is found. For Si we obtain

Vdiff=Vt lnNAND

ni2

= 0.65V, and for GaAs the result is Vdiff =1.12V

b) The maximum electric field in the junction is found by setting x = 0.

Subtituting the values for Si it is seen

EO =qNAeReO

dp

where the space charge region width in the p-semiconductor is found

dp(Si) =2e VdiffNDqNA

1

NA +ND

= 4.110- 7cm

dp(GaAS) =2e VdiffNDqNA

1

NA +ND

= 5.710- 7cm

Subtuting the values into the formula for the peak electric field we find

that in Si it is equal to EO = 6.4 103(V / cm)and for GaAs SO = 7.9 10

3(V/ cm) .

c) The distributions of the space charge, potential, and electric field areidentical to the figure 6-5 c - e

9.10

A BJT is operated at f= 750MHz(and with the S-parameters as follows:

S11 = 0.56 - 78O,S12 = 8.64 122

O ,S21 = 0.05 33O,S22 = 0.66 - 42

O). Attempt to

stabilize the transistor by finding a series resistor or shunt conductance for the

input and output ports.

Solution

In this problem, the values ofS12 and S21should have been reversed

S12 = 0.05 33O,S21 = 8.64 122

O. We first investigate and find that the transistor

does not meet the requirements of unconditional stability.

In fact,

k=1 - S11 2 - S22 2 + D 2

2 S12 S21= 0.6322, D = 0.5435

Then we plot the input and output the stability circuit then we got the result

gin'=

2.0

Gin'=gin

'

50W = 0.04Sfor the output resistance

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rout'

= 0.8Rout'

= 0.75 50W = 37.5W Using this resistance value, we can re-check the stability requierments by first

converting the output index into ABCD network representation followed by pre-

multiplication by converted S-parameter of the transistor. The resulting new set

of ABCD parameters is reconverted into a new parameter form and check for

stability below

The result is now : K=1.018 >1 and D = 0.5435