DEE Semiconductor Physics and Device (I)
Take-home Quiz.
Due date: 12/20/2012
1. (10%) Assume that at room temperature the electron mobility in Si is 1300 cm2/V-s. If an electric field of 100V/cm is applied. What is the excess energy of the electron? How does it compare with the thermal energy? If you assume that the mobility is unchanged, how does the same comparison work out at a field of 5V/cm? (Excess energy = , vd is the drift velocity)
2. (20%) Consider an ideal, long-base, silicon abrupt pn-junction diode with uniform cross section and constant doping on either side of the junction. The diode is made from 1W-cm p-type and 0.2W-cm n-type materials in which the minority-carrier lifetime are tn=10-6 and tp=10-8s, respectively. (Ideal implies that effects within space-charge region are negligible and the minority carriers flow only by diffusion mechanisms in the charge neutral regions)
(a) What is the value of the built-in voltage
(b) Calculate the density of the minority carriers at the edge of the space-charge region when the applied voltage is 0.589V (which is 23xkT/q)
(c) Sketch the majority- and minority-carrier currents as functions of distance from the junction on both sides of the junction, under the applied bias voltage of part (b).
(d) Calculate the locations of the planes at which the minority-carrier and majority-carrier currents are equal in magnitude for the applied bias voltage of part (b).
3. (15%) Calculate the intrinsic carrier concentration of Si, Ge and GaAs as a function of temperature from 4Kto 600K. Assume that the bandgap is given by
where Eg(0), a and b are given by
Si: Eg(0)=1.17eV, a =4.37x10-4K-1 and b=636K
Ge: Eg(0)=0.74eV, a =4.77x10-4K-1 and b=235K
GaAs: Eg(0)=1.519eV, a =5.4x10-4K-1 and b=204K
4. (10%) Calculate the magnitude of the built-in field in the quasi-neutral region of an exponential impurity distribution:
Let the surface dopant concentration be 1018cm-3 and l=0.4mm. Compare this field to the maximum field in the depletion region of an abrupt pn junction with acceptor and donor concentration of 1018cm-3 and 1015cm-3, respectively, on the two sides of the junction.
5. (15%) By considering collector current as charge in transit (Ic=qnvdA) use the known distribution of injected electrons in the base of an npn prototype transistor biased in the active mode to solve for the base transit time tB. That is, formulate the transit time as the he integrated sum of incremental path length divided by velocity and then carry out the integration to prove thattB is given by:
(i.e. take )
6. (15%) At high current densities, as significant fraction of the voltage applied across a diode can be dropped across the neutral regions of the device. Consider the current-voltage relation for a one-sided step junction with Nd donors on the lightly doped side of the junctions. Find the current and applied voltage Va at which 10% of Va appears across the n-type neutral region for a typical integrated-circuit diode. Assume that the n-type neutral region for a typical integrated-circuit diode. Assume that the cross-sectional area is 10-5 cm2, the length of the neutral region in the n-type silicon 10mm, Nd=5x1015cm-3, and tp=1ns.
7. (15%) An Si npn transistor at 300K has an area of 1mm2, base width of 1.0mm, doping of Nde=1018cm-3, Nab=1017cm-3 , Ndc=1016cm-3. The minority carrier lifetime are tE=10-7=tB;tc=10-6s. Calculate the collector current in the forward active mode for (a)VBE=0.5V, (b)IE=2.5mA, and (c)IB=5mA. The base diffusion coefficient is Db=20cm2s-1.