th The German University in Cairo Electronics 5 Semester Faculty of Information Engineering & Technology Semiconductors (Elct 503) Electronics Department Fall 2014
Problem Set 3
1- a) Find the resistivity of intrinsic Si at 300 k. b) If a shallow donor impurity is added to the extent of 1 atom per 108 Si atoms, find the resistivity.
2) An n-type semiconductor sample has an electron mobility of 500 cm2/V.sec. . Calculate the number of collision an electron suffers under the effect of a voltage difference of 200 volts, if the sample has a length of 2 cm . Assume m* = 0.2 mo .
3) An exactly compensated semiconductor is a one in which the mobile carrier concentrations are equal. Assuming complete ionization of all dopants, compute the conductivity for the exactly compensated Si at 300 K in which: 13 -3 a) NA = ND = 10 cm . 20 -3 b) NA = ND = 10 cm .
4) a- Find the value of the voltage source applied that causes the tilt shown in the energy band diagram.
b- Find the electric field and the carrier concentration given that T= 300 K 10 -3 ni = 1.5× 10 cm 0.1 e.v. EC 0.3 e.v.
EF
EV 3 cm
5) A semiconductor material is doped such that its doping concentration NA(x) varies with x as follows:
-xL NA(x) = NAo e x 0 L
≤ ≤ Where NA(x) >> ni for 0 x L. Express the hole diffusion current as a function of x and sketch this function.
6) Consider an n-type semiconducting sample 0.2 cm2 in cross-section and 3 cm long in which the electron concentration is 1015 cm-3.
a) Find the electron current density and the current if the applied voltage of 2V causes the electrons to drift at a velocity 900 cm/s. b) Calculate the electron mobility. c) Assuming the hole mobility equals half the electron mobility, calculate the hole current density. Compare the hole and electron current densities. 10 -3 (ni = 1.5 ×10 cm ).
7) The electron concentration in silicon decreases linearly from 1016 cm-3 to 1015 cm- 3 over a distance of 0.10 cm.The cross-sectional area of the sample is 0.05 cm-2. The electron diffusion coefficient is 25 cm2/s.Calculate the electron diffusion current.
15 -3 8) The hole concentration is given by p= 10 exp (-x/LP) cm for x>0 and the 14 exp -3 electron concentration is given by 5×10 (+ x /Ln) cm for x<0.The values of -4 -3 Lp and Ln are 5×10 cm and 10 cm respectively .The hole and electron diffusion coefficients are 10 cm2/s and 25 cm2/s respectively. The total current density is defined as the sum of the hole diffusion current density at x = 0 and the electron diffusion current density at x = 0. Calculate the total current density.
9) The total current in a semiconductor is constant and is composed of electron drift current and hole diffusion current. The electron concentration is constant and is equal to 1016 cm-3.The hole concentration is given by p= 1015 exp (-x/L) cm-3 x>0 2 where L=12µm .The hole diffusion coefficient is Dp = 12 cm /s and the electron 2 2 mobility is µn = 1000 cm /V.s. The total current density is J= 4.8A/cm .
Calculate: a) The hole diffusion current density versus x b) The electron current density versus x. c) The electric field versus x.
10) In n-type silicon,the Fermi energy level varies linearly with distance over a short -3 range.At x = 0, EF - Ei =0.4 e.v. and ,at x =10 cm EF - Ei =0.15 e.v. a) Write the expression for the electron concentration over the distance. 2 b) If the electron diffusion coefficient is Dn = 25 cm /s, calculate the electron diffusion current density at x = 0 and x = 5× 10-4 cm.
16 -3 11) A semiconductor,in thermal equilibrium ,has a hole concentration of Po = 10 cm and an intrinsic concentration of ni =1010 cm-3 . The minority carrier lifetime is 2× 10-7 s. a) Determine the thermal-equilibrium recombination rate of electrons b) Determine the change in the recombination rate of electrons if an excess electron concentration of n = 1012 cm-3 exists.
12) a) A sample of semiconductor has a cross-sectional area of 1 cm2 and a thickness of 0.1cm. Determine the number of E-H-p that are generated per unit volume per unit time by the uniform absorption of 1 watt of light at a wavelength of 6300 Aο .Assume each photon creates one E-H-p
b)If the excess minority carrier lifetime is 10µs, what is the steady-state excess carrier concentration.
13) A silicon sample with 1015donors is uniformly optically excited at room temperature such that 1019 cm-3 E-H- are generated per second. Find the separation of quasi Fermi levels and the change of conductivity upon shining the 2 2 light. [µn = 1300 cm /V.s. ,DP = 12 cm /s , = 10 µsec]
14) In a p-type Silicon bar with cross-sectional area 0.5cm2 and acceptor concentration 1017 cm-3.We inject holes such that the steady-state excess hole concentration is 5×1016 cm-3 at x = 0.What is the steady-state separation between 2 -10 EFP and EC at x = 1000 A ? [µp = 500 cm /V.s. , p = 10 sec]
15) A silicon sample is doped with 1015 cm-3 donors. Calculate the excess electron and hole concentration required to increase the sample’s conductivity by 15% at room temperature. What carrier generation rate is required to maintain these 10 -3 excess concentrations? [ µp = 0.3 µn , p = 1 µsec , ni = 1.5 × 10 cm ]
16) A bar of intrinsic silicon of 2 cm length has a 10 V battery connected across it. a) How long does it take an electron to drift the length of the bar? b) How much energy does an electron deliver to the lattice during this transit?
17) Consider the shown n-type semiconductor sample. The sample is maintained at room temperature and uniformly doped at 1014 cm-3 . Minority carriers are injected into the sample from terminal 1 . An electric field of 50 V/cm is applied between terminals 1 and 2 . The electric field moves the injected carriers a distance of 1 cm in 40 µs. a) State weather the minority carriers are electrons or holes. b) Determine the direction of the electric field vector (from 1 to 2 or from 2 to 1) . c) Calculate the minority carrier mobility. d) Calculate the minority carrier diffusion constant. (Hint for either electrons or holes D/µ = KT/e). e) Calculate the majority carrier mobility if a current density of 1.2 A/cm2 passes through the sample between 1 and 2 ( Hint : neglect currents due to minority carriers.) 3
1 2
4
State whether the following statements are true or false:
1) The electron mobility in a semiconductor is independent on temperature. 2) The conductivity of a semiconductor decreases with increasing temperature. 3) The conductivity of an intrinsic semiconductor increases exponentially with temperature. 4) Diffusion in semiconductors can occur in the absence of an externally applied electric field. 5) The electron mobility in a semiconductor is inversely proportional to the electrons effective mass. 6) The effective mass of a hole is higher than that of an electron. 7) The drift velocity of an electron increases linearly with the magnitude of the applied electric field at high electric fields. 8) For the same hole and electron concentration gradients (dn/dx = dp/dx )in a semiconductor, electron diffusion current = hole diffusion current. 9) Diffusion motion is due to the presence of an electric field. 10) If the same electric field is applied to two Si samples having the electron concentration distributions n(x) shown below, then sample (1) will have a higher drift current density at x= 0 than sample (2).
11) For the two Si samples having the electron concentration distributions n(x) shown above, then sample (1) will have a higher diffusion current density at x= 0 than sample (2). 12) Light emitting diodes (LEDs) are made from indirect gap semiconductors e.g. Si. 13) Semiconductors can be used for temperature measurements. When designing a semiconductor thermistor for this purpose to be used at room temperature, it is better to use an extrinsic semiconductor. 14) The electron mobility increases as the electron mean free time decreases.
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