# Tutorial3

**Tutorial 3**

- Consider a compensated n-type silicon at temperature T = 300K, with a conductivity of σ = 16 S/cm and an acceptor doping concentration of 10
^{17}/cm^{3}. Determine the donor concentration and the electron mobility. (A compensated semiconductor is one that contains both donor and acceptor impurities in the same region). µ_{n}is 510 cm^{2}/ V-s. - Find the electron and hole concentration, mobility and resistivity of Silicon sample at 300K for each of the following impurity concentrations. Note that electron and hole mobility is dependent on the impurity concentration. This dependency is shown in figure below. The red curve is for electron mobility and blue curve is for hole mobility.
- a) 5 * 10
^{15}boron atoms/cm^{3} ^{b) }2 * 10^{16}boron atoms /cm^{3}and 1.5 * 10^{16}arsenic atoms/cm^{3}and- c)5 * 10
^{15}boron atoms/cm^{3}, 10^{17}arsenic atoms/cm^{3}and 10^{17}gallium atoms/cm^{3}

- For a semiconductor with constant mobility ratio b = µ
_{n}/ µ_{p}> 1 independent of the impurity concentration, find the maximum resistivity (Rt_{max}) in terms of the intrinsic resistivity (Rt_{i}) and mobility ratio (b). - Given a silicon sample of unknown doping. Hall measurement provides the following information: W =0.05 cm, A = 1.6 * 10
^{-3}cm^{2}, Refer to the figure shown below. I_{x}= 2.5mA and the magnetic field (B_{z}) is 30nT (1T = 10^{-4}Wb/cm^{2}). If the hall voltage of 10mV is measured, find the Hall coefficient, conductivity type, majority carrier concentration, resistivity and mobility of the semiconductor sample. For computing resistivity you can use the graph given below. The graph plots the resistivity of p type silicon (blue) and n type silicon (red).

- Referring to the figure below consider a semiconductor bar with w =0.1mm, t = 10µm, and L=5mm. For magnetic field of 10kG (1kG= 10
^{-5}Wb/cm^{2}) as shown in the figure and current is 1mA, we have V_{AB}= -2mV and V_{CD}= 100mV. Find the type, concentration and mobility of the majority carriers.

- A semiconductor is doped with N
_{D}(N_{D}>> n_{i}) and has resistance R_{1}. The same semiconductor is then doped with the unknown amount of acceptors N_{A}(N_{A}>>N_{D}), yielding a resistance of 0.5R_{1}. Find N_{A}in terms of N_{D}if D_{n}/D_{p}=50 - Assume that in an n-type semiconductor at T = 300K, the electron concentration varies linearly from 1*10
^{18}to 7*10^{17}/cm^{3}over a distance of 0.1 cm. Calculate the diffusion current density if electron diffusion coefficient is D_{n}= 22.5 cm^{2}/s - Minority carriers (holes) are injected into a homogenous n-type semiconductor sample at a point. An electric field of 50V/cm is applied across the sample and the field moves these minority carriers a distance of 1cm in 100 µs. Find the drift velocity and diffusivity of the minority carriers.
- Find the resistivity at 300 K for a silicon sample doped with 1.0x 10
^{14}per cm^{3}of phosphorous atoms, 8.5 * 10^{12}cm^{-3}of Arsenic atoms, and 1.2 * 10^{13}cm^{-3}of boron atoms. Assume that the impurities are completely ionized and the mobility are µ_{n}= 1500 cm^{2}/V-s, and µ_{p}= 500 cm^{2}/V-s, independent of impurity concentrations. - A semiconductor has a resistivity of 1.0 ohm-cm, and a Hall coefficient of -1250cm
^{2}/C. Calculate the carrier density and mobility, assuming that only one type of carrier is present and the mean free time is proportional to the carrier energy i.e. Γ is directly proportional to E.

**References**

Q1 Q2 Q3 Q4 Q6 Q7 Q8 – “Semiconductor devices Physics and Technology” by SM Sze

Q5 – “Solid State Electronic Devices” by Ben Streetman and Sanjay Banerjee

Q9 Q10 – “ Physics of Semiconductor Devices” by SM Sze, Kwok Ng.

Graphs – “http://ecee.colorado.edu/~bart"