代写VE320 Intro to Semiconductor Devices Summer 2024 — Problem Set 4代做回归

VE320 Intro to Semiconductor Devices

Summer 2024 — Problem Set 4

Due: 11:59pm 30th June

Since we notice that there are several midterm exams next week, the due date is set on

next Sunday evening. But the next homework will still be posted on next Friday and due in one week.

1)  What are the two main mechanisms of scattering discussed in the lecture? State their effects on the electron’smobility.

2)    Consider a homogeneous gallium arsenide semiconductor at 300 K with

1016 cm −3 donors and  0cm−3 acceptors.  μp=310cm2/V-s,  μn =7500cm2/V-s.

a)    Calculate the thermal-equilibrium values of electron and hole concentrations.

b)    For an applied E-field of 10 V/cm, calculate the drift current density.

3)  Answer the following questions based on the band diagram below:

a)   Is it in equilibrium?

b)  Is this sample n-type or p-type or both?

c)   Is there an electric field?

d)  Is there a concentration gradient?

e)   Is there a drift current?

f)   Is there a diffusion current?

g)  Is there a net current?

4)  What’s the difference of direct(radiative) recombination and indirect(SRH)

recombination discussed in the lecture? Do they both contribute to the excess carrier lifetime?

5)    A Si bar is uniformly doped with  1017 cm −3 donors. Suppose complete

ionization. A light is casted to the left end (x = 0) of the bar, and excess carriers are only generated there. The lifetime of excess minority carrier is 1µs.  Dn =25cm2 /s,

Dp =10cm2 /s, δn(0) = δp(0) =  1015 cm −3 . Neglect the induced electric field.

a)    Calculate the concentration of steady-state excess holes as a function of x.

b)    Calculate the steady-state hole diffusion current density atx=10µm.

6)    We inject electrons instantly into a uniformly doped p-type 5µm long Si sample  at 300K such that the extra electron concentration varies linearly from  1020 cm −3 to

0 from left to right at that moment. The mobility of electrons is  500cm2/V-sin this doping condition.

a)    What is the current density at that moment if the induced electric field is

negligible? (Refer to the lecture slide chapter 5 if the induced electric field need to be considered)

b)    Qualitatively draw the energy band diagram of the semiconductor along its length at that moment, carefully labelling  Ec ,  Ev ,  Efi    and the quasi-Fermi energies  Efn ,  Efp.

7)    A Sisample is uniformly doped with  1016 cm −3 donors and is uniformly

optically excited such that  1019 cm −3s −1electron-hole pairs are generated. Optical excitation causes the sample to heat to 450K. Suppose the donors are completely ionized and the Si sample is in steady state. Excess electron and hole lifetimes are   both 10µs. At 450K,  Dp =12cm2 /s,  Dn =36cm2 /s  for Si in this doping condition.

a)  Find the quasi-Fermi levels  Efn ,  Efp    with respect to the intrinsic Fermi level Efi   at 450K

b)  Find the change in conductivity of the sample upon shining the light at 450K. Neglect the high electric field case.