An ideal silicon p-n junction at room temperature is doped with 𝑁𝐴 = 1017 𝑐𝑚−3(𝜇𝑛 = 680 𝑐𝑚2𝑉−1𝑠−1, 𝜇𝑝 = 320 𝑐𝑚2𝑉−1𝑠−1and𝑁𝐷 = 1016 𝑐𝑚−3 𝜇𝑛 = 1198 𝑐𝑚2𝑉−1𝑠−1, 𝜇𝑝 = 422 𝑐𝑚2𝑉−1𝑠−1 . And assume that 𝜏𝑛 = 𝜏𝑝 = 1 × 1 𝑚𝑠 𝑎𝑛𝑑 𝑡ℎ𝑒 𝑑𝑒𝑣𝑖𝑐𝑒 𝑎𝑟𝑒𝑎 𝑖𝑠 1 × 10−4 𝑐𝑚2.
1. Assume the p-n junction forms a step junction which is maintained at equilibrium. (a) Find the built-in potential. (b) Calculate the space-charge width. (c) Find electric field at x=0.
2. (a) Find the saturation current. (b) Calculate the forward currents at 0.05, 0.1, 0.2, and 0.5 V.
(c) Calculate the reverse currents at -0.05, -0.1, -0.2, and -0.5 V.
3. Under the condition of light off, find the J-V characteristic curve for the p-n junction by running AMPS-1D [i.e., 5pn_Si(Light 2015 05 14)]. * Plot the J-V characteristic curve under the condition of Off Light.
4. I-V characteristics of a solar cell are approximately modeled by the relationship, I = I0 eqVkT − 1 + IL
where IL is the current due to light. IL is always negative and a voltage-independent constant for a given level of illumination. (a) Find I0. (b) Construct a plot illustrating the general nature of the solar cell characteristics. Setting T=300K, simultaneously plot I/I0 versus V for the assumed values of IL/I0=0, -1, -2, and -4. Limit V to -0.5V≤V≤0.1V. (c) Plot the I-V characteristic curve.
5. Under the condition of light on, find the J-V characteristic curve for the p-n junction by running AMPS-1D [i.e., 5pn_Si(Light 2015 05 14)]. * Plot the light J-V characteristic curve under the condition of Light On.
Solar cell simulation by AMPS-1D Program
4. 1-p-Si
(1) Layer: 5000.0
(2) Center grid spacing: 200.0 (3) EPS: 11.90
(4) MUN: 212.6 (5) MUP: 71.01 (6) NA: 1.00e+019 (7) ND: 0.0
(8) EG: 1.12 (9) NC: 2.80e+019 (10) NV: 1.04e+019 (11) CHI: 4.05
5. 2-n-Si
(1) Layer: 200000.0
(2) Center grid spacing: 10000.0 (3) EPS: 11.90
(4) MUN: 725.5 (5) MUP: 318.3 (6) NA: 0
(7) ND: 1.00e+017 (8) EG: 1.12 (9) NC: 2.80e+019 (10) NV: 1.04e+019 (11) CHI: 4.05
Solar cell simulation by AMPS-1D Program
-0.7 0.0 0.7 0
100000 200000
C u rre n t D e n si ty(a mp e re s/ cm 2 )
Bias Voltage(Volts)
pn junction
-0.7 0.0 0.7
0 100000 200000
Current Density(amperes/cm2 )
Bias Voltage(Volts)
pn junction
Semiconductor Physics Final Exam
Instructor: Jonghun Lyou June 16, 2014
1. (50 points) At room temperature, an ideal step-junction diode has a doping concentration of 2.0×1016cm-3 on one side and the other side is unknown. It is given that the extension of the depletion region from the metallurgical junction into the p-type region is xp=0.04μm (4.0×10-6cm) and into the n-type region is xn=1.0μm (1.0×10-4cm).
a) (5 points) Is this a p+-n or n+-p diode? Explain!
b) (15 points) Draw the energy band diagram for the diode. Label all energy levels, and indicate on your plot numerical values for (Ei-EF)p and (EF-Ei)n in the quasi-neutral regions.
c) (20 points) Sketch the plots for doping profile, charge density, electric field, and voltage (electrostatic potential).
d) (10 points) Determine Vbi, the built-in voltage.
2. (45 points) The figure below shows a circuit for acquisition of I-V data for a p+-n Si step-junction diode at T=300K. The acquired data points are shown in the table. Doping on the n-side is 𝑁𝐷 = 1015 𝑐𝑚−3 𝜇𝑛 = 1400 𝑐𝑚2𝑉−1𝑠−1, 𝜇𝑝 = 450 𝑐𝑚2𝑉−1𝑠−1 . The junction area is A=1.0×10-4 cm2.
Review for final exam
VA(V) I(A)
0.8 8.07×10-1
0.7 1.70×10-1
0.6 3.68×10-3
0.5 7.87×10-5
0.4 1.68×10-6
0.3 3.59×10-8
0.2 8.10×10-9
0.1 1.64×10-9
a) (10 points) For the data shown in the table, in which region is this diode operating among forward bias, reverse bias, or reverse breakdown? Explain it.
b) (20 points) Determine I0 for the ideal diode model I = I0eqVA/kT by using the data in the table.
c) (20 points) Estimate the diffusion coefficient and the minority carrier diffusion length Lp for holes in the n-type material.
3. (40 points) Light generates electron-hole pairs of 1019/cm3 uniformly every second in a Si wafer doped with NA=1016 boron atoms/cm3 with τn= τp = 1 μsec at room temperature. (a) Calculate the equilibrium Fermi-level. (b) Find the electron and hole concentrations. (c) Find the electron and hole quasi-Fermi levels. (d) Find the recombination coefficient r.
11.8.
K F/cm, 10
8.85 ,
10 1.6 1eV C, 10 1.6 e 1 Si, for cm 10 1
*ni 10 -3 -19 -19J 0 -14 s
VA(V) I(A)
0.8 8.07×10-1
0.7 1.70×10-1
0.6 3.68×10-3
0.5 7.87×10-5
0.4 1.68×10-6
0.3 3.59×10-8
0.2 8.10×10-9
0.1 1.64×10-9
a) (10 points) For the data shown in the table, in which region is this diode operating among forward bias, reverse bias, or reverse breakdown? Explain it.
b) (20 points) Determine I0 for the ideal diode model I = I0eqVA/kT by using the data in the table.
c) (20 points) Estimate the diffusion coefficient and the minority carrier diffusion length Lp for holes in the n-type material.
3. (40 points) Light generates electron-hole pairs of 1019/cm3 uniformly every second in a Si wafer doped with NA=1016 boron atoms/cm3 with τn= τp = 1 μsec at room temperature. (a) Calculate the equilibrium Fermi-level. (b) Find the electron and hole concentrations. (c) Find the electron and hole quasi-Fermi levels. (d) Find the recombination coefficient r.
11.8.
K F/cm, 10
8.85 ,
10 1.6 1eV C, 10 1.6 e 1 Si, for cm 10 1
*ni 10 -3 -19 -19J 0 -14 s
