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Semiconductor quantum-dots are quantum systems with typical three-dimensional size of a few nanometers. They are being explored for optoelectronic application such as a quantum- dot laser. The figure below shows the infrared laser emission (middle) at 1 = 1.28 µm from InAs quantum-dots. Also shown is an AFM image (left) indicating the size of the InAs quantum-dots. You need to estimate the size of the quantum-dots by modeling the electron as confined in a nanocube of side L (right) and compare your result with the AFM measurement. V = 00 V = 00 →y V = 0 200 nm 1200 Wavelength (nm) 1100 1300 1400 1500 Atomic-Force Microscopy Lasing spectrum with emission at A = 1.28 um of as-grown InAs quantum dots (a) By direct substitution into the time-independent Schrödinger in three-dimensions, h2 [a2p(x,y, z) , ð²Þ(x,y, z) , a²µ(x, y, z)] ду? + V(x,y, z)¥(x) = EÞ(x,y,z) 2m show that the wavefunction of the electron is 3/2 L P'imn (x, y, x) sin х+ sin y + sin z + with the quantized energy levels given by E = En = -(1² + m² + n²) 2mL? where l, m, n = 1, 2, 3, .... (b) Assuming that the laser emission corresponds to the transition from the first excited state to the ground state, estimate the size L of the InAs quantum-dot. (Use m = 0.023m, for the effective mass of the electron in InAs.) Compare your estimate with the size of the quantum-dot obtained from the AFM measurement. Clectroluminescence intensity (

Semiconductor quantum-dots are quantum systems with typical three-dimensional size of a few nanometers. They are being explored for optoelectronic application such as a quantum- dot laser. The figure below shows the infrared laser emission (middle) at 1 = 1.28 µm from InAs quantum-dots. Also shown is an AFM image (left) indicating the size of the InAs quantum-dots. You need to estimate the size of the quantum-dots by modeling the electron as confined in a nanocube of side L (right) and compare your result with the AFM measurement. V = 00 V = 00 →y V = 0 200 nm 1200 Wavelength (nm) 1100 1300 1400 1500 Atomic-Force Microscopy Lasing spectrum with emission at A = 1.28 um of as-grown InAs quantum dots (a) By direct substitution into the time-independent Schrödinger in three-dimensions, h2 [a2p(x,y, z) , ð²Þ(x,y, z) , a²µ(x, y, z)] ду? + V(x,y, z)¥(x) = EÞ(x,y,z) 2m show that the wavefunction of the electron is 3/2 L P'imn (x, y, x) sin х+ sin y + sin z + with the quantized energy levels given by E = En = -(1² + m² + n²) 2mL? where l, m, n = 1, 2, 3, .... (b) Assuming that the laser emission corresponds to the transition from the first excited state to the ground state, estimate the size L of the InAs quantum-dot. (Use m = 0.023m, for the effective mass of the electron in InAs.) Compare your estimate with the size of the quantum-dot obtained from the AFM measurement. Clectroluminescence intensity (

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3. Semiconductor Quantum-Dot Laser Semiconductor quantum-dots are quantum systems with typical three-dimensional size of a few nanometers. They are being explored for optoelectronic application such as a quantum- dot laser. The figure below shows the infrared laser emission (middle) at 1 = 1.28 µm from InAs quantum-dots. Also shown is an AFM image (left) indicating the size of the InAs quantum-dots. You need to estimate the size of the quantum-dots by modeling the electron as confined in a nanocube of side L (right) and compare your result with the AFM measurement. V = c0 V = 00 > y 7. V = 0 L 200 nm L 1100 1200 Wavelength (nm) 1300 1400 1500 Atomic-Force Microscopy of as-grown InAs quantum dots Lasing spectrum with emission at A = 1.28 um (a) By direct substitution into the time-independent Schrödinger in three-dimensions, h2 [02p(x,y,z) , a²Þ(x,y,z) , 0²µ(x, y, z)] ду? + V(x,y, z)þ(x) = Ep(x,y,z) + 2m show that the wavefunction of the electron is 3/2 [MT Pimn (X, y, x) sin + sin y + sin z + L with the quantized energy levels given by E = En - (1² + m² + n²) 2ml? where l, m, n = 1,2, 3, ... (b) Assuming that the laser emission corresponds to the transition from the first excited state to the ground state, estimate the size L of the InAs quantum-dot. (Use m = 0.023m, for the effective mass of the electron in InAs.) Compare your estimate with the size of the quantum-dot obtained from the AFM measurement. aauaasaujunjoaa
Transcribed Image Text:3. Semiconductor Quantum-Dot Laser Semiconductor quantum-dots are quantum systems with typical three-dimensional size of a few nanometers. They are being explored for optoelectronic application such as a quantum- dot laser. The figure below shows the infrared laser emission (middle) at 1 = 1.28 µm from InAs quantum-dots. Also shown is an AFM image (left) indicating the size of the InAs quantum-dots. You need to estimate the size of the quantum-dots by modeling the electron as confined in a nanocube of side L (right) and compare your result with the AFM measurement. V = c0 V = 00 > y 7. V = 0 L 200 nm L 1100 1200 Wavelength (nm) 1300 1400 1500 Atomic-Force Microscopy of as-grown InAs quantum dots Lasing spectrum with emission at A = 1.28 um (a) By direct substitution into the time-independent Schrödinger in three-dimensions, h2 [02p(x,y,z) , a²Þ(x,y,z) , 0²µ(x, y, z)] ду? + V(x,y, z)þ(x) = Ep(x,y,z) + 2m show that the wavefunction of the electron is 3/2 [MT Pimn (X, y, x) sin + sin y + sin z + L with the quantized energy levels given by E = En - (1² + m² + n²) 2ml? where l, m, n = 1,2, 3, ... (b) Assuming that the laser emission corresponds to the transition from the first excited state to the ground state, estimate the size L of the InAs quantum-dot. (Use m = 0.023m, for the effective mass of the electron in InAs.) Compare your estimate with the size of the quantum-dot obtained from the AFM measurement. aauaasaujunjoaa
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