1. A silicon sample is doped by a group-V material of 2×10¹7 cm³³. (a) Determine the electron and hole concentrations in this sample, assume T= 300 K and ni = 10¹⁰ cm³. What is the carrier transport mechanism in the sample if an external voltage is applied? (b) If a voltage of 20 V is applied to the silicon sample (across 200 µm), determine the total current flows in the sample (mA). Assume un= 1200 cm²/V-s and µp= 400 cm²/V-s. (c) If the sample is connected to another silicon sample with the same geometry but doped by a group-III material to form a PN junction. Determine the doping concentration to obtain a built-in potential of 0.83 V at the interface (V₁= 26 mV). (d) The silicon sample resembles the channel of MOSFET, and the size is modified accordingly as shown below for the 40 nm technology. Determine the inversion layer thickness h (nm) to obtain an equivalent channel resistance of 100 ohm (across 40 nm). Assume the carrier density is the same with (a), but only need to consider the electrons. (a)-(c) 20 μm, 20 μm Uniformly doped Si 200 μm (d) 10 μm 40 nm th

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1. A silicon sample is doped by a group-V material of 2×10¹7 cm²³.
(a) Determine the electron and hole concentrations in this sample, assume T= 300 K
and n₁ = 10¹0 cm³. What is the carrier transport mechanism in the sample if an
external voltage is applied?
(b) If a voltage of 20 V is applied to the silicon sample (across 200 µm), determine
the total current flows in the sample (mA). Assume un 1200 cm²/V-s and μp 400
cm²/V.s.
(c) If the sample is connected to another silicon sample with the same geometry but
doped by a group-III material to form a PN junction. Determine the doping
concentration to obtain a built-in potential of 0.83 V at the interface (V₁= 26 mV).
(d) The silicon sample resembles the channel of MOSFET, and the size is modified
accordingly as shown below for the 40 nm technology. Determine the inversion layer
thickness h (nm) to obtain an equivalent channel resistance of 100 ohm (across 40
nm). Assume the carrier density is the same with (a), but only need to consider the
electrons.
(a)-(c)
20 μm,
20 μm
Uniformly doped Si
200 μm
(d)
10 μm,
40 nm
1th
Transcribed Image Text:1. A silicon sample is doped by a group-V material of 2×10¹7 cm²³. (a) Determine the electron and hole concentrations in this sample, assume T= 300 K and n₁ = 10¹0 cm³. What is the carrier transport mechanism in the sample if an external voltage is applied? (b) If a voltage of 20 V is applied to the silicon sample (across 200 µm), determine the total current flows in the sample (mA). Assume un 1200 cm²/V-s and μp 400 cm²/V.s. (c) If the sample is connected to another silicon sample with the same geometry but doped by a group-III material to form a PN junction. Determine the doping concentration to obtain a built-in potential of 0.83 V at the interface (V₁= 26 mV). (d) The silicon sample resembles the channel of MOSFET, and the size is modified accordingly as shown below for the 40 nm technology. Determine the inversion layer thickness h (nm) to obtain an equivalent channel resistance of 100 ohm (across 40 nm). Assume the carrier density is the same with (a), but only need to consider the electrons. (a)-(c) 20 μm, 20 μm Uniformly doped Si 200 μm (d) 10 μm, 40 nm 1th
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