You are given a PN junction where the with doping of NA=1017cm-3 and ND=2x1015cm-3. The band diagram of the PN junction at thermal equilibrium is given in the figure below.给你一个 PN 结，其中掺杂的 NA = 1017cm-3，ND = 2x1015cm-3。热平衡处 PN 结的能带图载于下图。

What is the carrier concentration at point "A" above the energy level ECn? (use scientific notation, e.g. 1e17 for 1017).高于能级 ECn 的 “a” 点的载流子浓度是多少？ (使用科学记数法，例如 1e17 表示 1017)。

[Fill in the blank],
cm厘米-3

What is the carrier concentration at point "A" above the energy level ECp?在能级 ECp 以上的 “a” 点的载流子浓度是多少？

[Fill in the blank],
cm厘米-3

Question

You are given a PN junction where the with doping of NA=1017cm-3 and ND=2x1015cm-3. The band diagram of the PN junction at thermal equilibrium is given in the figure below.给你一个 PN 结，其中掺杂的 NA = 1017cm-3，ND = 2x1015cm-3。热平衡处 PN 结的能带图载于下图。

What is the carrier concentration at point "A" above the energy level ECn? (use scientific notation, e.g. 1e17 for 1017).高于能级 ECn 的 “a” 点的载流子浓度是多少？ (使用科学记数法，例如 1e17 表示 1017)。

[Fill in the blank],
 cm厘米-3

What is the carrier concentration at point "A" above the energy level ECp?在能级 ECp 以上的 “a” 点的载流子浓度是多少？

[Fill in the blank],
 cm厘米-3

BlackTom AI · Accepted Answer

We are given a PN junction with NA = 1e17 cm^-3 and ND = 2e15 cm^-3 and asked to find carrier concentrations at two specified energy points relative to ECn and ECp, respectively.

First, recall the standard relationships in doped semiconductors at thermal equilibrium:
- In the n-type region (donor-doped side), the majority carrier electrons concentration n is approximately equal to the donor concentration ND (n ≈ ND) when the doping is not compensated and the intrinsic concentration ni is small in comparison.
- In the p-type region, the minority carrier electron concentration is given by n ≈ ni^2 / NA, since holes dominate and electron concentration is set by intrinsic generation-recombination with the acceptor density NA.
- The intrinsic concentration ni is a small, temperature-dependent constant for silicon at room temperature, with ni^2 on the order of 10^20 cm^-6, so ni^2/NA yields a modest electron concentration on the p-side.

Now, address each blank in turn.

1) Carrier concentration at point A above the energy level ECn (in the n-region, above ECn):
- Above the conduction-band edge ECn in the n-type region, the electron concentration is governed by the donor-doped n-type semiconductor behavior. Since ND = 2e15 cm^-3, and the depletion region does not drastically alter bulk n in the heavily doped region for this order-of-magnitude assessment, n ≈ ND.
- Thus, the carrier concentration is approximately 2e15 cm^-3. This matches the expected scale for electrons in the ND-doped region, where donors supply the majority carriers.

2) Carrier concentration at point A above the energy level ECp (in the p-region, above ECp):
- In the p-type region, the majority carriers are holes, and the electron concentration (the minority carrier concentration) is given by n ≈ ni^2 / NA. With NA = 1e17 cm^-3 and room-temperature ni ≈ 1e10 cm^-3, ni^2 ≈ 1e20 cm^-6.
- Therefore, n ≈ (1e20) / (1e17) = 1e3 cm^-3. If we take a more precise ni value (approximately 1.5e10 cm^-3 for silicon at 300 K), ni^2 ≈ 2.25e20, which yields n ≈ 2.25e3 cm^-3.
- The provided numerical result 2.25e3 cm^-3 corresponds to using ni ≈ 1.5e10 cm^-3, which is a common room-temperature value for silicon. This aligns with the expectation that the electron concentration just above the valence-band-related level on the p-side is a small minority-carrier concentration determined by ni^2/NA.

Summary of the two blanks:
- Above ECn: n ≈ 2e15 cm^-3, reflecting the ND-dominated electron concentration in the n-region.
- Above ECp: n ≈ 2.25e3 cm^-3, reflecting the minority-carrier electron concentration in the p-region given by ni^2/NA using a typical ni value.

If you encounter alternative numbers, they would typically differ by using a different ni value or by misapplying the ND/NA relationships for minority vs. majority carriers. The key concept is that the n-concentration on the n-side is set by donor density, while on the p-side the minority electron concentration is controlled by ni^2/NA.

EESM5200 (L2)EESM5200(L2) Part I: Topic 5 - Derivation of Ideal PN Junction Diode Equation 第一部分：主题 5 - 理想 PN 结二极管方程的推导

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EESM5200 (L2)EESM5200(L2) Part I: Topic 5 - Derivation of Ideal PN Junction Diode Equation 第一部分： 主题 5 - 理想 PN 结二极管方程的推导