Hole Diffusion Current of a P-N Junction

In summary, to calculate the hole diffusion current density on the n-side of the p+-n junction, you will need to use the equations for diffusion coefficient, hole mobility, built-in potential, and p-type doping concentration. Once these values are calculated, you can then use the equation for hole diffusion current density to find the answer.
  • #1
KasraMohammad
20
0

Homework Statement



A p+-n junction with the n-side donor concentration of 1016cm-3. If ni = 1010cm-3, the relative dielectric constant er = 12, Dn = 50cm2/s, Dp = 20cm2/s, tn = 100ns, tp = 50ns. Calculate the hole diffusion current density 2mm from the depletion edge on the n-side under a forward bias of 0.6V.

Homework Equations



J(p) [drift] = -qDpΔp

The Attempt at a Solution



My only understanding of how to solve this problem is by the relevant equation given above, yet i don't know how to find Δp from the given information. Perhaps there is another equation that suites better in solving this problem given the parameters at hand.
 
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  • #2
A:To solve this problem, you'll need to calculate the diffusion coefficient (Dp), the hole mobility ($\mu_p$), and the built-in potential ($V_{bi}$). To do this, you'll use the equations below. $$ D_{n/p} = \frac{k_BT}{q}\mu_{n/p} $$ $$ V_{bi} = k_BT\ln\left(\frac{N_A N_D}{n_i^2}\right) $$where $k_B$ is Boltzmann's constant, $T$ is the absolute temperature, and $q$ is the charge of an electron. Once you've calculated these three values, you can then calculate the p-type doping concentration ($N_A$) at the depletion region using the equation $$ N_A(x) = N_{A0}\exp\left(-\frac{qV(x)}{k_BT} + \frac{qV_{bi}}{k_BT}\right) $$where $V(x)$ is the voltage along the x-axis. Finally, you can use the equation you wrote down in your post to calculate the hole diffusion current density. $$ J_p(x) = -qD_p\left(N_{A0} - N_A(x)\right) $$Hope this helps!
 

1. What is hole diffusion current in a P-N junction?

Hole diffusion current in a P-N junction is the flow of holes (positively charged carriers) from the P-type region to the N-type region due to a concentration gradient. This current contributes to the overall current flow in a P-N junction diode.

2. How is hole diffusion current affected by temperature?

The hole diffusion current in a P-N junction increases with an increase in temperature. This is because at higher temperatures, there is a higher concentration of thermally generated holes in the P-type region, leading to a larger concentration gradient and therefore, a higher diffusion current.

3. What is the relationship between hole diffusion current and applied voltage?

Hole diffusion current is directly proportional to the applied voltage across a P-N junction. This means that as the applied voltage increases, the hole diffusion current also increases. However, at a certain voltage known as the breakdown voltage, the current suddenly increases due to a phenomenon called avalanche breakdown.

4. How does the doping concentration affect the hole diffusion current?

The doping concentration of the P-N junction affects the hole diffusion current by influencing the concentration gradient. A higher doping concentration in the P-type region leads to a larger concentration gradient, resulting in a higher diffusion current. On the other hand, a lower doping concentration results in a lower diffusion current.

5. What is the significance of hole diffusion current in P-N junctions?

The hole diffusion current is an important factor in the operation of P-N junctions. It helps in the formation of the depletion region, which is necessary for the diode to function properly. It also contributes to the overall current flow and plays a role in the forward and reverse biased characteristics of the diode.

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