In `mu_e` and `mu_h` are electron and hole mobility. E be the applied electric field, the current density `tau` for intristic semiconductor is equal to

Options

A. `n_ie(mu_e+mu_h)E`
B. `n_ie(mu_e-mu_h)E`
C. `(n_ie(mu_e+mu_h))/E`
D. `E/(n_ie(mu_e+muh))`

Answer

To solve the problem of finding the current density \( J \) for an intrinsic semiconductor, we will follow these steps:

### Step 1: Understand the Components of Current Density
In an intrinsic semiconductor, current density arises from the movement of both electrons and holes. The current density due to holes (\( J_h \)) and electrons (\( J_e \)) can be expressed as:
- For holes:
\[ J_h = q \cdot n_h \cdot \mu_h \cdot E \]
- For electrons:
\[ J_e = q \cdot n_e \cdot \mu_e \cdot E \]

Where:
- \( q \) is the charge of the carriers (for electrons, \( q = -e \), and for holes, \( q = +e \)),
- \( n_h \) is the concentration of holes,
- \( n_e \) is the concentration of electrons,
- \( \mu_h \) is the mobility of holes,
- \( \mu_e \) is the mobility of electrons,
- \( E \) is the applied electric field.

### Step 2: Identify Carrier Concentrations in Intrinsic Semiconductors
In intrinsic semiconductors, the concentration of electrons (\( n_e \)) is equal to the concentration of holes (\( n_h \)), which is denoted as \( n_i \):
\[ n_h = n_e = n_i \]

### Step 3: Substitute Carrier Concentrations into Current Density Equations
Substituting \( n_h \) and \( n_e \) with \( n_i \) in the equations for current density gives:
- For holes:
\[ J_h = q \cdot n_i \cdot \mu_h \cdot E \]
- For electrons:
\[ J_e = q \cdot n_i \cdot \mu_e \cdot E \]

### Step 4: Calculate Total Current Density
The total current density \( J \) is the sum of the current densities due to holes and electrons:
\[ J = J_h + J_e \]

Substituting the expressions for \( J_h \) and \( J_e \):
\[ J = q \cdot n_i \cdot \mu_h \cdot E + q \cdot n_i \cdot \mu_e \cdot E \]

### Step 5: Factor Out Common Terms
Factoring out the common terms gives:
\[ J = q \cdot n_i \cdot E \cdot (\mu_h + \mu_e) \]

### Step 6: Final Expression for Current Density
Thus, the current density \( J \) for an intrinsic semiconductor can be expressed as:
\[ J = n_i \cdot q \cdot E \cdot (\mu_e + \mu_h) \]

### Conclusion
The current density \( J \) for an intrinsic semiconductor is given by:
\[ J = n_i \cdot q \cdot E \cdot (\mu_e + \mu_h) \]