Which of the following equations correctly represents the temperature variation of energy gap between the conduction and valence bands for Si?

Options

A. `E_g(T)=0.70-2.23xx10^(-4)` T eV
B. `E_g(T)=0.70+2.23xx10^(-4)` T eV
C. `E_g(T)=1.10-3.60xx10^(-4)` T eV
D. `E_g(T)=1.10+3.60xx10^(-4)` T eV

Explanation

To determine the correct equation that represents the temperature variation of the energy gap between the conduction and valence bands for silicon (Si), we can follow these steps:

### Step 1: Understand the Energy Gap
The energy gap (E_g) in semiconductors like silicon is the energy difference between the conduction band and the valence band. It is known to vary with temperature.

### Step 2: Identify the Energy Gap at 0°C
At 0 degrees Celsius, the energy gap for silicon is given as:
\[ E_{g0} = 1.1 \, \text{eV} \]

### Step 3: Formulate the Temperature Dependence
The temperature dependence of the energy gap can be expressed with the formula:
\[ E_g(T) = E_{g0} - \frac{\alpha T^2}{T + \beta} \]
where:
- \( E_{g0} \) is the energy gap at 0°C,
- \( \alpha \) and \( \beta \) are constants that are positive for silicon,
- \( T \) is the temperature in degrees Celsius.

### Step 4: Substitute Known Values
Substituting the known value of \( E_{g0} \):
\[ E_g(T) = 1.1 - \frac{\alpha T^2}{T + \beta} \]

### Step 5: Analyze the Equation
Since both \( \alpha \) and \( \beta \) are positive, the term \( \frac{\alpha T^2}{T + \beta} \) will also be positive. Thus, as temperature increases, the energy gap \( E_g(T) \) decreases.

### Step 6: Select the Correct Equation
From the information provided, we can conclude that the equation representing the temperature variation of the energy gap for silicon is:
\[ E_g(T) = 1.1 - \frac{\alpha T^2}{T + \beta} \]

### Final Answer
The correct equation that represents the temperature variation of the energy gap between the conduction and valence bands for silicon is:
\[ E_g(T) = 1.1 - \frac{\alpha T^2}{T + \beta} \]

---