WEEK 3

 Week 3

TASK 4- determine the doping density 

 Doping density is one of the  factors that affect the the energy require to remove an electron from a material. it depends on the doping density because the position of the Fermi level is also affected by the doping density.
the formula used was

  

  In other to get   the doping density the equation was iterated seven times with initial value choosing to be N_{D0 =} 10²¹  

                                             

    Task 5- Determine the work function

  The energy required to remove an electron completely from a material is called the work function. that is the energy difference between the fermi level and the vacuum level. the energy band diagram is shown below

the work function of the capacitor was gotten as the difference between the work function of the metal given(gold)      and hat of the work function of the semiconductor shown below

the Fermi potential of the semiconductor gotten was 

.

the work function of the semiconductor was found to be 

the work function of the capacitor was gotten as the difference between the work function of the semiconductor and that of the metal was 

Task 6- Determining the flat band voltage

 This happens when the negative  voltage applied to the gate is slightly is decreasing until it is equal to zero. This reduces the accumulator capacitance and makes the capacitance to be defined as Debye. The used formulas are presented as following:

the formula for the debye length used was

               

the value of the derby length was




this was used to calculate the capacitance of the semiconductor



the equivalent circuit  of the total capacitance

the equivalent circuit  of the total capacitance

value gotten was

 

Hence, flatland voltage is equal to 0.53V.

                              

    Task 7-  Calculating the mid gap voltage

  The mid gap condition occurs when a negative voltage is applied to the gate , this forces majority carrier away from the from the surface of the semiconductor hence causing a depletion region. As a result of this the the oxide capacitance and the depletion capacitance will be in series. In mid gap, the surface potential will be equal to  the fermi potential.

 The capacitance at the depletion region was found the formula below

the depletion capacitance is

The total capacitance was found which comprises of a an equivalent circuit of oxide capacitor and the depletion capacitance in series, it was modeled by the following equation.

the value gotten for the total capacitance was 

with the total capacitance gotten, its  corresponding voltage was taking  (mid gap voltage) from the CV curve plotted and the value gotten was

Task 8- Find the oxide charge density

 

In flat band condition 

Where Vg equivalent to zero volts and  V_O =V_flat-band – V_{work function.}

V_O calculated was equal to 0.4424.

In midgap condition, differences between Fermi-level potential and mid-gap voltage 

With these parameters, in flatband condition

In midgap condition