Week 4

Week 4

Task 9- Comparison 

During this particle project, the percentage of high-k dielectric material in MOS capacitor was 50%. This specific percentage leads essence understanding on the function of using different percentage high-k dielectric in MOS capacitor. The determined oxide relative permittivity in 70%Hf and 30%Hf are approximately 11 and 5 respectively. By comparison of these result, using high percentage of Hf, high-k material, causes bigger relative permittivity. However leakage current conversely is increased due to high charge density. The percentage of high-k dielectric therefore needs to be justifying with regarding to correlation between permittivity and charge density.

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

WEEK 2 

TASK 2-DETERMINE THE OXIDE RELATIVE PERMITTIVITY

 The oxide relative permittivity  was calculated when the transistor was in the accumulation region because the capacitance is at its peak in this region. The capacitor of the MOS can be represented by circuit comprising of the series combination of the oxide capacitor and the accumulation layer capacitor.

the series combination of the capacitor was represented by the expression below.

The capacitor of the accumulation layer depends on the majority carriers which are holes for the p type substrate. The capacitor of the accumulation region is large because the majority carriers which are holes that accumulates depends exponentially  on the surface charge thereby making it very large for a negative voltage applied to the gate. this made the capacitance to be of the accumulation region to be ignored  
the value of Cmax given was 2.99×10^-9 

The area of the capacitor was found by using the this formula

The Area of silicon wafer calculated was equal to =2.6430×10^-7

The oxide capacitance consists of two layers which is represented in an electrical circuit as the parallel combination of the high k capacitor and the silicon oxide capacitor. which was represented in the formula below.


                                                                          


note: the capacitor of the accumulation region was ignored 
for the oxide relativity permittivity to be calculated the, the capacitance of the silicon oxide was initially calculated 

the value gotten for silicon oxide capacitance was 

with the capacitance value of the silicon oxide known the capacitance of the high-k material was gotten with the value of Cmax given by the our supervisor

the value gotten was

 this value gotten was used to calculate the oxide relative permittivity by using this formula

WEEK 2 

TASK 3-FIND THE EQUIVALENT OXIDE THICKNESS

The equivalent oxide thickness was by using the formula used to find the capacitance of the oxide which is the oxide capacitance given was 2.99×10^-9.

The thickness of the oxide was expressed in this form

The equivalent oxide thickness(EOT) is therefore equal to 3.03nm

This is the the thickness of the silicon oxide required to make the capacitance of the silicon oxide equivalent to the capacitance of the high k gate material.

 

     

WEEK 1 

TASK 1-Determine type of Substrate

 A group meeting was held with our supervisor, a file was sent to each member of the project. the file consisted of the capacitor values and its respective voltages. the values were us to determine the substrate of the semiconductor if it was a p type or a n type.

 

CAPACITANCE VOLTAGE CHARACTERISTICS OF A P-TYPE MOS CAPACITOR

 The type of substrate in MOS capacitor is clarified through plotting voltage-capacitance data. In terms of the conceptual approach, value of capacitance in p-type MOS became highest when negative voltage applied to gate terminal of MOS capacitor. In this context, type of substrate identification derived as p-type.