ece 584 semiconductor device fundamentals problem 1 : 1ece.gmu.edu/~qli/ece584/homework1...
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ECE 584 Semiconductor Device Fundamentals
Homework #1, due date: 09/19/2013
Problem 1: 1.1
Problem 2: 1.3
Problem 3: 1.5
Problem 4:
(i) Please find the Fermi level of a n-type Si with As dopant level at 1016 cm-3 from low temperature to high temperature (e.g., from 0 K to infinitely high temperature.) and draw EC, EF and EV vs. temperature)
(ii) Please find the Fermi level of a p-type Si with B dopant level at 1016 cm-3 from low temperature to high temperature (e.g., from 0 K to infinitely high temperature.) and draw EC, EF and EV vs. temperature)
Solve:
(i) consider n-type semiconductor
(a) At low temperature
� + ��� = �
���������� +
��
1 + ����������
= ���������
���������� +����
��������� = ���������
Both sides time �������
�� :
�� = ���������� �
�
= �������� + �����
��������� ≈ ��������������
where ��� = ����
��
�� is negligible at low temperature
so
� = ����������������
Use:
− = ��� ��
� � =�2
ln ��
��
� + − �
2
When T=0:
= + �
2
When T increases, Ef changes from the middle between Ec and Ed to below Ed linearly
(b) At medium temperature n = Nd+ = Nd and p= Na- = Na
Therefore Ef = Ei + kTln(Nd/ni)
(c) At high temperature, n and p are dominated by ni
� = �exp( −
� )
� = ��exp(� − � )
�� = ��� = ���exp(− �
�) Therefore, at high temperature �� ≈ ��� ≫ ������
For this intrinsic region, n=p=ni
So
� = � exp � −
� � = � = ��exp(� − � )
2 − ( + �)
� = ln(��
�
)
= + �
2+3
4kTln(��
∗
��∗)
From table 1.3, m*n = 0.26m0, m
*p = 0.386 m0
Therefore, as T increases, Ef will increase with Ei to approach Ec
(ii) similar method can be applied on p-type semiconductor
Problem 5: 1.15
E
Temperature
Ec
Ei
Ev
Ed
Ea
Efn
Efp
m*p m*
n>