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>