This document discusses the Hall effect and its analysis for determining properties of semiconductor materials. The Hall effect can be used to: 1) Distinguish whether a semiconductor is n-type or p-type based on the nature of doping. 2) Measure the majority carrier concentration. 3) Calculate the majority carrier mobility. The document provides equations to analyze the Hall effect for both n-type and p-type semiconductors and determine values such as Hall voltage, drift velocity, current density, and Hall coefficient.

1. Course: Electronic Devices
paper code: EC301
Course Coordinator: Arpan Deyasi
Department of Electronics and Communication Engineering
RCC Institute of Information Technology
Kolkata, India
8/4/2020 1Arpan Deyasi, RCCIIT
Topic: Hall Effect

2. 8/4/2020 2Arpan Deyasi, RCCIIT
Hall Effect
It is used to
I. distinguish whether a semiconductor material is n/p
type (nature of doping),
II. measure the majority carrier concentration,
III. calculate the majority carrier mobility

3. 8/4/2020 3Arpan Deyasi, RCCIIT
magnetic field (Bz)
d
W
L
Schematic Diagram

4. 8/4/2020 4Arpan Deyasi, RCCIIT
Analysis of Hall Effect
In steady state
[ ] 0q E v B+ × =
 
y x zE v B=
Consider p-type semiconductor

5. 8/4/2020 5Arpan Deyasi, RCCIIT
Analysis of Hall Effect
Induced electric field, called Hall Field,
produces a voltage across specimen,
named Hall Voltage
H HV E W=
H yV E W=
H x zV v B W=

6. 8/4/2020 6Arpan Deyasi, RCCIIT
Analysis of Hall Effect
Drift velocity
.
x
x
J
v
q p
=
. . .
x
x
I
v
W d q p
=
.
. . . . .
x x z
H x z
I I B
V v B W
W d q p d q p
= × =

7. 8/4/2020 Arpan Deyasi, RCCIIT 7
Analysis of Hall Effect
. .
x z
H
I B
p
d qV
=
Similarly for n-type semiconductor
. .
x z
H
I B
n
d qV
= −
Nature of doping is evaluated along with
carrier concentration

8. 8/4/2020 Arpan Deyasi, RCCIIT 8
Analysis of Hall Effect
Current density
. . .x p xJ q p Eµ=
. . .
.
x x
p
I V
q p
W d L
µ= External source
.
. . . .
x
p
x
I L
W d q pV
µ =

9. 8/4/2020 Arpan Deyasi, RCCIIT 9
Analysis of Hall Effect
Similarly for n-type semiconductor
.
. . . .
x
n
x
I L
W d q pV
µ = −
Carrier mobility is calculated

10. 8/4/2020 Arpan Deyasi, RCCIIT 10
Analysis of Hall Effect
. . .
.
x x
p
I V
q p
W d L
µ=
. . . . .x
x p
V
I q p W d
L
µ=
. . . .x xI q p v W d=
. . .
x
x
I
v
q pW d
=

11. 8/4/2020 Arpan Deyasi, RCCIIT 11
Analysis of Hall Effect
y x zE v B=
. . .
x
y z
I
E B
q pW d
=
1
. .
x z
y
I B
E
W d q p
= ×

12. 8/4/2020 Arpan Deyasi, RCCIIT 12
.
x z
y Hp
I B
E R
W d
= ×
Analysis of Hall Effect
where
1
.
HpR
q p
=
Similarly for n-type semiconductor
1
.
HnR
q n
= −
RHp: Hall resistance