Post on 01-Feb-2016
description
Doped semiconductors: donor impurities
A silicon lattice with a single impurity atom (Phosphorus, P) added.
As compared to Si, the Phosphorus has one extra valence electron which, after all bonds are made, has very weak bonding.
Very small energy is required to create a free electron from an impurity atom.
This type of impurity is called donor.
Note, that there is no hole created when a free electron comes from the impurity atom.
Free electron concentration in donor - doped semiconductors
For Si and other semiconductors, the typical doping levels are:
ND = 1015 cm-3 ….1018 cm-3
nD = 1015 cm-3 ….1018 cm-3 (compare to ni = 1.3×1010 cm-3 in intrinsic Si)
nD >> ni
Doping provides a flexible control over semiconductor conductivity.
The vast majority of microelectronic devices are based on doped semiconductors
If the concentration of donor impurity (e.g. Phosphor) in Si is ND, the concentration of free electrons,
n ≈ ND
When donor atoms are introduced into the semiconductor material, they are all ionized.
Each donor atom creates one free electron.
How much would be the resistance of the (1 cm×1cm× 1cm) Si sample doped with donor impurities with concentration 2×1016 cm-3?
Resistance of Donor-Doped Silicon sample
n = 2×1016 cm-3
µn = 1000 cm2/(V ×s)q = 1.6 ×10-19 C
σ = 1.6 ×10-19 C × 2×1016 cm-3 × 1000 cm2/(V ×s)
σ = 3.2 (Ohm × cm)-1
AL
ALR
qn
×==
=
σρ
µσ1
;
ρ = 0.325 Ohm × cm
R = 0.325 (Ohm × cm) ×1 cm /(1cm ×1cm) = 0.325 Ohm
The resistance of a doped Si crystal can be significantly lower than that of intrinsic Si
A silicon lattice with a single impurity atom (Boron, B) added. Boron has only three valence electrons, one electron less than the Si atom.Having only three valence electrons - not enough to fill all four bonds - it creates an excess hole that can be used in conduction.
This type of impurity is called acceptor.
There is no corresponding free electron created from acceptor impurity
Doped semiconductors: acceptor impurities
Hole concentration in acceptor - doped semiconductors
The vast majority of microelectronic devices using hole conductivity, are based on doped semiconductors
In doped semiconductors, the concentration of intrinsic electrons and holes can be neglected as compared to those coming from donor and acceptor impurities.
For Si and other semiconductors, the typical acceptor doping levels are:
NA = 1015 cm-3 ….1018 cm-3
pA = 1015 cm-3 ….1018 cm-3 (compare to ni = 1.3×1010 cm-3 in intrinsic Si);
pA >> ni
If the concentration of acceptor impurity (B atoms) in Si is NA, the hole concentration
pA ≈ NA
Concentration –temperature dependence in doped semiconductors
T
n, cm-3
Typical dependence for n-Si (i.e. donor-doped)(for p-Si (i.e. acceptor doped) the dependences are similar
Impurity electrons
Intrinsic electrons,intrinsic holes
ND
100 K 300 K 400 K200 K
Mobile charge carriers energy
Bound electron
Atom
Ec
Ev
Intrinsic material at low temperature. There are no free electrons or holes – no free carriers. The mobile charge energy does not make sense.
valence band
In semiconductors, the mobile charge carriers are the free electrons and holes
Conductance band energy
Free electron
Atom
When the electron in the valence band acquires sufficient extraenergy, it can be detached from its parent atom and reaches reach the “conductance band”The minimum energy of the conduction band is denoted as EC
conductance band
Hole
Ec
Ev
Energy Band Gap (Eg)
Generally no electron can have the energy between Ec and Ev
The “band-gap” is the energy difference between Ec and Ev:Eg=Ec-Ev
Ec
Ev
Forbidden Energyregion
Band-gap
Ec
Ev
Free electron
Atom
conductance band
Hole
Intrinsic material at high temperature. Temperature generates free electrons and holes in equal concentrations.
The energy of free electrons is close to EC; the energy of holes is close to EV
valence band
Mobile charge carriers energy
Ec
Ev
Average free carrier Energy – Fermi energyconductance
band
The energy of free electrons is close to EC; the energy of holes is equal to EV
valence band
The average energy of all the mobile charges in semiconductor:Eave Average [(Electron Average Energy + Hole Average Energy)] ≈(EC + EV)/2.
The average energy of all the mobile charges in semiconductor is called Fermi energy EF.In intrinsic semiconductor:EF ≈ (EC + EV)/2.
EF
n-type semiconductor
In the n-type material most of the mobile charges are free electrons.Therefore, the average energy of mobile charges is close to EC:
EF ≈ EC
EFn
Phosphorus (P) has 5 outer shell electrons.
Extra free electron
EC
EV
p-type semiconductor
In the p-type material most of the mobile charges are holes.Therefore, the average energy of mobile charges is close to EV:
EF ≈ EV
EFp
EC
EV
Boron (B) has 3 outer shell electrons.
Extra electron vacancy or hole
Carrier Concentration and Fermi level: n-type material
Electron concentration:
ND - Donor atoms concentration
n Dn N≈
Hole concentration in the n-type material:
2i
nn
npn
=
Fermi energy level: F CE E≈
2n n ip n n=
Carrier Concentration and Fermi level: p-type material
Hole concentration:
NA - Acceptor atoms concentration
p Ap N≈
Electron concentration in the p-type material:
2i
pp
nnp
=
Fermi energy level: F VE E≈
2n n ip n n=
Compensation
If both donor and acceptor are added to an intrinsic semiconductor then the semiconductor is said to be compensated
If ND > NA, the free electron concentration:n = ND-NA
If ND < NA, the hole concentration:p = NA-ND
Drift CurrentThe electric current due to electric field is called the
Drift Current.
E,n drift nJ q nEµ=
The electron current density (current per unit area):
µn is the electron mobility and n is the electron concentration.
Jn,drift
Jp,drift
Similarly the hole current density:
pEqJ pdrift,p µ=
µp is the hole mobility and p is the hole concentration.
…cont… Drift Current and conductivity
pEqnEq
JJJ
pn
drift,pdrift,ndrift
µ+µ=
+=
The total (electron + hole) drift current density:
( )drift n pJ q n p Eµ µ= +Conductivity:
( )n pq n pσ µ µ= + driftJ Eσ=
1 1( )n pq n p
ρσ µ µ
= =+
Resistivity:
Diffusion CurrentDiffusion is due to concentration difference between two regions of a semiconductorThe carriers will move from higher concentration region to the lower one.
Con
cent
ratio
n
x
Abr
upt c
once
ntra
tion
chan
ge
Con
cent
ratio
n
x
Gra
dual
con
cent
ratio
n ch
ange
Hole diffusion
Jp,diff
…continued… Diffusion CurrentThe electron diffusion current density: ,n diff n
dnJ qDdx
=
Dn is the diffusion coefficient of electrons
The hole diffusion current density: ,p diff pdpJ qDdx
=−
Ele
ctro
n C
once
ntra
tion
x
Electron diffusion
Jn,diff
Hol
e C
once
ntra
tion
x
Dp is the diffusion coefficient of holes
Total Currents in semiconductors with bothelectric field and concentration gradients
Electron current density
Hole current density:
, ,n n drift n diff n ndnJ J J q nE qDdx
µ= + = +
, ,p p drift p diff p pdpJ J J q pE qDdx
µ= + = −
Total current density: n pJ J J= +
Total current: ( )×An pI J A J J= × = + A is the sample cross-section area
Total electron current
n nI J A= ×
Total hole current
p pI J A= ×