7.7 EFFECTIV E MASS AND MOBILITY OF CHARGE CARRIERS
7.8.3 Reverse biasing the p-n junction
What happens if a voltage is applied to increase the potential difference across the junction?
Conversely, if the negative terminal of the DC power supply is connected to the p-type m aterial, the energy separation of the bands on either side of the junction is increased. This process is called negative or reverse biasing. In this case, because the height of the barrier is increased by AE = £ + e \\ as shown in Fig. 7.18, it becomes very difficult to drive electrons from the n-type into the p-type material. However electrons can move easily from the p-type to the n-type m aterial down the potential gradient of the conduction band in the vicinity of the interface. This results in an electrical current pulse and can occur for example if electrons are stimulated across the band gap by the absorption of photons in the junction itself. This means that the reverse-biased o-n junction can be used as a light detector (photodetector or photocell)
The current in a p-n junction diode therefore behaves non-linearly with the bias voltage as shown in Fig. 7.19. We see also that the simple p-n junction which we have described can act as a rectifier or diode by allowing current to flow in one direction only.
150 Electronic properties of semiconductors
n-type | j p-type
. ---
elec tro n
flo w — ► • • ♦ ằ •__________
* ve
EF" ' ' --- E t 6I V V ' ' w ’ _ ^ --- _
> ằ ằ ằ V * ằ * flowho'e
n +ve depletion
layer
Forward bias
n-type p-type
, / electron
i / # _ flow
depletion layer
Reverse bias
Fig. 7.18 Electron band structure of reverse-biased and forward-biased p-n junctions-
7 .8 .4 S e m i c o n d u c t o r d e v ic e s
How can we explain the device characteristics of a p-n junction, and what other device application can be found?
We have looked at the simplest case of a semiconductor device, the p-n ju n ctio n and shown that this can be used as a diode. We need to look at the op eratio n of the p-n junction in more detail so that the current/voltage characteristics
Current I (mA)
Semiconductor junctions 151
Pig. 7.19 V oltage/current characteristic of a p-n ju n c tio n shnu,i„„ . , . . L forward direction but no conduction in the reverse direction r c m conduci,on ,n the occurs at much higher reverse voltages, (Unt" electncal breakdow"
shown in Fig. 7.19 can ho understood in terms of the electronic properties Consider first the band structure diagram of the p-n junction shown in Fiằ 7 16c
Electrons in the conduction band of the n-type material cannot ¿ashy reach the p-type material because of the potential energy ramp which causes an internal electric field .£ However the higher density of electrons in the conduction band of the n-type material will cause a diffusion of electrons from this region of high concentration to the region of low concentration in the conduction band of the p-type material.
In diffusion the number of electrons passing through cross-sectional area A in unit time, dN /dt, is dependent on the rate of change of the number density Of electrons with position, dN/dx, according to the equation
D is the diffusion coefficient which in this case is given by e
where n is the mobility of the electrons (section 7.2.2), kn is Boltzmann’s constant, e is the charge on the electron and T is the temperature in degrees Kelvin.
Substituting for D in the diffusion equation
/ d / V \ _ - n k HT A i d N \
V d t ) " e V d.v )
We can therefore define a diffusion current density Jd for the ch arg e carriers in terms of the rate of change of the number density N with time.
e f d N \ /lV d t )
152 Electronic properties of semiconductors
by ^ convent! on a ^ Turrent' ‘dens i n ' s '0 n curre"t density must be balanced junction, y J' due t0 the v'oltage gradient at the p 'n
Jv = oÇ= NepÇ and equating the current densities, Jd = Jy
NepÇ= - p k BT - dx Rearranging and integrating gives,
v - = f i i
J e J N
and noting that when V = 0, N = N(0), and when V = V, N = N{V), this giveS V = — knT
-log,
r a m o o f reha te l thi dCMity o f e,ect^ n s N(V) at the to p o f th e p o t e n t ia l
N(0] at eiL ‘ ’ Inf , C ptype material) to the number density o f e le c t r o n s
If w ẻ T ° f ^ poiential ôôằP (in the n-type material)
If we look at the problem m more detail there is a hole current in a d d it io n
A e n s n . f Z * Semicondu“ or. We denote the electron current t h T Z l ™ " ' T r! Sr t0 !he p-‘yPe re6‘on (diffusion current) as currenn / CUcren the P*‘ype region to the n-type region (field a n dj ' !(field)' V " CUrrent densitles ean be denoted 7dh (diffusion) flo * ¡¡“ 3 VOltage V iS aPPlied t0 the P'n junction it causes currents to barrier r ‘h eJUn,Ct,° n A VO,tặe by convention reduces the p o t e n t ia l
mcreaseiTh K T ? h and hole\ whi<e a negative voltage by convention flowing U "16'' the Vo],age ,s lncreased the net electron current density flow n f r J n' tyPC re8' 0n mCreaSeS- Likewise thô ^ t hole current density owmg from the p-type reg.on mcreases. The current density for the diffusion
electrons can be determined from, _ e f d N ( 0 ) \
^-VN(e d 1',e<p(ùrr))
e dN(V) A
eV
* “ PU J
Semiconductor junctions 1 5 3
and replacing e(dN(V)/dt)/A by / vc we arrive at,
' - = ' - ex p( v F P)
and similarly for the hole current
The net electron current density is A = Jdc - Ac and the net hole current density is A = Ah — Ah- The total current flowing is then
Aoi = A + A
This is the diode equation, where A ' s the sum °f the current densities by the m inority carriers across the junction. We can now exf re^ 1 e £ u n _ q
flowing through a p -n junction in terms of the voltage across it. w hen 'ằpp
there is no current. When Fapp> 0 the current increases exponem ia >
applied voltage. W hen Kapp < 0 the current is small and negative. 1 his eqi describes the current voltage characteristics shown in Fig. 7.19.
A vast num ber of semiconductor devices based on the properties o semi conductor junctions exist [10]. These include devices which are designer or particular current/voltage characteristics, such as diodes and transistors, an optoelectronic devices such as photodetectors and photoemitters. The prtncip es of their o peration rem ain broadly the same. We have touched on the main concepts required for understanding them in this chapter. We will loo at so!j!
of these sem iconductor devices in more detail when we deal with spect a, applications in C hapters 11-15.