CHAPTER 7 The PN Junction Consider a uniformly doped PN junction, in which one region of the semiconductor is uniformly doped with acceptor atoms and the adjacent region is uniformly doped with donor atoms. Energy band diagram. A space charge region between the p and n regions. The electric field in the space charge region and the built in potential barrier. Analyze the changes that occur in the PN junction when a reverse biased voltage is applied. Derive expressions for space charge width and depletion capacitance. Analyze the voltage breakdown characteristics of a PN junction. Consider the properties of a non-uniformly doped PN junction. Specific doping profiles can lead to desirable properties of the PN junction.
7.1 BASIC STRUCTURE OF THE PN JUNCTION The interface separating the n and p region is referred to as the metallurgical junction.
7.1 BASIC STRUCTURE OF THE PN JUNCTION For simplicity, it is usually assumed that the P and N layers are uniformly doped at acceptor density N a, and donor density N d, respectively. This idealized PN junction is known as a step junction or an abrupt junction in which the doping concentration in uniform in the p and n region and there is an abrupt change in doping at the junction.
7.1 BASIC STRUCTURE OF THE PN JUNCTION A PN junction has rectifying current voltage (I V or IV) characteristics as shown in Fig. 4 2. As a device, it is called a rectifier or a diode. The PN junction is the basic structure of solar cell, light-emitting diode, and diode laser, and is present in all types of transistors.
7.1 BASIC STRUCTURE OF THE PN JUNCTION As electron diffuse from n to p region, positively charged donor are left in the n region. As holes diffuse from p to n region, negatively charged acceptor are left in the p region. The two region are referred to as the space charge region. The charges will induce electric field.
7.1 BASIC STRUCTURE OF THE PN JUNCTION Let us construct a rough energy band diagram for a PN junction at equilibrium or zero bias voltage. First draw a horizontal line for because there is only one Fermi level at equilibrium.
7.1 BASIC STRUCTURE OF THE PN JUNCTION Far from the junction, we simply have an N-type semiconductor on one side (with E c close to E F ), and a P-type semiconductor on the other side (with E v close to E F ).
7.1 BASIC STRUCTURE OF THE PN JUNCTION Finally, in we draw an arbitrary (for now) smooth curve to link the E c from the N layer to the P layer. E v of course follows Ec, being below Ec by a constant E g.
7.2 ZERO APPLIED BIAS Assumptions: Boltzmann approximation is valid. Each semiconductor region is non-degenerately doped. Complete ionization exists. The temperature of the PN junction is not too low. 7.2.1 Built in Potential Barrier In thermal equilibrium the Fermi energy level is constant. Ec and Ev are not flat. This indicates the presence of a voltage differential. The conduction and valence band must bend through the space charge region. V bi Fn Fp
7.2 ZERO APPLIED BIAS Assumptions: Boltzmann approximation is valid. Each semiconductor region is non-degenerately doped. Complete ionization exists. The temperature of the PN junction is not too low. 7.2.1 Built in Potential Barrier In thermal equilibrium the Fermi energy level is constant. Electron in the conduction band of the n region see a potential barrier when moving into the conduction band in the p region. This built-in potential barrier is denoted as ev bi V bi Fn Fp
7.2 ZERO APPLIED BIAS Assumptions: Boltzmann approximation is valid. Each semiconductor region is non-degenerately doped. Complete ionization exists. The temperature of the PN junction is not too low. 7.2.1 Built in Potential Barrier In thermal equilibrium the Fermi energy level is constant. This built-in potential barrier maintain equilibrium between i.majority carrier electron in the n region and minority electron carrier in the p region. ii.majority carrier holes in the p region and minority holes carrier in the n region. V bi Fn Fp
7.2.1 Built in Potential Barrier The built-in potential barrier is the difference between the intrinsic Fermi levels in the p and n regions V bi Fn Fp In the n region the electron concentration is given by ( EC EF) no NC exp kt which can also be written in the form ( EC EF ) EF EFi no NC exp ni exp kt kt
7.2.1 Built in Potential Barrier The built-in potential barrier is the difference between the intrinsic Fermi levels in the p and n regions V bi Fn Fp We can define potential F n in the n region as Thus, n 0 may be written as e Fn EFi EF EF EFi e Fn no ni exp ni exp kt kt
7.2.1 Built in Potential Barrier Taking the natural log of both sides of where n 0 = N d It becomes n o e Fn niexp kt Fn kt N d ln e ni
7.2.1 Built in Potential Barrier Similarly in the p region, the hole concentration is given as ( EF Ev ) ( EF EFi ) po Na Nv exp ni exp kt kt We can define potential F p Thus, p 0 may be written as e Fp EFi EF in the n region as p 0 n i ( EF exp[ kt E Fi ] n i e exp[ kt Fp ]
7.2.1 Built in Potential Barrier Taking the natural log of both sides of where n 0 = N d p 0 n i e exp[ kt Fp ] It becomes Fp kt N a ln e ni
7.2.1 Built in Potential Barrier Therefore, the built-in potential barrier becomes V bi Fn Fp kt N d kt N a ln ln e ni e ni kt NaN d NaN d ln V ln 2 t 2 e ni ni
Poisson s equation: 7.2.2 Electric Field
Poisson s equation: 7.2.2 Electric Field
7.2.3 Space Charge Width The total depletion or space charge width W is the sum of the two components.
7.3.1 Space Charge Width and Electric Field 1 N 1 N d 1 N a lighter 1 dopant density Does the depletion layer widen or shrink with increasing reverse bias?
7.3.1 Space Charge Width and Electric Field The maximum electric field at the metallurgical junction is that yield Maximum Electric Field E max en x en x d n a n s 2 e Vbi VR NN a d Emax s Na Nd The maximum electric field in the pn junction can also be written as E max 2 V bi V R W s 12
7.3.2 Junction Capacitance
7.3.3 One-Sided Junctions The built in potential of the junction can be determined by extrapolating the curve to the point where (1/C )2= 0. The slope of the curve is inversely proportional to the doping concentration of the low doped region in the junction.
7.4 JUNCTION BREAKDOWN At some particular voltage, the reverse biased current will increase rapidly. The applied voltage at this point is called the breakdown voltage. Junction Breakdown the Zener effect and the avalanche effect. Zener breakdown occurs in highly doped PN junctions through a tunneling mechanism. The avalanche breakdown process occurs when electrons and/or holes, moving across the space charge region, acquire sufficient energy from the electric field to create electron hole pairs by colliding with atomic electrons within the depletion region.
7.4 JUNCTION BREAKDOWN Zener Breakdown As the reverse voltage increases the diode can avalanche breakdown and zener breakdown. Zener breakdown occurs when the electric field near the junction becomes large enough for valence electrons directly tunneling into the conduction band and generate carriers
7.4 JUNCTION BREAKDOWN Avalanche Breakdown The avalanche process occurs when the carriers in the transition region are accelerated by the electric field to energies sufficient to free electron-hole pairs via collisions with bound electrons.
7.4 JUNCTION BREAKDOWN For most pn junctions, the predominant breakdown mechanism will be the avalanche effect. If we assume that a reverse biased electron current I n0 enters the depletion region at x = 0. The total current I is given by The avalanche breakdown condition is then given by
A one-sided p+n junction, the maximum electric field is given by The depletion width xn is given approximately as If we now define VR to be the breakdown voltage VB, the maximum electric field, Emax, will be defined as a critical electric field, Ecrit, at breakdown.
*7.5 NONUNIFORMLY DOPED JUNCTIONS 7.5.1 Linearly Graded Junctions The space charge density can be written as The potential through the junction:
7.5.1 Linearly Graded Junctions The junction capacitance is then
7.5.2 Hyperabrupt Junctions The generalized n-type doping concentration for x 0 is given by The case of m = 0 corresponds to the uniformly doped junction. m = +1 corresponds to the linearly graded junction just discussed. The cases of m= +2 and m = +3 shown would approximate a fairly low doped epitaxial n type layer grown on a much more heavily doped n+ substrate layer. When the value of m is negative, referred to as a hyperabrupt junction. The n type doping is larger near the metallurgical junction than in the bulk semiconductor.