Chapter 7. The pn Junction

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1 Chapter 7 The pn Junction

2 Chapter 7 PN Junction PN junction can be fabricated by implanting or diffusing donors into a P-type substrate such that a layer of semiconductor is converted into N type. Converting a layer of an N-type semiconductor into P type with acceptors would also create a PN junction

3 Chapter 7 PN Junction A PN junction has rectifying current voltage (I V or IV) characteristics as shown in Fig 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

4 7.1 Basic structure of the PN junction The interface separating the n and p region is referred to as the metallurgical junction

5 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.

6 8.1.2 Qualitative 7.1 Basic Description structure of of Charge the PN Flow junction in a pn Junction

7 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

8 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

9 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 ).

10 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.

11 7.2.1Built-in Potential Barrier 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

12 7.2.1Built-in Potential Barrier 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

13 7.2.1Built-in Potential Barrier 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

14 7.2.1Built-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

15 7.2.1Built-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 e Fn EFi EF Thus, n 0 may be written as EF EFi e Fn no ni exp ni exp kt kt

16 7.2.1Built-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

17 7.2.1Built-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 e Fp EFi EF Thus, p 0 may be written as in the n region as p 0 n i ( EF exp[ kt E Fi ] n i e exp[ kt Fp ]

18 7.2.1Built-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

19 7.2.1Built-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

20 7.3 Reverse applied bias W dep 2 s ( bi Vr ) 2 s qn potential barrier qn 1 N 1 N d 1 N a lighter 1 dopant density Does the depletion layer widen or shrink with increasing reverse bias?

21 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 s 12 E max 2 V bi V R W

22 7.4 Junction breakdown Junction Breakdown Zener Breakdown Avalanche Breakdown

23 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

24 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.

25 7.4 Junction breakdown The breakdown voltage can be given as V B E s 2eN 2 crit B Where N B is the semiconductor doping in the low-doped region of the one sided junction while E crit is actually E max at breakdown

26 Consider a silicon n+p junction diode. The critical electric field for breakdown in silicon is approximately E crit = V/cm. Determine the maximum p-type doping concentration such that the breakdown voltage is a)40v Example 1

27 Consider a silicon n+p junction diode. The critical electric field for breakdown in silicon is approximately E crit = V/cm. Determine the maximum p-type doping concentration such that the breakdown voltage is a)40v b)20 V V B N N B B s 2eN 2 crit B B or N cm a Example s crit 2eV

28 8.1.1 Qualitative Description of Charge Flow in a pn Junction In Figure 8.1c, the total potential barrier is reduced. There will be a diffusion of holes from the p region across the space charge region where they will flow into the n region. Similarly, there will be a diffusion of electrons from the n region across the space charge region where they will flow into the p region.

29 8.1.3 Boundary Conditions The electric field E app induced by the applied voltage is in the opposite direction to the thermal-equilibrium space charge electric field, so the net electric field in the space charge region is reduced below the equilibrium value. The electric field force that prevented majority carriers from crossing the space charge region is reduced ; majority carrier electrons from the n side are now injected across the depletion region int o the p material, and majority carrier holes from the p side are injected across the depletion region into the n material. V V N n n bi N a 2 ni d t NaN ln( 2 n n0 Nd, np0 p0 n i d ev exp( kt n0 bi ) n N ev exp( kt ) 2 i a bi ) 5

30 8.1.3 Boundary Conditions

31 8.1.4 Minority Carrier Distribution If a reverse biased voltage greater than a few tenths of a volt is applied to the pn junction, then we see from Equations (8.6) and (8.7) that the minority carrier concentrations at the space charge edge are essentially zero.

32 8.1.4 Minority Carrier Distribution

33 8.1.4 Minority Carrier Distribution

34 8.1.5 Ideal pn Junction Current

35 8.1.6 Summary of Physics Comment of Ex 8.4, We assumed, in the derivation of the current voltage equation, that the electric field in the neutral p and n regions was zero. Although the electric field is not zero, this example shows that the magnitude is very small thus the approximation of zero electric field is very good.

36 8.2.1 Generation Recombination Currents

37 8.2.1 Generation Recombination Currents The negative sign implies a negative recombination rate; hence, we are really generating electron hole pairs within the reverse biased space charge region.

38 8.2.1 Generation Recombination Currents

39 Forward Bias Recombination Current Generation Recombination Currents

40 8.2.1 Generation Recombination Currents At the center of the space charge region,

41 8.2.1 Generation Recombination Currents Total Forward Bias Current The total forward bias current density in the pn junction is the sum of the recombination and the ideal diffusion current densities. If some of the injected holes in the space charge region are lost due to recombination, then additional holes must be injected from the p region to make up for this loss. The flow of these additional injected carriers, per unit time, results in the recombination current.

42 8.2.2 High-Level injection

43 8.2.2 High-Level injection

44 8.2.2 High-Level injection In the high level injection region, it takes a larger increase in diode voltage to produce a given increase in diode current.

45 *8.4.1 The turn-off transient

46 the reverse biased density gradient is constant; thus, the minority carrier concentrations at the space charge edge decrease with time This reverse current IR will be approximately constant for 0< t< ts, where ts is called the storage time. *8.4.1 The turn-off transient

47 *8.5 The tunnel diode The tunnel diode is a pn junction in which both the n and p regions are degenerately doped. The depletion region width decreases as the doping increases and may be on the order of approximately 100 Å

48 *8.5 The tunnel diode (b) There is a finite probability that some of these electrons will tunnel directly into the empty states, producing a forward bias tunneling current (e) the tunneling current will be zero and the normal ideal diffusion current will exist

49 *8.5 The tunnel diode Electrons in the valence band on the p side are directly opposite empty states in the conduction band on the n side, so electrons can now tunnel directly from the p region into the n region, resulting in a large reversebiased tunneling current.

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